Estimation and Inference in Econometric Models with Asymptotic Discontinuities

具有渐近不连续性的计量经济模型中的估计和推理

• 批准号: 1058376
• 负责人: Donald Andrews
• 金额: $ 24.34万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-03-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1058376&HistoricalAwards=false
• 关键词: Estimation; Inference; Econometric; Models; Asymptotic

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.

该提案考虑了存在识别问题的模型的估计和推理方法。 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。 当模型被很好地识别后，可以使用文献中可用的标准方法来进行推理。 然而，当识别较弱或仅部分识别时，这种方法并不可靠。通常，它们会导致无效且可能误导性的推论。我们建议在识别能力较弱时研究标准方法的属性。 我们将考虑一类一般的估计和推理方法，并确定这些方法何时可靠、何时不可靠。 结果将应用于最大似然法、最小二乘法以及矩估计器和测试的广义方法。接下来，我们将开发对参数空间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广泛的横截面模型和时间序列模型。例如，它们将应用于主力自回归移动平均 (1, 1) 时间序列模型。 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以及劳工、公共财政和发展应用。将花费大量的时间和精力将一般结果应用于特定模型。在本提案中，我们还将开发新的方法，用于在模型中的识别完全崩溃时进行推理。 在这种情况下，不可能一致地估计模型中的未知参数。 然而，仍然可以构建有效的检验和置信区间。 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，这在许多不完整的经济模型中很常见。 例如，产业组织中使用的多重均衡博弈论模型就经常表现出这一特征。 我们将考虑存在大量（可能是无限）矩条件的情况，以及感兴趣的未知量是非参数量的情况。 在所有情况下，我们都将建立所提出方法的统一大样本有效性。我们还将解决模型选择后长期存在的测试问题。 这是经济学实证应用中的常见情况。 众所周知，忽略模型选择的方法不会表现出正确的大小。在之前的研究中，我们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，确定具有正确大小并且在特定意义上最优的方法。最近，在文献中引入了许多新方法，可以改进存在大量参数的问题中的估计器，比如有大量的回归参数，只有少量的非零参数。 具有这些属性的模型场景称为稀疏模型。 这些估计结果非常有用，并且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建置信区间。 该提案将研究稀疏模型中的最佳测试。 这些结果将产生有用的新方法或不可能的结果，表明现有方法无法得到显着改进。所提出的研究将通过改进的实证方法造福社会，从而导致更准确的实证研究，从而产生更明智的政策分析。 该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。 该研究将通过提供新的计算机软件供专业人士使用来增强基础设施。 研究结果将通过在国际会议上的演讲来广泛传播。