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

Define Δpt as the economy-wide average change in producer prices in period t.Then define zt= 1 (−1) if the proportion of industries with price falls in period t is lower (higher) than the proportion with price rises greater than 2Δpt. Finally, define Z = (z1+K+ZT)/T. Under the null hypothesis that price falls are as likely as price rises greater than 2Δpt, 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 Inline Equation is (approximately) a standard normal variable. For our sample of quarterly price changes, T = 87, Z = 5 / 87 and hence Inline Equation which is insignificantly different from zero. Hence, we accept the null hypothesis.