高级计量经济学王少平.ppt
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1、Some statistics in Econometrics and their developments Shaoping WangSchool of Economics,Huazhong University of Science and Technology,Wuhan,ChinaIntroductionClassic tests in EconometricsMore broadly:hypothesis could be set as linear or nonlinear.Likelihood Ratio test:Wald test:LM test:Three Prevaili
2、ng Tests in econometricsIntroduction DW test for first autocorrelation I(1)tests:t statistics and its distribution-DF and ADF distribution Whats difference for the DF and ADF distribution ADF test and PP test for I(1)process Some issues 3.1宏观计量非平稳(单位根I(1))过程:3.1宏观计量非平稳(单位根I(1))过程:单位根检验 时间序列yt,yt=yt-
3、1+ut,零假设和备择假设分别是,H0:=1,(yt I(1)H1:1,(yt I(0))3.1宏观计量非平稳(单位根I(1))过程:单位根检验 时间序列yt,yt=yt-1+ut,零假设和备择假设分别是,H0:=1,(yt I(1)H1:1,(yt I(0))用DF统计量进行单位根检验。t=DF distribution 3.1宏观计量非平稳(单位根I(1))过程:单位根检验 时间序列yt,yt=yt-1+ut,零假设和备择假设分别是,H0:=1,(yt I(1)H1:1,(yt I(0))用DF统计量进行单位根检验。t=DF distribution 协整 协整是对非平稳经济变量长期均衡关
4、系的统计描述.非平稳经济变量间存在的均衡关系称作协整关系.定义:如果 X1t,X2t,Xkt I(1),Zt=X I(0),=(1,2,k),那么X1t,X2t,Xkt 协整,记为,Xt CI(1,0),是协整向量.上图说明:X(t),Y(t)I(1),Z(t)=0.3Y(t)+0.5X(t)I(0)Introduction Panel unit root test:Survey by Hurlin and Mignon(2004)Assume cross sectional independence Levin and Lin(1992,1993);Levin,Lin and Chu(200
5、2);Harris and Tzavalis(1999);Im,Pesaran and Shin(1997,2003);Maddala and Wu(1999);Choi(1999,2001)Assume cross sectional dependence Flres,Preumont and Szafarz(1995);Tayor and Sarno(1998);Breitung and Das(2004);Bai and Ng(2001,2004);Moon and Perron(2004);Phillips and Sul(2003);Pesaran(2003);Choi(2002);
6、Chang(2002)Introduction Chang(2002)A NIV estimation Chang testPerformance of Chang test with moderate to high cross sectional dependencyl This Paperl A Two Step Testl Improved the performanceChangs Model(1):coefficient on the lagged dependent variable:error term which follows the AR(p)process:(2):la
7、g operator:autoregressive coefficient:some integer that is known and fixed We are interested in testing for all VS for some HypothesisModel Assumptions To ensure the AR(p)process in(2)is invertible Assumption 1:for all and To restrict the distribution of error term Assumption 2:Denote(1)are independ
8、ent and identically distributed and its distribution is absolutely continuous with respect to Lebesgue measure(2)has mean zero and covariance matrix(3)satisfies for some and has a characteristic function that satisfies for someNIV Estimation and Chang Test OLS estimation:Under,the asymptotic distrib
9、ution of obtained from(3)is asymmetric,and not the usual t-distribution NIV estimation:as instrument for,where is some function satisfying Assumption 3:is regularly integrable and satisfy Under assumption 1-3,Chang draw the key result:as and are asymptotically uncorrelated regardless of the cross se
10、ctional dependence And the test statistic has a limiting standard normal distributionNIV Estimation and Chang Test(contd)Findings about Chang(2002)The bigger the N is,the Smaller the correlation coefficient of cross-sectional units becomes.The test statistic does not fully follow the limiting standa
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