The Theory And Application Of Dynamic Factor Models

Over the past decade, dynamic factor models have received considerable attention. The reason why the dynamic factor model to get the attention, the most important starting point is to predict. Because the estimated factor contains a lot of information, so many researchers began to use the estimated factor in the different models. FAVAR model can solve the lack of information of the VAR. When we use the FAVAR model of monetary policy effects, the conclusions and the classical theory is consistent. 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, factor methodologies have got great progress in recent years. Dynamic factor model, there are still many obstacles unresolved, such as the basis of the model theory, the factor explained. However, after nearly ten years of rapid development, the dynamic factor model has become an important macroeconometric branch, and attracted more and more attention in the field of macroeconomic policy.In this context, this paper will focus on the theory and application of dynamic factor models. This article will study the prediction models based on dynamic factor models, FAVAR models and hierarchical dynamic factor models. For prediction perspective, we hope to explore the meaning of the factor and factor model. On this basis, FAVAR models focus on the use of the estimated factors. Hierarchical factor models are the expansion of the classic dynamic factor models. The three models also represent the three stages of development by the dynamic factor model. This article seeks to use a variety of estimation techniques, such as factor estimators and estimators of the number of factors in different sections. This paper take into account the abroad researches and domestic economic background, and strive to do innovative research based on a deep understanding of the basis of the model and methodology. The main conclusion of the study can be summarized as follows:First, the large model appears to be true prediction model. The estimated results show that 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 the predictive ability of the dynamic factor model, and we find that dynamic factor models behavior better than the classic AR and VAR models. We also find that the first factor provides a considerable incremental information when predicting M2. Correlation shows that the first factor combines real economic activities (the most important macroeconomic fundamental). This evidence suggests that the factor may be a combination of the most important macroeconomic fundamentals (or driving force).Second, we construct a large macroeconomic information set, from which we extract a few common factors. Based on a factor-augmented VAR, we evaluate candidate indicators of monetary policy shocks, and analyze their contribution to economic fluctuations. We find that shout-term interest rate innovations behave well as indicators of monetary policy shocks, because identified effects of monetary policy shocks are in line with basic consensus. Monetary policy shocks explain25.4percent,11percent and9.8percent of monetary policy, output and inflation, respectively. Historical decompositions show that most of sharp fluctuations in output and inflation were not explained by monetary policy shocks. Thus, monetary policy shocks are not the main source of China’s economic fluctuations.Third, we specifies a factor-augmented vector autoregression (FAVAR) based on economic theories and Chinese macroeconomic time series. The estimated macroeconomic factors show that the general economic conditions can be reflected by monetary policy and six latent factors. Then the fluctuations in sectoral inflation rates due to the macroeconomic factors are disentangled from those due to sector-specific conditions, and the effects of monetary policy shocks on sectoral inflation rates are identified in FAVAR models. The main finding is that macroeconomic shocks and sector-specific shocks are both important to sectoral inflation fluctuations, but macroeconomic shocks tend to have more persistent and sluggish effects on sectoral inflation rates. Therefore, monetary policy should focus on the effects of macroeconomic shocks and the macroeconomic components of sectoral inflation rates. The dynamic effects 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 come from disaggregate prices variations. Then, we conduct some typical impulse response of the CPI index to macroeconomic shocks. Our main finding is that the eight macroeconomic factors do capture important dimensions of Chinese macroeconomic movements. The analysis of macroeconomic component and its mean’s ratio to the mean of inflation rate itself provides a new sight for properties and sources of Chinese inflation in the different time periods. Typically, the ratio is134%in the2010-2011period of inflation, 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 demand rather than only monetary itself will effectively stabilize the inflation.Fifth, in hierarchical factor models, this paper extracts world inflation factor, regional inflation factor and the national inflation factor from65national and regional CPI indexes by sequential principal component estimation method. We find that the world inflation factor accurately characterize the global inflation situation, and has a significant influence on the national and regional CPI indexes. Thus, this study confirms the existence of the world inflation cycle. Judging by the results of the variance decomposition, the world factor is more important to developed countries and regions than to developing countries and regions. However, the national inflation factor has a strong explanatory power of national and regional CPI indexes.