Feasible Estimation of Firm-Specific Allocative Inefficiency through Bayesian Numerical Methods

The estimation of allocative and technical inefficiency has grown to an enormous body of literature, both theoretical and empirical. Ideally, one would estimate time-varying firm and input-specific parameters describing allocative inefficiency in order to minimize aggregation bias. However, this has never been previously accomplished. Typically, only industry-wide allocative efficiency parameters have been empirically identified. Our proposed solution is to employ Gibbs sampling to approximate posterior distributions from a Bayesian limited information model, embedding GMM moment conditions imposed via an instrumental variables step to obtain plant-specific parameters estimates that vary flexibly over time. For a panel of Chilean hydroelectric power plants, posterior distributions of these estimates display substantial differences in location and precision. By contrast, the standard GMM approach which produces industry-wide, time-varying allocative inefficiency parameters, not only fails to reveal the inter-plant differences by construction, but does not even produce posterior medians that approximate a weighted average of the plant-specific posterior medians.