A Control Function Approach to Endogeneity in Consumer Choice Models

TLDR

Endogeneity in consumer choice models, arising from omitted variables such as unobserved demand factors linked to price or advertising, causes standard estimators to be inconsistent. The study proposes a control function approach to address endogeneity in consumer choice models. The method derives controls from observed variables and theory, then applies both the control function and product‑market controls to households’ television package choices where unobserved programming quality is likely price‑correlated. Correcting for endogeneity flips the estimated demand curve from upward‑sloping to downward‑sloping, with both methods yielding comparable results.

Abstract

Endogeneity arises for numerous reasons in models of consumer choice. It leads to inconsistency with standard estimation methods that maintain independence between the model's error and the included variables. The authors describe a control function approach for handling endogeneity in choice models. Observed variables and economic theory are used to derive controls for the dependence between the endogenous variable and the demand error. The theory points to the relationships that contain information on the unobserved demand factor, such as the pricing equation and the advertising equation. The authors’ approach is an alternative to Berry, Levinsohn, and Pakes's (1995) product-market controls for unobserved quality. The authors apply both methods to examine households’ choices among television options, including basic and premium cable packages, in which unobserved attributes, such as quality of programming, are expected to be correlated with price. Without correcting for endogeneity, aggregate demand is estimated to be upward-sloping, suggesting that omitted attributes are positively correlated with demand. Both the control function method and the product-market controls method produce downward-sloping demand estimates that are similar.