Minimum Distance Estimation of Search Costs Using Price Distribution

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. (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 di¢ cult 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. Permanent repository linkWe show our estimator is consistent and has an asymptotic normal distribution. Its distribution can be consistently estimated by a bootstrap. Our estimator can be used to estimate the cost distribution nonparametrically on a larger support when prices from heterogeneous markets are available. We propose a two-step sieve estimator for that case. The …rst 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 …nd evidence that suggests search costs for consumers have fallen following a change in the British law that allows gambling operators to advertise more widely. JEL Classification Numbers: C13, C15, D43, D83, L13Keywords: Bootstrap, Generated Variables, M-Estimation, Search Cost, Sieve EstimationWe are very grateful to the authors of Moraga-González, Sándor and Wildenbeest (2013) for sharing their MATLAB code with us. We thank an anonymous referee for helpful comments and suggestions. We would also like to thank

Dynamic selection and distributional bounds on search costs in dynamic unit‐demand models

“…In this paper, we propose a dynamic model with forward‐looking consumers to estimate the population consumer search cost distribution. Like many other recent studies, such as Hong and Shum (), Moraga‐González and Wildenbeest () (henceforth MGW), Wildenbeest (), Moraga‐González, Sandor, and Wildenbeest (), and Sanches, Silva Junior, and Srisuma (), we focus on the case where only the distribution of prices in each period is observed, but no individual‐level data on consumers is available. We show that if consumers have the option to delay purchase until a later period, a dynamic selection problem exists that will cause estimates obtained from a static model to be biased.…”

“…Moraga‐González, Sandor, and Wildenbeest () estimated the search distribution more completely on an interval by pooling multiple markets with the same search technology and exploiting the variation in valuations and marginal costs across markets. Sanches, Silva Junior, and Srisuma () used a minimum distance approach, modifying Hong and Shum () to create a consistent and asymptotically normal estimator. Wildenbeest () tackled the problem when homogeneous products are sold by vertically differentiated sellers, while De los Santos, Hortaçsu, and Wildenbeest () estimated search costs for a differentiated product in a model with learning.…”

Price setting in Brazil from 1989 to 2007

“…The model is broadly based on Hong and Shum (2006), Moraga- González and Wildenbeest (2008), Sanches et al (2018), and Moraga- González et al (2017a). All of these authors propose a similar base model following the theoretical work of Burdett and Judd (1983) in order to structurally estimate search costs in markets of homogeneous goods using only observed price distribution data.…”

“…Where F p (p l ) solves the profit indifference condition of all stores in a symmetric Nash mixed strategy equilibrium 36 See also Hong and Shum (2006) for an empirical likelihood estimation (MEL) and Sanches et al (2018)…”

“…This is the estimation procedure on which the present chapter is based. Sanches et al (2018) propose a minimum distance estimator approach. All these methodologies are especially useful, since price data is widely available, while quantities supplied or demanded are not.…”