Sequential Search Models: A Pairwise Maximum Rank Approach

TL;DR

This paper introduces the pairwise maximum rank (PMR) estimator for sequential search models with unobserved quality and endogenous variables, enabling consistent estimation without full consideration set data.

Contribution

The paper proposes the PMR estimator, a novel method that achieves consistent parameter estimation in complex search models without requiring knowledge of the true match value distribution.

Findings

The position effect in Expedia hotel search is estimated between $0.11 and $0.36.

The true match value distribution is unlikely to be normal (0,1).

Ignoring endogeneity biases estimates upward by at least $1.17.

Abstract

This paper studies sequential search models that (1) incorporate unobserved product quality, which can be correlated with endogenous observable characteristics (such as price) and endogenous search cost variables (such as product rankings in online search intermediaries); and (2) do not require researchers to know the true distribution of the match value between consumers and products. A likelihood approach to estimate such models gives biased results. Therefore, I propose a new estimator -- pairwise maximum rank (PMR) estimator -- for both preference and search cost parameters. I show that the PMR estimator is consistent using only data on consumers' search order among one pair of products rather than data on consumers' full consideration set or final purchase. Additionally, we can use the PMR estimator to test for the true match value distribution in the data. In the empirical application, I apply the PMR estimator to quantify the effect of rankings in Expedia hotel search using two samples of the data set, to which consumers are randomly assigned. I find the position effect to be \$0.11-\$0.36, and the effect estimated using the sample with randomly generated rankings is close to the effect estimated using the sample with endogenous rankings. Moreover, I find that the true match value distribution in the data is unlikely to be N(0,1). Likelihood estimation ignoring endogeneity gives an upward bias of at least \$1.17; misspecification of match value distribution as N(0,1) gives an upward bias of at least \$2.99.