Quasi-Bayesian Alternative to M-Estimation

本研究发展了一类计量经济学的估计方法，称为拟贝叶斯估计，这是计算和实际吸引力。估计量被简单地定义为经济参数兴趣的准后验分布的平均值或中位数（或其他类似的量）。与传统的贝叶斯方法不同，准后验分布是通过转换可能没有任何似然解释的标准或目标函数（如GMM中的目标函数）来生成的。 该方法是有用的，新的一类“半参数”的问题，不强加刚性参数结构的经济模型的利益。 这种估计的主要应用包括非线性广义矩方法和各种其他结构计量经济模型，如工具中位数回归，其中传统的估计是非常困难或实际上不可行的计算。原则上，所有这些模型都可以在微观经济模型和经济政策评估的背景下回答非常有趣的经济问题。然而，这些模型的实际估算和使用面临着非常严峻的实施挑战。拟贝叶斯估计依靠马尔可夫链蒙特卡罗方法克服了这个问题。这使我们能够形成一类实用，易于使用，并具有优良的统计特性的估计。 该项目开发了一个类的半参数模型，落在传统的baidu推断的拟baidu估计的正式统计和计算特性。渐近正态性和一致性的估计证明，它表明，准后验分位数可以用于作出推论有关参数的声明。 该项目还实现了计算机程序，并通过模拟演示了整个方法的实用性。 还提出了一个实证应用。它使用递归非线性分位数（风险价值）模型来估计动态市场风险预测。这个应用程序对于法律要求每天和每周评估风险价值的金融公司和银行来说非常感兴趣。

This research develops a class of econometric estimation procedures, called quasi-bayesian estimators, which are computationally and practically attractive. The estimator is simply defined as the mean or median (or other quantity alike) of the quasi-posterior distribution of economic parameter interest. Unlike in the conventional bayesian approach, the quasi-posterior distribution is generated by transforming a criterion or objective function (such as that in GMM) which may not have any likelihood interpretation. The approach is useful and new for a class of ``semi-parametric" problems that do not impose rigid parametric structure on the economic model of interest. The main application of this estimation consists of nonlinear generalized method-of-moments and various other structural econometric models, such as instrumental median regression, in which the conventional estimates are very hard or practically infeasible to compute . All of these models allow, in principle, to answer very interesting economic questions in the context of microeconomic models and economic policy evaluation. However, the practical estimation and use of such models faces very severe implementation challenges. Quasi-bayesian estimation overcomes this problem by relying on the markov chain monte carlo methods. This allows us to form a class of estimators that are practical, easy to use, and that have excellent statistical properties. The project develops the formal statistical and computational properties of quasi-bayesian estimators for a class of semi-parametric models that fall outside the conventional bayesian inference. Asymptotic normality and consistency of the estimates are proven, and it is shown that the quasi-posterior quantiles can be used for making inferential statements about parameters of interest. The project also implements computer programs and demonstrates the usefulness of the entire approach through simulations. An empirical application is also presented. It deals with estimation of dynamic market risk forecasts using the recursive nonlinear quantile (value-at-risk) models. This application is of great interest to the financial firms and banks who are required by law to asses value-at-risk on a daily and a weekly basis.