RDP 9502: Price Stickiness and Inflation Appendix 1: Statistical Test: Are Price Falls Special?

Define Δp_t as the economy-wide average change in producer prices in period t.Then define z_t= 1 (−1) if the proportion of industries with price falls in period t is lower (higher) than the proportion with price rises greater than 2Δp_t. Finally, define Z = (z₁+K+Z_T)/T. Under the null hypothesis that price falls are as likely as price rises greater than 2Δp_t, and that price changes in each period are independent, it is straightforward to show that E(Z) = 0 and Va r(Z) = 1 / T. It follows from the central limit theorem that is (approximately) a standard normal variable. For our sample of quarterly price changes, T = 87, Z = 5 / 87 and hence which is insignificantly different from zero. Hence, we accept the null hypothesis.