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Related Theories And Applications Of High Dimension Factor Models

Posted on:2016-02-26Degree:DoctorType:Dissertation
Country:ChinaCandidate:G W CuiFull Text:PDF
GTID:1109330467496652Subject:Quantitative Economics
Abstract/Summary:PDF Full Text Request
To deal with high dimensional economic data, econometricians extended factor models to the high dimension factor models. Considering cross section dependence and serial correlation of economic data, they further proposed approximate factor models and (generalized) dynamic factor models. In macroeconomy, number of exogenous random shocks is a basic problem need investigated for economic fluctuation, however no study has yet solved this problem.(Generalized) dynamic factor models provide a chance to answer the above problem by the way of "letting the data speak for themselves", as the models well describe the mechanism of how exogenous random shocks occur and transmit, and the number of random shocks can be modeled as number of dynamic factors. However, there are many ways to estimate number of dynamic factors and the results likely to be different. With this, it’s hard to acquire the number of economic shocks.In addition, with a few factors, high dimension factor models well capture comovement fluctuation of macroeconomics variables. This advantage stimulates econometricians to augment factors in VAR and panel data models, and thus they derive flexible models like FAVAR, structural factor models and panel data models with interactive effects, which will be cornerstone models for economic forecasting and policy analysis. Such kinds of factor-augmented model all assume that the regression model is linear, which is not always true in reality. Nonlinearity in general cause standard factor-augmented models to make wrong inference conclusions. With these contexts, this paper investigates the above two topics, and the innovations are as follows:Firstly, to investigate the finite sample properties of estimators of number of dynamic factors systematically and comprehensively, this paper compares the estimated number of dynamic factors in a unified framework, and summarizes the advantage and weakness of those estimators while also providing instructions for empirical researchers to choose suitable estimators. Furthermore, this paper collects a data set which can mirror China macroeconomy in all dimensions, and lastly discovers5exogenous shocks. This confirms that real business cycle theory that only considers2shocks is not appropriate to China’s business cycle fluctuation. Considering macroeconomists have introduced as many as7economic shocks based on RBC framework, this indicates that at least2random shocks are not exogenous to the rest5shocks. Research has already introduced redundant economic shocks, so it reveals the limitations of the research pattern which analyzes economic shocks one by one. These conclusions show a direction to establish a business cycle model that befits Chinese economy.Secondly, this paper is the first to explicitly consider nonlinearity of regression, by combining factors as latent variables with structural break models, and proposes factor-augmented strucutral break models. To get close to reality, this paper allows the structural change date to be endogenous, latent factors can be arbitrarily correlated to explanatory variables and thus explanatory variables also can be endogenous. Factor-augmented strucutral break models are new models and this type of models can be widely applied to important empirical fields like economic forecasting and macroeconomy policy analysis. In this sense, they are substantial extensions for factor regression models.Thirdly, nonlinearities due to latent factors and structural breaks significantly increase the difficulty of estimation. However, this paper designs two stage least squares (2SLS) estimators for factor-augmented strucutral break models which are simple and feasible. To be specific, in the first stage, we use principal component analysis to estimate factors from high dimension data set; in the second stage we treat the estimated factors as the underlying factors, and thus factor-augmented structural break models reduce to standard structural break models, in which OLS can be applied to estimate break date and regression parameters. Later, this paper is the first to prove the consistency of2SLS estimators, to show rate of convergency and the corresponding limit distribution. Finally, Monte Carlo simulations are implemented to inspect the theoretical results, and show that the two-step estimator performs well in finite sample.Fourthly, this paper additionally studies the stability test of the regression parameters of factor-augmented models, in which involves two problems, that is, the factors are unobservable and endogenous strucutural change date can only be identifiable under alternative hypotheses. To tackle the above problems, this paper initiates feasible supremum Wald (SupWald) statistics. According to the2SLS estimations mentioned before, SupWald statistics can be derived by Andrews(1993). Later, this paper for the first time proves that under null hypotheses, the error in estimated factor doesn’t affect the large sample distributions of SupWald, then the asymptotic distribution and critical values of the feasible SupWald statistics can refer to Andrews(1993). Again, this paper designs simple Monte Carlo simulations to study the performance of test statistics, which well support the theoretical results and show good finite sample property.
Keywords/Search Tags:High dimension factor models, Number of dynamic factors, Factor augmentedstructural break models, 2SLS, SupWald, Monte Carlo simulations
PDF Full Text Request
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