The relationship between inflation and inflation uncertainty in emerging market economies.

1. Introduction

Friedman (1977) set out an informal two-part argument about the real effects of inflation. In the first part, an increase in inflation may induce an erratic policy response by the monetary authority and, therefore, lead to more uncertainty about the future rate of inflation. In the second part, inflation uncertainty has a negative effect on output. The causal effect of inflation uncertainty on inflation has been analyzed in the theoretical macro literature by Cukierman and Meltzer (1986) and Holland (1995). Cukierman and Meltzer show how, by providing an incentive for the monetary authority to create an inflation surprise in order to stimulate output growth, an increase in uncertainty about money growth and inflation will raise the optimal average inflation rate. Thus, a positive causal effect of inflation uncertainty on inflation is evidence of an 'opportunistic' central bank. In contrast, Holland claims that as inflation uncertainty rises due to increasing inflation, the central bank responds by contracting money supply growth in order to eliminate inflation uncertainty and the associated negative output effects. Thus, a negative causal effect of inflation uncertainty on inflation is evidence of a 'stabilizing' central bank. The different hypotheses on the link between inflation and inflation uncertainty have given rise to a large empirical literature, mainly with respect to the experience of the G7 advanced economics, where average inflation rates typically have been low (with the exception of a brief period in the late 1970s and early 1980s). Davis and Kanago (2000) review many of the early studies on the issue, highlighting the mixed results that partly reflect differences in the countries studied, sample periods, frequency of the data sets, and empirical methodologies, including the representation of inflation uncertainty. In the latter regard, recent studies have tended to use the estimated conditional variance from Generalized Autoregressive Conditional Heteroskedastic (GARCH) models to measure inflation uncertainty and generally have been supportive of the Friedman hypothesis. (1) These studies include Grier and Perry (1998) for the G7 countries; Fountas (2001) for the UK inflation experience over a long time span; Fountas, Ioannidis, and Karanasos (2004) for the inflation experience in five out of six European countries; and Conrad and Karanasos (2005) in a study of inflation in the United States, the United Kingdom, and Japan. In this paper, I focus on the inflation-uncertainty issue in emerging market economies. Specifically, I use the estimated conditional variance from a GARCH type model to measure inflation uncertainty and employ Granger methods to test for the direction of causality between inflation and inflation uncertainty in 12 emerging market economies. The results provide strong empirical support for the Friedman hypothesis that higher inflation rates raise inflation uncertainty, but are more mixed regarding the effect of inflation uncertainty on average monthly inflation.

2. The Model, Data, and Results

The GARCH time series studies that examine the link between inflation and inflation uncertainty use a variety of empirical methodologies. Following Fountas (2001), I use a GARCH (q,v) model of inflation extended to allow for the inclusion of the inflation rate as an exogenous regressor in the variance equation in which inflation, [y.sub.t], is an AR(p) process with time varying conditional variance:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

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where [alpha] > 0, [[alpha].sub.i] [greater than or equal to] 0, i = 1, ... q, [[beta].sub.j] [greater than or equal to] 0, j = 1, ..., [upsilon], and [[theta].sub.t] is the information available at time t, and where according to the Friedman hypothesis, [delta] > 0.

I use monthly data on the consumer price index (CPI) obtained from the International Monetary Fund's International Financial Statistics database for 12 emerging market economies with varying sample periods: Colombia, India, Malaysia, Mexico, South Africa (all 1957:1 to 2005:12), Thailand (1965:1 to 2005:12), Turkey (1970:1 to 2005:12), Indonesia (1968:1 to 2005:12), Korea (1970:1 to 2005:12), Israel (1975:1 to 2005:12), and Hungary and Jordan (both 1976:1 to 2005:12). The rate of inflation is measured as the monthly change in the log of the CPI and the number of observations (allowing for differencing) ranges between 359 and 587. The monthly inflation rates of the countries are plotted in Figure 1, from which it is clear that the series are very volatile. Summary statistics for the monthly inflation rates are presented in Table 1. The kurtosis and skewness statistics indicate that the distributions generally are nonnormal, being skewed to the right. The deviation from normality is confirmed by the large values of the Jarque-Bera statistics, and ARCH effects are indicated by the significant Q-statistics of the squared deviations of the monthly inflation rate from the sample means and the LM(12) statistics. The exceptions to these cases are India, where the distribution appears nonnormal, but also is wide and flat, and Mexico and Turkey, where there is no indication of ARCH effects in monthly inflation.

[FIGURE 1 OMITTED]

The next step is to consider the time series properties of inflation in each country. The authors of the studies cited above have tended to proceed as if inflation was a stationary series, though the empirical evidence on the issue is mixed with a substantial literature supporting nonstationarity. (2) A particular problem in the emerging market economies included in this study is the impact on the inflation series of the varying degrees of financial crisis and liberalization measures (including of administered prices) that each experienced during the sample periods under study. In this context, I use five different unit root tests to determine whether the inflation series are stationary. The first four tests are relatively common in the literature but have been criticized because of bias toward nonrejection of the null hypothesis in the presence of structural breaks and 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 by Elliott, Rothenberg, and Stock (1996), which is a modified Dickey-Fuller test that has improved 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 PP tests 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 that developed by Zivot and Andrews (1992) (ZA), which allows for one structural break in the series. The ZA test considers the null hypothesis of unit root with no break against the alternative of a stationary process with a break. The results from the tests that make no allowance for structural breaks are in Panel (a) of Table 2. The PP test statistics indicate that inflation is a stationary series in all cases. The other test statistics are less clear cut; however, the null hypothesis of a unit root is not rejected for Hungary, Israel, South Africa, and Turkey in the case of the ADF test and for Colombia, Hungary, Jordan, Korea, Mexico, and South Africa in the case of the DF-GLS test; and the null hypothesis of stationarity is rejected in the cases of Colombia, Mexico, South Africa, and Turkey. The results from the ZA test are given in Panel (b) of the table and suggest that the inflation series are stationary when structural breaks are taken into account. In each case, the null hypothesis of a unit root with no break against the alternative of a stationary process with a break is rejected.

The maximum likelihood estimates of the GARCH model are reported in Table 3. In carrying out the estimates, I began with an inflation lag length of 36 months, which was then shortened on the basis of the Schwartz Bayesian Criterion. The results strongly support the existence of a positive relationship between the level and variability of inflation. In all cases the reported parameters in the inflation and covariance equations are highly significant and of the hypothesized signs. The intercept in the conditional variance equation is positive, which is consistent with the nonnegativity of the variance. The sum of the ARCH and GARCH coefficients in the conditional variance equation is less than one, which is consistent with the conditional variance of inflation being stationary. Finally, the parameter 5 in the covariance equation is always positive and significant, and indicates that if inflation rises by one unit, its conditional variance goes up by between 0.01-0.008. (3) The Q-statistics for the standardized residuals and squared residuals show no patterns with the exceptions of a significant spike at the 12th lagged residual in the Thailand and Turkey data. (4)