TY - UNPB

T1 -  Higher Order Improvements for Approximate Estimators

AU - Kristensen, Dennis

AU - Salanié, Bernard

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

M3 - Working paper

BT -  Higher Order Improvements for Approximate Estimators

PB - Department of Economics, University of Copenhagen

ER -