The Cross-Sectional Price Equation: Reply - Wilder, Ronald P.; Williams, C. Glyn; Singh, Davinder (American Economic Review, 2016)
DeRosa and Goldstein (hereafter D-G) argue that the appropriate test for a pricing should regard only the sign of a05, the estimated coefficient of the cost change dummy variable (V1) and the sign and magnitude of a7, the estimated coefficient on the interaction term between the cost change dummy variable and the change in variable cost (V1 X AVC). In their words, Since a0 [the intercept term] in equation (2) is the estimated time trend of prices and cannot be uniquely identified with the hypothesis under investigation, it should not be used as evidence of an asymmetry (p. 880, fn. 6). We would argue instead that the magnitude of the intercept term in the price equation lies at the heart of the issue. The intercept term is the empirical manifestation of inflationary inertia, reflecting the expectations of price and wage setters. George Perry has called this phenomenon the inflationary norm. As discussed below, the estimated intercept terms in both crosssectional and time-series price equation studies have been positive and of relatively large magnitude, especially in the 1970's. (D-G's estimated intercept terms are 1.20 and 2.09 for the 1972-76 period.) The alternative configurations of a0 (the intercept term), and a5 (the coefficient on the cost-change dummy variable) are shown in Figure 1. In panel (a), a0 a ,5 = 0 and there is no asymmetry. In panels (b), (c), and (d), the basic result holds: namely, that a given percentage increase in variable cost produces a larger price increase than the decrease in price produced by a cost decrease of the same magnitude. Only in panel (e) does the work in the opposite direction. Generalizing, given a positive value of a0, the basic pricing result holds for all positive values of a5 and for negative values of a5 provided that j a5j > 2ao. Only when I a5 I > 2ao, a5 < 0, does the work in the opposite direction. This latter condition is met neither in our results nor in those reported by D-G.' Our point of agreement with D-G is in their argument that the negative sign on a5, the coefficient on the cost-change dummy variable, is not by itself the appropriate test for the asymmetry. We disagree with them, however, in the degree of importance to be attached to the intercept term.