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*-Chapter 4-* *-4.1 存在异方差时的稳健估计-*Example 8.1 Heteroscedastic Regressioninsheet using tablef9-1.csv,clear*keep if avgexp0 /有平均支出为零的去掉generate incomesq=income2regress avgexp age ownrent income incomesq*绘制残差rvpplot income,xlabel(0(2)12) xline(2 4 6 8 10,lstyle(grid) ylabel(-500(500)2000) /yline(0 500 1000 1500,lstyle(grid)*-*Example 8.2 The White Estimator*OLSregress avgexp age ownrent income incomesq *Robust Standard Errors.regress avgexp age ownrent income incomesq,vce(robust) *注意：这里给出的稳健标准误是Davidson/MacKinnon提出的修正1,到这里就可以了。*要获得最初White稳健标准误将协方差矩阵再乘以(n-K)/nmatrix b=e(b)matrix V=e(V)*(72-5)/72)ereturn post b Vereturn display /White Robust Standard Errors*Davidson/MacKinnon修正2regress avgexp age ownrent income incomesq,vce(hc2)*-Baum 6.1.2use /data/imeus/fertil2,clearregress ceb age agefbrth usemeth,vce(robust)regress ceb age agefbrth usemeth,vce(cluster children)*-*Newey-West *Example 19.4 Autocorrelation Consistent Covariance Estimationinsheet using TableF2-2.csv,cleartsset year*generate t=_ngenerate lnG=log(gasexp/(pop*gasp) /蓩吖腔詬谢貞私generate lnY=log(income)generate lnPG=log(gasp)generate lnPNC=log(pnc)generate lnPUC=log(puc)generate lnPPT=log(ppt)generate lnPN=log(pn)generate lnPD=log(pd)generate lnPS=log(ps)*regress lnG lnPG lnY lnPNC lnPUCpredict e,residtsline e,title(Autocorrelated Residuals from Gasoline Regression)*Newey-West estimatornewey lnG lnPG lnY lnPNC lnPUC,lag(3)*-use /data/imeus/ukrates,clearsummarize rs r20tsset monthregress D.rs LD.r20display _N(1/4)newey D.rs LD.r20,lag(5)*-4.3 异方差的检验-*Example 8.3 Testing for Heteroscedasticityinsheet using tablef9-1.csv,clearkeep if avgexp0 /有平均支出为零的去掉generate incomesq=income2*1.Whites Testquietly regress avgexp age ownrent income incomesq *White 异方差检验有一个专门的程序。whitetst.通过下面的命令安装ssc install whitetst /安装White Test 程序.whitetst*2. BreuschPagan Test:quietly regress avgexp age ownrent income incomesq *使用estat hettest 命令,注意其选项对应于不同情形*1.estat hettest,对因变量的拟合值进行检验*2.estat hettest,rhs 对所有解释变量进行检验*3.estat hettest varlist,iid 去除正态性假设的nR2得分检验*4.estat hettest varlist,mtest 将依次估计几个自变量 estat hettest income incomesq /针对变量 Income Incomesq estat hettest income incomesq,iid *是通过简单的附属回归获得其估计量 *Baum 6.2.1 WLS浼拌鐨勪緥瀛?-use /data/imeus/hprice2a,clearregress lprice rooms crime ldistestat hettest,iidestat hettest rooms crime ldist,iidwhitetst*Baum 6.2.1 加权最小二乘回归WLSgenerate rooms2=rooms2regress lprice rooms crime ldist aw=1/rooms2*- *Example 8.4 Multiplicative Heteroscedasticity.insheet using tablef6-1.csv,cleargenerate lnC=log(c)generate lnQ=log(q)generate lnQsq=lnQ2generate lnPf=log(pf)*这里省略了企业和年份虚拟变量，并且将载重因素（LF）变量出现在方差项而非OLSregress lnC lnQ lnQsq lnPf /OLS regression*Breusch-Pagan LM test or,bpagan LFestat hettest lf *predict double e,resid*robust std errregress lnC lnQ lnQsq lnPf,vce(robust) *FIGURE 8.2 Plot of Residuals Against Load Factortwoway scatter e lf,xlabel(0.4(0.05)0.7) yline(0,lcolor(1)xline(0.45 0.5 0.55 0.6 0.65,lstyle(grid) /| function y=0.8-2*x,range(0.4 0.61) lcolor(1) lpattern(longdash) /| function y=-0.8+2*x,range(0.4 0.61) lcolor(1)lpattern(longdash) legend(off) /title(FIGURE 8.2 Plot of Residuals Against Load Factor) xtitle(Load Factor)*-FGLS-generate double lne2=log(e2)regress lne2 lf /也可以使用非线性回归直接估计exp(za)predict double s2hatgenerate wi=exp(-s2hat)regress lnC lnQ lnQsq lnPf aweight=wi*-*Example 8.5 Groupwise Heteroscedasticity*数据整理quietly infile str20 COUNTRY YEAR LGASPCAR LINCOMEP LRPMG LCARPCAP /using gasoline.dat,cleardrop in 1gen ID=ceil(_n/19) / country IDlabel variable COUNTRY Name of countrylabel variable YEAR Year,1960-1978label variable LGASPCAR Log of consumption per carlabel variable LINCOMEP Log of per capita incomelabel variable LRPMGLog of real price of gasolinelabel variable LCARPCAP Log of per capita number of carslabel variable IDCountryquietly tab COUNTRY,gen(id) / generate country dummy variables*-*OLS Regressionregress LGASPCAR LINCOMEP LRPMG id2-id18 predict residual,residscatter residual ID,ylabel(-0.4(0.2)0.8) title(OECD石油消费数据中的群组异方差) /xline(5 10 15,lstyle(grid) *检验所有虚拟变量联合显著性testparm id*绋冲仴鏍囧噯璇?regress LGASPCAR LINCOMEP LRPMG id2-id18,vce(robust) /OLS with Robust Std.Errregress LGASPCAR LINCOMEP LRPMG id2-id18,vce(cluster ID) /OLS with Clustered Robust Std.Err*群组异方差的FGLS估计generate ressq=residual2 /OLS残差的平方by ID,sort:egen s2g=mean(ressq) /(8-36) 获得每个组的估计方差generate wi=1/s2gregress LGASPCAR LINCOMEP LRPMG id2-id18 aw=wi*-*异方差的检验quietly regress LGASPCAR LINCOMEP LRPMG id2-id18estat hettest id2-id18 /LM test 。注意书上结果有误*White-test 见书上的说明predict e,residgenerate e2=e2quietly regress e2 id2-id18display White-Statistics = e(N)*e(r2)*-*-4.3 序列相关-*Example 19.2 Autocorrelation Induced by Misspecification of the Modelinsheet using TableF2-2.csv,cleartsset year*generate t=_ngenerate lnG=log(gasexp/(pop*gasp) /人均汽油消费数量generate lnY=log(income)generate lnPG=log(gasp)generate lnPNC=log(pnc)generate lnPUC=log(puc)generate lnPPT=log(ppt)generate lnPN=log(pn)generate lnPD=log(pd)generate lnPS=log(ps)*quietly regress lnG lnPGpredict e1,residtsline e1,saving(figure1,replace) subtitle(lnG=&betasubscript:0+&betasubscript:1*lnPG+&epsilon)quietly regress lnG lnPG lnYpredict e2,residtsline e2,saving(figure2,replace) subtitle(lnG=&betasubscript:0+&betasubscript:1*lnPG+&betasubscript:2*lnY+&epsilon)quietly regress lnG lnPG lnY lnPNC lnPUC lnPPT lnPN lnPD lnPS tpredict e3,residtsline e3,saving(figure3,replace) subtitle(Full Model)quietly regress lnG lnPG lnY lnPNC lnPUC lnPPT lnPN lnPD lnPS t in 1/22predict e4 if e(sample)=1,residquietly regress lnG lnPG lnY lnPNC lnPUC lnPPT lnPN lnPD lnPS t in 23/52predict e42 if e(sample)=1,residreplace e4=e42 in 23/52tsline e4,saving(figure4,replace) subtitle(Seperated Model)*合并四个残差图graph combine figure1.gph figure2.gph figure3.gph figure4.gph,rows(2) /title(FIGURE 19.2 Unstandardized Residuals)*-*-自相关的检验-*检验自相关：汽油市场insheet using TableF2-2.csv,cleartsset year*generate t=_ngenerate lnG=log(gasexp/(pop*gasp) /人均汽油消费数量generate lnY=log(income)generate lnPG=log(gasp)generate lnPNC=log(pnc)generate lnPUC=log(puc)generate lnPPT=log(ppt)*1.普通最小二乘估计regress lnG lnY lnPG lnPNC lnPUC tpredict e,resid*Figure 19.4 Least Squares Residualstsline e,title(最小二乘残差)*Newey-West 自回归稳健标准误newey lnG lnY lnPG lnPNC lnPUC t,lag(3)*残差的自相关系数corrgram e,lag(5)*Box-Pierce Q 统计由于Box-Ljung Q的修正，基本不怎么使用，这里将计算列在下面matrix ac=r(AC)matrix ac=ac1,1.5matrix Q=ac*ac*52matrix list Q*Box-Ljung Q 统计量，实际上corrgram中也已列出.wntestq e,lag(5)*Bresuch and Godfrey LMquietly regress lnG lnY lnPG lnPNC lnPUC testat bgodfrey,lags(5) *也可以lags(1/5),列出1-5阶每一个*这里下面是计算的步骤，如下OLS回归和F联合检验，实际应用不需要forvalues i=1/5 quietly generate ei=Li.ereplace ei=0 in 1/iregress e lnY lnPG lnPNC lnPUC t e1-e5 display Bresuch and Godfrey LM = e(N)*e(r2)*Durbin-Watson.注意，上面进行了一个回归。要针对初始的估计进行检验quietly regress lnG lnY lnPG lnPNC lnPUC testat dwatson*ddL=1.34，因此存在自相关*-*Baum,6.3.1 英国政府长期和短期债券利率use /data/imeus/ukrates,clearregress D.rs LD.r20predict double eps,restat bgodfrey,lags(6)wntestq epsac eps*-应用：对自相关模型的估计insheet using TableF2-2.csv,cleartsset year*generate t=_ngenerate lnG=log(gasexp/(pop*gasp) /蓩吖腔詬谢貞私generate lnY=log(income)generate lnPG=log(gasp)generate lnPNC=log(pnc)generate lnPUC=log(puc)generate lnPPT=log(ppt)*prais lnG lnY lnPG lnPNC lnPUC t*结果与书上不同。stata软件进行多次迭代,直到 结果收敛，书上的结果未经迭代。*MLEarima lnG lnY lnPG lnPNC lnPUC t,ar(1)*非线性估计nl (lnG=rho=0.8*L.lnG+b0*(1-rho)+b1*(lnY-rho*L.lnY)+b2*(lnPG-rho*L.lnPG) /+b3*(lnPNC-rho*L.lnPNC)+b4*(lnPUC-rho*L.lnPUC)+b5*(t-rho*L.t) /,variables(lnG L.lnG lnY L.lnY lnPG L.lnPG lnPNC L.lnPNC lnPUC L.lnPUC t L.t)*-*-Chapter 6 面板数据模型-*- 为何使用面板数据-* 面板数据的组织：*Cornwell and Rupert(1988)年数据insheet using tablef8-1.csv,clear*生成一个id变量标注观测的个体gen id=ceil(_n/7)by id,sort:gen year=_nxtset id year*summarizelist id year lwage ed in 1/20,sep(7)xtdescribextsum lwage ed fem blk*面板数据分析的结构*平衡和非平衡面板数据。德国医疗数据quietly insheet using healthcare.csv,clearby id ,sort:gen Ni=_Ncollapse (count) Ni,by(id) tab Nihistogram Ni, freq title(Group Sizes for an Unbalanced Panel) /xlabel(1(1)7) *-*-*例9.1 工资方程（greene,edited 6)混合模型的面板稳健异方差*Cornwell and Rupert(1988)年数据insheet using tablef8-1.csv,cleargen id=ceil(_n/7)by id,sort:gen year=_nxtset id year*generate exp2=exp2global xlist exp exp2 wks occ ind south smsa ms union ed fem blk*OLSregress lwage $xlist*White std .errregress lwage $xlist,vce(robust)*cluster std.errregress lwage $xlist,vce(cluster id)/*bootstrap std.errtsset,clear*这个tsset,clear是清除掉前面xtset的设置，面板bootstrap要这一步。bootstrap,reps(100) cluster(id): regress lwage $xlist*/*可以使用xtreg,pa命令针对误差项可能存在的相关性进行设定。xtset id yearxtreg lwage $xlist,pa corr(ind)xtreg lwage $xlist,pa corr(ar 2) vce(robust)matrix list e(R)*-*例9.2*组间估计量，接上例xtreg lwage $xlist,be*orpreservextdata,be clearregress lwage $xlist / n=595*注意两者估计结果相同restore*-*一阶差分估计xtset id yearregress D.(lwage $xlist),vce(cluster id) noconstant*-*-6.3 固定效应模型-*Baum 9.1.1 One-Way FE MODELuse /data/imeus/traffic,clearxtset state yearxtdescribextsum fatal beertax spircons unrate perincK state year*FE MODELxtreg fatal beertax spircons unrate perincK,fe*- *Example 2:LSDV估计(E.9.4) 固定效应工资方程insheet using tablef8-1.csv,cleargen id=ceil(_n/7)by id,sort:gen year=_nxtset id yeargenerate exp2=exp2global xlist exp exp2 wks occ ind south smsa ms union *解释变量中去掉了不随时间变化的ed,fem,blk三个变量。*使用虚拟变量估计FEM,应用中部要使用该方法areg lwage $xlist,absorb(id) /use areg do LSDV*应当使用xtreg命令估计FE模型xtreg lwage $xlist,fe /FE model*个体固定效应的值alphapredict alphai,ureplace alphai=alphai+_b_cons /注意stata中FE包含常数项，因此固定效应是常数项+uipreservecollapse (mean) alphai,by(id) list alphai in 1/20histogram alphai,title(Fixed Effects from Cornwell and Rupert Wage Equation) kdensityrestore*Robust std.errsxtreg lwage $xlist,fe vce(cluster id) /Robust FEM*应该用xtreg进行估计。*-*-固定时间与群组效应-two way fixed effects*Two-Way FE,Baum 9.1.2use /data/imeus/traffic,clearxtset state year*One Way FE MODELxtreg fatal beertax spircons unrate perincK,fe*Two Way FEquietly tabulate year,gen(yr)*year dummy variables,7-1xtreg fatal beertax spircons unrate perincK yr1-yr6 ,fetestparm yr*Baum ,PP 198local j 0forvalues i=82/87 local +jrename yrj yriquietly replace yri=yri-yr7xtreg fatal beertax spircons unrate perincK yr82-yr87 ,fetestparm yr*RE Model Output,Baum 9.1.4xtreg fatal beertax spircons unrate perincK ,re*-*Example 9.4,Greene(6)insheet using tablef8-1.csv,cleargen id=ceil(_n/7)by id,sort:gen year=_nxtset id yeargenerate exp2=exp2global xlist exp exp2 wks occ ind south smsa ms union regress lwage $xlist,vce(cluster id) /OLS with cluster het*Time Effects*可以生成虚拟变量，然后使用F统计计算，F(6.4149)=191.11quietly tab year,gen(yr)regress lwage $xlist yr2-yr7testparm yr*个体效应模型使用xtreg,fe，下方直接报告F(594,3561)=38.25xtreg lwage $xlist,fe /Individul effects onlyxtreg lwage $xlist,fe vce(robust)/Individul effects with robust std.err.*利用test进行Wald检验xtreg lwage $xlist yr*,fetestparm yr*-*-*固定效应中不随时间变化的变量估计问题 *数据接上例xtreg lwage $xlist ed fem blk,fe*(1)yx估计FE，得到ai;(2)ai对z不随时间变量进行回归，得到残差hi;*(3) yx,z,hi估计global zlist fem ed blk /性别、教育、种族虚拟变量xtset id year*(1)xtreg lwage $xlist,fepredict ai,ureplace ai=ai+_b_cons*(2)regress ai $zlist if year=7predict hi,resid*(3)regress lwage $xlist $zlist hi*- Random Effects-*-*注：随机效应的结果与书上存在差异。原因在于stata 方差分解的方法与Nlogit不同。*如下例所示：insheet using tablef10-4.csv,clearxtset firm yearxtreg i f c,re/*下面的是Nlogit估计随机效应的命令import;file=e:greene7edtablef10-4.csv $setpanel;group=firm;pds=year $regress;lhs=i;rhs=one,f,c ;panel;random effects $*/*-* Example 9.5 Testing for Random Effectsinsheet using tablef8-1.csv,cleargen id=ceil(_n/7)by id,sort:gen year=_nxtset id yeargenerate exp2=exp2global xlist exp exp2 wks occ ind south smsa ms union *regress lwage $xlist,vce(cluster id) /Pooled OLSxtreg lwage $xlist,fe /Fixed Effectsxtreg lwage $xlist,re /Random Effects* xttest0 实施Breusch-Pagan LM test for random effects, a test that Var(v_i)=0.xttest0*随机效应模型的极大似然估计xtreg lwage $xlist,mle *-Mundlaks approach-*Example 9.8 Variable Addition Test for Fixed versus Random Effects*Hausman-Wu test.matrix.首先生成组均值变量foreach x of varlist $xlist by id,sort:egen xbar=mean(x)global xlistbar *barxtreg lwage $xlist $xlistbar,rematrix b=e(b)matrix V=e(V)matrix r=b1,10.18matrix V=V10.18,10.18matrix H=r*invsym(V)*rmatlist H*display invchi2tail(9,.05)*use testtest expbar exp2bar wksbar occbar indbar southbar smsabar msbar unionbar*ortestparm *bar*Mundlaks 方法处理FE中不随时间变化的变量xtreg lwage $xlist $xlistbar fem ed blk,re *-*Example 9.7 Hausman Test for Fixed versus Random Effects*数据接上quietly xtreg lwage $xlist,feest store FEquietly xtreg lwage $xlist,reest store REhausman FE RE*注意：(V_b-V_B is not positive definite)由于两个协方差矩阵的差不是正*定的。hausman FE RE,sigmamore*sigmamore 后缀意味着两个协方差矩阵使用相同的GLS的s2估计值。*或者使用Wu-附加变量检验，如上面Mundlak方法估计所示。*-*Hausman Robust Testxtreg lwage $xlist,rescalar theta=e(theta)foreach x of varlist $xlist by id:egen meanx=mean(x)gen mdx=x-meanxgen redx=x-theta*meanxglobal mdlist md*global redlist red*by id:egen meanlwage=mean(lwage)gen rlwage=lwage-theta*meanlwage*regress rlwage $redlist $mdlist,vce(cluster id)testparm md*-*-/*Example 9.6 Estimates of the Random Effects Model*求出来theta的值insheet using tablef8-1.csv,cleargen id=ceil(_n/7)by id,sort:gen year=_nxtset id yeargenerate exp2=exp2global xlist exp exp2 wks occ ind south smsa ms union quietly regress lwage $xlistscalar s2=e(rss)/e(df_r)quietly xtreg lwage $xlist,fescalar s2e=e(rss)/e(df_r)scalar s2u=s2-s2edisplay s2 s2e s2uscalar theta=1-sqrt(s2e/(s2e+7*s2u)display Theta = theta*利用FGLS计算随机效应，应用中不需要这样做。global yandX lwage exp exp2 wks occ ind south smsa ms unionforeach x of varlist $yandX by id,sort:egen xbar=mean(x)quietly generate xstar=x-theta*xbar*随机效应regress lwagestar expstar exp2star wksstar occstar indstar southstar /smsastar msstar unionstar*/*-嵌套随机效应模型（不介绍）-*GREENE ,ed 6 P216,example 9.9*import dataset and label variableinfile str20 STATE str20 ST_ABB YR P_CAP HWY WATER UTIL PC GSP EMP UNEMP /using PRODUC.txt,cleardrop in 1/1label variable STATE State name label variable ST_ABB State abbreviationlabel variable YR Yearlabel variable P_CAP Public capitallabel variable HWY Highway capitallabel variable WATER Water utility capitallabel variable UTIL Utility capitallabel variable PC Private capitallabel variable GSP Gross state productlabel variable EMP Employmentlabel variable UNEMP Unemployment rate*Generate log variableglobal yandx GSP PC HWY WATER UTIL EMP foreach x of varlist $yandx quietly generate lnx=log(x)label variable lnx LOG(x)*生成州IDgene