Dynamic Selection and Distributional Bounds on Search Costs in Dynamic Unit-Demand Models

This paper develops a dynamic model of consumer search that, despite placing very little structure on the dynamic problem faced by consumers, allows us to exploit intertemporal variation in within-period price and search cost distributions to estimate the population distribution from which consumers' search costs are initially drawn. We show that static approaches to estimating this distribution generally suffer from a dynamic sample selection bias because forward-looking consumers with unit demand for a good may delay their purchase in a way that depends on their individual search cost. We analyze identification of the population search cost distribution using only price data and develop estimable nonparametric upper and lower bounds on the distribution function and a nonlinear least squares estimator for parametric models. We also consider the additional identifying power of weak assumptions such as monotonicity of purchase probabilities in search costs. We apply our estimators to analyze the online market for two widely used econometrics textbooks. Our results suggest that static estimates of the search cost distribution are biased upwards, in a distributional sense, relative to the true population distribution. In a small-scale simulation study, we show that this is typical in a dynamic setting where consumers with high search costs are more likely to delay purchase than those with lower search costs.