Consumer search, productivity heterogeneity, prices, markups, and pass-through: Theory and estimation

We develop and estimate a search model in which identical consumers trade with price-setting firms that differ in productivity. In the model, equilibrium distributions of both prices and markups are non-degenerate and continuous with a firm's price decreasing as its productivity increases. Variation in markups across firms is more complicated and depends on the search process and the distribution of productivity, both of which are estimated using firm-level data on retail industries in Canada. We use the estimated model to characterize the qualitative and quantitative differences in prices and markups across firms. These differences stem from firm-level variation in demand elasticities driven by productivity heterogeneity and by imperfect information about prices. Additionally, we derive analytical expressions to determine how individual firm prices and markups respond to changes in cost and demand. This allows us to empirically analyze the heterogeneity in firms' pass-through of cost and demand shocks to prices and markups. Our findings reveal substantial heterogeneity in pass-through across firms, highlighting the distributional impact of shocks across consumers purchasing at different points of the price distribution. Finally, our analysis underscores the importance of accounting for individual firm price and markup adjustments to fully understand pass-through to average prices.