Collaborative Research: Factor-Augmented Vector Autoregressions [FAVARs] and the Analysis of Monetary Policy

已有相当多的文献使用向量自回归(VAR)方法试图确定货币政策创新对各种宏观经济变量的影响。这些方法通常提供对产出和价格等变量对政策冲击的动态反应的经验上可信的评估，它们已被广泛用于评估结构模型的适合性和政策应用。然而，各种基于VAR的方法当然也没有逃脱批评。对VAR方法用于货币政策识别的几个批评集中在低维VAR使用的信息量相对较少的问题上。典型的VAR分析中使用的稀疏信息集至少会产生两个潜在问题。首先，如果央行和私营部门拥有的信息没有在VAR系统中得到反映，那么对政策创新的衡量很可能会受到污染。这个潜在问题的一个标准例证是，在一些VAR中，价格对货币政策冲击的反常反应。有人认为，这种价格谜题是由于对央行可能掌握的有关未来通胀的信息控制不力造成的。在VAR分析中使用稀疏信息集产生的第二个问题是，只有包含在VAR中的变量才能观察到脉冲响应，这些变量通常只占我们关心的变量的一小部分。该项目开发了一种计量经济学方法，解决了这两个问题，同时保留了小维VAR分析的好处。具体地说，它结合了标准的VAR分析和因子分析。最近对动态因素模型的研究表明，来自大量时间序列的信息可以用少量的指数或因素来有效地总结。研究人员将估计因素添加到其他标准VAR中，得到了因子增广VAR(或FAVAR)。FAVAR可以用两步法或最大似然法来估计，这两种方法考虑了第二阶段VAR分析中因子估计的不确定性。初步工作表明，FAVAR可以帮助解决上述两个问题：第一，货币政策收益率的Favar分析合乎情理和严格估计的脉冲响应函数；特别是价格谜题得到了极大的改善。其次，FAVAR允许在单一的统一方法中估计各种宏观变量对政策冲击的反应。该项目对基本分析进行了若干扩展，既有计量经济学的，也有实质性的。计量经济学的扩展包括制定经验加权方案，以便更准确地衡量经济中的基本因素。实质性扩展包括开发实时测量潜在变量的方法，如产出缺口；对数据修订及其预测能力进行基于因素的分析；以及表征货币政策对股票价格的影响。

A considerable literature has developed that employs vector autoregression (VAR) methods to attempt to identify the effects of monetary policy innovations on various macroeconomic variables. These methods generally deliver empirically plausible assessments of the dynamic responses of variables such as output and prices to policy shocks, and they have been widely used both for assessing the fit of structural models and in policy applications. However, the various VAR-based approaches have certainly not escaped criticism. Several of the criticisms of the VAR approach to monetary policy identification center around the relatively small amount of information used by low-dimensional VARs. The sparse information sets used in typical VAR analyses create at least two potential problems. First, to the extent that central banks and the private sector have information not reflected in the VAR system, the measurement of policy innovations is likely to be contaminated. A standard illustration of this potential problem is the perverse response of prices to monetary policy shocks in some VARs. It is argued that this price puzzle results from imperfectly controlling for information that the central bank may have about future inflation. A second problem arising from the use of sparse information sets in VAR analyses is that impulse responses can be observed only for variables included in the VAR, which generally constitute only a small fraction of the variables that we care about. This project develops an econometric approach that addresses both of these issues while retaining the benefits of small-dimension VAR analyses. Specifically, it combines the standard VAR analyses with factor analysis. Recent research in dynamic factor models suggests that the information from large numbers of time series can be usefully summarized by a small number of indexes, or factors. The investigators add estimated factors to otherwise standard VARs, obtaining factor-augmented VARs (or FAVARs). FAVARs can be estimated by two-step methods or by maximum likelihood methods that account for uncertainty in the factor estimation in second-stage VAR analysis. Preliminary work shows that FAVARs can help solve both problems alluded to above: First, FAVAR analyses of monetary policy yield plausible and tightly estimated impulse response functions; in particular, the price puzzle is greatly ameliorated. Second, FAVARs allow estimates of the responses of a wide variety of macro variables to policy shocks within a single unified approach. This project pursues a number of extensions to the basic analysis, both econometric and substantive. Econometric extensions include the development of empirical weighting schemes to provide for more precise measurement of the underlying factors in the economy. Substantive extensions include developing methods for real-time measurement of latent variables such as the output gap; factor-based analysis of data revisions and their forecast ability; and characterization of the effects of monetary policy on stock prices.