Demand Estimation with Selection Bias: A Dynamic Game Approach with an Application to the US Railroad Industry

Abstract

This paper is motivated by the US freight railroad industry, which is characterized by a major restructuring over the last 30 years. In particular, the number of active firms decreased from 26 in 1978 to seven in 2006 due to several takeover waves. The empirical focus concerns the estimation of a structural demand model for the US railroad industry. Then, the demand estimates are used to compute the evolution of the mark-ups, the quality of the freight services provided, and the consumer surplus. The restructuring of this industry involves significant exit and takeovers. This implies that the data is characterized by an attrition issue, which generates a selection problem. A focus is to provide an estimation algorithm which takes explicitly into account this attrition issue. I find that the algorithm produces more plausible estimates of demand coefficients compared to standard estimation procedures. Moreover, using the model, I recover the evolution of the marginal costs, mark-ups, and the consumer surplus over time. I find that the takeover waves have led to efficiency gains by decreasing the marginal costs, and this was translated into lower prices and an increase in the consumer surplus. Finally, the takeovers have led to a reallocation of assets from the less efficient firms to the most efficient firms, which improved the quality of the freight services provided.