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

社会科学中的实证研究通常需要对非线性规划的最优值进行估计和得出可靠的推断。例子包括但不限于经济政策的因果效应分析;在弱假设下反事实结果（例如最优保留价格和最优收入）的分布特征;反事实投票份额和席位分配;政策干预的福利效应;合理性约束下的需求外推和福利分析;对货币政策的最大和最小反应。本研究的目的是建立一个通用的，正式的框架，并提供一种方法来估计和鲁棒推理的最优值的非线性规划的基础过程，产生了可观察的数据的弱限制。认识到该方法的计算可行性对于实证研究人员和社会更广泛的适用性和有用性至关重要，研究人员提供了用于计算拟议估计量和稳健置信区间的算法。本研究还提供了一个便携式计算机程序的集合，将与社区公开和免费或限制共享的方法，本研究的目的是开发强大的推理程序和计算方法的参数的计量经济模型，其特征是非线性规划的最优值。在这样的泛函上进行推理是不平凡的，因为底层优化问题的细微特征可能会影响推理。例如，最优解可能不是唯一的，可能是唯一的但仅弱识别的，或者可能由复杂的约束表征。由于这些具有挑战性的功能，现有的方法往往强加的假设，如约束条件的基本优化问题。这些在实践中很难验证。本研究的目的是开发推理方法，把很少的结构上的优化问题。此外，该项目旨在开发和研究可用于实施该程序的计算方法的收敛特性。非线性程序通常涉及通过模拟或求解复杂结构模型来计算的黑盒函数。该项目开发的算法以响应面法为基础，通过构建灵活的近似函数，并自适应地将评估点绘制到与找到最优值高度相关的区域，从而降低了计算成本。该奖项反映了NSF的法定使命，通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.