The antiPhillips curve
ABSTRACT In April 2009, we introduced a model representing the evolution of motor fuel price (a subcategory of the consumer price index of transportation) relative to the overall CPI as a linear function of time. Under our framework, all price deviations from the linear trend are transient and the price must promptly return to the trend. Specifically, the model predicted that “the price for motor fuel in the US will also grow by 50% by the end of 2009. Oil price is expected to rise by ~50% as well, from its current value of ~$50 per barrel.” The behavior of actual price has shown that this prediction is accurate in both amplitude and trajectory shape. Hence, one can conclude that the concept of price decomposition into a shortterm (oscillating) and longterm (linear trend) components is valid. According to the model, the price of motor fuel and crude oil will be falling to the level of $30 per barrel during the next 5 to 8 years.
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 SourceAvailable from: minneapolisfed.org[Show abstract] [Hide abstract]
ABSTRACT: This study evaluates the conventional wisdom that modern Phillips curvebased models are useful tools for forecasting inflation. These models are based on the nonaccelerating inflation rate of unemployment (the NAIRU). The study compares the accuracy, over the last 15 years, of three sets of inflation forecasts from NAIRU models to the naive forecast that at any date inflation will be the same over the next year as it has been over the last year. The conventional wisdom is wrong; none of the NAIRU forecasts is more accurate than the naive forecast. The likelihood of accurately predicting a change in the inflation rate from these three forecasts is no better than the likelihood of accurately predicting a change based on a coin flip. The forecasts include those from a textbook NAIRU model, those from two models similar to Stock and Watson's, and those produced by the Federal Reserve Board.Quarterly Review. 02/2001;  SourceAvailable from: Ivan Kitov[Show abstract] [Hide abstract]
ABSTRACT: In April 2009, we introduced a model representing the evolution of motor fuel price (a subcategory of the consumer price index of transportation) relative to the overall CPI as a linear function of time. Under our framework, all price deviations from the linear trend are transient and the price must promptly return to the trend. Specifically, the model predicted that “the price for motor fuel in the US will also grow by 50% by the end of 2009. Oil price is expected to rise by ~50% as well, from its current value of ~$50 per barrel.” The behavior of actual price has shown that this prediction is accurate in both amplitude and trajectory shape. Hence, one can conclude that the concept of price decomposition into a shortterm (oscillating) and longterm (linear trend) components is valid. According to the model, the price of motor fuel and crude oil will be falling to the level of $30 per barrel during the next 5 to 8 years.SSRN Electronic Journal 01/2007;
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Electronic copy available at: http://ssrn.com/abstract=1349707
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The antiPhillips curve
Ivan O. Kitov
Institute for the Geospheres’ Dynamics, Russian Academy of Sciences, ikitov@mail.ru
Abstract
There is no Phillips curve in the United States, i.e. unemployment does not drive inflation at any time horizon. There
is a statistically robust antiPhillips curve  inflation leads unemployment by 10 quarters. Apparently, the anti
Phillips curve would be the conventional one, if the time would flow in the opposite direction. Several tests for
cointegration do not reject the hypothesis that there exist a longterm equilibrium relation between inflation and
unemployment in the US.
The cointegrating relation between inflation and unemployment is not the proof of causality, however, and
both variables are driven by the same external force. Also presented are some statistical evidences that there exist
conventional Phillips curves in Germany and France, but there is no causality link between unemployment and
inflation as well.
Key words: the Phillips curve, inflation, unemployment, causality
JEL classification: E24, E31, E52, E58
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Electronic copy available at: http://ssrn.com/abstract=1349707
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Introduction
The Phillips curve is a fundamental axiom of the mainstream economics that links inflation to
unemployment. In some modern models, like the new Keynesian Phillips curves, other measures
of economic activity may be used instead of unemployment. The process behind the curve is so
crystal clear from the point of view of common wisdom, as introduced by A.W. Phillips (1958)
and elaborated by several generations of economists, that it has been easily accepted by major
schools of economic thought. Even central banks of the most advanced and richest countries do
not hesitate to use the Phillips curve in the prediction of price growth for purposes of inflation
targeting, which is the Holy Grail of monetary policy (Kohn, 2008). The only problem is left for
both theorists and practitioners – the Phillips curve does not work (Atkeson and Ohanian, 2001).
Essentially, even the simplest approach “tomorrow as today” gives better of comparable
predictions when the most elaborated model based on the Phillips curve (Stock and Watson,
2008). At best, the input of from unemployment or any other measures of economic activity in
the prediction of inflation at time horizons of one to two years is between 10 and 15 percent
(Piger and Rasche, 2006). The residual 85 to 90 percent is explained by autoregressive properties
of inflation itself. In other words, the accuracy of inflation prediction depends critically on the
predominant frequency in its spectrum. At time horizons sufficiently larger than the predominant
period, one should not observe any sound prediction.
There are two possible explanations of the absence of reliable correlation between
inflation and unemployment in the United States. One is banal – there is no link at all. Second
explanation is a more productive one – both variables are driven by some external force. The
failure of the Phillips curve is caused by the difference in time lags of inflation and
unemployment behind this driving force. We have found that in such developed countries as the
United States, Japan, Germany, France, Canada, and Austria this force is the change in the level
of labor force (Kitov, 2006ab, 2007ad; Kitov, Kitov, and Dolinskaya, 2007ab, 2008). In the US,
the lag of inflation behind the change in labor force is 2.5 years, and the lag of unemployment is
5 years. Accordingly, the inflation leads the unemployment by 30 months. One can formulate
such order in time as an antiPhillips curve. Due to the time lag, the unemployment could be by
mistake considered as a consequence of the inflation. This strict sequence in time is not
causality, however. The cause for both variables is of the same origin, but the
inflation/unemployment sequence varies between countries.
The main objective of this paper is to reveal the existence of an antiPhillips curve in the
United States and to estimate its statistical properties, including the conduction of appropriate
tests for cointegration. It is also important to demonstrate that the presence of a cointegrating
relation between inflation and unemployment is not the proof of causality and both variables are
driven by the same external force. In support to this conclusion, we present some statistical
evidences that there exist conventional Phillips curves in such developed countries Germany and
France.
The antiPhillips curve
We start with plotting of quarterly readings of inflation and unemployment, as measured by the
US Bureau of Labor Statistics (http://www.bls.gov/data/) and the Bureau of Economic Analysis
(http://bea.gov/national/nipaweb/), respectively. Straight away, Figure 1 reveals the existence of
the antiPhillips curve. In order to highlight the lead of inflation, represented by GDP deflator
(DGDP), ahead of unemployment (UE), the latter is scaled, displaced, and shifted by 2.5 years
(t+2.5) or 10 quarters back relative to its true time:
DGDP(t) = 1.444*UE(t+2.5)  0.0488 (1)
Both the slope and free term in (1) are determined by visual fit only, but with keeping the
average residual very close to 0. Overall, we tried matching the amplitude and timing of the
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highest peaks in 1973 and 1980 by the trailanderror method, with the emphasis on the latter
one. The consideration behind this approach is obvious – to obtain the best results one should
always fit the measurements with the highest signaltonoise ratio.
Effectively, the unemployment lags behind the GDP deflator by 2.5 years. The mean
difference between the observed and predicted inflation is 8.3E5 for the period from 1960Q1 to
2006Q2: one can use the reading of inflation only 10 quarters back from 2008Q4 (the last
reading currently available). The antiPhillips curve in its scatterplot form is displayed in Figure
2 (left panel). The goodnessoffit is 0.49 and the slope of the linear regression curve is 0.42.
Due to the presence of random (measurement) errors in both independent and dependent
variable, the slope is underestimated relative to that in Figure 1: 1/1.444=0.69.
0.05
0
1940
0.05
0.1
0.15
0.2
1960 19802000
2020
calendar year
inflation rate
1.444*UE(t+2.5)  0.049
DGDP
Figure 1. GDP deflator (DGDP) vs. scaled and lagged unemployment (UE) in the United States between
1950Q1 and 2006Q2. The DGDP and unemployment time series are represented by quarterly readings
(226 in total). The scaled unemployment is shifted by 2.5 years ahead (10 quarters), i.e. actual readings
start from 1952Q3.
y = 0.4219x + 0.0426
R2 = 0.4777
0
0.05
0.1
0.15
0 0.05 0.10.15
DGDP
UE(t+2.5)
2
1.5
1
0.5
0
1960
0.5
1
1970 1980199020002010
calendar year
{DGDP [1.444*UE(t+2.5) 0.049)]}/DGDP
Figure 2. Left panel: scatter plot: the DGDP vs. unemployment for the years between 1960Q1 and
2006Q2. The slope obtained by linear regression is slightly underestimated: 0.42 instead of 1/1.444=0.69,
as related to the uncertainty of the DGDP and unemployment estimates. This scatter plot is a textbook
example of the antiPhillips curve. Right panel: the residual of the observed and predicted DGDP
normalized to DGDP between 1968Q1 and 2006Q2. The average relative residual is 0.11 with standard
deviation of 0.5. The scatter is higher in the 1990s and 2000s supporting the conclusion by Stock and
Watson (2007) that inflation is getting harder to predict.
An important characteristic of the overall consistency is the residual of the observed and
predicted DGDP. The right panel of Figure 2 depicts this residual as normalized to the DGDP
between 1968Q1 and 2006Q2. Such normalization allows a different view on the residual as
related to the ratio of signal and noise. When amplitude of a signal is high relative to that of
noise, one can expect lower relative residuals because the input of the noise is negligible. When
the noise is of the amplitude of the signal, one should observe a higher scattering in the residual
due to partly stochastic character of the noise. The average residual in Figure 2 (right panel) is 
0.11 with standard deviation of 0.5. The scatter is higher in the 1990s and 2000s supporting the
conclusion of Stock and Watson (2007) that inflation is getting harder to predict. The cause is
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likely related to the constant level of absolute error in the measurements of inflation and
unemployment and, thus, objective.
The goodnessoffit is relatively low, however. The high scatter in Figure 2 is directly
mapped into large rootmeansquare forecasting error (RMSFE), as presented in Table 1 for the
empirical antiPhillips curve. In normal situation, the DGDP would be used to predict the UE,
but since we follow the conventional economic concept and the reversed time direction, i.e. the
antiPhillips curve, we predict the DGDP using future readings of the UE. Therefore, we obtain
a pseudo outofsample forecast, i.e. the forecast when “…, one simulates standing at a given
date and performing all model specification and parameter estimation using only the data
available at that date, then computing the h period ahead forecast” (Stock and Watson, 2008), but
from the future into the past. Otherwise, it is a standard pseudo outofsample forecast. (When
forecasting the UE using the DGDP, one is fully complying with the definition of pseudo outof
sample forecast.)
Table 1. Comparison of the RMSFE obtained in this study to those reported by Stock and Watson (2008)
for the same periods. Time horizons are 2.5 and 1 year, respectively. RMSFE for the DGDP MA(5) has a
time horizon of 2 years.
Length,
quarters antiPhillips
1960Q11967Q4 32 2.04
1968Q11976Q4 36 2.54
1977Q11984Q4 32 1.81
1985Q11992Q4 32 1.56
1993Q12000Q4 32 1.00
2001Q12006Q2 22 1.35
The unobserved componentstochastic volatility (UCSV) model developed by Stock and
Watson (2007) has a somewhat smaller RMSFE at a one year horizon than our model at a 2.5
year horizon. Stock and Watson (2008) have split the period between 1960 and 2007 into several
segments (see Table 1) in order to investigate the change in relative performance of various
models over time. For the most recent periods, RMSFE was 0.41% and 0.57%. Our model
provides 1% and 1.35%, respectively.
One of possible reasons for the scatter and larger RMSFEs consists in a higher
measurement noise associated with quarterly measurements. The DGDP is prone to continuous
revisions by the Bureau of Economic Analysis. The unemployment is measured in the Current
Population Surveys covering only 60,000 households. Both variables suffered numerous changes
in definitions over the past 60 years, which sometimes make them incompatible through time.
Therefore, the overall fit between the DGDP and UE should not be too high and one needs to use
some additional tools to suppress the measurement noise.
Moving average is a wellknow tool to reduce the influence of highfrequency noise. We
have applied a fivequarter (centered) moving window (MA(5)) to smooth the DGDP time
series. As a result, the horizon of pseudo outofsample forecast is now 8 quarters, or 2 years.
The prediction error has been sufficiently reduced, however, especially in the past 25 years,
when the measurement noise was the highest in relative terms. The RMSFE at a twoyear
horizon is only 0.72% between 1993 and 2000 compared to 0.41% for the UCSV model at a
oneyear horizon. At this stage, no autoregressive properties of both time series have been used
yet. This is the pure statistical link between the DGDP and UE.
The antiPhillips curve is not designated to kill the conventional Phillips curve, but to be
used for the prediction of the rate of unemployment in the United States using inflation. Figure 3
illustrates this possibility. Since the 1980s the DGDP and UE have been moving synchronously
(with 10 quarter shift) and the next move in the unemployment in the US should be down, from
the height it climbed in the end of 2008 and the beginning of 2009. Accurate prediction of such a
Period
RMSFE, % RMSFE, %
MA(5) DGDPUE
2.00
2.68
1.80
1.05
0.72
1.23
RMSFE, %
SW UCSV
0.72
1.76
1.28
0.70
0.41
0.57
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sudden and deep fall would be a good validation for relationship (1). This event should happen
because both variables are driven by the change in labor force (Kitov, 2006ab; Kitov, Kitov, and
Dolinskaya, 2007b).
We have also tested the link between the GDP deflator and unemployment for the
presence of cointegration relation. First, we used the difference of the measured and predicted
DGDP between 1960Q1 and 2006Q2 (186 readings) obtained by visual fit as a proxy to the
residual of corresponding linear regression. The augmented DickeyFuller test for unit root with
lags up to 4 gave test statistics of 3.64 with the 1% critical value of 3.48. At this level of
confidence, one can reject the hypothesis of the presence of unit root in the difference. The
PhillipsPerron unit root tests resulted in z(ρ)=54.0 (1% critical value 13.4) and z(t)=5.6 (1%
critical value 2.6). Therefore, both tests demonstrate that the difference between the observed
and predicted DGDP is an I(0) process and the variables are likely to be cointegrated.
0.05
0
1970
0.05
0.1
0.15
19801990 20002010
2020
calendar year
inflation rate
1.444*UE(t+2.5)  0.049
DGDP
Figure 3. Comparison of the DGDP and scaled unemployment in the United States between 1975Q1 and
2008Q4. A sudden and deep drop in the UE is expected in 20092010.
The Johansen (1988) approach allows both the test for cointegration and the
determination of its rank. With the maximum lag included in the underlying VAR model of 1
and trend specification “rconstant” we have obtained the eigenvalue of 0.15 and rank 1.
Corresponding statistics is as follows: trace statistics 6.4 (1% critical value 13.0, 5% critical
value 9.2), SBIC=13.39 and HQIC=13.4 – both maximum at rank 1. Hence, one cannot reject
the hypothesis that there exist a cointegrating relation between the DGDP and unemployment. In
other words, there exists a longterm equilibrium relation between these two variables with the
DGDP leading the unemployment by 10 quarters, and the linear regression shown in Figure 2 is
valid.
All in all, the antiPhillips curve revealed for the United States practically prohibits
predicting inflation by using unemployment. On the contrary, the existence of a cointegrating
relation allows improving the prediction of unemployment using its own autoregressive
properties and those of inflation. The best VECM with the largest lag of one quarter predicts the
rate of unemployment with RMSFE of 0.6 percent at 10 quarters horizon. The VAR provides
R2=0.84 and RMSFE also of 0.6 percent at the same horizon. Therefore, the antiPhillips curve
is much more practical than its counterpart.
The antiPhillips curve is a specific feature of the US economy, however. Other countries
demonstrate rather the presence of conventional Phillips curves. Figure 4 illustrates the link
between inflation (DGDP) and unemployment in Germany, where the former variable lags
behind the latter one by one year. Correspondingly, the slope obtained by linear regression is
negative. The relation obtained by visual fit is as follows:
UE(t+1) = 1.477*DGDP(t) + 0.1147
for the years between 1971 and 2008. Linear regression gives a slope of 1.50 with R2=0.86.
Therefore the Phillips curve in Germany is a reliable relationship between inflation and
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unemployment. Both are driven by the same external force – the change in labor force level
(Kitov, 2007c).
0
1960
0.04
0.08
0.12
0.16
19701980
calendar year
1990 20002010
rate
UE(t1) NAC
1.477*DGDP(t)+0.1147
y = 1.5044x + 0.1163
R2 = 0.8631
0
0.02
0.04
0.08
0.12
0.16
0 0.020.040.06 0.08
DGDP
UE(t1)
Figure 4. The antiPhillips curve in Germany is a conventional Phillips curve with inflation lagged behind
unemployment by one year.
In France, the Phillips curve existed before the Banque de France introduced a new
monetary policy restricting the emission of money (Kitov, 2007d; Kitov, Kitov, and Dolinskaya,
2007a). Figure 5 displays the observed DGDP annual time series and that predicted from
unemployment. The latter time series was obtained by the following relationship:
DGDP(t) = 1.3*UE(t4) + 0.155
i.e. the inflation lags the unemployment by four (!) years. The goodnessof fit as obtained from
linear regression, shown in Figure 5 (right panel), is 0.89 for the years between 1971 (the start of
the DGDP measurements) and 2007. The Phillips curve was a statistically reliable link between
unemployment and inflation; both are driven by the change in labor force level (dLF/LF), as
Figure 6 demonstrates. The change in labor force also leads inflation by four years, and thus is
contemporary with the unemployment. The agreement between the observed and predicted
curves is characterized by R2>0.9.
0.05
0.00
0.05
0.10
0.15
1965 19751985 19952005
calendar year
inflation
DGDP
1.3*UE(t4) + 0.155
y = 0.7213x + 0.117
R2 = 0.8905
0.00
0.07
0.13
0.050.00 0.05
DGDP
0.10 0.15
UE(t4)
Figure 5. The antiPhillips curve in France is a conventional Phillips curve with inflation lagged behind
unemployment by four years.
The slope of the regression line in Figure 5 is negative. Similar result was obtained for
Germany. In both countries, any decrease in unemployment indicates a delayed increase in
inflation, and vice versa. The French and German central banks should be very careful in
formulating a sound monetary policy. Our analysis demonstrates that inflation does no harm in
terms of real economic growth (Kitov, Kitov, and Dolinskaya, 2008), but high unemployment
directly affects the sustainability of social development.
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0.05
0.00
0.05
0.10
0.15
0.20
1965 19751985 1995 2005
calendar year
inflation
DGDP
4*dLF(t4)/LF(t4)UE(t4)+0.099
Figure 6. The link between the change in labor force level (dLF/LF), unemployment, and inflation in
France (Kitov, 2007d).
Conclusion
In addition to the US, Germany and France we have analyzed the link between the change in
labor force, unemployment and inflation in Japan (Kitov, 2007a), Canada (Kitov, 2007b), and
Austria (Kitov, 2007d). All these countries and other biggest developed countries (working
papers in preparation) demonstrate the presence of similar linear lagged relationships. In several
countries, the conventional Phillips curves are observed, but some central banks destroy the
statistical link between unemployment and inflation by monetary policy similar to that
introduced by the European central bank. All in all, the antiPhillips curve found in the United
States is just a funny peculiarity, not a fundamental bound. The Phillips curve has the same
nature.
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