A Method to Estimate Discrete Choice Models That Is Robust to Consumer Search

Overview

This research addresses the identification problem in discrete choice modeling when consumer preferences must be recovered from choice data generated under incomplete information. The authors establish sufficient conditions for identifying true preferences without requiring knowledge of the search process consumers employ. The core innovation is a method based on cross-derivatives of choice probabilities that remains valid across different search protocols and information structures, contrasting with conventional approaches that produce biased estimates of hidden attribute valuations.

Methods and approach

The study constructs a theoretical framework defining a search model in which: (i) econometricians observe attributes hidden to consumers; (ii) consumers follow a search rule by which goods with higher non-hidden utility components are also searched when lower-ranked alternatives are evaluated; and (iii) utility maximization occurs over the searched set. The proposed identification strategy employs cross-partial derivatives of choice probabilities rather than direct probability variation. The approach encompasses full information as a special case and permits specification testing to discriminate between informed and uninformed choice regimes. A laboratory experiment validates the methodology by measuring preference recovery accuracy when subjects engage in costly sequential search.

Results

The cross-derivative method successfully recovers consumer preferences under incomplete information conditions where canonical discrete choice estimators yield systematically biased parameter estimates, particularly for hidden attributes. Parameter values estimated through the proposed approach align with true preference structures revealed through experimental observation. The method achieves robustness across heterogeneous search protocols without requiring specification of the underlying search model. Tests for full information perform as predicted by theory within experimental conditions.

Implications

The findings establish that preference identification under incomplete information is achievable through choice data alone under explicitly stated behavioral restrictions, without requiring additional instruments or behavioral assumptions about search processes. This result expands the scope of discrete choice estimation to settings where complete information cannot be assumed, such as markets with search frictions, information asymmetries, or limited consumer attention. The approach enables researchers to distinguish between two sources of limited responsiveness to attribute variation: true preference indifference versus incomplete information, with significant consequences for policy simulations and market equilibrium analysis.