Inflation, inflation uncertainty, and relative price variability.

• Author: Aarstol, Michael

1. Introduction

   The early descriptive studies of the behavior of prices by Mills (1927) and Graham (1930) both found that the variability of relative price changes (henceforth, RPV) increased with inflation.(1) A modem literature beginning with Vining and Elwertowski (1976) and Parks (1978) has re-examined this finding in a variety of settings and searched for the particular aspect of inflation that is most closely associated with RPV. Defining RPV as the sum of the squared deviations of the rates of change of various price subindexes from the rate of change of some overall price index, this literature has generally confirmed the basic relationship found by Mills and Graham.(2) However, there is little agreement regarding which particular aspect of inflation is most highly correlated with RPV. For instance, Parks finds that RPV increases primarily with the absolute value of unexpected inflation, while Tang and Wang (1993) find that RPV increases with expected inflation as well as with the absolute value of unexpected inflation. At the same time, Fischer (1982) finds that RPV increases with expected inflation and positive instances of unexpected inflation but not with negative instances of unexpected inflation. Still others, such as Grier and Perry (1996), find that RPV increases only with ex ante inflation uncertainty.(3)

   Expected inflation, realized unexpected inflation, and ex ante inflation uncertainty have all been proposed as determinants of RPV in various well-specified theoretical models as outlined in section 2. Despite this, no empirical analysis of the relationship between inflation and RPV has simultaneously included all of these aspects of inflation as explanatory variables. All of the empirical studies other than that of Grier and Perry (1996) use only measures of expected and unexpected inflation as explanatory variables. At the same time, while Grier and Perry extend the empirical literature by including a plausible measure of inflation uncertainty obtained from a generalized autoregressive conditional heteroskedasticity (GARCH) model as an explanatory variable, they omit unexpected inflation from their model Specification.

   This paper investigates the empirical relationship between inflation and RPV in a model that incorporates measures of inflation uncertainty as well as expected and unexpected inflation. This allows a more complete test of the various competing theories of the inflation-RPV relationship. The finding is that no single theory explains the data and that, even in conjunction, the various proposed theories cannot explain the data.

   The rest of the paper proceeds as follows. Section 2 reviews three theories that have been proposed as possible explanations of the relationship between RPV and various aspects of inflation. Section 3 discusses the producer price index data used in this paper. Section 4 describes the model of inflation that is used to generate measures of expected inflation, unexpected inflation, and inflation variability. Section 5 estimates a model that relates RPV to these measures of expected inflation, unexpected inflation, and inflation variability. Section 6 checks the robustness of the results by dividing the sample into halves and also by re-estimating the key regression with food and energy prices removed from consideration. Section 7 offers a brief conclusion.

2. Theories Linking RPV and Inflation

   There are three well-developed theories that imply a relationship between RPV and inflation. These are (i) the signal-extraction model of Lucas (1972, 1973) and Barro (1976), (ii) the extension of the signal-extraction model by Hercowitz (1981) and Cukierman (1983), and (iii) the menu-costs model of Sheshinski and Weiss (1977) and Rotemberg (1983).(4) Each of these makes a distinct prediction regarding which aspect of inflation should be most closely related to RPV.

   The Lucas-Barro signal-extraction model predicts that RPV should increase with ex ante inflation uncertainty. The greater is the ex ante variability of aggregate demand shocks (and ex ante inflation uncertainty), the more various real local shocks will be interpreted as aggregate shocks and will be responded to with price changes rather than quantity changes. Realized aggregate demand shocks, on the other hand, have no effect on RPV in the Lucas-Barro model because all firms respond identically to any given aggregate shock.

   By contrast, realized aggregate demand shocks do affect RPV in the Hercowitz-Cukierman extension of the Lucas-Barro signal-extraction model in which price elasticities of supply differ across firms. In the Hercowitz-Cukierman model, firms with high elasticities of supply adjust prices less in response to a given unexpected aggregate demand shock than do firms in markets with low elasticities of supply. Moreover, the magnitude of the discrepancy in price adjustments across sectors increases with the magnitude of the aggregate demand shock. This leads to the prediction that RPV will be associated with the magnitude of unexpected inflation, whether positive or negative.

   Finally, anticipated changes in aggregate demand have no effect upon relative prices under either version of the signal-extraction model. Anticipated changes in aggregate demand simply result in a uniform increase or decrease in all nominal prices. By contrast, the menu-costs models of Sheshinski and Weiss (1977) and Rotemberg (1983) predict a positive relationship between RPV and expected inflation. These models predict that firms should use (S, s) pricing schemes if a fixed cost is incurred whenever output price is adjusted; that is, a firm should adjust its nominal price only when the real price of its good decays to its lower bound of s, at which time the price should be reset so that its real price equals the upper bound of S. Provided that firms do not adjust prices synchronously, these models predict that, as inflation increases, the difference between the optimal s and S will increase and more variability in relative price changes will be created. However, as noted by Danziger (1987), the period between observations on prices must be short compared to the period over which any given firm maintains a fixed nominal price for this prediction to hold. If, for instance, these two...