HIGH AND VARIABLE INFLATION: FURTHER EVIDENCE ON THE FRIEDMAN HYPOTHESIS

HIGH AND VARIABLE INFLATION: FURTHER EVIDENCE

ON THE FRIEDMAN HYPOTHESIS

john thornton*†

AbstractThis note, employing a GARCH model, finds a positive and significant relationship between thelevel and variability of inflation in South Africa in the period 1957:1-2005:9. This providesevidence in support of Friedman’s hypothesis that high inflation leads to more variable inflation.JEL Classification: C22, E31Keywords: Inflation, inflation uncertainty, conditional variance

1. INTRODUCTION

In a seminal paper, Friedman (1977) argued that increased variability of (or uncertaintyabout) inflation distorts relative prices and adds an additional risk to long termcontracting. In addition, he asserted that high levels of inflation are costly since they raiseinflation variability. This Friedman hypothesis has given rise to a host of empirical studiesexamining the link between inflation and inflation uncertainty. A review of the manyearly studies on the issue by Davis and Kanago (2000) highlights the mixed results, partlyreflecting differences in the countries studied, sample periods, frequency of the data sets,and empirical methodologies, including the representation of inflation uncertainty. Manyof the more recent studies have tended to favour the use of GARCH-based measures ofinflation uncertainty to test the Friedman hypothesis. These studies have typically eitherused the simultaneous estimation approach to determine whether a positive short-runrelationship between the mean and variance of inflation exists, and/or employed aGranger-causality approach to determine the direction of the impact of a change innominal uncertainty on inflation. Recent studies of this type generally have beensupportive of the Friedman hypothesis, including Fountas (2001) for the UK inflationexperience, Fountas et al. (2004) for the inflation experience in five out of six Europeancountries, and Conrad and Karanasos (2005) in a study of inflation in the USA, the UK,and Japan. In contrast, Hwang (2001) found no evidence that high inflation led to a highvariance of inflation using a long series of monthly US inflation data.

Most recent empirical tests of the Friedman hypothesis have been on the inflationexperience of one or more of the G7 advanced economies, where average inflation ratestypically have been low except for a brief period in the 1970s. This note contributes to theempirical evidence by using GARCH measures of inflation uncertainty to test for apositive short-run relationship between the mean and variance of inflation in South

* International monetary fund.Address for correspondence: Dr. John Thornton, International Monetary Fund, Fiscal AffairsDepartment, Room HQ2 6-811, 700 19th Street NW, Washington D.C. 20008, USA. Email:[email protected].† The views expressed in this paper are those of the author and should not be attributed to theInternational Monetary Fund.

South African Journal of Economics Vol. 74:2 June 2006

© 2006 The Author.Journal compilation © 2006 Economic Society of South Africa. Published by Blackwell Publishing, 9600 GarsingtonRoad, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

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Africa during 1957-2005, where the inflation experience has been more variable thanin the G7 economies. The results provide strong empirical support for the Friedmanhypothesis.

2. THE MODEL

Following Fountas (2001), the GARCH (p,q) model of inflation is extended to allow forthe inclusion of the inflation rate as an exogenous regressor in the variance equation inwhich inflation, yt, is specified as an AR(p) process with time varying conditionalvariance:

y y y E Var tt t 1 p t p t t t t t= + + + + ( ) = ( ) =∅ ∅ ∅− − − −0 1 1 120... ; ; ,ε ε θ ε θ σ (1)

σ α α ε α ε β σ β σ δυ2

0 1 1t yt 1 q t q t 1 v t t= + + + + + +− − − −2 2 2 2... ... , (2)

where a � 0, ai � 0, i = 1, ...q, bj � 0, j = 1, ..., u and qt is the information available attime t. According to the Friedman hypothesis, d � 0.

3. DATA AND RESULTS

I use monthly data for the South African consumer price index for 1957:1-2005:9 fromthe IMF’s International Financial Statistics database. Fig. 1 illustrates the volatility of theinflation series.1

Summary statistics for monthly inflation are given in Table 1. The distribution ofthe inflation series is skewed to the left, the large value of the Jarque-Bera statistics

1 The inflation series is constructed as log(CPI/CPI(-1)), where CPI is the consumer price index.

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

1957 1961 1965 1969 1973 1977 1981 1985 1989 1993 1998 2002

Figure 1. Monthly inflation, 1957-2005


© 2006 The Author.Journal compilation © Economic Society of South Africa 2006.

implies a deviation from normality, and the significant Q statistics of the squareddeviations of the inflation rate from the sample means indicates the existence of ARCHeffects. This evidence is also supported by the LM(12) statistic, which is highlysignificant.

I use five different unit root tests to determine whether inflation is a stationary series.The first four tests are relatively common in the literature but have been criticized becauseof bias towards nonrejection of the null hypothesis in the presence of structural breaksand their low power for near-integrated processes. These are the Augmented Dickey-Fuller (ADF) test developed by Dickey and Fuller (1979); the DF-GLS test developed byElliott, Rothenberg, and Stock (1996), which is a modified Dickey-Fuller test that hasimproved power in small samples; the Kwiatkowski, Phillips, Schmidt and Shin (1992)(KPSS) test; and the Phillips and Perron (1988) (PP) test. The ADF, DF-GLS and PPtests are of the null hypothesis of a unit root against the alternative of (trend) stationarity;the KPSS test is based on the null hypothesis of stationarity. The fifth test is thatdeveloped by Zivot and Andrews (1992) (ZA), which allows for one structural break inthe series and considers the null hypothesis of unit root with no break against thealternative of a stationary process with a break. Results from these tests are reported inTable 2. The Phillips-Perron test statistic indicates that inflation is a stationary series, butthe null hypothesis of a unit root is not rejected in the case of the ADF and DF-GLS tests,and the null hypothesis of stationarity is rejected in the case of KPSS test. However, theresults from the Zivot-Andrews test suggest that inflation is a stationary series whenaccount is taken of a structural break (identified in 1993:9) in that the null hypothesis ofa unit root with no break against the alternative of a stationary process with a break isrejected.

I therefore estimated GARCH models for monthly inflation where the inflation seriesfollows an ARMA model. Table 3 reports the results from a GARCH(p,q) model inwhich the AR process is chosen on the basis of the minimum value of the AkaikeInformation Criterion and the Schwarz Bayesian Criterion. I include a binary variableDUM in the inflation equation which takes the value of 1 when annual inflation is 10percent or greater to ensure that the results do not depend on the experience of highinflation. The results strongly support the existence of a positive relationship between thelevel and variability of inflation. The parameters in the inflation and covariance equationsare highly significant and of the hypothesized signs. The reported diagnostics indicate noserial correlation in the estimated squared residuals up to order 12. The intercept in the

Table 1. Summary statistics for inflation 1957:1-2005:9

Mean 0.0066Maximum 0.0421Minimum -0.0074Standard deviation 0.0065Skewness 1.1711Kurtosis 5.6522Jarque-Bera statistic 304.67Q2(12) (P-value) 95.93 (0.0000)LM(12) 6.7572 (0.0093)

Notes: Q2(12) is the Ljung-Box test for serial correlation in thesquared deviations of the inflation rate from its sample mean,where the 12 order test statistic is reported. LM is the Engel testfor ARCH effects.

169South African Journal of Economics Vol. 74:2 June 2006


conditional variance equation is positive, which is consistent with the nonnegativity ofthe variance. The sum of the ARCH and GARCH coefficients in the conditional varianceequation is less than one, which is consistent with the conditional variance of inflationbeing stationary. Finally, the positive and significant sign of the estimated parameter dindicates that if inflation rises by one unit, its conditional variance goes up by 0.008units.2

2 As the unit of measurement for the inflation series is 0.1 or 10 per cent, the unit of measurementfor the conditional variance is 0.01 or 1 per cent.

Table 2. Unit root test statistics for inflation, 1957:1-2005:9

P-P -23.79**ADF -2.21DF-GLS 1.42KPSS 1.14**ZA -9.00** Breakdate:1993:5

Notes: P-P is the Phillips-Perron test, ADF is the AugmentedDickey-Fuller test, DF-GLS is the modified Dickey-Fuller testdeveloped by Elliott, Rothenberg, and Stock (1996); in each casethe null hypothesis is of a unit root in the series. KPSS is theKwiatkowski-Phillips-Schmidt-Shin (1992) test for which thenull hypothesis is that the series is stationary. The ZA testconsiders the null hypothesis of unit root with no break againstthe alternative of a stationary process with a break. Lag length ischosen on the basis of the Schwartz Bayesian Criterion in the caseof the ADF test, the Newey-West criterion in the case of thePhillips-Perron test and KPSS tests, and the t-test in the case ofthe Zivot-Andrews test.** denotes statistical significance at the 1% levels.

Table 3. GARCH (1,1) model for inflation, 1957(1)-2005(9)

Variable Coefficient Standard error P-value

Inflation equation AR (1):Intercept 0.0000 0.0003 0.0395P(-1) 0.1102 0.5300 0.0377P(-3) 0.1421 0.0437 0.0012P(-6) 0.1189 0.0329 0.0003P(-9) 0.0896 0.0388 0.0210P(-12) 0.1770 0.0314 0.0000DUM 0.0026 0.0007 0.0002V ariance equation:Intercept 0.0000 0.0000 0.0094ARCH (1) 0.2055 0.0488 0.0000GARCH (1) 0.5288 0.0776 0.0000P 0.0008 0.0002 0.0000DiagnosticsR2 adj. 0.293AIC 0.005SBC -7.849Q2(4)/P-value 1.207 (0.877)Q2(12)/P-value 17.689 (0.125)

Notes: Q2(k) is the Box-Pierce statistic of the squared residuals(Critical values at the 5 significance level are Q2(4) = 9.49;Q2(12) = 21.03); AIC is the Akaike Information Criterion; andSBC is the Schwarz Bayesian Criterion.



4. CONCLUSIONS

Using a GARCH model of monthly inflation, I find a positive short-run relationshipbetween the mean and variance of inflation in South Africa for the period 1957:1-2005:9.The results are not sensitive to bouts of high inflation and are in line with those fromseveral recent studies that have used GARCH models to examine the inflation experiencein one or more of the G7 economies. The results provide further evidence in favor ofthe Friedman hypothesis that inflationary periods are associated with high inflationuncertainty.

REFERENCES

CONRAD, C. and KARANASOS, M. (2005). On the inflation-uncertainty hypothesis in the USA, Japan and the UK:a dual long memory approach. Japan and the World Economy, 17 August, 327-343.DAVIS, G.K. and Kanago B.E. (2000). The level and uncertainty of inflation: results from OECD forecasts. EconomicEnquiry, 38 January, 58-72.DICKEY, D. A. and FULLER, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root.Journal of the American Statistical Association, 74 June, 427-431.ELLIOTT, G., ROTHENBERG, T.J. and STOCK, J.H. (1996). Efficient tests for an autoregressive unit root.Econometica, 64 July, 813-836.FOUNTAS, S. (2001). The relationship between inflation and inflation uncertainty in the UK: 1885-1998. EconomicsLetters, 74 December, 77-83.FOUNTAS, S., IOANNIDI, A. and KARANASOS, M. (2004). Inflation, inflation uncertainty, and a common Europeanmonetary policy. Manchester School, 72 March, 221-242.FRIEDMAN, M. (1977). Inflation and unemployment. Journal of Political Economy, 85 June, 451-472.HWANG, Y. (2001). Relationship between inflation rate and inflation uncertainty. Economics Letters, 73 November,179-186.KWIATKOWSKI, D., PHILLIPS, P.C.B., SCHMIDT, P. and SHIN, Y. (1992). Testing the null hypothesis of stationarityagainst the alternative of a unit root: how sure are we that economic time series have a unit root. Journal of Econometrics,54 October, 159-178.PHILLIPS, P.C.B. and PERRON, P. (1988). Testing for a unit root in time series regression. Biometrika, 75 June, 335-346.ZIVOT, E. and andrews, D.W. K. (1992). Further evidence of the great crash, the oil price shock and the unit roothypothesis. Journal of Business and Economics Statistics, 10 July, 251-270.

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HIGH AND VARIABLE INFLATION: FURTHER EVIDENCE ON THE FRIEDMAN HYPOTHESIS