Robust Inference and Specification Analysis in Incomplete Models

社会科学中的实证研究人员经常面临他们的模型或数据不完整的情况。当研究人员不想对他们的模型的某些部分强加强烈的假设，或者一些数据由于研究人员不知道的原因而丢失时，就会出现这种不完整性。不完全模型存在于许多实证研究中，如策略投票、产品选择、学校选择、网络形成等。在评估公共或商业政策的研究中，对数据的不完整观察是常见的。这项研究将开发新的统计方法，使研究人员能够估计不完整的模型，并以不依赖于模型编写方式的方式进行假设检验。这项研究将为理解判断错误模型成本的最佳统计程序建立一个理论框架。该项目还将开发计算机程序，以实施拟议的估计和假设检验程序，并将通过网上储存库免费向公众分发。这项研究的结果将改善政策评估，从而确立美国在政策评估方面的全球领先地位。本研究将开发一个基于似然的框架，用于不完全模型中的稳健推理和规范分析。它将研究一类具有以下结构之一的模型：i)给定结构参数和可观测变量和不可观测变量，模型预测结果的一组值；或ii)给定结构参数和可观测变量和不可控变量，模型预测结果的唯一值，但研究人员只观察到集值结果。这样的模型是非标准的，因为它们可能会接受多个似然函数。基于矩不等式的辨识和推理方法近年来得到了广泛的研究，但另一种基于似然方法的研究较少。这项研究旨在开发一种新的框架，用于基于最不有利的可能性对及其相关分数构建稳健的估计和推理过程。此外，它将提供一个框架，用于理解在存在模型或数据不完整的情况下模型错误指定的后果，并引入伪真标识集的概念。本研究开发的方法将有助于政策评估，从而有助于在美国和其他地区有效地制定和实施有效的政策。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Empirical researchers in social science often face situations in which their models or data are in- complete. Such incompleteness arises when researchers do not want to impose strong assumptions on parts of their model or some of the data are missing for reasons not known to the researcher. Incomplete models occur in many empirical studies, such as strategic voting, product choice, school choice, and network formation. Incomplete observations of data are common in studies that evaluates public or business policies. This research will develop new statistical methods that allow researchers to estimate incomplete models and conduct hypothesis testing in a way that does not depend on how the model is written. The research will develop a theoretical framework for understanding the best statistical procedures to judge the costs of incorrect models. The project will also develop computer programs for implementing the proposed estimation and hypothesis testing procedures that will be freely distributed to the public through an online repository. The results of this research will improve policy evaluation, hence establish the US as the global leader in policy evaluation.This research will develop a likelihood-based framework for robust inference and specification analysis in incomplete models. It will study a class of models that have one of the following structures: i) given a structural parameter and observable and unboservable variables, the model predicts a set of values for an outcome; or ii) given a structural parameter and observable and unboservable variables, the model predicts a unique value of outcome, but the researcher only observes a set-valued outcome. Such models are nonstandard because they may admit multiple likelihood functions. Identification and inference methods based on moment inequalities have been extensively studied recently, but an alternative likelihood-based approach is less explored. The research aims at developing a novel framework for constructing robust estimation and inference procedures based on the least favorable pair of likelihoods and its associated scores. Furthermore, it will provide a framework for understanding the consequences of model misspecification in the presence of model or data incompleteness and introducing the notion of pseudo-true identified sets. The methods developed in this research will be useful for policy evaluation, hence contribute to effective policy formulation and implementation of efficient policies in the U.S. and elsewhere.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.