An Estimate Of The Number Of Mean Change Points In Panel Data

Since the 1960s,econometric economists have begun to pay attention to panel data.Especially in the past 20 years,with the development of econometric theory,statistical methods,and econometric analysis software,panel data econometric analysis has become the most active research in econometrics.One of the important branches.After years of development,the current panel data model has achieved a series of very mature results in the linear field.However,when the time length is long and the data appears to be non-stationary,how to build the model is still a hot field at the forefront.If this non-stationary process is ignored and the modeling is performed directly,it may lead to inconsistent estimates of the final result,which may lead to statistical inference errors.In the non-stationary field,there are two research viewpoints:one is to focus on random terms,such as unit root processes;the other is to focus on non-linear models that overthrow the original model settings,such as the mean shift model studied in this article.In the traditional sequence,it is assumed that the time series process has(weak)stationarity,that is,its moment does not change with time.The mean shift model assumes that the first-order moment changes with time and the second-order moment is stable.It is the simplest nonlinear model.This paper estimates the multivariate points based on the mean shift panel data model.The first chapter discusses the research background and current research status of mean shift at home and abroad through literature review,expounds the method evolution of change point estimation from time series to panel data,and puts forward his own motivation for selecting the topic based on the research ideas of the predecessors.And meaning.The second chapter elaborates on the specific process of the estimation method in this paper.The estimation problem of multi-change points is divided into two problems of posi-tion estimation and number estimation,the least squares(LS)sequential estimation and ratio methodis proposed for these two problems..For the estimation of the change point position,we extend the estimation process of Bai Jushan single change point mean shift to the case of multiple change points,and propose a least square sequential estimation.When the number of change points r₀is given,A consistent estimate of the position of the change point can be obtained.When the number of change points is undetermined,we find that the least squares sequential estimation will first estimate all the real change points,and then estimate the false change points,and the residual sum of squares caused by the real change points and the false change points decreases There is a dimensional difference in the quantity.On the basis of this discovery,we refer to the inflection point of distinguishing true and false factors in the factor model,and propose a ratio method to estimate the number of change points.Theoretical results show that the estimation of the number of change points is consistent.The third chapter uses Monte Carlo simulation experiments to simulate the two methods of position estimation and number estimation from two angles of N and T.The experimental results show that our method can obtain good estimation properties in the case of limited samples.The fourth chapter is empirical analysis.From the perspective of model conformity and practical significance,the birth rate data of 31 provinces in my country in 1949 to 2019 are selected for empirical analysis.The results show that there are 5 change points in my country's fertility rate,which can be divided into 6 stages.Combining the actual situation,according to the main reasons behind the restriction of my country's fertility rate,from natural factors,policy factors to economic factors,the six stages are summarized into three periods to reflect the changes in the fertility situation of the people since the founding of the People's Republic of China.