Bayesian Analysis Of Nonlinear Inflation Persistence

Inflation persistence, also known as inflation inertia, is the trend of convergence to equilibrium level and the process (Filippo Altissimo,Michael Ehrmann and Frank Smets,2006),when is subjected to a shock to the inflation rate deviate from the long-term equilibrium level. The higher inflation persistence,the longer lag time needed to monetary policy, which is more difficult playing a role in price fluctuations. In this case, the central bank to stabilize economic growth and inflation between the two goals to give greater weight to control inflation, achieve the policy objectives will increase the social cost (Fuhrer,1995).Many monetary authorities and economists have rised the attention of inflation persistence, the European countries have set up a research institution to study it (Inflation Persistence Network, referred to as IPN). In related studies, the nonlinear characteristics of inflation persistence caused some scholars interested in, some non-linear model has also been introduced, making model is complicated parameter estimation, parameters of high-dimensional integration problem has plagued these scholars.But as the MCMC sampling methods and the development of computers, these complex issues will be effectively resolved in the field of Bayesian statistics.In this context, this paper prepare to study China's non-linear features of inflation persistence, including the overall operating characteristics and regional metrics of innovation research,based on Bayesian analysis method. This study brings scientific basis to monetary policy which making forward-looking decision.This paper is divided into the following seven chapters:Chapter 1:Introduction. This chapter mainly presents the paper's research background, aims and significance, and also introduces the paper's research ideas, research content, research methods as well as the innovation.Chapter 2:Theory of Bayesian Analysis. This chapter mainly presents some basic theory (including the prior distribution, posterior distribution), MCMC sampling methods (including MH, Gibbs, Griddy-Gibbs sampling), MCMC convergence diagnostic methods (including graphical diagnosis, Raftery and Lewis method, Gelman and Rubin method, MC error method), model comparison and selection, etc.On the basis of these theories, this chapter also gives the logic flow chart of nonlinear inflation persistence from Bayesian analysis method.Chapter 3:The linear structure of inflation persistence. Using Bayesian analysis of inflation persistence in China,give statistical inference, conditions of distribution and MCMC parameter sampling process to linear model,and estimates the parameters using Bayesian analysis and maximum likelihood estimation methods,then compared eachother. The residual of this two different methods are tested by CUSUMSQ tests,to examine the structural stability for the parameters of linear structure model. Finally, gives BDS statistic test, and further show time series of inflation is noolinear structural. So it is necessary to study the nonlinear structure model of inflation persistence.Chapter 4:Nonlinear operation characteristics of inflation persistence. This chapter establish a linear dynamic and quantile characteristics model for the inflation persistence, From a historical perspective and the time-varying quantile point to study operation characteristics of inflation persistence.Using FFBS method to sampling in model of linear dynamic characteristics,and get time series graphics of persistence; Using MH algorithm method to sampling in model of Bayesian quantile characteristics,and get the track changes in different quantile of inflation.Chapter 5:Variable structure of inflation persistence. This chapter establish a changing structure model of inflation persistence,based on In Levin and Piger (2003) and Wang and Zivot (2000) views.Gives a specific Bayesian statistical inference and Gibbs sampling strategy. This chapter focuses on the structural changing in mean level,parameters of persistence, and then uses Bayes factor method to choose the number of changpoint. Found that persistence's coefficients have one changepoint in CPI,two changepoint in RPI, these changepoints occured one or two period after the inflation rate reached the highest point in the history.This conclusion shows the changing structure model of inflation is successful in this chapter, this method is very useful to measuring inflation persistence accurately in different time's region. Chapter 6:Threshold structure of inflation persistence. In Tong and Lim (1980)'modeling and Hansen (2000) point of view to establish the threshold structure model of inflation persistence, given a specific Bayesian Inference and Gibbs sampling strategy. This chapter focuses on the previous one's inflation and volatility of inflation measured GARCH models (taken Griddy-Gibbs sampling method available),take them as proxy variable for the threshold structure model. Found that:the number of spaces in inflation showed low persistence in regionof low inflation, high persistence in regionof high inflation; persistence is not sensitive to the volatility of inflation. It means advent of high inflation persistence when higher inflation and low fluctuations.Chapter 7:This chapter is the summary and outlook of this paper. This part summarizes the main points of view in this thesis and puts forward the major problems for the further study.The main innovations of the thesis:1. The introduction of Bayesian linear dynamic models and Bayesian quantile model of inflation persistence to study the characteristics of the overall operation. Constructed a Bayesian linear dynamic model of inflation persistence, statistical inference was carried out using the method with FFBS'MCMC sampling to estimate model parameters, obtained with time-varying parameters of inflation persistence time sequence diagram, depicts the inflation persistence changes in the time dimension on the History, found that since 1996, frequency of inflation persistence have became shorter,and cycle becomes longer, corresponds to 1996 years ago, the run trend remain the same as inflation trends.Constructed a Bayesian quantile model of inflation persistence, gave statistical inference, MH sampling, estimated the model's parameters, get the different persistence parameters in the corresponding quantile.Found that there existed a the "Logistic" smooth transition structure features in different quantile. It is indicating that different micro-economic subjects have different inflation expectations.2.Proposed a Bayesian changing the structure model of inflation persistence,based on the Wang and Zivot (2000) and Levin and Piger (2003)'s models.Gave a specific Bayesian statistical inference and Gibbs sampling strategy. Focused on the structural changing in mean level,parameters of persistence, and then uses Bayes factor method to choose the number of changpoint. Found that persistence's coefficients have one changepoint in CPI,two changepoint in RPI, these changepoints occured one or two period after the inflation rate reached the highest point in the history.This conclusion shows the changing structure model of inflation is successful in this chapter, this method is very useful to measuring inflation persistence accurately in different time's region.3. Proposed a Bayesian threshold model of inflation persistence,based on the Andrews and Chen (1994) and Tong and Lim (1980)'s models. Gave a specific Bayesian Inference and Gibbs sampling strategy. Focused on the previous one's inflation and volatility of inflation measured GARCH models (taken Griddy-Gibbs sampling method available),take them as proxy variable for the threshold structure model. Found that:the number of spaces in inflation showed low persistence in regionof low inflation, high persistence in regionof high inflation; persistence is not sensitive to the volatility of inflation. It means advent of high inflation persistence when higher inflation and low fluctuations.