Collaborative Research: Robust Inference and Computational Methods for Optimal Values of Nonlinear Programs

Trustees Of Boston University, Boston

Investigators

Abstract

Empirical research in the social sciences often entails estimating and drawing robust inference about optimal values of nonlinear programs. Examples include, but are not limited to, the analysis of causal effects of economic policies; features of the distribution of counterfactual outcomes (e.g. optimal reserve prices and optimal revenues) under weak assumptions; counterfactual vote shares and seats assignments; welfare effects of policy interventions; demand extrapolation and welfare analysis subject to rationality constraints; maximum and minimum responses to monetary policies. This research aims at establishing a general, formal framework and providing a methodology for estimation and robust inference on optimal values of nonlinear programs under weak restrictions on the underlying process that has generated the observable data. Recognizing that the computational feasibility of the method is crucial for its applicability and usefulness for empirical researchers and society more broadly, the investigators deliver algorithms for computation of the proposed estimators and robust confidence intervals. This research also delivers a collection of portable computer programs implementing the methodology that will be shared with the community openly and free of charges or restrictions. This research aims at developing robust inference procedures and computational methods for parameters in econometric models that are characterized as optimal values of nonlinear programs. Making inference on such functionals is nontrivial because subtle features of the underlying optimization problem may affect inference. For example, the optimal solution may not be unique, may be unique but only weakly identified, or may be characterized by intricate constraints. Due to these challenging features, existing methods often impose assumptions such as constraint qualifications on the underlying optimization problem. These are hard to verify in practice. This research aims at developing inference methods that place very little structure on the optimization problem. Further, the project aims at developing and investigating the convergence properties of a computational method that can be used to implement the procedure. Nonlinear programs often involve black-box functions that are computed by simulation or by solving a complex structural model. The algorithm developed in this project, which is based on the response surface method, mitigates the computational cost by constructing flexible approximations to such functions and adaptively drawing evaluation points to regions that are highly relevant for finding the optimal value. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.