Computationally Intensive Strategies for Structural Modelling

本提案要求继续支持一个研究非线性计量经济学方法的项目。这条研究路线的动机是，关于经济学的思想、理论和模型的计量经济学推断应该在不妥协于学科的情况下进行：经济模型不应该被简化或粗略地近似，以适应计量经济学理论施加的限制。先前拨款下的研究主要集中在参数和半参数结构模型的估计上，这些模型非常复杂，只能通过模拟方法进行估计。这个想法是要求由结构模型模拟确定的力矩与某个截断筛的分数相匹配。这种估计方法与最大似然方法一样有效，因此被称为有效矩法或EMM。开发了基于分数的诊断方法，可以确定模型失败的原因。这些方法在数据丰富的情况下，如金融计量经济学，效果很好。当应用于数据稀疏的领域（如宏观经济学）时，允许的最大截断点变得如此之小，以至于诊断无法检测到模型无法跟踪数据的重要特征（如条件尺度），并且通过诊断测试证明模型充分性的声明变得可疑。该奖项支持类似于EMM的方法的开发，这些方法在数据稀疏时工作得很好。最有希望的是贝叶斯方法，该方法将结构模型作为截断筛上的先验。这样做的好处是，先验相当于降低了维数，使得在数据稀疏时计算变得可行。先前的松弛导致信息性诊断。为该贝叶斯估计量开发的马尔可夫链蒙特卡罗计算策略也可以应用于频率估计量。由于该方法比传统的准牛顿爬坡方法具有更强的鲁棒性，因此使用非标准准则函数进行估计是可行的。克莱默-冯·米塞斯标准是一个有趣的例子，因为当经济模型被公认为错误指定时，它是可以辩护的，并且它在应用中给出的结果在性质上似乎与贝叶斯方法相似。本文寻求克拉默-冯·米塞斯估计的理论依据。该项目还继续了一项正在进行的实证工作计划，该计划利用了计量经济学研究计划下开发的新方法。初步工作将侧重于确定能够通过基于宏观时间序列数据的模型充分性测试的结构性宏观模型，在需要另外面对来自资产横截面的现金流量数据时，是否还能继续这样做。广泛的影响：是否有切实可行的方法从数据中确定足够丰富的实质性模型的参数，以准确地表示目标现象，是否有方法评估这些模型的充分性，具有相当大的社会重要性。该计划中开发的方法已应用于科学，商业和政府。在科学领域，传播是广泛的；在非经济和非统计期刊上引用的样本如下：《美国流行病学杂志》、《美国博物学家》、《人类生物学年鉴》、《生态学》、《药物动力学和生物制药杂志》、《精神病学研究杂志》、《自然》、《物理学D》和《地球物理与化学c》。向商业和政府的传播主要是通过将项目中开发的方法纳入商业统计软件包（如SAS）中。

This proposal requests continued support for a program of research in nonlinear econometric methods. The motivation for this line of research is that econometric inference regarding the ideas, theories, and models from economics should be made without compromise to the discipline: Economic models should not be simplified or crudely approximated to accommodate limits imposed by econometric theory.Research under the previous grant focused on estimation of parametric and semiparametric structural models that are so complex that they can only be estimated by simulation methods. The idea was to require that moments determined by simulation from the structural model match the scores of a certain truncation sieve. This estimator is as efficient as maximum likelihood would be were it feasible and is termed efficient method of moments or EMM for that reason. Diagnostics based on the scores that can pinpoint the reasons for model failure were developed. These methods work well when data is abundant such as financial econometrics. When applied in areas where data is sparse, such as macroeconomics, the maximum permissible truncation point becomes so small that the diagnostics cannot detect a model's inability to track important features of the data such as conditional scale and a claim that passing the diagnostic tests certifies a model's adequacy becomes suspect.This award supports the development of methods similar to EMM that work well when data is sparse. The most promising is a Bayesian approach for which the structural model is taken as the prior on a truncation sieve. The advantage is that the prior amounts to a dimensionality reduction that makes computations feasible when data is sparse. Relaxation of the prior leads to informative diagnostics. The Markov chain Monte Carlo computational strategy developed for this Bayesian estimator can also be applied to frequentist estimators. Because it is more robust than traditional quasi Newton hill climbing methods, estimation using nonstandard criterion functions becomes practicable. The Cramer-Von Mises criterion is an instance that is interesting because it is defensible when the economic model is admittedly misspecified and it gives results that seem qualitatively similar to the Bayesian approach in applications. A theoretical justification of Cramer-Von Mises estimates is sought. This project also continues an ongoing program of empirical work that exploits new methodologies developed under this program of econometric research. Initial work will focus on determining whether structural macro models that can pass tests of model adequacy based on macro time series data will continue to do so when required to confront, in addition, data on cash flows from a cross section of assets.Broad impact: The availability of practicable methods to determine from data the parameters of substantive models rich enough to accurately represent target phenomena and the availability of methods to assess the adequacy of such models is of considerable societal importance. The methods developed within the program have been applied in science, business, and government. In thesciences diffusion has been broad; a sample of citations in non-economic and non-statistical journals is the following: American Journal of Epidemiology, American Naturalist, Annals of Human Biology, Ecology, Journal of Pharmacokinetics and Biopharmaceutics, Journal of Psychiatric Research, Nature, Physica D, and Physics and Chemistry of the Earth C. Diffusion to business and government has been primarily through inclusion of methods developed within the project in commercial statistical packages such as SAS.