Inflation Expectation And Its Uncertainty Based On The Bayesian Learning Algorithm

Inflation expectation represents the economic agents’ expectation of future inflation based on the available information at present.Inflation expectations play an important role in the macroeconomy.On the one hand,inflation expectation can affect the headline inflation by influencing the price and wage level.On the other hand,the environment of monetary policy tools is different when the state of inflation expectation changes.Monetary policy works better when inflation expectations are stable or anchored.A strand of literature suggests that policy makers need to observe the state of inflation expectations when controlling inflation and making forward-looking monetary policies.In recent years,China’s central bank and related economic departments have issued a series of policy documents on the management of inflation expectations.In2009,The State Council issued the 12 th Five-Year Plan.In the 12 th Five-Year Plan,The State Council put forward the economic concept of inflation expectation management for the first time.Subsequently,the "Decision of the CPC Central Committee on Some Major Issues concerning Comprehensively Deepening Reform" issued by the government in 2013 continued to stress the need for forwardlooking management of future changes in price levels.In 2018-2019,the three Central Economic Work Conferences continuously emphasized the importance of stabilizing inflation expectations,and made stabilizing inflation expectations a target of macroeconomic regulation along with stabilizing inflation.Since 2020,China has set the economic goals of "six guarantees" and "six stability".Among them,the goals of "ensuring residents’ employment","stabilizing employment" and "stabilizing expectations" are closely related to inflation expectations.These economic policies indicate that the nation and government attaches great importance to the state of inflation expectations.Inflation expectations include the information of its level and uncertainty.How should the relevant economic departments measure inflation expectation and its uncertainty,and how should they use the measure information to control inflation and manage the macroeconomy? The above questions are of great practical significance,and relevant researches have not reached a unanimous conclusion.There is insufficient research on the measure of inflation expectation and its uncertainty,the impact of inflation expectation and its uncertainty on economy,and the impact of relevant economic policies on inflation expectation and its uncertainty,while the relevant theoretical basis and empirical evidence are also weak.There is room for further improvement and supplement in the measurement and application of inflation expectation and its uncertainty,which is worthy of further discussion and analysis by scholars.Taking the deficiencies of previous literatures as the starting point,this paper uses Bayesian learning algorithm to study the measurement of inflation expectation and its uncertainty,and compares and analyzes the relationship between the level and fluctuation of inflation expectation and other macroeconomic variables under different measurement frameworks.Specifically,the research content of this paper is divided into four parts: measure analysis,correlation research,influence mechanism analysis and equilibrium theory interpretation.The four major parts correspond to the third chapter,the fourth chapter,the fifth chapter and the sixth chapter respectively.The main contents and research findings of each chapter are provide as follows.(1)Measuring Inflation expectation and its uncertainty based on Bayesian learning.First,this chapter extends the benchmark measurement model according to the economic reality,which is considering the heavy tails of inflation and the information of the inflation expectation uncertainty implied by the interest rate term structure of the national debt under the framework of unobserved component stochastic volatility model.Secondly,conbining Bayesian learning algorithm and the measurement model to endowing the model with ability of belief updating.Finally,this chapter obtains real-time posterior estimates of inflation expectation and its uncertainty through state variable identification and parameter learning.In the empirical analysis,this chapter compares and analyzes the difference between real-time and non-real-time inflation expectation and its uncertainty,discusses the stability of Chinese inflation expectations in different time periods,and discusses the accuracy of inflation prediction under the framework of various comparable models.The empirical results of this chapter show that: first,the real-time inflation expectations reflect the movement of inflation more accurately.According to the results of real-time estimates,China’s inflation expectations showed relatively sharp fluctuations during the global financial crisis and the COVID-19 pandemic.In 2008 and 2020,inflation expectations changed in a wide range and a high frequency.Secondly,conbining Bayesian learning algorithm improves the performance of insample characterization and out of sample prediction of models.Thirdly,considering the heavy tail of inflation and the implicit information of the term structure of the interest rate of national debt is helpful to improve the model’s portrayal of the dynamic process of inflation and to improve the accuracy of inflation prediction.(2)Correlation between inflation expectation and inflation.This chapter aims to explore the effects of different measures of inflation expectations on actual inflation.First,this chapter examines the correlation between the survey-based measure of inflation expectation and the actual inflation,and examines the effect of the inflation trend information contained in the survey-based measure of inflation expectation.Secondly,this chapter discusses the limitations of using survey-based measure of inflation expectation,and the advantages of using real-time inflation expectations measures in this correlation study.Finally,on the premise of considering the influence of inflation expectation,this chapter explores the relationship between inflation and a series of common factors(such as unemployment rate),and uses these factors to investigate the deciding factors of inflation expectation.The empirical results of this chapter show that: first,the survey-based measures of inflation expectations contain inflation trend information,thus can explain actual inflation.Stripped of the real-time inflation trend contained in the survey-based measures of inflation expectations,they do not significantly explain inflation fluctuations.Second,compared with the survey-based and non-real-time measures of inflation expectations,real-time inflation expectation is more in line with the changes of actual inflation and has stronger explanatory ability for actual inflation.Third,considering the impact of real-time inflation expectations on actual inflation,the change of unemployment rate has no significant ability to explain the change of inflation.Moreover,changes in unemployment rate and money supply cannot significantly explain changes in inflation expectations.(3)Analysis of the relationship among inflation expectation,its uncertainty and monetary policy.This chapter aims to explore the relationship among different measures of inflation expectations,their uncertainty and different types of monetary policies.First,this chapter considers the interaction between five macroeconomic variables when constructing the vector autoregressive model,namely,inflation,inflation expectation,inflation expectation uncertainty,market interest rate and money supply.Interest rate and money supply represent price and quantitative monetary policy tools respectively.Secondly,this chapter uses real-time and nonreal-time measures of inflation expectations and their uncertainty respectively,then compares the differences and similarities of impulse response results corresponding to different measures.The empirical results of this chapter show that: first,the impact direction of price-based monetary policies on different measures of inflation expectations and their uncertainty is roughly the same,and the impact duration is different.Second,implementing tight price monetary policy could curb inflation expectations and reduce the medium-and long-term inflation expectation uncertainty.Third,the corresponding impulse response results of the real-time inflation expectation and its uncertainty show that loosing quantitative monetary policy could restrain the inflation expectation uncertainty in the short term.(4)The intrinsic impact mechanism of monetary policy on inflation expectation.This chapter explores the intrinsic impact mechanism of monetary policy on Chinese inflation expectations under the structure of equilibrium theory.First,this chapter constructs a small-scale dynamic stochastic general equilibrium model involving households,firms and central banks,and considers the impact of inflation expectation management targets,interest rates and technological innovation under this framework.Second,in the empirical analysis,real-time inflation expectation measure and non-real-time inflation expectation measure are used respectively,and the intrinsic impact mechanism under the two scenarios is compared.The empirical results of this chapter show that the intrinsic impact mechanism of monetary policies on inflation expectations is as follows: in a small-scale economy,after implementing tight monetary policies(raising market interest rates),households tend to reduce current consumption and use their wealth to buy bonds to obtain higher interest rates.Household consumption decreased in the current period resulting in a decline in aggregate demand for products.When total demand for products falls,total output also falls.At this time,the demand for labor decreases,and the wages that enterprises are willing to pay decrease.When part of enterprises can adjust the optimal price at current period,they tend to reduce the price to stimulate consumption,and the optimal price of the current period will decline.Accordingly,the current level of inflation and the optimal level of inflation fall,and households,firms and central banks adjusted their expectations of inflation,and inflation expectations fall.This paper enriches and improves the research on measuring and applying inflation expectation and its uncertainty from the aspects of research method,content and perspective.It also provides an economic equilibrium explanation for central bank to control inflation and regulate macroeconomy.Compared with the existing literature,this paper has the following four contributions and innovations:(1)This paper innovatively combines Bayesian learning algorithm with the bivariate heavy-tailed unobserved component stochastic volatility model,endowing the measure model with belief updating ability.Applications of Bayesian learning algorithm and bivariate unobserved component stochastic volatility model exist respectively,but few literatures have matched the algorithm with the models.The bivariate heavy-tailed state space model constructed in this paper can measure the real-time inflation expectation and its uncertainty,which is more flexible and accurate than the measures provided by other methods.(2)This paper explores the limitations of the survey-based measures of inflation expectations and verifies the superiority of real-time inflation expectation measure in the study of the correlation between inflation expectation and inflation.The research on the correlation between inflation expectation and inflation in this paper is different from the traditional thoughts of related literature.In the past related literature,survey-based inflation expecation is widely used,but the limitation of the survey-based measure of inflation expecation is rarely considered,and the real-time inflation expectation has not been applied.(3)This paper focuses on the differences and similarities of the relationship among different types of monetary policies,different measures of inflation expectations and their uncertainty.Different from the existing literature,this paper uses real-time and non-realtime measures of inflation expectations and their uncertainty for comparative analysis,with a novel research perspective,richer and more comprehensive research content.(4)This paper uses real-time and non-real-time inflation expectations to explore the internal impact mechanism of monetary policy on inflation expectations under the framework of dynamic stochastic general equilibrium framework.Different from the existing literature,this paper makes a comparative analysis of the internal impact mechanism of monetary policies on different measures of inflation expectations from the perspective of economic equilibrium,and obtains a more robust conclusion.