Unification of Bayesian and Frequentist Inference in Econometrics

在实证经济学中，描述模型参数和预测的不确定性有两种主要方法：经典方法，也被称为频率论方法，根据它们在许多可能数据集上的平均表现来评估推断和估计过程。相比之下，贝叶斯方法专注于给定的数据集，并在此数据集上有条件地执行推理。贝叶斯（条件）和经典（频率论）属性的可取性在经验经济学中以及更一般地在统计学文献中得到了很好的理解。在一大类标准估计问题中，经典和贝叶斯方法提供了近似相等的结果。因此，通常的经典估计程序有吸引力的频率和条件属性。然而，近年来，实证经济学的大量注意力都集中在非标准估计问题上，这两种方法之间的等价性可能会失败。例如，非标准问题出现在高度持久的时间序列模型中。许多经济时间序列，如通货膨胀和利率是高度持续的。另一类重要的非标准问题包括部分或弱识别参数的问题，换句话说，这些问题中的数据只包含关于感兴趣的数量的相对少量的信息。模型参数和预测的不确定性通常由集合估计量描述，对于给定的数据，它提供了一组感兴趣的数量的可能值。现有的经典方法的建设集估计不一定提供令人信服的描述非标准问题的不确定性，因为他们可能有不良的条件属性。本研究的第一部分旨在发展一套评估和建构非标准计量经济学问题的集合估计量的方法。在这个框架下，吸引集估计具有频率和条件性质。所提出的方法包括理论结果和数值算法。它将在一些经常出现在经济学应用中的非标准问题上进行说明。经典方法和贝叶斯方法之间的关系尚未完全理解的另一个重要领域是高维参数的灵活模型。这种模型在经济应用中很有用，因为它们通过施加更少的先验限制“让数据说话”。拟议的研究的第二部分，旨在促进文学如何构建灵活的模型，贝叶斯和经典属性。

There are two main approaches to describing uncertainty about model parameters and forecasts in empirical economics.The classical approach, which is also known as the frequentist approach, evaluates inference and estimation procedures in terms of how they perform on average over many possible datasets. In contrast, the Bayesian approach focuses on a given dataset and performs inference conditionally on this dataset. The desirability of both Bayesian (conditional) and classical (frequentist) properties is well understood in empirical economics and, more generally, in the statistics literature.In a large class of standard estimation problems, the classical and Bayesian approaches deliver approximately equivalent results. Thus, usual classical estimation procedures have attractive frequentist and conditional properties. In recent years, however, though, a lot of attention in empirical economics has been devoted to non-standard estimation problems, where the equivalence between the two approaches can fail. For instance, non-standard problems arise in models for highly persistent time series. Many economic time series such as inflation and interest rates are highly persistent. Another important class of non-standard problems includes problems with partially or weakly identified parameters, in other words, problems in which data contain only a relatively small amount of information about a quantity of interest.Uncertainty about model parameters and forecasts is usually described by set estimators, which for given data provide a set of likely values for a quantity of interest. Existing classical methods for construction of set estimators do not necessarily provide compelling descriptions of uncertainty in non-standard problems as they might have poor conditional properties. The first part of the proposed research intends to develop a methodology for evaluation and construction of set estimators in non-standard econometric problems. In this framework, attractive set estimators possess both frequentist and conditional properties. The proposed methodology includes theoretical results and numerical algorithms. It will be illustrated on a number of non-standard problems that routinely arise in economics applications.Another important area where the relationship between the classical and Bayesian approaches has not been completely understood is flexible models with high-dimensional parameters. Such models are useful in economic applications as they "let data speak" by imposing fewer a priori restrictions. The second part of the proposed research seeks to contribute to the literature on how to construct flexible models that posses both Bayesian and classical properties.