Common threshold in quantile regressions with an application to pricing for reputation

Abstract

<p>The paper develops a systematic estimation and inference procedure for</p><p>quantile regression models where there may exist a common threshold</p><p>effect across different quantile indices. We first propose a sup-Wald test for</p><p>the existence of a threshold effect, and then study the asymptotic proper-</p><p>ties of the estimators in a threshold quantile regression model under the</p><p>shrinking threshold effect framework. We consider several tests for the</p><p>presence of a common threshold value across different quantile indices</p><p>and obtain their limiting distributions. We apply our methodology to study</p><p>the pricing strategy for reputation through the use of a data set from</p><p>Taobao.com. In our economic model, an online seller maximizes the sum</p><p>of the profit from current sales and the possible future gain from a tar-</p><p>geted higher reputation level. We show that the model can predict a jump</p><p>in optimal pricing behavior, which is considered as“reputation effect” in</p><p>this paper. The use of threshold quantile regression model allows us to</p><p>identify and explore the reputation effect and its heterogeneity in data.</p><p>We find both reputation effects and common thresholds for a range of</p><p>quantile indices in seller’s pricing strategy in our application.</p>