What Happens When Demand is Estimated with a Misspecified Model?

Abstract:     
We conduct Monte Carlo experiments to investigate the biases in structural estimation of demand for differentiated products when the assumed demand functional form is misspecified. We focus on aggregate data (i.e. not individual purchase decisions) and generate stochastic equilibrium price and quantity data for four types of markets; each market has a different demand specification: linear, log-linear, Almost Ideal Demand System (AIDS), and logit, but all markets share the same cost specification. Using instrumental variables, we then estimate demand with the correct and the misspecified functional forms. Biases in estimates of own- and cross-price elasticities are typically largest when "continuous choice" models (linear, log-linear, AIDS) are used to estimate the discrete choice model (logit), and vice versa. However, when misspecified, logit's biases in own- and cross-price elasticities disappear as the assumed market potential approaches a specific value. This advantage of the logit model can also play against it (if the econometrician only observes aggregate quantity data): if the assumed market potential is incorrect, logit will fail to recover the true elasticities even when correctly specified. Conversely, continuous choice models estimates are not biased when correctly specified or when the wrong continuous choice model is employed. We conduct merger simulations to analyze a misspecified model's accuracy in post-merger predictions and confirm the importance of the assumed market potential in logit estimation. Our overall results tend to favor the use of a logit model even when the discreteness of the purchase decision is questionable.

Keywords: Demand, discrete choice, mergers, misspecification, differentiated products, structural estimation

JEL Classification: C15, L11, L41

Accepted Paper Series