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Higher Order Improvements for Approximate Estimators

Dennis Kristensen; Bernard Salanie

Title:
Higher Order Improvements for Approximate Estimators
Author(s):
Kristensen, Dennis
Salanie, Bernard
Date:
Type:
Working papers
Department:
Economics
Permanent URL:
Series:
Department of Economics Discussion Papers
Part Number:
0910-15
Publisher:
Department of Economics, Columbia University
Publisher Location:
New York
Abstract:
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.
Subject(s):
Economic theory
Item views:
209
Metadata:
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