Inflation, Deflation, Inflation Uncertainty, & the Dispersion of Relative Prices
by
Kevin B. Grier
Mark J. Perry
Department of Economics University of Oklahoma Norman OK 73019
Department of Economics University of Michigan-Flint Flint MI 48502
[email protected]
[email protected]
December 2000
Inflation, Deflation, Inflation Uncertainty, & the Dispersion of Relative Prices
I. Introduction
It is often taken as a given that trend inflation causes, or at least is correlated with, the dispersion of relative prices.1 The existence of this correlation is often cited as prima facie evidence that there are substantial nominal rigidities in the economy, either in prices or wages.2 The empirical evidence most often cited is Parks (1978) and Vining & Elwertowski (1976). However, the fragility of Parks’ results are well documented.3 Further, as Grier & Perry (1996) point out, Vining and Elwertowski actually make an argument about the volatility of inflation and the dispersion of relative prices. A signal extraction model (e.g., Lucas (1973), Barro (1976)), or a search model (Benabou & Gertner (1993)) can predict this type of relationship, where inflation uncertainty raises relative price dispersion (hereafter RPD). Grier & Perry (1996) construct a test of whether trend inflation or inflation uncertainty best explains the dispersion of relative prices and find that inflation uncertainty dominates trend inflation as a predictor of RPD. Recently though, Jaramillo (1999) argues that the effect of trend inflation on relative price dispersion is much more robust if one allows it to be asymmetric. He argues that negative inflation rates (i.e.deflation) raise RPD significantly more than do positive rates of inflation. Previous studies have used either the absolute value of inflation or the square of inflation, enforcing symmetry on the effects of equal sized positive and negative inflation rates. In this paper we test for the effects of inflation, deflation, and inflation uncertainty on relative price dispersion simultaneously in a multivariate statistical model. The three main results are: (1) inflation uncertainty still dominates trend inflation as a predictor of RPD over a longer sample than that originally used by Grier & Perry (1996), (2) using a long monthly dataset, there is no evidence
2
of the type of asymmetry of the effects of inflation on RPD claimed by Jaramillo, and (3) to the extent that any asymmetry in the effect of trend inflation on RPD exists, positive inflation raises RPD while negative inflation has no impact, which is exactly the opposite of Jaramillo’s claim. In what follows below, section II describes our data and statistical approach and presents an extension of the empirical work in Grier & Perry (1996). Section III presents several tests for the asymmetric effect of average inflation on RPD, and section IV contains a discussion and an evaluation of the empirical evidence on how the inflation process affects the dispersion of relative prices.
II. Statistical model and initial results We simultaneously estimate a multivariate model of the evolution of inflation, its conditional variance, RPD, and the covariance between the errors of the inflation equation and the RPD equation.4 In this way, both average inflation variables and the conditional variance of inflation (a measure of inflation uncertainty) can be included as explanatory variables in the RPD equation. We model the conditional mean and variance of inflation as ARMA processes, the conditional mean of RPD as an ARMA plus inflation variables process, and the covariance of the errors with a constant correlation model. We choose the number of ARMA terms in our equations to ensure that the residuals, cross-residuals and squared residuals have no exploitable patterns. For ease of computation and reporting, we adopt the convention of dropping insignificant terms from the ARMA process. None of the results in the paper change if these terms are kept in the estimated equations.5 We assume the error terms are distributed jointly normal and use the BHHH algorithm to obtain maximum likelihood estimates of the model’s parameters.6
3
Our RPD variable is calculated from PPI (producer price index) data on 14 commodity groupings. There are 15 such groupings available; the categories are shown in Table 1. We do not use the oil sector to compute RPD because of the frequent assertion that oil prices drive the relationship between inflation and RPD.7 We begin by estimating the effect of average inflation, lagged one month, on RPD with the potential effect of inflation uncertainty constrained to be zero. Following common practice in the literature since Parks, we measure trend inflation by its square. Parks explicitly argues that the inflation - price dispersion relation should be symmetric. Using the square forces an x% rate of deflation to have the same impact on RPD as an x% rate of inflation. We relax this assumption below when considering Jamarillo’s claim that the inflation - price dispersion relation is significantly asymmetric.8 The initial results are presented in equations (1)- (4) below. The symbol At represents the average rate of inflation in month t. Equation (1) explains the mean of inflation with its first, second, and sixth lag along with an MA(12) term. Equation (2) is a GARCH(1,1) equation for the conditional variance of inflation. Equation (3) represents the mean of RPD with its second and fifth lags, an MA(8) term, and lagged, squared inflation, while equation (4) reports the cross-equation error correlation. The sample is monthly, 1948.01 through 1997.12, a sample of 600 observations spanning 50 years. At = .102 + .256 At-1 + .081 At-2 + .083 At-6 + .142 ,t-12 + ,t (4.00) (5.67) (1.83) (1.89) (3.97)
(1)
F
(2)
2
,t
= .017 + .152 ,2t-1 + .779 F2,t-1 (3.35) (3.59) (18.2)
4
RPDt = .610 + .148 RPDt-2 + .113 RPDt-5 + .144
