  Multinomial choice models are fundamental for empirical modeling of economic
choices among discrete alternatives. We analyze identification of binary and
multinomial choice models when the choice utilities are nonseparable in
observed attributes and multidimensional unobserved heterogeneity with
cross-section and panel data. We show that derivatives of choice probabilities
with respect to continuous attributes are weighted averages of utility
derivatives in cross-section models with exogenous heterogeneity. In the
special case of random coefficient models with an independent additive effect,
we further characterize that the probability derivative at zero is proportional
to the population mean of the coefficients. We extend the identification
results to models with endogenous heterogeneity using either a control function
or panel data. In time stationary panel models with two periods, we find that
differences over time of derivatives of choice probabilities identify utility
derivatives "on the diagonal," i.e. when the observed attributes take the same
values in the two periods. We also show that time stationarity does not
identify structural derivatives "off the diagonal" both in continuous and
multinomial choice panel models.
