A Limited Information Approach to the Simultaneous Estimation of Wage and Price Dynamics

This paper analyzes the dynamics of prices and wages using a limited information approach to estimation. I consider a two-equation model for the determination of prices and wages derived from an optimization-based dynamic model, where both goods and labor markets are monopolistically competitive, prices and wages can be re-optimized only at random intervals, and, when not re-optimized, can be partially adjusted to the previous period inflation. The estimation procedure is a two-step minimum distance estimation, which exploits the restrictions that the model imposes on a time series representation of the data. Specifically, in the first step I estimate an unrestricted autoregressive representation of the variables of interest. In the second step, I express the model solution in the form of a constrained autoregressive representation of the data, and define the distance between unconstrained and constrained representations as a function of the structural parameters that characterize the joint dynamics of inflation and labor share. This function summarizes the cross-equation restrictions between the model and the time series representations of the data. The parameters of interest are then estimated by minimizing a quadratic function of that distance. I find that the estimated dynamics of prices and wages track actual dynamics quite well, and that the estimated parameters are consistent with the observed length of nominal contracts.