This paper studies the comovement between output and inflation in the EU15 countries. Following den Haan (2000), I use the correlations of VAR forecast errors at different horizons in order to analyze the output-inflation relationship. The empirical results show that eight countries display a significant positive comovement between output and inflation. Moreover, the empirical evidence suggests that a Phillips curve phenomenom is more likely to be detected in countries where inflation is more stable.comovement of output and inflation, VAR forecast errors

Vázquez Pérez, Jesús

English

Research Papers in Economics

IS THERE A PHILLIPS CURVE IN THE
U.S. AND THE EU15 COUNTRIES? An
empirical investigation∗
Jesús Vázquez†
Universidad del País Vasco
November, 2001
(Preliminary draft)
Abstract
This paper studies the comovement between output and inﬂation
in the EU15 countries. Following den Haan (2000), I use the corre-
lations of VAR forecast errors at diﬀerent horizons in order to ana-
lyze the output-inﬂation relationship. The empirical results show that
eight countries display a signiﬁcant positive comovement between out-
put and inﬂation. Moreover, the empirical evidence suggests that a
Phillips curve phenomenom is more likely to be detected in countries
where inﬂation is more stable.
Key words: comovement of output and inﬂation, VAR forecast errors
JEL classiﬁcation numbers: E31, E47
∗Financial support from Ministerio de Ciencia y Tecnología, Gobierno Vasco and
Universidad del País Vasco (Spain) through projects BEC2000-1393, PI-1999-131 and
9/UPV00035.321-13511/2001, respectively, is gratefully acknowledged.
†Correspondence to: Jesús Vázquez, Departamento de Fundamentos del Análisis
Económico, Universidad del País Vasco, Av. Lehendakari Aguirre 83, 48015 Bilbao, Spain.
Phone: (34) 94-601-3779, Fax: (34) 94-601-3774, e-mail: jepvapej@bs.ehu.es
11I N T R O D U C T I O N
For long economists widely accepted that output and inﬂation displayed a
positive correlation at least in the short-run. For a large group of economists,
the positive short-run correlation between output and inﬂation (the so-called
Phillips curve phenomenon) is still considered a necessary building block of
business cycle theory (for instance, Mankiw (2001)). Yet, this view is rather
controversial in the literature. For instance, Kydland and Prescott (1990)
a r g u et h a t“ any theory in which procyclical prices ﬁgure crucially in account-
ing for postwar business cycle ﬂuctuations is doomed to failure.”M o r e o v e r ,
Cooley and Ohanian (1991) ﬁnd evidence that the U.S. correlation between
output and prices is negative during the postwar period. Furthermore, Atke-
son and Ohanian (2001) show that Phillips curve-based models are no better
for forecasting a change in the inﬂation rate than a naive forecast based on
ac o i nﬂip.
Den Haan (2000) argues that an important source of disagreement in the
literature is the focus on only the unconditional correlation between output
and prices. As an alternative, Den Haan proposes to use the correlations of
VAR forecast errors at diﬀerent horizons. Proceeding in this way one can
take into account valuable information about the comovement of variables.
Moreover, variables need not to be stationary to analyze their comovement
(that is, previous ﬁltering of variables is not required). Den Haan (2000),
Sumner and Den Haan (2001) and Vázquez (2001) have studied the comove-
ment between output and prices using the correlations of VAR forecast errors
at diﬀerent horizons. Using U.S. data from the postwar period, Den Haan
(2000) ﬁnds that the comovement between output and prices is positive in
the short-run (up to two years horizons) and negative in the long-run (be-
tween ﬁve and seven years horizons). Sumner and Den Haan (2001) analyze
data from the G7 countries. They ﬁnd a negative long-run relationship for
all countries. However, the evidence of a positive short-run comovement be-
tween output and prices is weaker. Similar to Sumner and Den Haan (2001),
Vázquez (2001) ﬁnds evidence of a negative long-run relationship for a large
group of EU15 countries, but only few countries (France, Italy and Portugal)
exhibit a type of Phillips-curve eﬀect, that is, a positive comovement between
output and prices in the short-run.
In this paper, we argue that there are two another important sources of
disagreement on the Phillips curve. One source is the variables involved in
this relationship. Many papers have studied the comovement between output
(or another indicator of economic activity) and prices. However, traditional
and new Phillips curve proponents claim that the presence of a positive short-
run correlation between output (or another indicator of economic activity)
2and inﬂation. As pointed out by Mankiw (2001), the dynamics of prices and
inﬂation; and thus, the comovement of output with one of these variables,
can be rather diﬀerent. For instance, in the models of staggered price ad-
justment, the price level adjusts slowly, but the rate of inﬂation can jump
instantaneously. Another source of disagreement is the deﬁnition of business
cycle used. While real business cycle researchers look at horizons between
two and eight years, new keynesian macroeconomists seem to look at closer
horizons.
This paper carries out the methodology suggested by Den Haan (2000) to
study the comovement between output and inﬂa t i o ni nt h ep o s t w a rp e r i o d
using data from U.S. and the EU15 group of countries.1 The aim of this paper
is twofold. First, I analyze whether there is signiﬁcant positive correlation
between output and inﬂation. Second, by comparing the results found in
this paper with those obtained by Vázquez (2001), I shall assess whether
the comovement between output and inﬂation is similar to the comovement
between output and prices. The empirical results show that U.S. and seven of
EU15 countries (Belgium, Finland, France, Germany, Italy, Netherlands and
United Kingdom) display a signiﬁcant positive comovement between output
and inﬂation at forecast horizons up to seven years. The empirical results
also show that a Phillips curve is more likely to be observed in countries
where inﬂation volatility is lower. Moreover, for almost all countries the
comovement pattern of output and inﬂation is rather diﬀerent from that
found for output and prices.
The rest of the paper is organized as follows. Section 2 brieﬂy describes
how to use a VAR to study the correlation structure of output and inﬂation
at several forecast horizons. Section 3 presents and discusses the empirical
evidence. Section 4 shows the conclusions.
2 MEASURING CORRELATIONS AT DIF-
FERENT FORECAST HORIZONS
For illustrative purposes, this section describes the methodology suggested
by Den Haan (2000) in order to measure correlations at diﬀerent forecast
horizons. Readers who are familiar with this methodology should skip this
description and move on to Section 3.
1In alphabetical order, the EU15 group of countries includes Austria (AU), Belgium
(BE), Denmark (DE), Finland (FI), France (FR), Germany (G), Greece (GR), Ireland
(IR), Italy (IT), Luxembourg (LU), Netherlands (NE), Portugal (PO), Spain (SP), Sweden
(SW) and United Kingdom (UK). The abbreviated name of each country is in parenthesis.
3Let us consider an N-vector of random variables Xt. The vector Xt may
include any combination of stationary processes and integrated processes of
arbitrary order. In order to characterize the comovement of output, Yt,a n d
inﬂation, πt, Xt must contain at least (the log of) Yt and πt.C o n s i d e r t h e
following VAR
Xt = α + βt + γt
2 +
L X
l=1
AlXt−l + Ut, (1)
where α, β,a n dγ denote ﬁxed N-vectors of constants, Al are ﬁxed N x
N coeﬃcient matrices. Ut is an N-dimensional white noise process, that
is, E(Ut)=0 , E(UtU0
t)=Ωu and E(UtU0
s)=0for s 6= t. L is the total
number of lags included. The K-period ahead forecast and the K-period
ahead forecast error of the random variable Yt are denoted by EtYt+K and
Y ue
t+K,t, respectively. Similarly, we can deﬁne Etπt+K and πue
t+K,t.L e t u s
denote the correlation coeﬃcients between Y ue
t+K,t and πue
t+K,t by COR(K).
As pointed out by Den Haan (2000), if all time series included in Xt are
stationary, then the correlation coeﬃcient of the forecast errors will converge
to the unconditional correlation coeﬃcient between Yt and πt as K goes to
inﬁnity. If Xt includes integrated processes, then correlation coeﬃcient may
not converge but they can be estimated consistently for ﬁxed K.
Using the correlation coeﬃcient of the forecast error to analyze the output-
inﬂation relationship at a particular horizon K can be viewed, roughly speak-
ing, as involving an implicit trend-cycle decomposition where the ‘trend’
components of output and inﬂation are given by EtYt+K and Etπt+K, respec-
tively; whereas the ‘cycle’ components of output and inﬂation are Y ue
t+K,t and
πue
t+K,t, respectively. Therefore, when we analyze the correlations of the VAR
forecast errors at diﬀerent horizons we are studying the comovement between
the “cyclical” components of output and inﬂation.
3 THE COMOVEMENT BETWEEN OUT-
PUT AND INFLATION
In this section, I implement the procedures describe in Section 2 to study the
comovements between output and inﬂation in the EU15 group of countries
and U.S. during the postwar period. The data for the EU15 countries used are
monthly data taken from the OECD’s Main Economic Indicators as released
on line through license by DSI Data Service and Information GmbH, except
for Ireland which is quarterly data since monthly data are not available. U.S.
data were download from Den Haan’s web-site. The price time series used
4for each country studied is the consumer price index. The output time series
are index of industrial production.
Table 1 shows Phillips-Perron unit root tests applied to each country
studied. These unit root tests provide strong support for the hypothesis that
πt is a stationary process. For a small group of countries (Greece, Ireland,
Sweden and U.S.), the log of output is an I(1) process. For the rest of
countries, log(Yt) seems to be stationary around a deterministic trend.
I estimate correlation coeﬃcients based on VAR’s that only includes out-
put and inﬂation. The characteristics of these VAR’s are described in Table
2. Akaike information criterion was used to determine the number of lags
and whether linear and quadratic trend terms should be included. When
estimating the VAR’s for the countries for which log(Yt) is nonstationary,
the ﬁrst-diﬀerence of log(Yt) is included in Xt instead of log(Yt) (that is, the
unit restriction on output is included).
Following Den Haan (2000), we estimate the correlation coeﬃcients of
VAR forecast errors by, calculating the forecast errors for each horizon con-
sidered (from one quarter to 28 quarters) as the diﬀerence between the real-
izations and the corresponding forecasts and then calculating the correlations
of these forecast errors for each horizon.2 Since the estimated correlation co-
eﬃcients are subject to sampling variation, conﬁdence bands are constructed
using bootstrap methods. More speciﬁcally, for each estimated VAR and its
bootstrapped errors are used to generate 2500 simulated data sets. Then, for
each simulated data set the correlation coeﬃcients at diﬀerent horizons are
estimated and standard conﬁdence bands are calculated.3
Figures 1-4 display a set of graphs, one for each country analyzed. Each
graph shows the estimated correlation coeﬃcients and the 10% − 90% and
5% − 95% conﬁdence bands constructed using bootstrap methods. Looking
at these graphs, we observe that eight countries (Belgium, Finland, France,
Germany, Italy, Netherlands, United Kingdom and U.S.) exhibit a signiﬁcant
positive comovement between output and inﬂation at horizons up to seven
years (28 quarters), but U.S. where a signiﬁcant comovement between output
and inﬂation does not appear for horizons greater than six quarters. For the
2Den Haan and Sumner (2001) use an alternative method to estimate the correlation
coeﬃcients. This alternative method uses the covariance obtained from the VA Rcoef-
ﬁcients and the variance-covariance matrix of the white noise process, Ut. They argue
that using this method leads to eﬃciency gains especially in estimating the correlation
coeﬃcients associated with long-term forecast horizons. However, they also report that
bias is larger with this second method.
3The programs for estimating the correlation coeﬃcients and the conﬁdence bands
are adapted versions of programs written in RATS that were download from Den Haan’s
web-site.
5rest of EU15 countries there is no evidence of a signiﬁcant correlation between
output and inﬂation. Only Sweden exhibits evidence of a negative correlation
between output and inﬂation at horizons ranging from 10 to 28 quarters. The
ﬁrst two columns in Table 3 summarize the comovement between output and
inﬂation at the diﬀerent ranges of forecast horizons. The third and fourth
columns summarize the evidence on comovement between output and prices
found by Vázquez (2001). In general, one may conclude that the comovement
between output and prices is rather diﬀerent from the comovement between
output and inﬂation.
Figure 5 ranks the EU15 countries and U.S. according to two sample
statistics that measure inﬂation volatility: the standard deviation of inﬂation
and the variation coeﬃcient of inﬂation. Inside of a circle are the abbreviated
names of the countries for which a signiﬁcant positive correlation between
output and inﬂation is found. We observe that the two volatility measures
of inﬂation support the hypothesis that the Phillips curve is easier to detect
(that is, a positive comovement between output and inﬂation is more likely)
in those countries where inﬂation volatility is lower.
4C O N C L U S I O N S
This paper uses the correlation coeﬃcients of forecast errors at diﬀerent fore-
cast horizons obtained from estimated VAR’s to analyze the comovement
between output and inﬂation in the EU15 countries and U.S. The empiri-
cal results show that eight countries (Belgium, Finland, France, Germany,
Italy, Netherlands, United Kingdom and U.S.) exhibit a signiﬁcant positive
comovement between output and inﬂation at horizons up to seven years (28
quarters), except U.S. where a signiﬁcant comovement between output and
inﬂation does not appear for horizons greater than six quarters. For the
rest of EU15 countries there is no evidence of a signiﬁcant correlation be-
tween output and inﬂation. Moreover, the empirical evidence suggests that
a Phillips curve phenomenon is more likely to be detected in countries where
inﬂation volatility is lower.
References
[1] Atkeson, Andrew, and Lee E. Ohanian (2001) “Are Phillips curves useful
for forecasting inﬂation?,” Federal Reserve Bank of Minneapolis Quar-
terly Review 25, 2-11.
6[2] Cooley, Timothy F., and Lee E. Ohanian (1991) “The cyclical behavior
of prices,” Journal of Monetary Economics 28, 25-60.
[3] Den Haan, Wouter J. (2000) “The comovement between output and
prices,” Journal of Monetary Economics 46, 3-30.
[4] Den Haan, Wouter J., and Steven Sumner (2001) “The comovement be-
tween real activity and prices in the G7,” National Bureau Economic
Research Working Paper 8195.
[5] Kydland, Finn E., and Edward. C. Prescott (1990) “Business cycles: real
facts and a monetary myth,” Federal Reserve Bank of Minneapolis Quar-
terly Review 14, 3-18.
[6] Mankiw, N. Gregory (2001) “The inexorable and mysterious trade-oﬀ
between inﬂation and unemployment,” Economic Journal 111, C45-61.
[7] Vázquez, Jesús (2001) “The comovement between output and prices in
the EU15 countries: An empirical investigation,” Universidad del País
Vasco, mimeo.
7Table 1. Phillips-Perron Zρ tests
Country-Period Variable With Trend Without Trend
Yt −127.39 −3.88
Austria Pt 1.30 −0.71
1962:1-2001:1 ∆Yt −372.11 −372.10
∆Pt −355.03 −355.75
Yt −234.04 −26.20
Belgium Pt 1.77 −0.64
1962:1-2001:1 ∆Yt −428.29 −428.92
∆Pt −279.92 −264.02
Yt −68.14 −0.20
Denmark Pt −1.53 −2.12
1974:1-2001:1 ∆Yt −363.83 −364.25
∆Pt −290.30 −268.51
Yt −85.09 −16.57
Finland Pt −8.29 −1.60
1990:1-2001:2 ∆Yt −134.60 −134.83
∆Pt −109.69 −108.01
Yt −259.22 −46.27
France Pt −2.18 −0.64
1962:1-2001:1 ∆Yt −474.95 −474.96
∆Pt −170.21 −145.30
Yt −65.35 −9.61
Germany Pt −0.59 −0.26
1962:1-1994:12 ∆Yt −263.90 −264.01
∆Pt −268.13 −267.11
Notes: The Phillips-Perron Zρ statistics are corrected for fourth-order se-
rial correlation. The results are qualitatively similar to those obtained when
considering augmented Dickey-Fuller tests, or when considering alternative
orders of the serial correlation correction in computing Phillips-Perron statis-
tics. For a sample size of 500 observations, the critical values for the Phillips-
Perron Zρ test are: with trend: 10%, -18.1; 5%, -21.5; 1%, -28.9; without
trend: 10%, -11.2; 5%, -14.0; 1%, -20.5. A table displaying the critical values
for the Phillips-Perron Zρ test is reported in Fuller (1976, p. 371).
8Table 1. Phillips-Perron Zρ tests (continued)
Country-Period Variable With Trend Without Trend
Yt −12.79 −5.48
Greece Pt −3.66 0.36
1962:1-2000:11 ∆Yt −490.93 −492.25
∆Pt −366.06 −364.76
Yt −4.93 −1.54
Ireland Pt −2.59 −2.57
1975:3-2000:4 ∆Yt −154.33 −158.73
∆Pt −71.53 −29.46
Yt −448.25 −113.07
Italy Pt 1.18 −0.35
1962:1-2001:1 ∆Yt −561.28 −561.29
∆Pt −117.74 −113.27
Yt −261.29 −28.99
Luxembourg Pt 1.24 −0.49
1962:1-2000:12 ∆Yt −494.79 −494.80
∆Pt −465.23 −459.26
Yt −65.32 −12.97
Netherlands Pt 0.40 −1.08
1962:1-2000:12 ∆Yt −379.60 −379.66
∆Pt −453.46 −455.25
Yt −232.31 −5.11
Portuguese Pt 0.51 −0.21
1962:1-2001:1 ∆Yt −535.75 −535.84
∆Pt −389.02 −388.64
9Table 1. Phillips-Perron Zρ tests (continued)
Country-Period Variable With Trend Without Trend
Yt −373.03 −110.17
Spain Pt 2.01 −0.61
1962:1-2001:1 ∆Yt −563.11 −563.15
∆Pt −535.85 −529.74
Yt −13.70 −1.75
Sweden Pt 2.81 −0.48
1975:3-2000:4 ∆Yt −553.55 −553.58
∆Pt −469.66 −465.54
Yt −231.21 −20.31
United Kingdom Pt 1.42 −0.49
1962:1-2001:1 ∆Yt −388.58 −388.58
∆Pt −276.09 −267.66
10Table 2. Characteristics of the estimated bivariate VAR’s
Country Sample Unit Root No. Lags Linear Quadratic
Period for Output Trend Trend
Austria 1962:1-2001:1 No 24 Yes Yes
Belgium 1962:1-2000:12 No 27 Yes No
Denmark 1974:1-2001:1 No 25 Yes Yes
Finland 1990:1-2001:2 No 27 Yes Yes
France 1962:1-2001:1 No 24 Yes Yes
Germany 1962:1-1994:12 No 26 Yes No
Greece 1962:1-2000:11 Yes 27 Yes No
Ireland 1975:3-2000:4 Yes 26 Yes No
Italy 1962:1-2001:1 No 25 Yes Yes
Luxembourg 1962:1-2000:12 No 28 Yes Yes
Netherlands 1962:1-2000:12 No 25 Yes Yes
Portugal 1962:1-2001:1 No 27 Yes Yes
Spain 1962:1-2001:1 No 25 Yes Yes
Sweden 1962:1-2001:1 Yes 12 Yes No
UK 1962:1-2001:1 No 28 Yes Yes
U.S.A 1960:2-1997:6 Yes 7 Yes No
11Table 3. Summary of the results
Output vs Inﬂation Output vs Prices
Horizons Horizons
C o u n t r y u pt o6 f r o m6t o2 8 up to 6 from 6 to 28
Austria No No No Negative
Belgium Positive Positive No Negative
Denmark No No No No
Finland Positive Positive No No
France Positive Positive Positive Negative
Germany Positive Positive No Negative
Greece No No No Negative
Ireland No No No No
Italy Positive Positive Positive Negative
Luxembourg No No No Negative
Netherlands No Positive No No
Portugal No No Positive No
Spain No No No Negative
Sweden No Negative No Negative
UK No Positive No Negative
U.S.A Positive No Positive Negative
Notes: the word “Positive” (“Negative”) means that the correlation between
t h et w ov a r i a b l e si ss i g n i ﬁcantly positive at a standard conﬁdence level. “No”
means that the correlation is not signiﬁcant. Horizons are measured in quar-
ters.
12Figure 1:
13Figure 2:
14Figure 3:
15Figure 4:
16FI US G BE FR
0
IT NE UK LU AU DE SW SP PO GR IR
π σ
0
BE NE LU GR PO SW DE LU IR SP UK G FI FR IT US
π σ π / ) ( E
Figure 5: Ranking of countries according to two measures of inﬂation volatil-
ity
17

Are Phillips curves useful for forecasting inﬂation?,” Federal Reserve Bank of

Business cycles: real facts and a monetary myth,” Federal Reserve Bank of

The comovement between output and prices in the EU15 countries: An empirical investigation,” Universidad del País Vasco,

The comovement between output and prices,”

The comovement between real activity and prices

The inexorable and mysterious trade-oﬀ between inﬂation and unemployment,”

Is there a Phillips Curve in the US and the EU15 Countries? An empirical investigation

https://addi.ehu.es/bitstream/10810/6808/1/wp2002-32.pdf

Is there a Phillips Curve in the US and the EU15 Countries? An empirical investigation

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