Four Essays on Applied Bayesian Econometrics
Transcript of Four Essays on Applied Bayesian Econometrics
Charles University
Faculty of Social SciencesInstitute of Economic Studies
DISSERTATION (PRE-DEFENSE VERSION)
Four Essays on Applied BayesianEconometrics
Author: Tomas Adam
Supervisor: prof. Ing. et Ing. Lubos Komarek Ph.D., MSc., MBA
Academic Year: 2018/2019
Acknowledgements
I would like to express my gratitude to my adviser Lubos Komarek for super-
vising this work. I would also like to thank my colleagues at Charles University,
the Czech National Bank and the European Central Bank and all referees for
their comments and useful feedback. In addition, I would like to thank the
CNB and ECB for funding several courses in Bayesian econometrics, which
greatly helped me understand techniques used in the thesis.
I would also like to thank my family and friends for their support and encour-
agement to finalize the thesis.
Bibliographic Record
Adam, Tomas: Fours Essays on Applied Bayesian Econometrics. Dissertation
thesis. Charles University in Prague, Faculty of Social Sciences, Institute of
Economic Studies. xxx 2019, pages xxx. Advisor: prof. Ing. et Ing. Lubos
Komarek Ph.D., MSc., MBA.
Typeset in LATEX 2εusing the IES Thesis Template.
Contents
Abstract v
List of Tables vii
List of Figures viii
1 General Introduction 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2 Assessing the External Demand of the Czech Economy: Now-
casting Foreign GDP Using Bridge Equations 11
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3 Methodology and the design of the nowcasting and forecasting
exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.A Data used for the analysis . . . . . . . . . . . . . . . . . . . . . 34
2.B Major trading partners of the Czech Republic: stylized facts . . 37
2.C Monthly indicators in univariate models (BMA, correlations) . . 40
2.D Multivariate model equations . . . . . . . . . . . . . . . . . . . 41
2.E Root mean square errors . . . . . . . . . . . . . . . . . . . . . . 43
3 Modeling Euro Area Bond Yields Using a Time-Varying Factor
Model 45
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
3.2 Methodology and data . . . . . . . . . . . . . . . . . . . . . . . 48
3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Contents iv
3.4 Discussions of the results . . . . . . . . . . . . . . . . . . . . . . 63
3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
3.A Estimation of the FAVAR with time-varying loadings and stochastic
volatility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.B Time-varying loadings on factors and exogenous varibales . . . . 77
3.C Time-varying impact responses to structural shocks . . . . . . . 79
3.D Correlations with factors . . . . . . . . . . . . . . . . . . . . . . 80
4 Financial Stress and Its Non-Linear Impact on CEE Exchange
Rates 81
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
4.2 Financial stress and exchange rates . . . . . . . . . . . . . . . . 84
4.3 A model of portfolio rebalancing . . . . . . . . . . . . . . . . . . 89
4.4 The effects of financial stress on CEE currencies . . . . . . . . . 94
4.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.A Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.B Estimated regime probabilities . . . . . . . . . . . . . . . . . . . 111
4.C Impulse responses . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.D Setting the priors and Gibbs sampling . . . . . . . . . . . . . . 113
5 Time-Varying Betas of Banking Sectors 117
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
5.2 Systematic risk and the banking sector . . . . . . . . . . . . . . 119
5.3 Approaches to the estimation of systematic risk . . . . . . . . . 121
5.4 Time-varying betas of the banking sectors . . . . . . . . . . . . 125
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.A Estimating CAPM betas in a Bayesian state-space framework . 136
5.B Estimating the global factor . . . . . . . . . . . . . . . . . . . . 138
5.C Banking and stock market indices . . . . . . . . . . . . . . . . . 139
5.D Banking betas: rolling regression estimates . . . . . . . . . . . . 140
5.E Banking Sector Betas - estimation using M–GARCH model . . . 141
5.F Banking Sector Betas - estimation using Bayesian state space
model with stochastic volatility . . . . . . . . . . . . . . . . . . 143
Abstract
The dissertation consists of four papers which apply Bayesian econometric tech-
niques to monitoring macroeconomic and macro-financial developments in the
economy. Its aim is to illustrate how Bayesian methods can be employed in
standard areas of economic research (estimating systemic risk in the banking
sectors, nowcasting GDP growth) and also in more original areas (monitor-
ing developments in sovereign bond markets, the effects of changes in financial
stress on foreign exchange rate dynamics in the CEE region).
In the first essay, we address a task which analytical departments in central
or commercial banks face very often - nowcasting foreign demand of a small
open economy. On the example of the Czech economy, we propose an approach
to nowcast foreign GDP growth rates for the Czech economy. For presentation
purposes, we focus on three major trading partners: Germany, Slovakia and
France. We opt for a simple method which is very general and which has proved
successful in the literature: the method based on bridge equation models. A
battery of models is evaluated based on a pseudo-real-time forecasting exer-
cise. The results for Germany and France suggest that the models are more
successful at backcasting, nowcasting and forecasting than the naive random
walk benchmark model. At the same time, the various models considered are
more or less successful depending on the forecast horizon. On the other hand,
the results for Slovakia are less convincing, possibly due to the stability of the
GDP growth rate over the evaluation period and the weak relationship between
GDP growth rates and monthly indicators in the training sample.
In the second essay, we turn to monitoring developments in euro area sover-
eign bond markets. To study the period since October 2005, with a particular
focus on the financial and sovereign debt crises, we employ a factor model with
time-varying loading coefficients and stochastic volatility, which allows for cap-
turing changes in the pricing mechanism of bond yields. Our key contribution
is exploring both the global and the local dimensions of bond yield determin-
ants in individual euro area countries using a time-varying model. Using the
Contents vi
reduced form results, we show decoupling of periphery euro area bond yields
from the core countries’ yields following the financial crisis and the scope of
their subsequent re-integration. In addition, by means of the structural analysis
based on identification via sign restrictions, we present time varying impulse re-
sponses of bond yields to EA and US monetary policy shocks and to confidence
shocks.
The third essay studies the dynamics of selected CEE (“satellite curren-
cies”) currencies following an increase in financial stress in the euro area and
also in global financial markets (“the core currency”). We suggest that this
reaction might be non-linear; the “safe haven” status of a satellite currency
may hold in calm periods, but breaks down when risk aversion is elevated. A
stylized model of portfolio allocation between assets denominated in euro and
the satellite currency suggests the presence of two regimes characterised by
different reactions of the exchange rate to increased stress in the euro area.
In the “diversification” regime, the satellite currency appreciates in reaction
to an increase in the expected variance of EUR assets, while in the “flight
to safety” regime, the satellite currency depreciates in response to increased
expected volatility. We suggest that the switch between regimes is related to
changes in risk aversion, driven by the level of strains in the financial system as
captured by financial stress indicators. Using the Bayesian Markov-switching
VAR model, the presence of these regimes are identified in the case of the Czech
koruna, the Hungarian forint and the Polish zloty.
The final essay analyses the evolution of the systematic risk of the banking
industries in eight advanced countries using weekly data from 1990 to 2012.
Time-varying betas are estimated using a Bayesian state-space model with
stochastic volatility, whose results are contrasted with those of the standard
M-GARCH and rolling-regression models. We show that both country-specific
and global events affect the perceived systematic risk, while the impact of the
latter differs considerably across countries. Finally, our results do not support
fully the previous findings that equity prices did not reflect the build-up of
systematic risk of the banking sector before the last financial crisis.
List of Tables
2.1 Data used for the analysis . . . . . . . . . . . . . . . . . . . . . 34
2.1 Correlation coefficients between GDP growth rates and industral
production growth rates . . . . . . . . . . . . . . . . . . . . . . 39
2.1 Root mean square errors: Germany . . . . . . . . . . . . . . . . 43
2.2 Root mean square errors: Slovakia . . . . . . . . . . . . . . . . . 44
2.3 Root mean square errors: France . . . . . . . . . . . . . . . . . 44
3.1 Bond yields: sign restrictions on (impact) responses to structural
shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.2 Descriptive statistics for sovereign bond yields and euro/dollar
exchange rate (USDEUR) . . . . . . . . . . . . . . . . . . . . . 54
4.1 Results summary: the response of investors to an increase in the
expected variance of core-currency assets . . . . . . . . . . . . . 94
5.1 Banking betas: data used for the analysis . . . . . . . . . . . . . 125
5.2 Banking sector systematic risk: percentage of the variation ex-
plained by the global factor . . . . . . . . . . . . . . . . . . . . 129
5.3 Cross-border exposures of banking sectors . . . . . . . . . . . . 131
List of Figures
2.1 Timing scheme of the forecasting exercise . . . . . . . . . . . . . 20
2.2 RMSE: Germany . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 RMSE: Slovakia . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4 RMSE: France . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.1 GDP growth rates in the considered countries . . . . . . . . . . 37
2.2 EA country weights based on the Czech export shares (2018 Q1) 37
2.3 EA country weights based on the Czech export shares, correla-
tions of gdp growth rates with industrial production growth . . 38
2.4 GDP and industrial production growth rates . . . . . . . . . . . 38
2.5 GDP and industrial production growth rates . . . . . . . . . . . 39
2.1 Variables selected based on BMA and correlations: Germany . . 40
2.2 Variables selected based on BMA and correlations: Slovakia . . 40
2.3 Variables selected based on BMA and correlations: France . . . 40
3.1 Sovereign bond yields and euro/dollar exchange rate (USDEUR) 53
3.2 Cumulative sums of estimated factors and exogenous variables . 55
3.3 Stochastic volatility of idiosyncratic shocks to bond yields: pos-
terior median, 16th and 84th quantiles. . . . . . . . . . . . . . . 56
3.4 Evolution of loadings of bond yields on factors . . . . . . . . . . 57
3.5 Semiannually cumulated structural shocks . . . . . . . . . . . . 58
3.6 Cumulative impulse responses to structural shocks: posterior
median, 16th and 84th quantiles. x-axis: weeks . . . . . . . . . 59
3.7 Impact coefficients to the euro area and US monetary policy
shocks - annual averages . . . . . . . . . . . . . . . . . . . . . . 61
3.8 Historical decomposition of annual changes in bond unobserved
factors, bond yields in the US and EMEs. . . . . . . . . . . . . 63
3.9 Evolution of loadings of bond yields on factors (1) . . . . . . . . 77
3.10 Evolution of loadings of bond yields on factors (2) . . . . . . . . 78
List of Figures ix
3.11 Evolution of loadings of bond yields on factors (3) . . . . . . . . 78
3.12 Posterior median responses (on impact) of bond yields to struc-
tural shocks over time. . . . . . . . . . . . . . . . . . . . . . . . 79
3.13 Posterior median responses (on impact) of bond yields to struc-
tural shocks over time. . . . . . . . . . . . . . . . . . . . . . . . 79
3.14 Correlations of each country with factors. . . . . . . . . . . . . . 80
4.1 Financial stress indicators . . . . . . . . . . . . . . . . . . . . . 86
4.2 Mean-variance frontier of the portfolio . . . . . . . . . . . . . . 91
4.3 Optimal λsat for changing σ2core, for different values of γ . . . . . 92
4.4 Optimal λsat for changing σ2core, constrained σ2
p . . . . . . . . . . 93
4.5 CEE currencies vis-a-vis the euro . . . . . . . . . . . . . . . . . 98
4.6 Transition matrices . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.7 Expected durations of regimes . . . . . . . . . . . . . . . . . . . 100
4.8 Estimated regimes and average levels of the CISS index in the
estimated regimes . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.9 Responses of exchange rates to shocks to financial stress indices
(higher values indicate a depreciation of a given currency) . . . 104
4.10 Estimated regime probabilities . . . . . . . . . . . . . . . . . . . 111
4.11 Responses to a 1 s.d. shock to financial stress indices . . . . . . 112
5.1 Banking sector systematic risk: the global factor . . . . . . . . . 129
5.2 Banking sector betas: data used for the analysis . . . . . . . . . 139
5.3 Banking betas: rolling regression estimates . . . . . . . . . . . . 140
5.4 Banking betas: M-GARCH estimates 1 . . . . . . . . . . . . . . 141
5.5 Banking betas: M-GARCH estimates 2 . . . . . . . . . . . . . . 142
5.6 Banking betas: Bayesian state-space model estimates 1 . . . . . 143
5.7 Banking betas: Bayesian state-space model estimates 2 . . . . . 144
Chapter 1
General Introduction
Bayesian econometric methods have become increasingly popular among eco-
nomists in recent years. Their primary advantage stems from the possibility to
incorporate prior beliefs on the parameters of interest in the estimation proced-
ure. This merit is valuable particularly in macroeconomics, where often only a
limited number of observations is available to the researcher.
As an example, vector autoregression models are heavily used in macroeco-
nomics for forecasting but also structural analysis. These models suffer from
the problem of overparameterization, as the number of coefficients in models
growth very fast when additional variables are included. Bayesian VAR models
overcome this model by imposing prior information on the parameters. This
information can originate from knowledge on the behaviour of inflation dynam-
ics, for example, which tends to be stable between two periods (Doan et al.,
1984) or approaches the inflation target in the medium-run (Villani, 2009).
Predictions from these models tend to have more precise credible intervals
(“confidence bands”) and also smaller forecast errors, compared to standard
VAR models. Since the models are usually simulated using Monte-Carlo tech-
niques, it is straightforward to draw inferences around quantities of interest,
such as impulse response functions (Baumeister and Hamilton, 2015; Rubio-
Ramirez et al., 2010) or forecasts, without the need to use bootstrapping or
other complicated methods.
In the case of macroeconomic models build on micro-foundations (An and
Schorfheide, 2007), one often has prior knowledge on several parameters, which
stems either from economic theory or empirical studies. Imposing these into
the estimation leads to more meaningful estimates of parameters on which no
information is available and often also to better predictions and more plausible
1. General Introduction 2
impulse response functions.
Another reason for the popularity of Bayesian techniques in macroeconomics
has been their ability to simulate state-space models (Carter and Kohn, 1994),
which in classical econometrics rely on often unstable optimisation methods.
These techniques allow researchers to estimate more complex unobserved pro-
cesses (Stock and Watson, 2007), including stochastic volatility models Kim
et al. (1998), time-varying coefficient models (Primiceri, 2005), or factor mod-
els (Bernanke et al., 2005).
In addition, the increase in computational power and the reduction of its
costs in recent years have contributed to the embrace of Bayesian techniques by
many economists. Since posterior distributions in Bayesian econometric models
can be rarely solved analytically, Markov Chain Monte Carlo methods (Chib
and Greenberg, 1996, 1995; Casella and George, 1992) are used to simulate
draws from posterior distributions and compute characteristics of posterior
distributions (e.g., mean, mode, variance). These methods, although known
for a long time, had been prohibitively computationally costly until recently.
Finally, the publication of several relatively non-technical books and sources
on the topic (Koop et al., 2010; Blake et al., 2012) made Bayesian techniques
accessible to the broad public.
This dissertation illustrates the power of Bayesian econometric techniques
in four areas of economic research. The overarching topic of the four essays is
monitoring macroeconomic and macro-financial developments in the economy.
The models used in the essays can, therefore, be used as one of the inputs for
economic analysts and policymakers. The first paper applies Bayesian model
averaging technique as a variable selection tool to nowcast GDP growth rates.
The second paper studies the developments in euro area sovereign bond mar-
kets using a factor model with time-varying loading coefficients and stochastic
volatility. In the third paper, a Bayesian Markov switching VAR model is used
to detect unobserved regimes of the reaction of CEE exchange rates to increased
financial stress in the euro area and global financial markets. Finally, the fourth
paper estimates a measure of systematic risk (CAPM betas) in banking sectors
using a state space model, where state variables are simulated using Bayesian
techniques.
The use of Bayesian techniques in the first paper is relatively standard in
economic research, while their application is rather original in the subsequent
three essays. The models and methods applied in all four articles encompass a
broad spectrum of the Bayesian toolkit - simple linear regression, Bayesian VAR
1. General Introduction 3
models, the time-varying parameter regression model, the model of stochastic
volatility, Markov switching VAR models, Bayesian model averaging, factor
models and factor models with time-varying loadings. The appealing fea-
ture of Bayesian econometrics is that once several fundamental techniques are
mastered, they can be combined to estimate rich models, for example, a factor-
augmented vector autoregression model (FAVAR) with time-varying loadings
and stochastic volatility presented in the second essay.
In the first essay (published as (Adam and Novotny, 2018)), we address a
challenge that forecasters of a small economy very often face - nowcasting for-
eign demand growth. Successful forecasts of a small open economy need to take
into account developments abroad, so a researcher needs to make reasonable
assumptions about the external economic environment. These assumptions
are often taken from external sources (such as Consensus Forecasts), which,
however, provide outlooks only for yearly GDP growth rates. These annual
numbers are disaggregated into a quarterly frequency by a mechanical pro-
cedure, which often does not take into account timely monthly indicators on
current economic developments.
To overcome the gap between external yearly forecasts and available indic-
ators on the economy, we introduce a semi-automatic approach to nowcasting
foreign GDP growth rates for the Czech economy1. This approach is based on
the bridge equation models (BEQ), which “bridge” information from monthly
indicators (e.g. industrial production) into quarterly ones (GDP growth rates)
using a simple linear regression model. The estimated linear relationship is sub-
sequently used for nowcasting. Since a lot of monthly indicators are available,
we reduce the space of possible models by grouping them into three categor-
ies: univariate models, more complex multivariate models, and finally models
based on common components. In the first category, we average predictions of
univariate models into five categories. One of the categories contains variables
selected using Bayesian model averaging, which identifies the best possible can-
didates for explaining GDP growth.
The paper illustrates the suggested technique on backcasting, nowcasting
and one-quarter ahead forecasting GDP growth rates for Germany, Slovakia
and France. The evaluation exercise takes into account 58 available time series,
starting in January 1999. The calculated nowcasts are compared on an evalu-
ation period starting in the first quarter of 2012. The models are re-estimated
1Although the paper is written specifically for a small open economy, the techniques canalso be used in other contexts, where many variables need to be nowcasted in a short time.
1. General Introduction 4
every quarter on currently available data, and the pseudo-real-time forecasting
exercise takes into account the publication lags of the monthly indicators.
The forecasting exercise suggests that the performance of various competing
BEQ models is not constant and varies based on the forecasting horizon con-
sidered (i.e. backcast, nowcast and one-quarter-ahead forecast). In line with
intuition, the forecasting ability of the models containing leading indicators is
strongest at longer horizons, but diminishes for nowcasting and backcasting.
At the same time, the power of the models containing industrial production is
higher in the case of nowcasting and backcasting (compared to forecasting), es-
pecially in the third month, when the industrial production index is published
for the first month of the current quarter.
The second essay (published as (Adam and Lo Duca, 2017)) studies the de-
velopments in the euro area sovereign bond markets, with a particular emphasis
on the financial and sovereign debt crises. These two events demonstrated that
understanding the pricing mechanism and the drivers of bond yields is essential
to monitor risks, decide on policies and assess their effectiveness. On the one
hand, a part of the literature suggests that at the peak of the sovereign debt
crisis, euro area bond yields reflected fundamentals, in particular, the expected
deterioration of the macro environment and fiscal positions. Another strand of
literature suggests that risk aversion, panic and irrational investors’ behaviour
drove bond yields.
Against this backdrop, the essay presents a new model to assess the pricing
mechanism of euro area sovereign bond yields from a dynamic perspective. It
employs a factor model with time-varying loading coefficients and stochastic
volatilities to determine the drivers of sovereign bond yields in the euro area.
The time variation in factor loading coefficients allows for capturing changes in
the pricing mechanism of bond yields, consistent with the evidence emerging
from other empirical studies. Exploring both the global and local dimensions
of bond yield determinants in individual euro area countries is one of our key
contributions. Specifically, our model studies the drivers of country-specific
yields separating between (i) euro area core and periphery factors to assess
integration, spill-overs and contagion within the euro area (ii) US and Emerging
Market Economies (EMEs) market factors to assess spill-overs to the euro area
from the rest of the world. Finally, time-varying impulse responses to monetary
policy shocks and confidence shocks are identified via sign restrictions and
studied.
The results support the view that the pricing mechanism of bond yields
1. General Introduction 5
evolved during the European banking and sovereign crisis. The analysis iden-
tifies three distinct phases in euro area sovereign bond markets. In the first,
initial phase, bond markets were almost fully integrated. In the second, when
the crisis escalated, bond markets became disintegrated. In this phase, the
pricing of euro area sovereign bonds depended on different factors and the
transmission of monetary policy shocks became heterogeneous across countries.
Lastly, in the third phase of partial re-integration, the pricing mechanism of
bonds approached the pre-crisis conditions, according to loading coefficients
and structural impulse responses.
Our results have implications for the debate on the impact of unconven-
tional monetary policy on sovereign bond markets in the euro area. While
the literature predominantly quantifies the impact of unconventional monet-
ary policy on bond yields and it assesses the transmission channels (e.g. the
signalling channel vs the portfolio balance channel), our results also shed light
on the impact of policies on the pricing mechanism of yields. Specifically, we
highlight a link between euro area unconventional policies, the way different
factors are priced into bond yields and the reaction of bond yields to monetary
policy shocks. We find that, when looking at loading coefficients and structural
impulse responses, the announcement of Outright Monetary Transactions by
the ECB was a game changer leading to gradual normalisation of the pricing
mechanism of bond yields to the pre-crisis situation. Finally, another inter-
esting finding shows that yields in troubled euro area countries became more
responsive to EA monetary policy shocks during the crisis periods. This sug-
gests that the ECB mix of unconventional monetary policy was particularly
effective in those markets where monetary accommodation was needed.
The essay is valuable also from the methodological perspective since it ex-
tends the method by Chan and Jeliazkov (2009) to simulate draws from more
complex models, such as the FAVAR model used in this paper. State variables
in these models can follow a higher order VAR process so that the covariance
matrix of shocks in the transition matrix is singular. This method is relat-
ively straightforward to implement and computationally more efficient than
the algorithms used routinely in the literature (e.g., (Carter and Kohn, 1994)).
The third essay (published as (Adam et al., 2018)) explores the response
of selected CEE currencies to an increase in the euro area or global financial
markets uncertainty. The motivation for the paper was the puzzling feature
of some CEE currencies (the Czech koruna, in particular), which appreciated
strongly before the peak of the financial crisis in 2008 when the level of fin-
1. General Introduction 6
ancial strains in the euro area was already elevated. Many commentators and
even policymakers suggested that the currency could serve as a “safe haven” for
investors. Nevertheless, around the peak of the financial crisis, the CEE cur-
rencies depreciated strongly, although the fundamentals deteriorated markedly
abroad and not initially in the countries of interest. The presence or the ab-
sence of the haven status and the reaction of currencies following deteriorated
fundamentals abroad are worth exploring further since foreign exchange devel-
opments are one of the critical factors for macroeconomic developments and
financial-stability in small open economies.
To study these phenomena, the paper introduces a simple theoretical model
of portfolio allocation between assets denominated in a “core” and a “satellite”
currency. On an example of the EUR- and CZK- denominated assets, the model
suggests the existence of two regimes characterized by different reactions of the
exchange rate to increased stress in the euro area. The “diversification” regime
is characterized by an appreciation of the koruna in reaction to an increase in
the expected variance of EUR assets, while in the “flight to safety” regime, the
koruna depreciates in response to increased variance. The paper argues that
this non-linear reaction of asset prices to increased variance can originate from
two sources - either from discontinuous changes in investors’ risk aversion or
from reaching constraints given by value-at-risk portfolio management.
Since the two factors leading to non-linearity in the portfolio allocation
are unobserved, we employ the Bayesian Markov-switching VAR model. This
model assumes that a latent underlying process determines how the asset value
(in our case reflected in exchange rate movements) reacts to changes in the
variance (captured by financial stress indicators) of the core countries.
The empirical results support the idea that the reaction of CEE currencies
to financial stress switches between several regimes. Although the “flight to
safety” regime prevails when financial stress indicators are peaking, in trans-
ition periods (run-up to a crisis or crisis aftermath), we often observe the “di-
versification” regime where CEE currencies respond to an increase in financial
stress by appreciation. Interestingly, in calm periods, when the levels of stress
are low, we observe a third regime characterized by lower volatility, but also neg-
ative correlations between financial stress and satellite exchange rates, which
are otherwise typical for the “flight to safety” regime.
To put the results into a wider perspective, the paper illustrates that with
deepening financial integration, external financial conditions and changes in
investors’ sentiment can play a substantial role in exchange rate dynamics,
1. General Introduction 7
especially in the short run when international parity based on macroeconomic
fundamentals is less reliable.
The results have two important implications for policymaking in the CEE
region. Firstly, the paper shows that a CEE currency can depreciate in re-
sponse to an increase in financial stress in the euro area even if fundamentals
in a given country do not change. If the central bank does not respond to
such shocks with foreign exchange interventions, policy-makers can take pre-
cautionary measures and induce the banking sector to generate capital buffers,
which would strengthen its resilience to such shocks. Next, even if a currency
seemingly has a safe haven status in some periods (i.e., it appreciates after
stress increases in the euro area), this status can be easily lost even though
domestic fundamentals do not change. This again speaks for creating buffers
and hedging for unexpected moves in exchange rates (in both ways) by the
private sector.
The final essay (published as (Adam et al., 2012)) analyzes the evolution
of systematic risk in the banking sectors. The inherent fragility of banks and
the opacity of their businesses raise the question of whether markets can price
the risk correctly. The excessive risk-taking by US banks before the market
meltdown in 2007 is an example of a period when the correct evaluation of
risk is questionable. Surprisingly, not even the ex-post literature provides any
clear-cut answer to this question, so it remains unanswered whether markets
were fully aware of the risks connected with mortgage loan securitization. As we
show in this paper, the answer depends on how the systematic risk is estimated.
The paper extends the evidence from the current literature in several ways.
First, it applies a Bayesian state-space model with stochastic volatility for the
estimation of the CAPM betas of banking sectors. According to the CAPM
theory, the betas should capture the systematic risk of the industry. It is now
widely held that betas are not time-invariant, and methods such as the rolling-
regression model, classic state-space models, and the GARCH model have so
far been used frequently to estimate the evolution of betas. Still, these methods
have several shortcomings, such as arbitrary choice of window size (in the case of
rolling regression), assumed homoskedasticity of residuals (in both the rolling-
regression and the state-space approaches), and a large amount of noise present
in the estimates (estimation based on the GARCH model). On the other hand,
the model that we use links the advantages of both the state-space approach
(estimating the beta as an unobservable process in a state-space model) and
the approach based on the M-GARCH model (allowing for heteroskedasticity
1. General Introduction 8
of residuals).
We demonstrate how the estimates can be used by policymakers as an in-
dicator of systematic risk. Some studies argue that in the US, the pre-crisis
build-up of instability in the banking sector was not reflected in stock prices.
Our analysis on the contrary shows that the banking sector risk in this seem-
ingly calm period increased. In other words, the results do not support fully the
previous findings that the systematic risk of the banking sector was significantly
underestimated before the last financial crisis.
Next, we show that both country-specific and global events affect the per-
ceived systematic risk, and the strength of the global factor differs considerably
across countries. The previous literature has investigated the betas of financial
sectors as a whole or has studied trends between sub-sectors in one individual
country. On the other hand, the final essay explores potential global trends
in the perceived riskiness of banking sectors. To evaluate the degree of co-
movement, we estimate a global factor and calculate the percentage of the
variation explained by the global factor for individual countries.
The results suggest that the banking sectors in some countries (the US, the
UK, and Germany) share similar patterns in the evolution of their systemic
risk; on the other hand, the sectors in other countries (Japan and Australia)
look more isolated. The paper presents one of several possible explanations:
the degree to which banking sectors are financially interconnected by cross-
border exposures. It seems that the most influential financial centres exhibit
the highest sensitivity to global developments and the degree to which the
banking sector is internationalized can affect the sector’s systemic risk.
To conclude, the thesis demonstrates how Bayesian econometric techniques
can be employed in a broad spectrum of applications relevant to both eco-
nomic research, but also to practitioners. Regarding economic research, the
thesis shows applications in heavily studied areas - nowcasting, analyzing bond
yield and exchange rate developments and estimating CAPM betas. For prac-
titioners, the thesis suggests several tools useful for monitoring macroeconomic
and macro-financial developments. As a result, these techniques can be used
as one of the inputs for the economic analysis and also for policymakers.
1. General Introduction 9
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Chapter 2
Assessing the External Demand of
the Czech Economy: Nowcasting
Foreign GDP Using Bridge
Equations
Abstract
We propose an approach to nowcasting foreign GDP growth rates for
the Czech economy. For presentational purposes, we focus on three
major trading partners: Germany, Slovakia and France. We opt for
a simple method which is very general and which has proved success-
ful in the literature: the method based on bridge equation models. A
battery of models is evaluated based on a pseudo-real-time forecasting
exercise. The results for Germany and France suggest that the models
are more successful at backcasting, nowcasting and forecasting than the
naive random walk benchmark model. At the same time, the various
models considered are more or less successful depending on the forecast
horizon. On the other hand, the results for Slovakia are less convincing,
possibly due to the stability of the GDP growth rate over the evalu-
ation period and the weak relationship between GDP growth rates and
monthly indicators in the training sample.
The paper was co-authored with Filip Novotny and published in CNB Working Paper Series (paper no.18/2018). The work was supported by Czech National Bank Research Project No. B1/17. We would liketo thank Jan Bruha, Marek Rusnak and Marcel Tirpak for valuable comments in their referee reports. Wewould also like to thank Michal Franta, Petr Kral and other seminar participants at the Czech National Bankfor their valuable feedback and comments. The views expressed in this paper are those of the authors andnot necessarily those of the Czech National Bank.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 12
2.1 Introduction
GDP growth nowcasting has long been a topic of interest to both economic
practitioners and academics. For forecasters, assessing the current state of
the economy is of utmost importance, since the most recent observations are
what drives forecasts to a significant extent, especially at the short ends of
forecast horizons. Unfortunately, estimates of GDP growth are available with
substantial lags, so estimates of the current (or even the last) GDP growth
rates have to be produced. On a theoretical level, nowcasting has been of
particular interest, since the techniques used face the challenge of extracting
meaningful signals from a multitude of variables representing different parts of
the economy. At the same time, these indicators are available with various lags
and can be subject to significant measurement errors.
Forecasters of a small open economy face a challenge in that a successful
forecast needs to take into account developments abroad. Very often, effect-
ive aggregates of foreign GDP growth, inflation rates and interest rates are
constructed and assumptions are made about their future paths to produce
forecasts for the domestic economy. In the case of the Czech Republic, the core
forecasting model of the Czech National Bank assumes the paths of “effective”
euro area aggregates of GDP and PPI inflation rates, which are constructed as
trade-weighted averages of variables of the 17 most important euro area trading
partners of the Czech Republic. These assumptions are taken from Consensus
Forecasts (produced by Consensus Economics), which are published at monthly
frequency. However, the forecasts are produced for yearly data and have to be
disaggregated into quarterly frequency. Currently, the temporal disaggregation
is based on a simple mechanistic approach which does not take into account
timely data from the economy and available leading indicators.
This paper introduces an approach to producing nowcasts, backcasts and
one-quarter-ahead forecasts of foreign GDP for the Czech economy, which
drives foreign demand in the Czech National Bank’s core forecasting model.
The main aim of producing these estimates is to improve the current mech-
anistic approach to disaggregating the forecasted annual growth rates of GDP
produced by external institutions which operate in the economies of interest.
In addition, producing backcasts, nowcasts and one-quarter-ahead forecasts
can provide a basis for making expert adjustments to the Consensus Forecast
projections, which tend to reflect new information slowly.
The share of exports to the euro area in overall Czech exports is about 65%.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 13
Since we face the challenge that many (17) countries enter the forecast-
ing process at the Czech National Bank, we opt for one of the simplest, but
also most successful, nowcasting methods, based on bridge equations. This
approach “bridges” information from timely monthly indicators to quarterly
GDP growth rates. For the sake of brevity, the paper presents the results for
the three most important trading partners of the Czech Republic, Germany,
Slovakia and France, which cover about 70% of exports to the euro area. The
results are presented for a battery of models, starting with simple univariate
bridge equation models, followed by more complex multivariate models and
finishing with models containing principal components, which capture the co-
movement among all relevant variables.
The results suggest that in the case of Germany and France, even most
of the simplest models beat the naive forecasts at all horizons (i.e. when we
consider backcasting, nowcasting and forecasting performance). The models
containing leading indicators perform best at the one-quarter-ahead forecasting
horizon in the case of Germany and to a smaller extent in the case of France.
For shorter horizons (nowcasting and backcasting), the power of the models
containing coincident indicators increases, especially in the third month of the
quarter, when the industrial production index is published for the first month of
the quarter. Finally, the model containing common components performs well
at all horizons, especially in the case of nowcasting the current GDP growth
rate. On the other hand, the results for Slovakia are not as successful. This
stems primarily from low correlations of monthly indicators with GDP growth
rates. In addition, GDP growth exhibited very low volatility over our evaluation
period, so the naive forecast performs best.
2.2 Literature review
Short-term forecasting tools are used widely by policy institutions, since ap-
propriate policy measures need to take into account timely information on
macroeconomic developments. Specifically, data on GDP growth, which is
published with a substantial time lag (typically 6 to 8 weeks), are observed
closely by policymakers. Nowcasting of quarterly GDP growth has thus be-
come very common at central banks. Traditional nowcasting methods used by
central banks include bridge equation (BEQ) models and dynamic factor mod-
els (DFMs). These two groups of models are supplemented by other related
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 14
models, e.g. OLS models with more explanatory variables, ARMAX models,
mixed frequency VARs and MIDAS equations.
Feldkircher et al. (2015) apply both BEQ models and DFMs to Central and
Eastern European countries. The models are estimated for the period from the
first quarter of 2000 to the second quarter of 2008. Their evaluation period then
ranges to the third quarter of 2014, covering the period since the Great Reces-
sion. They follow the standard practice when evaluating out-of-sample fore-
casting accuracy, which is measured by the root mean squared error (RMSE)
with the latest available GDP growth figures (quasi out-of-sample forecasts).
Their small-scale nowcasting models outperform a simple AR(1) model, but
the model performance varies strongly across countries. Additionally, Hucek
et al. (2015) show that BEQ models and DFMs outperform ARMA models in
the case of the Slovak economy. Moreover, BEQ models may offer an advantage
over DFMs, since they are simple to construct and easy to understand.
Similarly, Antipa et al. (2012) forecast German GDP growth rates for the
current quarter using factor and bridge models. They show that changing
the bridge model equations by including newly available monthly information
generally provides more precise forecasts and is preferable to maintaining the
same equation over the horizon of the exercise. Importantly, the forecast errors
of the BEQ models are smaller than those of the DFMs. Furthermore, the BEQ
models not only provide very accurate forecasts, but are also straightforward to
interpret. Indicators that appear to be unrelated or only loosely linked to the
target variable can be neglected. The datasets are therefore relatively small and
thus not costly to update. Second, BEQ model predictions allow for a better
description of the forecast based on the evolution of the explanatory indicators.
The ability to identify and interpret the drivers of forecasts is a useful feature,
especially in periods characterized by significant or changing volatility.
This paper focuses on BEQ models due to their above-mentioned advant-
ages over other types of models, particularly DFMs. BEQ models were intro-
duced by Klein and Sojo (1989) as a regression-based system for GDP growth
forecasting. BEQ models are essentially regressions relating quarterly GDP
growth to one or a few monthly variables (such as industrial production or
various survey indicators, especially leading ones) aggregated to quarterly fre-
quency. The forecasting accuracy of bridge equations seems to rely on selecting
the “right” higher frequency indicators conditional on the forecast horizon (Tre-
han, 1992). Since only partial monthly information is usually available for the
target quarter, the monthly variables are forecasted using auxiliary models such
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 15
as ARIMA models (Banbura et al., 2013). In order to exploit the information
content from several monthly predictors, bridge equations are sometimes pooled
(see, for example, (Kitchen and Monaco)). Since BEQ models are designed to
be used on a monthly basis, the industrial production index is probably the
most relevant and widely analysed high-frequency indicator.
The underlying structure of BEQ models is different from standard mac-
roeconomic models, which are built around behavioural and causal relations
between the variables. The gains of forecasts based on BEQ models relative
to naive constant growth models are substantial, especially at very short hori-
zons, and most of all for the current quarter, according to Baffigi et al. (2004).
The high accuracy of forecasts at shorter horizons implies that these models
should be used primarily to forecast growth in the current and previous quar-
ters. In addition, it is straightforward to incorporate new data as soon as it is
released. Early in the quarter, soft indicators have been found to be extremely
important, especially since hard data (e.g. industrial production) is not yet
available.
Furthermore, Giannone et al. (2008) propose a method which consists of
bridging quarterly GDP with monthly data via regressing GDP growth rates on
factors extracted from a large panel of monthly series with different publication
lags. Angelini et al. (2011) show on euro area data that bridging via factors
produces more accurate estimates than traditional bridge models. The factor
model thus improves the pool of bridge equation models. They also show that
survey data and other “soft” information are valuable for nowcasting. BEQ
models for France, Germany, Italy and the euro area over the period from 1980
to 1999 are estimated by Baffigi et al. (2004). They conclude that BEQ models
are far better than selected ARIMA and VAR models and a structural model.
Moreover, over a forecasting horizon one- to two-steps ahead, the aggregation
of forecasts by country performs better in forecasting euro area GDP and also
offers information on the state of the single economies.
ECB staff use a set of bridge equations in their regular monitoring of eco-
nomic activity in the euro area (Diron, 2008; Runstler and Sedillot, 2003). In
Germany, the higher volatility of GDP growth rates probably stems from the
country’s reliance on the industrial sector and exports, which are sensitive to
the global business cycle. Deutsche Bundesbank operates factor models and
bridge equations for GDP growth forecasts. It updates its forecasts twice a
month and concentrates on nowcasting the current quarter or backcasting the
last quarter using all the available indicator-based information. In addition,
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 16
one-quarter-ahead prediction (forecasting) is conducted (Bundesbank, 2013;
Gotz and Knetsch, 2019). Recently, Pinkwart (2018) argues that the fore-
cast performance of BEQ models can be substantially improved in the case of
Germany by combining the production side and the demand side projections.
Mogliani et al. (2017) use a model which relies exclusively on business survey
data in industry and services conducted directly by the Banque de France.
Some soft indicators are even used by the French national statistics institute
(INSEE) to compile its GDP figures. The National Bank of Slovakia regularly
publishes its nowcast of the real economy in its monthly bulletin. To this end,
it uses several approaches, including BEQ models. Incomplete monthly series
of economic indicators are forecasted by ARMA models and then bridge equa-
tions are estimated by OLS for each explanatory variable. Finally, the average
of the individual BEQ models is weighted by the AIC Hucek et al. (2015); Tvrz
(2016).
This paper concentrates on techniques for nowcasting foreign economic vari-
ables (specifically the GDP growth of the Czech Republic’s main trading part-
ners). The variety of BEQ models used ranges from simple univariate BEQ
models to models based on common components. The main motivation is that
a small open economy is substantially influenced by external developments.
On the other hand, the research into short-term forecasting at the Czech
National Bank has so far focused exclusively on the Czech economy. Benda and
Ruzicka (2007) evaluate nowcasts of Czech GDP growth using principal com-
ponent analysis (PCA) and seemingly unrelated regression estimation (SURE)
with monthly and quarterly explanatory variables. They show that these meth-
ods provide relatively accurate nowcasts and near-term forecasts of GDP fluc-
tuations. Similarly, Arnostova et al. (2011) forecast the quarterly GDP growth
of the Czech economy up to three quarters ahead using six competing simple
econometric models. Furthermore, Rusnak (2016) employs a dynamic factor
model (DFM) to nowcast Czech GDP growth. Havranek et al. (2010) evaluate
to what extent financial variables improve the forecasts of Czech GDP growth
and inflation. More recently, the impact of financial variables on Czech macroe-
conomic developments is investigated by Adam and Plasil (2014) and Franta
et al. (2016), who use various mixed-frequency data models to forecast Czech
GDP growth. Babecka and Bruha (2016) present nowcast models for Czech
external trade. This is a novel approach, since no nowcast model for trade has
been described previously in the literature. They apply four empirical mod-
els: principal component regression, elastic net regression, the dynamic factor
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 17
model and partial least squares.
2.3 Methodology and the design of the nowcast-
ing and forecasting exercises
This paper employs the method based on bridge models (Runstler and Sedillot,
2003; Baffigi et al., 2004; Diron, 2008). This method is one of the most straight-
forward, but also most general and successful, techniques used for nowcast-
ing and, as a result, it is widely used in practice. Models from this class
“bridge” information from timely monthly indicators into quarterly frequency.
The method used to extract the information on the dynamics of a quarterly
variable from monthly indicators is simple linear regression. This section de-
scribes the approach taken by the paper to forecasting GDP growth in a given
quarter using one model. It subsequently describes the strategy used for the
selection, aggregation and evaluation of several competing models.
2.3.1 The case of one model
Bridge models exploit statistical relations between monthly and quarterly in-
dicators. For example, the coefficients of correlation between changes in GDP
growth rates and quarterly averages of changes in several indicators exceed 0.7
in the case of Germany and France (Figures 2.1, 2.2 and 2.3). This relation
is intuitive and reflected in the nature of the business cycle, which exhibits
co-movements among many economic indicators (Burns and Mitchell, 1947).
Formally, in line with Antipa et al. (2012), let Yt denote the quarter-on-
quarter GDP growth rate and Xt denote the quarterly averages of q monthly
explanatory variables (also referred to as indicators). The bridge model can be
specified as:
Yt = α +m∑i=1
βiYt−1 +
q∑j
k∑i
δj,iXj,t−i + εt, (2.1)
where m is the number of autoregressive parameters and k is the number of
lags for the explanatory variables. In all specifications, we opt for m = 0. This
Throughout the paper, the term forecast can have two meanings – either a proper forecastof future GDP growth or a fitted value from a model, which could also denote a nowcast ofGDP growth in the current quarter or even a backcast of GDP growth in the last quarter.
In line with Mariano and Murasawa (2003), quarterly growth rates are constructed bytaking moving averages of monthly growth rates.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 18
choice is common in the literature (Diron, 2008; Arnostova et al., 2011) and is
aimed at reducing the persistence of forecasts (and thus improving forecasting
power when fundamentals change abruptly). In addition, the lagged GDP
growth rate is not observed in the first two months of a given quarter and
its extrapolation would add additional noise to the forecasts. Finally, one can
argue that the lagged series is highly collinear with the monthly indicators,
which leads to larger forecast sampling errors. Regarding the number of lags
of each explanatory variable, parameters k were set based on an automatic
selection procedure where the Akaike information criterion was minimized on
the training sample (1999Q1–2011Q4).
Equation 2.1 is estimated using a simple ordinary least squares estimator.
The estimated relationship can subsequently be used for the nowcasting and
forecasting of a given quarter provided that the variables on the right-hand side
(Xt) are known. This is rarely the case (with the exception of backcasting) and
one hence needs to extrapolate observations of monthly indicators so that all
observations are known in a given quarter. The literature uses simple AR,
ARMA or VAR models for this task. For the sake of computational simplicity,
we opt for AR models.
One can infer various sources of forecast errors. First, even if all the monthly
indicators are known precisely (i.e. without any measurement errors), the GDP
figures may not be estimated accurately (using bridge equations, or by other
approaches). Next, since the models are estimated using simple OLS regres-
sions, the choice of indicators matters and it is not clear what variables ex-
plain GDP growth rates best. In addition, the coefficients in Equation 2.1 are
only estimated and are subject to statistical uncertainty. Finally, not all the
monthly indicators are known in a given quarter and the missing figures are
extrapolated, which very likely leads to further errors.
2.3.2 The evaluation of nowcasts and forecasts
In order to compare the performance of various competing models, we perform
a pseudo-real-time out-of-sample forecasting exercise. For each month in a
given quarter (denoted as M1, M2 and M3 in the paper), forecasts for three
horizons are considered: (i) a backcast (estimating GDP growth in the last
quarter when the figure has not yet been published), (ii) a nowcast (estimating
Preliminary estimates suggested that the forecasting performance gain from using ARMAmodels compared to AR models is negligible. At the same time, the computational cost ofselecting the optimal lag structure of AR and MA parameters was large.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 19
GDP growth in the given quarter), (iii) a forecast of GDP growth in the next
quarter. It is assumed that the forecasts are made at the end of the month, so
that all indicators which are published during the given month are known.
The models are estimated since the first quarter of 1999 (provided the data
is available) and the evaluation period starts in the first quarter of 2012. For
each month since January 2012, we take the following steps:
1. Missing observations are introduced at the tail of the sample according to
the publication lag, in order to simulate “pseudo” real-time data vintages.
2. Observations from complete quarters are used in order to estimate the
parameters in Equation 2.1.
3. The missing observations of monthly indicators are subsequently extra-
polated using the AR models described in the previous subsection and
aggregated to quarterly frequency. One should note that we extrapolate
not only the missing observations due to the procedure described in the
first step, but also the observations of the remaining months in the given
and next quarters.
4. The estimated model is fitted in order to obtain a backcast, a nowcast
and a forecast and the estimates are saved.
In other words, the forecast evaluation is performed recursively and the
model is re-estimated every quarter. For each of the months considered, we
obtain three sets of forecasts (a backcast, a nowcast and a forecast; panels (i)
and (ii) in Figure 2.1) and for each quarter, we obtain nine sets of forecasts de-
pending on the forecasting horizon (panel (iii) in Figure 2.1). For presentation
purposes, we drop one of the horizons – the backcast in the third month, since
the GDP figure for the last quarter is already published by then.
The models are compared based on the root mean square error for each
forecast horizon. This is because one could expect the forecasting performance
of each model to vary across the forecasting horizon and the month of the
forecast. In the first month of a given quarter, when only leading indicators
are available, one could expect these models to perform best for nowcasting.
All publication lags are described in Table 2.1 in the Appendix. The lags are denoted inmonths, i.e. 0 means that the data are available at the end of the given month at the latest;1 means that the data are published by the end of the following month at the latest.
The order of the AR models is selected automatically based on the Akaike informationcriterion for each variable separately.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 20
Figure 2.1: Timing scheme of the forecasting exercise
(i) Forecasting exercise in January 2012
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
(ii) Forecasting exercise in May 2012
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
(iii) 9 estimates obtained for the second quarter 2012
1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
I/11 II/11 III/11 IV/11
backcasting nowcasting forecasting
III/11 IV/11 II/12 III/12 IV/12
II/11 II/12 III/12 IV/12I/11
I/11 II/11
IV/11 I/12III/11
I/12
I/12 II/12 III/12 IV/12
of II/12
backcastnowcastforecast
of II/12 of II/12
training sample testing sample
training sample testing sample
On the other hand, in the third month of a given quarter, when hard data from
industry are available for the first month, models with industrial production
may perform better.
In the presentation of the results, the benchmark model is a naive model
based on a random walk forecast. This model assumes that GDP growth in the
last, current and next quarters remains the same as the last published GDP
growth figure.
2.3.3 Three types of models
The next section describes the variables considered in the forecasting exercise.
In total, we have amassed 58 variables. In order to obtain results which are
relatively easy to compare and present, we consider the following three groups
of models for each country:
Univariate bridge equation models
In these models, only one variable is used as an indicator in the bridge equation
(we also consider its lags, as described in Section 2.3.1). At the same time, we
average the outcomes of these models (in line with Arnostova et al. (2011), for
example) and group them into the following categories:
1. BMA
2. correlations
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 21
3. leading indicators
4. financial variables
5. foreign variables
The BMA category includes indicators selected based on Bayesian model
averaging, which accounts for the model uncertainty. Specifically, priors on
regression parameters are set as non-informative and priors on probabilities
are set as uniform. The posterior probabilities of the models are approximated
using the simple Bayesian Information Criterion. The BMA category considers
all variables whose posterior probabilities of inclusion exceed 0.1%.
Similarly, the correlations category contains 15 variables, which were se-
lected based on their correlations with GDP growth rates. The probability
threshold and the number of variables in the correlations category were chosen
arbitrarily. However, this led to approximately the same number of indicat-
ors in each category, and variables from each important category (hard, soft,
foreign indicators) were also selected.
Multivariate models
Multivariate models include multiple variables selected on the basis of economic
intuition and also of their correlations with GDP growth. For each country,
we consider (i) two models containing only a combination of two leading in-
dicators; (ii) four models containing various coincident indicators (usually a
combination of the industrial production index, the retail sales index and a
measure of unemployment); (iii) two models containing both leading and coin-
cident indicators. The precise model specifications are described in Appendix
2.D.
Models based on common components
The last model we consider is based on common components which capture the
comovement among all the indicators relevant to a particular country. Since
some of the observations are missing, especially at the start of the training
sample, a method based on the EM algorithm (described by (Josse and Husson,
2012)) is used to extract the common components, estimate the loadings and
impute the missing observations on the training sample. The iterative PCA
The R library by Raftery et al. (2018) was used for the computations.The package by Josse and Husson (2016) was used for the estimation.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 22
algorithm starts by replacing missing observations with the initial values (such
as the mean of the variable). It is followed by PCA of this provisional dataset
and by imputing initially missing observations using the extracted common
components and loadings. The process is then iterated until convergence is
achieved.
The nowcasting procedure described above is modified slightly. First, the
loadings of the principal components are obtained on the training sample using
the method cited in the previous paragraph. Then, missing values are then
imposed for each of the variables (based on their publication lags), which are
then extrapolated using an AR process. Finally, the principal components are
fitted based on the loadings estimated on the training sample, and the GDP
growth forecast is subsequently obtained.
2.4 Data
2.4.1 The choice of countries
Seventeen euro area countries are currently used in the CNB’s forecasting pro-
cess (only Luxembourg and Malta are excluded from the total aggregate). GDP
growth rates and measures of the inflation of these countries are weighted in
order to generate “effective” euro area aggregates. The weights used for the
aggregation are based on the trade weights of Czech exports. Nowcasting all 17
countries puts enormous demands on data processing, which is naturally prone
to mistakes. In addition, when choosing the number of countries to include in
the forecasting process, one faces a trade-off between covering a higher export
share on the one hand and the ability to make expert judgments on the fore-
casts. This is partly because with 17 countries, the time-consuming process can
lead to poor monitoring of individual countries. This is one of the advantages
of BEQ models.
To reduce the computational burden of nowcasting the full aggregate, and
in order to make the presentation of the results concise, we focus only on the
three most important euro area countries weighted by their shares in Czech
exports: Germany, France and Slovakia. We argue that, firstly, these three
countries cover more than 70% of total Czech exports to the euro area (Figure
2.2). This share increases to more than 83% when we include another two
countries (Austria and Italy). Nevertheless, one could argue that including
The weight of Czech exports to the euro area in all Czech exports is about 65%.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 23
more countries is not necessary from the economic point of view, since the GDP
growth rates of both Austria and Italy are highly correlated with German GDP
growth (Figure 2.3).
2.4.2 Data used for the analysis
The dataset used in the nowcasting and forecasting exercises was obtained at
the beginning of October 2018. In the terminology of the previous section, the
exercise is performed in the third month (M3) of the third quarter of 2018.
The data set starts in January 1999, i.e. at the inception of the euro area and
the date when most of the time series start to be available. As stated in the
previous section, the training sample spans 1999Q1–2011Q4 and the evaluation
period is 2012Q1–2018Q3.
The downloaded variables represent various sectors of the economy and
can be grouped into the following categories: (i) production and turnover in
industry and construction, (ii) labour market variables, (iii) consumer and busi-
ness surveys, (iv) external trade data, (iv) financial variables. In addition, since
the economies studied in the paper are linked closely to the car industry, we use
a variable on new passenger car registrations. Finally, as these economies are
also very open, we use several indicators for the United States, which capture
the global business cycle and foreign demand.
In total, 58 variables were downloaded from publicly available sources. Some
of these variables are country-specific but the definitions are the same across
countries (such as the industrial production index); some variables are country-
specific and unique to a given country (such as the ZEW index indicator in the
case of Germany). There are also some indicators which are shared by models
in every country (such as US leading or financial indicators). The complete list
of variables (along with their precise definitions) can be found in Table 2.1 in
the Appendix. The data are downloaded in an automatic way using the APIs
of the data providers (in the case of Eurostat, the ECB, Deutsche Bundesbank,
Federal Reserve Economic Data (FRED) and Yahoo Finance) or directly from
the ZEW and CESifo websites and can be routinely updated.
All the data, with the exception of financial variables, were seasonally ad-
justed by the publishing institutions. The nowcasting and forecasting exercises
In the case of Slovakia, the case for including US variables is weaker, since the countrytrades mostly with other euro area member states. To address this feature of the Slovakeconomy, we included a German leading indicator in one of the multivariate models to capturethe foreign demand channel (Model 2).
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 24
rely on stationary variables, i.e. we used log-differences or differences of vari-
ables that were non-stationary (I(1)).
Unfortunately, we were not able to obtain historical data vintages. As a res-
ult, the analysis is performed not in real time, but on the most recently available
data. Nevertheless, as stated in the previous section, the analysis is performed
on pseudo-real-time vintages, which take into account the publication lag of
each time series (the lags are described in Table 2.1 in the Appendix).
2.5 Results
This section summarizes the results of the forecast evaluation exercise. All
computations were performed in R, primarily using libraries in the Tidyverse
collection. Charts were generated using the ggplot2 library.
The text uses various names for the forecast horizon: longer horizons denote
proper forecasting of next-quarter GDP growth, while shorter horizons denote
nowcasts and backcasts. The figures in this section summarize the root mean
square errors of the forecasts at each horizon graphically. The precise figures
can be found in Section 2.E in the Appendix. It is worth noting that the
numbers on the horizontal axes of the figures denote the months in the quarters
when the forecast is performed. As a result, the information sets (or data)
available to the forecaster are the same for each month.
2.5.1 Germany
In the case of Germany (Figure 2.2), all the models considered based on bridge
equations perform better than the naive random walk benchmark model. Re-
garding univariate models, the models based on leading indicators perform best
at the long forecast horizon. However, their forecasting ability declines as the
horizon of the forecast gets shorter both in absolute terms (slightly) and com-
pared to some of the other competing models (considerably). The models based
on BMA perform moderately well at longer horizons but improve when the ho-
rizon is shorter. The same holds for the models based on variables selected
based on the correlation coefficients and for the models containing industrial
production indicators, especially in the case of backcasting. On the other hand,
R Core Team (2018)Wickham (2017)Wickham (2016)
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 25
foreign variables do not necessarily improve nowcasting much compared to the
benchmark model, but such models still perform better than those containing
financial variables.
The evaluation exercise based on multivariate and common component
models provide similar results to the univariate models. First, the models based
on leading indicators perform best at the long end of the forecasting horizon,
but their performance worsens for nowcasting and backcasting. Compared to
the models based on leading indicators, those based on coincident and mixed
indicators perform moderately worse at the longer end of the horizon, but their
performance improves in the case of nowcasting and backcasting. The model
based on common components performs relatively poorly at the longer end of
the forecasting horizon, but its forecasting ability still beats that of the bench-
mark model. The performance of the common components model improves in
the case of nowcasting and backcasting and is comparable to the best models
from the other two groups.
2.5.2 Slovakia
The performance of the bridge models is considerably worse in the case of
Slovakia (Figure 2.3). None of the models considered outperforms the random
walk benchmark model, and the root mean square errors are more dispersed
than in the case of Germany. The poor performance of the models for Slovakia
can be explained by several factors. First, the volatility of GDP growth is very
low in the case of Slovakia (Figure 2.1), which leads to very high performance
of the benchmark model. Interestingly, the performance of the AR(2) model is
worse than that of the random walk model, due to the stability of GDP growth
rates. In addition, looking at the correlations between GDP growth rates and
industrial production, the coefficient is significantly lower for Slovakia than
for Germany and France (Figure 2.4, Table 2.5). Strikingly, the correlation
coefficients between the two variables were even negative before the financial
crisis (2.1). They subsequently turned positive, but were still lower than in
the other two countries analysed. This signals issues with the measurement of
GDP before the financial crisis.
Still, one can identify several features shared with the results for Germany.
The models containing the industrial production index perform moderately
We tried to eliminate the extreme GDP growth rates observed before the crisis, but thisdid not improve the performance of the models significantly.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 26
well. Interestingly, however, the root mean square errors of the two multivariate
models based on coincident indicators (coincident indicators 2 and 3) perform
worse for nowcasting in the third month compared to the previous two months.
As in the case of Germany, financial and foreign variables also do not add much
information to the forecasts. The performance of the model based on common
components can be assessed as consistently satisfactory.
2.5.3 France
In the case of France, almost all the models considered outperform the bench-
mark random walk model based on the random walk forecast. One major
exception is the model containing financial variables, which performs worse in
the case of the nowcast (in months 1 and 2) and the forecast (in month 3).
This feature is similar to the cases of the two countries discussed previously.
The performance of all the other models considered is very similar at the
long end of the forecasts. Looking at nowcasting, the performance of the models
based on correlations and BMA improves, as does that of the multivariate
models based on coincident and mixed indicators. The two models with mixed
indicators perform best at the nowcasting horizon, both in absolute terms and
compared to other models. Finally, the forecasts based on common components
yield consistently satisfactory results.
2.5.4 Discussion of the Results
To sum up, the forecasting performance of the various competing models is not
constant and varies based on the forecasting horizon considered. In line with
intuition, the forecasting ability of the models containing leading indicators is
strongest at longer horizons, but diminishes for nowcasting and backcasting.
At the same time, the power of the models containing industrial production is
increasing in the case of nowcasting and backcasting (compared to forecasting),
especially in the third month, when the industrial production index is published
for the first month of the current quarter. The ability of the industrial pro-
duction index to explain GDP growth is highest in the case of Germany and
France and lower in the case of Slovakia. This finding is not surprising in the
case of Germany, as German economic output relies largely on industry (espe-
cially manufacturing) and the industrial production index is one of the sources
used to compute the GDP figures.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 27
Figure 2.2: RMSE: Germany
forecast nowcast backcast
RW
AR(2)
0.2
0.3
0.4
0.5
0.6
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
bmacorrelationsfinancial variables
foreign variablesindustrial productionleading indicators
Univariate models: DE
forecast nowcast backcast
RW
AR(2)
0.2
0.3
0.4
0.5
0.6
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
leading indic. 1leading indic. 2coincident indic. 1
coincident indic. 2coincident indic. 3coincident indic. 4
mixed indic. 1mixed indic. 2
Multivariate models: DE
forecast nowcast backcast
RW
AR(2)
0.2
0.3
0.4
0.5
0.6
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
pcaPCA model: DE
Figure 2.3: RMSE: Slovakia
forecast nowcast backcast
RW
AR(2)
0.0
0.2
0.4
0.6
0.8
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
bmacorrelationsfinancial variables
foreign variablesindustrial productionleading indicators
Univariate models: SK
forecast nowcast backcast
RW
AR(2)
0.0
0.2
0.4
0.6
0.8
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
leading indic. 1leading indic. 2coincident indic. 1
coincident indic. 2coincident indic. 3coincident indic. 4
mixed indic. 1mixed indic. 2
Multivariate models: SK
forecast nowcast backcast
RW
AR(2)
0.0
0.2
0.4
0.6
0.8
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
pcaPCA model: SK
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 28
Figure 2.4: RMSE: France
forecast nowcast backcast
RW
AR(2)
0.1
0.2
0.3
0.4
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
bmacorrelationsfinancial variables
foreign variablesindustrial productionleading indicators
Univariate models: FR
forecast nowcast backcast
RW
AR(2)
0.1
0.2
0.3
0.4
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
leading indic. 1leading indic. 2coincident indic. 1
coincident indic. 2coincident indic. 3coincident indic. 4
mixed indic. 1mixed indic. 2
Multivariate models: FR
forecast nowcast backcast
RW
AR(2)
0.1
0.2
0.3
0.4
1 2 3 1 2 3 1 2 3month in a quarter (horizon)
root
mea
n sq
uare
erro
r
pcaPCA model: FR
The models for Slovakia perform very poorly even when they are contrasted
with the naive random walk model. This is due to the low volatility of GDP
growth observed in recent years, especially after 2012, and the relatively high
volatility of the monthly indicators. At the same time, the contemporaneous
correlations between industrial production and GDP growth are small relative
to the cases of Germany and France (Figure 2.2).
Overall, the forecasting performance of most of the models is highest for
backcasting, followed by nowcasting and forecasting. This result is in line
with the size of the information set available at the time of the forecast. The
relatively poor performance of bridge models for forecasting stems from the
extrapolation of monthly indicators, which sometimes involves producing more
than ten monthly observations using simple AR models (the forecast horizon
is nine months, plus the publication lag is up to two months). As a result,
alternative models such as VAR or structural models might be useful for short-
term forecasting.
On the other hand, bridge models exploit a significant amount of inform-
ation from monthly indicators to produce nowcasts and backcasts. However,
even these estimates are crucial for forecasting GDP growth many quarters
ahead, since assessing the current state of the economy is critical in order to
produce meaningful forecasts.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 29
2.6 Conclusion
This paper introduced a new approach to nowcasting foreign GDP growth for
the Czech economy. Although the current state of the Czech economy is as-
sessed on a regular basis, no method for routinely nowcasting the foreign GDP
growth of several countries has been proposed yet. To this end, the paper em-
ployed a relatively simple, but general and successful technique based on bridge
models. These models extract information from timely monthly indicators to
infer GDP growth rates in the past, current and even next quarters.
The method of bridge equations was employed to perform backcasts, now-
casts and short-term forecasts of GDP growth rates in three major trading
partners of the Czech Republic: Germany, Slovakia and France. A pseudo-
real-time forecasting exercise was performed for the three horizons for each of
the three months in a given quarter for the whole evaluation period. The es-
timates were subsequently evaluated based on the root mean square errors for
each forecast horizon.
The results for Germany and France confirmed economic intuition and the
findings in the literature, in that the various models are more or less successful
depending on the forecast horizon. Overall, most of the models considered in
the paper outperform the benchmark model based on random walk forecasts.
The models with industrial production indices are most successful for nowcast-
ing and backcasting, notably when the industrial production index has already
been published for a given quarter. On the other hand, the models containing
leading indicators are more successful at the longer ends of forecasts, especially
in the case of Germany, for which many soft indicators are constructed. In addi-
tion, the model containing common components capturing the overall dynamics
shared by the monthly indicators performs well at all horizons, particularly in
the case of nowcasting the current GDP growth rate.
On the other hand, the performance of the models for Slovakia is not as
successful. Their poor performance stems from two major factors. The first is
the very low volatility of GDP over the evaluation period, which is reflected in
the highest performance of the random walk benchmark model. Second, the
correlation coefficient between the industrial production index and GDP growth
rates was negative before the crisis, signalling issues with the measurement of
GDP in the first half of the sample.
The models based on bridge equations perform best for the nowcasting and
backcasting horizons, but they can also be valuable for assessing the direction
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 30
of GDP growth in the coming quarter. In addition, having accurate estimates
of the last and current GDP growth rates enables one to impose more pre-
cise initial conditions in more complex models. As a result, the techniques in
this paper can be considered the first step for future research into time series
forecasting of external economic developments for the Czech economy.
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 31
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34
2.A Data used for the analysis
Table 2.1: Data used for the analysis
ticker keys lags DE SK FR EA19 US
Eurostat
GDP growth
GDP qoq growth SCA gdp qoq namq 10 gdp:
Q.CLV PCH PRE.SCA.B1GQ.
5 x x
GDP qoq growth SA gdp qoq namq 10 gdp: Q.CLV PCH PRE.SA.B1GQ. 5 x
production in industry
industry total ip total sts inpr m: M.PROD.B-D.SCA.PCH PRE. 2 x x x
manufacturing ip manufacturing sts inpr m: M.PROD.C.SCA.PCH PRE. 2 x x x
electricity, gas, steam and air conditioning supply ip energy sts inpr m: M.PROD.D.SCA.PCH PRE. 2 x x x
mining and quarrying ip mining quarrying sts inpr m: M.PROD.B.SCA.PCH PRE. 2 x x x
intermediate goods industry ip intermediate sts inpr m:
M.PROD.MIG ING.SCA.PCH PRE.
2 x x x
capital goods industry ip capital goods sts inpr m:
M.PROD.MIG CAG.SCA.PCH PRE.
2 x x x
durable consumer goods industry ip durables sts inpr m:
M.PROD.MIG DCOG.SCA.PCH PRE.
2 x x x
non-durable consumer goods industry ip nondurables sts inpr m:
M.PROD.MIG NDCOG.SCA.PCH PRE.
2 x x x
production in construction
production in construction construction sts copr m: M.PROD.F.SCA.PCH PRE. 2 x x x
deflated turnover in retail trade
retail trade, except of motor vehicles and motorcycles retail excl vehicles sts trtu m: M.TOVV.G47.SCA.PCH PRE. 2 x x x
retail trade of non-food products (except fuel) retail nonfood sts trtu m:
M.TOVV.G47 NFOOD X G473.SCA.PCH PRE.
2 x x x
turnover in industry
mining and quarrying it mining quarrying sts intv m: M.TOVT.B.SCA.PCH PRE. 2 x x x
manufacturing it manufacturing sts intv m: M.TOVT.C.SCA.PCH PRE. 2 x x x
turnover in industry; domestic market
mining and quarrying it dom mining quarrying sts intvd m: M.TOVD.B.SCA.PCH PRE. 2 x x x
manufacturing it dom manufacturing sts intvd m: M.TOVD.C.SCA.PCH PRE. 2 x x x
turnover in industry; non-domestic market
mining and quarrying it nondom mining quarrying sts intvnd m: M.TOVE.B.SCA.PCH PRE. 2 x x x
manufacturing it nondom manufacturing sts intvnd m: M.TOVE.C.SCA.PCH PRE. 2 x x x
labour market
unemployment rate total unrate total une rt m: M.SA.TOTAL.PC ACT.T. 1 x x x
2.Assessing
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35
ticker keys lags DE SK FR EA19 US
unemployment rate, 25 years and over unrate 25over une rt m: M.SA.Y25-74.PC ACT.T. 1 x x x
unemployment rate, under 25 years unrate 25under une rt m: M.SA.Y LT25.PC ACT.T. 1 x x x
consumer and business surveys
consumer confidence indicator ecs consumer confidence ei bsco m: M.BS-CSMCI.SA.BAL. 0 x x x
consumer unemployment expectations ecs consumer exp unem ei bsco m: M.BS-UE-NY.SA.BAL. 0 x x x
industry confidence indicator ecs industry confidence ei bsin m r2: M.BS-ICI.SA.BAL. 0 x x x
industry employment expecations ecs industry exp employment ei bsin m r2: M.BS-IEME.SA.BAL. 0 x x x
services confidence indicator ecs services confidence ei bsse m r2: M.BS-SCI.SA.BAL. 0 x x x
services employment expectations ecs services exp employment ei bsse m r2: M.BS-SEEM.SA.BAL. 0 x x x
retail confidence indicator ecs retail confidence ei bsrt m r2: M.BS-RCI.SA.BAL. 0 x x x
retail employment expectations ecs retail exp employment ei bsrt m r2: M.BS-REM.SA.BAL. 0 x x x
construction confidence indicator ecs construction confidence ei bsbu m r2: M.BS-CCI-BAL.SA. 0 x x x
construction employment expectations ecs construction exp empl ei bsbu m r2: M.BS-CEME-BAL.SA. 0 x x x
external trade
exports outside of the EU, current value exports ex eu ext st 28msbec:
M.EXP.TRD VAL SCA.EXT EU28.TOTAL.
2 x x x
exports, current value exports world ext st 28msbec:
M.EXP.TRD VAL SCA.WORLD.TOTAL.
2 x x x
ECB
car registrations
new passenger car registration mom, sa car registrations STS.M.I8.Y.CREG.PC0000.3.PER 2 x
Buba
orders received
industry, constant prices orders industry BBDE1.M.DE.Y.AEA1.A2P300000.F.C.I15.A 2 x
intermediate goods, constant prices orders intermediates BBDE1.M.DE.Y.AEA1.A2P310000.F.C.I15.A 2 x
capital goods, constant prices orders capital goods BBDE1.M.DE.Y.AEA1.A2P320000.F.C.I15.A 2 x
consumer goods, constant prices orders consumer goods BBDE1.M.DE.Y.AEA1.A2P350000.F.C.I15.A 2 x
Fred
foreign variables
Industrial production: manufacturing us manufacturing IPMAN 1 x
Industrial production index us ip total INDPRO 1 x
University of Michigan: consumer sentiment us umcsent UMCSENT 0 x
Motor vehicle retail sales: domestic autos us dom cars DAUTOSA 1 x
Retail sales us retail RETAILSMSA 2 x
OECD consumer confidence indicator for the US us oecd consop CSCICP03USM665S 2 x
OECD business confidence indicator for the US us oecd business surveys BSCICP03USM665S 2 x
Other
leading indicators - Germany
ifo business climate, industry and trade ifo industry climate 0 x
ifo business situation, industry and trade ifo industry situation 0 x
ifo business expectations, industry and trade ifo industry expectations 0 x
2.Assessing
theExternal
Dem
andof
theCzech
Econom
y:Now
castingForeign
GDPUsing
Bridge
Equations
36
ticker keys lags DE SK FR EA19 US
ifo business climate, manufacturing ifo manufacturing climate 0 x
ifo business situation, manufacturing ifo manufacturing situation 0 x
ifo business expectations, manufacturing ifo manufacturing expectations 0 x
ZEW indicator of economic sentiment, Germany zew sentiment 0 x
ZEW indicator of economic situation, Germany zew situation 0 x
financial variables
DAX performance index dax yahoo: ˆGDAXI 0 x
CAC 40 cac40 yahoo: ˆFCHI 0 x
Euro Stoxx 50 stoxx50 yahoo: ˆSTOXX50E 0 x
S&P 500 Index sp500 yahoo: ˆGSPC 0 x
Note:
Data sources are printed in bold. Keys column denotes the name of the database (in the case of Eurostat) and other identification dimensions / tickers.
Column lags denotes the publication lag in weeks (i.e., zero indicates that the variable is published by the end of a given month).
Variables in the Other category were downloaded from the websites of publishing institutions (CESifo or Center for European Economic Research, ZEW) or from Yahoo Finance (financial variables).
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 37
2.B Major trading partners of the Czech Republic:
stylized facts
Figure 2.1: GDP growth rates in the considered countries
FR
DE SK
00 02 04 06 08 10 12 14 16 18
00 02 04 06 08 10 12 14 16 18 00 02 04 06 08 10 12 14 16 18
-8
-6
-4
-2
0
2
4
6
-4
-3
-2
-1
0
1
2
-1.5
-1.0
-0.5
0.0
0.5
1.0
q-o-q, %, SAGDP growth rates
Source: Eurostat
Figure 2.2: EA country weights based on the Czech export shares(2018 Q1)
DE
50.5
SK
11.7
FR
7.9
AT
6.8
IT
6.3
NL
4.7
ES
4.4
BE
3.5
FI
0.9
SI
0.7
IE
0.6
LT
0.6
PT
0.5
EL
0.4
EE
0.3
LV
0.2
CY
0.1
EA3: 70.1%
0
20
40
60
80
100
0
25
50
75
100
%, based on shares in Czech exportsCountry weights in the current effective euro area aggregate
Source: Eurostat, CZSO
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 38
Figure 2.3: EA country weights based on the Czech export shares,correlations of gdp growth rates with industrial produc-tion growth
AT
BE
CY
DE
EE
EL
ES
FI
FR
IE
IT
LT
LV
NL
PT
SI
SK
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50Need to nowcast?
(country weight in the effective EA)
Easy
to n
owca
st?
(cor
rela
tion
of G
DP
grow
th w
ith in
dust
rial p
rodu
ctio
n gr
owth
)
Correlation of GDP (q-o-q) with the German GDP 25 50 75 100
Source: Eurostat
Figure 2.4: GDP and industrial production growth rates
DE FR SK
00 02 04 06 08 10 12 14 16 18 00 02 04 06 08 10 12 14 16 18 00 02 04 06 08 10 12 14 16 18
-10
0
10
-5
0
-15
-10
-5
0
5
gdp_qoq ip_manufacturing
GDP and industrial production growth rates
Note: industrial production is transformed into quarterly frequency using the approach described by Mariano and Murasawa (2003)
Source: Eurostat
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 39
Figure 2.5: GDP and industrial production growth rates
DE FR SK
-15 -10 -5 0 5 -5 0 -10 0 10
-5
0
5
-1
0
1
-4
-2
0
2
ip_manufacturing
gdp_
qoq
before 2009 after 2009
GDP and industrial production growth rates
Note: industrial production is transformed into quarterly frequency using the approach described by Mariano and Murasawa (2003)
Source: Eurostat
Table 2.1: Correlation coefficients between GDP growth rates and in-dustral production growth rates
before 2009 after 2009
DE 0.68 0.94FR 0.90 0.85SK -0.06 0.62
Source: Eurostat
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 40
2.C Monthly indicators in univariate models (BMA,
correlations)
Figure 2.1: Variables selected based on BMA and correlations: Ger-many
BMA: posterior probabilities of inclusion Absolute value of correlations with GDP (q-o-q)
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0ecs_industry_confidence
orders_intermediatesus_manufacturing
exports_ex_euip_durables
exports_worldifo_industry_situation
ip_capital_goodsifo_manufacturing_situation
ip_intermediateit_nondom_manufacturing
ip_totalip_manufacturing
it_dom_manufacturingit_manufacturing
it_dom_mining_quarryingconstruction
ecs_construction_confidenceecs_construction_exp_employment
ifo_manufacturing_climateip_mining_quarrying
ifo_manufacturing_expectationsunrate_25over
ip_nondurablesit_manufacturing
ecs_services_confidenceecs_retail_confidence
exports_ex_euip_durables
Variables selected based on BMA and correlations: DE
Figure 2.2: Variables selected based on BMA and correlations: Slov-akia
BMA: posterior probabilities of inclusion Absolute value of correlations with GDP (q-o-q)
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0it_mining_quarrying
us_dom_carsit_dom_mining_quarrying
ecs_industry_exp_employmentip_durables
stoxx50us_ip_total
exports_ex_euecs_consumer_confidence
it_dom_manufacturingsp500
us_manufacturingecs_retail_confidence
retail_excl_vehiclesretail_nonfood
constructionip_manufacturing
ecs_retail_exp_employmentus_manufacturing
ecs_consumer_exp_unemploymentip_nondurables
it_nondom_manufacturingecs_construction_confidence
sp500us_oecd_business_surveys
ecs_construction_exp_employmentretail_excl_vehicles
us_umcsentip_durables
retail_nonfood
Variables selected based on BMA and correlations: SK
Figure 2.3: Variables selected based on BMA and correlations: France
BMA: posterior probabilities of inclusion Absolute value of correlations with GDP
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0us_retail
it_dom_manufacturingecs_industry_confidence
exports_worldecs_services_confidence
us_ip_totalecs_construction_exp_employment
ip_capital_goodsecs_industry_exp_employment
ecs_construction_confidenceus_manufacturing
it_manufacturingip_intermediate
ip_manufacturingip_total
ecs_services_confidence
us_oecd_business_surveys
it_manufacturing
ecs_construction_exp_employment
stoxx50
sp500
it_nondom_manufacturing
retail_excl_vehicles
car_registrations
it_nondom_mining_quarrying
ip_total
us_manufacturing
unrate_total
Variables selected based on BMA and correlations: FR
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 41
2.D Multivariate model equations
2.D.1 Germany
Models with leading indicators:
• Model 1: gdp qoq∼ ecs industry exp employment + ecs industry exp employment lag
+ ifo manufacturing expectations lag
• Model 2: gdp qoq∼ ifo manufacturing expectations + ifo manufacturing expectations lag
+ zew sentiment
Models with coincident indicators:
• Model 3: gdp qoq ∼ ip total + retail nonfood
• Model 4: gdp qoq ∼ ip manufacturing + retail nonfood
• Model 5: gdp qoq ∼ ip manufacturing + orders industry lag + retail nonfood
• Model 6: gdp qoq ∼ ip manufacturing + retail nonfood + unrate 25over
Models with leading and coincident indicators:
• Model 7: gdp qoq ∼ ifo manufacturing expectations + ip manufacturing
• Model 8: gdp qoq∼ ifo manufacturing expectations + ip manufacturing + retail nonfood
2.D.2 Slovakia
Models with leading indicators:
• Model 1: gdp qoq∼ ecs consumer exp unemployment + ecs consumer exp unemployment lag
+ ecs construction exp employment
• Model 2: gdp qoq∼ ecs consumer exp unemployment + ifo manufacturing expectations
Models with coincident indicators:
• Model 3: gdp qoq ∼ ip manufacturing + ip manufacturing lag + retail excl vehicles
• Model 4: gdp qoq ∼ ip durables + ip durables lag + retail nonfood
• Model 5: gdp qoq ∼ ip manufacturing lag + retail excl vehicles + unrate total +
unrate total lag
• Model 6: gdp qoq ∼ ip total + ip total lag + retail excl vehicles + us manufacturing
Models with leading and coincident indicators:
• Model 7: gdp qoq∼ ip total lag + retail excl vehicles lag + ecs consumer exp unemployment lag
• Model 8: gdp qoq∼ ip total lag + retail excl vehicles lag + ecs construction exp employment
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 42
2.D.3 France
Models with leading indicators:
• Model 1: gdp qoq sim ecs industry exp employment + ecs construction exp employment
• Model 2: gdp qoq sim ecs industry confidence + ecs services confidence
Models with coincident indicators:
• Model 3: gdp qoq ∼ ip total + ip total lag + retail excl vehicles
• Model 4: gdp qoq ∼ ip manufacturing + ip manufacturing lag + retail excl vehicles
• Model 5: gdp qoq ∼ ip manufacturing + ip manufacturing lag + unrate total
• Model 6: gdp qoq ∼ ip total + us manufacturing lag
Models with leading and coincident indicators:
• Model 7: gdp qoq ∼ ip total + ip total lag + ecs industry exp employment
• Model 8: gdp qoq∼ ip total + ip total lag + retail nonfood + ecs industry exp employment
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 43
2.E Root mean square errors
Table 2.1: Root mean square errors: Germany
Backcast Nowcast Forecast
model M1 M2 M3 M1 M2 M3 M1 M2 M3
benchmark modelsAR(2) 0.423 0.423 NA 0.401 0.401 0.417 0.410 0.410 0.432random walk 0.548 0.548 NA 0.500 0.500 0.578 0.568 0.568 0.556
common component modelpca 0.280 0.266 0.248 0.448 0.447 0.434 0.455 0.418 0.336
economic modelscoincident indicators 1 0.317 0.282 0.272 0.437 0.443 0.436 0.488 0.469 0.389coincident indicators 2 0.312 0.265 0.257 0.457 0.443 0.437 0.501 0.485 0.391coincident indicators 3 0.308 0.264 0.254 0.459 0.442 0.436 0.501 0.482 0.387coincident indicators 4 0.303 0.257 0.248 0.455 0.440 0.444 0.507 0.473 0.379leading indicators 1 0.442 0.442 0.422 0.352 0.397 0.402 0.430 0.426 0.419leading indicators 2 0.455 0.455 0.424 0.350 0.383 0.385 0.427 0.441 0.454mixed indicators 1 0.309 0.269 0.263 0.467 0.451 0.433 0.498 0.475 0.387mixed indicators 2 0.312 0.265 0.253 0.457 0.442 0.437 0.501 0.485 0.392
pairwise modelsbma 0.333 0.327 0.318 0.375 0.380 0.383 0.388 0.370 0.347correlations 0.310 0.306 0.298 0.423 0.414 0.409 0.448 0.412 0.341financial variables 0.489 0.489 0.472 0.445 0.493 0.502 0.499 0.487 0.489foreign variables 0.457 0.455 0.442 0.433 0.433 0.449 0.456 0.464 0.470industrial production 0.302 0.283 0.276 0.431 0.422 0.412 0.432 0.418 0.347leading indicators 0.366 0.366 0.355 0.339 0.357 0.365 0.377 0.371 0.368
2. Assessing the External Demand of the Czech Economy: Nowcasting ForeignGDP Using Bridge Equations 44
Table 2.2: Root mean square errors: Slovakia
Backcast Nowcast Forecast
model M1 M2 M3 M1 M2 M3 M1 M2 M3
benchmark modelsAR(2) 0.285 0.285 NA 0.327 0.327 0.297 0.312 0.312 0.287random walk 0.193 0.193 NA 0.307 0.307 0.237 0.236 0.236 0.186
common component modelpca 0.433 0.427 0.418 0.346 0.352 0.352 0.380 0.385 0.430
economic modelscoincident indicators 1 0.379 0.368 0.353 0.348 0.347 0.392 0.392 0.376 0.365coincident indicators 2 0.527 0.498 0.466 0.359 0.357 0.373 0.363 0.389 0.552coincident indicators 3 0.459 0.454 0.438 0.422 0.417 0.474 0.490 0.438 0.435coincident indicators 4 0.628 0.625 0.599 0.464 0.509 0.535 0.602 0.599 0.645leading indicators 1 0.766 0.766 0.715 0.627 0.662 0.669 0.788 0.774 0.766leading indicators 2 0.661 0.661 0.620 0.389 0.408 0.398 0.605 0.641 0.628mixed indicators 1 0.755 0.755 0.706 0.630 0.694 0.757 0.753 0.757 0.752mixed indicators 2 0.643 0.643 0.614 0.352 0.394 0.559 0.584 0.628 0.645
pairwise modelsbma 0.413 0.412 0.398 0.375 0.381 0.385 0.410 0.404 0.409correlations 0.435 0.434 0.420 0.391 0.398 0.400 0.445 0.414 0.419financial variables 0.656 0.656 0.635 0.599 0.644 0.647 0.647 0.647 0.639foreign variables 0.519 0.519 0.498 0.397 0.427 0.445 0.497 0.515 0.517industrial production 0.422 0.423 0.410 0.345 0.348 0.388 0.417 0.423 0.429leading indicators 0.445 0.445 0.427 0.445 0.434 0.439 0.447 0.451 0.446
Table 2.3: Root mean square errors: France
Backcast Nowcast Forecast
model M1 M2 M3 M1 M2 M3 M1 M2 M3
benchmark modelsAR(2) 0.306 0.306 NA 0.298 0.298 0.283 0.281 0.281 0.307random walk 0.362 0.362 NA 0.393 0.393 0.345 0.339 0.339 0.364
common component modelpca 0.232 0.246 0.231 0.277 0.272 0.260 0.242 0.224 0.229
economic modelscoincident indicators 1 0.230 0.223 0.215 0.280 0.281 0.290 0.288 0.263 0.250coincident indicators 2 0.246 0.233 0.224 0.279 0.279 0.293 0.280 0.247 0.247coincident indicators 3 0.246 0.226 0.217 0.284 0.286 0.282 0.277 0.249 0.254coincident indicators 4 0.254 0.231 0.226 0.292 0.297 0.293 0.299 0.284 0.276leading indicators 1 0.328 0.328 0.315 0.293 0.260 0.304 0.289 0.286 0.297leading indicators 2 0.299 0.299 0.290 0.273 0.307 0.308 0.330 0.305 0.294mixed indicators 1 0.223 0.211 0.205 0.287 0.279 0.287 0.297 0.274 0.249mixed indicators 2 0.210 0.212 0.203 0.282 0.272 0.282 0.283 0.260 0.235
pairwise modelsbma 0.241 0.248 0.241 0.275 0.275 0.275 0.268 0.254 0.249correlations 0.218 0.218 0.212 0.269 0.262 0.266 0.249 0.231 0.222financial variables 0.369 0.369 0.354 0.320 0.352 0.362 0.360 0.357 0.357foreign variables 0.317 0.316 0.306 0.296 0.301 0.304 0.311 0.305 0.312industrial production 0.265 0.266 0.249 0.287 0.288 0.301 0.279 0.273 0.264leading indicators 0.286 0.286 0.276 0.278 0.267 0.283 0.281 0.280 0.278
Chapter 3
Modeling Euro Area Bond Yields
Using a Time-Varying Factor
Model
Abstract
In this paper, we study the dynamics and drivers of sovereign bond
yields in euro area countries using a factor model with time-varying
loading coefficients and stochastic volatility, which allows for cap-
turing changes in the pricing mechanism of bond yields. Our key
contribution is exploring both the global and the local dimensions
of bond yield determinants in individual euro area countries using
a time-varying model. Using the reduced form results, we show de-
coupling of periphery euro area bond yields from the core countries’
yields following the financial crisis and the scope of their subsequent
re-integration. In addition, by means of the structural analysis
based on identification via sign restrictions, we present time vary-
ing impulse responses of bond yields to EA and US monetary policy
shocks and to confidence shocks.
This paper was co-authored by Marco Lo Duca (ECB). It was published in ECB workingPaper Series as a paper No 2012/February 2017. The authors would like to thank for helpfuldiscussions and valuable feedback to: Giorgio Primiceri, Fabio Canova, Roberto De Santis,Giulio Nicoletti, Mahir Binici, Marek Jarocinski, Joshua Chan, participants to the INFINITI2016 Conference, and to participants to internal seminars of the European Central Bank.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 46
3.1 Introduction
Sovereign bond markets have increasingly drawn the attention of policy makers
and academics in recent years. As the global financial crisis and the European
banking and sovereign crises demonstrated, understanding the pricing mech-
anism and the drivers of bond yields is essential to monitor risks, decide on
policies and assess their effectiveness.
First, sovereign bonds are benchmark financial instruments used for pricing
of a large variety of financial assets, including bank loans and derivatives. As
a consequence, sovereign bond yields have implications for the broader macro
financial environment and the transmission of monetary policy.
Second, as short term rates hit the zero lower bound across advanced econ-
omies, central banks resorted to unconventional monetary policies, including
large purchases of sovereign bonds, with the aim of providing stimulus by lower-
ing long term yields. This led the academic and policy communities to step up
the efforts to analyse bond markets to assess the effectiveness, the transmis-
sion channels and international spill-overs of unconventional monetary policy
((Gagnon et al., 2011), (D’Amico and King, 2013), (Wright, 2012), (Joyce et al.,
2011) for the UK; (Hancock and Passmore, 2011), (Stroebel et al., 2012), (Hat-
tori et al., 2016), (Rosa, 2012), (Gilchrist et al., 2014), (Neely et al., 2010),
(Chen et al., 2012), (Fratzscher et al., 2013), (Rogers et al., 2014), (Bowman
et al., 2015), (Christensen and Rudebusch, 2012), (Bauer and Neely, 2014),
(Krishnamurthy and Vissing-Jorgensen, 2011), (Bauer and Rudebusch, 2014)).
Finally, the European sovereign and banking crisis showed the importance
of understanding signals from bond markets in order to assess the underly-
ing pricing factors and design appropriate policy responses ((De Santis, 2012),
(De Santis, 2015), (De Grauwe and Ji, 2013), (Beirne and Fratzscher, 2013)).
On the one hand, a number of contributions suggest that, at the peak of the
sovereign debt crisis, euro area bond yields reflected fundamentals, in particu-
lar the expected deterioration of the macro environment and of fiscal positions.
On the other hand, a number of other contributions suggest that risk aversion,
panic and irrational investors’ behaviour drove bond yields.
Overall, the evidence presented on the European crisis supports the view
that the pricing mechanism of sovereign bond yields might change over time,
consistent with the existence of multiple equilibria and market imperfections.
Against the background of the importance of understanding the drivers of
bond yields, especially in a crisis/post crisis environment, this study contributes
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 47
to the policy debate and the academic literature by presenting a new model to
assess the pricing mechanism of euro area sovereign bond yields from a dynamic
perspective. In particular, we use a factor model with time varying loading
coefficients and stochastic volatilities to assess the drivers of sovereign bond
yields in euro area countries. The time variation in factor loading coefficients
allows for capturing changes in the pricing mechanism of bond yields, consistent
with the evidence emerging from other empirical studies. Exploring both the
global and local dimensions of bond yield determinants in individual euro area
countries is one of our key contributions. Specifically, our model studies the
drivers of country specific yields separating between (i) Euro area core and
periphery factors to assess integration, spill-overs and contagion within the
euro area (ii) US and Emerging Market Economies (EMEs) market factors to
assess spill-overs to the euro area from the rest of the world. Finally, time
varying impulse responses to monetary policy shocks and confidence shocks
are identified via sign restrictions and studied.
From a financial stability perspective, the model presented in this article
allows for the detection of anomalies or rapid changes in the pricing mechanism
of bonds. For example, the model can detect early signs of de-coupling among
euro area bond markets when idiosyncratic volatilities increase and when the
role of the loading coefficient of the ”core” euro area factor decreases. It can
detect early signs of contagion when the loading coefficient of the ”periphery”
euro area factor increases. It can also be used to monitor the intensity of the
spill-overs from the rest of the world by looking at the loading coefficients on
the external variables. Relevant benchmarks for assessing the level of anomalies
in the pricing mechanism are provided by loading coefficients, volatilities and
shape of impulse responses in the pre-crisis and crisis periods. From a monet-
ary policy perspective, the model provides useful information on whether the
pricing mechanism changes in response to policy actions.
From an academic perspective, this study improves on the existing literature
((Boysen-Hogrefe, 2013), (D’Agostino and Ehrmann, 2013)) by adding external
factors (US and EMEs) and other variables into a dynamic factor model with
time varying loading coefficients for euro area bond yields. Furthermore, the
study presents new evidence based on time varying impulse responses to discuss
how the transmission of EA and US monetary policy shocks has evolved during
the crisis. In addition, from the econometric point of view, the study shows
how a recently proposed precision-based simulator of state-space models by
Chan and Jeliazkov (2009) can be used to sample factors in a FAVAR model
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 48
after a correction of singularity in the transition matrix.
The empirical analysis presented in the paper shows that there is substantial
time variation in the loading coefficients of factors and in the impulse responses
of yields to different shocks. This supports the view that the pricing mechanism
of bond yields is not stable across periods, suggesting the existence of multiple
equilibria where the pricing factors for bonds differ. In particular, the model
captures well the unfolding of the European sovereign and banking crisis as
of 2010 and the subsequent re-integration of markets after 2012. As of 2010,
when the crisis escalated, idiosyncratic volatilities in a number of euro area
countries spiked, bond yields in the periphery gradually became more sensitive
to the euro area ”periphery” factor and less sensitive to the ”core” factor. At
the same time the impulse responses of bond yields in some countries changed
shape, suggesting changes in the transmission of monetary policy shocks. After
2012, the pricing mechanism gradually approached the situation prevailing in
the pre-crisis periods.
The results of the analysis have implications for the debate on the im-
pact of unconventional monetary policy on sovereign bond markets in the euro
area. Specifically, our results suggest a link between euro area unconventional
policies, the way different factors are priced into bond yields and the reaction
of bond yields to monetary policy shocks. A notable finding is that the an-
nouncement of Outright Monetary Transactions by the ECB appears to have
led to the gradual normalisation of the pricing mechanism of bond yields to-
wards the pre-crisis situation. Another interesting finding is that the ECB mix
of unconventional monetary policy gained particular traction in those markets
experiencing distress where accommodation was needed.
The remainder of the paper is organised as follows. The next section
presents the model and the data used for the empirical analysis. The sub-
sequent two sections discuss the results and their implications for financial
stability surveillance and for the analysis of monetary policy. The final section
concludes.
3.2 Methodology and data
3.2.1 Model setup
To study the dynamics of bond yields, we use a FAVAR model with time-
varying loadings. In our benchmark model, first differences of bond yields of N
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 49
euro area countries are assumed to be driven by two euro area factors, dynam-
ics of bond yields in the United States and in emerging markets, by changes in
USD/EUR exchange rate and finally by country-specific idiosyncratic shocks.
The five driving factors in turn evolve according to a VAR(p) process, which al-
lows us to study interactions between the factors themselves and also responses
of each euro area government bond yields to these factors.
More formally, let yi,t denote bond yield of country i (i = 1, ...N) at time t,
iust , iemet denote the US and emerging market factors, st denote the USD/EUR
exchange rate and λi,j,t denote loading of i-th country on j-th factor at time t.
This notation leads to the following measurement equation:
yi,t = λi,1,tf1,t + λi,2,tf2,t + λi,3,tiust + λi,4,ti
emet + λi,5,tst + vi,t, (3.1)
vi,t ∼ N(0, σ2vi,t
) (3.2)
We assume that the loadings on the five factors driving euro area bond
yields are time-varying. This allows us to study how the pricing mechanism
changes over time. Another approach to allow for time-varying parameters in
the FAVAR is taken by Mumtaz et al. (2011), who allow for changing para-
meters in the VAR part of the model. We opt for the first specification, since
our emphasis is on the identification of drivers (factors) driving bond yields in
each euro area country.
In line with the literature (e.g., Primiceri (2005)) and in order to reduce
dimensionality of the model, we assume that time-varying loadings follow a
random walk process:
λi,j,t = λi,j,t−1 + εi,j,t, εi,j,t ∼ N(0, σ2εi,j
), (3.3)
where shocks εi,j,t are uncorrelated across equations, explanatory variables
and time (indices i, j, t, respectively).
In addition to loadings, idiosyncratic shocks to the measurement equation
are allowed to be time-varying and follow a random walk stochastic volatility
process:
log σ2vi,t
= log σ2vi,t−1
+ εvt , εvt ∼ N(0, σε2v) (3.4)
The common factors and ”exogenous” variables evolve according to a stand-
ard VAR process:
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 50
Yt = Φ(L)Yt + et, et ∼ N(0,Σ), (3.5)
where Yt = f1,t, f2,t, iust , i
emet , st, Φ(L) is a multivariate lag polynomial
(which includes an intercept in each VAR equation) and Σ is a general covari-
ance matrix, i.e., we allow for non-zero correlation between shocks to the VAR
equations.
Identification of factors
The factors f1,t and f2,t are identified using the strategy suggested by Bernanke
et al. (2005) by assuming restrictions on the first two rows of matrix Lt, which
stacks the row vectors (λi,1,t, λi,2,t, λi,3,t, λi,4,t, λi,5,t) across index i. Specifically,
we assume that λi,j,t = 1 for i = j and λi,1,t = 0 otherwise, for i = 1, 2.
This identification strategy allows us to interpret the common factors, when
ordering of variables is chosen properly. In our case, we choose the first two
bond yield series to represent bond yields of Belgium and Greece, respectively.
This means that bond yield dynamics of Belgium is contemporaneously unaf-
fected by movements in the second factor, bond yields in the US and emerging
markets. Similarly, in other words, movements in Greek government bond
yields are contemporaneously driven only by the second factor and idiosyn-
cratic shocks. As a result of this identification, we can loosely interpret the
first euro area factor as the core factor (λcorei,t ≡ λi,1,t) and the second euro area
factor as the periphery factor (λperipheryi,t ≡ λi,2,t).
One may argue why German yields were not chosen to be ordered first,
instead of Belgian. We do not opt for this possibility, since due to safe haven
effects observed in the recent years, it is not reasonable to assume that λperipheryDE,t
would be always zero. Instead, one can expect λperipheryDE,t to be often negative.
In addition, a robustness check for this alternative identification strategy did
not yield substantially different results.
It is worth noting that the first factor estimated using the baseline setup is mostlycorrelated with changes in yields in Finland (91%) and Germany (90%), while the correlationcoefficients with changes in yields in Belgium is 75%. The second factor is mostly correlatedwith yields in Italy (43%), Greece (38%) and Spain (37%). This confirms that the chosennormalization of factors does not predetermine the shape of the estimated factors and alsomotivates the names of the factors (core / periphery). The correlations are also depicted inFigure.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 51
Table 3.1: Sign restrictions on responses (on impact) to structuralshocks
EA core EA periphery US EME USD/EUR
EA monetary policy shock + + + +
US monetary policy shock + + -
Risk aversion shock - + -
Note: The plus sign in the USD/EUR column denotes the appreciation of eurovis-a-vis the US dollar.
Identification of structural shocks
In order to identify structural shocks in the model and draw impulse responses,
we use an identification scheme based on contemporaneous sign restrictions
(see Table 3.1). We focus on three structural shocks. The tightening EA
monetary policy shock is characterized by an increase in the euro area core and
periphery factors, by an appreciation of the euro vis-a-vis the US dollar and
by an increase in bond yields in emerging markets. This set of sign restrictions
is motivated by standard assumptions on the impact of monetary policy on
quasi-risk free yields, as captured by the core factor, and on the exchange rate
. In addition, we impose that the periphery factor, which prices in sovereign
risk in troubled euro area countries, and emerging market yields, which prices
in other risk factors, increase with monetary policy tightening, consistent with
the findings on the impact on monetary policy on risk (Fratzscher et al. (2016),
Bekaert et al. (2013)). Similarly to the euro area monetary policy shock, the
tightening US monetary policy shock is characterized by an increase in the US
and EME yields and by an appreciation of the US dollar. Finally, the risk
aversion shock (or negative shock to market confidence) leads to higher yields
in emerging markets, US dollar appreciation and lower US yields, reflecting safe
haven flows. For the risk aversion shock, we leave responses in the euro area
core and periphery factors unrestricted. We discuss the identified structural
shocks and potential alternative approaches in Section 5.
Yields are expected to increase and the exchange rate to appreciate in response to mon-etary tightening
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 52
Estimation
The model is estimated using Bayesian techniques, where posterior distribu-
tions of parameters are approximated by the Gibbs sampler. Technical details
of the estimation are provided in the Appendix. Worth to note is that the di-
mension of the model is large, both in terms of the number of observations and
parameters. The unobserved variables (factors, factor loadings and stochastic
volatilities of idiosyncratic shocks) are usually estimated using simulation al-
gorithm, such as that proposed by Carter and Kohn (1994). In contrast, we use
a relatively recent precision-based simulator suggested by Chan and Jeliazkov
(2009), which significantly reduces the computational burden in that it avoids
the Kalman filtering step used in the standard algorithms. We run the Gibbs
sampler 55,000 times and discard the first 50,000 draws as a burn-in sample.
The subsequent 5,000 draws of parameters are used to compute posterior quant-
ities.
3.2.2 Data
We use weekly data on 10 year government bond yields for the analysis, starting
in October 2005 and ending at the end of August 2016. The data are plotted in
Figure 3.1. We difference the data to achieve stationarity required for the factor
analysis and subsequently standardize them for computational purposes.
We use a common standardization, i.e., demeaning and dividing by a standard deviation.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 53
Figure 3.1: Sovereign bond yields and euro/dollar exchange rate (US-DEUR)
0
2
4
2006 2008 2010 2012 2014 2016
AT BE DE FI FR NL
0
10
20
30
40
2006 2008 2010 2012 2014 2016
ES IE IT PT GR
2
4
6
8
2006 2008 2010 2012 2014 2016
US EME
1.0
1.2
1.4
1.6
2006 2008 2010 2012 2014 2016
USD/EUR exchange rate
Source: Datastream
3.3 Results
The model described in the previous section yields several outputs, which we
study subsequently.
3.3.1 Reduced-form results: estimated factors, idiosyncratic
volatilities and loading coefficients
The raw estimated factors are not very informative on their own, since they
are estimated on stationary time series and therefore capture co-movements
of weekly bond yield changes, which can be very noisy. To obtain a more
informative insight from the factors, we focus on their cumulative sums (Figure
3.2), which show general directions of bond yield movements. A number of
stylised facts are worth noting. First, the euro area core factor displays a
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 54
Table 3.2: Descriptive statistics for sovereign bond yields andeuro/dollar exchange rate (USDEUR)
Levels Differences
Variable n min max mean median sd min max mean median sd
AT 559 0.24 4.84 2.83 3.24 1.27 -0.28 0.39 -0.01 -0.01 0.08
BE 559 0.37 5.41 3.11 3.58 1.28 -0.65 0.57 0.00 -0.01 0.10
DE 559 0.00 4.64 2.48 2.67 1.30 -0.30 0.27 -0.01 -0.01 0.08
EME 559 5.24 8.48 6.59 6.58 0.51 -0.48 0.44 0.00 -0.01 0.08
ES 559 1.20 7.25 3.99 4.10 1.27 -1.22 0.62 0.00 0.00 0.14
FI 559 0.22 4.89 2.71 2.93 1.28 -0.31 0.30 0.00 -0.01 0.08
FR 559 0.39 4.81 2.87 3.22 1.19 -0.27 0.35 -0.01 -0.01 0.08
GR 559 3.39 38.35 9.61 7.65 6.97 -19.60 5.11 0.01 0.01 1.11
IE 559 0.68 14.02 4.51 4.32 2.40 -1.89 1.59 0.00 -0.02 0.21
IT 559 1.19 7.05 4.00 4.25 1.23 -1.00 0.57 0.00 -0.01 0.12
NL 559 0.23 4.82 2.72 2.92 1.28 -0.25 0.28 -0.01 -0.01 0.08
PT 559 1.65 15.60 5.43 4.44 2.81 -2.26 1.91 0.00 0.00 0.29
US 559 1.44 5.21 3.08 2.88 1.05 -0.41 0.31 0.00 -0.01 0.10
USDEUR 559 1.06 1.59 1.31 1.32 0.11 -0.06 0.10 0.00 0.00 0.02
Source: Datastream
similar pattern to core euro area countries’ bond yields, as observed in Figure
4.5. Second, the euro area periphery factor captures well the evolution of
sovereign tensions across the euro area. In particular, the periphery factor
started to follow an upward trend in 2010 reaching a peak in 2012. It stabilised
in early 2012, following the three year ECB long-term refinancing operations
(LTROs) and reverted in the second part of the year after the ECB announced
the possibility of Outright Monetary Transactions (OMT). After the summer of
2012, the periphery factor followed a generally declining trend. This evidence
suggests a role of ECB policies in bringing the pricing mechanism of bond
yields to “normal” times. Another interesting finding is that the downward
trend in the periphery factor did not revert during the summer 2015, the period
of large uncertainty related to the extension of the macroeconomic adjustment
programme in Greece. This suggests that the latter episode of turmoil remained
largely contained. A last finding is that one can observe a decoupling of the
euro area core factor from US yields after 2013, when monetary policy in the
euro area and in the US started diverging.
Turning to the stochastic volatility of idiosyncratic shocks (Figure 3.3), it
was generally elevated during the peak of the financial crisis of 2008, reflecting
the turmoil in financial markets. Another generally observed peak coincides
with the beginning of 2012, i.e. around the peak of the sovereign debt crisis.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 55
Figure 3.2: Cumulative sums of estimated factors and exogenous vari-ables
SMPLTRO1LTRO2
OMT
EAPP
SMP
LTRO1LTRO2OMT
EAPP
SMP
LTRO1LTRO2
OMT
EAPP
core periphery
us eme
usd/eur
-10
0
10
20
30
-10
0
10
20
-10
0
10
-10
0
10
20
30
0
10
20
30
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
06 07 08 09 10 11 12 13 14 15 16 17
Note: exogenous variables used for the analysis were stationarized andstandardized, subsequently.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 56
Figure 3.3: Stochastic volatility of idiosyncratic shocks to bond yields:posterior median, 16th and 84th quantiles.
AT BE DE
ES FI FR
GR IE IT
NL PT
0
2
4
0
2
4
0
2
4
0
2
4
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
Interestingly, stochastic volatility in Greece evolves relatively smoothly com-
pared to other countries. This reflects the high standard deviation of changes in
Greek bond yields on which the model is estimated and additionally its loading
on the periphery factor, which explains Greek bond movements relatively well
on average. Nevertheless, stochastic volatility of idiosyncratic shocks of Greek
bonds was elevated during the summer 2015, reflecting the uncertainty around
the extension of the adjustment programme.
Turning to factor loadings (Figures 3.4 and 3.9 - 3.11), there are a number
of interesting findings. First, at the beginning of the sample, loadings on both
the core and the periphery factors were homogeneous, reflecting the integra-
tion of the euro area bond markets. Second, following the financial crisis of
2008, loadings of all countries on the core factor generally declined. Third,
the loadings of IT, PT, IE, ES started decoupling from the loadings of other
countries in 2009. Their loadings on the core factor declined significantly, while
the loading on the periphery factor substantially increased. Consistently with
the dynamics of the periphery factor, the decoupling reached its peak in 2012,
after which countries became again more homogeneous (as measured by the
similarity of loading coefficients). It is worth noting that the reversal in the
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 57
Figure 3.4: Evolution of loadings of bond yields on factors
(a) Loadings on the core factor (b) Loadings on the periphery factor
0.0
0.5
1.0
0.0
0.5
1.0
1.5
2006 2008 2010 2012 2014 2016 2006 2008 2010 2012 2014 2016
AT DE ES FI FR IE IT NL PT
dispersion among loading coefficients coincides with the announcement of the
OMT programme in summer 2012 (denoted in figures in the Appendix). The
OMT brought about a change in the pricing mechanism of sovereign bonds,
leading to “re-integration” between the periphery and the core of the euro
area. Nevertheless, at the end of the sample, loadings on the core factor were
still lower than at the beginning of the sample, while loadings on the periphery
factor were higher (particularly in the case of Portugal, Spain, and Italy). In-
terestingly, the loadings of Germany and Finland on the periphery factor are
generally negative, which reflects their safe haven status. The safe haven status
of these two countries is further reflected by periods of large positive loadings
on the exchange rate (Figure 3.9), which signals that depreciation of the euro
tends to be associated with declining yields in Germany and Finland on aver-
age.
3.3.2 Structural form results
Regarding the structural analysis, it is worth checking the evolution of struc-
tural shocks in order to assess the plausibility of the imposed sign restrictions.
To facilitate the identification of periods of “prevailing” monetary accommod-
ation, Figure 3.5 plots semi-annually cumulated euro area and US monetary
policy shocks. In the euro area, significant loosening of monetary policy occurs
in the second half of 2008 and 2011, in the first half of 2010 and during 2012
On July 26 2012, the ECB president hinted to the imminent adoption unconventionalmonetary policy measure during his speech in London. The OMT was finally announced inAugust 2012.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 58
Figure 3.5: Semiannually cumulated structural shocks
EA monetary policy shocks US monetary policy shocks
-5
0
5
06-1 07-1 08-1 09-1 10-1 11-1 12-1 13-1 14-1 15-1 16-1 06-1 07-1 08-1 09-1 10-1 11-1 12-1 13-1 14-1 15-1 16-1
Cummulated structural shocks
and 2014. All of these periods coincide with important monetary policy ac-
tions. The detected accommodation in the second half of 2008 corresponds to
aggressive rate cuts and provision of liquidity in the aftermath of the collapse of
Lehman Brothers. Accommodation in 2010 and 2011 corresponds to the intro-
duction and the re-activation of the Security Market Program (SMP). Easing in
2012 reflects the unprecedented provision of long term loans via the three year
long term refinancing operations and the announcement of Outright Monetary
Transactions (OMT). Finally, accommodation in 2014 reflects the progressive
building up of expectations and the final announcement of the Extended Asset
Purchase Program (EAPP). Turning to the US monetary policy shocks, one
can observe loosening in the second half of 2008, and 2011 in response to the
introduction of different rounds of bond purchases. On the other hand, the
model correctly captures the announcement of tapering of bond purchases in
2013 and the build-up of expectations of monetary policy tightening in 2015.
To validate our identification scheme, we also check the largest identified
shocks. For euro area the largest accommodative monetary policy shocks oc-
curred in the weeks when the SMP (May 2010) and the EAPP (January 2015)
were announced. The largest accommodative US monetary policy shocks coin-
cided with the initial announcement of the LSAP programme (November 2008)
and its expansion to government securities (March 2009). On the other hand,
one of the largest tightening shock for the US was in June 2013, when the
”tapering” of the QE programme by the Fed was anticipated.
Figure 3.6 depicts responses to the identified shocks described in the meth-
odology section (euro area and the US monetary policy shocks, respectively,
and the risk aversion shock). The shocks are priced in quickly, reflecting the
fast behaviour of financial markets. In addition, the speed of responses is lowest
in emerging market economies.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 59
Figure 3.6: Cumulative impulse responses to structural shocks: pos-terior median, 16th and 84th quantiles. x-axis: weeks
CORE PERIPHERY US EME USD/UER
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
-1.0
-0.5
0.0
0.5
1.0
EA
m.p
. sh
ock
US
m.p
. sh
ock
Ris
k av
ersi
on
sh
ock
1 3 5 7 9 1 3 5 7 9 1 3 5 7 9 1 3 5 7 9 1 3 5 7 9
The responses to the euro area (tightening) monetary policy shock are sig-
nificant for the core and periphery factors, as well as for the exchange rate,
leading to an appreciation of the euro vis-a-vis the US dollar. The same shock
leads to positive responses of the US (not specified by the sign restrictions)
and emerging market yields, although the reaction is statistically insignificant
in the first two weeks in case of the United States. A tightening US monetary
policy shock leads to a significant positive response in emerging markets and
to a significant appreciation of the dollar vis-a-vis the euro. The same shock
leads to a positive, significant, response in the euro area core factor, which is
not implied by the sign restrictions. Finally, increasing risk aversion, which by
definition leads to the appreciation of the dollar accompanied by rising yields
in the EMEs and declining yields in the United States, leads to a decrease in
yields in the core and an increase in the periphery, although the responses in
the periphery are insignificant. This can be explained by a various nature of
the risk aversion shocks (global vs local, for example).
The impulse response functions presented so far have been computed using
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 60
the VAR equation of the FAVAR model based on the assumption of constant
coefficients. These results can be transformed using time-varying loadings into
time-varying impact responses of each country to each structural shock, which
are depicted in Figures 3.7. The time varying impulse responses provide inter-
esting insights on how the transmission of monetary policy has evolved during
recent years, reflecting market conditions and different policy mixes.
The results suggest that at the beginning of the sample, the responses of
sovereign yields to all shocks were relatively homogeneous across countries,
consistent with a high degree of financial integration in Europe. Focusing on
the euro area monetary policy shock, the responses of PT, ES, IT and IE
started decoupling from the other countries in 2008. Overall, between 2008
and 2014 impulse responses remained dispersed across euro area countries. At
the end of the sample, responses were homogenous again across the euro area,
with the exception of PT, IT and ES. The latter result suggests at least partial
normalisation of the transmission mechanism of monetary policy to bond yields
in the euro area.
Interestingly, bond yields in troubled euro area countries (PT, IT, IE and
ES) became more sensitive to euro area monetary policy as the crisis escal-
ated. This finding apparently contradicts the narrative that the transmission
mechanism of monetary policy in the euro area became impaired during the
crisis. While this may indeed be the case for the transmission of conventional
monetary policy via short term rates, other forms of unconventional monet-
ary policy were introduced during the crisis specifically to overcome the lack of
”grip” of conventional monetary policy. By relying on the identification scheme
based on sign restrictions on the movement of factors and the exchange rate,
our approach captures the impact of the overall mix of monetary policy on
bond yields. Against this backdrop, the finding that yields in troubled euro
area countries react more to the mix of monetary policy is not surprising. This
supports the view that new forms of monetary policy were most effective where
they were needed, i.e. in bond markets of troubled euro area countries.
Turning to US monetary policy shocks, the responses of euro area bond
yields were also homogeneous at the beginning of the sample, suggesting strong
integration in European sovereign bond markets. Similarly to the responses
to euro area monetary policy shocks, the dispersion of responses increased
significantly starting from 2010, when the euro area banking and sovereign
crisis escalated, and peaked in 2012. At the end of the sample, responses were
homogenous again across the euro area, with the exception of IE, IT and PT. It
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 61
Figure 3.7: Impact coefficients to the euro area and US monetarypolicy shocks - annual averages
DEATNLFIFR
ITIE
ES
PT
0.02
0.04
0.06
2004 2006 2008 2010 2012 2014 2016
EA m.p. shock
PT
IT
IEESATFINLFRDE
-0.02
0.00
0.02
2004 2006 2008 2010 2012 2014 2016
US m.p. shock
DE
FINLATFR
IEESIT
PT
0.01
0.02
0.03
2004 2006 2008 2010 2012 2014 2016
Risk aversion shock
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 62
is worth noting how countries largely driven by the periphery factor during the
acute phase of the European crisis (PT, IT, IE, ES) were ”isolated” from the
US monetary policy shocks. The higher and more stable impact coefficients
of the euro area other countries could be related to substitutability of their
bonds with US Treasuries in portfolios of global bond investors. The impulse
response analysis suggests that this substitutability was lost by troubled euro
area countries after the financial crisis of 2008. At the same time, yields of
these countries started to react more sensitively to risk aversion shocks and
this sensitivity diminished somewhat only after 2012.
The impulse response analysis described so far suggests how yields of each
country react over time to shocks of the same size. In order to assess the drivers
of changes in bond yields, one can employ an historical decomposition (plotted
in Figure 3.8). The results show that the euro area core factor was driven to
a large extent by euro area monetary policy shocks, which led to declines in
yields particularly in 2008, 2012 and 2014, i.e. years when the ECB either cut
interest rates or announced programmes to further ease monetary conditions.
Furthermore, one can observe the opposite effect of expectations of tightening
the US monetary policy in 2013 and 2015. Changes in the periphery factor
were largely driven by unexplained shocks, which plausibly capture the local
risk aversion and worsening fundamentals, i.e. effects we are not able to identify
using our relatively parsimonious model. On the other hand, loosening of the
euro area monetary policy in 2012, 2014 and 2015 was successful in driving
down the periphery factor.
Regarding the US factor, one can observe that changes in the euro area
monetary policy had relatively small impact on its changes. In addition, the
model identifies significant loosing in 2008 and 2011 and tightening in 2013 and
2015. Finally, the US monetary policy had a significant loosening effect on EME
yields in 2011 and 2012, reflecting portfolio rebalancing effect of unconventional
monetary policy. On the other hand, the tapering announcement in 2013 and
expectations of tightening the US monetary policy in 2015 contributed to an
increase in EME bond yields.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 63
Figure 3.8: Historical decomposition of annual changes in bond un-observed factors, bond yields in the US and EMEs.
-10
0
10
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
ea m.p. resid risk aversion us m.p.
core
-10
-5
0
5
10
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
ea m.p. resid risk aversion us m.p.
periphery
-10
0
10
20
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
ea m.p. resid risk aversion us m.p.
us
-10
0
10
2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
ea m.p. resid risk aversion us m.p.
eme
3.4 Discussions of the results
3.4.1 Implications for financial stability surveillance
The results discussed in the previous section support the view that the pricing
mechanism of bond yields evolved during the European banking and sover-
eign crisis. First, a new pricing (periphery) factor associated to the euro area
troubled countries emerged during the acute phase of the crises. Second, load-
ing coefficients of bond yields on the different factors changed substantially
during the crisis. Specifically, the loading coefficients of troubled countries on
the periphery factor increased, while those on the core factor decreased. The
opposite was true for other euro area countries. Third, the reaction of yields
to US and Euro area monetary policy shocks also evolved according to market
conditions.
The results support the view of three distinct phases in euro area sovereign
bond markets between 2006 and early 2016. In an initial phase of almost
full integration, only one pricing factor mattered for euro area sovereign bond
yields (i.e. the core factor). Also, loading coefficients and impulse responses
to shocks where homogeneous across sovereign bond markets in this period. In
the second phase, when the crisis escalated, bond yields decoupled: some bond
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 64
yields remained tightly linked to the core factor, while others became linked
to the periphery factor. During this phase, also the transmission of monetary
policy was heterogeneous across countries. Lastly, in the third phase of partial
re-integration of bond markets, the pricing mechanism appeared to approach
the pre-crisis conditions according to loading coefficients and impulse responses.
Concerning potential explanations of the above findings, as discussed in
((Lo Duca, 2012)), there are several reasons why the determinants of asset
prices could change across periods. First, during turbulent periods, informa-
tion asymmetries could prevent the market to clear at a given price ((Stiglitz
and Weiss, 1981)). Second, heterogeneous investors have different allocation
strategies, therefore pricing changes across periods are reflecting the mix of
active investors. The latter is likely to have changed substantially during the
crisis, especially for sovereign bonds in troubled euro area countries. In partic-
ular, evidence suggests that the pool of active investors in these bond markets
shrank and liquidity got much thinner. Third, during periods of market turbu-
lence, investors might face binding constraints as, for example, margin calls, or
the need to sell certain assets to preserve the risk profile of their portfolios. In
this context, investment decisions are either increasingly influenced by certain
events, as rating actions, or become increasingly related to the dynamic of cer-
tain variables as, for example, the price or the volatility of certain benchmark
assets. As pointed by Adrian et al. (2010), this can generate self-enforcing
de-leveraging cycles that increase the sensitivity of prices and flows to common
factors. Fourth, the information set that investors use to price assets might
change over time. This might have been the case during the European banking
and sovereign crisis when ex-ante unlikely fears of euro break up started being
priced into sovereign bonds (Draghi (2012), De Santis (2015)).
The above results suggest a framework to assess the gravity of distress
in bond markets based on the model presented in this paper. First, spiking
idiosyncratic volatilities are a first sign of market turbulence. Although, as
demonstrated by the 2015 Greek episode, a spike in the idiosyncratic volatility
in one market does not necessarily transmit to other markets. Idiosyncratic
volatilities could be benchmarked to average levels in the pre-crisis and in
the crisis periods. Second, looking at the pricing of the periphery and the core
factors across bond markets is important to assess the degree of integration and
spill-overs across countries. Significant turbulence would be detected when the
loading on the periphery factor increases in one country. A dangerous situation
of contagion would emerge when the loading coefficient of the periphery factor
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 65
increases in more countries. Generally, the dispersion of the loading coefficients
for each factor could be benchmarked to the levels observed during the acute
phase of the crisis.
3.4.2 Impact of monetary policy on the pricing mechanism
of sovereign bond yields
Our results have implications for the debate on the impact of unconventional
monetary policy on bond markets. While the literature predominantly quanti-
fies the impact of unconventional monetary policy on bond yields and it assesses
the transmission channels (e.g. signalling channel vs portfolio balance chan-
nel), our results shed light on the impact of policies on the pricing mechanism of
yields. Specifically, our results suggest an intriguing link between euro area un-
conventional policies, the way different factors are priced into bond yields and
the reaction of bond yields to monetary policy shocks. While it is extremely
difficult to formally test the link between unconventional monetary policy and
changes in the pricing mechanism of sovereign bond yields, a number of stylised
facts appear to support the view that the announcement of Outright Monetary
Transactions by the ECB was a game changer leading to a turning point in
several indicators of markets stress. Conversely, several other unconventional
monetary policy actions, including the Security Market Programme (SMP),
other purchases programmes and liquidity injections, while having visible pos-
itive effects (Fratzscher et al. (2016)), only temporarily halted the escalation
of the crisis. Specifically, the OMT announcement coincides (i) with turning
points in the cumulated dynamics of the periphery factor which started decreas-
ing the second half of 2012, (ii) with a gradual normalisation of the loading
coefficients of bond yields on the core and periphery factors towards pre-crisis
levels and (iii) with gradual normalisation of the reaction of euro area bond
yields to monetary policy shocks.
Another interesting finding relates to the dynamic response of sovereign
yields to euro area monetary policy shocks. In particular, over time, yields in
troubled euro area countries became more responsive to EA monetary policy
shocks. At the same time, the response of yields in other euro area countries did
not display substantial changes. This suggests that ECB mix of unconventional
monetary policy was particularly effective in those markets in distress where
risk premia rose and where accommodation was needed.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 66
3.4.3 Robustness analysis
We check the robustness of our findings along several dimensions. Regarding
the reduced form analysis, we test alternative assumptions to identify the core
and periphery factors. In our benchmark specification, we identify the signs
and magnitudes of the factors by assuming that changes in the Belgian sov-
ereign yields on the core factor have loading equal to one and zero elsewhere.
Symmetrically, the Greek sovereign bond yield loads only on the periphery
factor by the coefficient equal to one. In the robustness check, we replace the
Belgian bond yields by German bond yields, while we replace the Greek bond
yields with Portuguese yields. The results are substantially unaffected by this
change . Generally the results are broadly stable as long as the core factor is
identified by mean of a non-troubled euro area sovereign bond yield and the
periphery factor by one euro area troubled country. While the shape of the
factors might slightly change across specifications, the key results about time
variation in loading coefficients and impulse response functions remain stable.
Regarding the identification of structural shocks and the related impulse
responses, we perform two additional robustness checks. In the first one, we
want to check how restrictive our assumption on fixed coefficients in the VAR
part of the model is (i.e., Φ(L),Σ in Equation 3.2.1). Our motivation for this
is that one may expect that the transmission mechanism has changed due to
the introduction of non-standard measures of monetary policy. Therefore, we
estimate (endogenously in one model) two sets of system matrices (Φ(L),Σ),
where the first set is used for filtering the state variables in the first part of
the sample (up to the end of 2010) and the second set is used for the filtering
in the remaining sample. The resulting factors are highly correlated with the
baseline results (with correlation coefficients of the two factors of 0.99, 0.93,
respectively). Also the impulse responses that we obtain in this setting confirm
the findings of our benchmark specification.
Second, we extend the model to include an additional exogenous variables
which helps identifying shocks. We note that demand shocks might results in
similar effects to US monetary policy shocks in the set of variables that we
include in the model and use for identification. Essentially, a demand shock in
the US might push US yields and the US dollar up, the same conditions that we
use for identifying US monetary policy shocks. In order to disentangle between
The correlation between the first factors (core factor) in the two different specificationsis 0.98, while the correlation between the second factors (periphery factor) is 0.9.
In our view, this is less of a problem in the euro area, where a demand shock would most
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 67
the two type of shocks, we include US breakeven inflation among the variables
in the model. While a demand shock would push inflation up, a tightening
monetary policy shock would push it down. The results in this setting confirm
a large part of our benchmark specification. However, this alternative model
specification identifies monetary policy tightening in the US in 2009, which is
not very plausible. In order to keep the model parsimonious, we decided to
drop the measure of break-even inflation from the baseline model.
3.5 Conclusion
The paper studies movements in euro area sovereign bond yields using a factor
model with time-varying loadings, which capture potential changes in the pri-
cing mechanism of bond yields. Impulse responses to three structural shocks
(EA monetary policy, US monetary policy and risk aversion) are also analysed
over time. The structural identification strategy based on sign restrictions
yields overall plausible results when assessed against key monetary policy ac-
tions during the period under review.
The results support the view that the pricing mechanism of bond yields
evolved during the European banking and sovereign crisis. The analysis iden-
tifies three distinct phases in euro area sovereign bond markets. First, an
initial phase when bond markets were almost fully integrated. A second phase
of dis-integration in bond markets when the crisis escalated. In this phase
the pricing of euro area sovereign bonds depended on different factors and the
transmission of monetary policy shocks became heterogeneous across countries.
Lastly, a third phase of partial re-integration, when the pricing mechanism of
bonds approached the pre-crisis conditions, according to loading coefficients
and structural impulse responses.
The above results suggest a framework to assess the gravity of distress in
bond markets based on the model presented in this paper. The framework
could rely on benchmarking idiosyncratic volatilities, loading coefficients and
impulse responses to the averages observed during the pre-crisis and during
the crisis periods. Spiking idiosyncratic volatilities would be a first sign of
market turbulence. The pricing of the periphery and the core factors across
likely lead to a decrease in risk and therefore to a decrease in the periphery factor, which isthe opposite of a tightening monetary policy shock.
Measured as 10-year breakeven inflation rate, downloaded from Federal Reserve Eco-nomic Data (ticker T10YIE).
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 68
bond markets could be used to assess the degree of integration and spill-overs
across countries. Generally, the dispersion of the loading coefficients for each
factor and of the impact coefficients of impulse responses to structural shocks
could be informative of anomalies in the pricing of bonds.
Our results have implications for the debate on the impact of unconventional
monetary policy on sovereign bond markets in the euro area. While the literat-
ure predominantly quantifies the impact of unconventional monetary policy on
bond yields and it assesses the transmission channels (e.g. the signalling chan-
nel vs the portfolio balance channel), our results also shed light on the impact
of policies on the pricing mechanism of yields. Specifically, our results suggest
a link between euro area unconventional policies, the way different factors are
priced into bond yields and the reaction of bond yields to monetary policy
shocks. We find that the announcement of Outright Monetary Transactions by
the ECB was a game changer leading to a gradual normalisation of the pricing
mechanism of bond yields to the pre-crisis situation, when looking at loading
coefficients and structural impulse responses. Finally, another interesting find-
ing shows that yields in troubled euro area countries became more responsive
to EA monetary policy shocks during the crisis periods. This suggests that
ECB mix of unconventional monetary policy was particularly effective in those
markets where accommodation was needed.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 69
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3.A Estimation of the FAVAR with time-varying
loadings and stochastic volatility
The model given by Equations 3.2, 3.3 gives rise to the following blocks of
parameters:
• Factors f1,t, f2,t
• Time-varying factor loadings λi,j,t, i = 1, . . . , N , j = 1, 2, 3, 4
• Idiosyncratic shocks volatilities σ2v,t
• VAR model parameters B and Σ
3.A.1 Gibbs sampling
The marginal posterior distributions and their quantiles are approximated us-
ing the Gibbs sampler by drawing parameters from their conditional posterior
distributions, most of which are standard in the literature. Time-varying load-
ings were sampled by applying the algorithm by Chan and Jeliazkov (2009);
the VAR model parameters were drawn from their conditional posterior distri-
butions which are standard in the Bayesian VAR literature. Variances of the
idiosyncratic shocks were sampled using the approach by Kim et al. (1998).
What deserves a deeper explanation is sampling of factor themselves.
Conditional on other parameters of the model, factors can be routinely
extracted as an unobserved variable in a state space model, which can be
written in the following way:
The observation equation relates the observed variables to unobserved state
variables:
y1,t
y2,t
...
yN,t
iust
iemet
︸ ︷︷ ︸
yt
=
λ1,1 λ1,2 λ1,3 λ1,4
λ2,1 λ2,2 λ2,3 λ2,4
......
......
λN,1 λN,2 λN,3 λN,4
0 0 1 0
0 0 0 1
︸ ︷︷ ︸
Ht
f1,t
f2,t
iust
iemet
︸ ︷︷ ︸
βt
+
e1,t
e2,t
...
eN,t
eus,t
eeme,t
︸ ︷︷ ︸
et
(3.6)
In this appendix, we focus on the case of a VAR(1) process, however higher order pro-cesses can be incorporated by re-defining the F matrix.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 74
where
R = cov(et) = diagσ1,t, σ2,t, . . . σN,t, 0, 0 (3.7)
The transition equation describes the dynamics of state variables:
f1,t
f2,t
iust
iemet
︸ ︷︷ ︸
βt
=
a1
a2
a3
a4
︸ ︷︷ ︸
µ
+
φ11,1 φ12,1 φ13,1 φ14,1
φ21,1 φ22,1 φ23,1 φ24,1
φ31,1 φ32,1 φ33,1 φ34,1
φ41,1 φ42,1 φ43,1 φ44,1
︸ ︷︷ ︸
F
f1,t−1
f2,t−1
iust−1
iemet−1
︸ ︷︷ ︸
βt−1
+
v1,t
v2,t
vus,t
veme,t
︸ ︷︷ ︸
vt
(3.8)
cov(vt) = Σ =
[Σ11 Σ12
Σ21 Σ22
], (3.9)
where Σii is a 2x2 block of matrix Σ.
Note that exogenous variables (iust and iemet ) are both in the observation and
transition equations and the relationship between them is achieved by imposing
ones in Equation 3.6 and zero variances in Equation 3.7.
The unobserved factors can be relatively easily sampled, for example, using
the algorithm by Carter and Kohn (1994), which is, however, prohibitively
slow for our purposes. Therefore we use the ideas from the algorithm by Chan
and Jeliazkov (2009), whose variant adjusted for our purposes is described
subsequently.
First, in order to correct for singularity of matrix R we reduce the number
of our state variables only to the number of factors. As a result, we can write
our observation equation as:
yt =
y1,t − λ1,3i
ust − λ1,4i
emet
y2,t − λ2,3iust − λ2,4i
emet
...
yN,t − λN,3iust − λN,4iemet
=
λ1,1,t λ1,2,t
λ2,1,t λ2,2,t
......
λN,1,t λN,2,t
[f1,t
f2,t
]+
e1,t
e2,t
...
eN,t
︸ ︷︷ ︸
et
(3.10)
and the transition equation as:
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 75
[f1,t
f2,t
]= µt +
[φ11,1 φ12,1
φ21,1 φ22,1
][f1,t−1
f2,t−1
]+ vt (3.11)
where
cov(vt) = Σ = Σ11 − Σ12Σ−122 Σ21 (3.12)
and
µt =
[a1
a2
]+ Σ12Σ−1
22
[v1,t
v2,t
](3.13)
,
which follows from the properties of conditional normal distributions.
Let
Lt =
λ1,t,1 λ1,t,2
λ2,t,1 λ2,t,2
...
λN,t,1 λN,t,2
(3.14)
and
ft = (f1,t, f2,t)T (3.15)
We can rewrite the measurement equation asy1
y2
...
yT
=
L1 0 0 0
0 L2 0 0
0 0. . . 0
0 0 0 LT
f1
f2
...
fT
+
e1
e2
...
eT
(3.16)
or, in line with Chan and Jeliazkov (2009), as
y = Gη + ε (3.17)
The stacked version of the transition equation can be written as:
Hη = Zγ + ν (3.18)
where
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 76
H =
I2
−F I2
−F I2
. . . . . .
−F I2
(3.19)
and
Zγ =
a1
a2
a1
a2
...
(3.20)
This specification of the model is now in line with (Chan and Jeliazkov,
2009) and their algorithm can be used to sample the unobserved factors.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 77
3.B Time-varying loadings on factors and exogen-
ous varibales
Figure 3.9: Evolution of loadings of bond yields on factors
DE FI NL
0.6
0.8
1.0
-0.2
0.0
0.0
0.1
0.2
-0.05
0.00
0.05
0.00
0.05
0.10
CORE
PERIPH.
US
EME
USD/EUR
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
LOADINGS
SMP LTRO1 LTRO2 OMT EAPP
Note: posterior median, 16th and 84th quantiles.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 78
Figure 3.10: Evolution of loadings of bond yields on factors
AT FR IE
0.5
1.0
0.00.51.01.5
-0.2
0.0
0.00.10.20.3
-0.1
0.0
0.1
CORE
PERIPH.
US
EME
USD/EUR
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
LOADINGS
SMP LTRO1 LTRO2 OMT EAPP
Note: posterior median, 16th and 84th quantiles.
Figure 3.11: Evolution of loadings of bond yields on factors
ES IT PT
0
1
0
1
2
-0.4
-0.2
0.0
-0.10.00.10.2
-0.2
0.0
0.2
CORE
PERIPH.
US
EME
USD/EUR
06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17 06 07 08 09 10 11 12 13 14 15 16 17
LOADINGS
SMP LTRO1 LTRO2 OMT EAPP
Note: posterior median, 16th and 84th quantiles.
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 79
3.C Time-varying impact responses to structural
shocks
Figure 3.12: Posterior median responses (on impact) of bond yieldsto structural shocks over time.
DE AT FI FR NL
0.020
0.025
0.030
0.035
0.020
0.025
0.030
0.035
0.005
0.010
0.015
EA
m.p
. sho
ckU
S m
.p. sh
ock
Risk aversio
n sh
ock
07 09 11 13 15 17 07 09 11 13 15 17 07 09 11 13 15 17 07 09 11 13 15 17 07 09 11 13 15 17
Figure 3.13: Posterior median responses (on impact) of bond yieldsto structural shocks over time.
IE IT PT ES
0.02
0.04
0.06
-0.02
0.00
0.02
0.02
0.03
EA
m.p
. sho
ckU
S m
.p. sh
ock
Risk aversio
n sh
ock
07 09 11 13 15 17 07 09 11 13 15 17 07 09 11 13 15 17 07 09 11 13 15 17
3. Modeling Euro Area Bond Yields Using a Time-Varying Factor Model 80
3.D Correlations with factors
Figure 3.14: Correlations of each country with factors.
88
75
90
38
91
88
−10
19
34
95
6
−6
5
−30
37
−23
−4
38
32
43
−16
33
92
91
91
70
90
96
16
29
76
98
26
−7
1
−26
17
−19
−10
34
35
22
−9
35
84
64
89
23
92
82
−16
11
16
93
−1
−6
7
−35
45
−26
−1
43
29
52
−22
34
Whole sample Subsample 1 Subsample 2
PT
NL
IT
IE
GR
FR
FI
ES
DE
BE
AT
Core Periphery Core Periphery Core Periphery
0 50Correlations with factors
Note: Subsample 1: October 2005 - December 2010. Subsample 2: January2011 - August 2015.
Chapter 4
Financial Stress and Its Non-Linear
Impact on CEE Exchange Rates
Abstract
This paper studies the reaction of selected CEE (satellite) curren-
cies to increased financial stress in the euro area (core) and also in
global financial markets. We suggest that this reaction might be
non-linear; the “safe haven” status of a satellite currency may hold
in calm periods, but breaks down when risk aversion is elevated. A
stylized model of portfolio allocation between assets denominated
in euro and the satellite currency suggests the presence of two re-
gimes characterized by different reactions of the exchange rate to
an increased stress in the euro area. In the “diversification” re-
gime, the satellite currency appreciates in reaction to an increase in
the expected variance of EUR assets, while in the “flight to safety”
regime, the satellite currency depreciates in response to increased
expected volatility. We suggest that the switch between regimes is
related to changes in risk aversion, driven by the level of strains
in the financial system as captured by financial stress indicators.
Using the Bayesian Markov-switching VAR model, the presence of
these regimes is identified in the case of the Czech koruna, the Hun-
garian forint and the Polish zloty.
This paper was co-authored by Sona Benecka and Jakub Mateju. It was published in Journal of FinancialStability (volume 36, pp. 346-360) in June 2018. Its earlier version had been published as a CNB WorkingPaper No. 7/2014. This work was supported by Czech National Bank Research Project No. B5/2013. TomasAdam and Sona Benecka acknowledge support from the Grant Agency of the Czech Republic under ProjectNo. 13-06229S. We thank Tomas Konecny and Kamil Galuscak (both CNB), Marco Lo Duca (ECB), andEvzen Kocenda (IES FSV UK) and two anonymous referees for their valuable comments.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 82
4.1 Introduction
One of the financial stability challenges of central European economies (CEE)
outside of the euro area stems from foreign exchange risk. Like in other small
open economies, movements in exchange rates affect balance sheets and earn-
ings of private firms involved in international trade by altering the value of
their exports and imports. On the financial side, corporations and households
are exposed to foreign exchange risk due to the currency mismatch of their
assets and liabilities. The impact of foreign exchange movements on the finan-
cial position of the real sector is further complicated in the CEE region by the
ownership structure of its banks. Since the major banks, on which the private
sector is dependent, are foreign owned and the parent companies are located
in the euro area, investor’s perception of their health can affect the exchange
rates in the CEE countries. It is therefore plausible that a financial shock in
the euro area countries (“core”) directly unrelated to the CEE (“periphery”)
countries can result in the depreciation of the latter’s currencies.
This paper explores the impact of financial stress in the “core” countries on
exchange rates in the “periphery” countries. It suggests that the relationship
can be non-linear and dependent on the degree of risk aversion. Our analysis is
novel in several aspects. The previous literature has often considered the reac-
tion of exchange rates to stress with the focus on carry trades and has assumed
that the “safe haven” status of a currency is time-invariant. Here we take a
more elaborate approach, recognizing that currencies which are “safe havens”
in some periods may lose this status in more turbulent times. Further, we the-
oretically link these distinct regimes (labelled “diversification” and “flight to
safety”) to the attitute of institutional investors towards risk - risk aversion in
general terms. Finally, we empirically test for the presence of such regimes in
CEE currencies, finding that the Czech koruna (CZK), the Polish zloty (PLN)
and the Hungarian forint (HUF) have switched the regimes several times, and
those switches have coincided with periods of elevated risk aversion.
There are two major challenges for studying the link between exchange rate
dynamics, financial stress and risk aversion. First, risk aversion as a behavioral
characteristic of financial agents is an unobserved variable, and there are only
estimates and proxies available. At the same time, risk aversion supposedly
rises when the degree of financial stress itself is elevated. Therefore we are
forced to reduce the three-dimensional problem into a two-dimensional one,
investigating the reaction of exchange rates to financial stress and interpreting
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 83
the non-linear responses and observed regime switches as related to elevated
risk aversion causing behavioral change. At the same time, we argue that the
regime switches do not occur at specific thresholds, as the measures of financial
stress themselves are imperfect and a commonly measured level of stress in
recent years may exceed peaks in previous decade, reflecting also structural
changes in financial markets. Therefore, a more elaborate approach to the
regime switching process is needed, and we opt for Bayesian Markov-switching
VAR model.
Second, the existing literature has often suggested a simple link: an increase
in risk aversion causes funds to be withdrawn from emerging economies and
their currencies to depreciate. In contrast to this finding, we suggest that the
reaction of emerging currencies (CZK, PLN and HUF) to increased uncertainty
depends on the level of risk aversion in the core advanced economy (the euro
area in our case). When euro area financial markets are calm and hence risk
aversion is low, the search-for-yield effect drives trades in emerging currencies,
including carry trades. This may lead to emerging currencies appreciating in
response to a mild increase in uncertainty in the euro area. On the other hand,
when advanced markets become turbulent, funds start to be withdrawn from
satellite economies and an increase in financial stress causes the satellite curren-
cies to depreciate. As a result, the link can be non-linear and the relationship
can operate in several regimes.
This paper fills the gap in the literature on the link between financial stress
and exchange rate movements in the CEE region in that it provides both the-
oretical background and empirical evidence. To start with, we present a simple
model of a stylized currency portfolio where the endogenously selected weights
of assets denominated in the “core” and “satellite” currencies in the optimal
portfolio respond to changes in the variance (uncertainty) of euro area assets.
In this model we identify two regimes (related to the degree of risk aversion and
portfolio management strategy) based on the different reactions of the exchange
rate to increased uncertainty. The “diversification” regime is characterized by
the koruna appreciating in response to increasing uncertainty of euro asset
returns, while the “flight to safety” regime is characterized by the koruna de-
preciating in response to increasing uncertainty of euro asset returns. Finally,
using the Markov-switching model we manage to identify different exchange
rate reaction regimes in the case of the CZK and HUF in reaction to financial
stress captured by the CISS indicator of euro area financial stress, while the
evidence for PLN is more mixed. Also, we do not find different regimes in the
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 84
reaction of exchange rates to global stress captured by the VIX index, as the
global stress does not directly relate to euro area domestic uncertainty and is
therefore more likely to affect satellite currencies more uniformly in the “flight
to safety” fashion.
The paper is structured as follows. First, it reviews relevant literature re-
lated to the concept of financial stress, its measures, and its impact on exchange
rates. Next, based on a model of portfolio rebalancing, it provides a theoretical
motivation for the link between the exchange rate and risk aversion. Finally,
it estimates how have CZK, PLN and HUF reacted to the evolution of fin-
ancial stress in the euro area and the global economy in the various regimes
identified.
4.2 Financial stress and exchange rates
Financial stress can be described as a situation where the normal (smooth)
functioning of financial markets is severely impaired. Under these conditions,
the financial system is threatened by substantial losses. Financial stress is
marked by a higher degree of perceived risk (a wider distribution of probable
losses) as well as uncertainty (decreased confidence in the shape of that dis-
tribution), according to Misina and Tkacz (2008). The uncertainty leads to
increased volatility of asset prices, which can then alter the risk aversion of
traders. As a recent study by Kandasamy et al. (2014) shows, during peri-
ods of extreme market volatility traders’ attitude toward taking risks changes.
We make use of this link when exploring the reaction of a selected currency
exchange rate to increased uncertainty in foreign financial markets.
4.2.1 Measuring financial stress
Financial stress indicators aggregate a set of stress measures, such as volatilities
and spreads, from various market segments, such as the money market, bond
market, stock market, and foreign exchange market, into a single time series.
Even early papers on financial stress, which used simply constructed stress
indicators (in terms of the aggregation methods or variables used), were able
to capture most stressful events as perceived by experts (Illing and Liu, 2006).
Some studies additionally include macroeconomic or financial stability indicators (such asprivate credit) to capture the overall economic conditions. We stick to the financial marketscontext as we intend to assess the impact of financial stress only.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 85
But over time, more elaborate indices have been constructed. In particular, the
global financial crisis gave a strong impulse to research in this field, highlighting
the importance of financial stress for real economic activity.
The construction of indices varies both in the stress measures included and
in the methods used to aggregate them. To the best of our knowledge, there
is little theoretical background for modeling financial stress, so these choices
are often arbitrary. Several indicators have been constructed for individual
economies (such as the U.S., the euro area, and Canada) as well as more general
ones to be used across countries (Cardarelli et al., 2009). A number of studies
have shown the impact of financial stress on real or financial variables as well as
on monetary policy, but the financial stress indicators themselves seem difficult
to predict according to Slingenberg and de Haan (2011) and their potential use
in forecasting so far seems to be limited.
In the post-crisis period, the focus has shifted to the construction of fin-
ancial stress indicators to capture systemic risk. The contagion effect is an
import element of systemic risk, so these indices should reflect situations where
stress materializes simultaneously in several interconnected markets. Brave
and Butters (2012) constructs a state-space representation of the level of sys-
temic stress. This approach takes into consideration the cross-correlations of a
large number of financial variables (100 indicators) and the past development
of the index to set the weights for each sub-index. Standard portfolio theory is
used by Hollo et al. (2012), who aggregate sub-indices in a way which reflects
their cross-correlation structure. This approach has been applied to Czech data
(Adam and Benecka, 2013) and Hungarian data (Hollo, 2012), but generally
the attention paid to the role of financial stress in the Central European region
(CEE) has been relatively limited.
In this paper, we build on the financial stress literature and use two financial
stress indices for the euro area in our analysis. The Composite Indicator of
Systemic Stress (CISS) by Hollo et al. (2012) will be employed first as a an
index of financial stress in the “core” economy (euro area). Its construction
not only incorporates information about conditions in individual markets, based
primarily on volatility, but also captures the effect of simultaneous stress in each
of them. The CISS index is updated on a weekly frequency and is regularly
used as a measure of euro area systemic stress by the ECB, in the ESRB Risk
Dashboard and has been also employed in academic studies (Vasıcek et al.,
Due to the importance of banking sectors in CEE compared to other financial segments,the focus has been on developing banking-oriented or broader financial stability indices.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 86
2017; Dovern and van Roye, 2014; Gelman et al., 2015). As an alternative,
we will use the VIX index of implied option volatilities in S&P 500 index
to capture the level of global stress. Figure 4.1 shows the evolution of both
indicators starting from the launch of the euro area in 1999.
Figure 4.1: Financial stress indicators
Composite indicator of systemic stress (CISS) VIX index
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18
10
20
30
40
50
60
70
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Financial stress indicators
4.2.2 Modelling exchange rate dynamics
Although the exchange rate dynamics has been frequently modelled in the lit-
erature, exploring the impact of financial stress on exchange rate movements
is a relatively new topic. Traditionally, empirical models have been often rely-
ing on the link to their theoretical fundamental values. The prime theoretical
model for exchange rates is the uncovered interest rate parity (UIP). In its
basic version, the UIP suggests that the expected exchange rate appreciation
is linked to the interest rate differential and a risk premium. Sarno et al.
(2004) document the long run relationship to nominal fundamentals but also
find that the exchange rate regime is an important determinant of the speed
of reversion towards values implied by the fundamentals. Some studies (Beck-
mann and Czudaj, 2017a) link exchange rate dynamics to current account
balance. However, the UIP fundamentals have been shown to perform poorly
in out-of-sample forecasts. Sarno and Valente (2009) estimate a time-varying
relationship between exchange rate movements and fundamentals to suggest
that there might not be a single fundamental model but the set of fundamental
drivers can change over time, possibly reflecting the changing nature of ex-
change rate expectations formation. Other potential reasons for the ”exchange
rate disconnect puzzle” are discussed by Sarno (2005).
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 87
The determinants of CEE currencies have been also investigated by previous
studies, often finding that the role of UIP fundamentals is relatively weak in
explaining currency movements in the CEE region. Egert and Kocenda (2014)
establish the effects of macroeconomic news and central bank communication
on CEE exchange rates. Feldkircher et al. (2014) find on a large sample of
countries and indicators that previous price stability is a good predictor for
exchange rate reactions to the global crisis. Similarly to the findings of this
paper, Bubak et al. (2011) suggest that the nature of the volatility spill-overs
from global markets to CEE exchange rates may have changed with the onset
of global crisis. Finally, it is important to note that the CEE currencies have
often operated in a managed float regimes with (symmetric or asymmetric)
target bands. Fidrmuc and Horvath (2008) show that exchange rates tend to
be more volatile if far away from target rates.
Because we need to explicitly model different regimes of exchange rate re-
actions to financial stress, we employ the Markov switching VAR model. A
similar methodology has been previously used for modelling exchange rates. In
a classic paper, Engel (1994) finds that Markov switching models can improve
the prediction of the direction of future exchange rate movements. Cheung
and Erlandsson (2005) find evidence for the Markov switching dynamics for
GBP, DEM and FFR against the USD. Other studies suggest non-linearities
in exchange rate reversion toward mean (Taylor et al., 2001) or fundamental
values (Sarno and Valente, 2006). The usage of the Markov switching VAR
model to model different regimes of reaction to financial stress may be new in
the exchange rate literature and therefore we discuss it in a more detail later
in the text.
4.2.3 The Impact of Financial Stress on Exchange Rate Dy-
namics
A number of studies investigate the role of traditional exchange rate determ-
inants, but financial measures such as financial stress have attracted relatively
little attention from researchers. The link between exchange rate movements
and risk aversion (measured by the VIX index) is investigated, for example, in
De Bock and Carvalho Filho (2013). During risk-off episodes, when risk aver-
sion dominates globally, the Japanese yen, the Swiss franc, and the U.S. dollar
appreciate against other G-10 and emerging market currencies. Ranaldo and
Soderlind (2010) also document the safe-haven or hedge function of selected
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 88
currencies. Habib and Stracca (2012) establish fundamental determinants of
currencies’ “safe haven” status, and find that net foreign asset position, low
external vulnerability, large economy and past hedge status predict if a cur-
rency will function as a safe haven. Beckmann and Czudaj (2017b) investigate
the precision of exchange rate expectations and find that safe haven status can
even come as a surprise to markets, such as in the case of USD in 2009. At the
same time, the profitability of currency carry trades is found to be procyclical
in financial stress (Brunnermeier et al., 2009; Menkhoff et al., 2012).
The question of how the conditions in financial markets affect exchange
rate portfolio allocations has been treated to some extent in the literature. Ac-
cording to Raddatz and Schmukler (2012), both investors and fund managers
relocate their portfolios when facing a stressful event either in the domestic
country or in a foreign country where their investment is exposed. As a result,
the investors and their fund managers have a substantial impact on capital flows
during periods of financial stress. These capital flows then have a direct impact
on the exchange rates under scrutiny. Closer to our approach, Lo Duca (2012)
discusses the time-varying nature of capital flows, where push and pull factors
have a different impact based on market conditions. Also Sarno et al. (2016)
find that over 80% of variation in bond and equity flows to satellite countries
can be attributed to push factors from the US. When market tensions are elev-
ated, investors pay attention to regional developments in emerging economies.
But when panic occurs, uncertainty and risk aversion start to drive flows and
regional developments play a marginal role.
To sum up, the literature suggests that financial stress plays some role in
exchange rate dynamics. In the traditional view, calm conditions in advanced
countries’ financial markets stimulate carry trades to high-yielding currencies
of emerging economies, which then tend to appreciate. An increased level of
risk aversion leads to appreciation of safe haven currencies, while emerging
markets are hit by capital outflows and their currencies depreciate vis-a-vis the
U.S. dollar (with carry trade reversal too). In the following section, we show
that satellite currencies can operate in several regimes – they appreciate in
response to increased external financial stress in the “diversification” regime,
and they depreciate in response to increased financial stress in the “flight to
safety” regime, while we relate the switch from the former to the latter to the
changes in risk aversion. The distinction between safe-haven and high-yielding
currency status is therefore no longer time-invariant, but depends on global
investors’ changing attitude to risk.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 89
4.3 A model of portfolio rebalancing
In this section we present a highly stylized model of portfolio allocation where
investors decide about the composition of a portfolio consisting of assets de-
nominated in the “core” and “satellite” currencies. The purpose is to invest-
igate the possibly non-linear relationship between risk aversion and the ex-
change rate, i.e., a different reaction of the relative exchange rate to increased
uncertainty based on the level of risk aversion and different portfolio man-
agement strategies. This relates to the findings of Cenedese et al. (2016) who
acknowledge that stock market returns and exchange rate returns can be either
positively or negatively correlated, and build a similar model of international
currency portfolios, drawing implications for systematic profitability of carry
trades. In contrast to them, we exploit the effects of changes in risk aversion
and of different types of risk management strategies. Also note that we do not
aim to build a fundamental model of portfolio flows. The assumed expected
return and variance on assets denominated in each currency can then be inter-
preted as reflecting the fundamentals, but for this stylized model it is sufficient
to assume they are fixed in the short run.
We will consider two types of portfolio risk management: a simple mean-
variance utility maximization and an optimization with a constraint on the
maximum variance of the portfolio. We include the limit on the total portfolio
return variance as an analogy to the value-at-risk indicator which has become a
widely used tool in portfolio risk management over the last few decades. Sub-
sequently, two regimes (related to the degree of risk aversion and the portfolio
risk management strategy) can be identified based on the different reactions
of the exchange rate to increased uncertainty. The “diversification” regime is
characterized by the satellite currency appreciating in reaction to increasing
uncertainty of asset returns in the core economy, while the “flight to safety”
The model is therefore static, which is sufficient to illustrate our point that in somesituations, a currency can be a ”safe haven”, but lose this status when risk attitude changes.For the discussion of fundamental drivers of exchange rates and the relevant literature seeSection 2.
Value-at-risk (VaR) has been considered also for currency portfolios, see eg. Yamai andYoshiba (2005) or Berger and Missong (2014) who also show that VaR is notoriously difficultto forecast. Note that in reality the VaR constraint may be combined with mean-varianceoptimization, and the moment when it becomes binding (a regime switch) might be related e.gto re-estimated, higher return variance after negative shocks have been observed. Therefore,it is likely that after turbulent financial market events, VaR constraints may become strictlybinding for majority of portfolios.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 90
regime is characterized by the satellite currency depreciating in response to
increasing uncertainty of core-currency asset returns.
Moreover, we investigate the reasons for regime switching – we suggest
that regime switches may occur due to changes in investors’ behavior, notably
to shifts in the degree of risk aversion, and possibly also to changes in fund
managers’ objectives related to changes in the perception of risk. In particular,
we will show that either an increase in risk aversion or a change from simple
mean-variance optimization to value-at-risk-constrained optimization (or both
at the same time) causes a switch from the “diversification” to the “flight to
safety” regime.
4.3.1 The Portfolio Composition
We model the behavior of an investor deciding about the composition of a
portfolio where one class of assets is denominated in a core currency, while
the other class is denominated in a satellite currency. Matching the stylized
facts for CZK, PLN and HUF, we assume that the expected return on satellite-
currency assets is higher than that on core-currency assets,
E[Rsat] ≥ E[Rcore] (4.1)
and the variance of satellite-currency asset returns is higher than that of core-
currency asset returns.
σsat ≥ σcore (4.2)
Assume a portfolio P , composed of satellite-currency and core-currency assets.
The expected return on the portfolio is
E[RP ] = λsatE[Rsat] + (1− λsat)E[Rcore] (4.3)
where λsat is the weight of satellite-currency assets. The variance of the
portfolio returns is then
σ2P = λ2
satσ2sat + (1− λsat)2σ2
core + 2λsat(1− λsat)σsat,core (4.4)
The aim is to study the changes in portfolio allocation (particularly the
share of assets denominated in satellite currency λsat) in response to increased
uncertainty related to the returns on core-currency assets, i.e., an increase
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 91
Figure 4.2: Mean-variance frontier of the portfolio
0 0.005 0.01 0.015 0.02 0.0251
1.02
1.04
1.06
1.08
1.1
1.12
Exp
ecte
d po
rtfo
lio r
etur
n
Portfolio return variance
in σcore. Figure 4.2 shows the mean-variance frontier of the portfolio for a
particular parametrization. The preferences of investors increase toward the
north-west of the diagram. It is clear that very low values of λsat are strictly
dominated by their higher counterparts with equal variance but higher returns.
The preference schedule also implies that the allocation with minimum variance
(the vertex of the mean-variance parabola) is usually not the optimal one, as the
investor can achieve higher expected returns with an infinitely small increase
in the return variance.
We consider two types of portfolio management: mean-variance utility max-
imization and optimization with a constraint on the maximum variance. The
latter is identical to a constraint on theoretical value-at-risk, a widely used tool
for portfolio risk management.
4.3.2 The Mean-variance Utility Maximization
First we consider an investor who maximizes her mean-variance utility derived
from the portfolio return. The problem is to choose the share of satellite-
Parameter values: E[Rsat] = 1.1, E[Rsat] = 1.01, σsat = 0.15, σcore = 0.08Value-at-risk, V aRα, is defined as the α-quantile of the return distribution and can be
interpreted as the loss amount which will not be exceeded with probability (1 − α). Underthe assumption of return normality, the constraint on the α-quantile is equivalent to theconstraint on the variance.
It can be shown that maximizing the exponential utility function U = −e−γRP , whereγ is a coefficient of absolute risk aversion, is equivalent to maximizing the mean-varianceobjective MV = E[RP ]− γ
2σ2P .
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 92
Figure 4.3: Optimal λsat for changing σ2core, for different values of γ
0
20
40
60
80
1000 20 40 60 80 100 120
−5
−4
−3
−2
−1
0
1
2
3
4
5
σ2coreγ
λ sat
currency assets λsat to maximize
maxλsatE[RP ]− γ
2σ2P (4.5)
where γ is the Arrow-Pratt coefficient of absolute risk aversion. The first-
order conditions illustrate the optimal allocation. The investors are, in general,
allowed to hold negative amounts of any of the assets (short-sell).
Figure 4.3 shows the optimal share λsat of satellite-currency assets, with
increasing uncertainty in core-currency assets, and for different values of the
risk aversion parameter. Most importantly, for low values of the risk aversion
parameter γ, the investor optimally reacts to increased core uncertainty by
switching to satellite-currency assets, increasing the share λsat. For higher val-
ues of γ, however, the relationship reverses: with increased core uncertainty,
the investor’s optimal response is to reduce the share of satellite-currency as-
sets. This is because satellite-currency asset returns still have relatively higher
variance, and an increase in core uncertainty in the case of high risk aversion
calls for a “flight to safety”.
Parameter values: E[Rsat] = 1.1, E[Rsat] = 1.01, σsat = 0.15, σcore ∈ (0, 0.9σsat),γ ∈ (3, 100)
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 93
Figure 4.4: Optimal λsat for changing σ2core, constrained σ2
p
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.05
0.1
0.15
0.2
0.25
0.3
0.35
λ sat
σ2core
4.3.3 The optimization with a variance constraint
The second type of investor behavior is motivated by the widespread use of the
Value-at-Risk (VaR) indicator as a risk management tool in the last decade.
When risk concerns dominate the portfolio allocation decision, it is reasonable
to assume that portfolio managers are forced to pay more attention to VaR-
type indicators. The major modeling difference from the previous case is that
the portfolio managers have to fulfill the constraint of maximum variance. The
objective is the following:
maxλsatE[RP ] s.t. σ2
P ≤ σ2P (4.6)
Because E[Rsat] ≥ E[Rcore], the decision consists of choosing the highest λsat
such that σ2P = σ2
P . Figure 4.4 presents the variance-constrained optimal
choices of the share of satellite-currency assets in the portfolio with changing
core-currency asset return variance.
When the portfolio manager faces a binding constraint on the portfolio
return variance, the share of satellite-currency assets decreases with higher
uncertainty of core-currency returns. As the variance of core-currency asset
returns rises, the manager needs to reduce the exposure to satellite-currency
assets, which are still riskier.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 94
Table 4.1: Results summary: the response of investors to an increasein the expected variance of core-currency assets
M-V optimization VaR constraintlow risk aversion diversification flight to safetyhigh risk aversion flight to safety flight to safety
4.3.4 The implications for exchange rate behavior
The results are summarized in Table 4.1. Based on the risk attitude and object-
ives of the investors and/or portfolio managers, the share of satellite-currency
assets in the model portfolio can switch between regimes, which we call “di-
versification” and “flight to safety.” When portfolio managers maximize their
mean-variance utility and risk aversion (γ) is low, satellite-currency assets serve
as a diversification tool and their share in the representative portfolio increases
with increasing uncertainty of core-currency asset returns. When risk aversion
rises, the attitude toward satellite-currency assets changes to “flight to safety”
– the share of satellite-currency assets declines with increased core uncertainty.
When the portfolio decision is made with a constraint on the portfolio variance
(or VaR), the “flight to safety” regime dominates.
We suggest that the described changes in investors’ attitude toward satellite-
currency assets induce international capital flows, which translate into analog-
ous behavior of exchange rates. The simple and stylized model presented above
offers an explanation of the regime switches observed in the reaction of the satel-
lite currency exchange rate to stress in the core economy. When risk aversion
is low and portfolio managers operate in standard mode (mean-variance util-
ity maximization), the satellite currency may serve for “diversification” when
uncertainty in the core economy increases. On the contrary, if risk aversion
rises, or portfolio managers start to operate under strictly binding constraints
on the portfolio return variance (such as VaR), the regime switches to “flight
to safety,” where the satellite currency reacts to increased uncertainty in the
core economy by depreciation.
4.4 The effects of financial stress on CEE curren-
cies
In this section, we estimate the reaction of three CEE exchange rates to shocks
to financial stress. In line with the proposed theoretical model, we believe that
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 95
the reaction may be non-linear, i.e., the same shock may lead to a different
reaction under different regimes. In the first, “diversification”, regime, a cur-
rency appreciates in response to elevated financial stress due to the portfolio
diversification motive. However, this behavior may alter in times of financial
panic, when investors resort to safe assets in advanced countries (due to in-
creased risk aversion) and thus the currency depreciates again (the “flight to
safety” regime).
We do not assume that the regimes are defined only by the level of financial
stress or by its value relative to an estimated threshold. Instead, we assume
that regime switching is driven endogenously, by unobserved variables such as
risk aversion or credit constraints. The reason why we do not associate regimes
with the level of financial stress is path dependency – investors may react to a
rise in the level of stress in a different way when the stress has been at elevated
levels for a long time than they do when it rises by the same amount in calm
times, for example. As mentioned in Section 2, increased volatility of asset
prices can alter the risk aversion of traders. Also, after a substantial shock
to a financial system the credit constraints change. Investors hence are more
sensitive to market volatility, which is an unobserved variable to be treated
using endogenous regime switching.
As a result, we opt for the Markov-switching vector autoregression model,
where regime switching is driven endogenously by an unobserved Markov pro-
cess. This is in contrast to threshold VAR, which would define regimes based on
the level of stress relative to an estimated threshold. We also assume that the
transition probabilities of switching from one regime to another are constant
and do not depend on the level of financial stress due to the path dependency
mentioned above.
4.4.1 Bayesian Markov-switching VAR methodology
The Markov-switching VAR is a non-linear variant of the VAR model where two
or more VAR models switch over time according to an endogenous unobserved
Markov chain process. This model is convenient in our context, as we aim to
study the response of an endogenous variable (the exchange rate) to shocks
to another variable (a financial stress index) and we assume that the reaction
The Markov-switching VAR model, or its variants, have been routinely estimated in theliterature on exchange rate dynamics, as is described in Section 4.2.2. However, we are notaware of any of its applications to model the responses of exchange rates to financial stressmeasures.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 96
is state contingent, with the regime depending on the state of an unobserved
variable.
We estimate the model in the Bayesian setting, since we want to include
our prior information regarding the nature of the exchange rate and financial
stress (they should be close to a random walk). In addition, we have strong
prior information that shocks to the CEE exchange rates do not affect financial
stress in the euro area (or stress on the global scale), but the exchange rate itself
reacts to changes in financial stress. Finally, this estimation method allows us
to draw impulse response functions easily and does not suffer from convergence
problems as in the case of MLE.
Let et be the exchange rate of a CEE currency against the euro, yt be an
(m x 1 ) vector of endogenous variables at time t and let N be the number of
regimes. In our case, we have m = 2, yt = (indt, et), and N = 2 or N = 3. A
Markov-switching vector autoregression model can be written as follows:
yt = µst +B1,styt−1 + . . .+Bp,styt−p + (Σst)12 εt (4.1)
where εt ∼ i.i.d.N(0, Im). We assume that the unobserved state variable st
indicating the realization of the regime at time t follows a first-order Markov
chain with N regimes and transition probabilities
pij = Prob(st+1 = j|st = i), ∀i, j ∈ 1, . . . , N ,N∑j=1
pij = 1 (4.2)
This means that both the coefficients in the VAR model and the variances
of shocks are governed by the same endogenous Markov process (some studies
assume that the coefficients are governed by one process and the variances by
another – see Krolzig (1997) for example; this reference also provides models
where only the coefficients or covariance matrices are regime-dependent).
In the Bayesian setting, the parameters of the model are regarded as ran-
dom variables. Let us define the vector of parameter blocks to be estimated
as Θ = B1, B2, B3,Σ1,Σ2,Σ3, P, St, t = 1, . . . , T, where T is the number of
observations, St is the state variable indicating the regime at time t, and P is
the transition matrix:
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 97
P =
p11 p12 · · · p1N
p21 p22 · · · p2N
......
. . ....
pN1 pN2 · · · pNN
(4.3)
The method of estimating Bayesian Markov-switching VAR models can be
seen as an extension of estimating Markov-switching univariate autoregressive
processes to a multivariate setting. The former, in the two- and three-regime
cases, is described in Kim and Nelson (1999), for example, while the multivari-
ate extension is described in Krolzig (1997).
In order to draw further inferences regarding the model parameters and
impulse response functions, we need to choose the number of regimes to be
estimated, to impose priors on the parameters, and to simulate approximations
of the marginal posterior distributions of each parameter. The choice of the
number of regimes was done informally and we arrived at three regimes, as is
described in the next section. The latter two steps – setting the priors and
simulating draws from the posterior distribution by means of Gibbs sampling
– are described in Appendix 4.D.
4.4.2 Data
We estimate a set of six bi-variate Markov-switching VAR model in order to
check the validity of the theoretical model. In each considered model, the
two endogenous variables represent the exchange rate of one particular CEE
currency vis-a-vis the euro and one financial stress index.
Regarding the exchange rates, we consider the Czech koruna (CZK), the
Polish zloty (PLN) and the Hungarian forint (HUF), i.e., the most traded
currencies in the CEE region. The exchange rates (plotted in Figure 4.5) are
expressed as the number of currency units per euro (e.g., CZK/EUR), which
implies that an increase in exchange rates corresponds to the weaker local
currency.
Since 1990s, the CEE region has been characterized by strong capital in-
flows and convergence process, which followed the economic transformation
from centrally-planned economies. Therefore the fundamental drivers of ex-
change rates differ from those in advanced economies (expected interest rate
differentials, monetary aggregates etc.). In order to isolate movements driven
by fundamental variables (capital flows, net investment positions, productivity
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 98
growth differentials, converging prices of non-tradeables), and work with resid-
uals, as the theoretical model assumes, we opt for a simple Hodrick-Prescott
filter and run estimations on log-gaps from the trend (plotted in bottom panels
of Figure 5). As a cross-check, we contrasted these deviations with deviations
from the BEER model estimated by the Czech National Bank. The two series
are correlated with the correlation coefficient of 0.75, thus we believe our choice
is reasonable.
Figure 4.5: CEE currencies vis-a-vis the euro
gap
czkeur
gap
hufeur
gap
plneur
levels
czkeur
levels
hufeur
levels
plneur
00 02 04 06 08 10 12 00 02 04 06 08 10 12 00 02 04 06 08 10 12
00 02 04 06 08 10 12 00 02 04 06 08 10 12 00 02 04 06 08 10 12
3.5
4.0
4.5
-0.1
0.0
0.1
250
275
300
-0.10
-0.05
0.00
0.05
0.10
0.15
25
30
35
-0.10
-0.05
0.00
0.05
0.10
exchange rates of a currency against the euroData used for the analysis
Regarding the financial stress indices, we consider the CISS index and the
VIX index (Figure 4.1). Since the CISS index is constructed on a weekly fre-
quency, we estimate the six models using weekly data. The CISS indicator
and exchange rate time series were downloaded from the ECB Statistical Data
Warehouse. The VIX index was downloaded from the Federal Reserve Eco-
nomic Data (FRED) website.
The behavioural equilibrium exchange rate model estimates the equilibrium value ofa currency given its determinants. The CNB, in particular, uses variables affecting long-term exchange rate developments, such as productivity differentials and the inflow of foreigninvestments.
Note: The smooth lines in upper panels denote HP filtered trends of the exchange rates.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 99
Our estimation sample spans the period between January 1999 (the intro-
duction of the euro) and August 2012, because in the following months the
Czech National Bank started to verbally intervene on the foreign exchange
market and we believe that this date could coincide with a structural break in
the relationship we are estimating. In addition, in the same period, the ECB
launched the Outright Monetary Transaction programme, which served as a
backstop in the European sovereign debt crisis and could also contribute to the
structural break.
4.5 Results
Using the Markov-switching model, we identified three regimes of the reaction
of exchange rates to changes in financial stress. Figure 4.6 presents estimated
transition matrices, which summarise the probabilities of switching from re-
gime i to regime j. One can observe that transitions between regimes tend to
be smooth, i.e., it is unlikely that regimes would switch from Regime 1 (low
volatility) to Regime 3 (high volatility) and vice versa directly. This is con-
sistent with the observation that there are distinct periods of run-ups to crises
and aftermaths of crises, with different dynamic characteristics to calm periods
and periods of crises.
The transition matrices can be transformed in order to compute expected
durations of staying in a given regime, once the regime is reached (Figure 4.7).
Their values indicate that durations of the calm regime tend to be longest,
around 1 year for the CISS index. For the VIX index, the durations of the
calm regime are also longest, albeit significantly shorter (less than or around
20 weeks), which indicates that the VIX index may be less suitable for capturing
investors’ activity in the CEE region. This can reflect the fact that the VIX
index captures financial stress related to the US stock market, while the CISS
Initially, we estimated econometric models consistently with the theoretical model, i.e.,we considered models with two regimes. Under this initial setting, the direction of impulseresponse functions was consistent with the theoretical model. However, the estimation un-certainty was very high and impulse responses were often insignificant. This indicated thatsome regime included responses of two regimes - one leading to appreciation and anotherto depreciation - which led to the insignificance of impulse responses when the two regimeswere collapsed into one. Therefore we opted for the specification with three regimes, whichwe consistently applied to models of all three CEE currencies.
We would like to remind the reader that volatility of shocks to financial stress indicesare increasing across regimes by assumption on labelling the regimes, as described in theprevious section.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 100
index captures several dimension of financial (systemic) stress in euro area,
which is clearly more relevant for the CEE currencies.
Figure 4.6: Transition matrices
0.98
0.02
0
0.02
0.96
0.06
0
0.03
0.94
0.92
0.13
0
0.07
0.87
0.1
0.02
0
0.9
0.98
0
0
0.02
0.94
0.09
0
0.06
0.91
0.95
0.05
0
0
0.95
0.18
0.05
0
0.82
0.98
0.01
0
0.02
0.96
0.1
0
0.03
0.9
0.91
0.14
0
0.09
0.83
0.15
0
0.03
0.85
czkeur-vix hufeur-vix plneur-vix
czkeur-ciss hufeur-ciss plneur-ciss
1 2 3 1 2 3 1 2 3
1 2 3 1 2 3 1 2 3
3
2
1
3
2
1
3
2
1
3
2
1
3
2
1
3
2
1
to
from
Transition matrices
Figure 4.7: Expected durations of regimes
czkeur hufeur plneur
ciss vix ciss vix ciss vix0
20
40
60
dura
tion
regime 1 regime 2 regime 3
Expected durations of regimes
Note: Numbers in the tables denote the probabilities of switching from regime i to regimej, where is are denoted on the vertical axis and js are denoted on the horizontal axis.
Note: Bars denote expected durations of staying in a given regime (durations in week).
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 101
Figure 4.8 summarises the estimated probabilities of each regime, in that it
indicates which regime had the highest probability in a given period. It can be
observed that Regime 3 (high volatility) emerged in similar periods for all the
considered currencies - around the period of financial crisis (2008 - 2009) - and
in the second half of 2011 (sovereign debt crisis). Interestingly, periods when
Regime 3 is identified using the VIX index are subsets of those identified using
the CISS index. This can be explained by the nature of the VIX index, which
considers stress in a narrow segment of financial markets (stock market in the
US). VIX index also has a more global nature, and euro area financial stress
was only partially caused by global factors. Regime 2 (medium volatility)
was identified in the run-up to the financial crisis and between the financial
and sovereign debt crisis for the Czech koruna and the Polish zloty. For the
Hungarian forint, Regime 2 was identified in similar periods and also in period
between 2004 - 2006.
The lower panel of Figure 4.8 presents the average level of financial stress
(captured by the CISS index) in each of the estimated regimes, separately
on two sub-samples (1999 - end of 2005, 2006 - 2013). The ranking of the
regimes by average financial stress coincides with the ranking by the volatility
with the exception of the Polish zloty (1999-2006), for which Regime 2 was
associated with higher stress than Regime 3. It is also worth mentioning that
the average level of financial stress in each regime was generally lower in the
first sub-sample than in the second sub-sample, indicating that there is no
fixed threshold for the regime switch. This is caused by the structural changes
in financial markets which may have adapted to higher levels of stress, or by
an imperfect measurement of financial stress by the stress indices. These two
findings support our choice of the Markov switching model compared to a
threshold VAR model, in that the reaction of a currency to the same shock
does not depend on a fixed threshold of a stress index but on an unobserved
factor (which, according to our model, may be related to risk aversion).
Regarding the reaction of exchange rate dynamics to financial stress shocks,
Figure 4.9 suggests their highly non-linear nature. In Regime 3 (high volatility),
satellite currencies depreciate in response to a shock to financial stress, with
A chart showing the time series of exact probabilities for each regime is provided inFigure 4.10 the Appendix.
Note: The tiles in the upper chart indicate which regime had the highest probability ina given period.
Impulse response functions with their confidence bands are summarised in Figure 4.11
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 102
Figure 4.8: Estimated regimes and average levels of the CISS indexin the estimated regimes
hufeur-vix
hufeur-ciss
plneur-vix
plneur-ciss
czkeur-vix
czkeur-ciss
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13
regime 1 regime 2 regime 3
Estimated regimes
vix
ciss
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13
99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.00.10.20.30.40.50.60.70.8
10203040506070
czkeur hufeur plneur
regime 1 regime 2 regime 3 regime 1 regime 2 regime 3 regime 1 regime 2 regime 3
0.0
0.2
0.4
0.6
1999-2006 2006-2013
Average level of the CISS index in the estimated regimes
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 103
the exception of the Polish zloty, where the reaction is not significant. The
depreciation in response to stress shock can be the result of safe haven flows,
when investors shift their funds to safe assets due to increased risk aversion (as
suggested by our model) or due to herd behaviour. In the case of the Polish
zloty, the reaction is not significant, which could reflect that the Polish economy
is more closed compared to the Czech and Hungarian economies, or that it has
retained some of the safe have status also during the more severe phases of past
crises.
In Regime 2, the reaction of currencies in models with the CISS index is also
consistent with our model and corresponds to the “diversification” regime. As
a result of an increased stress in the euro area, investors diversify their portfolio
and shift a part of funds to the CEE region, which leads to the appreciation
of CEE currencies. On the other hand, shocks to the VIX index still lead to
the depreciation of satellite currencies. Therefore, in reaction to global stress
shocks, we do not observe the “diversification” regime, which is very reasonable
as the uncertainty in such cases may not originate from euro area.
Compared to the behaviour of exchange rates in Regime 3 and Regime
2, their behaviour in Regime 1 (which is characterized by low volatility and
mild levels of stress) is less clear-cut. In response to a financial stress shock
captured by the CISS index, the Czech koruna and the Polish zloty depreciate,
while the reaction of the Hungarian forint is insignificant. This may reflect
some of the business-as-usual behavior when increase in uncertainty triggers a
limited rebalancing involving mild outflows from satellite markets. A further
increase in financial stress may then lead to a switch to Regime 2 in a search
for safe haven outside of the core (euro area) economy. At such medium levels
of financial stress, CEE currencies may still qualify for the safe haven status.
This does not hold anymore when the further surge in financial stress triggers
the swithc to Regime 3.
Overall, the results provide supportive evidence for our theoretical motiva-
tion. The emerging market currency can have different responses to increased
stress based on actual financial market conditions. When the financial stress
to the euro intensifies, low risk aversion leads to an increase in diversification
motives and currency appreciation. A panic on financial markets causes risk
aversion to increase, leading to capital withdrawals and depreciation of emer-
ging market currencies.
In the model with the HUF, Regime 1 was observed only in period 2000 - 2001.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 104
Figure 4.9: Responses of exchange rates to shocks to financial stressindices (higher values indicate a depreciation of a givencurrency)
plneur
ciss
plneur
vix
hufeur
ciss
hufeur
vix
czkeur
ciss
czkeur
vix
0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 500
1
2
-0.5
0.0
0.5
1.0
0.0
0.5
1.0
-0.40.00.40.8
-0.25
0.00
0.25
0.50
-0.6-0.30.00.30.6
regime 1 regime 2 regime 3
Responses to 1 s.d. shock to financial stress
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 105
4.6 Conclusion
This paper has analyzed how changes in financial stress and risk aversion in
the euro area and on the global level affect the exchange rates of satellite CEE
currencies. Using a highly stylized model of international currency portfolio
allocation, we have illustrated that the impact of elevated stress in the core
economy (euro area) on the exchange rates of satellite currencies can be non-
linear and can operate in regimes: In the the well-known “flight to safety”
regime, the satellite currency depreciates in response to an increase in financial
stress. In the second, “diversification” regime, the CEE currencies have a
safe haven status. We relate switches between the regimes to changes in risk
aversion and changes in portfolio risk management strategy.
The empirical results based on Markov-switching VAR models support the
idea that the reactions of CEE currencies to financial stress operate in differ-
ent regimes. Although the “flight to safety” regime prevails when financial
stress indicators are peaking, in transition periods (run up to crisis or crisis
aftermath) we often observe the “diversification” regime where CEE curren-
cies respond to an increase in financial stress by appreciation. Interestingly, in
calm periods when the levels of stress are low, we observe a third regime char-
acterized by lower volatility, but also negative correlations between financial
stress and satellite exchange rates which are otherwise typical for the “flight to
safety” regime.
These results have two important implications for policy making in the CEE
region. Firstly, we have shown that a CEE currency can depreciate in response
to an increase in financial stress in the euro area even if fundamentals in a given
country do not change. If the central bank does not respond to such shocks
with foreign exchange interventions, the best precautionary measure against
these developments is inducing the banking sector to generate capital buffers,
which would make the banking sector resilient to such shocks. Next, even if a
currency seemingly has a safe haven status in some periods (i.e., it appreciates
after stress increases in the euro area), this status can be easily lost even though
domestic fundamentals do not change. This again speaks for creating buffers
and hedging for unexpected moves in exchange rates (in both ways) by the
private sector.
To put the results into a wider perspective, we have illustrated that with
deepening financial integration, outside financial conditions and changes in in-
vestors’ sentiment can play substantial role in exchange rate dynamics, es-
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 106
pecially in the short run when international parity based on macroeconomic
fundamentals is less reliable. This paper thus also proposes a potential avenue
for future research: the questions to be answered include issues of incorporat-
ing financial stress indicators into exchange rate forecasting and into practical
monetary policy decision making.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 107
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4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 111
4.A Appendix
4.B Estimated regime probabilities
Figure 4.10: Estimated regime probabilities
plneur-ciss plneur-vix
hufeur-ciss hufeur-vix
czkeur-ciss czkeur-vix
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13
99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 99 00 01 02 03 04 05 06 07 08 09 10 11 12 130.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
0.00
0.25
0.50
0.75
1.00
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 112
4.C Impulse responses
Figure 4.11: Responses to a 1 s.d. shock to financial stress indices
plneur-ciss
regime 1
plneur-ciss
regime 2
plneur-ciss
regime 3
plneur-vix
regime 1
plneur-vix
regime 2
plneur-vix
regime 3
hufeur-ciss
regime 1
hufeur-ciss
regime 2
hufeur-ciss
regime 3
hufeur-vix
regime 1
hufeur-vix
regime 2
hufeur-vix
regime 3
czkeur-ciss
regime 1
czkeur-ciss
regime 2
czkeur-ciss
regime 3
czkeur-vix
regime 1
czkeur-vix
regime 2
czkeur-vix
regime 3
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 500
1
2
3
4
-1.0
-0.5
0.0
0.5
1.0
1.5
-1
0
1
2
0.0
0.2
0.4
0.6
0.0
0.3
0.6
0.9
0.0
0.5
-0.2
0.0
0.2
0.0
0.1
0.2
0.3
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.0
0.5
1.0
1.5
-0.4
0.0
0.4
-1.0
-0.5
0.0
0.5
-0.8
-0.4
0.0
-0.3
-0.2
-0.1
0.0
-0.5
0.0
0.5
0.0
0.2
0.4
0.6
0.8
-0.05
0.00
0.05
0.10
0.00
0.25
0.50
0.75
Responses to a 1 s.d. shock to financial stress
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 113
4.D Setting the priors and Gibbs sampling
4.D.1 Priors
We want to produce results that are as independent of our priors as possible,
so we set most of the priors as non-informative. The only block of parameters
which we set as informative is the block regarding the regression parameters,
matrices BS. All the priors are described subsequently.
VAR Regression coefficients: BS,ΣS
For the coefficients in the VAR models in each regime, we specify relatively
standard priors. Also, since we do not want to make any specific assumptions
regarding the regimes, we assume the same priors for each regime.
We assume an independent normal-inverse-Wishart prior for the VAR coef-
ficients. The VAR coefficients BS (S ∈ 1, ...N) have Minnesota prior form
as described in Banbura et al. (2009), for example. Therefore, we assume the
following prior BSt ∼ N(B, VB):
(Bk)ij =
bi, if i = j, k = 1
0 otherwise(4.4)
V(Bk)ij =
(λ1
kλ3
)2, if i = j(
σiλ1λ2
σjkλ3
)2
otherwise(4.5)
µS ∼ N(0, c) (4.6)
The AR coefficients are set very close to one (the priors are estimated
using univariate AR(1) regression), which is a very plausible prior for exchange
rates and also stress indicators. The prior covariances between the regression
parameters were set to zero, which is common practice. The variances are
assumed to be distributed according to the inverse-Wishart distribution with
scale matrix S and prior degrees of freedom T (in our case, S−1 = 0 and T = 0,
which is a non-informative prior as described in Koop and Korobilis (2010)):
Σ−1S ∼ W (S−1, T ) (4.7)
In addition, as we have a prior belief that shocks to the Czech koruna do not
affect the level of stress in the eurozone (and thus the value of stress indices), we
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 114
incorporate a tight prior on the parameters reflecting the effect of the exchange
rate on the stress index: bik ∼ N(0, c) (where i is the equation for the stress
index and k indicates all parameters pertaining to the lagged exchange rate
values), where c is a very small constant.
The number of lags in the VAR model in each regime was chosen using the
information criteria in the frequentist VAR model. Although a more rigorous
way would be to select the number of lags using the marginal likelihood, we
opted for the approach based on the information criteria due to its simplicity. In
addition, changing the number of lags does not change the results dramatically.
As for the prior hyperparameters on the B coefficients in each VAR model,
we chose the ones suggested in Canova (2007) (which are very loose in our
case). The prior on the constants in the VAR model is also set as very loose
(c = 10, 000).
Finally, one more prior assumption was imposed to alleviate the so-called
label switching (identification) problem (Fruhwirth-Schnatter, 2006), which
Markov-switching models suffer from when the priors are symmetric, as in
our case. A possible solution is to assume a ranking of some coefficients across
regimes and order the draws accordingly (as applied in Billio et al. (2013), for
example). A plausible way to choose such a ranking is to order the regimes
according to the variance of some shocks. This is the solution we chose. In our
case, we assume that σind,1 < σind,2 < σind,3, that is, the reduced-form shocks to
financial stress indicators have the lowest volatility in Regime 1 and the highest
volatility in Regime 3.
Priors on transition matrix P
In the case where the state variable has two states, we follow Kim and Nelson
(1999) and assume a beta prior on the diagonal elements of the transition
matrix (due to the adding-up property, one needs to impose only one prior in
each row of the transition matrix). Specifically, pij ∼ beta(uij, uij). We opt
for a non-informative version of the prior beta(0.5, 0.5). In the case of three
regimes, we assume a non-informative Dirichlet distribution prior (which is an
extension of the beta distribution to multivariate random variables) for each
row of the transition matrix: pi ∼ Dir(0.5, 0.5, 0.5).
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 115
Priors on state variable St
Similarly to the algorithm by Carter and Kohn (1994), it can be shown that
due to the Markov property, all posterior distributions of St depend on S0
(Kim and Nelson, 1999). Since we draw the parameters conditionally on other
parameters, we assume an ergodic solution for the initial St for a given draw
of transition matrix P .
4.D.2 Gibbs sampling
Since no analytical solution of the model exists, we employ the Gibbs sampling
algorithm to draw samples from the joint posterior distribution of the para-
meters:
Θ = BS,ΣS, St, t ∈ 1, . . . , T , pij, i, j ∈ 1, . . . , N (4.8)
We can draw from the conditional distributions of each block of parameters,
which, after a sufficient number of iterations, converges to draws from the joint
posterior distribution. The steps are similar to those sketched in Krolzig (1997):
1. Filtering and smoothing step: draw indicators of state (regime) St for
each t. This is done using multi-move sampling, which first employs the
Hamilton filter to obtain the posterior distribution of the state variable
at time T and then samples backward states at each time t given a draw
at t+ 1. This procedure is in principle very akin to the Carter and Kohn
algorithm in linear state-space models (Carter and Kohn, 1994).
2. Hidden Markov chain step: draw the elements of transition matrix P from
the posterior beta (Dirichlet) distribution as in Kim and Nelson (1999).
3. Regression step: given the draws of the state variable, the whole sample
can be split into N sub-samples. For each sub-sample, parameter Bs can
be drawn from the same conditional posterior distribution (multivariate
normal) as in the standard Bayesian VAR model, e.g. Koop and Korobilis
(2010).
4. Similarly to the previous step, covariance matrices can be drawn for each
sub-sample from its conditional posterior distribution, which is from the
inverse-Wishart family.
4. Financial Stress and Its Non-Linear Impact on CEE Exchange Rates 116
5. Draw impulse response functions: given the draws of B and Σ, we draw
impulse response functions identified using recursive identification (where
we assume that the shock to stress comes first, so the shock from the
koruna does not affect it contemporaneously).
We iterated this procedure 105,000 times, discarded the first 100,000 draws
as a burn-in sample, and retained the remaining 5,000 draws, from which pos-
terior quantiles were taken.
Chapter 5
Time-Varying Betas of Banking
Sectors
Abstract
This paper analyzes the evolution of the systematic risk of the bank-
ing industries in eight advanced countries using weekly data from
1990 to 2012. Time-varying betas are estimated by means of a
Bayesian state-space model with stochastic volatility, whose results
are contrasted with those of the standard M-GARCH and rolling-
regression models. We show that both country-specific and global
events affect the perceived systematic risk, while the impact of the
latter differs considerably across countries. Finally, our results do
not support the previous findings that the systematic risk of the
banking sector was underestimated before the last financial crisis.
5.1 Introduction
Systematic risk has been among the most studied issues in the financial liter-
ature, particularly when the systematic risk of banking sectors is considered.
The inherent fragility of banks and the opacity of their businesses raise the
question of whether markets are able to price the risk correctly. The excessive
risk-taking by US banks before the market meltdown in 2007 is an example of
a period when the correct evaluation of risk is questionable. Surprisingly, not
even the ex-post literature provides any clear-cut answer to this question, so it
This paper was co-authored by Sona Benecka and Ivo Jansky. It was published in theCzech Journal of Economics and Finance (no. 6/2012). Its earlier version had been publishedas an IES Working Paper 23/2012.
5. Time-Varying Betas of Banking Sectors 118
is not clear whether markets were aware of the risks connected with mortgage
loan securitization. As we show in this paper, the results depend on how the
systematic risk is estimated.
The paper extends the evidence from the current literature in several ways.
First, it applies a Bayesian state-space model with stochastic volatility for the
estimation of the CAPM betas of banking sectors. According to the CAPM
theory (e.g., (Sharpe, 1964), (Lintner, 1975), (Mossin, 1966)), the betas should
capture the systematic risk of the industry. It is now widely held that betas are
not time-invariant, and methods such as the rolling-regression model, classic
state-space models, and the GARCH model have so far been used frequently
to estimate the evolution of betas. Still, these methods have several shortcom-
ings, such as arbitrary choice of window size (in the case of rolling regression),
assumed homoskedasticity of residuals (in both the rolling-regression and the
state-space approaches), and a large amount of noise present in the estimates
(estimation based on the GARCH model). On the other hand, the model that
we use links the advantages of both the Kalman filter approach (estimating
the beta as an unobservable process in a state-space model) and the approach
based on the M-GARCH model (allowing for heteroskedasticity of residuals).
Next, the paper presents the results for three methods—the rolling-regression
model, the GARCH model, and the state-space model with stochastic volatil-
ity—and, on the example of US banking betas in the pre-crisis period, shows
how these estimates can be useful for policymakers. This period was character-
ized by a build-up of instability in the banking sector, which was not reflected
in stock prices according to some studies. Nevertheless, our analysis shows that
the banking sector risk in calm periods could still be priced in if the estimation
techniques used in this paper were employed.
Third, we analyze the time-varying betas of banking sectors across differ-
ent advanced countries. The previous literature has investigated the betas of
financial sectors as a whole or has studied trends between sub-sectors in one
individual country. On the other hand, our estimation allows us to look at po-
tential global trends in the perceived riskiness of banking sectors. To evaluate
the degree of co-movement, we estimate a global factor and calculate the per-
centage of the variation explained by the global factor for individual countries.
The results suggest that the banking sectors in some countries (the US, the UK,
and Germany) share similar patterns in the evolution of their systemic risk; on
the other hand, the sectors in other countries (Japan and Australia) look more
isolated. The paper presents one of many possible explanations: the degree
5. Time-Varying Betas of Banking Sectors 119
to which the countries are financially interconnected. Thus, we compare our
results with previous findings on international banking and the transmission of
financial stress. It seems that the most influential financial centres exhibit the
highest sensitivity to global developments and the degree to which the banking
sector is internationalized can be reflected in the sector’s systemic risk.
We believe that our proposed estimation method could enhance the analyses
by equity capital investors, bank managers as well by financial supervisors.
This innovative approach can be applied to the banking sector as a whole or
individual banks’ data. Hence, it can be used to estimate the cost of capital
more accurately or to identify the determinants of systemic risk. It may also
help in the identification of instability accumulation in tranquil times, as this
phenomenon remains a crucial issue for financial stability.
5.2 Systematic risk and the banking sector
The concept of the capital asset pricing model (CAPM) has been under the
relentless attention of both academicians and practitioners for almost 50 years.
One of the most important implications of this model is that we can use the
contribution of an asset to the variance of the market portfolio (the asset’s
beta) as a measure of the asset’s systematic risk. This risk is determined by
general market conditions and cannot be diversified away.
The assessment of systematic risk is vital both for academic research when
testing asset-pricing models and market efficiency, and for investment decisions
such as portfolio choice, capital budgeting, and performance evaluation. In
recent years, it has also become used for financial stability purposes to estimate
the cost of equity (Barnes and Lopez, 2006) or even to measure the level of
financial stress.
Our study is unique in that it compares time-varying betas in banking
sectors across different countries. Betas of banking sectors have usually been
estimated in the literature as a part of sectoral analyses in the financial industry.
For example, Mergner and Bulla (2008) estimate the time-varying betas of a
financial sector (including insurance companies) in a pan-European portfolio. A
similar exercise is performed by Groenewold and Fraser (1999) on Australian
sectors. Estimation is performed on an individual stock level by Lie et al.
(2000), who estimate the time-varying betas of 15 financial sector companies in
Australia on daily data. They use the GARCH model and the Kalman filter,
which generates better results based on in-sample MAE and MSE.
5. Time-Varying Betas of Banking Sectors 120
Another pure banking-sector analysis is by King (2009), who estimates the
costs (required rate of return) of capital in six developed countries using rolling
regression. The author claims that the costs declined in all countries except in
Japan until 2005 when they started to rise. The decline in costs reflects both a
declining beta and a declining risk-free rate. He also suggests that a low beta
may point to mispricing of banking shares.
More recently, Caporale (2012) performs tests for structural breaks in a
market model of the US banking sector. He identifies three structural breaks
— 1960M12, 1989M09, and 2000M03, after which banking betas were at historic
lows (the sample ended in 2008). He suggests that the risk was mispriced (i.e.,
the systematic risk was underestimated), as the banks took the highest leverage
and risk in this time, while the expected risk was low. On the other hand,
Bhattacharyya and Purnanandam (2011) look at the evidence of excessive risk-
taking of US banks in the pre-crisis period on an individual bank level. They
conclude that financial markets were able to identify banks engaged in risky
operations before the meltdown.
Another stream of literature investigates the determinants of systematic
risk. In particular, several studies examine the question of whether more lever-
aged banks bear a higher systematic risk. While Yang and Tsatsaronis (2012)
show a positive correlation between leverage and beta on a sample of 50 banks
from OECD countries, di Biase and Elisabetta (2012) do not find a strong link
in the Italian sector. Also, the cost of equity (which is determined based on
beta) is still a key issue mainly for banking sector supervision and financial sta-
bility purposes. A recent paper by Yang and Tsatsaronis (2012) extends this
stream by showing that leverage and business cycles influence the systematic
component of banking risk, so bank equity financing is cheaper in booms and
dearer during recessions. Altunbas et al. (2010) identify several determinants
of individual bank riskiness, accounting for banking sector characteristics such
as GDP, housing prices, and the yield curve.
The impact of banking globalization on banking sector risk has not been
investigated in this context thoroughly. Individual bank data from Germany
were studied by Buch et al. (2012), who show that internationalization in-
creases the riskiness of banks. Similarly, Cetorelli and Goldberg (2012) show
that banking globalization is leading to faster transmission of global shocks, so
increased financial linkages between banking sectors worldwide increase their
vulnerability to financial shocks.
5. Time-Varying Betas of Banking Sectors 121
5.3 Approaches to the estimation of systematic
risk
For the purposes of this paper (estimating betas of the banking sectors), we
consider the standard CAPM result, summarized in the following equation:
E(Ri) = βiE(Rm) (5.1)
where Ri = Ri − rf is the excess return on asset i (rf is the return on
the reisk-free asset) and Rm = Rm − rf is the excess return on the market
portfolio. This equation asserts that in equilibrium, the returns on an asset
depend linearly only on the returns on the market portfolio (thus, it is a one-
factor model). This model should hold ex-ante, but it can be estimated only
on historical data, so the following market model regression is used for the
estimation:
Rit = αi + βiRmt + εit, εit ∼ N(0, σ2i ). (5.2)
The original model implies an equilibrium relation, which should be stable
or time-invariant. However, the stability of this relation has been challenged
several times in the literature and there is now a consensus that βi is not
constant. For instance, Fabozzi and Francis (1978) claim that betas may be
random coefficients, which could explain the large variance of betas estimated
using OLS, the poor performance in estimating the returns on assets, and
the rejection of the CAPM in many stock markets. Despite these findings,
no consensus has been found on the method for estimating time-varying betas.
Usually, the Kalman filter or a GARCH model are used (e.g., (Faff et al., 2000),
(Mergner and Bulla, 2008), (Lie et al., 2000)) with differing results.
In order to draw credible conclusions from our analysis, we employ three
approaches to estimating betas and compare their results. The first approach is
based on a simple rolling-regression model. The second approach is based on the
M-GARCH model introduced by Bollerslev (1990), which is based on estimating
the conditional covariances between the returns on the market portfolio and
the asset under consideration. The third approach is based on a Bayesian state-
space model with stochastic volatility, which estimates betas as an unobserved
component and allows for time-varying variance of shocks.
5. Time-Varying Betas of Banking Sectors 122
5.3.1 Rolling regression
As a starting point, we employ a method based on rolling-regression estimates,
where time-varying betas are estimated by OLS on a moving window of a given
number of observations. The drawback of this method is its sensitivity to the
choice of window size and the sensitivity of OLS to outliers. As this method is
used only as a benchmark against which we compare the other two methods,
the size of the window is chosen informally.
5.3.2 M-GARCH
First, let us assume without loss of generality that Rjt = εjt, where j = i,M ,
and the error terms are assumed to be (εit, εMt)′ = H
1/2t zt, and zjt ∼ N(0, 1)
are uncorrelated. Since εjt|Ψt−1 ∼ N(0, Ht), the equation 5.3 represents a con-
ditional covariance matrix between the banking sector returns and the market
returns:
Ht =
(hii,t hiM,t
hMi,t hMM,t
)(5.3)
Following the analysis by Rippel and Jansky (2011), we opt for a GARCH(1,1)
process, which leads to the M-GARCH model described by the vector Equation
5.4. The same equation can be rewritten in a more compact way (Equation 5.6)
using a vech operator that stacks in one column all non-redundant elements of
a symmetric matrix that are either on or below the diagonal (Hamilton, 1994).
hii,t
hiM,t
hMM,t
=
c11
c12
c22
+
a11 a12 a13
a21 a22 a23
a31 a32 a33
× ε2
i,t−1
(εi,t−1)(εM,t−1)
ε2M,t−1
+ (5.4)
b11 b12 b13
b21 b22 b23
b31 b32 b33
× hii,t−1
hiM,t−1
hMM,t−1
(5.5)
(vech)Ht = C + A(vech)ε+B(vech)Ht−1 (5.6)
A disadvantage of the multivariate M-GARCH model is its overparameter-
ization. For example, the M-GARCH(1,1) model has 21 unknown coefficients
and the number is growing at a polynomial rate as the number of time series
5. Time-Varying Betas of Banking Sectors 123
involved rises (Pagan, 1996). Some authors, such as Bollerslev (1990), suggest
setting all coefficients above and below the diagonal to zero. This simplification
leads to a substantially reduced form of the general equation and it allows us
to describe the model by equations 5.7, 5.9 and 5.8 with only seven coefficients.
The correlation between the returns of a banking sector and the market, de-
noted ρ, is by Bollerslev (1990) assumed to be constant. This simplification
leads to the following system of equations:
hii,t = c11 + a11ε2i,t−1 + b11hii,t−1 (5.7)
hMM,t = c22 + a33ε2M,t−1 + b33hMM,t−1 (5.8)
hiM,t = ρ√hii,thMM,t (5.9)
Having estimated the three equations above, the time-varying beta can be
easily calculated. The standard CAPM model calculates the β as a ratio of
covariance between an asset and the market and the market volatility. Since
the variance-covariance matrix in the M-GARCH model is time dependent, the
time-varying beta can be calculated using the respective conditional covariance
matrix Ht. In other words, a time-varying beta calculated using an M-GARCH
model has a form described by the following equation:
βit =covt(Rit, RMt)
vart(RMt)=
hiM,t
hMM,t
(5.10)
5.3.3 Bayesian state space model with stochastic volatility
The drawback of the previous approach is that it contains a lot of noise because
the betas can change substantially every period, which is not plausible. To
overcome this problem, we model the betas as an unobservable process which
follows a random walk. We assume the following state-space model (note that
the analyzed asset’s index i is omitted):
5. Time-Varying Betas of Banking Sectors 124
Rt = αt + βtRmt + ut, ut ∼ N(0, σ2t ), t = 1, 2, ..., T (5.11)
Bt =
(αt
βt
)=
(αt−1
βt−1
)+
(vα,t
vα,t
),
(vα,t
vα,t
)∼ N(0,Σ) (5.12)
log σt = log σt−1 + ηt, ηt ∼ N(0,W ) (5.13)
This state-space model is similar to those used in the literature. However,
those models, estimated using the Kalman filter, assume that the residuals ut
are homoskedastic, i.e., σt is fixed. This can bring bias into the results (i.e., the
betas can be overestimated or underestimated, depending on the value of σt),
because σt is used in the Kalman filtering and presumably varies over time.
Therefore, we assume a variant of stochastic volatility, i.e., the volatility is
modelled as a latent process σt which is not a simple function of the past or
current values of the observables, as is the case with a GARCH process, for
example. We assume the simplest version of the stochastic volatility process,
where the volatility follows a geometric random walk.
This kind of model is usually estimated using Bayesian inference, which
overcomes the problem of failure to find local maxima, as is the case with the
MLE approach. In addition, Bayesian methods in this context are relatively
easy to implement and can be extended to find the posterior distributions of
parameters in very complex models. The major difference between the MLE
and Bayesian approaches to state-space modeling is that the latter assumes
that the parameters of the state/observational equations (i.e., the variances of
the error terms) are not fixed parameters to be estimated, but are random vari-
ables. Also, the state variables (Bt and σt) are regarded as random variables as
well. The estimation starts by assuming the prior distributions of the hyper-
parameters and the starting values of the state variables, and solving for the
posterior densities of all these variables (by means of Bayes’ theorem). Because
the joint posterior density function is intractable in this case, a simulation us-
ing Markov chain Monte Carlo methods is performed. Its details are described
in the Appendix 5.A
5. Time-Varying Betas of Banking Sectors 125
Table 5.1: Data used for the analyss
Country Risk-Free Rate Stock Market Index
United Kingdom UK Interbank 3M FTSE 100France Euribor 3M CAC 40Germany Euribor 3M DAX 30Switzerland Swiss Liquidity Financing Rate 1M SMIUnited States US 3M T-Bill NYSE COMPOSITEJapan 3M Interbank NIKKEI 225Hong Kong HKD Depo 1M Hang SengAustralia Dealer bill 90 day rate ALL ORDS
Source: Thomson Reuters Datastream
5.4 Time-varying betas of the banking sectors
5.4.1 Data used for the analysis
We estimate the time-varying betas of the banking industries in eight advanced
countries—the United States, the United Kingdom, Germany, France, Switzer-
land, Japan, Hong Kong, and Australia. The countries were chosen based on
their market capitalization and the number of banks operating in the coun-
try. The major stock market indices were used as the indices representing the
market portfolio. In some cases, banking sector indices are published by stock
exchanges, but to ensure consistency we opted for banking sector indices con-
structed by Thomson Reuters. Finally, the risk-free rates of most countries
were chosen as those recommended by Datastream (available on its intranet,
for example), while the risk-free rate of Hong Kong was chosen based on the
literature. All the data were downloaded from Datastream and are summar-
ized in Table 5.1. The normalized stock indices are plotted in Figure 5.2 in
Appendix 5.C.
Weekly data spanning January 1990 to February 2011 are used for the
analysis. The exceptions are Germany and France, whose data start in January
1999, when the Euribor rate was introduced. The sample could have been
extended by using the national money market rates before 1999, but we wanted
to ensure consistency of the results, so this extension was skipped.
5. Time-Varying Betas of Banking Sectors 126
5.4.2 Results: systemic risk of the banking sectors
We estimated the time-varying betas of each banking sector using the three ap-
proaches mentioned in the previous section—the rolling-regression model, the
multivariate GARCH model, and finally the state-space model with stochastic
volatility. Figure 5.3 in Appendix 5.D presents the results from the rolling
regression with a window spanning 50 observations, which corresponds to ap-
proximately one year. This approach has two major drawbacks—there is no
means of estimating the optimal size of the window, and the technique is sensit-
ive to outliers. Therefore, the technique would yield different results depending
on the size of a chose window.
Next, Figures 5.4 and 5.5 in Appendix 5.E presents estimates using the
multivariate GARCH. The drawback of this method is that the resulting time
series contains a large amount of noise, which causes them to be very erratic.
Since each new observation affects the volatility of both the market and the
indices and, therefore, the betas, changes between two consecutive observations
should be interpreted cautiously.
Finally, Figures 5.6 and 5.7 in Appendix 5.F present the posterior medi-
ans and two posterior quantiles of the latent processes of the betas and the
stochastic volatility simulated using the Gibbs sampler. The burn-in sample
has 8,000 iterations, and the following 2,000 iterations were used to form the
quantiles. One can observe that the most substantial differences between this
approach and the former two occur at times of increased volatility, which is
because the last method filters out the noise brought about by every new ob-
servation. The ability of this method to filter out noise from the signals is why
we introduced this third method.
All three approaches strongly support the idea of the time-varying nature
of the beta, and several important features are apparent. First, we do not
observe any steady decline in the banking sector beta after 1990. This finding
is in contrast with King (2009), who concludes that the bank betas trended
downward for most countries over a 20-year period, with a substantial increase
only in the latest period. He used bank level estimates that are lower than the
equity sub-index estimates we employ. The differences are unusually large in
the case of the UK and increased during the recent crisis period (mainly due to
a different weighting and sample). Still, our focus is not on the cost of capital,
but on investors’ reasoning (perceived riskiness) and global factors for the most
important banking groups.
5. Time-Varying Betas of Banking Sectors 127
Second, our beta estimates indicate that the banking sector risk in quiet
times could still have been reflected in asset prices. As for the period after
2005, it is often argued in the literature that market expectations of banking
risk in the US were low while bank leverage and risk-taking were rising during
the housing market credit boom. Still, our findings are not consistent with
the notion that this instability build-up was mispriced. The US banking beta
started to rise as early as July 2006 from levels close to 0.6, growing steadily
to 1.5 two years later when the financial crisis had fully developed. Similarly,
the sovereign debt crisis was expected to hit mainly the French banking sector,
so its beta remained at elevated levels (more than 1.6) in most of 2010. In
the first months of 2011, the beta for the French banking sector started to rise
again, reaching 2.5 at the end of 2011.
Third, the reaction of the markets to the recent crises also differed substan-
tially. While the dot-com bubble in 2000 increased the perceived riskiness of
the American banking sector and lowered it for other countries, the global fin-
ancial crisis increased the betas of many banking sectors all around the world at
the same time. The same pattern, i.e., synchronized increase in the systematic
risk, although to a lesser extent, can be found in the data for the more recent
euro area sovereign debt crisis. This may be due to the systemic nature of the
crisis, as the transmission of shocks was facilitated by the international bank-
ing network. The growth of banking sector linkages between several countries
(such as the US, the UK, and Germany) could have contributed to the higher
perceived riskiness of their banking sectors.
To explore the similarities among the movements of banking sector betas
across countries more precisely, we estimate a global factor of systematic risk
and assess its synchronization with the individual countries’ betas.
5.4.3 Extension: exploring the global development of sys-
temic risk
As we have pointed out, some banking sectors share similar patterns in the
evolution of their systematic risk. That is, in most of the studied countries,
their betas generally declined until 2005, after which they started to rise. Aus-
tralia and Japan were exceptions, and the systematic risk of their banking
sectors looks isolated to a large extent from global developments. Therefore, it
seems that changes in the perceived riskiness of some banking sectors are more
sensitive to global shocks in some countries than in others. To quantify the hy-
5. Time-Varying Betas of Banking Sectors 128
pothesis that the systematic risk of some banking sectors is more isolated from
global developments, we extract a common (global) factor to all the betas and
compute the proportion of the variation of each beta explained by the global
factor. If more variation is explained, the banking sector is more sensitive to
global developments.
For further analysis, we use posterior medians estimated using Bayesian
inference as described above. This is because this method filters out noise and
outliers that are present in the results obtained by the GARCH and rolling-
regression models. Since we have assumed that the process of betas follows a
random walk, it is not surprising that the hypothesis of a unit root is not rejec-
ted by the Dickey-Fuller test. To achieve stationarity, we first differenced the
original time series and then normalized them, so the value of the transformed
series has the interpretation of the deviation from the mean, where the unit of
measurement is the standard deviation of the estimated sample.
The dynamic factor model, described in the Appendix 5.A, was estimated
using the MLE approach and the Kalman filter, and the estimated global factor
is plotted along with its cumulative sum in Figure 5.1. The magnitude of the
factor is not directly interpretable, but one can observe that the sharp decline
in the beta after the dot-com bubble in 2000 was followed by a period when the
average beta for our sample rose and moved around unity. At the beginning of
2003, the betas of the banking sectors in several countries fell sharply again.
The trend reversed only in 2007 when the financial crisis spread globally. The
sovereign debt crisis had a smaller impact than the financial crisis, but the
betas in several countries (France, UK, and Germany, among others) still rose
substantially.
To quantify the extent to which the global factor explains the dynamics
of each beta, we estimate a regression over the whole period and another two
regressions over two sub-periods: 1999–2006 and 2006–February 2012 . Next,
in order to check the robustness of the results, we estimate another two factors,
one for each sub-period, and estimate Equation 5.20 over the sub-periods. This
step is done to make sure that the results do not change when matrix P is
estimated using the split sample. If the results are to be robust, R2 should not
The choice of 2006 was driven by two reasons in addition to a robustness check. First, wewanted to include in the second sub-period the onset of the crisis in the US. Then, accordingto Garratt et al. (2011), a substantial shift in international banking occurred in 20006Q1when Switzerland moved away from the most important financial centers in the sense offinancial stress transmission. This structure remained broadly unchanged until recently. Forfurther explanation see the remaining text.
5. Time-Varying Betas of Banking Sectors 129
Figure 5.1: The global factor of the systematic risk of the bankingsector and its cumulative sum
00 02 05 07 10
−3
−2
−1
0
1
2
3
00 02 05 07 10
−40
−30
−20
−10
0
10
20
differ much. Unfortunately, there is no statistical test to test for the equality
of the two approaches, since different dependent variables are used, so the
differences are assessed only informally.
Table 5.2: Banking sector systematic risk: percentage of the variationexplained by the global factor
Factor Time period US UK DE FR JP CH HK AUFactor 1 1999-2012Feb 0.27 0.38 0.19 0.31 0.01 0.17 0.23 0.13
1999-2006 0.15 0.32 0.15 0.32 0.01 0.14 0.24 0.142006-2011 0.37 0.44 0.24 0.32 0.01 0.22 0.22 0.13
Factor 2 1999-2006 0.11 0.3 0.16 0.31 0.02 0.13 0.28 0.19Factor 3 2006-2012Feb 0.39 0.46 0.23 0.32 0.01 0.2 0.22 0.12
Note: The first part of the table shows the results when the global factor isestimated for the whole period. The second part shows the results when twofactors are estimated for the two sub-periods.
The results are reported in Table 5.2. The highest percentage of the vari-
ation explained by the global factor both across sub-samples and over the whole
sample is for the United Kingdom, while its value increased over time as well.
It is followed by the United States, France, and Germany. On the other hand,
the beta for Japan seems unrelated to global developments.
5.4.4 Systematic risk and global banking
One potential explanation for the level of sensitivity to global developments is
the extent to which countries are financially interconnected. Ideally, interna-
5. Time-Varying Betas of Banking Sectors 130
tionalization per se is a diversification strategy reducing a bank’s risk, which
depends on the correlation between domestic and foreign assets and the volat-
ility of foreign markets. However, Buch et al. (2009), for example, found that
internationalization increases the risk of German banks, although the results
depend strongly on the type and the size of the bank.
Also, the global financial crisis has shown that international integration
exposes banks to additional risk, especially through the global banking net-
work. Internationalization has dominated banking in the last ten years, with
the amount of global international claims having increased by 400% since 2000,
mainly in advanced countries. Cetorelli and Goldberg (2012) show how globally
active banks contribute to the international propagation of shocks. A global
bank responds to a domestic liquidity shock by adjusting its funds interna-
tionally. The financial stability dimension of global banking has led to several
attempts to limit these activities (BIS, 2009).
Therefore, an interesting question arises whether investors are aware of
cross-country banking sector linkages when pricing risk. There is still no simple
measure of the degree to which a country’s banking sector is internationally
integrated. One possible simple measure is the volume of loans from non-
resident banks as a percentage of GDP (presented in Table 5.3). Switzerland,
Hong Kong, and the UK have had a dominant position in international lending
during the last ten years, while Japan and Australia have remained rather
isolated. Another important development is the rise in offshore activities, which
are related to operations of hedge funds and shadow banking. The country
ranking is similar.
More sophisticated measures are based on the BIS bilateral claims database,
taking into account both debtor and creditor positions. Garratt et al. (2011)
use this dataset to identify important financial centers. Using an information
map equation, they divide banking groups from 21 countries into a structure
which shows a map of financial stress contagion. They conclude that the most
influential centers became smaller but more contagious. As for the structure,
the most prestigious centers in 2000 were the UK, the US, Germany, and Japan.
In 2006, Japan and Switzerland ceased to be dominant while France became
dominant. In 2009, the most influential centers were the US, the UK, France,
and Germany, in line with our beta findings. Any identification of the determ-
inants of the pricing of perceived risk is beyond the scope of this paper, but
one can conclude that the most influential financial centers exhibit the highest
sensitivity of betas to the global factor.
5. Time-Varying Betas of Banking Sectors 131
Table 5.3: Banking sector external relations: cross country compar-ison
Loans from Offshore banknon-resident banks deposits / domestic(amt. outstanding / GDP) bank deposits
United Kingdom 1999 83.3% 10.5%2004 112.3% 23.5%2009 204.7% 21.1%
Germany 1999 24.50% 6.3%2004 30.1% 9.2%2009 35.7% 8.7%
United States 1999 13.90% 9%2004 17.8% 13.1%2009 33.8% 23%
Hong Kong, China 1999 172% 11.7%2004 90.3% 15.6%2009 129.7% 38.6%
France 1999 27.4% 5.7%2004 35.9% 9.8%2009 72% 12%
Switzerland 1999 101.3% 18.6%2004 137.9% 29.4%2009 284.4% 61.8%
Japan 1999 15% 0.5%2004 12.4% 1.2%2009 11.5% 2.4%
Australia 1999 14% 4.5%2004 12.6% 5.1%2009 26.8% 4.1%
Source: Beck et al. (2009)
5. Time-Varying Betas of Banking Sectors 132
5.5 Conclusion
In this paper, we estimated the time-varying betas of the banking sectors in
eight advanced countries. We showed that the systematic risk of the indus-
tries varies considerably over time using three approaches—a rolling-regression
model, an M-GARCH model, and a Bayesian state-space model. The choice
of method can have a substantial impact on the assessment of whether mar-
kets can price the risk correctly. Our approach, based on Bayesian inference,
provides some new evidence, and, contrary to some previous literature, we do
not find strong evidence of declining systematic risk before the recent finan-
cial and sovereign crises; according to the literature, such a decline would have
signalled the mispricing of risk.
Finally, we investigated the cross-country differences in banking sector betas.
The systematic risk of banking sectors is primarily determined by domestic
factors, but some countries share a degree of co-movement in their banking
sector betas. The subsequent discussion showed that the growth of interna-
tional banking linkages and faster transmission of financial shocks could have
contributed to more significant comovement in some countries.
5. Time-Varying Betas of Banking Sectors 133
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Appendix
5.A Estimating CAPM betas in a Bayesian state-
space framework
As we have noted in the main body of the text, we use a relatively standard
approach for estimating a states space model with stochastic volatility. This
approach is described well in a multivariate setting in (Primiceri, 2005) or
(Koop and Korobilis, 2010). Here, we only review our choice of the priors and
the Gibbs sampling.
Choice of priors
Before the vector of parameters can be sampled from their joint posterior dis-
tribution, prior distributions and their hyperparameters must be chosen. For
our purposes, the priors were set broadly in line with Primiceri (2005). That
is, we have chosen a training sample of size t0, on which the starting values of
time varying parameters were estimated. The OLS estimates on the training
sample have been used as a reference value for the priors:
(α0
β0
)∼ N
((αOLS
βOLS
), 3 . ΣOLS
)(5.14)
log σ0 ∼ N(log σOLS, 1) (5.15)
Σ ∼ IW (to . k2Q. ˆΣOLS, t0) (5.16)
W ∼ IG(4 . k2W , 4) (5.17)
The means of the initial values of state variables (α0, β0, log σ0) were set at
their OLS values, but with a larger variance. The prior on the error variance of
B (the distribution of Σ) has been set to belong to the inverse-Wishart family,
with the scale parameter set as a fraction of the OLS variance of estimates of
B. The degrees of freedom parameter was chosen as t0. This is in line with the
interpretation of the inverse-Wishart distribution parameters: sum of squared
errors and the number of observations. It is worth noting that the choice of the
inverse-Wishart distribution implies that covariance matrix Σ is not diagonal,
5. Time-Varying Betas of Banking Sectors 137
i.e. shocks to αt and βt may be correlated (this is not the case in some studies
using the Kalman filter). Finally, the prior on the variance of the error term to
the volatility process, W was chosen as a noninformative conjugate prior from
the inverse-gamma distribution.
Gibbs sampling
The state-space model in this subsection is a relatively complex one and we
simulate it by drawing from its joint posterior density function. The variables of
interest are not only variances Σ and W , but also state variables. Together, we
sample from the joint posterior distribution of the following vector of random
variables: Ω =BT , σT ,Σ,W
.
Draws from joint posterior density functions in the state-space models are
done by means of the Gibbs sampler, which draws in turns from the condi-
tional posterior densities of each block of random variables. If the sampling
is performed a sufficient number of times, the distribution of draws generated
using the Gibbs sampler converges to draws from the joint posterior density.
The conditional sampling is done in the following five steps:
1. Initialize BT , σT ,Σ,W
2. Draw BT from p(BT |yT , σT ,Σ,W )
3. Draw σ from p(σT |yT , BT ,Σ,W )
4. Draw Σ from p(Σ|BT , σT ,W )
5. Draw W from p(W |BT , σT ,Σ)
The blocks are initialized at their OLS values and then a large number
of repetitions n of steps 2-5 are performed. In order to skip draws before
the Markov chain converges, we omit the first n1 burn-in observations. The
remaining n− n1 observations are used for the analysis.
Step 2 is performed using a variant of the Bayesian simulation smoother
of state-space models, proposed by Carter and Kohn (1994). In this step, we
obtain draws from the posterior density of the vector BT . Conditional on draws
BT and variance hyperparameters, we can obtain the estimates of residuals uT
and apply the algorithm by Kim et al. (1998) combined with the previous
algorithm to obtain draws of a latent stochastic volatility process. The steps
The symbol xT denotes x1, x2, ..., xT
5. Time-Varying Betas of Banking Sectors 138
are summarized in the appendix of (Primiceri, 2005). Step 3 is a standard
one of drawing the covariance matrix in a SURE model when we assume a
conjugate inverse Wishart prior. Finally, Step 4 is a standard one of drawing
the variance in a linear regression model, assuming a conjugate inverse gamma
prior.
5.B Estimating the global factor
One approach to extracting a global component of banking sector betas is
the principal components analysis, which is widely used in similar settings.
However, as we want to allow for the autocorrelation of shocks to the global
factor, we estimate it as an unobserved component f in the following dynamic
factor model:
yt = Pft + ut, ut ∼MN(0,Σu) (5.18)
ft = Aft−1 + νt, νt ∼ AR(1) (5.19)
where yt stacks the estimated betas transformed to achieve stationarity (this
is described in the text).
The proportion of variation explained by the global factor is estimated by
estimating the following linear regression:
yit = ai + bift + ηit (5.20)
and examining R2. If R2 is higher, we claim that the global factor explains the
sector beta better.
5. Time-Varying Betas of Banking Sectors 139
5.C Banking and stock market indices
Figure 5.2: Stock market (dark line) and banking sector indices,weekly values.
90 92 95 97 00 02 05 07 10
50
100
150
(a) United States
90 92 95 97 00 02 05 07 10
20
40
60
80
100
120
(b) United Kingdom
90 92 95 97 00 02 05 07 10
20
40
60
80
100
120
(c) Germany
90 92 95 97 00 02 05 07 10
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100
150
200
(d) France
90 92 95 97 00 02 05 07 10
50
100
150
200
250
(e) Japan
90 92 95 97 00 02 05 07 10
50
100
150
(f) Switzerland
90 92 95 97 00 02 05 07 10
50
100
150
(g) Hong Kong
90 92 95 97 00 02 05 07 10
50
100
150
200
(h) Australia
Note: Weekly averages, the values were normalized so that their values are 100 inthe first week of 2000.Source: Thomson Reuters Datastream.
5. Time-Varying Betas of Banking Sectors 140
5.D Betas estimated using rolling regressions
Figure 5.3: Rolling regression estimates of banking betas over win-dows of 50 observations
92 95 97 00 02 05 07 10
1
1.5
2
(a) United States
92 95 97 00 02 05 07 10
1
1.5
2
(b) United Kingdom
00 01 02 03 04 05 06 07 08 09 10 11 120.6
0.8
1
1.2
1.4
1.6
(c) Germany
00 01 02 03 04 05 06 07 08 09 10 11 12
0.5
1
1.5
(d) France
92 95 97 00 02 05 07 10
0.2
0.4
0.6
0.8
1
1.2
1.4
(e) Japan
92 95 97 00 02 05 07 10
0.6
0.8
1
1.2
1.4
1.6
1.8
(f) Switzerland
92 95 97 00 02 05 07 10
0.6
0.8
1
1.2
1.4
(g) Hong Kong
92 95 97 00 02 05 07 10
0.4
0.6
0.8
1
1.2
1.4
(h) Australia
5. Time-Varying Betas of Banking Sectors 141
5.E Banking Sector Betas - estimation using M–
GARCH model
Figure 5.4: Betas estimated using M-GARCH model
92 95 97 00 02 05 07 10
1
1.5
2
2.5
3
(a) United States
92 95 97 00 02 05 07 10
1
1.5
2
2.5
3
(b) United Kingdom
00 01 02 03 04 05 06 07 08 09 10 11 12
0.5
1
1.5
2
(c) Germany
00 01 02 03 04 05 06 07 08 09 10 11 12
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
(d) France
5. Time-Varying Betas of Banking Sectors 142
Figure 5.5: Betas estimated using M-GARCH model
92 95 97 00 02 05 07 10
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
(a) Japan
92 95 97 00 02 05 07 10
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
(b) Switzerland
92 95 97 00 02 05 07 10
0.6
0.8
1
1.2
1.4
1.6
(c) Hong Kong
92 95 97 00 02 05 07 10
0.6
0.8
1
1.2
1.4
1.6
(d) Australia
5. Time-Varying Betas of Banking Sectors 143
5.F Banking Sector Betas - estimation using Bayesian
state space model with stochastic volatility
Figure 5.6: Posterior medians, 5-th and 95-th percentiles of betas (up-per panels) and stochastic volatility (lower panels)
0.5
1
1.5
2
92 95 97 00 02 05 07 10
0.02
0.04
0.06
0.08
0.1
(a) United States
0.5
1
1.5
2
2.5
92 95 97 00 02 05 07 10
0.02
0.04
0.06
0.08
0.1
0.12
(b) United Kingdom
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
99 00 01 02 03 04 05 06 07 08 09 10 11 12
0.02
0.04
0.06
0.08
0.1
0.12
(c) Germany
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
99 00 01 02 03 04 05 06 07 08 09 10 11 12
0.02
0.04
0.06
0.08
0.1
0.12
(d) France
5. Time-Varying Betas of Banking Sectors 144
Figure 5.7: Posterior medians, 5-th and 95-th percentiles of betas (up-per panels) and stochastic volatility (lower panels)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
92 95 97 00 02 05 07 10
0.02
0.04
0.06
0.08
(a) Japan
0.5
1
1.5
2
92 95 97 00 02 05 07 10
0.02
0.04
0.06
(b) Switzerland
0.2
0.4
0.6
0.8
1
1.2
1.4
92 95 97 00 02 05 07 10
0.02
0.04
0.06
(c) Hong Kong
0
0.5
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2
92 95 97 00 02 05 07 10
0.01
0.02
0.03
0.04
0.05
(d) Australia