Efficient Two-Step Estimation via Targeting

Abstract

The standard description of two-step extremum estimation amounts to plugging-in a first-step estimator of nuisance parameters to simplify the optimization problem and then deducing a user friendly, but potentially inefficient, estimator for the parameters of interest. In this paper, we consider a more general setting of two-step estimation where we do not necessarily have ‘nuisance parameters’ but rather awkward occurrences of the parameters of interest. The efficiency problem associated with two-step estimators in this context is more difficult than with standard nuisance parameters as even if the true unknown value of the parameters were plugged-in to alleviate the awkward occurrences of the parameters, the resulting second-step estimator may not be efficient. In addition, standard approaches to restore efficiency for two-step procedures may not work due to a consistency issue. To alleviate this potential issue, we propose a new computationally simple two-step estimation procedure that relies on targeting and penalization to enforce consistency, with the second-step estimators maintaining asymptotic efficiency. We compare this new method with existing iterative methods in the framework of copula models and asset pricing models. Simulation results illustrate that this new method performs better than existing iterative procedures and is (nearly) computationally equivalent.