Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models

This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties. Our method is similar to Rust's Nested Fixed-Point algorithm (NFXP), but the order of the two nested algorithms is swapped. First, we prove that this method produces the maximum likelihood estimator under the same conditions as NFXP. However, our procedure requires significantly fewer policy iterations than NFXP. Second, based on this algorithm, we define a class of sequential consistent estimators, K -stage Policy Iteration (PI) estimators, that encompasses MLE and Holz-Miller, and we obtain a recursive expression for their asymptotic covariance matrices. This presents the researcher with a 'menu' of sequential estimators reflecting a trade-off between efficiency and computational cost. Using actual and simulated data we compare the relative performance of these estimators. In all our experiments, the benefits in efficiency of using a two-stage PI estimator instead of a one-stage estimator (i.e., Hotz-Miller) are very significant. More interestingly, the benefits of MLE relative to two-stage PI are small.