A Mixture Model for Filtering Firms' Profit Rates

Existing methods for sample selection from noisy profit rate data in the industrial organization field of economics tend to be conditional on a covariate's value that risks discarding valuable information. We condition sample selection on the profit rate data structure instead by use of a Bayesian mixture model. In a two-component (signal and noise) mixture that reflects the prior belief of noisy data, each firm profit rate observation is assigned an indicator latent variable. Gibbs sampling determines the latent variables' posterior densities, sorting profit rate observations to the signal or noise component. We apply two model specifications to empirical profit rate cross-sections, one with a normal and one with a Laplace signal component. We find the Laplace specification to have a superior fit based on the Bayes factor and the profit rate sample to be time stationary Laplace distributed, corroborating earlier estimates of cross-section distributions. Our model retains 97%, as opposed to as little as 20 %, of the raw data in a previous application.