This proposal investigates three projects on the numerical implementation of econometric estimation and inference methods.
The first project studies a numerical Delta method for inference on a directionally differentiable function of regular parameters. This method is computationally efficient, does not require analytic knowledge of the structure of the function of interest, and provides uniformly valid inference for testing a one-sided hypothesis of a convex function of the parameters. In situations where the first order Delta method limiting distribution is degenerate, the second (or higher) order Delta method may provide the necessary nondegenerate large sample approximation.
The second project, studies a more general resampling technique which will be called the numerical bootstrap, that can consistently estimate the limit distribution in many cases where the conventional bootstrap is not valid and where subsampling has been the most commonly used inference approach, and where the parameters are not known to be directionally differentiable. Applications include constrained and unconstrained M-estimators converging at both regular and nonstandard rates such as the maximum score model, partially identified models, misspecified simulated GMM models, and many sample size dependent statistics.
The third project studies classical extremum estimators and Laplace-type Bayesian estimators subject to general nonlinear constraints through a variety of penalization methods of including l0, l1 and l2 norms. These estimators offer computationally attractive alternatives to nonlinear programming alternatives. The penalized posterior locations achieve first order asymptotic efficiency implied by the imposition of the constraints under general conditions that allow for nonsmooth and simulation based models. Bayesian credible intervals are asymptotically valid confidence intervals in a pointwise sense, providing exact asymptotic coverage for general functions of the parameters. Furthermore, the proposed project allows for nonadaptive and adaptive penalizations, and both estimated and simulated constraints.