“Estimating the New Keynesian Philips Curve for the UK”

Submitted to:

Dr. Stephen Millard

Advanced Macroeconomics (L14010)

Authors:

Mohammad Alali (4295448)

Moosa Yousuf (4297530)

Ziya Ekrem Bayrak (4311388)

10th May 2018

Introduction

The New Keynesian Phillips curve (NKPC) delivers a simple relationship between

inflation and output by taking into consideration the expected inflation and real

marginal cost of private agents. It has been beneficial for its simplicity when

conducting theoretical policy analysis. Gali and Gertler (1999) were one of the first

researchers who estimated the NKPC. They used quarterly US data from 1960 to

1977 and found that their model was a good fit. In particular, the real marginal cost

was quantitatively important and statistically significant. On the contrary, Roberts

(2001) argued that the NKPC did not fit the US Data very well, and for it to fit the

data, rational expectations needed to be augmented by additional lags of inflation.

Hence, he argued that the backward-looking component of the NKPC was the most

important determinant indicating that most of the population just uses a univariate

rule to forecast inflation. Vašíček (2014) in a relatively recent study on a panel of four

central European countries (Poland, Hungary, Czech and Slovakia) argued that the

NKPC vaguely fits the data. He finds that inflation is driven by external factors and

its past values both. Furthermore, he disputed the NKPC claims that the real marginal

cost is the main inflation forcing variable. In contrast, Scheufele (2010) tested the

NKPC and its hybrid variant on German data and found a purely forward-looking

behavior. Despite the large amount of research devoted to the validity of the NKPC,

the issue is still subject to debate.

NKPC in the UK

As for the UK, Batini et al (2005) use an open-economy NKPC and find that external

factors such as real oil prices; competitive pressure and relative prices of imported

inputs are all significant determinants of future inflation, as they make modifications

to the baseline NKPC model. Furthermore, they adjust for price stickiness in their

model using a framework based on Rotemberg (1982). A study aimed at considering

inflation uncertainty by Groth et al (2006) tests the validity of the NKPC by

examining the fit between fundamental and actual inflation series for UK and US

data. Their findings for the UK data had narrower confidence bounds than the US,

which allowed for identification of factors that may have contributed towards the

inability of the NKPC to fit actual data for certain periods. Initially, there was a shift

in the monetary policy around 1979, which was followed by a drastic fall in inflation.

Next, the NKPC failed to predict a rise in inflation during the second-half of the

1980s. However, since the adoption of inflation targeting set at two percent in 1992, a

relatively stable economic environment has accompanied low inflation and a low

level of uncertainty regarding it. Since then, it could be fairly said that the

fundamental inflation predicted by the NKPC has tracked actual inflation reasonably

well. Our goal for this paper will be to extend previous studies on the verification of

the NKPC, by examining if it fits the relatively recent UK data. We shall be studying

a hybrid version of the NKPC that studies both backward and forward-looking

components of inflation.

Data and Methodology

𝝅𝒕 − 𝝅 =  𝜷𝟏𝑴𝑪+ 𝜷𝟐(𝝅𝒆 − 𝝅)+ 𝜷𝟑(𝝅𝒕!𝟏 − 𝝅) (1) 𝝅𝒕 − 𝝅 =  𝜸𝟏(𝝅𝒕!𝟏 − 𝝅)+ 𝜸𝟐(𝝅𝒕!𝟐 − 𝝅)+ 𝜸𝟑(𝝅𝒕!𝟑 − 𝝅)+ 𝜸𝟒(𝝅𝒕!𝟒 − 𝝅) (2) 𝝅𝒕 − 𝝅 =  𝜽𝟏(𝝅𝒕!𝟏 − 𝝅)+ 𝜽𝟐(𝝅𝒕!𝟐 − 𝝅)+ 𝜽𝟑(𝝅𝒕!𝟒 − 𝝅) (3)

The empirical estimations in the following section are based on quarterly data from

1955 Q1 until 2016 Q3, gathered from the Bank of England database. We have

constructed the real marginal cost (RMC) based on the log deviation of labor share

from its mean, and specified instrumental variables for the generalized method of

moments (GMM) estimation based on Gali et al (2005). Accordingly, we specify four

lags for inflation and two lags each, for de-trended real GDP, nominal wage inflation

and RMC. In order to estimate the NKPC (given in Equation 1), we construct three

models based on different forms of expected inflation:

1. We use an AR process to forecast future inflation using the 1st, 2nd and 4th

lags. The AR (4) model is depicted in Equations 2, which we estimated and

found an insignificant coefficient for the 3rd lag, hence used its reduced form

illustrated in Equation 3.

2. Assuming rational expectations, we could expect inflation in the next period to

be the actual inflation plus a random expectational error. Doing so, we use πt+1

as the expected inflation.

3. Expected inflation is also available from survey forecasters at the Bank of

England. We use these values in our third model, however, since these values

start from 1996, leaving us with relatively fewer observations than the first

two models.

We calculate inflation as !"#!!"#!!!

− 1 ∗ 400. The steady state inflation rate used in

our framework is 2% for the post 1992 period, based on inflation target set by the

central bank, and 6.5% prior to 1992 based on the mean inflation for 1955 Q1 to 1991

Q4. Labor share is computed as !!!!!"#$  !"#!

, where Wt and Nt correspond to real wages

and the number of people employed respectively.

Figure 1 depicts the expected inflation differential from its steady state based on the

AR (4) reduced model, plotted against actual values. The expected inflation seems to

fit well with the actual values, though it has a lower variation as the series takes more

balanced values based on the 1st, 2nd and 4th lags. On the other hand, the values for

expected inflation based on survey forecasts minus the steady state value of 2%

appears to be very close to zero throughout 1996 – 2016 period and doesn’t fit well

with actual inflation differential series from its steady state. Perhaps, this is since

forecasts on average, expect that the central bank would commit to the target, which

is observed to be the case in the long run where average inflation based on CPI over

the inflation targeting period starting from 1992 is found to be very close to 2%.

-‐15  

-‐10  

-‐5  

0  

5  

10  

15  

20  

25  

30  

1955  

1958  

1961  

1964  

1967  

1970  

1973  

1976  

1979  

1982  

1985  

1988  

1991  

1994  

1997  

2000  

2003  

2006  

2009  

2012  

2015  

Figure 1 Actual inflation differential from its steady state and its expectation

based on AR process

Actual  

AR  expected  

Empirical Results

Table 1: Summary of regression outputs

Dependent Variable: CPI Inflation Linear estimation with 1 weight update

Choice of Expected Inflation

Independent Variables Rational

Expectations (Model 1)

AR Process (Model 2)

Survey Forecasts (Model 3)

Real Marginal Cost 0.017 (1.33) 0.002 (0.12)

0.017 (0.74)

Expected Inflation 0.517*** (6.41) 1.045***

(9.42) -0.651 (0.26)

Lagged inflation 0.125* (1.95) -0.123**

(2.35) -0.252**

(2.33) R-squared 0.22 0.48 0.00

J-statistic 26.2 9.8 15.8 Cragg-Donald F-statistic 1659.7 13.8 5.6 Number of observations 241 242 82 Instrument rank 10 10 10

Instrument specification: Constant; 4 lags of CPI Inflation; 2 lags of Real Marginal

Cost; 2 lags of De-trended Real GDP; 2 lags of Nominal Wage Inflation. Estimation weighting matrix: HAC (Bartlett kernel, Newey-West fixed bandwidth = 5.00 for Models 1 and 2, and 4.00 for Model 3). Standard errors and covariance are computed using estimation weighting matrix. Numbers in parentheses are the absolute (Newey West) t-statistics that have been corrected for heteroscedasticity and serial auto-correlation. Significant coefficients are indicated by *p

There are different methods that contribute to the estimation of NKPC like the Non-

Linear Least Squares, Maximum Likelihood Estimation, Limited Information

Maximum Likelihood Estimation and the Generalized Method of Moments (GMM).

However, we have used GMM since it is among the best estimators able to deal with

potential endogeneity issues. Doing so, we have introduced a set of 10 instruments

based on different number of lags of 4 variables, as suggested by Gali et al (2005).

Results for each of the three models are presented in Table 1.

It is essential that we test for the strength of these instruments for robustness. We do

this by comparing the Cragg-Donald F-statistic with the Stock-Yogo critical values.

Based on the results, we reject the “null hypothesis of weak instruments” at the 5%

level for Model 1, and 10% level for Model 2. However, we fail to reject the “null

hypothesis of weak instruments” for Model 3. Furthermore, Model 3 has an r-squared

of zero, indicating that it lacks predictive power. We therefore disregard it from our

analysis and examine the NKPC under expected inflation based on rational

expectations and the AR process. Next, we test for over-specification based on the J-

statistic given by our GMM estimation. Using a significance threshold of 1%, our

results indicate that none of the models severely suffer from the over-specification

problem.

Inferences on the expected inflation and the backward looking component:

The coefficients of expected inflation for Models 1 and 2 are both positive and

statistically significant, underlying a strong forward-looking component. In Model 1,

we assume rational expectations, suggesting that current inflation heavily depends on

the actual one period ahead inflation with an expectational error. There is also a

significantly positive backward looking component implying inflation tends to be

higher in periods that follow high inflation in the most immediate period.

Surprisingly, the opposite is true for lagged inflation in Model 2, in which case

consumers expect inflation to be lower at times succeeding periods of high inflation.

Nonetheless, the backward looking component is of a lower magnitude than the

forward looking component in both Models 1 and 2, suggesting that the NKPC is

predominantly forward looking. Additionally, our coefficient for expected inflation in

Model 2 (which uses an AR process to estimate expected inflation) is highly

significant and closer to one. This supports the general claim in Roberts (2001) that

most people just use a univariate rule when estimating inflation.

Comments on the real marginal cost:

In theory, the RMC forms a major component of the NKPC as it is expected to

positively influence inflation. Accordingly, the signs of coefficients for RMC are

theoretically correct in each of the three models we have estimated, however, neither

are statistically significant. This could be due to the inherent limitations for measuring

RMC or using labor share to proximate it. Mazumder (2010) mentions two main

reasons why labor share used by Gali et al (2005) is an unsuitable proxy for RMC.

Firstly, he argues that while marginal cost should be pro-cyclical (in theory), labor

share tends to be countercyclical. Secondly, he criticizes the assumption that labor

input is freely adjusted at a fixed real wage, since in reality, due to labor contracts,

hiring and training costs, labor is not fully flexible in the short-run.

Conclusion and further recommendations In conclusion, we found expected inflation to be the most valuable contributor in the NKPC, since the coefficients of expected inflation in both Models 1 and 2 are statistically significant and quantitatively important. As for the lagged inflation, although it is statistically significant in both models, it carries a relatively lower magnitude than its forward-looking counterpart. This conclusion is also found in Gali and Gertler (1999) who suggested the forward-looking component has a dominant role in the NKPC. Furthermore, the RMC is statistically insignificant across all three models; partially due to the limitation of using labor share to proximate RMC. Finally, we would like to suggest alternatives to studying inflation dynamics. We recommend using financial and money market variables such as interest and forward rates as they are closely linked with inflation. For countries that actively participate in international trade, introducing variables such as average inflation rates in trading partner countries and exchange rates could help in identifying any potential spillovers. Cottarelli et al (1998) suggest a number of non-monetary determinants of inflation such as the central bank independence, exchange rate regimes, degree of price liberalization and fiscal policy variables that they find significant. Furthermore, it may be a good idea to revisit the classical Philips curve to study interactions between inflation and unemployment, though this relation could only last in the short run as unemployment is determined by real factors in the long run when markets adjust their expectations over time (Friedman, 1977).

References

Batini, N., Jackson, B. and Nickell, S., 2005. An open-economy new Keynesian Phillips curve for the UK. Journal of Monetary Economics, 52(6), pp.1061-1071. Cottarelli, M.C., 1998. The Nonmonetary determinants of inflation: A panel data study. International Monetary Fund. Friedman, M., 1977. Nobel lecture: inflation and unemployment. Journal of political economy, 85(3), pp.451-472. Gali, J. and Gertler, M., 1999. Inflation dynamics: A structural econometric analysis. Journal of monetary Economics, 44(2), pp.195-222. Gali, J., Gertler, M. and Lopez-Salido, J.D., 2005. Robustness of the estimates of the hybrid New Keynesian Phillips curve. Journal of Monetary Economics, 52(6), pp.1107-1118. Groth, C., Jääskelä, J.P. and Surico, P., 2006. Fundamental inflation uncertainty. Mazumder, S., 2010. The new Keynesian Phillips curve and the cyclicality of marginal cost. Journal of Macroeconomics, 32(3), pp.747-765. Roberts, J., 2001. How Well does the new Keynesian Sticky Price Model Fit the Data?. Rotemberg, J.J., 1982. Sticky prices in the United States. Journal of Political Economy, 90(6), pp.1187-1211. Scheufele, R., 2010. Evaluating the german (new keynesian) phillips curve. The North American Journal of Economics and Finance, 21(2), pp.145-164. Vašíček, B., 2011. Inflation dynamics and the new Keynesian Phillips curve in four Central European Countries. Emerging Markets Finance and Trade, 47(5), pp.71-100.