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We propose to combine smoothing, simulations and sieve approximations tosolve for either the integrated or expected value function in a general classof dynamic discrete choice (DDC) models. We use importance sampling toapproximate the Bellman operators defining the two functions. The randomBellman operators, and therefore also the corresponding solutions, aregenerally non-smooth which is undesirable. To circumvent this issue, weintroduce a smoothed version of the random Bellman operator and solve for thecorresponding smoothed value function using sieve methods. We show that one canavoid using sieves by generalizing and adapting the `self-approximating' methodof Rust (1997) to our setting. We provide an asymptotic theory for theapproximate solutions and show that they converge with root-N-rate, where $N$is number of Monte Carlo draws, towards Gaussian processes. We examine theirperformance in practice through a set of numerical experiments and find thatboth methods perform well with the sieve method being particularly attractivein terms of computational speed and accuracy.

Solving Dynamic Discrete Choice Models Using Smoothing and Sieve Methods