Estimation and Inference in Econometric Models with Asymptotic Discontinuities

这项建议考虑了对出现识别问题的模型的估计和推断方法。这样的模型在经济学和其他社会科学的许多领域以及生物科学中都很常见。当模型被很好地识别时，可以使用文献中可用的标准方法来进行推理。然而，当识别能力较弱或只有部分识别能力时，这种方法是不可靠的。通常，它们会导致无效的和潜在的误导性推理。我们建议在识别能力较弱的情况下调查标准方法的性质。我们将考虑一类一般的估计和推断方法，并确定这些方法何时可靠，何时不可靠。这些结果将适用于最大似然法、最小二乘法和广义矩估计法和检验。下一步，我们将开发对参数空间的部分弱识别的存在具有鲁棒性的方法。这些结果将适用于经济学中使用的一大类横截面和时间序列模型。例如，它们将应用于工作-自回归-移动平均(1，1)时间序列模型。所得结果也适用于非线性回归模型、平稳过渡自回归模型、二元选择模型和工具变量模型。这些模型通常用于宏观经济学的时间序列应用程序以及劳工、公共财政和发展应用程序。在将一般结果应用于特定模型时，将花费大量的时间和精力。在这项建议中，我们还将开发新的方法，在模型中存在完全识别故障时进行推理。在这种情况下，不可能一致地估计模型中的未知参数。然而，仍有可能构建有效的测试和可信区间。当所考虑的模型指定了许多条件矩不等式和/或等式时，我们将这样做，这在许多不完全经济模型中是常见的。例如，产业组织中使用的具有多个均衡的博弈论模型经常表现出这一特征。我们将考虑存在大量的、可能是无限的矩条件的情况，以及感兴趣的未知量是非参数的情况。在所有情况下，我们都将建立建议方法的统一大样本有效性。我们还将解决长期存在的模型选择后的测试问题。在经济学的实证应用中，这是一个常见的场景。众所周知，忽略模型选择的方法不会显示正确的大小。在以前的研究中，我们已经开发了一些方法来绕过这个问题。在这里，我们的目标是更进一步，确定具有正确的规模和在特定意义上最优的方法。最近，在文献中，已经有许多新的方法被引入，以改善存在大量参数的问题的估计量，例如大量的回归参数，而只有少量的非零参数。具有这些属性的模型场景称为稀疏。这些估计结果非常有用，并正越来越多地被用于经济学中。然而，在稀疏模型中进行测试和构造可信区间的方法很少。这项建议将研究稀疏模型中的最优测试。这些结果要么产生有用的新方法，要么产生不可能的结果，表明现有方法无法显著改进。拟议的研究将通过改进的经验方法造福社会，从而导致更准确的经验研究，从而更有见地的政策分析。这项研究将通过使用研究生作为研究助理和合作研究人员来促进教学和培训。这项研究将通过为该行业提供新的计算机软件来加强基础设施。研究结果将通过在国际会议上介绍的方式广泛传播。

This proposal considers estimation and inference methods for models that exhibit problems with identification. Such models are common in many areas of economics and other social sciences, as well as biological sciences. When a model is well identified, standard methods available in the literature can be used to carry out inference. However, when identification is weak or when identification is only partial, such methods are not reliable. Typically, they lead to invalid and potentially misleading inference.We propose to investigate the property of standard methods when identification is only weak. We will consider a general class of estimation and inference methods and determine when the methods are reliable and when they are not. The results will apply to maximum likelihood, least squares, and generalized method of moments estimators and tests. Next, we will develop methods that are robust to the existence of weak identification in parts of the parameter space. These results will apply to a broad class of cross-section and time series models used in economics. For example, they will apply to the work-horse autoregressive-moving average (1, 1) time series model. The results also will apply to nonlinear regression models, smooth transition autoregressive models, binary choice models, and instrumental variables models. These models are employed routinely in macroeconomics times series applications and labor, public finance, and development applications. Considerable time and effort will be spent in applying the general results to specific models.In this proposal, we will also develop new methods for carrying out inference when there is a complete breakdown of identification in a model. In this case, it is not possible to consistently estimate the unknown parameters in the model. However, it still is possible to construct valid tests and confidence intervals. We will do this when the models under consideration specify a number of conditional moment inequalities and/or equalities, as is common in many incomplete economic models. For example, game theory models with multiple equilibria, which are used in industrial organization, often exhibit this feature. We will consider the case where there are a large, possibly infinite, number of moment conditions, as well as the case where the unknown quantity of interest is a nonparametric quantity. In all cases, we will establish the uniform large sample validity of the proposed methods.We will also address long-standing issues of testing subsequent to model selection. This is a common scenario in empirical applications in economics. It is well-known that methods that ignore model selection do not exhibit correct size. In previous research, we have developed some methods that circumvent this problem. Here we aim to go a step further and determine methods that have correct size and are optimal in a specific sense.Recently in the literature, there have been a number of new methods introduced that improve estimators in problems where there are a large number of parameters, such as a large number of regression parameters, with only a small number of non-zero parameters. Model scenarios with these properties are called sparse. These estimation results are quite useful and are being employed increasingly in economics. However, few methods are available for carrying out tests and constructing confidence intervals in sparse models. This proposal will investigate optimal tests in sparse models. Such results will yield either useful new methods or impossibility results showing that existing methods cannot be improved upon significantly.The proposed research will benefit society through improved empirical methods that lead to more accurate empirical research and, consequently, better informed policy analysis. The research will promote teaching and training through the use of graduate students as research assistants and collaborative researchers. The research will enhance infrastructure by making new computer software available for use by the profession. The results of the research will be disseminated broadly via presentation at international conferences.