Higher Order Improvements for Approximate Estimators
Kristensen
Dennis
author
Columbia University. Economics
Salanie
Bernard
author
Columbia University. Economics
Columbia University. Economics
originator
contributor
text
Working papers
New York
Department of Economics, Columbia University
2010
English
Many modern estimation methods in econometrics approximate an objective function, through simulation or discretization for instance. The resulting "approximate" estimator is often biased; and it always incurs an efficiency loss. We here propose three methods to improve the properties of such approximate estimators at a low computational cost. The first two methods correct the objective function so as to remove the leading term of the bias due to the approximation. One variant provides an analytical bias adjustment, but it only works for estimators based on stochastic approximators, such as simulation-based estimators. Our second bias correction 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 finer degree of approximation. The NR step removes some or all of the additional bias and variance of the initial approximate estimator. A Monte Carlo simulation on the mixed logit model shows that noticeable improvements can be obtained rather cheaply.
Economic theory
Department of Economics Discussion Papers
0910-15
http://hdl.handle.net/10022/AC:P:9187
NNC
NNC
2010-07-06 17:17:33 -0400
2011-08-02 13:09:38 -0400
1668
eng