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

社会科学的实证研究通常需要估计和绘制关于非线性规划的最优值的稳健推断。例子包括，但不限于，对经济政策因果效应的分析；弱假设下反事实结果（如最优储备价格和最优收入）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；理性约束下的需求外推与福利分析对货币政策的最大和最小反应。本研究旨在建立一个通用的形式化框架，并提供一种方法，用于在产生可观测数据的底层过程的弱限制下对非线性规划的最优值进行估计和鲁棒推断。认识到该方法的计算可行性对于其对经验研究人员和更广泛的社会的适用性和有用性至关重要，研究人员提供了计算所提出的估计量和稳健置信区间的算法。这项研究还提供了一组实现该方法的便携式计算机程序，这些程序将与社区公开、免费或有限制地共享。本研究旨在开发具有非线性程序最优值特征的计量经济模型参数的鲁棒推理程序和计算方法。对这样的函数进行推断是非常有意义的，因为底层优化问题的细微特征可能会影响推断。例如，最优解可能不是唯一的，可能是唯一的但只是弱识别的，或者可能具有复杂的约束条件。由于这些具有挑战性的特征，现有的方法经常对潜在的优化问题施加约束条件等假设。这些很难在实践中得到证实。本研究的目的是开发推理方法，在优化问题上投入很少的结构。此外，该项目旨在开发和研究可用于实现该程序的计算方法的收敛性。非线性程序通常涉及通过模拟或通过求解复杂结构模型来计算的黑盒函数。本课题开发的算法基于响应面法，通过对这些函数构造灵活的近似，并自适应地将评价点绘制到高度相关的区域，以寻找最优值，从而降低了计算成本。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识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.