Estimating dynamic discrete choice models with aggregate data: Properties of the inclusive value approximation

We investigate the use of the inclusive value based approach for estimating dynamic discrete choice models of demand with aggregate data. The inclusive value sufficiency (IVS) approach approximates a multi-dimensional state space with a single “sufficient statistic” in order to mitigate the curse of dimensionality and tractability estimate model primitives. Although in widespread use, the conditions under which IVS is appropriate have not been examined. Theoretically, we show that the estimator is biased and inconsistent. We then use Monte Carlo simulations (of a simple model of dynamic durable goods adoption) to demonstrate the degree of bias associated with the inclusive value approximation estimator under an array of parameterizations and data generating processes. In our examination, we show that the estimator performs better when the discount factor is smaller and/or when the price sensitivity of the consumer is larger. Examining how the bias impacts economic quantities of interest, we find that the IVS method under estimates the true long-run own-price elasticities and over estimates the change in profits as prices change. Theses findings highlight the importance of correctly specifying how consumers form expectations. As a result, researchers should consider how to empirically support their assumption for the underlying consumer belief structure.