Appendix A. Constructing Firm-Specific Markups
Our construction of firm-specific markups closely follows De Loecker and Warzynski (2012). A firm i at time t produces output using the following production technology:
The only restriction we impose on Qit to derive an expression of markup is that Qit is continuous and twice differentiable with respect to its arguments.
Cost-minimizing producers consider the following Lagrangian function:
where wit and rit denote a firm’s input cost for labor and capital, respectively. The first-order condition with respect to labor input is
where the marginal cost of production at a given level of output is λit as
Define markup μ as the ratio of price over marginal cost,
Based on equation (22), once the labor elasticity, θi, is obtained from the production function estimation and the share of labor costs in total sales,