Estimation and Inference in Econometric Models with Asymptotic Discontinuities

该建议考虑了模型的估计和推理方法，这些模型表现出识别问题。 这种模型在经济学和其他社会科学以及生物科学的许多领域都很常见。 当一个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，当识别能力较弱或识别能力不强时，这种方法就不可靠。通常情况下，它们会导致无效的和潜在的误导性的推断。我们建议调查的标准方法的属性时，识别只是弱。 我们将考虑一般类的估计和推理方法，并确定何时方法是可靠的，何时不可靠。 结果将适用于最大似然，最小二乘法，和广义矩估计和测试的方法。接下来，我们将开发对部分参数空间中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广泛的横截面和时间序列模型。例如，它们将应用于工作马自回归移动平均（1，1）时间序列模型。 这些结果也适用于非线性回归模型、平滑过渡自回归模型、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时间序列应用和劳动力，公共财政和发展应用。相当多的时间和精力将花费在将一般结果应用到特定的model.In本提案中，我们还将开发新的方法进行推理时，有一个完全故障的识别模型。 在这种情况下，不可能一致地估计模型中的未知参数。 然而，仍然可以构造有效的检验和置信区间。 我们将这样做时，考虑的模型指定了一些条件矩不等式和/或等式，这是常见的许多不完全的经济模型。 例如，在产业组织中使用的具有多重均衡的博弈论模型经常表现出这一特征。 我们将考虑的情况下，有一个大的，可能是无限的，数量的矩条件，以及情况下，未知量的利益是一个非参数量。 在所有情况下，我们将建立所提出的方法的统一大样本有效性。我们还将解决长期存在的问题，测试后，模型选择。 这是经济学中经验应用的常见场景。 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规避这个问题。在这里，我们的目标是更进一步，并确定方法，有正确的大小，并在特定sense.Recently在文献中，已经有一些新的方法介绍，提高估计的问题，有大量的参数，如大量的回归参数，只有少数非零参数。 具有这些属性的模型方案称为稀疏。 这些估计结果是非常有用的，并在经济学中得到越来越多的应用。 然而，很少有方法可用于在稀疏模型中进行测试和构造置信区间。 本提案将研究稀疏模型中的最优检验。 这些结果将产生有用的新方法或不可能的结果，表明现有的方法无法显着改善，拟议的研究将通过改进的实证方法，导致更准确的实证研究，从而更好地知情的政策分析，造福社会。 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。 这项研究将通过提供新的计算机软件供专业人员使用来加强基础设施。 研究结果将通过在国际会议上介绍而广泛传播。

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.