Minimum Distance Estimation of Search Costs Using Price Distribution

It has been shown that equilibrium restrictions in a search model can be used to identify quantiles of the search cost distribution from observedprices alone. These quantiles can be difficult to estimate in practice. This article 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-square 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 bootstrap. Our estimator can be used to estimate the cost distribution nonparametrically on a larger support when prices from heterogenous markets are available. We propose a two-step sieve estimator for that case. 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. Supplementary materials for this article are available online.

已有研究证实，搜索模型中的均衡约束仅需通过观测价格即可识别搜索成本分布的分位数。但实际应用中，这类分位数的估计往往颇具难度。本文采用最小距离法开展估计，该方法计算简便易行。本文提出的某类估计量可转化为非线性最小二乘问题，能够在STATA等统计软件中直接编程实现。本文证明该估计量具有相合性与渐近正态分布，其分布可通过自助法（bootstrap）进行一致估计。当可获取异质性市场的价格数据时，本估计量可在更大的支撑集上非参数估计成本分布，针对该情形本文提出了两步筛估计量（two-step sieve estimator）：第一步对各市场的分位数进行估计，第二步将这些估计得到的分位数作为生成变量，执行非参数筛估计。本文推导了该筛估计量的一致收敛速度，可用于量化跨市场插值数据所产生的估计误差。为展示方法的应用效果，本文采用英格兰足球联赛赛事的在线博彩赔率作为价格数据，实证结果表明，英国修订允许博彩运营商更广泛开展宣传的法律后，消费者的搜索成本有所下降。本文的补充材料可在线获取。