  We study the use of Temporal-Difference learning for estimating the
structural parameters in dynamic discrete choice models. Our algorithms are
based on the conditional choice probability approach but use functional
approximations to estimate various terms in the pseudo-likelihood function. We
suggest two approaches: The first - linear semi-gradient - provides
approximations to the recursive terms using basis functions. The second -
Approximate Value Iteration - builds a sequence of approximations to the
recursive terms by solving non-parametric estimation problems. Our approaches
are fast and naturally allow for continuous and/or high-dimensional state
spaces. Furthermore, they do not require specification of transition densities.
In dynamic games, they avoid integrating over other players' actions, further
heightening the computational advantage. Our proposals can be paired with
popular existing methods such as pseudo-maximum-likelihood, and we propose
locally robust corrections for the latter to achieve parametric rates of
convergence. Monte Carlo simulations confirm the properties of our algorithms
in practice.
