Is there any asymmetry in the effect of inflation on relative price variability?

a r t i c l e i n f o Keywords: Asymmetry Inflation Relative price variability (RPV) U-shape JEL classification: E30 E31 E52 It is widely perceived that relative prices are more dispersed in periods of price decreases than in periods of price increases. We show that the asymmetry results from misspecifying the true, U-shaped, underlying model with a piecewise linear regression model. Ever since Parks (1978) first noted that relative prices get more dispersed in periods of price falls than in periods of price rises, the asymmetric effect of inflation on the relative price variability (hereafter, RPV) has been supported by extensive empirical work [e. to cite a few]. At a theoretical level, Ball and Mankiw (1994) outline a model of asymmetric price adjustments in which negative inflation shocks trigger a slower adjustment of firms' desired prices and thus yield a larger variation in relative prices than do positive shocks of the same size. Jaramillo (1999) provides further theoretical explanations based on a simple two-sector model with downward price rigidity. The asymmetry also bears a crucial implication for monetary policy as it stipulates different policy responses to different inflation shocks. By studying disaggregated CPI data for three countries, Canada, Japan, and the U.S., this note makes two major arguments with regard to the asymmetry. First, the ample empirical evidence of asymmetry established in the literature largely results from the misspecification of the regression model. When the usual piecewise linear regression model is applied, we could find evidence of asymmetry, but the degree of asymmetry is not stable over time. Instead, asymmetry dwindles as trend inflation decreases before vanishing completely when trend inflation falls to zero. It is reversed when trend inflation goes below zero as seen in Japan during the period of deflation. We attribute this time-varying behavior of the asymmetry to misspecify-ing the true underlying model of a nonlinear U-shape with the piecewise linear model. In the trend inflation (deflation), the model misspecification causes a spurious asymmetry by overstating the response of RPV to price decreases (increases), while understating the response to price increases (decreases). Indeed, we find compelling evidence of a U-shaped relationship between inflation and RPV in all countries under study, consistent with the recent findings by Fielding and Mizen (2008) and Choi (2009). Second, in the U-shaped profile, what matters for the response of RPV is not the direction of price changes but the …