Nonlinear Price Adjustment and the Lifetime of a Price Level

The objective of this paper is to develop and test empirically a new model of imperfect price adjustment. The new model offers two extensions of classical models. First, it allows for a variable proportion of price-setters adjusting their prices at any given period. Second, the duration of deviation of the price level from the equilibrium level depends on the inflationary environment. In the high-inflation economies, price adjustment is much faster than in the low-inflation economies. Using the existing partial equilibrium models of monopolistic competition [Spence (1976), Dixit and Stiglitz (1977)] and models of imperfect price adjustment [Calvo (1983), Caplin and Spulber (1987)], we construct a new model and show that the inflationary environment (approximated by the average inflation rate) has a positive impact on the number of agents who adjust their prices and negative impact on the duration of the price level. The latter relationship is nonlinear. To test the model we use a sample of data on the price level and the money supply (both M1 and M2) covering the period from 1969 to 1999, consisting of 138 (M1) and 115 countries (M2). After checking for non-stationarity and using the Johansen procedure, we estimate the cointegration relationship between the money supply and the price level. Afterwards, we test the impact of inflationary environment on obtained estimates. We find that the average inflation rate in the analysed period has significant impact on the estimates. First, the cointegrating parameter increases (in absolute value) with the average inflation rate. It means that in high inflation countries the price level follows the money supply more tightly. Second, the error correction parameter increases (also in absolute value) with inflation. This, in turn, means that deviations of the price level from the equilibrium (dictated by the money supply) are corrected much faster in high-inflation economies and that the duration of the price level in these economies is much shorter. We find that this relationship is indeed nonlinear, as predicted by the theoretical model.