动态因子模型的理论和应用研究
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摘要
近十年来，动态因子模型的理论和方法获得极大的发展，已经成为计量经济学新的研究领域和重要的学术前沿。动态因子模型的主要特征为：估计的动态因子包含了丰富的宏观和微观信息；基于估计的因子组成VAR模型，即FAVAR模型，可以解决VAR的信息缺失等。近十年的快速发展，使得动态因子模型已经成为宏观计量经济学的重要分支，并广泛应用于宏观经济政策的评估。对我国而言，系统地研究动态因子模型的相关文献还较少。在此背景下，本文系统地研究动态因子模型的理论和应用，以期对因子模型的理论和应用有所扩展和创新。
从理论上，本文重点研究动态因子模型的三个重要分支：预测模型、FAVAR模型和分层动态因子模型。基于预测的视角，本文发掘了因子和因子模型的内涵。在此基础上，本文重点解析FAVAR模型。而分层因子模型则是经典动态因子模型在结构上的拓展。这三个分支的关系层层递进，也代表了动态因子模型发展的三个阶段。在具体的计量方法上，本文尝试对不同或者相同的问题，使用多种估计方法，以进行对比分析，如因子的估计、因子个数等。由此体现了本文对因子模型的理论研究深度。在实证研究方面，本文针对国内的经济背景和数据，综合考虑国外既有研究，在深刻理解模型和方法论的基础上，对我国通胀的宏观成分、CPI的波动源、世界通胀因子及其对我国的影响、货币政策冲击的度量、宏观预测等，进行了深入的研究，产生具有创新性的研究成果。本文的主要研究内容和研究结论及其创新意义可以概述如下：
第一，对于预测模型，我们发现，大型模型的结构反映了真实的预测模型的特征。而增量的R2表明，大型模型的结构可以浓缩为动态因子模型。上述分析说明，动态因子模型反映真实的经济结构，从而使预测的理念和结果更为先进。本文的上述分析与和西方学者的研究结论近似。本文还认为，动态因子模型的预测能力显著优于经典的AR和VAR模型。典型的，以M2为例，使用单个因子就可以改进AR模型的预测结果，从而使预测精度提高26%；使用7个因子导致预测精度的提高接近40%。本文还发现，第一个因子对预测M2提供了重要的增量信息。相关性显示，第一个因子综合了实际经济活动内容（宏观经济最重要的基本面）。这个证据提示，因子综合了宏观经济重要的基本面因素（或驱动力量）。
第二，在FAVAR模型的研究中，本文构建了代表中国宏观经济各方面信息的宏观经济信息集，应用最新的因子提取方法，从这个宏观经济信息集中提取因子并建立关于因子和可观测的共同因子的FAVAR模型。本文将FAVAR模型用于货币政策冲击的度量。研究结论表明，和常用的货币新息不同，短期利率的新息是我国货币政策冲击的准确测度。本文进而在FAVAR模型中扩展方差分解和历史分解方法。方差分解显示，我国货币政策冲击解释了产出和通胀方差的11%和9.8%，历史分解也显示，我国货币政策冲击不是任何一次产出和通胀大幅持续波动的主要原因。所以，本文认为，货币政策冲击不是我国经济波动的主要冲击源。上述模型和结论，体现了本文的创新。
第三，在FAVAR模型的基本框架内，本文进行应用性的扩展和创新：将FAVAR模型用于通胀波动源的分解，考察中国通胀分类指数的波动源及其性质。具体而言，将我国CPI的8大类分解为宏观成分与特质成分，并根据宏观因子组成的VAR识别货币政策冲击的动态效应。本文发现，宏观冲击和特质冲击都是CPI大类的重要波动源，但是宏观冲击的效应相对持久。所以，货币政策需要重点关注宏观冲击的效应并盯住CPI大类的宏观成分。货币政策冲击的动态效应显示，货币政策冲击对各大类的传导存在一定的规律性。据我们所查阅的文献，本文系国内第一次使用FAVAR模型揭示我国CPI大类的波动源，从这个角度来说，本文的研究具有开拓性意义。
第四，本文基于FAVAR的理论和本文的实证结果，进一步精炼宏观成分的理论概念和理论解释。我们根据FAVAR模型的估计结果，计算我国CPI的宏观成分并且揭示宏观冲击效应。主要结果为，我国的宏观信息集存在八个宏观因子，它们基本准确地刻画了我国宏观经济运行的动态特征。样本期5个不同的通胀（通缩）期，宏观成分的均值占通胀均值的比，度量了通胀的程度，揭示了通胀的来源。典型的是2010~2011年的通胀期，其宏观成分占比达到134%，证实了这是一轮由宏观因素驱动的严重通胀。宏观冲击效应显示，针对宏观因素驱动的通胀，紧缩货币和需求而不是单纯地紧缩货币，将有效地抑制通胀的上涨和反复。从上述可知，本文基于我国的现实和估计结果，具体精炼和解释了宏观成分。
第五，由于众多批评家认为估计的因子难以解释，由此产生了分层动态因子模型。分层动态因子模型将变量分块，同时估计共同因子和分块因子，部分地解决了如何解释因子的难题。本文采用序贯主成分的估计方法，从65个国家（地区）和区域CPI中提取世界通胀因子、区域通胀因子和国家通胀因子。本文发现，世界通胀因子基本准确地刻画了全球通胀形势，对各国、各区域具有重要影响力。本文的研究证实了世界通胀周期的存在性。从方差分解的结果来看，世界通胀因子对发达国家和发达区域CPI方差的贡献强于发展中国家和发展中区域。对整个样本区间，世界通胀因子对我国通胀的影响较小，但是近年来影响力逐渐增强。但是，国家通胀因子对发展中国家和区域具有很强的解释力。据我们查阅的文献，上述研究是我国关于分层动态因子的首次研究，体现了本文对国际前沿的紧密跟踪和应用性创新。
Over the past decade, dynamic factor models have received considerableattention. The reason why the dynamic factor model to get the attention, the mostimportant starting point is to predict. Because the estimated factor contains a lot ofinformation, so many researchers began to use the estimated factor in the differentmodels. FAVAR model can solve the lack of information of the VAR. When we use theFAVAR model of monetary policy effects, the conclusions and the classical theory isconsistent. Many critics believe that the estimated factor is difficult to explain.Hierarchical factor models estimate the common factor and block factor at the same time.The estimated factors can then be interpreted. Driven by empirical researches, factormethodologies have got great progress in recent years. Dynamic factor model, there arestill many obstacles unresolved, such as the basis of the model theory, the factorexplained. However, after nearly ten years of rapid development, the dynamic factormodel has become an important macroeconometric branch, and attracted more and moreattention in the field of macroeconomic policy.
In this context, this paper will focus on the theory and application of dynamic factormodels. This article will study the prediction models based on dynamic factor models,FAVAR models and hierarchical dynamic factor models. For prediction perspective, wehope to explore the meaning of the factor and factor model. On this basis, FAVAR modelsfocus on the use of the estimated factors. Hierarchical factor models are the expansion ofthe classic dynamic factor models. The three models also represent the three stages ofdevelopment by the dynamic factor model. This article seeks to use a variety of estimationtechniques, such as factor estimators and estimators of the number of factors in differentsections. This paper take into account the abroad researches and domestic economicbackground, and strive to do innovative research based on a deep understanding of thebasis of the model and methodology. The main conclusion of the study can besummarized as follows:
First, the large model appears to be true prediction model. The estimated results showthat the model structure can be concentrated to a dynamic factor model. In other words, dynamic factor models can reflect the real economic structure. This paper considers thepredictive ability of the dynamic factor model, and we find that dynamic factor modelsbehavior better than the classic AR and VAR models. We also find that the first factorprovides a considerable incremental information when predicting M2. Correlation showsthat the first factor combines real economic activities (the most important macroeconomicfundamental). This evidence suggests that the factor may be a combination of the mostimportant macroeconomic fundamentals (or driving force).
Second, we construct a large macroeconomic information set, from which we extracta few common factors. Based on a factor-augmented VAR, we evaluate candidateindicators of monetary policy shocks, and analyze their contribution to economicfluctuations. We find that shout-term interest rate innovations behave well as indicators ofmonetary policy shocks, because identified effects of monetary policy shocks are in linewith basic consensus. Monetary policy shocks explain25.4percent,11percent and9.8percent of monetary policy, output and inflation, respectively. Historical decompositionsshow that most of sharp fluctuations in output and inflation were not explained bymonetary policy shocks. Thus, monetary policy shocks are not the main source of China'seconomic fluctuations.
Third, we specifies a factor-augmented vector autoregression (FAVAR) based oneconomic theories and Chinese macroeconomic time series. The estimatedmacroeconomic factors show that the general economic conditions can be reflected bymonetary policy and six latent factors. Then the fluctuations in sectoral inflation rates dueto the macroeconomic factors are disentangled from those due to sector-specificconditions, and the effects of monetary policy shocks on sectoral inflation rates areidentified in FAVAR models. The main finding is that macroeconomic shocks andsector-specific shocks are both important to sectoral inflation fluctuations, butmacroeconomic shocks tend to have more persistent and sluggish effects on sectoralinflation rates. Therefore, monetary policy should focus on the effects of macroeconomicshocks and the macroeconomic components of sectoral inflation rates. The dynamiceffects of monetary policy shocks on sectoral inflation rates indicate some regularities.
Fourth, we decompose the fluctuations in China’s CPI index into macroeconomic component that are due to macroeconomic factors and idiosyncratic shocks which comefrom disaggregate prices variations. Then, we conduct some typical impulse response ofthe CPI index to macroeconomic shocks. Our main finding is that the eightmacroeconomic factors do capture important dimensions of Chinese macroeconomicmovements. The analysis of macroeconomic component and its mean’s ratio to the meanof inflation rate itself provides a new sight for properties and sources of Chinese inflationin the different time periods. Typically, the ratio is134%in the2010-2011period ofinflation, which shows this is a serious inflation and is driven by macroeconomic factors.The effects of macroeconomic shocks imply that tightening of both monetary and demandrather than only monetary itself will effectively stabilize the inflation.
Fifth, in hierarchical factor models, this paper extracts world inflation factor, regionalinflation factor and the national inflation factor from65national and regional CPI indexesby sequential principal component estimation method. We find that the world inflationfactor accurately characterize the global inflation situation, and has a significant influenceon the national and regional CPI indexes. Thus, this study confirms the existence of theworld inflation cycle. Judging by the results of the variance decomposition, the worldfactor is more important to developed countries and regions than to developing countriesand regions. However, the national inflation factor has a strong explanatory power ofnational and regional CPI indexes.
从理论上，本文重点研究动态因子模型的三个重要分支：预测模型、FAVAR模型和分层动态因子模型。基于预测的视角，本文发掘了因子和因子模型的内涵。在此基础上，本文重点解析FAVAR模型。而分层因子模型则是经典动态因子模型在结构上的拓展。这三个分支的关系层层递进，也代表了动态因子模型发展的三个阶段。在具体的计量方法上，本文尝试对不同或者相同的问题，使用多种估计方法，以进行对比分析，如因子的估计、因子个数等。由此体现了本文对因子模型的理论研究深度。在实证研究方面，本文针对国内的经济背景和数据，综合考虑国外既有研究，在深刻理解模型和方法论的基础上，对我国通胀的宏观成分、CPI的波动源、世界通胀因子及其对我国的影响、货币政策冲击的度量、宏观预测等，进行了深入的研究，产生具有创新性的研究成果。本文的主要研究内容和研究结论及其创新意义可以概述如下：
第一，对于预测模型，我们发现，大型模型的结构反映了真实的预测模型的特征。而增量的R2表明，大型模型的结构可以浓缩为动态因子模型。上述分析说明，动态因子模型反映真实的经济结构，从而使预测的理念和结果更为先进。本文的上述分析与和西方学者的研究结论近似。本文还认为，动态因子模型的预测能力显著优于经典的AR和VAR模型。典型的，以M2为例，使用单个因子就可以改进AR模型的预测结果，从而使预测精度提高26%；使用7个因子导致预测精度的提高接近40%。本文还发现，第一个因子对预测M2提供了重要的增量信息。相关性显示，第一个因子综合了实际经济活动内容（宏观经济最重要的基本面）。这个证据提示，因子综合了宏观经济重要的基本面因素（或驱动力量）。
第二，在FAVAR模型的研究中，本文构建了代表中国宏观经济各方面信息的宏观经济信息集，应用最新的因子提取方法，从这个宏观经济信息集中提取因子并建立关于因子和可观测的共同因子的FAVAR模型。本文将FAVAR模型用于货币政策冲击的度量。研究结论表明，和常用的货币新息不同，短期利率的新息是我国货币政策冲击的准确测度。本文进而在FAVAR模型中扩展方差分解和历史分解方法。方差分解显示，我国货币政策冲击解释了产出和通胀方差的11%和9.8%，历史分解也显示，我国货币政策冲击不是任何一次产出和通胀大幅持续波动的主要原因。所以，本文认为，货币政策冲击不是我国经济波动的主要冲击源。上述模型和结论，体现了本文的创新。
第三，在FAVAR模型的基本框架内，本文进行应用性的扩展和创新：将FAVAR模型用于通胀波动源的分解，考察中国通胀分类指数的波动源及其性质。具体而言，将我国CPI的8大类分解为宏观成分与特质成分，并根据宏观因子组成的VAR识别货币政策冲击的动态效应。本文发现，宏观冲击和特质冲击都是CPI大类的重要波动源，但是宏观冲击的效应相对持久。所以，货币政策需要重点关注宏观冲击的效应并盯住CPI大类的宏观成分。货币政策冲击的动态效应显示，货币政策冲击对各大类的传导存在一定的规律性。据我们所查阅的文献，本文系国内第一次使用FAVAR模型揭示我国CPI大类的波动源，从这个角度来说，本文的研究具有开拓性意义。
第四，本文基于FAVAR的理论和本文的实证结果，进一步精炼宏观成分的理论概念和理论解释。我们根据FAVAR模型的估计结果，计算我国CPI的宏观成分并且揭示宏观冲击效应。主要结果为，我国的宏观信息集存在八个宏观因子，它们基本准确地刻画了我国宏观经济运行的动态特征。样本期5个不同的通胀（通缩）期，宏观成分的均值占通胀均值的比，度量了通胀的程度，揭示了通胀的来源。典型的是2010~2011年的通胀期，其宏观成分占比达到134%，证实了这是一轮由宏观因素驱动的严重通胀。宏观冲击效应显示，针对宏观因素驱动的通胀，紧缩货币和需求而不是单纯地紧缩货币，将有效地抑制通胀的上涨和反复。从上述可知，本文基于我国的现实和估计结果，具体精炼和解释了宏观成分。
第五，由于众多批评家认为估计的因子难以解释，由此产生了分层动态因子模型。分层动态因子模型将变量分块，同时估计共同因子和分块因子，部分地解决了如何解释因子的难题。本文采用序贯主成分的估计方法，从65个国家（地区）和区域CPI中提取世界通胀因子、区域通胀因子和国家通胀因子。本文发现，世界通胀因子基本准确地刻画了全球通胀形势，对各国、各区域具有重要影响力。本文的研究证实了世界通胀周期的存在性。从方差分解的结果来看，世界通胀因子对发达国家和发达区域CPI方差的贡献强于发展中国家和发展中区域。对整个样本区间，世界通胀因子对我国通胀的影响较小，但是近年来影响力逐渐增强。但是，国家通胀因子对发展中国家和区域具有很强的解释力。据我们查阅的文献，上述研究是我国关于分层动态因子的首次研究，体现了本文对国际前沿的紧密跟踪和应用性创新。
Over the past decade, dynamic factor models have received considerableattention. The reason why the dynamic factor model to get the attention, the mostimportant starting point is to predict. Because the estimated factor contains a lot ofinformation, so many researchers began to use the estimated factor in the differentmodels. FAVAR model can solve the lack of information of the VAR. When we use theFAVAR model of monetary policy effects, the conclusions and the classical theory isconsistent. Many critics believe that the estimated factor is difficult to explain.Hierarchical factor models estimate the common factor and block factor at the same time.The estimated factors can then be interpreted. Driven by empirical researches, factormethodologies have got great progress in recent years. Dynamic factor model, there arestill many obstacles unresolved, such as the basis of the model theory, the factorexplained. However, after nearly ten years of rapid development, the dynamic factormodel has become an important macroeconometric branch, and attracted more and moreattention in the field of macroeconomic policy.
In this context, this paper will focus on the theory and application of dynamic factormodels. This article will study the prediction models based on dynamic factor models,FAVAR models and hierarchical dynamic factor models. For prediction perspective, wehope to explore the meaning of the factor and factor model. On this basis, FAVAR modelsfocus on the use of the estimated factors. Hierarchical factor models are the expansion ofthe classic dynamic factor models. The three models also represent the three stages ofdevelopment by the dynamic factor model. This article seeks to use a variety of estimationtechniques, such as factor estimators and estimators of the number of factors in differentsections. This paper take into account the abroad researches and domestic economicbackground, and strive to do innovative research based on a deep understanding of thebasis of the model and methodology. The main conclusion of the study can besummarized as follows:
First, the large model appears to be true prediction model. The estimated results showthat the model structure can be concentrated to a dynamic factor model. In other words, dynamic factor models can reflect the real economic structure. This paper considers thepredictive ability of the dynamic factor model, and we find that dynamic factor modelsbehavior better than the classic AR and VAR models. We also find that the first factorprovides a considerable incremental information when predicting M2. Correlation showsthat the first factor combines real economic activities (the most important macroeconomicfundamental). This evidence suggests that the factor may be a combination of the mostimportant macroeconomic fundamentals (or driving force).
Second, we construct a large macroeconomic information set, from which we extracta few common factors. Based on a factor-augmented VAR, we evaluate candidateindicators of monetary policy shocks, and analyze their contribution to economicfluctuations. We find that shout-term interest rate innovations behave well as indicators ofmonetary policy shocks, because identified effects of monetary policy shocks are in linewith basic consensus. Monetary policy shocks explain25.4percent,11percent and9.8percent of monetary policy, output and inflation, respectively. Historical decompositionsshow that most of sharp fluctuations in output and inflation were not explained bymonetary policy shocks. Thus, monetary policy shocks are not the main source of China'seconomic fluctuations.
Third, we specifies a factor-augmented vector autoregression (FAVAR) based oneconomic theories and Chinese macroeconomic time series. The estimatedmacroeconomic factors show that the general economic conditions can be reflected bymonetary policy and six latent factors. Then the fluctuations in sectoral inflation rates dueto the macroeconomic factors are disentangled from those due to sector-specificconditions, and the effects of monetary policy shocks on sectoral inflation rates areidentified in FAVAR models. The main finding is that macroeconomic shocks andsector-specific shocks are both important to sectoral inflation fluctuations, butmacroeconomic shocks tend to have more persistent and sluggish effects on sectoralinflation rates. Therefore, monetary policy should focus on the effects of macroeconomicshocks and the macroeconomic components of sectoral inflation rates. The dynamiceffects of monetary policy shocks on sectoral inflation rates indicate some regularities.
Fourth, we decompose the fluctuations in China’s CPI index into macroeconomic component that are due to macroeconomic factors and idiosyncratic shocks which comefrom disaggregate prices variations. Then, we conduct some typical impulse response ofthe CPI index to macroeconomic shocks. Our main finding is that the eightmacroeconomic factors do capture important dimensions of Chinese macroeconomicmovements. The analysis of macroeconomic component and its mean’s ratio to the meanof inflation rate itself provides a new sight for properties and sources of Chinese inflationin the different time periods. Typically, the ratio is134%in the2010-2011period ofinflation, which shows this is a serious inflation and is driven by macroeconomic factors.The effects of macroeconomic shocks imply that tightening of both monetary and demandrather than only monetary itself will effectively stabilize the inflation.
Fifth, in hierarchical factor models, this paper extracts world inflation factor, regionalinflation factor and the national inflation factor from65national and regional CPI indexesby sequential principal component estimation method. We find that the world inflationfactor accurately characterize the global inflation situation, and has a significant influenceon the national and regional CPI indexes. Thus, this study confirms the existence of theworld inflation cycle. Judging by the results of the variance decomposition, the worldfactor is more important to developed countries and regions than to developing countriesand regions. However, the national inflation factor has a strong explanatory power ofnational and regional CPI indexes.
引文
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[17] Banerjee, A., M. Marcellino and I. Masten,2007, Forecasting MacroeconomicVariables Using Diffusion Indexes in Short Samples With Structural Change,forthcoming in Forecasting in the Presence of Structural Breaks and ModelUncertainty, ed. by D. Rapach and M. Wohar, Elsevier.
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[12] Bai, J. and S. Ng,2006, Determining the Number of Factors in Approximate FactorModels, errata, manuscript, Columbia University.
[13] Bai, J., and S. Ng (2007), Determining the Number of Primitive Shocks in FactorModels, Journal of Business and Economic Statistics,25,52-60.
[14] Bai, J. and S. Ng,2008, Large Dimensional Factor Analysis, Foundations andTrends in Econometrics,3,89-163.
[15] Banerjee, A. and M. Marcellino,2008, Factor Augmented Error Correction Models,CEPR WP6707.
[16] Banerjee, A., M. Marcellino and I. Masten,2009, Forecasting withFactor-augmented Error Correction Models, mimeo, European University Institute.
[17] Banerjee, A., M. Marcellino and I. Masten,2007, Forecasting MacroeconomicVariables Using Diffusion Indexes in Short Samples With Structural Change,forthcoming in Forecasting in the Presence of Structural Breaks and ModelUncertainty, ed. by D. Rapach and M. Wohar, Elsevier.
[18] Bernanke B.S. and A. Blinder,1992, The Federal Funds Rate and the Channels ofMonetary Transmission, American Economic Review,82,901-921.
[19] Bernanke B.S. and I. Mihov,1998, Measuring Monetary Policy, The QuarterlyJournal of Economics,113,869-902.
[20] Bernanke B.S., J. Boivin and P. Eliasz,2005, Measuring the Effects of MonetaryPolicy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach, TheQuarterly Journal of Economics,120,387-422.
[21] Bernanke, B.S. and Blinder, A.,1992, The Federal Funds Rate and the Channels ofMonetary Transmission, American Economic Review,82,901-921.
[22] Bernanke, B.S. and Mihov, I.,1998, Measuring Monetary Policy, QuarterlyJournal of Economics,113,869-902.
[23] Beyer A., Famer R., Henry J. and M. Marcellino,2008, Factor Analysis in aNew-Keynesian Model, Econometrics Journal, forthcoming.
[24] Blanchard, O.J., and D. Quah,1989, Dynamic Effects of Aggregate Demand andSupply Disturbances, American Economic Review,79,655-673.
[25] Boivin J. and S. Ng,2006, Are More Data Always Better for Factor Analysis?,Journal of Econometrics,132,169-194.
[26] Boivin J., M.P. Giannoni and I. Mihov,2009, Sticky Prices and Monetary Policy:Evidence from Disaggregated US Data, American Economic Review,99,350-384.
[27] Boivin, J., and M. Giannoni,2006, DSGE Models in a Data-Rich Environment,NBER Working Paper no.12772.
[28] Boivin, J., and S. Ng,2005, Understanding and Comparing Factor-Based Forecasts,International Journal of Central Banking,1,117-151.
[29] Breitung, J. and S. Eickmeier,2009, Testing for Structural Breaks in DynamicFactor Models, Deutsche Bundesbank Economic Studies Discussion Paper No.2009.
[30] Brillinger, D.R.,1964, A Frequency Approach to the Techniques of PrincipalComponents, Factor Analysis and Canonical Variates In the Case of StationaryTime Series, Invited Paper, Royal Statistical Society Conference, Cardiff Wales.
[31] Brillinger, D.R.,1981, Time Series: Data Analysis and Theory, expanded edition,San Francisco: Holden-Day.
[32] Cattell, R. B.,1966, The Scree Test for the Number of Factors, MultivariateBehavioral Research,1,245-76.
[33] Chamberlain, G. and M. Rothschild,1983, Arbitrage Factor Structure, andMean-Variance Analysis of Large Asset Markets, Econometrica,51,1281-1304.
[34] Chib, S. and E. Greenbergm1996, Markov Chain Monte Carlo SimulationMethods in Econometrics, Econometric Theory,12,409-431.
[35] Christiano L.J., E. Eichenbaum and C. Evans,1996, The Effects of MonetaryPolicy Shocks: Evidence from the Flow of Funds, The Review of Economics andStatistics,78,16-34.
[36] Christiano L.J., E. Eichenbaum and C. Evans,1998, Monetary Policy Shocks:What Have We Learned and to What End?, NBER Working Paper, No.6400.
[37] Connor, G., and R.A. Korajczyk,1986, Performance Measurement with theArbitrage Pricing Theory, Journal of Financial Economics,15,373-394.
[38] D’Agostino, A. and Domenico Giannone,2006, Comparing Alternative PredictorsBased on Large-Panel Factor Models, ECB Working Paper680.
[39] Doz, C., D. Giannone and L. Reichlin,2006, A Quasi Maximum LikelihoodApproach for Large Approximate Dynamic Factor Models, ECB Working Paper674.
[40] Eickmeier, S., C. Ziegler,2008, How successful are dynamic factor models atforecasting output and inflation? A meta-analytic approach, Journal of Forecasting,27,237-265.
[41] El Karoui, N.,2007, Tracy-Widom Limit for the Largest Eigenvalue of a LargeClass of Complex Sample Covariance Matrices, Annals of Probability,35,633-714.
[42] Engle, R.F. and M.W. Watson,1981, A One-Factor Multivariate Time SeriesModel of Metropolitan Wage Rates, Journal of the American StatisticalAssociation,76,774-781.
[43] Engle, R.F. and M.W. Watson,1983, Alternative Algorithms for Estimation ofDynamic MIMIC, Factor, and Time Varying Coefficient Regression Models,Journal of Econometrics,23,385-400.
[44] Favero, C.A., M. Marcellino and F. Neglia,2005, Principal Components at Work:The Empirical Analysis of Monetary Policy With Large Datasets, forthcoming,Journal of Applied Econometrics.
[45] Foerster, A.T., Sarte, P.G. and Watson, M.W.,2011, Sectoral versus AggregateShocks: A Structural Factor Analysis of Industrial Production, Journal of PoliticalEconomy,119,1-38.
[46] Forni, M. and L. Reichlin,1998, Let’s Get Real: A Dynamic Factor AnalyticalApproach to Disaggregated Business Cycle, Review of Economic Studies,65,453-474.
[47] Forni, M., D. Giannone, M. Lippi and L. Reichlin,2009, Opening the Black Box:Structural Factor Models with Large Cross Sections, Econometric Theory,25,1319-1347.
[48] Forni, M., M. Hallin, M. Lippi and L. Reichlin,2000, The Generalized FactorModel: Identification And Estimation, Review of Economics and Statistics,82,540–554.
[49] Forni, M., M. Hallin, M. Lippi and L. Reichlin,2004, The Generalized FactorModel: Consistency and Rates, Journal of Econometrics,119,231-255.
[50] Forni, M., M. Hallin, M. Lippi and L. Reichlin,2005, The Generalized DynamicFactor Model: One-Sided Estimation and Forecasting, Journal of the AmericanStatistical Association,100,830-839.
[51] Geweke, J.,1977, The Dynamic Factor Analysis of Economic Time Series, inLatent Variables in Socio-Economic Models, ed. by D.J. Aigner and A.S.Goldberger, Amsterdam: North-Holland.
[52] Geweke, J. and R. Meese,1981, Estimating Regression Models of Finite butUnknown Order, International Economic Review,22,1,55-70.
[53] Giannone, D., L. Reichlin and D. Small,2008, Nowcasting: The Real-TimeInformational Content of Macroeconomic Data, Journal of Monetary Economics,55,665-676.
[54] Giannone, D., Reichlin, L. and Sala, L.,2004, Monetary Policy in Real Time,NBER Macroeconomics Annual,2004,161-200.
[55] Granger, P. and C.W.J. Newbold,1974, Spurious Regressions in Econometrics,Journal of Econometrics2,111-120.
[56] Hallin, M. and Li ka, R.,2007, The Generalized Dynamic Factor Model:Determining the Number of Factors, Journal of the American StatisticalAssociation,102,603-617.
[57] Hamilton, J.D.,1989, A New Approach to the Economic Analysis of NonstationaryTime Series and the Business Cycle, Econometrica,57,357-384.
[58] Harvey, A.C.,1989, Forecasting, Structural Time Series Models and the KalmanFilter. Cambridge, U.K.: Cambridge University Press,1989.
[59] Johnstone, I.M.,2001, On the Distribution of the Largest Eigenvalue in PrincipalComponent Analysis, Annals of Statistics,29,295-327.
[60] Jungbacker, D. and S.J. Koopman,2008, Likelihood-Based Analysis for DynamicFactor Models, manuscript, Tinbergen Institute.
[61] Jungbacker, D., S.J. Koopman and M. van der Wel,2009, Dynamic FactorAnalysis in the Presence of Missing Data, Tinbergen Institute Discussion Paper2009-010/4.
[62] Kapetanios, G. and M. Marcellino,2008, Factor-GMM Estimation with Large Setsof Possibly Weak Instruments, manuscript, EUI
[63] Kim, C.J. and C. Nelson,1998, Business Cycle Turning Points, A New CoincidentIndex, and Tests of Duration Dependence Based on a Dynamic Factor Model withRegime-Switching, Review of Economics and Statistics,80,188-201.
[64] King, Robert G., C.I. Plosser, J.H. Stock and M.W. Watson,1991, StochasticTrends and Economic Fluctuations, American Economic Review81,819-840.
[65] Kitagawa, G.,1987, Non-Gaussian State Space Modeling of Non-Stationary TimeSeries, with discussion, Journal of the American Statistical Association,82,1032-1063.
[66] Kloek, T. and L.B.M. Mennes,1960, Simultaneous Equations Estimation Based onPrincipal Components of Predetermined Variables,‖Econometrica,28,45-61.
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