Collaborative Research: Identification, Estimation, and Inference of DSGE Models

本计画发展动态随机一般均衡（DSGE）模型之辨识理论，并研究其对估计与推论之意涵。 动态随机一般均衡模型现在已经达到可以分析重要宏观经济问题的复杂程度。 尽管这些模型中的参数过去是经过校准的，但过去二十年来数值方面的进步使人们有可能估计具有多达一百个参数的模型。然而，研究人员意识到，由于识别问题，并非所有感兴趣的参数都可以一致地估计：不同的结构参数可能导致无法区分的结果。 尽管认识到这一识别问题，一个程序还没有开发，告诉我们有多少参数是可识别的，如果是这样的，这一项目的第一个目标是研究条件下，DSGE模型是可识别的。分析是非标准的，因为经典的识别条件依赖于DSGE模型中通常不成立的假设。 我们的建议是使用DSGE模型的紧密结构，以建立新的秩和顺序的识别条件。这些条件尚未在文献中提出。重点是协方差平稳过程，第一步是精确的意义下，两个动力系统可以有观测等价的谱密度。适应控制理论的结果，它表明，马尔可夫（脉冲响应）参数和等效DSGE模型的误差方差必须通过相似变换。 这些限制，然后用来建立条件下，DSGE模型是可识别的可观测量的频谱。 我们将表明，DSGE模型是可识别的，即使其简化形式的参数是不。 将制定正式的识别条件，以明确处理测量误差的存在。本项目的第二个目标是研究DSGE模型参数的估计。 众所周知，无法识别的参数无法得到一致的估计。这对频率论和贝叶斯分析都有重要的影响，因为当使用平坦先验时，局部非识别会导致后验的奇怪行为。尽管这个问题的重要性，文献上的非确定DSGE模型的全信息估计是相对较少的。 DSGE约简形式参数不能从谱中识别的结果对于仅使用自协方差子集的有限信息估计具有重要意义。 该项目将提供一个完整的表征的“可识别的减少形式”组成的动态方程和身份。 充分和有限的信息估计的挑战是降低秩的误差方差。 本计画的第三个目标是研究DSGE模型的推论。 部分识别的模型对测试提出了挑战性的问题。 该项目侧重于两个问题。 第一，在DSGE模型等奇异系统中，当感兴趣的参数是点可辨识的，而讨厌的参数不是点可辨识的时，如何检验统计假设。 第二，如何在动态和可能的奇异模型中进行推理，当感兴趣的参数本身仅被识别时。 这些问题是具有挑战性的，但也相关的DSGE框架外。智力优点：目前，不存在正式的识别结果DSGE模型，允许更少的冲击比内生变量。 该项目提供了易于评估的等级和顺序条件，以供从业者检查。 降阶形式参数未知时的结构参数估计与推断以及广义系统的集合辨识都是新的研究课题。 更广泛的影响：DSGE模型越来越多地用于政策分析，因此这项工作的影响超出了更好地理解线性动力系统的方法。 这项工作也是相关的估计和推理的其他奇异模型，如需求系统。 部分识别的动态模型的推断是普遍感兴趣的。 计算机代码将提供给科学界用于非商业、研究和教育目的。

This project develops the theory for identification of dynamic stochastic general equilibrium (DSGE) models and studies its implications for estimation and inference. DSGE models have now reached the level of sophistication to permit analysis of important macroeconomic issues. Whereas the parameters in these models used to be calibrated, numerical advances in the last two decades have made it possible to estimate models with as many as a hundred parameters. Researchers are, however, aware that not all the parameters of interest can be consistently estimated because of identification problems: that different structural parameters can lead to indistinguishable outcomes. In spite of the recognition of this identification issue, a procedure has yet to be developed that tells us in a systematic manner how many parameters are identifiable, and if so which ones.The first goal of this project is to study conditions under which a DSGE model is identifiable. The analysis is nonstandard as classical conditions for identification rely on assumptions that do not generally hold in DSGE models. Our proposal is to use the tight structure of DSGE models in order to establish new rank and order conditions for identification. Such conditions have not yet been proposed in the literature. T he focus is on covariance stationary process and the first step is to make precise the sense in which two dynamical systems can have observationally equivalent spectral densities. Adapting results from control theory, it is shown that the Markov (impulse response) parameters and the error variance of equivalent DSGE models must be related through a similarity transformation. These restrictions are then used to establish conditions under which DSGE models are identifiable from the spectrum of the observables. We will show that a DSGE model is identifiable even when its reduced form parameters are not. Formal identification conditions will be developed to explicitly handle the presence of measurement errors. The second goal of this project is to study the estimation of DSGE model parameters. It is a well known fact that parameters that are not identifiable cannot be consistently estimated. This has important implications for both frequentist as well as Bayesian analysis as local non-identification leads to strange behavior of posteriors when flat priors are used. In spite of the importance of this problem, the literature on full information estimation of non-identified DSGE models is relatively small. The result that DSGE reduced form parameters are not identifiable from the spectrum has important implications for limited information estimation which uses only a subset of the autocovariances. The project will provide a complete characterization of an 'identifiable reduced form' consisting of dynamic equations and identities. The challenge for both full and limited information estimation is an error variance of reduced rank. The project will develop new estimation methods for singular systems without throwing away information or adding stochastic errors.The third goal of the project is to focus on inference in DSGE models. Partially identified models pose challenging problems for testing. The project focuses on two issues. First, how to test statistical hypothesis in singular systems such as DSGE models when the parameters of interest are point identified but the nuisance parameters are not. Second, how to conduct inference in dynamic and possibly singular models when the parameters of interest are themselves only set identified. These problems are challenging, but are also relevant outside of the DSGE framework.Intellectual Merit: Currently, there exists no formal identification results for DSGE models that allow for fewer shocks than endogenous variables. This project provides easy to evaluate rank and order conditions for identification that practitioners can check. Estimation and inference of structural parameters when the reduced form parameters are not identified, and set identification in singular systems are both new research topics. The results will be a new contribution to econometric theory.Broader Impacts: DSGE models are increasingly used in policy analysis, so the impact of this work goes beyond a better methodological understanding of linear dynamical systems. The work is also relevant to estimation and inference of other singular models such as demand systems. Inference of partially identified dynamic models is of general interest. The computer code will be made available to the scientific community for non-commercial, research, and educational purposes.