Identification Of Discrete Choice Models Research Articles

Nonparametric identification of discrete choice models with lagged dependent variables

Variation in covariates can be used to nonparametrically identify a discrete choice model with a lagged dependent variable and discrete unobserved heterogeneity (Kasahara and Shimotsu, 2009; Browning and Carro, 2014). In some cases the number of support points of the unobserved heterogeneity distribution is restricted only by the number of points of support in the distribution of the covariates. This paper provides conditions under which these models can be identified with continuous heterogeneity using continuous variation in the covariates. The identification argument is related to that of Honore and Lewbel (2002) in that it requires a “special regressor” (Lewbel, 1998), but it does not assume an additively separable latent index. Identification requires only 3 time periods, neither stationarity nor time homogeneity is imposed, and the distribution of the initial condition is not restricted apart from conditions required for the special regressor. I demonstrate the result through a Monte Carlo simulation.

A note on identification of discrete choice models for bundles and binary games

We study nonparametric identification of single‐agent discrete choice models for bundles (without requiring bundle‐specific prices) and of binary games of complete information. We show that these two models are quite similar from an identification standpoint. Moreover, they are mathematically equivalent when we restrict attention to the class of potential games and impose a specific equilibrium selection mechanism in the data generating process. We provide new identification results for the two related models. Discrete choice demand binary games identification bundles complements substitutes entry games potential games C14 C35 C57 C72

Identifying the Discount Factor of Forward Looking Consumers Based on Consumption from Inventory

In this paper we study the identification of discrete choice models of dynamically optimizing consumers. We first provide additional formal results for existing identification solutions. We then investigate the ‘last in, last out’ (LILO) constraint on consuming from the inventory as a means to identifying the discount factor in these models. We find that the LILO constraint (over-)identifies the discount parameter in the absence of assumptions about consumers’ expectations and show how LILO results in efficient estimates in a parametric, maximum likelihood framework using simulated data. Finally, we report survey based empirical evidence for the relevance of LILO strategies in four different categories.

Masking identification of discrete choice models under simulation methods

We present examples based on actual and synthetic datasets to illustrate how simulation methods can mask identification problems in the estimation of discrete choice models such as mixed logit. Simulation methods approximate an integral (without a closed form) by taking draws from the underlying distribution of the random variable of integration. Our examples reveal how a low number of draws can generate estimates that appear identified, but in fact, are either not theoretically identified by the model or not empirically identified by the data. For the particular case of maximum simulated likelihood estimation, we investigate the underlying source of the problem by focusing on the shape of the simulated log-likelihood function under different conditions.