A Forest Approach for Analyzing the Heterogeneous and Nonlinear Effects of Sellers’ Response Time

Problem definition: In online-marketplace bargaining, how fast to respond to a buyer’s offer is a question many sellers face. Whereas a fast response signals the seller’s eagerness to sell, a slow response signals the seller’s insincerity or irresponsibility. In this paper, we use a unique dataset from eBay’s best-offer platform to study the effect of the seller’s response time on the buyer’s concession. Methodology/results: We first use a multiple instrumental variable (IV) regression to study the average effect of the seller’s response time. We find that the effect of the seller’s response time on the buyer’s concession first increases and then decreases (i.e., following an inverted-U shape). We then develop a new multi-treatment IV forest approach, which incorporates a multiple IV regression into a forest, to study the heterogeneous and nonlinear effects of the seller’s response time. We find that the effect of the seller’s response time varies widely across different items. Finally, we use the results from our empirical analyses to derive the best response time for the seller. We find that using the best response time leads to a sizeable increase in the buyer’s concession. Managerial implications: Our results are helpful to online marketplaces, because we find that the effect of the seller’s response time is nonlinear and heterogeneous across different items. Our results are also helpful to the seller, because we find the best response time that increases the buyer’s concession. Finally, our results are helpful to academia, because we develop a new causal machine learning method for analyzing the heterogeneous effects of multiple treatments with endogeneity issues.