计量期末复习笔记.docx
- 文档编号:26657571
- 上传时间:2023-06-21
- 格式:DOCX
- 页数:20
- 大小:325.58KB
计量期末复习笔记.docx
《计量期末复习笔记.docx》由会员分享,可在线阅读,更多相关《计量期末复习笔记.docx(20页珍藏版)》请在冰豆网上搜索。
计量期末复习笔记
Stata部分(30’~40‘)
单选&多选:
Stata哪个命令正确?
填空:
做某件事需要哪个命令?
写小程序或者解释小程序:
解释某个命令是干什么的
计量原理部分(10’+5’)
大题:
证明OLS估计的某个性质,写出证明过程
其他课上重点讲解的部分
课本部分
Part1Thelinearregressionmodel
第一章Anoverview
●Threetypesofdata:
-Timeseriesdata
Asetofobservationsthatavariabletakesatdifferenttimes,suchasdaily(e.g.,stockprices),weekly(e.g.,moneysupply),monthly(e.g.,theunemploymentrate),quarterly(e.g.,GDP),annually(e.g.,governmentbudgets),quinqueniallyoreveryfiveyears(e.g.,thecensusofmanufactures),ordecenniallyoreverytenyears(e.g.,thecensusofpopulation).
Theproblemofautocorrelation
Atimeseriesdatasetisstationaryifitsmeanandvariancedonotvarysystematicallyovertime.
-Cross-sectionaldata
Cross-sectionaldataaredataononeormorevariablescollectedatthesamepointintime.ExamplesarethecensusofpopulationconductedbytheCensusBureauevery10years,opinionpollsconductedbyvariouspollingorganizations,andtemperatureatagiventimeinseveralplaces.
Theproblemofheterogeneity
-Panel,longitudinalormicro-paneldata
Paneldatacombinesfeaturesofbothcross-sectionandtimeseriesdata.
●EightassumptionstheClassicalLinearRegressionModel(CLRM)
A-1:
Linearintheparameters;itmayormaynotbelinearinthevariablesYandtheXs.系数线性
A-2:
Theregressorsareassumedtobefixedornonstochasticinthesensethattheirvaluesarefixedinrepeatedsampling.回归元X假定为不变的或者非随机的,即其值在重复抽样中是固定的。
A-3:
GiventhevaluesoftheXvariables,theexpected,orthemean,valueoftheerrortermiszero.Thatis,
给定X变量的值,其误差项的条件期望为零(知道X就一定知道Y)
A-4:
Homoscedastic,orconstant,varianceof
or
.给定X的值,每一个
的方差都是不变的,或者说它们具有同方差性(变化有规律)
A-5:
Noautocorrelation,Thereisnocorrelationbetweentwoerrorterms.两个误差项之间不相关,不存在自相关性
A-6:
Nomulticollinearity,ornoperfectlinearrelationshipsamongtheXvariables.
A-7:
Nospecificationbias.模型设计正确,观察值的数目n要比待估参数的数目多
A-8:
尽管不是CLRM的一部分,我们还是假定误差项服从零均值和(不变)方差
的正态分布
若再增加假设8,在正态性假设下CLRM称为正态经典线性回归模型NCLRM
●在A1-7这些假设条件下,OLS估计量是最佳线性无偏估计量(BLUE:
bestlinearunbiasedestimators)
(1)EstimatorsarelinearfunctionsofthedependentvariableY.
(2)Theestimatorsareunbiased;inrepeatedapplicationsofthemethod,theestimatorsapproachtheirtruevalues.
(3)Intheclassoflinearestimators,OLSestimatorshaveminimumvariance;i.e.,theyareefficientestimator,orthe“best”estimators.
●Thet-testofstatistics
wherese(
isthestandarderrorofcoefficient
H0:
Bk=0;H1:
Bk≠0,Ifthisvalueisgreaterthanthecriticaltvalue,wecanrejectH0
ttestsofsignificance,
=10%,5%and1%,levelsofsignificance,typeofⅠerror
|t|
才稳定,ttest检验的是某个系数是否接近0,某个变量的显著性、引入的恰当性
Thep-valuegivestheexactlevelofsignificance,orthelowestlevelofsignificanceatwhichwecanrejectH0.
Alowp-valuesuggeststhattheestimatedcoefficientisstatisticallysignificant.P值越小越显著
●Ftest
整个方程设计是否合理testthehypothesisthatalltheslopecoefficientsare0(即对X无解释能力)
多元回归中才需要做,一元回归用t-test
H0:
R2=0(B1=B2…=Bk=0);H1:
R2≠0(Bj至少有一个不为0)
IfthisvalueisgreaterthanthecriticalFvalue,rejectH0.
●拟合优度R2
thecoefficientofdetermination判定系数,isanoverallmeasureofgoodnessoffitoftheestimatedregressionline.Givesthepercentageofthetotalvariationinthedependentvariablethatisexplainedbytheregressors.y的变动中能被x解释的比例
Itisavaluebetween0(nofit)and1(perfectfit).经济学上,>0.85;管理学,>0.6
调整R2
如果在模型中增加了一个变量,则R2的值就会增加,因此进行自由度的调整
由于调整后的R2通常比未调整的R2小,因而看起来像是对添加过多回归元进入模型而施加的惩罚
●明白线性回归的系数的意义
Thefemalecoefficientof
means,holdingallothervariablesconstant(ceterisparibus),thattheaveragefemalehourlywageislowerthantheaveragemalehourlywagebyabout3dollars.
Theeducationcoefficientsuggeststhattheaveragehourlywagesincreasesbyabout$1.37foreveryadditionalyearofeducation,holdingallothervariablesconstant(ceterisparibus).
第二章
●如何产生对数值的新序列?
Genlog*=log(*)EX:
genlogoutput=log(output)
●如何将线性约束纳入进来以对回归模型进行估计
Unrestrictedregression(URS)
Restrictedregression(RS)
●画图命令
散点图:
scatterrgdptime
加线散点图:
twoway(scatterrgdptime)(lfitrgdptime)
●不同模型系数表达的意义不同
对数线性模型有一个有趣的特征,其斜率系数可以被解释为弹性:
它给出了在其他条件不变的情况下劳动投入的百分比变化所引致的产出的百分比变化。
TheinterpretationofthecoefficientoflnLABORofabout0.47isthatifweincreasethelaborinputby1%,onaverage,outputgoesupbyabout0.47%.
线性生产函数中,如果劳动投入增加一个单位,在资本投入不变的情况下,产出平均增加约48个单位;同样,如果资本投入增加一个单位,在其他条件不变的情况下,产出平均增加约10个单位。
Iflaborinputincreasesbyaunit,theaverageoutputgoesupbyabout48units,holdingcapitalconstant.Similarly,ifcapitalinputgoesupbyaunit,output,onaverage,goesupbyabout10units,ceterisparibus.
●AIC和SIC信息标准对添加过多回归元进入模型施加了更为严重的惩罚,在比较两个或更多个回归模型时,值越小的越好。
第三章
●Dummyvariables/indicatorvariables/categoricalvariables/qualitativevariables哑变量产生语句
gensex=.
replacesex=1ifgender=male
replacesex=0ifgender=female
Part2Criticalevaluationoftheclassicallinearregressionmodel
第四章multicollinearity
●Oneoftheassumptionsoftheclassicallinearregression(CLRM)isthatthereisnoexactlinearrelationshipamongtheregressors.Ifthereareoneormoresuchrelationshipsamongtheregressors,wecallitmulticollinearity,orcollinearityforshort.
●Perfectcollinearity:
Aperfectlinearrelationshipbetweenthetwovariablesexists.
Imperfectcollinearity:
Theregressorsarehighly(butnotperfectly)collinear
●Ifcollinearityisnotperfect,buthigh,severalconsequencesensue:
-TheOLSestimatorsarestillBLUE,buttheyhavelargevarianceandcovariances.Oneormoreregressioncoefficientshavelargestandarderrorsrelativetothevaluesofthecoefficients,therebymakingthetratiossmall.
-Eventhoughsomeregressioncoefficientsarestatisticallyinsignificant,theR2valuemaybeveryhigh.
-Therefore,onemayconclude(misleadingly)thatthetruevaluesofthesecoefficientsarenotdifferentfromzero.
-Also,theregressioncoefficientsmaybeverysensitivetosmallchangesinthedata,especiallyifthesampleisrelativelysmall.
(预测模型不会影响,相关性依然存在;分析x对y的边际影响,危害较大。
)
●方差膨胀因子Variance-InflationFactor:
VIFisameasureofthedegreetowhichthevarianceoftheOLSestimatorisinflatedbecauseofcollinearity.R2大,VIF大(>10不能接受),变量之间高度相关。
ToleranceFactor(TOL,theinverseofVIF)
estatvif
第五章heteroscedasticity
●Oneoftheassumptionsoftheclassicallinearregression(CLRM)isthatthevarianceofui,theerrorterm,isconstant,orhomoscedastic.Heteroscedasticity(unequalvariance)intheerrortermisoneoftheproblemscommonlyencounteredincross-sectionaldata.
●Ifheteroscedasticityexists,severalconsequencesensue:
-TheOLSestimatorsarestillunbiasedandconsistent.
-ButOLSestimatorsarenolongerofminimumvarianceorefficient,makingstatisticalinferencelessreliable(i.e.,theestimatedtvaluesmaynotbereliable)OLS估计量不再是最小方差或有效的估计量
-Thus,Estimatorsarenotbestlinearunbiasedestimators(BLUE);theyaresimplylinearunbiasedestimators(LUE).
-Inthepresenceofheteroscedasticity,theBLUEestimatorsareprovidedbythemethodofweightedleastsquares(WLS).
●对异方差性的简单检验
-残差平方和SIS的柱状图Graphhistogramofsquaredresiduals
predicte,r
gene2=e^2
histograme2
-GraphsquaredresidualsagainstpredictedY
predictyhat
scattere2yhat
●Dectionofheteroscedasticity
-BPtestp值小,拒绝零假设(Ho:
Constantvariance),存在异方差hettest
estathettest,iid
-White’stestp值大,接受零假设(White'stestforHo:
homoskedasticity),异方差
estatimtest,white
TheWhitetestismoregeneralandmoreflexiblethantheBPtest.
●Remedialmeasures-UsemethodofWeightedLeastSquares(WLS)加权最小二乘法
Divideeachobservationbythe(heteroscedastic)σiandestimatethetransformedmodelbyOLS(yettruevarianceisrarelyknown).Ifthetrueerrorvarianceisproportionaltothesquareofoneoftheregressors,wecandividebothsidesoftheequationbythatvariableandrunthetransformedregression将每个观测值除以其方差(方差不相同)而得到BLUE估计量,从而根据OLS估计其转换形式
第六章Autocorrelation
●Oneoftheassumptionsoftheclassicallinearregression(CLRM)isthatthecovariancebetweenui,theerrortermforobservationi,anduj,theerrortermforobservationj,iszero.
-Morecommonintimeseriesdata(时间序列设定tssettime)
●Iftheerrortermattimetiscorrelatedwiththeerrortermatt-1oranyothererrorterminthepast,severalconsequencesensue:
-TheOLSestimatorsarestillunbiasedandconsistent.
-Theyarestillnormallydistributedinlargesamples.
-Theyarenolongerefficient,meaningthattheyarenolongerBLUE.
-Inmostcasesstandarderrorsareunderestimated.OLS标准误被低估,估计出来的t值是有些夸大了,给人的感觉是系数比它实际的情况要更显著,t检验和F检验可能会不再有效
-Thus,thehypothesis-testingprocedurebecomessuspect,sincetheestimatedstandarderrorsmaynotbereliable,evenasymptotically(i.e.,inlargesamples).
●Testofautocorrelation
-回归reglnconsumplndpilnwealthinterest
得到残差predicte,r
用残差对滞后一期回归(不要常数项)regel.e,nocons
得到e=0.3246707
说明存在残差项自相关0.3246707→
-Graphicalmethod
genle=l.e
twoway(scatterele)(lfitele)
自相关、偏相关
ace
pace
corrgrame
-Durbin-Watsontestdwstat
0:
残差序列正相关;4:
负相关;2:
比较好
-Breusch-Godfrey(BG)testbgodfrey,lags(#)
P<0.05拒绝原假设,存在自相关
●Remedialmeasures
-First-DifferenceTransformation一阶差分转换
-
GeneralizedTransformation广义差分模型
取得的参数的估计,称为可行性广义最小二乘(FGLS)估计量
gennewlnconsump=lnconsump-0.3246*l.lnconsump
gennewlndpi=lndpi-0.3246*l.lndpi
gennewlnwealth=lnwealth-0.3246*l.lnwealth
gennewinterest=interest-0.3246*l.interest
regnewlnconsumpnewlndpinewlnwealthnewinterest
-Newey-WestMethod
neweylnconsumplndpilnwealthinterest,lag(3)
确定滞后期estaticAIC值大小大,最小的一个
第七章modelspecificationerrors
●Omissionofrelevantvariables
Ifth
- 配套讲稿:
如PPT文件的首页显示word图标,表示该PPT已包含配套word讲稿。双击word图标可打开word文档。
- 特殊限制:
部分文档作品中含有的国旗、国徽等图片,仅作为作品整体效果示例展示,禁止商用。设计者仅对作品中独创性部分享有著作权。
- 关 键 词:
- 计量 期末 复习 笔记