delhi seminar

8/11/2019 Delhi Seminar

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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



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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*



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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*


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*



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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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THANK YOU

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