The missing link: intra-country evidence on the relationship between high and uncertain inflation from high-inflation countries.

• Author: Davis, George K.

1. Introduction

   The notion that high inflation breeds high uncertainty about future inflation is widely accepted.(1) This acceptance is based largely on a positive correlation between the mean and variability of inflation across countries.(2) This positive relationship is taken as evidence that high inflation creates high uncertainty.(3) Recently though, Driffill, Mizon, and Ulph [10] have questioned the relevance of this cross-country evidence for making inferences about welfare issues within countries. They argue that it is the relationship between the time-series mean and variance within a country that is important when considering the potential costs of inflation. In this paper we examine the within country time-series link between the level and uncertainty of inflation for ten countries that experienced a period of very high inflation. We use data generated from regression based forecasts of inflation, and historical data on actual forecasts. Our sample does not provide evidence of a general positive link within these countries.

   The ten countries we study are: Argentina, Bolivia, Brazil, Chile, Colombia, Israel, Mexico, Peru, Turkey, and Uruguay. In these countries the average annualized rate of inflation from the quarterly data in our sample was about 54% per year, and the average sample standard deviation, a measure of variability, was about 38%.(4) Further, the countries with the highest inflation tend to be the ones with the most variable inflation. Our presumption is that if a positive relationship exists within countries between the level of inflation and the squared forecast errors, it should reveal itself in these countries.

   Earlier studies of the within-country time series link between the level and uncertainty of inflation forecasts have produced mixed results. Most of these studies develop inflation regressions, and then test to see if some function of the errors of the regressions are related to the level of inflation. The function of the errors is intended to serve as an indicator of the unpredictability of inflation, a measure of uncertainty.

   Engle [13] argues that the variance of the errors from the forecasting equation may vary over time according to an ARCH model. He finds for the United States that the ARCH generated time-varying variance, which is a function of past squared-errors, is not significantly related to the lagged inflation rate. Pagan, Hall, and Trivedi [22] use a forecasting equation, corrected for serial correlation, for Australia and find "weak evidence" of a relation between the squared forecast error and lagged inflation. Holland [16] finds mixed results for the U.S. using the Pagan, Hall, and Trivedi approach, but finds a positive link using the Livingston survey data. Recently, Holland [17] finds evidence that high inflation precedes high inflation uncertainty for this data.

   A series of studies examine the experience of the Latin American countries. Glezakos and Nugent [14] generate inflation forecasts for 23 countries over the period 1950 to 1975 with an adaptive expectations model and find a positive relationship between the absolute value of the forecast error and the current rate of inflation for about 80% of the countries in the sample. Darrat and Lopez [8] use a rational expectations approach to generate inflation forecasts for 14 countries from 1950 to 1983. They find a significant positive link for 10 of the 14 countries. In contrast, Pourgerami and Maskus [24], also using a rational expectations approach, find a positive relationship that is significant at or above the 5% level in only 2 of 7 countries using quarterly data from 1968 to 1985. Glezakos and Nugent [15] attribute the difference between their earlier results and those of Pourgerami and Maskus primarily to the inclusion of additional explanatory variables rather than the sample period or the sample frequency of the data. Maskus and Pourgerami [20] later construct errors based on regression constructed forecasts in which the regression coefficients are based only on data that would have been available to forecasters at the time of the forecast. Using this rolling regression procedure they find a significant negative relationship in Argentina, a significant positive relationship in Brazil, and no significant relation for the remaining countries.

   There are two general problems with the methodology used in the Latin American studies. The first problem arises from the form of the test. The absolute value of the forecast error is regressed on the current rate of inflation.(5) This specification leads to an inconsistent estimate of the coefficient on current inflation. Pagan, Hall, and Trivedi [22] suggest a regression of lagged inflation on the squared forecast error that yields a consistent estimate, and we follow their suggestion.(6)

   The second difficulty is also a specification issue. If there is a structural change in the sample period, perhaps from the implementation of a stabilization program, any positive relationship may be an artifact of misspecification. On this score it is interesting to note that Pourgerami and Maskus [24], whose results do not support the existence of a strong link, use the shortest, and most homogeneous, sample period. Moreover, they find the strongest evidence of a link for Chile which instituted a stabilization policy in 1975. Furthermore, Glezakos and Nugent [15] find that for some countries their results are reversed when they estimate over the same relatively regime-change free period as Pourgerami and Maskus.

   We address this specification issue by performing stability tests. We use the Chow test, and a test for time-varying parameters. We also construct our sample to avoid major regime shifts, and to provide us with reasonably consistent data. Our sample begins in 1972 after the demise of Bretton Woods, and ends in 1985 before many of the countries in our sample embarked on stabilization programs.(7) Even so, three of the countries we examine had possible regime shifts over the period we study. Chile instituted a stabilization policy in 1975 and Turkey did so in 1980. Bolivia floated the Peso in March 1982, and consequently made drastic changes in fiscal and monetary policy.(8) Below we consider what happens in shorter samples for Chile and Bolivia.

   We also employ tests for heteroskedasticity. We perform ARCH tests, and several general tests such as White's test. Evidence of these types of heteroskedasticity ought to be accounted for, as in Engle [13], when testing for a link between the level and uncertainty of inflation.

   In the next section we provide an overview of the paper. This is followed by a description of our inflation regressions. In Section IV we discuss the heteroskedasticity tests that we performed, and the results we obtained. In Section V we examine the robustness of our results, and in Section VI present evidence using actual forecasts. In Section VII we discuss the relationship between the time-series results and cross-section results. We end with some concluding remarks.

2. Overview

   For each country we run several simple inflation forecasting equations. We then examine the squared residuals from these equations for each country to see if there is evidence for a time-varying variance of the forecast error. With the possible exceptions of Bolivia, Chile, and Turkey, we cannot reject the hypothesis that the variance of the forecast error was constant. Indeed, the forecast variance for these countries appears to be stable over a period of time during which inflation was highly variable.

   More specifically, for most countries the squared residuals are not positively related to lagged inflation. This result is not reversed when other variables are included with lagged inflation. In short, a battery of tests generally fail to find any evidence of heteroskedasticity in our regressions. Our results are robust to scrutiny of the forecasting equations. In addition to the heteroskedasticity tests, we test for misspecification in the OLS regressions with Chow, RESET, and serial correlation tests. For the few countries where it is necessary, we make corrections according to the tests. We continue to find, within almost all countries, that no such link exists. Thus, there is little evidence that high inflation creates unusually large forecast errors within countries.

   It is possible that regression forecasts fail to adequately capture the history of forecasts actually made at the time. Consequently, some studies for the U.S. have used time series of survey-generated forecasts and their errors to test for a link between the unpredictability and level of inflation. Pagan, Hall, and Trivedi [22] consider the errors from the median value of an Australian survey of inflation. Ungar and Zilberfarb [26] use various measures of uncertainty from a survey concerning inflation in Israel. These studies generally find a positive link. However, Ungar and Zilberfarb find that the link for Israel is weaker when estimating the relation separately for two regimes rather than over the entire period.

   So, in addition to our regression based results, we also present results from a time series of published inflation forecasts for Latin America. These forecasts are further differentiated from the regression results by the forecast horizon. The regression based results use a forecast period of one quarter, while the actual forecasts have a one year horizon. The results using the errors from these actual forecasts reinforce our regression based evidence. That is, using the errors from the actual forecasts, we still find little evidence of a link between the uncertainty and level of inflation.

   Although we fail to find a link within the countries we study, our sample does exhibit a strong positive relationship across countries between average inflation rates and inflation variability, and also between average inflation rates and the standard errors from an inflation regression...