Minimum Distance Estimation of Search Costs using Price Distribution

Hong and Shum (2006) show equilibrium restrictions in a search model can be used to identify quantiles of the search cost distribution from observed prices alone. These quantiles can be difficult to estimate in practice. This paper uses a minimum distance approach to estimate them that is easy to compute. A version of our estimator is a solution to a nonlinear least squares problem that can be straightforwardly programmed on softwares such as STATA. We show our estimator is consistent and has an asymptotic normal distribution. Its distribution can be consistently estimated by a boostrap. Our estimator can be used to estimate the cost distribution nonparametrically on a larger support when prices from heterogeneous markets are available. There we propose a two-step sieve estimator. The first step estimates quantiles from each market. They are used in the second step as generated variables to perform nonparametric sieve estimation. We derive the uniform rate of convergence of the sieve estimator that can be used to quantify the errors incurred from interpolating data across markets. To illustrate we use online bookmaking odds for English football leagues’ matches, as prices, and find evidence that suggests search costs for consumers have fallen following a change in the British law that allows gambling operators to advertise more widely.