Inflation and relative price variability: new evidence for the United States.

• Author: Becker, Sascha S.

1. Introduction

   Various economic theories predict that inflation increases relative price variability (RPV) and thus, impedes the efficient allocation of resources. In fact, recent macroeconomic models put much emphasis on the distorting impact of inflation on relative prices, yet the empirical relationship between inflation and RPV seems underresearched. (1) In particular, recent theoretical and empirical contributions suggest that the impact of expected inflation on RPV may depend on the level of inflation. This article reexamines the empirical relationship between U.S. inflation and RPV in order to shed more light on the role of expected inflation during the recent low inflation period.

   Since the seminal study by Parks (1978), the empirical evidence on inflation's impact on RPV has been mixed and elusive. While most studies (see Jaramillo 1999) find a significant positive impact of inflation on RPV, the relationship has broken down, according to Lastrapes (2006), while Reinsdorf (1994) concludes that RPV decreases with inflation. Bick and Nautz (2008) partly reconcile this contradicting evidence by allowing for inflation thresholds where the marginal impact of inflation on RPV varies with the inflation regime.

   Many empirical studies on the inflation-RPV nexus do not account for the different effects of expected and unexpected inflation emphasized by the theoretical literature. For example, menu cost models imply that RPV is increased only by expected inflation. An early attempt to account for the implications of economic theories relating inflation and RPV is provided by Aarstol (1999). Using U.S. producer price data from 1973 to 1997, he finds that both expected and unexpected inflation significantly increase RPV. Yet recent theoretical contributions question the stability of the empirical relationship between inflation and RPV. In particular, the monetary search model introduced by Head and Kumar (2005) suggests that the influence of expected inflation on RPV may have changed during the recent low inflation period. In order to investigate the empirical relevance of this prediction, the focus of our empirical analysis is on the (changing) role of expected inflation for the U.S. inflation-RPV nexus. However, to ensure that our results concerning expected inflation are not driven by further instabilities in the empirical relationship between inflation and RPV, we will also account for breaks in the role of unexpected inflation and inflation uncertainty.

   Adopting the empirical framework of Aarstol (1999), we find that the effect of expected inflation on RPV becomes insignificant if the sample includes the recent low-inflation period. The instability of the relationship between inflation and RPV can be confirmed for different price indices, disaggregation levels, and RPV measures. In order to shed more light on the changing role of expected inflation for RPV, we employ endogenous break-point tests to identify the timing and to test for the significance of a structural break. In line with recent evidence obtained for Germany (Nautz and Scharff 2005) and the Euro area (Nautz and Scharff 2006), our results indicate that the influence of expected inflation on RPV has already disappeared since the early 1990s, when U.S. monetary policy made interest rates more responsive to inflation and, thereby, stabilized inflation expectations on a lower level (see, e.g., Judd and Trehan 1995; Mankiw 2001).

   This article is organized as follows: Section 2 reviews theory and empirical evidence on the relationship between inflation and RPV. Section 3 provides first results suggesting a changing role of expected inflation for the U.S. inflation-RPV nexus. Section 4 uses endogenous breakpoint tests to assess the timing and significance of the structural break in the relationship between expected inflation and RPV, where we controlled for possible changes in the effects of unexpected inflation and inflation uncertainty on RPV. Section 5 concludes.

2. Inflation and Relative Price Variability: Theory and Evidence

   Theoretical Literature

   The theoretical literature on the relationship between inflation and RPV consists mainly of three types of models: menu cost models, signal extraction models, and monetary search models. Interestingly, the implications of these models concerning the role of expected and unexpected inflation are very different.

   Menu Cost Models

   Menu cost models assume that nominal price changes are subject to price adjustment costs (Sheshinski and Weiss 1977; Rotemberg 1983; Benabou 1992). In this case, it can be shown that firms set prices discontinuously according to an (S, s) pricing rule. Because of inflation, the firm's real price begins at S and then falls to s over time. At that point, the firm raises its nominal price so that the real price once again equals S. In case of deflation, a firm decreases its nominal price accordingly. Since the width of the (S, s) band depends on the size of its menu costs, firm-specific menu costs lead to staggered price setting, distorted relative prices, and an inefficient increase of RPV. The crucial point is that only the anticipated part of inflation affects the width of the (S, s) band. Therefore, increases in expected inflation amplify the distorting effect of menu costs on relative prices. Because of the symmetry in firms' pricing strategy, menu cost models typically imply that RPV is increasing in the absolute value of expected inflation.

   Signal Extraction Models

   Signal extraction models share the assumption that inflation is not always anticipated correctly. As a consequence, firms and households confuse absolute and relative price changes. For example, according to Lucas (1973), Barro (1976), and Hercowitz (1981), higher inflation uncertainty makes aggregate demand shocks harder to predict. Solving the implied signal extraction problem, firms adjust output less in response to all shocks, including idiosyncratic real demand shocks. As a result, increases in unexpected inflation and inflation uncertainty will raise RPV.

   Monetary Search Models

   Monetary search models emphasize that buyers have only incomplete information about the prices offered by different sellers. In these models, the overall effect of inflation on RPV is not always obvious (Reinsdorf 1994; Peterson and Shi 2004). On the one hand, higher expected inflation lowers the value of flat money, which increases sellers' market power and thereby, the dispersion of prices. On the other hand, higher expected inflation also raises the gains of search, which lowers sellers' market power and, thus, RPV. As inflation rises, the RPV increasing effect will eventually dominate. Yet there will be a region within which small changes in expected inflation have little effect on RPV. Head and Kumar (2005) showed that expected inflation may increase RPV only if it exceeds a critical value.

   Empirical Literature

   The early empirical evidence on the relationship between inflation and relative price variability is typically based on linear regressions of RPV on inflation. In line with menu cost and signal extraction models, most empirical contributions find a significant positive coefficient of expected inflation, unexpected inflation, or inflation uncertainty (Grier and Perry 1996; Parsley 1996; Debelle and Lamont 1997; Aarstol 1999; Jaramillo 1999). Yet there are notable exceptions. In particular, according to Lastrapes (2006) the relationship between U.S. inflation and RPV broke down in the mid-1980s, while Reinsdorf (1994) demonstrates that the relationship is negative even during the disinflationary early 1980s. Similarly, Fielding and Mizen (2000) and Silver and Ioannidis (2001) show for several European countries that RPV decreases in inflation.

   In accordance with the implications of monetary search models, more recent evidence suggests that the relationship between inflation and RPV might be more complex. In particular, several studies have found that the impact of inflation on RPV is different for high- and low-inflation periods and countries with different inflationary contexts (Caglayan and Filiztekin 2003; Caraballo, Dabfls, and Usabiaga 2006). Using nonparametric methods, Fielding and Mizen (2008) find that the U.S. inflation-RPV linkage is nonlinear. Nautz and Scharff (2006) apply panel threshold models to price data of Euro-area countries. In line with Head and Kumar (2005), they find evidence in favor of threshold effects in the European link between expected inflation and RPV. Similar threshold effects are found by Bick and Nautz (2008) using price data from U.S. cities, although they do not differentiate between expected and unexpected inflation. Finally, analyzing price observations from bazaars, convenience stores, and supermarkets in Turkey, Caglayan, Filiztekin, and Rauh (2008) show that the relationship between RPV and expected inflation confirms the predictions of monetary search models. In particular, expected inflation increases RPV only if it exceeds a certain threshold.

   Given the overall decline of U.S. inflation and inflation expectations over the past decades, the focus of our analysis is on the impact of expected inflation on RPV in the United States. In light of the recent theoretical and empirical literature, a changing role of expected inflation should be reflected in a structural break of the traditional inflation-RPV nexus.

3. The Empirical Relation between Inflation and RPV

   Data and Variables

   Our benchmark measures of inflation ([[pi].sup.PPI]) and relative price variability (RPV) use monthly price data of the U.S. Producer Price Index (PPI). At the two-digit disaggregation level, the corresponding RPV measure, [RPV.sub.PPI-2], is based on the prices of the complete set of 15 subcategories. In order to check the robustness of our results, we additionally employ four alternative inflation and RPV measures typically applied in the empirical literature. Specifically, we consider...