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Friedman-Ball Hypothesis for Inflation Revisited:
Evidence from some OECD Countries
Kushal Banik Chowdhury
Economic Research Unit
Indian Statistical Institute, Kolkata
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In his key note address, Friedman (1977) blames bad economic
policies for large and inefficient fluctuations. He argues that when
inflation is low, policymakers try to keep it low. To the extent they
are successful, inflation remains low and stable. However, when it is
high, policymakers are more likely to adopt disinflationary policies.
These policies suffer from some serious problems such as the
problem of choosing the inside lag (i.e., the time gap between a
shock to the economy and the policy action responding to that
shock) and outside lag (indicating the time between a policy action
and its influence on the economy) and as a result, uncertainty about
future inflation rises, and consequently the economy gets affected
more.
FRIEDMANS HYPOTHESIS
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Ball (1992) has formalised Friedmans hypothesis by
introducing a game theoretic framework between public and
policy makers about their response to high inflationary situation.
There exists a positive relationship between inflation and inflation
uncertainty, i.e., when inflation increases, inflation uncertainty
also increases.
This hypothesis has given rise to many empirical studies examining
the link between inflation and inflation uncertainty.
Outcome of Friedman-Ball hypothesis
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After the introduction of autoregressive conditional
heteroskedasticty (ARCH) and generalised ARCH (GARCH)
model by Engle (1982) and Bollerslev (1986), respectively
several studies use it as a measure of inflation uncertainty thatunderpin the dynamic nexus between inflation and inflation
uncertainty.
,
where stands for the rate of inflation and for its
conditional variance.
Measure of uncertainty
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With an ARCH process, Engle (1982) found a weak evidence to
support Friedmans hypothesis. Bollerslev (1986) who has
generalised the ARCH, called the GARCH process, also found
that his analysis does not support the Friedman-Ball hypothesis.
This evidence is also same in Cosimano and Jansen (1988) study.
Important empirical results
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In their study, Evans and Watchtel (1993) have emphasized on
the consequences of regime switching behaviour of inflation in
dealing with inflation uncertainty. They also claimed that the
resultant model will seriously underestimate both the degree ofuncertainty and its impact if one neglects this regime switching
feature of inflation. One serious limitation with the (symmetric)
GARCH model is that it does not incorporate the possibility of
structural instability due to regime changes.
Criticism of the above studies
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Further, Brunner and Hess (1993) have pointed out a reason
behind the failure of finding any support to the above
hypothesis. According to them, for testing Friedman-Balls
hypothesis directly, conditional variance should be a function of
lagged inflation.
Subsequently, with the advancement of exponential GARCH
(EGARCH) model of Nelson (1991), threshold GARCH
(TGARCH) model of Glosten et al. (1993), recent studies have
used these variants of GARCH model to allow asymmetries in
the conditional variance.
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Following Brunner and Hess (1993) and Fountas et al. (2000), the
conditional variance specification of inflation is assumed to explicitly
include a lag inflation term. With the conditional mean specification being
an AR(k) model, the model, designated as AR(k)-GARCH(1,1) L(1) for
describing inflation, consists of the following specifications for the
conditional mean and conditional variance.
,
where stands for the (rate of) inflation at time t, the conditional
variance at t and k the optimal lag order in the conditional mean
specification. Here the coefficient depicts the link between inflation
uncertainty and inflation.
Econometr ic models
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AR(k)-TGARCH(1,1) L(1)
A Threshold GARCH (TGARCH) model where the lag inflation is
included in the conditional variance equation can be written as
follows.
whereI[.] is an indicator function.
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1.
Now, we raise a question, namely that, if a regime switching
behaviour or asymmetry is allowed in the conditional variance
specification, then why should it be only reflected in the
coefficient of lag squared error term (as in the case of EGARCH
and TGARCH model), and why not in the other parameters,
especially the coefficient which captures the link between
inflation and uncertainty. As argued by Friedman (1977), Ball
(1992), Ungar and Zilberfarb (1993), Brunner and Hess (1993)
and Baillie et al. (1996) that for the high inflationary period
there is a significant positive link between inflation and its
uncertainty, whereas it does not exist for the low inflationary
SOME IMPORTANT QUESTIONS
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period. Keeping this in mind, it is quite obvious to attach regime
specific behaviour to the coefficients which captures the link.
2.Subsequently, another question arises, how high (low) is a high
(low) inflation rate? In other words, does a threshold level of
inflation exist? Thus from the policy perspective, it is quite
important for the policymakers to know the threshold level of
inflation rate above which significant increase in uncertainty
may occur.
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To address these two questions in our framework of analysis we have adoptedasymmetric nonlinear smooth transition ARCH (ANSTARCH) model, as
proposed by Anderson et al. (1999) and Nam et al. (2002). We have extended it
to allow for the inclusion of lag inflation as an exogenous regressor in the
conditional variance equation.
,
PROPOSED MODELS
AR(k)-ANSTGARCH(1,1)-L(1)
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,
Here comprises the coefficients of both
conditional mean and conditional variance specifications for the th regime
where stands for , denoting the low and high inflation regimes,
respectively. Apart from the usual GARCH coefficients, and describe the
link between inflation uncertainty and inflation in the two regimes, respectively.
STAR(k)-ANSTGARCH(1,1)-L(1)
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The regimes are governed by the transition function .
A popular choice for the transition function is the logistic
function which is defined as
where is a threshold variable corresponding to a threshold
value.
We have used a lag inflation term, , as our thresholdvariable, and accordingly the regimes are defined as the lag
inflation is greater or smaller than an unknown threshold level
of inflation. Thus, in the transition equation we replace by
as a probable candidate for the threshold variable.
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In this empirical study, we have considered monthly time series on
consumer price index from January 1960 to December 2009 for 13
different OECD (Organisation for Economic Co-operation and
Development) countries viz., Canada, France, Germany, I taly, Japan,
the U.K., the U.S.A., Austr ia, Belgium, F in land, Greece, Luxembourg
and Spain. All the time series have been downloaded from the official
website of Federal Reserve Bank of St. Louis. The time series of
inflation, denoted as , has been obtained as
where is the seasonally adjusted consumer price index of a particular
country.
Empirical analysis
Data
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Country
Estimate
Canada France Germany Italy Japan The U.K. The U.S.A.
Conditional variance parameters
0.014* 0.033* 0.015* 0.000*** 0.005 0.005** 0.001
0.191* 0.172* 0.458* 0.150* 0.104** 0.405* 0.102*
0.665* 0.000 0.324* 0.848* 0.867* 0.647* 0.897*
0.016 -0.001 0.026*** 0.000 -0.004 0.002 0.001
Autocorrelation in standardized residuals
Q(1) 0.781 0.137 0.040 0.486 0.013 1.124 0.047
Q(10) 1.836 3.355 1.071 1.894 1.607 8.732 4.119
Autocorrelation in squared standardized residualsQ (1) 0.060 1.425 0.379 1.802 0.323 0.013 3.450
Q2(5) 1.206 2.173 2.442 2.159 2.303 3.037 6.333
Q2(10) 3.228 2.780 4.797 7.203 3.020 5.021 9.879
[*, ** and *** indicate significance at 1%, 5% and 10% levels of significance, respectively.]
Parameter estimate and results of residual diagnostic tests for the AR(k)-
GARCH(1,1)L(1) model
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Country
Austria Belgium Finland Greece Luxembourg Spain
Conditional variance parameters
0.004* 0.007* 0.008* 0.002 0.005* 0.018*
0.197* 0.045 0.224* 0.089** 0.151* 0.764*
0.766* 0.845* 0.750* 0.910* 0.807* 0.381*
0.005 0.021* 0.012 0.003 0.002 0.044*
Autocorrelation in standardized residuals
Q(1) 2.012 0.057 0.000 0.005 0.010 0.097
Q(5) 2.692 1.594 1.840 0.640 0.812 3.418
Q(10) 6.044 2.698 3.324 1.587 2.139 4.992
Autocorrelation in squared standardized residuals
Q2(1) 6.285** 0.179 0.719 3.360 1.990 0.019
Q (5) 8.618 1.922 3.294 4.355 6.904 1.879
Q2(10) 12.252 11.187 15.601 7.679 11.841** 3.279
[*, ** and *** indicate significance at 1%, 5% and 10% levels of significance, respectively.]
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The finding of no such significant relationship between inflation uncertainty and
inflation for the remaining ten countries may be due to the consideration of
single regime in the modelling of inflation and inflation uncertainty which may
mask potentially different realizations due to the regime shift of inflation,
especially because the span of the data set is quite large.
Comment
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We first test for our assumption of nonlinearity based on own
transition effect as captured by . To that end, we use Lagrange
multiplier (LM) test statistic as developed by Luukkonen et al. (1988),
to test linearity against nonlinearity as represented by STAR model.
Test for nonlinearity (AR Vs STAR)
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LM test statistic values
Country Test statistic value
Canada 48.27***
France 84.82*
Germany 50.11**
Italy 133.23*
Japan 91.66*
The U.K. 70.28*
The U.S.A. 90.03*
Austria 227.67*
Belgium 62.34*
Finland 28.04***
Greece 97.86*
Luxembourg 69.60***
Spain 147.83*
[*, ** and *** indicate significance at 1%, 5% and 10% levels of significance, respectively.]
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Country
Estimate
Canada France Germany Italy Japan The U.K. The U.S.A.
Conditional variance parameters in the first regime
0.037** 0.027* 0.011* 0.000 0.010 0.002 0.000
0.559* 0.778* 0.636* 0.000 0.063 0.545* 0.050***
0.221 0.000 0.380* 0.973* 0.459* 0.677* 0.914*
0.047 0.070* 0.020 -0.002 -0.185** -0.005 -0.012**
Conditional variance parameters in the second regime
0.005 0.034 0.000 0.005 0.000 0.000 0.022**
0.000 0.303** 0.000 0.491* 0.142 0.000 0.000
0.657* 0.000 0.000 0.215 1.035* 0.873* 1.145*
0.099** -0.082 0.211* 0.029 -0.010 0.048*** -0.046
Smooth transition parameters
3.3410 16.38 6.5310 3.84 29.75 62.13 8.99
0.015 0.216* 0.185** 0.533* 0.056** 0.077* 0.273*
[*, ** and *** indicate significance at 1%, 5% and 10% levels of significance, respectively.]
Parameter estimate and results of residual diagnostic tests for the STAR(k)-
GARCH(1,1)L(1) model
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Country Austria Belgium Finland Greece Luxembourg Spain
Conditional variance parameters in the first regime
0.010* 0.036* 0.010 0.000 0.028* 0.011*
0.630* 0.584* 0.283** 0.046 0.122 0.841*
0.472* 0.000 0.786* 0.898* 0.035 0.409*
0.030 0.067** 0.030 -0.064*** -0.231* 0.025**
Conditional variance parameters in the second regime
0.000 0.087* 0.000 0.005 0.056* 0.000
0.245* 0.000 0.000 0.000 0.000 0.059
0.561** 0.000 0.654* 0.884* 0.000 0.000
0.027 0.007 0.149* 0.115** 0.115** 0.311*
Smooth transition parameters
8.77105 2.2410
17 1.0710
6 3.34 5.8710
18 29.61
0.255* 0.098 0.012*** 0.000 0.057*** 0.541*
[*, ** and *** indicate significance at 1%, 5% and 10% levels of significance, respectively.]
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Lastly, we make a statistical comparison between AR(k)-GARCH(1,1)-L(1)
model which may be taken as a benchmark model and the proposed STAR( k)-ANSTGARCH(1,1)L(1) model by means of likelihood ratio (LR) test.
Country Model I
versusModel II
Canada 31.32**France 63.62*Germany 45.4*
Italy 38.9*Japan 20.52
The U.K. 56.58*
The U.S.A. 48.98*Austria 51.14*Belgium 25.56Finland 15.24
Greece 24.98Luxembourg 24.36***
Spain 85.54*[Model I: AR(k)-GARCH(1,1)L(1) and Model II: STAR(k)-ANSTGARCH(1,1)L(1). *, ** and *** indicate
significance at 1%, 5% and 10% levels of significance, respectively.]
Likelihood Ratio test (AR(k)-GARCH(1,1)-L(1) Vs STAR(k)-
ANSTGARCH(1,1)L(1)STAR))
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The paper has revisited this hypothesis by proposing a new
model, called STAR(k)-ANSTGARCH(1,1)L(1) where the
conditional mean as well as the conditional variance for
inflation are based on consideration of two regimes for inflation
below and above a certain level of inflation- and which is
determined endogenously.
There exists a threshold level of inflation in case of 10 out of 13
countries considered. This means that the control of inflation
would crucially depend on this threshold level of inflation which
is estimated endogenously.
Concluding Remarks
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The parameter capturing the effect of inflation on inflation
uncertainty in the specification of conditional variance clearly
shows that this coefficient is different in the two inflation
regimes. It is observed from the results that the Friedman-Ball
hypothesis holds for six countries viz., Canada, Germany, the
U.K., Finland, Greece and Luxembourg in the high-inflation
regime, two countries (France and Belgium) in the low-inflation
regime and one country (Spain) in both the regimes.
The improvement in terms of maximized log likelihood value is
significant for the proposed model as compared to the
benchmark AR(k)-GARCH(1,1)L(1) model for 9 out of 13
countries.
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