Author: Serob Asatrjan Supervisor: Dr. M.A.J. Theebe
Student number: 6092411 Second reader: Prof. dr. M.K. Francke
Faculteit Economie & Bedrijfskunde
Business Economics, Real Estate Finance
Universiteit van Amsterdam
November 2010
EX ANTE IDENTIFICATION OF HOUSING BUBBLES:
INTRODUCING THE MOVING EXTREMA APPROACH
Master’s Thesis
ABSTRACT
In this thesis, I propose an early warning system for identifying bubbles in house
prices – the moving extrema approach. This methodology monitors a number of
indicators that were noted to display certain directional dynamics prior to the
occurrence of housing bubbles in the past. The dynamics in question – the moving
extremum cycle phases – are moving intervals of time where the last value is the
largest or the smallest among other values (each extrema seen as a signal). When the
same moving extremum cycle phases in a time series of a variable occur within a
fixed number of periods prior to every bubble (i.e. signaling horizon), such signals
are tested for the randomness of their occurrence. To reduce the number of false
signals (noise) in those variables that were proven to issue signals non-randomly,
several variables are tested in combination, bound by the length of their signaling
horizons. When these variables achieve their predetermined extrema within specific
for each variable cycle phases, such co-movements are interpreted as signals for an
upcoming bubble. This method was tested on the US long-term data (24 variables for
the period of 1890-2007 and 16 variables for the period of 1930-2007). The
indicators that displayed the best performance within the in-sample tests were: a) 2-
year lagged real house price, residential investment to GDP, real residential
investment, and nominal exchange rate of GDPUSD currency pair – all expressed as
growth rates [based on the long sample of 1890-1990]; b) real farm value of land and
improvements per acre expressed as growth rates, and price-to-rent ratio in levels
[based on the short sample of 1930-1990]. Their out-of-sample performance was
exceptionally good – the bubble that occurred in the US in the beginning of the 21st
century was called with no false alarms.
KEYWORDS
Moving extrema approach, housing bubbles, early warning system, long-term data
ACKNOWLEDGEMENTS
I want to thank dr. Marcel Theebe for support and guidance in the right direction, for
patience and encouragement to develop something new. I am also thankful to prof. dr.
Marc Francke for useful corrections and remarks.
TABLE OF CONTENTS
INTRODUCTION ....................................................................................................... 4
1. OVERVIEW OF THE LITERATURE................................................................. 9 1.1 What is a bubble? .................................................................................................................9 1.2 Housing bubble identification methodologies....................................................................10
1.2.1 Fundamental price models ..........................................................................................10 1.2.2 Logit/probit models.....................................................................................................12
1.3 Ex post bubble identification..............................................................................................13 1.4 Variables explaining house prices......................................................................................18
2. METHODOLOGY................................................................................................ 21 2.1 Kaminsky-Lizondo-Reinhart leading indicators ................................................................21
2.1.1 One-indicator KLR .....................................................................................................22 2.1.2 Composite KLR indicator ...........................................................................................25
2.2 From KLR thresholds to moving extrema..........................................................................25 2.3 Moving Extrema approach .................................................................................................29
2.3.1 In-sample application: one-indicator moving extrema ...............................................31 2.3.2 In-sample application: composite indicator ................................................................33 2.3.3 Out-of-sample application ..........................................................................................35
3. EMPIRICAL ANALYSIS..................................................................................... 37 3.1 Data and variables ..............................................................................................................37
3.1.1 Variables .....................................................................................................................37 3.2 In-sample analysis and results............................................................................................41
3.2.1 1890-1990 (long sample) ............................................................................................41 3.2.2 1930-1990 (short sample) ...........................................................................................45
3.3 Out-of-sample analysis and results ....................................................................................50 3.3.1 1991-2007 (long sample) ............................................................................................50 3.3.2 1991-2007 (short sample) ...........................................................................................52
3.4 Comparing composite indicators........................................................................................54
CONCLUSION.......................................................................................................... 56
REFERENCES .......................................................................................................... 59
DATA SOURCES...................................................................................................... 65
APPENDICES............................................................................................................ 68
INTRODUCTION
Relevance of housing bubbles
It is intuitively clear that the information about the existence or the build-up of a
housing bubble would interest the most prospective buyers (buy-side investors) both
because of the potential negative gearing and margin calls in case of mortgage
financing, or the consequent loss of equity in case the property is bought out with
cash. Such information may also influence sell-side decisions, as it would be
convenient to sell during overvaluation and repurchase after the bust. It would also be
of interest to mortgage portfolio holders or any market participant who may be
exposed to the risk of lending without sufficient future asset coverage, which includes
investors who take positions in the housing market via RMBS.
In the light of the severe worldwide recession that started in 2007, the question of
central banks’ intervention into the formation of housing bubbles during the boom
stages is becoming gradually one of the hottest topics for academicians and central
bankers.1 While some specialists advise non-intervention and others propagate
policies of “leaning against the wind”2, such attention to housing bubbles arises from
the macroeconomic consequences that they tend to bring forth. Black et al. (2005: 10)
stated that housing crashes lasted on average for 5 years with the average aggregate
price depreciation of 30%.3 Cecchetti (2006: 3) concluded that as opposed to equity
booms, house price booms that ended with a bust were “bad in virtually every way
imaginable”: decreasing the output gap, while increasing its volatility and GDP at
risk, such housing booms downgraded economic growth outlook for several years
ahead. Adalid and Detken (2007: 17) distinguished between high and low-cost booms
with the main criterion being the post-boom 3-year period GDP growth. They found
that high-cost booms were associated with much larger residential investment during
the boom episodes and much deeper declines in house prices during the bust. Bunda
and Ca’Zorzi (2009: 15) found that a booming housing market signaled 81% of the
episodes of financial pressure (decline in nominal exchange rate and currency
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
1 The number of papers concerned with monetary policy influence on house prices published by the researchers from BIS, ECB,
FED, etc. speaks in support of this statement.
2 Ahearne et al. (2005).
3 Industrial countries, 1970-2002.
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reserves) or even banking crisis.4 Andre and Girouard (2008: 19) noted that the
potential negative outcomes for the economic growth, employment and the stability of
the financial infrastructure caused by house price busts could justify the actions taken
by central bankers to reduce price escalation; another question being the effectiveness
of such intervention.
Identification of housing bubbles
As about half of the total household wealth depends on the movement of house
prices5 and housing bubbles may have such vicious consequences on the economy, it
is surprising, that no method for preventing bubble formation has yet been introduced
during the preceding years. A key issue here is the ability to prove the existence or the
absence of a bubble with a sufficient degree of confidence. The main argument of the
skeptics of “real time” bubble exploration is that it is hard to exclude the possibility of
a major shift in the underlying fundamentals even for the most famous events
generally perceived as bubbles6; that the ability to predict or identify bubbles by
central banks (as the institutions responsible for price stability) would imply an
informational advantage over the private markets; and that detecting bubbles using
econometric methods is impossible with a sufficient level of confidence7. These views
could be summed up by Malkiel’s words: asset price bubbles are “virtually impossible
to identify ex ante” (Malkiel 2010: 17).
Still, there were those who were warning of the existence of a bubble in several
countries already in 2002-2003, both in the media8 and more importantly in the
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
4 Despite the fact, that no causality was set out to be proven, the occurrence of such events in a successive pattern should not be
ignored.
5 Wolff (2010) showed that the gross value of the principal residences in the US in 2007 constituted 33% of the total household
wealth, reaching 44% if accounted for other real estate holdings; Goldbloom and Craston (2008) stated that the total dwelling
assets in the aggregate portfolio of Australian households constituted 66% of the total wealth in 2007; Halifax report (2010) on
the household wealth in the United Kingdom indicated that the housing assets in 2009 comprised approximately 48% of the total
household wealth.
6 Garber (1990) provided explanations for the three most prominent events perceived as bubbles, namely the Dutch Tulipmania
(1634-1637), the Mississippi Bubble (1719-1720) and the South Sea Bubble (1720), stating that, for example, the annual
depreciation of the price of a tulip bulb during the “bubble” period did not differ so categorically from that registered in the 18th
century.
7 See, for example, Gurkaynak (2005).
8 Krugman (2005) suggested that there was a bubble in the US both in geographically and zoning-restricted areas with inelastic
supply and the midland cities, remarking though, that the prices and sales volumes were already deteriorating.
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academic circles9. These studies prove that “real time” identification of bubbles in the
housing markets is not impossible.
Aim and research questions
The aim of this thesis is to propose a specific early warning system for timely (ex
ante) identification of housing bubbles – the moving extrema approach – targeted at
homebuyers as the primary users.
The following research questions were addressed in this paper:
1. What are the available methodologies for identifying housing bubbles?
2. How does the moving extrema approach work?
3. How did the moving extrema approach perform in out-of-sample mode?
An overview of the proposed methodology
The moving extrema approach was inspired by another early warning system
developed initially for currency crisis ex ante identification by Kaminsky, Lizondo
and Reinhart in 1998. The main idea of the moving extrema approach is to seek for
association between the dynamics of certain explanatory variables and the occurrence
of housing bubbles, and exploit that association to identify housing bubbles ex ante.
The dynamics in question – the moving extremum cycle phases – are moving
intervals of time where the last value is the largest or the smallest among other values
– thus, either moving maximum or minimum. Observing data this way allows
extracting certain directional movements in explanatory variables. When the same
moving extremum cycle phases of a variable occur within certain signaling horizons
(fixed number of periods prior to each bubble), such a variable is filtered out and
tested for the randomness of such occurrences to establish if the same cycle phase is
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9 Among others, Baker (2002) stated that the nominal house prices in the US had risen by 47% in the period of 1995-2001, of
which the inflationary increase had been only 18%, the 29% gap could be explained by only 10% increase in rents and the
remaining 19% increase of price of owning relative to renting was a bubble. Case and Shiller (2003) also concluded that the US
housing market concealed regional bubbles. Bodman and Crosby (2003) found that houses in the two of the five most populated
cities in Australia were overvalued by 15% and 25%. Hawksworth (2004) suggested that the UK market was overpriced by 20-
40%, and Black et al. (2005) calculated the premium of actual house prices over their fundamental value in the same market
being around 25% by the third quarter of 2004. Ayuso and Restoy (2006) reported that the price-to-rent ratio in the Spanish
housing market was about 24-32% higher than its long-term equilibrium value.
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occurring in a variable mostly prior to bubbles or all the time – randomly. To bring
the number of false signals down, several variables are tested in combination, bound
by the same length of signaling horizon – when all of these variables achieve their
respective largest or smallest values at the same time (within specific for each
variable cycle phases), such co-movements are interpreted as signals for an upcoming
bubble. The aim of this approach is to find such co-movements that lower the number
of false alarms, but are still able to call all the bubble episodes inside the sample.
Then there is sufficient evidence to use these variables trying to identify bubbles ex
ante.
Data
An important condition set for the moving extrema approach is to analyze as long
time series as possible, for that reason and the issue of public availability of data in
English, the US housing market was chosen. I would like to stress the amount of work
undertaken to acquire data series for 24 variables for the period of 1890-2009, which
taking into account different transformations and rationing were compiled into 70
time series, which then entered the analysis. Data for another 16 variables,
unavailable from 1890, were collected for the period of 1930-2009, resulting in 71
time series after various transformations (in total 40 variables and 141 series).
Results
The best-performing composite indicators, based on in-sample tests, were both 3-year
signaling-horizon indicators (bubble imminent to occur in a 3-year time window after
the signal):
• 2-year lagged real house price, residential investment to GDP, real residential
investment, and nominal exchange rate of GDPUSD currency pair – all
expressed as growth rates [based on the long sample of 1890-1990];
• real farm value of land and improvements per acre expressed as growth rates,
and price-to-rent ratio in levels [based on the short sample of 1930-1990].
The out-of-sample results were more than satisfactory: both composite indicators
named above were successful at identifying the out-of-sample bubble with no false
alarms. A potential user – homebuyer – could have benefited greatly relying on
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forecasts of these indicators, as the whole of the housing bubble that occurred in the
beginning of the 21st century could have been avoided.
Structure of the paper
The remainder of this thesis is organized as follows: chapter 1 is concerned with the
overview of literature, chapter 2 describes the methodological issues, and chapter 3
the empirical analysis.
Chapter 1 deals with the definition of a bubble (section 1.1); discusses the existing
“real time” and ex ante bubble identification approaches most commonly applied to
house prices (section 1.2); describes the choice of ex post bubble dating methodology
used in the thesis (section 1.3); and lists the variables considered and found
significant as explanatory variables of house prices (section 1.4).
Chapter 2 describes the starting point of the proposed approach – the KLR
methodology (section 2.1); explaines the transition from thresholds to moving
extrema (section 2.2); and gives a thorough overview of the proposed methodology
(section 2.3).
Chapter 3 describes the data and the variables tested in the thesis (section 3.1);
describes the in-sample analysis of single indicators, on which the composite
indicators are based (section 3.2); discusses the out-of-sample performance of the
composite indicators (section 3.3); and compares the composite indicators with a
potential competitor (section 3.4).
An overview of the completed work and results together with suggestions regarding
further development of the ideas raised in the thesis at hand is presented in the final
section i.e. Conclusions.
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1. OVERVIEW OF THE LITERATURE
The literature overview chapter is divided into four sections: 1) issues of definition; 2)
overview of the most frequently used methods for identifying housing bubbles in the
“real time” and ex ante; 3) methods for dating bubbles ex post; 4) variables that have
been found effective in explaining house price dynamics.
1.1 What is a bubble?
Before approaching the issues of bubble detection, it is necessary to answer the
question: What is the concept of a bubble? In their 2003 paper, Karl Case and Robert
Shiller studied the origin of the term “housing bubble” collecting data on its
occurrence in the major English language newspapers from 1980-2003, and found
that the term had almost been not used at all until 200210
contrary to the “housing
boom”, which had been very popular since 1980s. They suggested that journalists did
not want to use the word “bubble” without very strong evidence of the magnitude of
the stock market crashes in 1987 and 2000. Nevertheless, the concept of a bubble in
asset prices has pervaded the academic literature and there are plenty of sources to
which to refer.
There are numerous definitions of an asset price bubble. The most famous definition
is the one by Stiglitz (1990): “if the reason that the price is high today is only because
investors believe that the selling price will be high tomorrow – when “fundamental”
factors do not seem to justify such a price – then a bubble exists”. This could be
understood as a substitution of fundamentals with expectations. Such a formulation
does not require a decline in prices to prove the existence of a bubble: if it is possible
to show that the prices have grown out of line with fundamentals, such an
overvaluation could go on for extended periods of time and still qualify as a bubble.
Another prominent definition was presented by Kindleberger in 1987: “a sharp rise in
price of an asset in a continuous process, with the initial rise generating expectations
of further rises and attracting new buyers – generally speculators interested in profits
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10 Case and Shiller (2003) stated that the term “housing bubble” came up several times after the stock market crash in 1987, but
vanished shortly after.
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from trading rather than in its use or earning capacity. The rise is then followed by a
reversal of expectations and a sharp decline in price often resulting in severe financial
crisis.”11
This implies that an important condition for identifying the existence of a
bubble is the bursting. The definition of a bubble for this study is derived by further
abandoning the expectations component from Kindleberger’s formulation. The
reasoning is that the prospective end-users of the model presented in this paper – buy-
side investors – would not discriminate between fundamentally sound price and
overpricing (a bubble) that would go on for the next two centuries (meaning that the
price would not drop for 200 years ahead), as concrete evidence of a bubble, that
could hurt their interests, can only emerge through a burst.12
Thus, the definition
chosen for this paper stipulates the following: when there is a sufficient (in terms of
magnitude) spike-like movement in the price, it can be defined as a bubble.
1.2 Housing bubble identification methodologies
The most commonly implemented methodologies dealing with house price bubble
identification are, first of all, the fundamental price approach and then probit
modeling. In the two following sections, the general idea of these methodologies is
described along with several examples from the respective studies.
1.2.1 Fundamental price models
A frequently used “umbrella” of methodologies for house price bubble exploration is
the fundamental price approach. Its root is to model the fundamental (equilibrium)
price and then compare it to the actual price. A good example of such a model can be
found in Case and Shiller (2003). In this paper, the regional US house prices were
regressed on the following fundamentals: percentage change in population and
employment, mortgage and unemployment rates in levels, number of housing starts,
income per capita, and the ratio of the latter to annual mortgage payments. The
positive difference between the actual price and the fundamental price calculated this
way was interpreted as overvaluation. The authors concluded that a bubble was
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11 Several other definitions can be found in Flood and Hodrick (1990), Muellbauer and Murphy (2008), Shiller (2007), Smith
and Smith (2006).
12 In addition, the ax ante signaling approach presented in this paper is not based on the concept of deviation from fundamentals,
but merely on the property of certain dynamics in various macroeconomic and other variables to lead house price bubbles.
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concealed in several cities – in addition to the regression results, this conclusion was
supported by the existence of “elements of speculative bubbles – the strong
investment motive, the high expectations of future price increases, and the strong
influence of word-to-mouth discussion”, which they derived from their survey (Case
and Shiller 2003: 341).
An essential part of fundamental price models is the error term specification that
seeks to explain the gap between the actual and the fundamental price. An often-cited
example was demonstrated in a study by Abraham and Hendershott (1996), where an
error term was set to account for the bubble-building lagged house price growth and
the bubble-bursting difference between the lagged fundamental and actual price. The
higher the appreciation rate of house prices in the previous period, the more it would
be likely for the price to develop into a bubble during the current period. On the other
hand, the larger the gap between the actual price and the fundamental lagged price,
the stronger the pressure on the bubble to burst.
The next level is not just to explain the gap, but to model the short-term dynamics of
the price adjusting back to equilibrium – such models are called error correction
models (ECM). Malpezzi (1999) proposed, in addition to a linear error correction
model, an ECM using cubic terms to enforce the notion, that a larger positive gap
between actual and fundamental price implied larger (faster) adjustment effects than
smaller overvaluation. Despite the fact, that only the linear adjustment was found
statistically significant, the idea of proportional reactions is worth mentioning. For
other examples of ECM, see, among others, Abelson et al. (2005), Cameron et al.
(2005), Sorbe (2008).
An important prerequisite for the error correction models to be viable is cointegration
between the dependent and the independent variables, meaning that they act within a
long-term relationship and cannot wonder apart for too long without a bound. If the
latter is true, the deviations between such variables are temporary and can be
explained by an error correction term. When it comes to cointegration between house
prices and (assumed) fundamentals, various empirical studies report both the
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existence and the lack of such relationships.13
Despite the mixed results, fundamental
price models remain a widely accepted and used methodology.
1.2.2 Logit/probit models
While fundamental price models set out to establish the equilibrium price of housing
for a certain moment in time and the bubble is exposed via the positive gap between
the actual and the calculated fundamental price, logit/probit models are constructed to
indicate the probability of events14
. Thus, it is not the difference between the positive
and the normative, but the association between events that matters within the latter
methodology. Logit/probit models are limited dependent variable models that are
programmed to calculate the probability of an event using the cumulative logistic
distribution in the case of logit models, and the cumulative normal distribution in the
case of probit models. This solves the problem of the linear probability model,
transforming the probability function into an S-shaped curve bound between 0 and 1.
The two studies that are relevant to the theme of this paper were conducted by
Agnello and Schuknecht (2009) and Noord (2006). Both studies applied probit
analysis to house prices, with the former study concentrating on booms and busts and
the latter on house price peaks. Agnello and Schuknecht (2009: 28) included the
following variables in their probit model: growth rate of real GDP per capita; growth
rate of global-liquidity variable (growth of broad money aggregate M3 of the
countries in the sample other than (minus) the respective national M3 of the particular
country under observation); level of nominal short-term interest rate; growth of
working-age population; banking crisis dummy and market deregulation dummy. All
variables entered the analysis with a lag. This model was tested on panel data of 18
countries (including the US) for the period of 1980-2007. Panel data were used to
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13 For example, Black et al. (2005: 15) found cointegration between UK house prices and real disposable income for a period of
31 years; Abelson et al. (2005: 15) reported cointegration between Australian house prices and explanatory variables for a period
of 33 years. Gallin (2003: 3) found no cointegration between the US national-level house price and the assumed economic
fundamentals such as income per capita, population, stock market index, construction wages and personal consumption deflator
within a period of 27 years. Schnure (2005: 11) reported that cointegration tests for regional housing prices and income in the US
(for a period of 26 years) failed to find evidence of such a relationship. Mikhed and Zemcik (2007: 12) further supported Gallin’s
findings, having found no cointegration between aggregate house prices and personal income per capita, consumer price index,
population, mortgage rate, construction wage, the stock market and rent in the US for a period of 24 years.
14 Such events may occur in “real time”, but due to their latent nature, cannot be observed directly, or they may occur in a
certain time window – dependent on the setup of the model.
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enhance the robustness of the model, as the sample period was too short to extract
reliable results on single-country basis.
The probit regression with house price booms being the dependent variable returned
the following results: all variables were found significant at 1% apart from real credit
growth, which was found significant at 5% and deregulation dummy variable, which
was found significant at 10%. Regarding the bust sequence being the dependent
variable: all variables were significant at 1% apart from population growth, which
was significant at 10% and the deregulation dummy, which was not significant even
at 10% level. The model performed extremely well predicting booms in the US house
prices during 1982-2007 issuing only one false signal in 1997. The prediction of busts
was somewhat less successful with two false signals in the beginning of the period
and, more importantly, failure to indicate a bust during 1993-1997.
Noord’s (2006: 15) probit regression with the dependent variable being the peaks in
the US house prices included the following variables: simple average of short- and
long-term interest rate; real house price gap (calculated as the log of real house price
minus the log-linear trend of real house price); and inflation, which were all found
significant at 5%. The conclusions reported were generally successful: as of the end
of the 4th
quarter of 2005, the real house price gap (overvaluation) was found to be
26%. The probability of a peak in house prices was calculated to be 98,5%. This
probability was upgraded to 100% if the housing prices were to increase in 2006 at
the same pace as in 2005 and/if the interest rates were to increase by 100-200 basis
points. Although the timing of the peak was not forecasted precisely – the peak, as we
know now, occurred in 2007 – the conclusion of this paper could have been quite
useful for buy-side decisions.
1.3 Ex post bubble identification
Although it may seem easy to identify asset price bubbles ex post, there are several
issues that need prior clarification. The definition of a bubble elected for this paper
doesn’t require delving deeper into the matters of explaining prices – what matters is
the fact that there was a sufficient boom and a bust. But how much does the price
have to increase and decline and in what time frame for an episode to qualify as a
boom/bust sequence (a bubble)? There are two main approaches commonly used by
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academicians; one of them is for purely ex post decisions and the other for “real time”
estimation.
Bry and Boschan’s (1971) algorithm is the more frequently encountered approach that
deals with the identification of turning points ex post.15
The algorithm prescribes the
exact procedures for identification: correction for outliers, identification of peaks and
troughs, alternation condition, phase and total cycle length etc. The main problem of
this methodology is that it leaves the ends of the series unused, which is somewhat
inappropriate for this thesis, as using this methodology would exclude the last bubble
episode (the one in the beginning of the 21st century) from analysis and that episode is
chosen as the out-of-sample test event.
The second approach is based on a “normal” level and a deviation threshold for time
series for recursive estimations, meaning that the available data is sufficient to
conclude if there is a boom or a bust at a given period. The root of the method is to
establish a deviation threshold from some long-term average or moving average,
which, if crossed, would mean a boom or a bust.16
Adalid and Detken (2007) studied the impact of liquidity shocks on asset price cycles,
defining a boom as at least 4 consecutive quarters where the price index exceeds its
very slow adjusting trend (Hodrick-Prescott filter with !=100,000) by minimum 10%.
This is the most suitable methodology to date bubbles in this thesis in my view, as a
smoothed price trend would reveal the long-term price dynamics which buyers have
to face, and the temporary deviations from this price trend by more than a certain
percentage would mean being exposed to a possibility of a bubble.
Identifying US housing bubbles
The foundation for the upcoming analysis is the house price series produced by Case
and Shiller. First of all, it is necessary to check if the series are stationary, as such a
case would imply mean reverting price dynamics and any major deviation from the
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15 Noord (2006) dated booms and busts in house prices using the Bry-Boschan procedures and defined a peak as a period, prior
and preceding which the price had been rising and then falling for at least 6 quarters. In addition, prices had to rise at least 15%
to qualify as a boom phase. Among other papers, where Bry-Boschan algorithm was implemented, are Girouard (2006), OECD
(2007), Helbling and Terrones (2003).
16 The following papers are a few who have used this method: Alessi and Detken (2009), Bordo and Jeanne (2002), Gerdesmeier
et al. (2009).
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mean could then be seen as a bubble. The traditional Augmented Dickey-Fueller test
was implemented to test for unit roots in the real price series. The results are
presented in appendix 1 and show that there is a unit root in the levels, so the test is
repeated in differences (house prices are expressed in natural logs) and the more
negative value of the test statistic than the critical value at 99% confidence level
allows to reject the unit root in the growth rates of house prices. Thus, the series is
integrated in the order of 1, allowing for an important conclusion that the series is not
mean reverting – at least, based on the analyzed data.
The definition of a bubble in this paper states that a bubble is any sufficient spike-like
movement in real house prices in terms of magnitude. To date the bubbles in the
house price series for the US market, this definition is taken as the basis together with
the threshold method described previously. Within the threshold methodology, the
series are to be smoothed using the Hodrick-Prescott filter to reveal the long-run
dynamics of the series. No assumptions are made if this long-term path is in
accordance with the fundamentals – only the facts based on data. Agnello and
Schuknecht (2009) and Adalid and Detken (2007) used very strong smoothing
parameters of !=10,000 and of !=100,000, applying which smoothes the series too
much, approaching a more “linear” shape the higher the parameter is set (see figure
1).
Figure 1. The real house price index (1890=100) and the smoothed series using HP
filter with !=10,000 and 100,000, period of 1890-2009
Source: S&P / Case-Shiller Home Price Index, author’s calculations
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Setting the filter parameter to !=100, generates a more reasonable result with the
smoothed series moving closer to the actual price, smoothing out the excess volatility
(see figure 2).17
Figure 2. The real house price index (1890=100) and the smoothed series using HP
filter with !=100, period of 1890-2009
Source: Ibid., author’s calculations
Next, the difference between the smoothed values and the actual prices are calculated
for each year. It is, thus, needed to choose a minimum deviation value between these
two series for an episode to qualify as a bubble. Adalid and Detken (2007: 14) set the
deviation threshold of their composite index of asset prices from the smoothed trend
to 10%; Noord (2006: 8) used the value of 15% for the sequence to qualify as a boom
or a bust. In this case, it is not the difference between the trough and the peak that
needs to be considered, but the positive gap between the actual price and the
smoothed series, so the threshold of 10% was considered at first. The bubbles
identified in such a way are shown in table 1 - the overvaluation is shown for every
year, where the actual price exceeded the smoothed series by more than 10%.
Table 1. Bubble episodes from 1890-2007 with 10% deviation threshold
1894 1895 1907 1916 1946 1947 1989 2004 2005 2006 2007
20.7% 13.4% 10.3% 10.1% 15.4% 14.3% 10.7% 10.5% 21.8% 29.5% 11.5%
Source: S&P / Case-Shiller Home Price Index, author’s calculations
Comparing the deviations shown in table 5 with the deviations of actual price from
smoothed series in figure 2, it becomes obvious that the bubble in the end of the 70’s
is left unaccounted. Decreasing the threshold to 9%, brings the episode into the
observations, without adding any other event into the picture (see table 2).
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
17 !=100 is also the default setting for annual data smoothing within statistical software packages.
" &#"
Table 2. Bubble episodes and overvaluation in each year with 9% deviation threshold
1894 1895 1907 1916 1946 1947 1979 1989 1990 2004 2005 2006 2007
20.7% 13.4% 10.3% 10.1% 15.4% 14.3% 9.3% 10.7% 9.8% 10.5% 21.8% 29.5% 11.5%
Source: Ibid.
The duration and the magnitude of the bubbles are denoted in figure 3 bubble
episodes are marked with red arrows. These are the final episodes, around which all
of the following analysis is constructed.
Figure 3. The real house price index (1890=100), the smoothed series using HP filter
with !=100, and the bubble episodes during the period of 1890-2009
Source: Ibid., author’s calculations
A problem with HP filter treating the beginning and the end parts of the sample with a
bias towards the values at those ends was described in St-Amant and Norden (1997:
13). This problem may have an impact on this particular analysis, as the beginning of
the overpriced periods is of primary interest. If the house price in the coming future
(beyond 2010) were to decrease further, the smoothed series would look much flatter
closer to the end of the series, meaning that the overvaluation period had started
earlier - closer to 2000. It would also mean that the market was still overvalued after
2007 - under the present assumptions the overvaluation ended in 2007. An attractive
alternative solution that could reduce the above-mentioned problem is the unobserved
component model (see, for example, Harvey (2006)). Nevertheless, as HP filter was
used in numerous studies with similar aims and is easier to implement and
understand, it is chosen as the preferred methodology for this thesis.
&$"
1.4 Variables explaining house prices
In this section, various variables from academic sources that were found significant in
explaining house prices or predicting housing boom/bust episodes are presented in a
way that mimics that of Lestano and Kuper (2003: 7), where potential indicators were
listed with the general interpretation of each variable and its respective references.18
Table 3. Variables explaining house prices from existing research with comments and
references
Variable Comments References
1 After-tax interest rate The default assumption of interest rates’ impact on housing prices is
that low and/or declining rates favor house price appreciation, as cheap
credit increases demand. An important issue here is the tax burden,
which in the US is lowered due to mortgage interest deductibility.
Abraham and
Hendershott
(1996)
2 Budget balance Fiscal deficit narrows prior to the peak and widens considerably
afterwards.
Ahearne et al.
(2005)
3 Construction cost Growing construction costs, ceteris paribus, increase house prices, as
the reproduction cost becomes higher and arbitrage opportunities may
arise in case house prices respond with a lag.
Abraham and
Hendershott
(1996)
4 Construction share in
GDP
There is a positive association between construction share and house
prices (in the US): rising house prices push construction up, with the
peak of the construction share in GDP generally occurring in close
proximity to the peak in house prices.
Ahearne et al.
(2005)
5 Current account to GDP It was reported that peaks in house prices were associated with
substantial deterioration in balance of the current account. Although
Kole and Martin (2009) concluded that there was no systematic
relationship between current account and house price, such association
may still be useful within the setup of the model presented in this
paper.
Kole and Martin
(2009)
6 Disposable income Disposable income (after-tax personal income) is one of main
determinants of housing demand, i.e. growing disposable income
pushes housing prices up.
Abelson et al.
(2005),
Sorbe (2008)
7 Employment Employment growth is generally associated with increasing consumer
inflation (Phillips curve), which in its turn increases house prices.
Abraham and
Hendershott
(1996), Case and
Shiller (2003)
8 Exchange rate In large cities of the countries with open economies, decreasing
exchange rates may increase house prices, making housing more
attractive for foreigners. In addition to that, depreciating home currency
supports export growth, resulting in increased economic activity and
higher demand.
Abelson et al.
(2005)
9 Gap between lagged
actual and fundamental
house price
Widening gap implies a bubble and also proximity to the peak of house
prices, as overvaluation cannot go on forever. Tsounta (2009) used
long-run house price instead of the fundamental price.
Abraham and
Hendershott
(1996), Noord
(2006)
10 GDP GDP is, in principle, a business cycle variable. The growth in GDP,
similarly to income growth, ceteris paribus, would imply growth in
house prices via increased economic activity and housing demand.
Prolonged GDP growth may lead to a perception of higher level life-
time income and motivate potential buyers to spend more on housing,
taking on more debt. Tsatsaronis and Zhu (2004) presented the results
of variance decomposition of housing prices, which prescribed rather
moderate 7% in the US house price variance to shocks to GDP (the
number was calculated as an average for the group including the US).
Agnello and
Schuknecht
(2009), Kole and
Martin (2009),
Schnure (2005),
Tsatsaronis and
Zhu (2004)
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
18 Some research involved only comparative analysis without using regression techniques – in such case, the variables
considered there are also listed as significant in table 3.
" &%"
Variable Comments References 11 Government spending/
revenue
Government expenditure was found to have a positive effect on
housing prices: government expenditure fuels economic activity via
investment etc, which transforms into rising house prices. There is an
association between government revenue and housing price, which
could potentially have predictive power - high government revenue is
usually the result of strong economic activity.
Afonso and Sousa
(2009)
12 Housing costs to
consumption
Increased housing expenditures (imputed and tenant-occupied rent) to
consumption could be associated with higher house prices. The ratio of
housing costs to income was used by Hogue (2010) as a measure of
both affordability and overvaluation.
Shiller (2007)
13 Housing starts Increases in house prices (positive returns) bring forth more investment
activity with housing starts’ peaks usually leading house price peaks.
Schnure (2005)
14 Housing stock per capita Housing stock p.c. is a supply variable that is negatively related to
house prices: increase in housing stock per capita, ceteris paribus,
should lead to a decrease in house prices, as demand would not cover
supply.
Abelson et al.
(2005)
15 Income p.c. to annual
mortgage payment ratio
Ratio of income per capita to annual mortgage payment measures
affordability. High ratio suggests possible bubble development, if the
increase comes from low interest rates and softening mortgage
conditions. The subsequent decline in the ratio may indicate the
proximity to the peak in house prices as worries of overpricing result in
tighter credit supply and higher interest rates.
Case and Shiller
(2003)
16 Inflation rate High consumer inflation pushes house prices up as rents are usually
indexed with CPI change and real estate is often perceived as a hedge
against inflation. Tsatsaronis and Zhu calculated the variance
decomposition of the US housing prices and prescribed 42% of house
prices’ total variation to inflation, that was equally the largest
contributor (the number was calculated as an average for the group
including the US).
Noord (2006),
Tsatsaronis and
Zhu (2004)
17 Labor force Labor force is comprised of individuals that are employed or are
seeking employment. Growth in labor force increases house prices via
additional demand.
Schnure (2005)
18 Lagged house price
growth
Lagged house price growth is a primary measure of expectations.
Krainer (2002) concluded that the primary driver of house prices in the
US by the end of 2001 was not the drop in mortgage rates, but price
appreciation in previous periods, implying a bubble based on
expectations.
Abraham and
Hendershott
(1996), Kole and
Martin (2009),
Krainer (2002),
Lecat and
Messonnier
(2005), Sorbe
(2008), Tsounta
(2009)
19 Long-term interest rate Decreasing long-term interest rate in “normal” economic conjuncture
increases house prices, as more entities wish and are able to borrow at
lower cost, which increases the demand for housing. The question often
raised is the applicability of nominal vs. real interest rates: although
theory suggests that real rates are those that should matter to borrowers,
practice shows that nominal rates are more influential, as that is what
mortgagors have to pay and what banks follow within DSCR.
Adalid and Detken
(2007), Afonso
and Sousa (2009),
Kole and Martin
(2009), Noord
(2006),
20 Money aggregate M3 Broad money growth usually peaks before house prices and is
positively correlated with real GDP and household borrowing.
Adalid and Detken
(2007), Agnello
and Schuknecht
(2009), Ahearne et
al. (2005)
21 Mortgage interest rate In general, decreasing or low mortgage interest rates have a positive
impact on house price growth. What makes this variable different from
long-term interest rate is the specific to the housing market risk
premium, which fluctuates depending on the perception of risk in the
housing market.
Abelson et al.
(2005), Cutts and
Nothaft (2005),
Krainer (2002),
Malpezzi (1999),
Sorbe (2008)
22 Moving average of
house price growth
Two-quarter MA of house price growth was found significant for
predicting house price peaks for a panel of 17 countries, but not for the
US within country-specific testing. This variable accounts for
expectations (similar to the lagged price growth), taking into account a
longer base for the development of such expectations. In this thesis,
two-year MA is considered instead of two-quarter variable.
Noord (2006)
23 Output gap Positive output gap (difference between actual and potential GDP) is
associated with house price growth, as during house price booms real
GDP grows faster than potential GDP, which then reverses into a
negative gap after the house price peak.
Ahearne et al.
(2005), Sorbe
(2008)
('"
Variable Comments References
24 Personal income As mentioned under disposable income, income variables are widely
considered as the main determinants of house prices. The difference
between personal and disposable income arises from personal current
taxes – thus, changes in disposable income account for the effects
emerging through the buyers/rents channels, while changes in personal
income reflect on a wider level (somewhat similar to GDP growth, as
the latter includes taxes payable to the government).
Case and Shiller
(2003), Cutts and
Nothaft (2005),
Schnure (2005),
Sorbe (2008)
25 Population Although population is not as good a variable for house prices as
number of households or the ratio of young households to total (the
latter often ignored due to data availability issues), it is a generally
accepted demand determinant, where population growth, ceteris
paribus, increases house price via increased demand.
Case and Shiller
(2003), Cutts and
Nothaft (2005),
Malpezzi (1999),
Tsounta (2009)
26 Price-to-income ratio Substantial upward deviations of price-to-income ratio from its long-
term trend are generally perceived as a sign of overvaluation. Malpezzi
(1999) implemented price-to-income ratio with various lags to account
for different magnitude deviations’ error correction.
Andersen and
Kennedy (1994),
Malpezzi (1999),
Black et al. (2005)
27 Price-to-rent ratio Price-to-rent ratio is the gross rent multiplier, which is the third main
affordability ratio. As in the case of price-to-income ratio, upward
deviations from the long-term trend may indicate a bubble
development.
Ayso and Restoy
(2006), Gallin
(2004), Girouard
(2006)
28 Private sector credit Growth of credit to private sector should be correlated with growing
house prices. Additional “kick” is given by the growing house prices,
which increase the collateral value and that, in is turn, increases house
prices further. Helbling (2005) concluded that private credit booms,
measured via large upward deviations in the credit-to-GDP ratio from
long-term trend, coincided with housing boom-bust cycles.
Agnello and
Schuknecht (2009)
29 Productivity Labor productivity (output per hour of work) influences house prices
via changes in income and expectations of future income growth.
Kahn (2008)
30 Rapid house price
appreciation
Helbling (2005) concluded that rapid house price growth during short
periods (as opposed to extended periods of moderate house price
appreciation) were relatively good indicators of a developing bubble.
Helbling (2005)
31 Residential investment to
GDP
Residential investment is, in its principle, similar to housing starts: the
peaks in residential investment to GDP ratio usually precede the
housing price peaks in the US (Dokko 2009).
Dokko (2009),
Musso et al.
(2010), Shiller
(2007)
32 Short term interest rate Although it is the mortgage rate that seem to matter the most among
different types of interest rates where housing prices are concerned,
short term rate is often monitored as an indicator of monetary policy
direction. Helbling (2005) noted that monetary policy via short rates
tightening triggered the bursting of house price bubbles. Thus, initially
low rates support the boom in house prices, which is later deflated into
a bust by a sharp increase in the short rate.
Agnello and
Schuknecht
(2009), Helbling
(2005), Lecat and
Mesonnier (2005),
Tsatsaronis and
Zhu (2004)
33 Stock market index Using stock prices is a simple way to include fluctuations in wealth.
Another application is reflecting on the possible substitution effects
from stock to housing markets after stock market crashes. Thus, there
are two theoretical principles: first of all, increasing stock prices
increase wealth, which pushes house prices up; secondly, stock market
crashes may cause a flow of funds from stocks to real estate also
increasing the prices of the latter.
Abelson et al.
(2005), Lecat and
Mesonnier (2005)
34 Term spread Term spread is an indicator of future economic growth: narrowing gap
between long and short rates indicates the increased perception of
riskiness by the lenders – proximity of a recession; a widening spread
usually means higher growth in the future, as central banks try to
stimulate the economy lowering the short rate.
Tsatsaronis and
Zhu (2004)
35 Unemployment rate Decreasing unemployment rate usually brings forth increased inflation
(Phillips curve), which is transmitted into higher house prices; also
allows access to ownership to individuals in the labor force that do not
yet own a home, thus increasing demand and house prices.
Abelson et al.
(2005), Case and
Shiller (2003),
Schnure (2005)
36 User cost of housing User cost of housing (mortgage rate adjusted for taxation and inflation
less the lagged capital gains) could be viewed as the negative-signed
net return. Rising user cost decreases housing prices.
Andersen and
Kennedy (1994),
Krainer (2002)
37 Working-age to total
population
Growth in working-age population increases house prices via growing
demand, especially when supply lags are taken into account. Long-term
increase in the working-age to total population ratio implies that the
composition of population is generally on the younger side, which
favors formation of new households that need housing – increasing
demand leads to price appreciation.
Agnello and
Schuknecht
(2009), Andersen
and Kennedy
(1994)
Variables tested within the empirical analysis are based on table 3 with several
exceptions due to the public availability of data in sufficient length.
" (&"
2. METHODOLOGY
As stated in the introduction section, the aim of this paper is to introduce a new early
warning system for identifying housing bubbles ex ante – the moving extrema
approach. The root of this idea is to find regularity in the dynamics of various
indicators and house prices (particularly housing bubbles), so that if certain indicators
act in a specific way, a signal is issued by the system that means that a housing bubble
is imminent in a certain time period. This method was inspired by Kaminsky, Lizondo
and Reinhart’s leading indicators approach (KLR) and several elements of the latter
are taken as the foundation of the moving extrema methodology. This chapter
explains the proposed methodology by, first, describing KLR; then discussing why
KLR is not ideal for dealing with country-specific long-term data; and finally
describing the moving extrema approach itself.
2.1 Kaminsky-Lizondo-Reinhart leading indicators
KLR leading indicators approach is an ex ante signaling model developed by
Kaminsky, Lizondo and Reinhart (1998) for currency crisis and has since been used
for banking, debt crisis and asset price bubble identification. It has not been applied to
housing bubbles so far.
A few words about the background of this method: Stock and Watson (1989: 2)
revisited the leading indexes that were developed by the National Bureau of
Economic Research in 1937 for “summarizing and forecasting the state of
macroeconomic activity”. In 1996, Kaminsky and Reinhart proposed several leading
indicators for their currency and banking crisis prediction methodology, which they
said had taken its roots from the above-mentioned Stock and Watson, and Diebold
and Rudebusch (1989) – both papers concerned with turning points forecasting. In
1998, Kaminsky and Reinhart in cooperation with Lizondo revised the 1996 model
and formulated what is generally referred to as the Kaminsky-Lizondo-Reinhart
leading indicators – in this paper (as in many others) this model is abbreviated to
“KLR”. Two domains of KLR can be differentiated: the traditional approach
introduced in 1996 and developed further in 1998 dealt with single indicators. In
(("
2002, a composite indicator approach was presented by Kaminsky. In the following
paragraphs both of these methods are described in some detail.
2.1.1 One-indicator KLR
KLR “monitors the evolution of a number of economic variables and when one of
these variables deviates from its “normal” level beyond a certain “threshold” value,
this is taken as a warning signal about a possible [currency] crisis within a specified
period of time” (Kaminsky et al. 1998: 15). The general shape of such a process could
be described as follows:
(1)
!
Dumt=1 if
!
"Xt# "X
max/min$threshold{ } ,
where
!
"Xt is the change in the indicator at time t, and
!
"Xmax/min#threshold is the chosen
maximum or minimum threshold, depending on the nature of the indicator.19
Dummy
variable issues a signal, when its value is 1.
Several definitions are specified thereafter. First, the meaning of “crisis” should be
established precisely. Second, the signaling horizon should be chosen, indicating the
number of periods prior to the occurrence of a crisis that an indicator should issue a
signal. Third, the thresholds, as the minimum levels of deviation for an indicator to
issue a signal, are chosen so that the noise-to-signal ratio (explained later on) is the
lowest. Thresholds have to be country-specific and are derived “in relation to
percentiles of the distribution of observations of the indicator” (Ibid.: 17). What it
means is that, for example, 10% or 20% of the highest growth rates up to a certain
point in time registered for one or another indicator were chosen as the threshold –
this also made it possible to analyze 16 variables for 20 countries (320 thresholds),
which would be exceedingly time-consuming to be carried out manually.
The next stage of KLR approach is involved with analyzing the results, trying to
answer the question if the signals are effective via table 4 (the matrix is slightly
modified to account for any event, not only a currency crisis).20
A is the number of
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
19 Several indicators were analyzed in levels – for example, interest rates; others both in levels and first differences of logs.
20 This type of analysis could be implemented to any kind of signaling approach, not only KLR. For example, Gerdesmeier et al.
(2009: 23) applied this matrix to the results of a probit model. Lestano and Kuper (2003) used a similar set-up for comparing
various EWS models (probit, logit and several other signaling approaches).
" ()"
periods (dependent on the specifications) in which the indicator issued a correct signal
(predicted the event), B is the number of periods with false alarms (noise), C is the
number of periods where the event occurred without the indicator’s signal and D is
the number of periods where no signal was needed and neither any was issued. It is
clear that an ideal indicator would generate A- and D-type signals only.
Table 4. KLR indicators’ performance matrix
Event No event
Signal issued A B
No signal issued C D
Source: Kaminsky et al. (1998: 18)
There are three main ratios to assess the efficiency of the model. The measure of
correct signals over all signals that could have been issued correctly:
(2)
!
A
A+C .
The ratio of incorrect signals over all signals that could have been issued falsely:
(3)
!
B
B+D .
The ratio of equation (3) to (2) is the adjusted noise-to-signal ratio:
(4)
!
B
B+D÷
A
A+C ,
which is the nucleus of all performance evaluation in KLR: it shows that the model
issues random signals if the ratio is 1, and the lower the outcome is, the better the
model performs (ideally 0).
Berg and Pattillo (1999: 564) noted that the ratio actually measured the proportion of
correct to incorrect signals (B/A), with the (A+C)/(B+D) being the frequency of the
event in tranquil times that could not be optimized using different thresholds for the
indicators. In addition, neither (B/A) nor the adjusted noise-to-signal ratio account for
missed events – for example, the ratio may be quite low, but the value of such an
indicator system is questionable, if only 70% of the events were predicted and the low
(*"
value of the ratio came from the numerous signals issued correctly for the most, but
not all events in the sample. In this thesis, this problem is tackled seriously, setting the
condition of predicting all the events in the sample as a necessary condition.21
Alessi and Detken (2009: 12) stated that the noise-to-signal ratio below 1 could only
be treated as a necessary and not a sufficient condition. The reasoning behind this
notion is as follows – if the model gives an approximately equal number of correct
and false signals, the potential end-users (in their paper – policy-makers) may be
reluctant to take any notice of it at all. They proposed what they called a “loss
function”:
(5)
!
L ="C
A+C+ (1#" )
B
B+D ,
where
!
" was the user’s relative risk aversion between type I (signaling failed to
indicate the event: C/(A+C)), and type II errors (false alarms: B/(B+D)). If the
relative risk aversion is more than 0,5, then the user is prepared to accept more false
signals, so that she won’t miss the correct ones and vice versa. In addition to this, the
gap between the conditional and the unconditional probabilities – the difference
between the ratio of correct to all issued signals and the ratio of all possible good
signals to the total sample (to see if the there were proportionally more correct signals
than events in the sample) – was proposed in KLR:
(6)
!
A
A+ B"
A+C
A+ B+C +D ,
which shows the increasing quality of the indicator the larger it is and must be at least
non-negative.
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
21 Another efficiency measure proposed in KLR was the average lead-time of each particular indicator, which showed the
number of periods prior to the event when the first signal was issued. Also the persistence of a signal was calculated to see what
was the difference between the “normal” and pre-crisis times in the average number of signals per period. These measures are
not fully applicable to the analysis at hand as an important issue here is the frequency of data – months in KLR, annual data in
this thesis.
" (+"
2.1.2 Composite KLR indicator
In the concluding chapter of their 1998 paper, Kaminsky, Lizondo and Reinhart stated
that the natural extension of their analysis would have been the construction of a
composite index for simultaneous signals. In 2000, Kaminsky presented a paper on
this topic, where she suggested four composite indices for currency and banking
crisis. The only composite indicator, that could be potentially interesting for this
thesis, combined single indicators into a system by weighing their respective
importance using the inverse noise-to-signal ratio:
(7)
!
It =Stj
" j
j=1
m
# ,
where
!
Stj equals 1 if the indicator j crosses the critical threshold in period t,
!
" j is the
noise-to-signal ratio of the indicator j (defined as
!
" j=
B
B+D÷
A
A+C from equation
(4)), and m is the number of observations. This composite indicator has several
advantages and disadvantages: the main disadvantage is that the outcome of this
system is not binary anymore and thus, a threshold for the indicator itself is needed to
decide whenever the probability should be treated as a call for an event. Among the
advantages of this system is the fact, that the same non-binary outcomes
(probabilities) allow for the KLR system to be compared with the logit/probit
methodology using the log and the quadratic probability scores – such formulation
then allows for various ex ante, i.e. logit/probit and signaling-based, systems to be
compared statistically (Kaminsky 2000: 16).
2.2 From KLR thresholds to moving extrema
The unfitness of KLR thresholds to issue a sufficient number of signals working with
long-term country-specific data becomes evident when levels and growth rates of
variables, that were found significant, for example, within the probit models discussed
in section 1.2.2 (house price boom/busts and peaks forecasting), are plotted and
compared in the pre-bubble periods. The idea of using thresholds to indicate a signal,
when deviations in the variable’s dynamics are sufficient (growth rates or the values
(!"
in levels exceed a threshold), can only be justified if the history of such deviations
supports the theory.
Figure 4, where the nominal long-term interest rates are presented in levels (covering
the whole sample), allows for such comparison in combination with Figure 5 - the
same indicator’s values prior to all bubble episodes within 3-year windows,
explaining the aforementioned notion.
Figure 4. Nominal long-term interest rate (in levels), period of 1891-2009
Source: Officer (2010), author’s calculations, bubble episodes (in red)
Figure 5. Nominal long-term interest rates (in levels) during the 3-year windows
preceding each bubble episode, 7 episodes
Source: Ibid.
The default assumptions regarding the long-term interest rate would suggest that the
low/declining rate would boost the demand for housing by lowering the cost of
capital, increasing the demand for loans and creating additional liquidity, with which
potential buyers can bid prices up. Figures 4 and 5, though, clearly show that such a
" (#"
single threshold cannot be defined, as there is no clear pattern for the interest rates
being lower during pre-bubble times than during tranquil times.
Even the usage of percentiles, implemented in KLR, would not give sufficient results,
as it is not the case for, at least, the nominal long rate to have lower level of values
with each bubble episode. Expressing the indicator in percentage change does not
improve the picture either (see figures 6, 7).
Figure 6. Nominal long-term interest rate (growth), period of 1891-2009
Source: Ibid.
Figure 7. Nominal long-term interest rate (growth) during the 3-year windows
preceding each bubble episode, 7 episodes
Source: Ibid.
The long rates do display negative change prior to the bubble episodes (figure 7), but
the magnitude of the decline is not sufficient for determining particular thresholds – in
Figure 6 one could notice many periods of much larger declines during tranquil times.
For a similar display in relation to several other variables found significant predicting
house price peaks and boom/busts, respectively in Noord (2006) and Agnello and
Schuknecht (2009), see Appendix 2.
($"
The ongoing global economic crisis that started in 2007 reminded the market
participants of the cyclicality in economic trends, proving once again that what goes
up, has to come down – despite the magnitude and the persistence of the upward
trend. The cyclical nature of long rate dynamics is barely noticeable in 3-year
windows (as in figure 7), but extending the length of these windows to 8 years,
enables a clearer view (see figure 8 – the cycle phases marked with green have a
purely visualization purpose). It becomes evident that prior to an event of
overvaluation, the growth rate of the nominal long-term interest rate declines. The
same variables from Agnello and Schuknecht (2009) and Noord (2006) are
demonstrated in appendix 3 in support of more general upward/downward phases in
explanatory variables prior to bubbles.
Figure 8. Growth of nominal long-term interest rate (in blue) during the 8-year
windows preceding each of the 7 bubble episodes (in red), and cycle phases (in green)
Source: Officer (2010), author’s calculations
Such cyclicality is practically impossible to include in a long-term model using
thresholds – even if the latter are expressed in percentiles: different cycle phases have
different magnitudes and the large growth rates during preceding boom phases distort
the actual size of the previously chosen percentiles, pushing them too high up. The
notion depicted in figure 8 gave me the impulse to put the KLR threshold concept
aside and consider the local maxima/minima in the cycle phases of various lengths
instead. The method developed this way is referred to as the Moving Extrema.22
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
22 I wish to acknowledge, that the methodology proposed here has been developed independently from the more advanced
moving-maximum models, described in Hall et al. (2002). The derivation of the methodology at hand is extremely simple and
intuitive and any similarities with the named study are either natural or coincidental.
" (%"
2.3 Moving Extrema approach
The moving extrema (ME) approach is an early warning system that, similarly to
KLR, follows the dynamics of several variables that were proven to lead certain
events - housing bubbles. Unlike KLR, the moving extrema approach does not follow
such variables crossing predetermined thresholds, but seeks for certain moving
extremum cycle phases observable prior to bubbles. A moving extremum cycle phase
is a number of periods, where the value (of the variable under observation) in the last
period achieves the highest or the lowest value compared to other values inside the
phase. It is important to note, that inside the local extremum phases, values are not
necessarily moving incessantly in the same direction. A theoretical example of a cycle
phase of incessant growth and a moving maxima cycle phase is presented in figure 9
(two cycle phases are independent).
Figure 9. Incessant growth cycle phase (in red) and a moving maxima cycle phase (in
blue); arrows denote the length of moving maxima cycle phases
What figure 9 shows, is an approach somewhat similar to smoothing of data series. It
would have been perfect if variables were to display continuous-change cycle phases,
which could be associated with certain events, but the reality is that there is a
substantial amount of extraneous deviations in the dynamics of variables. For this
reason, a condition that variables have to grow continuously is replaced with moving
extremum cycle phases: in figure 9 the arrow “5” denotes the maximum within the 5-
period cycle phase; the arrow “9” shows the 9-period maximum cycle phase, i.e. the
maximum value during the last 9 periods. The idea of this method is to find similar
ME cycle phases and associate them with the occurrence of bubbles.
)'"
Herring and Wachter (2002: 7) formulated the underlying postulate regarding the
ability to estimate the probability of an upcoming event23
based on historical data - if
the underlying causal structure of the economic system changes each time an event
occurs, previous events cannot be taken as evidence for new estimations; only if the
structure is stable, probabilities of an event can be estimated with a known
confidence. This is the first assumption for constructing an early warning system: the
causal structure of the underlying economic forces is assumed to be stable through
time.
Developing an early warning system constitutes a tradeoff between the amount of
false signals and episodes predicted. Under the KLR methodology in the literature
review section, the loss function, defined by Alessi and Detken (see equation (5)),
looked into this problem by including the user’s relative risk aversion factor to
differentiate between users that are more neutral towards Type I errors (the indicator
fails to signal the upcoming event) than Type II (false signal). Homebuyers, the
primary intended users of this methodology, would generally try to avoid Type I
errors (missed events) for their wrong decisions to purchase real estate during a
bubble may lead to taking large obligations and the risk of losing a substantial part of
their equity. As in any optimization exercise, it is not possible to optimize both sides
of the problem – one should be fixed and the other minimized or maximized.
Following the homebuyer logic, the condition to be enforced at all times is the
requirement that for any separate or composite indicator to be considered within this
analysis, it should be able to predict all the in-sample bubbles (Type I errors must
equal 0). Only then we can work on minimizing the number of false alarms (Type II
errors).
Below, all stages of the moving extrema methodology are described in some detail:
the process of choosing indicators one by one based on their ability to lead bubbles is
presented in section 2.3.1; the procedure of combining separate indicators into
composite indicators is discussed in section 2.3.2; and the procedures for identifying
oncoming bubbles using the composite indicators developed in the preceding section
are described in section 2.3.3.
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
23 In their formulation, an event was a shock.
" )&"
2.3.1 In-sample application: one-indicator moving extrema
To present this methodology as clearly as possible, keeping in mind the targeted final
users of this approach, the required procedures are presented as a user’s manual
flowchart with concrete steps (see figure 10) and comments to these steps.
Figure 10. A flow diagram explaining the implementation procedure of the one-
indicator stage of the moving extrema approach
Comments to Step 1. The number of countries with the amount of sufficiently long-
term data regarding housing prices and explanatory economic variables is limited.
Some of such countries are the Netherlands, Norway, the United Kingdom and the
United States. Housing bubbles can be dated ex post using methods from chapter 1.3.
Comments to Step 2. The more data sets of explanatory variables there are, the higher
the probability of finding variables able to predict all in-sample events with low
number of false alarms. Therefore, different variations and ratios of the same
variables are considered as separate variables: for example, GDP per capita and GDP
per working age population denoted both in levels and as growth rates are treated as
four separate variables.
)("
Comments to Step 3. The idea of the moving extremum cycle phases was described
above. The lengths of these phases (n) are 2, 3, 4, 5, 6, 7, 8 years, all tested
simultaneously and compared in search of the best-performing phase lengths. A
theoretical example of determining moving extremum cycle phases is presented in
table 5. Hypothetical values of a hypothetical variable are taken for a period of seven
years. The moving extremum cycle phase lengths vary from 2 to 7 years. First of all,
as the values in this short series are alternating, there are both moving minimum and
maximum cycles of 2-year length. There is a 3-year moving minimum cycle phase in
1908. The main purpose of this example is to show that the value of a variable in a
certain year can be a moving extremum cycle phase of various lengths – see how a
variable’s value is a 2-, 3- and 4-year moving maxima phase in 1909. The year in
which we start to count makes all the difference.
Table 5. An example of determining moving extremum cycle phases
Year 1906 1907 1908 1909 1910 1911 1912
Values 5 6 2 7 3 9 1
max2 min2 max2 min2 max2 min2
min3 max3 max3 min3
max4 max4 min4
max5 min5
max6 min6
min7
Comments to Step 4. The signaling horizon indicates the number of periods (m),
during which a bubble is expected after an indicator has issued a signal. Three
signaling horizons are simultaneously tested and compared: 1-, 2- and 3-year
horizons. A 3-year signaling horizon means that if an indicator has issued a signal in
1995, a high probability of a bubble exists in 1996, 1997 and 1998.
Comments to Step 5. It is important to develop the notion suggested under the
comment to Steps 2 and 3. If a number of combinations of moving extremum cycle
phases and signaling horizons of one variable were able to call all the in-sample
events, all of those are considered separately. For example, a variable might have
been able to call all the bubbles via moving minimum cycle phases of 4,5 and 6 years
with signaling horizons of 2 and 3 years. In this case, all 6 combinations of the same
variable make it to the next round. In addition, the moving extremum cycle phase
cannot vary within one successful variable. It means that only cycle phases with the
" ))"
same length, direction (maximum or minimum) and signaling horizon that have called
all the bubbles in the sample are to be seen as successful. For example, each time the
moving maximum of 4-year phase of a variable had been observed and a bubble
within 2-year signaling horizon had occurred - this makes this variable a candidate for
the next round.
Comments to Step 7. Having obtained the noise-to-signal ratios for all of the variables
(keeping in mind various cycle phase lengths and signaling horizons) choose one
best-performing combination using the lowest noise-to-signal ratio for each variable.
In case of identical ratios consult other evaluation procedures: correct to all signals
issued, the average number of wrong signals issued per bubble, and the ratios from
KLR (correct signals to all possible correct signals - equation (2); wrong signals to all
possible wrong signals - equation (3); and the conditional/unconditional probability
gap - equation (6)).24
The end result of the one-indicator stage should emerge as one or several tables
(dependent on the number of signaling horizons) with different variables listed by the
ascending noise-to-signal ratio. The outcome of such analysis, described later on in
this paper, can be seen in appendices 5 and 6.
2.3.2 In-sample application: composite indicator
After the results for all of the variables are obtained from the one-indicator stage,
indicators that succeeded in predicting all the events in the sample with noise-to-
signal ratios below 1 are extracted for analysis at the composite level.
The reasoning behind the composite signal is this: different indicators may display
their local minimum and maximum values influenced by various exogenous factors –
it is when several indicators achieve their local maxima/minima at the same time in a
pattern supported by occurrence of bubble in the past immediately after such co-
movements, it is not unreasonable to expect a bubble in the near future. The final
target in such a case would be to “clean” all the false signals out, lowering the noise-
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
24 See appendix 4 for the summary tables of the variable “Nominal long-term interest rate” in levels – this is a suggestion of how
to organize such an analysis in practice.
)*"
to-signal ratio, though keeping in mind the condition that all the bubbles in the sample
have to be predicted by the composite indicator under consideration.
Constructing such an aggregate system is intuitive: if the one-indicator approach is
able to predict all the preceding events with noise-to-signal ratio lower than 1 (1
would mean random signals), then such single indicators can be connected into
systems by signaling horizons and only those signals counted that had been issued by
all indicators. Indicators are included into the system step by step in the order of the
ascending noise-to-signal ratios. Once again, these procedures are presented as a
flowchart in figure 11.
Figure 11. A flow diagram explaining the development procedure of the composite
indicator stage of the moving extrema approach
At first, the first two variables with the lowest noise-to-signal ratios are combined: if
the resulting composite indicator is still able to predict all the in-sample events with a
synergy in terms of a lower noise-to-signal ratio, then the pair is fixed and the next
indicator is included to try for a 3-indicator system. If the third (or any other
consecutive) variable fails to raise the quality of the composite system in terms of
lowering the noise-to-value ratio, it is ignored and the next one on the list is tested.
The limit for the number of indicators included in the composite system is 4, if the
noise-to-signal of 0 has not been reached first. The reason for the maximum number
" )+"
of variables being fixed to 4 is the fact that the marginal decrease in the noise-to-
signal ratio becomes less than the danger of losing good signals and missing bubbles
somewhere after the fourth indicator.25
The evaluation of these composite indicators
is carried out using the same ratios from the one-indicator stage (see comments to
Step 7 in the previous section). These were the actions to be undertaken to develop
composite indicators. The next section describes the process of implementing these
composite indicators to real-life bubble monitoring.
2.3.3 Out-of-sample application
The purpose of developing an early warning system is to use it in the “real time” to
identify specific upcoming events ex ante. Figure 12 describes the specific actions to
use the composite indicators from the moving extrema approach.
Figure 12. A flowchart explaining the implementation procedure of the composite
indicators to “real-time” data
Comments to Step 1. A rather complicated issue to be assessed before implementation
of the composite indicators out of sample is determining if the bursting stage of the
previous bubble is already over. No comprehensive cross-country approach is
suggested in this paper, but the following remark seems to be proper for the US house
prices: during a period of 1890-2000, each bursting bubble had at least two years of
non-negative price change after the deflation of prices. Similar simple analysis
regarding other countries may be appropriate.
Comments to Step 3. For example, if a composite indicator with a 2-year signaling
horizon contains three single indicators – the nominal mortgage rate (with 4-year
moving minimum cycle phase), the growth rate of housing starts (with 3-year moving
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
25 Data series with few missing values that do not coincide with bubbles can still be included into the composite indicator – the
signals issued by all other variables are analyzed in such cases.
)!"
maximum cycle phase) and the M0 money aggregate growth rate (with 5-year moving
maximum cycle phase), a signal will be issued next time when the nominal mortgage
rate will be at its lowest within a moving time window of 4 years, the housing starts’
growth rate has been the highest within a time window of 3 years and the M0 growth
rate has been the highest within a time window of 5 years. Such a signal means that
during the following 2 years there would be a high probability of overvaluation in
house prices.
Comments to Step 4. If there is more than one composite indicator developed within
the in-sample stage, the signals of all of these composite indicators should be
observed in combination and the conclusions made depending on the in-sample
performance of each composite indicator.
" )#"
3. EMPIRICAL ANALYSIS
3.1 Data and variables
The empirical analysis in its entirety is based on one country – the United States of
America - for the period of 1890-2009. The main reason for this was the author’s
desire and interest to develop an early warning system based on long-term trends of a
single country, rather than merging data from various countries into a panel26
, and the
US is the country with the largest amount of publicly available backward looking
statistics in English. There were doubts about the usage of such data as historical
sources are generally more prone to error, not all time series are available in the
desired length, and many fragments of similar variables are not exactly compatible.
On the other hand, pooling countries together would result in an implicit assumption
that the same economic forces accompany housing prices equally and that might lead
to wrong or unsatisfactory results.27
In addition, the usage of annual frequency makes
the necessity to seasonally adjust data redundant, while keeping in place important
underlying trends.
3.1.1 Variables
The choice of indicators/variables to be tested within this thesis was based on table 3,
limited by the availability (or the quality) of data series with sufficient length. There
are two blocks of data analyzed within this thesis categorized by the length of the
series: 1890-2007 and 1930-2007.28
The first block is further divided by three themes:
macroeconomic, housing sector and other variables; the second has an additional set
of affordability variables (see tables 6 and 7).29
Forty different variables were
collected, 24 of which with the sample length of 1890-2009 and 16 with the sample
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
26 Altough
Fuertes and Kalotychou (2006) expressed their support for the panel analysis and argued that it was much more
efficient in terms of forecast performance.
27 Berg et al. (2008), Bunda and Ca’Zorzi (2009), Calza et al. (2009) among others supported this view.
28 Limiting samples to 2007 is dictated by methodological issues (the bubble dating procedure in section 1.3. were based on full
sample length – i.e. 1890-2009).
29 Demographic variables were listed under the macroeconomic theme.
)$"
length of 1930-2009. Due to the signaling nature of the model developed and tested in
this paper, only those variables are considered in levels that may display sufficient
cyclical dynamics expressed in levels.
Table 6. List of variables with data available for 1890-2007 and the number of time
series that entered the analysis
Macroeconomic Levels Growth No of series
Real consumption per capita + 1
Nominal exchange rate: GBPUSD + + 2
Employed persons + 1
GDP deflator ratio + 1
Real GDP + 1
Real GDP per capita + 1
Real GDP per person in labor force, per employed person + 2
Interest rate: nominal and real: short, long, term spread + + 12
Labor force + 1
Real money supply: M0, M2 + 2
M2 multiplier (M2/M0 ratio) + + 2
Real output gap + + 2
P/E ratio: S&P 500 + + 2
Population + 1
Labor force to population + + 2
Real productivity: nonfarm business output per hour + 1
Stock market index: S&P 500 real price + 1
Unemployment rate + + 2
Inflation rate + 1
TOTAL Macroeconomic 38
Housing sector
Real construction cost + 1
Housing starts + 1
Mortgage rate: nominal, real, gap + + 8
Real residential investment + 1
Share of real residential investment in GDP + + 2
Real residential nonfarm wealth, per capita ratio + 2
Real residential nonfarm wealth to labor force + 1
Real residential nonfarm wealth per employed person + 1
Real residential nonfarm wealth to M0; M2 + + 4
TOTAL Housing Sector 21
Other
Gap between real house price and its 5-year MA + + 2
Lagged real house price (1,2,3-year lags) + 3
Rapid real house price growth (>2%) + 1
2;3- year moving average of growth in real house prices + 2
Real price of gold ounce + 1
House price/gold ounce price (levels and growth) + + 2
TOTAL Other 11
TOTAL 70
* - Data in levels start from 1890; growth rate data start from 1891
" )%"
Table 7. List of variables with data available for 1930-2007 and the number of time
series that entered the analysis
Macroeconomic Levels Growth
No of
Series
Real federal budget balance + 1
Federal budget balance to GDP + 1
Real current account + + 2
Current account to GDP + + 2
Real government expenditure + 1
Government expenditure to GDP + 1
Real government net saving + + 2
Government net saving to GDP + 1
Real government revenue + 1
Government revenue to GDP + + 2
Real personal and disposable income + 2
Real personal and disposable income per capita + 2
Real personal and disposable income to labor force + 2
Real personal and disposable income per employed person + 2
Personal and disposable income to GDP + + 4
Real personal saving + 1
Personal saving to GDP + + 2
Real personal saving per capita + 1
Real personal saving to labor force + 1
Real personal saving per employed person + 1
Real gross private domestic investment + 1
Gross private domestic investment to GDP + + 2
Residential investment to gross private domestic investment + + 2
Real M1 + 1
M1/M0, M2/M1 + + 4
TOTAL Macroeconomic 42
Housing sector
Real rental price of tenant occupied nonfarm housing + 1
Real imputed rental price (owner-occupied) nonfarm housing + 1
Real housing and utilities expenditures growth + 1
Housing and utility expenditures % from disposable income + + 2
Housing and utility expenditures % from consumption + + 2
Real nonfarm mortgage debt + 1
Nonfarm mortgage debt to GDP + + 2
Real nonfarm residential mortgage debt + 1
Nonfarm residential mortgage debt to GDP + + 2
Real mortgage interest cost + 1
TOTAL Housing sector 14
Affordability ratios
Price-to-income + + 2
Price-to-rent + + 2
Total mortgage interest cost to total disposable income + + 2
TOTAL Affordability ratios 6
Other
Gap between actual and 5-year price-to-income, price-to-rent + + 4
Gap between current saving and 5-year MA + + 2
Real farm value (land + buildings) per acre + 1
TOTAL Other 7
TOTAL 71
* - Data in levels start from 1929; growth rate data start from 1930
Where applicable, data is analyzed both in levels and per annum growth rates. The
following variables, listed in table 3 and likewise interesting within this analysis, were
omitted due to the lack of data: after-tax interest rate, credit to the private sector,
housing stock, working age population, and the user cost of housing. Apart from
these, all the variables that were touched upon in table 3 were presented in the
*'"
analysis with some additions. The collected data consist of series extracted from
original sources and those derived from the latter. The description of such data
transformation follows next.
1. The GDP deflator, which is the broader measure of inflation, is calculated as the
ratio of nominal to real GDP.
2. The size of the labor force was calculated using the unemployment rate and the
total persons employed data:
(8)
!
LF = E +uE
1"u ,
where LF is the size of the labor force, u is the unemployment rate, E is the number of
employed persons.
3. The term spread and the mortgage rate spread are calculated as the difference
between respectively the long-term and the short-term interest rate; and the mortgage
rate and the short-term interest rate (separately real and nominal).
Figure 13. Real GDP index (1980=100) and the smoothed trend using HP filter with
!=1600, period of 1890-2009
Source: 1890-1928 – Grebler et al. (1956) Appendix B; 1929-2009 – NIPA: Table 1.1.5; author’s
calculations
4. The real output gap was calculated by smoothing the real GDP series with the
Hodrick-Prescott filter (!=1600) and then the gap between the actual and the
" *&"
smoothed (potential) GDP was divided by the smoothed value (the results are
displayed in figure 3).30
5. A more controversial variable (in terms of reliability and applicability) is the total
real mortgage interest cost and its ratio to the total disposable income. As respective
data could not be obtained for the required period, this variable was calculated as the
product of the mortgage rate and the total amount of residential nonfarm mortgages
outstanding, although it is known that adjustable rate mortgages are not the
predominant product in the US housing market.31
Thus, the conclusions arising from
the possible usage of this variable should be treated cautiously.
3.2 In-sample analysis and results
To assess the fair value of the developed model, the recursive testing could be
implemented for the whole sample period, reproducing the analysis that could have
been performed after the first bubble (in this sample) of 1894-1895, moving further to
predict each following event. On the other hand, 141 data sets available for analysis
make it more reasonable to mimic only the prediction process of the last episode of a
housing bubble that was measured to have started in 2004, trying to see if this
methodology could have helped to predict the bubble in advance of 1-3 years.
3.2.1 1890-1990 (long sample)
One-indicator stage
For the period of 1890-1990 6 bubbles were identified ex post (see table 2 or figure
3). Each time a series from table 6 enters the analysis so that the predictive ability of
those variables can be tested on the sample of the first 6 bubbles in search of existing
cyclical dynamics. If the tests return satisfactory results, meaning that all 6 bubbles
are predicted with the noise-to-signal ratio being lower than 1, a variable can be called
successful, allowing it to qualify for the next round. No assumptions are made about
the direction of extrema (minima or maxima) that would predict all in-sample events
""""""""""""""""""""""""""""""""""""""""""""""""""""""""
30 St-Amant and Norden (1997) concluded that the usage of HP filtering is not always a reliable method to measure the output
gap; nevertheless, within this thesis the output gap is merely a variable among others and an in-depth analysis of the latter using
more sophisticated methodologies would be outside the scope of this paper.
31 Girouard (2006: 28) stated that adjustable rate mortgages constituted only 33% of all mortgages in the US by 2005.
*("
with little noise, as the transition mechanisms for the most of the variables could be
described in both ways. For example, declining interest rate (maximum-type phase)
could be an indication of possible overheating in the housing market, but at the same
time increasing values of this variable could indicate the proximity to the peak of the
housing bubble (minimum-type phase). The summary of the five best-performing
indicators is presented in tables 8 and 9 (see full results in appendix 5).
Table 8. The best five indicators that predicted all 6 bubbles during 1890-1990 with
signal-to-noise ratios lower than 1; 2-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
3-year lagged real
house price G max 3 0.49 0.26 4.67 0.11
2
Real house price
and 5-year MA gap L max 2 0.58 0.23 6.00 0.08
3
Res. n-f wealth to
M0 G max 2 0.59 0.23 6.17 0.08
4 Real mortgage rate L max 3 0.60 0.23 5.67 0.08
5
Real res. n-f wealth
to labor force G max 2 0.67 0.21 6.33 0.06
Comment: complete results in appendix 5.1
Table 9. The best five indicators that predicted all 6 bubbles during 1890-1990 with
signal-to-noise ratios lower than 1; 3-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Real construction
cost G max 4 0.50 0.35 2.50 0.14
2
Nominal long term
rate G min 5 0.53 0.33 2.67 0.12
3
2-year lagged real
house price G max 3 0.55 0.32 4.17 0.11
4 Housing starts G max 3 0.56 0.32 3.50 0.11
5
Residential
investment to GDP G max 3 0.56 0.32 3.50 0.11
Comment: complete results in appendix 5.2
The initial results contained two variables that displayed their best results within 1-
year signaling horizon framework: real and nominal mortgage rate analyzed in levels.
These were merged with the next better-performing horizon – 2-year signaling
window category. Note how with the lengthening signaling horizon increases the
length of cycle phases, giving more space to the latter to be revealed, ignoring the
random exogenous effects. Out of 70 data series, 53 managed to predict all the events
" *)"
in the sample with noise-to-ratios below 1. From these, 8 achieved noise-to-signal
ratios below 0,6 and 19 indicators below 0,7. Each fourth signal issued by the 3-year
lagged real house price is good, and there are approximately 5 false alarms per called
bubble. The real construction cost performs better with each third signal appropriate
and only 2-3 false alarms per called bubble. These results may seem somewhat not
too encouraging at first, but the problem of a large amount of false signals will be
solved within the composite indicator stage.
Composite indicators
The composite indicators are built keeping in mind the respective signaling horizon (2
or 3 years in the case of the long sample), where the single indicators from appendix 5
are added step by step. The results of such composition are presented in tables 10 and
12. The best performing (in terms of noise-to-signal ratios) single-indicators that
entered the 2-year signaling horizon composite indicator were: 1) gap between the
real house price and its 5-year moving average in levels, 2) real residential nonfarm
wealth to labor force expressed in growth rates; 3) real residential nonfarm wealth per
employed person expressed in growth rates; and 4) real price of gold ounce expressed
in growth rates.
Table 10. Composite indicator that predicted all 6 bubbles during 1890-1990; 2-year
signaling horizon
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals/
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
2 indicators 100% 0.39 0.31 3.33 0.60 0.16 0.24
3 indicators 100% 0.33 0.35 2.83 0.60 0.20 0.20
4 indicators 100% 0.24 0.43 2.00 0.60 0.28 0.14
Indicators in order of inclusion: gap between the real house price and its 5-year moving
average (in levels); real residential nonfarm wealth to labor force (growth); real residential
nonfarm wealth per employed person (growth); real price of gold ounce (growth)
Comparing this composition with table 8, one would notice that several single
indicators that scored lower noise-to-signal ratios than some of those that entered the
composite indicator were excluded from the composite. The reason for that is their
inability to cooperate with other indicators, either failing to predict in-sample events
or under-achieving in terms of reduced level of noise.
**"
The 2-year horizon composite model does not perform ideally in-sample: noise-to-
signal ratio does drop to 0,24, but there are still too many false alarms – 2 per called
bubble. This can be viewed in the following way: 15% of the tranquil times false
alarms arrive, which means that during 1890-1990 (101 years) there were wrong
signals 15 times. The fact that there are quite many signals issued is seen also via the
high number of good to all possible good signals, which is 0,6, good on the one hand,
but also potentially dangerous, as it implies higher proportion of random signals.
Looking at each bubble episode separately gives some insights into the consistency of
the composite indicator’s performance (see table 11). The performance has been quite
homogenous and most of the bubbles had 1-2 false alarms per each bubble episode.
The noise-to-signal ratio has also persisted at the same level, with a large deviation
during the first bubble period mainly due to the length of that period (6 years). The
fact that the period during the 1948-1979 had 5 wrong signals raises some doubt,
although the following prediction of the bubble in the end of the 80s was overall
successful.
Table 11. Composite indicator’s performance over the period of 1890-1990; 2-year
signaling horizon; details for 6 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals/
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 6 0.24 0.43 2.00 0.60 0.28 0.14
1890-1895 1 1.50 0.67 1.00 0.67 -0.08 1.00
1896-1907 1 0.20 0.50 1.00 0.50 0.33 0.10
1908-1916 1 0.29 0.50 1.00 0.50 0.28 0.14
1917-1947 1 0.07 0.60 2.00 1.00 0.50 0.07
1948-1979 1 0.33 0.17 5.00 0.50 0.10 0.17
1980-1990 1 0.75 0.33 2.00 0.33 0.06 0.25
Indicators: see footer of table 10
The 3-year signaling horizon composite indicator consists of the following indicators:
1) 2-years lagged house price expressed in growth rates; 2) ratio of residential
investment to GDP expressed in growth rates of the ratio; 3) real residential growth
expressed in growth rates; and 4) nominal exchange rate GBPUSD expressed in
growth rates (see table 12). The results clearly improve with the 3-year signaling
horizon model, where the noise-to-signal ratio declines to the level of 0,13 and there
is a false alarm only per every second bubble.
" *+"
Table 12. Composite indicator that predicted all 6 bubbles during 1890-1990; 3-year
signaling horizon
Bubbles
called Noise-to-signal ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
2 indicators 100% 0.30 0.47 1.33 0.33 0.26 0.10
3 indicators 100% 0.27 0.50 1.17 0.33 0.29 0.09
4 indicators 100% 0.13 0.67 0.50 0.29 0.46 0.04
Indicators in order of inclusion: 2-years lagged house price (growth); residential investment
to GDP (growth); real residential investment (growth); nominal exchange rate GBPUSD
(growth)
Table 13. Composite indicator’s performance over the period of 1890-1990; 3-year
signaling horizon; details for 6 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 6 0.13 0.67 0.50 0.29 0.46 0.04
1890-1895 1 N/A 1.00 0.00 0.25 0.00 N/A
1896-1907 1 0.00 1.00 0.00 0.33 0.75 0.00
1908-1916 1 0.50 0.50 1.00 0.33 0.17 0.17
1917-1947 1 0.00 1.00 0.00 0.25 0.87 0.00
1948-1979 1 0.21 0.33 2.00 0.33 0.24 0.07
1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00
Indicators: see footer of table 12
Table 13 indicates a relatively consistent performance with no false signals in 4 out of
6 bubbles. In addition, the last two bubble episodes were forecasted with low noise-
to-signal ratio. All the performance measures and the length of the signaling window
indicate that this is the reliable model from the long-sample group.
3.2.2 1930-1990 (short sample)
A similar analysis to the one described in the previous section was undertaken for the
short sample (period of 1930-1990). This time there were enough single-indicators
performing well within 1-year signaling horizon to form a separate group. The results
for the first 5 successful indicators with 1-, 2- and 3-year signaling horizons are
presented in tables 14,15,16 (for complete results see appendix 6).
*!"
Table 14. The best five indicators that predicted all 3 bubbles during 1930-1990; 1-
year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Real government net
saving L max 4 0.25 0.27 3.67 0.18
2
Government net saving to
GDP L max 4 0.27 0.25 4.00 0.17
3
Government expenditure to
GDP G min 4 0.31 0.22 4.67 0.14
4 Personal income to GDP G max 3 0.36 0.20 6.67 0.12
5
Mortgage interest to disp.
Income G max 4 0.38 0.19 7.00 0.11
Comment: complete results in appendix 6.1
Table 15. The best five indicators that predicted all 3 bubbles during 1930-1990; 2-
year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Price-to-income and 5-year
MA gap L max 7 0.15 0.50 2.33 0.37
2
Price-to-rent and 5-year MA
gap L max 5 0.26 0.36 4.67 0.23
3 Price-to-income L max 3 0.28 0.35 3.67 0.22
4
Federal budget balance to
GDP L max 4 0.33 0.31 3.67 0.18
5 Real federal budget balance L max 3 0.35 0.30 4.67 0.17
Comment: complete results in appendix 6.2
Table 16. The best five indicators that predicted all 3 bubbles during 1930-1990; 3-
year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1 Real farm value per acre G max 8 0.18 0.56 1.33 0.38
2 Real government expenditure G min 8 0.22 0.50 1.33 0.32
3 Price-to-rent L max 8 0.25 0.47 3.00 0.29
4
Saving-to-GDP and 5-year
MA gap L min 7 0.26 0.46 2.33 0.28
5 Price-to-income G max 7 0.26 0.45 2.00 0.27
Comment: complete results in appendix 6.3
For the shorter sample, 66 out of 71 time series were able to predict all 3 bubbles, of
which 11 achieved noise-to-signal ratio levels below 0,3. Especially low ratios were
registered for the variables: gap between price-to-income ratio and its 5-year moving
" *#"
average in levels (0,15) and real farm value per acre (0,18) with 2- and 3-year
signaling horizons respectively.
It is crucial to underline the importance of the smaller sample on the reliability of the
results: when there is a decline in sample size in regression models, it results in a
smaller number of degrees of freedom, which then pushes the critical values for the
test statistics up, requiring smaller standard errors of coefficients for the latter to be
statistically significant at the same confidence level. As the moving extrema approach
does not have statistical testing behind it, it is difficult to implement a precise
requirement to account for the shortened sample, although there is one condition that
can be enforced to make the results more viable: to lower the acceptable threshold of
the noise-to-signal ratio - in appendix 6 this is expressed as highlighted areas, where
the indicators that scored noise-to-signal ratios above 0,5 are marked with grey. These
indicators should not be considered as candidates for the composite indicators.
Composite indicators
The larger number of successful indicators with 3 different signaling horizons allows
to built 3 composite indicators on the same principles as described above (see tables
17,19,21).
The 1-year signaling horizon model consists of the following indicators: 1) real
government net savings in levels; 2) government net saving to GDP in levels; 3)
government expenditure to GDP expressed in growth rates; 4) personal income to
GDP expressed in growth rates (see table 17).
Table 17. Composite indicator that predicted all 3 bubbles during 1930-1990; 1-year
signaling horizon
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals /
Tranquil
times
2 indicators 100% 0.25 0.27 3.67 0.80 0.18 0.2
3 indicators 100% 0.12 0.43 1.33 0.6 0.35 0.07
4 indicators 100% 0.03 0.75 0.33 0.60 0.67 0.02
Indicators in order of inclusion: real government net savings (in levels); government net
saving to GDP (in levels); government expenditure to GDP (growth); personal income to
GDP (growth)
*$"
Table 18. Composite indicator’s performance over the period of 1930-1990; 1-year
signaling horizon; details for 3 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals /
Tranquil
times
TOTAL
PERIOD 3 0.03 0.75 0.33 0.60 0.67 0.02
1930-1947 1 0.00 1.00 0.00 0.50 0.88 0.00
1948-1979 1 0.00 1.00 0.00 1.00 0.97 0.00
1980-1990 1 0.22 0.50 1.00 0.50 0.32 0.11
Indicators: see footer of table 17
It is the riskiest indicator of those analyzed in this paper, as it enforces the strictest
condition: the issued signal indicates a bubble within the next year, not during two or
three years. Taking this into account, the model performs very well in-sample: with
the noise-to-signal ratio of 0,03; 3 signals out of 4 being correct, and with only one
wrong signal per 3 bubbles. Also the consistency of predictions is quite good: all
bubbles called with noise-to-signal ratios close to 0 (see table 18). Despite good in-
sample performance, the riskiness of this indicator (due to the signaling horizon and
the sample length) should definitely be treated cautiously while relying on out-of-
sample forecasts.
Table 19. Composite indicator that predicted all 3 bubbles during 1930-1990; 2-year
signaling horizon
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signal /
Tranquil
times
2 indicators 100% 0.11 0.58 1.67 0.88 0.45 0.09
3 indicators 100% 0.09 0.63 1.00 0.63 0.49 0.06
4 indicators 100% 0.05 0.75 0.33 0.38 0.62 0.02
Indicators in order of inclusion: gap between the current price-to-income ratio and its 5-
year moving average (in levels); gap between the current price-to-rent ratio and its 5-year MA
(in levels); price-to-income ratio (in levels); gap between the current price-to-income and its
5-year MA (growth)
The composite indicator based on the 2-year signaling horizon was composed of 1)
the gap between the current price-to-income ratio and its 5-year moving average in
levels; 2) the gap between the current price-to-rent ratio and its 5-year MA in levels;
3) price-to-income ratio in levels; 4) gap between the current price-to-income and its
5-year MA expressed in growth rates (see table 19). A noise-to-ratio level of 0,05 and
only 2% of false signals during tranquil times makes the indicator rather attractive and
" *%"
dependable. The consistency of predictions shown in table 19 is sufficient: two last
bubbles were called with 0 noise-to-signal ratios. It is very similar to the previous
specification in terms of performance, but the 2-year signaling window makes it less
risky.
Table 20. Composite indicator’s performance over the period of 1930-1990; 2-year
signaling horizon; details for 3 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 3 0.05 0.75 0.33 0.38 0.62 0.02
1930-1947 1 0.21 0.50 1.00 0.33 0.32 0.07
1948-1979 1 0.00 1.00 0.00 0.50 0.94 0.00
1980-1990 1 0.00 1.00 0.00 0.33 0.73 0.00
Indicators: see footer of table 19
The 3-year signaling horizon composite indicator displayed the best results within the
in-sample analysis with the following two variables: 1) real farm value (land +
improvements) per acre expressed in growth rates and 2) the price-to-rent ratio in
levels (see tables 21 and 22).
Table 21. Composite indicator that predicted all 3 bubbles during 1930-1990; 3-year
signaling horizon
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
2 indicators 100% 0.00 1.00 0.00 0.27 0.82 0.00
Indicators in order of inclusion: real farm value (land + improvements) per acre (growth);
price-to-rent ratio (in levels)
A noise-to-signal of 0,00 means no false alarms. At the same time only 27% of all
possible good signals were issued. It may be due to the cycle phase length of the
variables, 8 years, filtering out the longest phases in the development of these
variables. This is the second most reliable indicator, after the long-sample 3-year
signaling horizon composite indicator and should be considered in a combination with
the latter for more reliable forecasting.
+'"
Table 22. Composite indicator’s performance over the period 1930-1990; 3-year
signaling horizon; details for 3 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 3 0.00 1.00 0.00 0.27 0.82 0.00
1930-1947 1 0.00 1.00 0.00 0.25 0.76 0.00
1948-1979 1 0.00 1.00 0.00 0.33 0.91 0.00
1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00
Indicators: see footer of table 21
3.3 Out-of-sample analysis and results
The in-sample results are sufficient, but the only way to appraise the predictive
quality of a model is to test (or carry out a simulation simulation of) it in the out-of-
sample mode. The most reliable composite indicators based on in-sample
performance and the intrinsic nature of the signaling horizon were the two 3-year
signaling window models. The importance of the longer signaling horizon in terms of
reliability comes from simple probabilities: if there is a period of 10 years which
contains one event, then an indicator with 3-year signaling horizon is approximately 3
times more likely to randomly predict the event than the 1-year signaling horizon
model.
Below, both long sample models with 2- and 3-year signaling horizons and the three
short sample models with 1-,2- and 3-year signaling horizon are tested, seeking to
find if they were able to predict the bubble that, according to the chosen ex post
identification methodology, had developed in 2004 and continued till 2007.
3.3.1 1991-2007 (long sample)
With the 2-year signaling horizon indicator the expectations of possible mediocre
performance came true (see table 23). In in-sample mode, there were two false alarms
per bubble. The ratio has increased to 2.3 for the complete sample with all seven
bubbles. This was due to the fact that during out-of-sample testing the indicator issued
five signals, only one of which was correct.
" +&"
Table 23. Composite indicator’s performance over the total sample period of 1890-
2007; 2-year signaling horizon; details for 7 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 7 0.33 0.38 2.29 0.50 0.21 0.17
1890-1895 1 1.50 0.67 1.00 0.67 -0.08 1.00
1896-1907 1 0.20 0.50 1.00 0.50 0.33 0.10
1908-1916 1 0.29 0.50 1.00 0.50 0.28 0.14
1917-1947 1 0.07 0.60 2.00 1.00 0.50 0.07
1948-1979 1 0.33 0.17 5.00 0.50 0.10 0.17
1980-1990 1 0.75 0.33 2.00 0.33 0.06 0.25
1991-2007 1 1.67 0.20 4.00 0.20 -0.09 0.33
Indicators in order of inclusion: gap between the real house price and its 5-year moving
average (in levels); real residential nonfarm wealth to labor force (growth); real residential
nonfarm wealth per employed person (growth); real price of gold ounce (growth)
In other words, the 2004-2007 bubble was called, but with way too many false alarms
– 4. With a whopping 1,67 noise-to-signal ratio it can be concluded that this indicator
was overall unsuccessful, though expectedly so. In its defense, it should be
mentioned, that the correct signal was issued in 2002, having predicted the first year
of overvaluation (see table 28).
The more reliable, at least based on the in-sample testing results, 3-year signaling
horizon long-sample indicator was tested next (see table 24).
Table 24. Composite indicator’s performance over the total sample 1890-2007; 3-
year signaling horizon; details for 7 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 7 0.11 0.73 0.43 0.30 0.49 0.03
1890-1895 1 N/A 1.00 0.00 0.25 0.00 N/A
1896-1907 1 0.00 1.00 0.00 0.33 0.75 0.00
1908-1916 1 0.50 0.50 1.00 0.33 0.17 0.17
1917-1947 1 0.00 1.00 0.00 0.25 0.87 0.00
1948-1979 1 0.21 0.33 2.00 0.33 0.24 0.07
1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00
1991-2007 1 0.00 1.00 0.00 0.33 0.65 0.00
Indicators in order of inclusion: 2-years lagged house price (growth); residential investment
to GDP (growth); real residential investment (growth); nominal exchange rate GBPUSD
(growth)
+("
The model performed very well, having predicted the out-of-sample event with no
false alarms. The in-sample noise-to-signal ratio of 0,13 dropped further to the total
sample ratio of 0,11. Though only every third good signal of all possible good signals
was issued (from possible six signals, that could have been issued for the last bubble,
only two were actually indicated), this result is still more than satisfactory, as the
timing of these signals was very convenient: the first signal was issued in 2002,
meaning that the time-window of 2003-2005 could be potentially bubbly; the second
signal was issued in 2004, covering the period of 2005-2007 (see table 28). As this
indicator was claimed to be the most reliable already during the in-sample tests, a user
(a buy-side investor) consulting this indicator could have avoided making a costly
mistake of entering the overvalued market altogether.
3.3.2 1991-2007 (short sample)
As can be seen from the last row of table 25, there had been cause for alarm that arose
during the in-sample testing – the short sample composite indicator of 1-year
signaling horizon issued no signals during 1991-2007 at all.
Table 25. Composite indicator’s performance over the total sample 1930-2007; 1-
year signaling horizon; details for 4 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 3 0.07 0.67 0.50 0.44 0.55 0.03
1930-1947 1 0.00 1.00 0.00 0.50 0.88 0.00
1948-1979 1 0.00 1.00 0.00 1.00 0.97 0.00
1980-1990 1 0.22 0.50 1.00 0.50 0.32 0.11
1991-2007 0 - - - - - -
Indicators in order of inclusion: real government net savings (in levels); government net
saving to GDP (in levels); government expenditure to GDP (growth); personal income to
GDP (growth)
Fortunately, it was possible to foresee the shortcomings of this indicator already prior
to the tests, and in “real” life the potential user would have been cautious and most
probably consulted it last among others. The 1-year signaling horizon is too narrow
for in-sample testing of only 3 bubbles to give reliable indicator specifications.
" +)"
The 2-year signaling horizon model derived from the short sample variables
performed much better, having predicted the last bubble episode with a noise-to-
signal ratio of 0,42 (see table 26).
Table 26. Composite indicator’s performance over the total sample 1930-2007; 2-
year signaling horizon; details for 4 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signals/
Tranquil
times
TOTAL
PERIOD 4 0.10 0.67 0.50 0.31 0.50 0.03
1930-1947 1 0.21 0.50 1.00 0.33 0.32 0.07
1948-1979 1 0.00 1.00 0.00 0.50 0.94 0.00
1980-1990 1 0.00 1.00 0.00 0.33 0.73 0.00
1991-2009 1 0.42 0.50 1.00 0.20 0.21 0.08
Indicators in order of inclusion: gap between the current price-to-income ratio and its 5-
year moving average (in levels); gap between the current price-to-rent ratio and its 5-year MA
(in levels); price-to-income ratio (in levels); gap between the current price-to-income and its
5-year MA (growth)
There were two signals issued: one false alarm in 1999, covering the period of 2000-
2001; and the other – a correct signal – in 2004, covering the period of 2005-2006
(see table 28). A potential user basing her decisions purely on this indicator, could
end up having somewhat insufficient forecast material, as year 2004 – the first year of
overvaluation – was not blocked out. Apart from this, the indicator performed rather
well, keeping in mind that it was not considered top quality.
The second most reliable indicator from all five moving extrema approach composite
indicators did not let the potential user down, having predicted the last bubble with no
false alarms, similar to its long sample counterparty (see table 27).
Table 27. Composite indicator’s performance over the total sample 1930-2007; 3-
year signaling horizon; details for 4 bubble episodes
Bubbles
called
Noise-to-signal
ratio
Good to
all
signals
Wrong
signals /
Called
Bubbles
Good/All
Possible
Good
Signals
Conditional -
Unconditional
Probability
Wrong
signal /
Tranquil
times
TOTAL
PERIOD 4 0.00 1.00 0.00 0.29 0.78 0.00
1930-1947 1 0.00 1.00 0.00 0.25 0.76 0.00
1948-1979 1 0.00 1.00 0.00 0.33 0.91 0.00
1980-1990 1 0.00 1.00 0.00 0.25 0.64 0.00
1991-2009 1 0.00 1.00 0.00 0.33 0.65 0.00
Indicators in order of inclusion: real farm value (land + improvements) per acre (growth);
price-to-rent ratio (in levels)
+*"
Of six possible good signals two were issued in a timely manner (see table 28). The
first signal was issued in 2002, preventing the potential user from buying a property
during 2003-2005; the second signal was issued in 2005, covering the period of 2006-
2008. In other words, the buy-side investor having consulted this indicator (especially
in combination with the 3-year signaling horizon composite indicator based on the
long-sample variables) could have successfully avoided the bubbly US housing
market of the first decade of the 21st century.
Table 28. The chronological representation of the issued signals, 1991-2007
91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07
2y + + + + + LONG
3y + +
1y
2y + +
Moving
Extrema SHORT
3y + +
Comment: “+” indicates an issued signal; the highlighted gray area and the bold borders
denote the coverage of the correctly issued signals; the diagonal pattern denotes the bubble
3.4 Comparing composite indicators
As we touched upon the composite indicator methodology proposed by Kaminsky
(2000), it is appropriate to compare the outcomes of these two methods. Kaminsky-
type composite indicator (see equation 7) used all the available variables with noise-
to-signal ratio lower than 1 to weigh single-indicators by the inverse of their noise-to-
signal to receive a probability-type distribution (between 0 and 1). After the in-sample
tests are performed, a critical threshold, that would transform the probabilities of an
event into yes/no signals, is to be chosen. This threshold is chosen such that all the in-
sample events are predicted with the lowest possible noise-to-signal. When there is no
marginal gain from raising the threshold (meaning that the noise-to-signal ratio does
not decline any further), its level is fixed for out-of-sample testing.
The summary of the results from such composition is presented in table 29. The in-
sample performance was very good, but not better than the methodology proposed in
this thesis (noise-to-signal ratios for Kaminsky-type indicator were, on average,
higher).
" ++"
Table 29. Performance summary of Kaminsky-type composite indicator
Signaling
horizon IN-SAMPLE
Bubbles
called
Noise-
to-
signal
ratio OUT-OF-SAMPLE
2004-
2007
bubble
called
Noise-
to-
signal
ratio
6 bubbles (1890-
1990)
7 bubbles (1890-
2007)
2y 100% 0.18 NO 0.24
3y 100% 0.19 NO 0.27
3 bubbles (1930-
1990)
4 bubbles (1930-
2007)
1y 100% 0.04 NO 0.07
2y 100% 0.08 YES 0.10
3y 100% 0.07 NO 0.09
Indicators: Long 2-years gap between the real house price and its 5-year moving average
(in levels); real residential nonfarm wealth to labor force (growth); real residential nonfarm
wealth per employed person (growth); real price of gold ounce (growth). Long 3-years : 2-
years lagged house price (growth); residential investment to GDP (growth); real residential
investment (growth); nominal exchange rate GBPUSD (growth). Short 1-year: real
government net savings (in levels); government net saving to GDP (in levels); government
expenditure to GDP (growth); personal income to GDP (growth). Short 2-years: gap between
the current price-to-income ratio and its 5-year moving average (in levels); gap between the
current price-to-rent ratio and its 5-year MA (in levels); price-to-income ratio (in levels); gap
between the current price-to-income and its 5-year MA (growth). Short 3-years: real farm
value (land + improvements) per acre (growth); price-to-rent ratio (in levels).
The out-of-sample performance, on the other hand, was insufficient, with only one of
the indicators being able to predict the bubble of 2004-2007. Not only is this type of
composition unsuitable in terms of results but the manual work behind weighing each
signal by the inverse of its noise-to-signal ratio, is substantial. Moving extrema
composite indicators clearly outperform Kaminsky-type composite indicators. It is
important to note, though, that Kaminsky-type composite indicator approach was
developed for different kind of data – panel medium-term data as opposed to long-
term country-specific data in the case of the moving extrema approach.
+!"
CONCLUSION
The aim of this thesis was to propose an early warning system for timely housing
bubble identification – the moving extrema approach – with homebuyers kept in mind
as the target users.
To do so, three research questions were addressed:
1. What are the available methodologies for identifying housing bubbles?
The two main methodologies most commonly used within house price bubble
identification were discussed: the fundamental price models and probit models. The
fundamental price models compare the positive house prices with the normative
equilibrium prices calculated on a set of assumed economic fundamentals. Some
fundamental models contain error correction specifications (ECM), which are
programmed to explain the path of the price moving back from overvaluation to
equilibrium. Under the limited dependent variable models, two studies that
implemented probit models to identifying housing peaks and house price boom/bust
sequences were described.
2. How does the moving extrema approach work?
The moving extrema approach was inspired by another early warning system
developed initially for currency crisis ex ante identification by Kaminsky, Lizondo
and Reinhart. The root of the moving extrema approach is to find association between
the dynamics of certain explanatory variables and the occurrence of housing bubbles.
Two central definitions were explained: 1) moving extremum cycle phase – a moving
interval of time within which a variable’s value is either the maximum or the
minimum among other values; seven lengths of moving extremum cycle phases were
considered simultaneously in this paper – from 2 to 8 years. Each occurrence of an
extremum in such a moving interval was viewed as a signal; 2) signaling horizon – a
time interval between a signal from moving extremum cycle phase and the occurrence
of a bubble; three signaling horizons were simultaneously tested – 1-, 2- and 3-year
horizons.
" +#"
At first, those variables (with fixed moving extremum cycle phases and signaling
horizons within one series), that were issuing signals prior to each bubble in the
sample, were filtered out as the potentially suitable ones. Then, the noise-to-signal
ratios for each variable were calculated to see if those signals were issued randomly
or if there were relatively more correct signals than wrong ones. Those indicators that
passed this test (didn’t issue signals randomly) were sorted in the ascending order by
the noise-to-signal ratio, divided into groups by signaling horizons.
The best-performing variables were considered within the composite indicators
grouped by the respective signaling horizon: signals issued by two single indicators
with the same signaling horizons were combined and only those counted, that were
issued by both. The requirements for inclusion into a composite indicator were: 1) the
ability to call all bubbles in the sample; 2) synergy from signals issued by several
single indicators in terms of lowered noise-to-signal ratio. The maximum number of
single indicators in the composite indicator was prescribed to 4.
3. How did the moving extrema approach perform out-of-sample?
The best-performing composite indicators, based on in-sample tests, were both 3-year
signaling horizon indicators:
• 2-year lagged real house price, residential investment to GDP, real residential
investment, and nominal exchange rate of GDPUSD currency pair – all
expressed as growth rates [based on the long sample of 1890-1990];
• real farm value of land and improvements per acre expressed as growth rates,
and price-to-rent ratio in levels [based on the short sample of 1930-1990].
These and other less reliable composite indicators were tested under conditions close
to “real”-life, inserting data from 1991 to 2007 to see if these indicators had been able
to identify the bubble that occurred in the beginning of the 21st century if used at the
time. The out-of-sample results were more than satisfactory: both composite
indicators listed above managed to identify the bubble with no false alarms. A
potential user – homebuyer – could have benefited greatly relying on forecasts of
these indicators, as the whole of the housing bubble of 2004-2007 could have been
successfully avoided. Less reliable indicators were not as successful: the riskiest
composite indicator with 1-year signaling horizon failed to indicate the bubble; two
+$"
others did predict the bubble, but issued some false alarms. In defense of this
methodology, it should be said that the potentially unreliable nature of the latter was
obvious already during the in-sample tests.
How could the results of this analysis be used in future?
After the deflation of house prices in the US has stopped and a period of two years of
non-negative growth has been registered, the methodology suggested in this thesis can
be of assistance anew. If one doesn’t wish to carry out all of the analysis undertaken
in this paper to determine the best-performing composite indicators on the new total
sample (including the 1991-2007), and is only interested in checking for a new
possible US housing bubble using the already developed indicators, a shortcut would
be to monitor the developments in the following composite indicators (especially
together):
a) when the 2-years lagged house price growth rate and the growth rate of residential
investment to GDP ratio are both the largest within a 3-year moving cycle phase, the
growth rate of real residential investment is the largest within a 2-year moving cycle
phase and the growth rate of the nominal exchange rate of pound-dollar currency pair
is the largest within a 4-year moving cycle phase, a potential homebuyer should be
cautious of an upcoming bubble during the next 3 years.
b) when the growth rate of real farm value of land and improvements per acre and the
price-to-rent ratio in levels are both the largest within an 8-year moving cycle phase,
once again a bubble is imminent to occur during the following 3 years.
There are many ways in which future research could move further using the outputs
of this thesis. Similar analysis could be carried out on the housing markets of
countries such as the Netherlands, Norway, the UK and others, where data are
available in sufficient length. The moving extrema approach could be developed
further, upgrading the simple method with thresholds, same-direction continuous
change conditions and other modifications to extract maximum utility out of the
cyclical dynamics’ forecasting ability. As this approach lacks the possibilities of
statistical tests, other tests that could help prescribe statistical significance to the
composite and single indicators would be another major improvement.
" +%"
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" !+"
DATA SOURCES Variable Period Source
Real House Price
Index
1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
Real Building
Cost Index
1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
U.S. Population 1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
CPI 1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
Nominal S&P
500 Price
1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
Real p.c.
Consumption
1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
P/E Ratio (S&P) 1890-2009 Online Data Robert Shiller,
http://www.econ.yale.edu/~shiller/data.htm
Long-Term
Interest Rate
1890-2009 Lawrence H. Officer, "What Was the Interest Rate Then?"
MeasuringWorth, 2010. URL:
http://www.measuringworth.org/interestrates/
Short-Term
Interest Rate
1890-2009 Lawrence H. Officer, "What Was the Interest Rate Then?"
MeasuringWorth, 2010. URL:
http://www.measuringworth.org/interestrates/
Mortgage Rate 1890-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix O.
http://www.nber.org/books/greb56-1
Mortgage Rate 1963-2009 Economic Report of the President. Table B-73, Bond yields and
interest rates, 1929-2008.
http://www.gpoaccess.gov/eop/tables09.html
Housing Starts 1890-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix B.
http://www.nber.org/books/greb56-1
Housing Starts 1953-1958 Nonfarm Housing Starts 1889-1958. Bulletin No. 1260.
http://www.michaelcarliner.com/files/Data/BLS59HousingStarts188
9-1958.pdf
Housing Starts 1962-2009 Economic Report of the President. Table B-56, Bond Yields and
Interest Rates, 1929-2008.
http://www.gpoaccess.gov/eop/tables09.html
Federal Budget
Balance
1901-2008 Budget of the US Government. Historical Tables.
http://www.whitehouse.gov/sites/default/files/omb/budget/fy2008/p
df/hist.pdf
Rental of Tenant-
Occupied
Nonfarm Housing
1929-2009 National Income and Product Accounts: Table 2.5.5
http://www.bea.gov/national/nipaweb/SelectTable.asp
Imputed Rent of
Owner-Occupied
Nonfarm
1929-2009 National Income and Product Accounts: Table 2.5.5
http://www.bea.gov/national/nipaweb/SelectTable.asp
Unemployment
rate
1890-1930 Romer, C. (1986), Spurious Volatility in Historical Unemployment
Data. The Journal of Political Economy, 94(1): 1-37.
Unemployment
rate
1931-1939 Coen, R.M. (1973), Labor Force and Unemployment in the 1920's
and 1930's: A Re-Examination Based on Postwar Experience. The
Review of Economics and Statistics, 55(1): 46-55.
Unemployment
rate
1940-2009 Houshold Data Annual Averages. Civilian Labor Force.
ftp://ftp.bls.gov/pub/special.requests/lf/aat1.txt
!!"
Real housing and
utilities
expenditures
1929-2009 National Income and Product Accounts: Table 2.3.3
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal GDP 1890-1928 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix B.
http://www.nber.org/books/greb56-1
Nominal GDP 1929-2009 National Income and Product Accounts: Table 1.1.5
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal
Residential
Investment
1890-1928 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix B.
http://www.nber.org/books/greb56-1
Nominal
Residential
Investment
1929-2009 National Income and Product Accounts: Table 1.1.5
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal
Government
Current Receipts
1929-2009 National Income and Product Accounts: Table 3.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal
Government
Current
Expenditures
1929-2009 National Income and Product Accounts: Table 3.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal Net
Government
Saving
1929-2009 National Income and Product Accounts: Table 3.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal Price of
Gold Ounce
1890-2009 Lawrence H. Officer, "The Price of Gold, 1257-2009,"
MeasuringWorth, 2010. URL:
http://www.measuringworth.org/gold/
Nominal Current
Account
1929-2009 National Income and Product Accounts: Table 4.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal
Nonfarm
Mortgage Debt
1896-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix L.
http://www.nber.org/books/greb56-1
Nominal
Nonfarm
Mortgage Debt
1953-1954 Economic Report of the President. Table B-75, Bond yields and
interest rates, 1929-2008.
http://www.gpoaccess.gov/eop/tables09.html
Nominal
Nonfarm
Mortgage Debt
1955-2009 US Flow of Funds, Annual Flows and Outstandings.
http://www.federalreserve.gov/releases/z1/current/data.htm
Nominal
Nonfarm
Residential
Mortgage Debt
1896-1952 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix L.
http://www.nber.org/books/greb56-1
Nominal
Nonfarm
Residential
Mortgage Debt
1953-1954 Economic Report of the President. Table B-75, Bond yields and
interest rates, 1929-2008.
http://www.gpoaccess.gov/eop/tables09.html
Nominal
Nonfarm
Residential
Mortgage Debt
1955-2009 US Flow of Funds, Annual Flows and Outstandings.
http://www.federalreserve.gov/releases/z1/current/data.htm
Nominal
GBPUSD
1890-2009 Lawrence H. Officer, "Exchange Rates Between the United States
Dollar and Forty-one Currencies," MeasuringWorth, 2009. URL:
http://www.measuringworth.org/exchangeglobal/
Nominal
Residential
Nonfarm Wealth
1890-1953 Grebler, L., Blank, D.M. and Winnick, L. (1956), Capital Formation
in Residential Real Estate: Trends and Prospects. Princeton
University Press, p. 549. Appendix D.
" !#"
http://www.nber.org/books/greb56-1
Nominal
Residential
Nonfarm Wealth
1955-2009 US Flow of Funds, Annual Flows and Outstandings.
http://www.federalreserve.gov/releases/z1/current/data.htm
Nominal Personal
Income
1929-2009 National Income and Product Accounts: Table 2.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nominal
Disposable
Income
1929-2009 National Income and Product Accounts: Table 2.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Farm Value (land
and buildings)
per acre
1929-2008 Farm Land Values. Department of Agricultural Economics,
University of Missouri.
http://extension.missouri.edu/publications/DisplayPub.aspx?P=G40
4
Owner’s equity
as percentage of
household real
estate
1929-2008 US Flow of Funds, Annual Flows and Outstandings. B-100.
http://www.federalreserve.gov/releases/z1/current/data.htm
Nominal Net
Worth
1929-2008 US Flow of Funds, Annual Flows and Outstandings. B-100.
http://www.federalreserve.gov/releases/z1/current/data.htm
Rent-to-Price
ratio
1960-2009 Davis, Morris A., Lehnert, Andreas, and Robert F. Martin, 2008,
"The Rent-Price Ratio for the Aggregate Stock of Owner-Occupied
Housing," Review of Income and Wealth, vol. 54 (2), p. 279-284;
data located at Land and Property Values in the U.S., Lincoln
Institute of Land Policy http://www.lincolninst.edu/resources/ (data
for the perid of 1930-2009 was calculated using inputs from the
source above.
Nominal Personal
Saving
1929-2009 National Income and Product Accounts: Table 2.1
http://www.bea.gov/national/nipaweb/SelectTable.asp
Gross Private
Domestic
Investment
1929-2009 National Income and Product Accounts: Table 1.1.5
http://www.bea.gov/national/nipaweb/SelectTable.asp
Nonfarm
Business
Productivity
Output per hour
1890-1946 Kendrick, J.W. (1961), Productivity Trends in the United States.
Appendix A. http://www.nber.org/books/kend61-1
Nonfarm
Business
Productivity
Output per hour
1947-2009 Bureau of Labor Statistics. http://www.bls.gov
Employed
Persons in All
Sectors of
Economy
1890-2009 1890-1954: Kendrick, J.W. (1961), Productivity Trends in the
United States. Appendix A. http://www.nber.org/books/kend61-1
1955-2009: OECD: http://www.oecd.org/statsportal
Nominal M1 1929-1935 Friedman, M. and Schwartz, A.J. (1971), A Monetary History of the
United States, 1867-1960. Table A-1.
Nominal M1 1936-1947 Federal Reserve of St. Louis http://www.stlouisfed.org
Nominal M1 1948-2009 Money Stock Measures. Federal Reserve.
http://www.federalreserve.gov/releases/h6/hist/h6hist1.txt
Nominal M2 1890-1946 Anderson, R.G. (2003), Some Tables of Historical US Currency and
Monetary Aggregates Data. Working Paper 006A.
http://research.stlouisfed.org/wp/2003/2003-006.pdf
Nominal M2 1947-1958 Rasche web page.
https://www.msu.edu/~rasche/research/money.htm
Nominal M2 1959-2009 Money Stock Measures. Federal Reserve.
http://www.federalreserve.gov/releases/h6/hist/h6hist1.txt
Monetary Base 1890-1917 Anderson, R.G. (2003), Some Tables of Historical US Currency and
Monetary Aggregates Data. Working Paper 006A.
http://research.stlouisfed.org/wp/2003/2003-006.pdf
Monetary Base 1918-2009 Federal Reserve of St. Louis http://www.stlouisfed.org
!$"
APPENDICES
APPENDIX 1
1.1 ADF test output (natural logs of house prices in levels)
Null Hypothesis: HOUSEPRICE has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic based on SIC, MAXLAG=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -1.587205 0.4860
Test critical values: 1% level -3.486064
5% level -2.885863
10% level -2.579818
1.2 ADF test output (natural logs of house prices in first differences)
Null Hypothesis: D(HOUSEPRICE) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic based on SIC, MAXLAG=12)
t-Statistic Prob.*
Augmented Dickey-Fuller test statistic -10.48549 0.0000
Test critical values: 1% level -3.486064
5% level -2.885863
10% level -2.579818
" !%"
APPENDIX 2
2.1 Inflation rate (in levels) during 1891-2009; and the 3-year windows preceding
each bubble episode, 7 bubbles, period of 1891-2003
2.2 2-year moving average of house price growth during 1892-2009; and the 3-year
windows preceding each bubble episode, 7 bubbles, period of 1892-2003
#'"
2.3 Gap between the real house price and its 5-year MA (in levels) during 1890-2009;
and the 3-year windows preceding each bubble episode, 7 bubbles, period of 1891-
2003
2.4 Growth in real GDP per capita during 1891-2009; and the 3-year windows
preceding each bubble episode, 7 bubbles, period of 1891-2003
" #&"
APPENDIX 3
3.1. Inflation rate in levels (in blue): 8-year windows preceding each of the 7 bubble
episodes (in red), cycle phases (in green), period of 1891-2007
Comment: the level of inflation rate declines prior to a bubble
3.2. 2-year moving average of house price growth (in blue): 8-year windows
preceding each of the 7 bubble episodes (in red), cycle phases (in green), period of
1891-2007
Comment: the MA growth mostly increases prior to a bubble
3.3 Gap (%) between the real house price and its 5-year MA in levels (in blue): 8-year
windows preceding each of the 7 bubble episodes (in red), cycle phases (in green),
period of 1891-2007
Comment: the gap increases (or the negative gap decreases) prior to a bubble
The cycle phases marked in green have a purely visualization purpose.
#("
3.4 Growth of real GDP per capita (in blue): 8-year windows preceding each of the 7
bubble episodes (in red), cycle phases (in green), period of 1891-2007
Comment: the cyclicality in this indicator is harder to observe, nevertheless, there is an
upward trend prior to a bubble (taking into account the signaling horizon of 2-3 years)
3.5 Real short-term interest rate in levels (in blue): 8-year windows preceding each of
the 7 bubble episodes (in red), cycle phases (in green), period of 1891-2007
Comment: a mild upward trend prior or during the first years of overvaluation can be
observed clearly
The cycle phases marked in green have a purely visualization purpose.
" #)"
APPENDIX 4
4.1 Moving minima analysis table for the variable nominal long-term interest rate in
levels
MOVING
MINIMA
Horizon of
prediction /
Moving
extremum
Bub
bles
calle
d
Number
of
bubbles
Noise-to-
signal
ratio
Good /
All
signals
Wrong signals per
called bubble
Good
signa
ls /
Possi
ble
good
signa
ls
Bad
signals
/
Possibl
e bad
signals
P(bubble/signal)
-P(bubble)
Formula A' 6
[B/(B+D)
] /
A/(A+C)
A/(A+B
) B/A'
A/(A
+C)
B/(B+
D)
A/(A+B)-(A+C)
/ (A+B+C+D)
1 year
2 Year MM 3 6 1.11 0.08 15.00 0.44 0.49 -0.01
3 Year MM 2 6 1.15 0.08 17.50 0.33 0.38 -0.01
4 Year MM 1 6 1.34 0.07 27.00 0.22 0.30 -0.02
5 Year MM 1 6 1.19 0.08 24.00 0.22 0.26 -0.01
6 Year MM 1 6 1.04 0.09 21.00 0.22 0.23 0.00
7 Year MM 1 6 0.99 0.09 20.00 0.22 0.22 0.00
8 Year MM 1 6 0.99 0.09 20.00 0.22 0.22 0.00
2 year
2 Year MM 6 6 0.78 0.18 6.67 0.60 0.47 0.03
3 Year MM 4 6 0.94 0.16 8.00 0.40 0.38 0.01
4 Year MM 2 6 1.10 0.14 12.50 0.27 0.29 -0.01
5 Year MM 1 6 1.35 0.12 23.00 0.20 0.27 -0.03
6 Year MM 1 6 1.18 0.13 20.00 0.20 0.24 -0.02
7 Year MM 1 6 1.12 0.14 19.00 0.20 0.22 -0.01
8 Year MM 1 6 1.12 0.14 19.00 0.20 0.22 -0.01
3 year
2 Year MM 6 6 0.82 0.24 6.17 0.57 0.47 0.03
3 Year MM 4 6 0.86 0.24 7.25 0.43 0.37 0.03
4 Year MM 3 6 1.02 0.21 7.67 0.29 0.29 0.00
5 Year MM 2 6 1.12 0.19 10.50 0.24 0.27 -0.02
6 Year MM 2 6 0.96 0.22 9.00 0.24 0.23 0.01
7 Year MM 2 6 0.90 0.23 8.50 0.24 0.22 0.02
8 Year MM 2 6 0.90 0.23 8.50 0.24 0.22 0.02
* - pink denotes the best indicator
Comment: the table presents a summary of analysis sheets with 1-, 2- and 3-year signaling
horizons and 2,3,4,5,6,7 and 8-year moving minima. In this particular case, the best settings
were determined as the 2-year moving minima with 100% in-sample prediction performance
(6 out of 6 bubbles called); noise-to-signal ratio of 0,78; almost each 5th
signal issued was
good, and 3 signals out of 5 possible good signals were issued. At the same time, half of all
possible bad signals are present; and per each called bubble there are approximately 7 false
alarms
#*"
4.2 Moving maxima analysis table for the variable nominal long-term interest rate in
levels
MOVING
MAXIMA
Horizon of
prediction /
Moving
extremum
Bub
bles
calle
d
Number
of
bubbles
Noise-to-
signal
ratio
Good /
All
signals Wrong signals per
called bubble
Good
signals
/
Possib
le
good
signals
Bad
signals /
Possible
bad
signals
P(bubble/sign
al)-P(bubble)
Formula A' 6
[B/(B+D)
] /
A/(A+C)
A/(A+B
) B/A'
A/(A+
C) B/(B+D)
A/(A+B)-
(A+C) /
(A+B+C+D)
1 year
2 Year MM 5 6 0.89 0.10 9.00 0.56 0.49 0.01
3 Year MM 5 6 0.65 0.13 6.60 0.56 0.36 0.04
4 Year MM 3 6 1.05 0.09 10.67 0.33 0.35 0.00
5 Year MM 3 6 0.96 0.09 9.67 0.33 0.32 0.00
6 Year MM 3 6 0.96 0.09 9.67 0.33 0.32 0.00
7 Year MM 3 6 0.92 0.10 9.33 0.33 0.31 0.01
8 Year MM 3 6 0.89 0.10 9.00 0.33 0.30 0.01
2 year
2 Year MM 5 6 1.29 0.12 8.80 0.40 0.52 -0.03
3 Year MM 5 6 1.16 0.13 6.60 0.33 0.39 -0.02
4 Year MM 3 6 1.88 0.09 10.67 0.20 0.38 -0.06
5 Year MM 3 6 1.71 0.09 9.67 0.20 0.34 -0.06
6 Year MM 3 6 1.71 0.09 9.67 0.20 0.34 -0.06
7 Year MM 3 6 1.65 0.10 9.33 0.20 0.33 -0.05
8 Year MM 3 6 1.59 0.10 9.00 0.20 0.32 -0.05
3 year
2 Year MM 5 6 1.40 0.16 8.40 0.38 0.53 -0.05
3 Year MM 5 6 1.18 0.18 6.20 0.33 0.39 -0.03
4 Year MM 3 6 1.59 0.14 10.00 0.24 0.38 -0.07
5 Year MM 3 6 1.44 0.16 9.00 0.24 0.34 -0.05
6 Year MM 3 6 1.44 0.16 9.00 0.24 0.34 -0.05
7 Year MM 3 6 1.38 0.16 8.67 0.24 0.33 -0.05
8 Year MM 3 6 1.33 0.17 8.33 0.24 0.32 -0.04
Comment: the table presents a summary of analysis sheets with 1-, 2- and 3-year signaling
horizons and 2,3,4,5,6,7 and 8-year moving maxima
" #+"
APPENDIX 5
5.1. Indicators that predicted all 6 bubbles during 1890-1990 with signal-to-noise
ratios lower than 1; 2-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
3-year lagged real
house price G max 3 0.49 0.26 4.67 0.11
2
Real house price
and 5-year MA gap L max 2 0.58 0.23 6.00 0.08
3
Res. n-f wealth to
M0 G max 2 0.59 0.23 6.17 0.08
4 Real mortgage rate L max 3 0.60 0.23 5.67 0.08
5
Real res. n-f wealth
to labor force G max 2 0.67 0.21 6.33 0.06
6
Real res. n-f wealth
per employed p. G max 2 0.67 0.21 6.33 0.06
7
Real price of gold
ounce G max 2 0.67 0.21 7.00 0.06
8
Real GDP per
employed person G max 3 0.71 0.20 4.67 0.05
9
Real res. nonfarm
wealth G max 2 0.71 0.20 6.67 0.05
10
Real res. nonfarm
wealth p.c. G max 2 0.71 0.20 6.67 0.05
11
Res. n-f wealth to
M2 G max 2 0.71 0.20 6.00 0.05
12
Nominal mortgage
rate G max 2 0.74 0.19 7.67 0.04
13
Nominal long term
rate L min 2 0.78 0.18 6.67 0.03
14 M2/M0 G min 2 0.78 0.18 6.67 0.03
15 Real output gap L max 2 0.79 0.18 8.17 0.03
16 Real mortgage rate G max 2 0.79 0.18 7.50 0.03
17 Real long term rate G min 2 0.82 0.18 6.17 0.03
18 Real long term rate L max 2 0.84 0.17 7.17 0.02
19
Real GDP per
capita G min 2 0.86 0.17 7.33 0.02
20
Rapid price growth
>2% L max 3 0.86 0.17 7.33 0.02
21
Res. n-f wealth to
M0 L max 2 0.88 0.17 8.33 0.02
22
Nominal mortgage
rate L max 2 0.94 0.16 8.00 0.01
23 Real output gap G min 2 0.98 0.15 8.33 0.00
24
Real GDP to labor
force G max 2 0.98 0.15 6.50 0.00
Comment: the third column shows if the data is expressed in levels or growth rates; the fourth
column marks the direction of the phase; the fifth column marks the length of a phase in
years; the sixth column shows the ratio of good signals to all possible good signals; the
seventh column shows the number of wrongly issued signals per called bubble; the last
column denotes the difference between the conditional and unconditional probabilities: if the
gap is close to zero or negative, it means that signals were issued more or less randomly with
the right predictions happening by chance
#!"
5.2. Indicators that predicted all 6 bubbles during 1890-1990 with signal-to-noise
ratios lower than 1; 3-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Real construction
cost G max 4 0.50 0.35 2.50 0.14
2
Nominal long term
rate G min 5 0.53 0.33 2.67 0.12
3
2-year lagged real
house price G max 3 0.55 0.32 4.17 0.11
4 Housing starts G max 3 0.56 0.32 3.50 0.11
5
Residential
investment to GDP G max 3 0.56 0.32 3.50 0.11
6 Real M0 G max 4 0.60 0.31 3.00 0.10
7 GDP defltaor G min 3 0.64 0.29 4.00 0.08
8 Inflation rate L min 3 0.64 0.29 4.00 0.08
9
Real residential
investment G max 2 0.65 0.29 5.33 0.08
10
Nominal short term
rate L min 4 0.66 0.29 3.33 0.08
11
House price to gold
ounce price G max 2 0.69 0.28 5.17 0.07
12
Nominal exchange
rate: GBPUSD L max 3 0.69 0.28 5.17 0.07
13
Nominal exchange
rate: GBPUSD G max 4 0.70 0.28 3.50 0.07
14
Residential
investment to GDP L max 2 0.73 0.27 5.50 0.06
15 Real mortgage gap L max 4 0.73 0.27 3.67 0.06
16 Unemployment rate L min 4 0.74 0.26 4.67 0.05
17 Nominal term spread L min 3 0.78 0.26 5.83 0.05
18
Nominal short term
rate G max 3 0.83 0.24 4.67 0.03
19 P/E ratio G max 2 0.85 0.24 5.83 0.03
20 P/E ratio L max 2 0.86 0.24 6.50 0.03
21 Unemployment rate G max 2 0.87 0.23 6.00 0.02
22 Real term spread L min 3 0.88 0.23 5.50 0.02
23
1-year lagged real
house price G max 2 0.89 0.23 6.67 0.02
24
Labor force to
population G max 3 0.90 0.23 4.50 0.02
25
House price to gold
ounce price L max 3 0.91 0.23 6.83 0.02
26 Real M2 G max 3 0.91 0.23 4.00 0.02
27
Nominal mortgage
gap L max 3 0.92 0.23 5.17 0.02
28 S&P real price G max 2 0.97 0.21 5.50 0.00
29 Productivity G max 2 0.99 0.21 6.83 0.00
" ##"
APPENDIX 6
6.1. Indicators that predicted all 3 bubbles during 1930-1990; 1-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Real government net
saving L max 4 0.25 0.27 3.67 0.18
2
Government net saving to
GDP L max 4 0.27 0.25 4.00 0.17
3
Government expenditure to
GDP G min 4 0.31 0.22 4.67 0.14
4 Personal income to GDP G max 3 0.36 0.20 6.67 0.12
5
Mortgage interest to disp.
Income G max 4 0.38 0.19 7.00 0.11
6 Disposable income to GDP G max 3 0.42 0.17 6.33 0.09
7
Real housing and utilities
expendit. G max 3 0.48 0.16 5.33 0.08
8 Real M1 G min 2 0.49 0.15 7.33 0.07
9 Real tenant-oc. rental price G min 2 0.54 0.14 8.00 0.06
10
Hous. and util. exp. to
consumption G min 2 0.54 0.14 8.00 0.06
11 M1/M0 L min 3 0.56 0.14 8.33 0.06
12
Real mortgage interest cost
(calc) G max 2 0.57 0.14 10.67 0.05
13
Real per. income per empl.
person G min 2 0.60 0.13 9.00 0.05
14
Real perosnal income to
labor force G min 2 0.67 0.12 10.00 0.04
15
N-f residential mortgage
debt to GDP L max 2 0.68 0.12 12.67 0.03
16 Real government revenue G max 2 0.71 0.11 8.00 0.03
17
Nonfarm mortgage debt to
GDP L max 4 0.76 0.11 11.33 0.02
18
Mortgage interest to disp.
Income L max 2 0.83 0.10 12.33 0.02
19
Government revenue to
GDP G max 2 0.83 0.10 9.33 0.01
Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered
from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient
#$"
6.2. Indicators that predicted all 3 bubbles during 1930-1990; 2-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1
Price-to-income and 5-year
MA gap L max 7 0.15 0.50 2.33 0.37
2
Price-to-rent and 5-year MA
gap L max 5 0.26 0.36 4.67 0.23
3 Price-to-income L max 3 0.28 0.35 3.67 0.22
4
Federal budget balance to
GDP L max 4 0.33 0.31 3.67 0.18
5
Real federal budget balance in
levels L max 3 0.35 0.30 4.67 0.17
6
Real n-f residential mortgage
debt G max 8 0.40 0.27 2.67 0.14
7 Disposable income to GDP L min 5 0.45 0.25 4.00 0.12
8
Real disp. income per empl.
person G max 3 0.48 0.24 5.33 0.11
9
Price-to-income and 5-year
MA gap G min 5 0.49 0.24 4.33 0.10
10
Res.inv. to gross priv. dom.
inv. G min 3 0.51 0.23 5.67 0.10
11 Real disposable income G max 2 0.53 0.22 7.00 0.09
12
Real disposable income per
capita G max 2 0.53 0.22 7.00 0.09
13 Real imputed rental price G max 4 0.53 0.22 4.67 0.09
14
Real disposable income to
labor force G max 4 0.55 0.21 3.67 0.08
15 Real nonfarm mortgage debt G max 4 0.57 0.21 5.00 0.08
16 M1/M0 G min 3 0.60 0.20 5.33 0.07
17 Real government net saving G min 3 0.68 0.18 6.00 0.05
18
Hous. and util. exp. to dispos.
income G max 2 0.75 0.17 10.00 0.04
19 Personal saving to GDP G max 2 0.75 0.17 6.67 0.04
20 M2/M1 L max 2 0.78 0.16 12.00 0.03
21
Real personal saving to labor
force G max 2 0.79 0.16 7.00 0.03
22 Real personal income G max 2 0.87 0.15 7.67 0.02
23
Real personal income per
capita G max 2 0.87 0.15 7.67 0.02
24
Real per. saving per empl.
person G max 2 0.87 0.15 7.67 0.02
Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered
from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient
" #%"
6.3. Indicators that predicted all 3 bubbles during 1930-1990; 3-year signaling horizon
Name
Growth
/ Levels
Moving
Extremum
Length
of
phase
Noise-
to-
signal
ratio
Good /
All
signals
Wrong
signals
per
called
bubble
Conditional -
Unconditional
Probability
1 Real farm value per acre G max 8 0.18 0.56 1.33 0.38
2 Real government expenditure G min 8 0.22 0.50 1.33 0.32
3 Price-to-rent L max 8 0.25 0.47 3.00 0.29
4
Saving-to-GDP and 5-year
MA gap L min 7 0.26 0.46 2.33 0.28
5 Price-to-income G max 7 0.26 0.45 2.00 0.27
6
N-f residential mortgage debt
to GDP G max 7 0.28 0.44 1.67 0.26
7 Personal saving to GDP L min 6 0.39 0.36 2.33 0.18
8
Gross priv. domestic inv. to
GDP G max 5 0.39 0.36 2.33 0.18
9
Hous. and util. exp. to
consumption L min 3 0.44 0.33 4.67 0.15
10
Price-to-rent and 5-year MA
gap G max 4 0.50 0.31 3.00 0.13
11
Saving-to-GDP and 5-year
MA gap G max 4 0.50 0.31 3.00 0.13
12 Real current account L min 4 0.51 0.30 4.67 0.12
13
Res.inv. to gross private dom.
Inv. L max 3 0.51 0.30 4.67 0.12
14
Nonfarm mortgage debt to
GDP G max 4 0.53 0.29 4.00 0.11
15 Personal income to GDP L min 5 0.55 0.29 3.33 0.11
16 Real current account G min 3 0.57 0.28 6.00 0.10
17 Price-to-rent G max 3 0.57 0.28 6.00 0.10
18
Real gross priv. domestic
investment G max 2 0.58 0.28 7.00 0.10
19 Government revenue to GDP L max 2 0.83 0.21 10.00 0.03
20 M2/M1 G min 3 0.83 0.21 5.00 0.03
21 Real personal saving G min 2 0.94 0.19 10.00 0.01
22
Real personal saving per
capita G min 2 0.94 0.19 10.00 0.01
23
Hous. and util. exp. to dispos.
income L max 2 0.97 0.18 10.33 0.00
Comment: due to the smaller sample, the noise-to-signal ratio acceptable had to be lowered
from 1 to 0,5. The highlighted indicators therefore do not qualify as sufficient
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