# Price Synchronization in the Calvo Model

In the paper Gorodnichenko, Sheremirov and Talavera (2014) the authors compute empirically the degree of price synchronization across different goods. In a nutshell their definition of synchronization is given by: $$sync^h_i = \frac{(A− 1)}{(B − 1)} \text{ provided A > 0 and B > 1}$$ where $A$ is the number of sellers of good $i$ that change their prices and $B$ is the total number of sellers of good $i$. The measure is computed over an horizon $h$ in weeks.

They then compare this empirical measure with what would be implied by the Calvo (1983) model of price adjustment. In page 16 they argue that the degree of synchronization at horizon $h$ in the Calvo (1983) model is given by:

$$sync_{calvo} = 1 - (1 - \bar{f})^{h+1}$$

where $\bar{f}$ is the median frequency of price adjustment. I have two questions regarding the last equation:

1) Why does the calvo model imply this degree of price synchronization? 2) What should be the frequency at which $\bar{f}$ is computed? Is it annual? Weekly? Something tells me it should be a daily measure of the frequency of price adjustment ... But if that is the case the figure 2 on their paper below, implies that a 0 week horizon, $\bar{f}$ should be 0.2. I have no idea where this number comes from (definitely does not seem consistent with their estimates of price adjustment in table 5).