Higher Order Improvements for Approximate Estimators

Abstract

Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. Approximations typically impart additional bias and variance to the resulting estimator. We here propose three methods to improve the properties of such \approximate estimators at a low computational cost. The rst method provides an analytical bias adjustment for estimators based on stochastic approximators, such as simulation-based estimators. Our second proposal is based on ideas from the resampling literature; it eliminates the leading bias term for non-stochastic as well as stochastic approximators. Finally, we propose an iterative procedure where we use Newton-Raphson (NR) iterations based on a much ner degree of approximation. The NR step removes much of the additional bias and variance of the initial approximate estimator. A Monte Carlo simulation on the mixed logit model shows that combining these approaches can yield spectacular improvements at a low cost.