State-Dependent Demand Estimation with Initial Conditions Correction

Abstract

The authors analyze the initial conditions bias in the estimation of brand choice models with structural state dependence. Using a combination of Monte Carlo simulations and empirical case studies of shopping panels, they show that popular, simple solutions that misspecify the initial conditions are likely to lead to bias even in relatively long panel data sets. The magnitude of the bias in the state dependence parameter can be as large as a factor of 2–2.5. The authors propose a solution to the initial conditions problem that samples the initial states as auxiliary variables in a Markov chain Monte Carlo procedure. The approach assumes that the joint distribution of prices and consumer choices is in equilibrium, which is plausible for the mature consumer packaged goods products commonly used in empirical applications. In Monte Carlo simulations, the approach recovers the true parameter values even in relatively short panels. Finally, the authors propose a diagnostic tool that uses common, biased approaches to bound the values of the state dependence and construct a computationally light test for state dependence.