A simple way to identify the degree of collusion under proportional reduction

Proportional reduction is a common cartel practice, in which cartel members reduce their output by the same percentage. We develop a simple method to quantify this reduction relative to a benchmark market equilibrium scenario. Our measure is continuous, has a simple interpretation as the "degree of collusion" and nests the earlier models in the existing literature. More importantly, by exploiting firms ex post heterogeneity and optimality conditions, Corts (1999) critique can be addressed by estimating time-varying degree of industry monopolization from a short panel of firm-level observations. We illustrate the method in Monte-Carlo simulations and in application to the data from the Joint Executive Committee railroad cartel.