计量经济学英文重点知识点考试必备Word格式文档下载.docx
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7)
8)
●Step2:
收集数据
Ø
Threetypesofdata三类可用于分析的数据
3)Pooleddata合并数据〔上两种的结合〕
●Step3:
设定数学模型
1.plotscatterdiagramorscattergram
2.writethemathematicalmodel
●Step4:
设立统计或经济计量模型
CLFPRisdependentvariable应变量
CUNRisindependentorexplanatoryvariable独立或解释变量〔自变量〕
WegiveacatchallvariableUtostandforalltheseneglectedfactors
Inlinearregressionanalysisourprimaryobjectiveistoexplainthebehaviorofthedependentvariableinrelationtothebehaviorofoneormoreothervariables,allowingforthedatathattherelationshipbetweenthemisinexact.线性回归分析的主要目标就是解释一个变量〔应变量〕与其他一个或多个变量〔自变量〕只见的行为关系,当然这种关系并非完全正确
●Step5:
估计经济计量模型参数
Inshort,theestimatedregressionlinegivestherelationshipbetweenaverageCLFPRandCUNR简言之,估计的回归直线给出了平均应变量和自变量之间的关系
Thatis,onaverage,howthedependentvariablerespondstoaunitchangeintheindependentvariable.单位因变量的变化引起的自变量平均变化量的多少。
●Step6:
核查模型的适用性:
Thepurposeofdevelopinganeconometricmodelisnottocapturetotalreality,butjustitssalientfeatures.
●Step7:
检验自模型的假设
Whydoweperformhypothesistesting?
Wewanttofindourwhethertheestimatedmodelmakeseconomicsenseandwhethertheresultsobtainsconformwiththeunderlyingeconomictheory.
第二章
1.Themeaningofregression〔回归〕
Regressionanalysisisconcernedwiththestudyoftherelationshipbetweenonevariablecalledthedependentorexplainedvariable,andoneormoreothervariablescalledindependentorexplanatoryvariables.
2.Objectivesofregression
1)Estimatethemean,oraverage,andthedependentvaluesgiventheindependentvalues
2)Testhypothesesaboutthenatureofthedependence-----hypothesessuggestedbytheunderlyingeconomictheory
3)Predictorforecastthemeanvalueofthedependentvariablegiventhevaluesoftheindependents
4)Oneormoreoftheprecedingobjectivesbined
3.PopulationRegressionLine〔PRL〕
Inshort,thePRLtellsushowthemean,oraverage,valueofYisrelatedtoeachvalueofXinthewholepopulation
4.ThedependenceofYonX,technicallycalledtheregressionofYonX.
5.Howdoweexplainit?
Astudent’sS.A.T.score,say,theithindividual,correspondingtoaspecificfamilyinecanbeexpressedasthesumoftwoponents
1)Theponentcanbecalledthesystematic,ordeterministic,ponent.
2)Maybecalledthenonsystematicorrandomponent
6.WhatisthenatureofU(stochasticerror)term?
2)Someintrinsicrandomnessinthemathscoreisboundtooccurthatcannotbeexplainedevenweincludeallrelevantvariables.即使模型包括了决定性数学分数的所有变量,内在随机性也不可防止,这是做任何努力都无法解释的。
3)Umayalsorepresenterrorsofmeasurement.U还代表了度量误差
4)TheprincipleofOckham’srazor-thedescriptionbekeptassimpleaspossibleuntilprovedinadequate-wouldsuggestthatwekeepourregressionmodelassimpleaspossible.“奥卡姆剃刀原如此〞,描述应该尽可能简单,只要不遗漏重要信息。
这明确回归模型应尽可能简单。
7.HowdoweestimatethePRF〔populationregressionfunction〕?
Unfortunately,inpractice,Werarelyhavetheentirepopulationinourdisposal,oftenwehaveonlyasamplefromthispopulation.
8.GrantedthattheSRFisonlyanapproximationofPRF.Canwefindamethodoraprocedurethatwillmakethisapproximationascloseaspossible?
SRF仅仅是PRF的近似,那么能不能找到一种方法使这种近似尽可能接近真实呢?
9.Specialmeaningof“linear〞
1)Linearityinthevariables变量线性
Theconditionalmeanvalueofthedependentvariableisalinearfunctionoftheindependentvariables
2)LinearityintheParameters参数线性
Theconditionalmeanofthedependentvariableisalinearfunctionoftheparameters,theB’s;
itmayormaynotbelinearinthevariables.
第三章
1.UnlesswearewillingtoassumehowthestochasticUtermsaregenerated,wewillnotbeabletotellhowgoodanSRFisasanestimateofthetruePRF.只有假定了随机误差的生成过程,才能判定SRF对PRF拟合的是好是坏。
2.ClassicalLinearRegressionModel
1)Assumption1:
Theregressionmodelislinearintheparameters.Itmayormaynotbelinearinthevariables.回归模型是参数线性的,但不一定是变量线性的。
2)Assumption2:
TheexplanatoryvariablesXisuncorrelatedwiththedisturbancetermU.X’sarenonstochastic,Uisstochastic.解释变量X与扰动误差项u不相关.X是非随机的,U是随机的。
3)Assumption3:
GiventhevalueofXi,theexpected,ormeanvalueofthedisturbancetermUiszero.给定Xi,扰动项的期望或均值为零。
DisturbanceUrepresentallthosefactorsthatarenotspecificallyintroducedinthemodel干扰项U代表了所有未纳入模型的影响因素。
4)Assumption4:
ThevarianceofeachUiisconstant,orhomoscedastic.U的方差为常数,或同方差。
●Homoscedasticity〔同方差〕:
a.ThisassumptionsimplymeansthattheconditionaldistributionofeachYpopulationcorrespondingtothegivenvalueofXhasthesamevariance.该假定明确,与给定的X相对应的每个Y的条件分布具有同方差。
b.TheindividualYvaluesarespreadaroundtheirmeanvalueswiththesamevariance.即每个Y值以一样的方差分布在其均值周围。
5)Assumption5:
Thereisnocorrelationbetweentwoerrorterms,thisistheassumptionofno-autocorrelation.无自相关假定,即两个误差项之间不相关。
6)Assumption6:
Theregressionmodeliscorrectlyspecified.回归模型是正确假定的。
Thereisnospecificationbiasorspecificationerrorinthemodel.实证分析的模型不存在设定偏差或设定误差。
●Thisassumptioncanbeexplainedinformallyasfollows.Aneconometricinvestigationbeginswiththespecificationoftheeconometricmodelunderlyingthephenomenonofinterest.
3.VariancesandStandarderrorsofOLSestimators普通最小二乘估计量的方差与标准误:
OneimmediateresultoftheassumptionsintroducedisthattheyenableustoestimatethevariancesandstandarderrorsoftheOLSestimatorsgiveninEq.(2.16)and(2.17).
4.Weshouldknow:
●Variancesoftheestimators
●Standarderrorsoftheestimators
5.Whatisthevalueofσ
●Thehomoscedasticσisestimatedfromformula
6.StandardErroroftheRegression(SER)回归标准误
●IssimplythestandarddeviationoftheYvaluesabouttheestimatedregressionline.Y值偏离估计回归的标准差。
7.SummaryofmathS.A.T.scorefunction
1)Interpretation
●Thestandarddeviation,orstandarderror,is0.000245,isameasureofvariabilityofb2fromsampletosample.
●Ifwecansaythatourputedb2lieswithinacertainnumberofstandarddeviationunitsfromthetrueB2,wecanstatewithsomeconfidencehowgoodtheputedSRFisasanestimatorofthetruePRF.
2〕SamplingDistribution抽样分布
Oncewedeterminethesamplingdistributionofourtwoestimators,thetaskofhypothesistestingbeesstraightforward.一旦确定了两个估计量的抽样分布,那么假设检验就是举手之劳的事情。
8.WhydoweuseOLS?
●ThepropertiesofOLSestimators
●ThemethodofOLSisusedpopularlynotonlybecauseitiseasytousebutalsobecauseithassomestrongtheoreticalproperties.OLS法得到广泛使用,不仅是因为它简单易行,还因为它具有很强的理论性质。
9.Gauss-Markovtheorem高斯-马尔科夫定理
Giventheassumptionsoftheclassicallinearregressionmodel(CLRM),theOLSestimatorshaveminimumvarianceintheclassoflinearestimators.TheOLSestimatorsareBLUE(bestlinearunbiasedestimators)满足古典线性模型的根本假定,如此在所有线性据计量中,OLS估计两具有最小方差性,即OLS是最优线性无偏估计量〔BLUE〕
10.BLUEproperty最优线性无偏估计量的性质
1)B1andB2arelinearestimators.B1和B2是线性估计量
2)Theyareunbiased,thatisE(b1)=B1,E(b2)=B2.B1和B2是无偏估计两
3)TheOLSestimatoroftheerrorvarianceisunbiased.误差方差的OLS估计量是无偏的
4)b1andb2areefficient
Var(b1)islessthanthevarianceofanyotherlinearunbiasedestimatorofB1
Var(b2)islessthanthevarianceofanyotherlinearunbiasedestimatorofB2
11.MonteCarlosimulation蒙特卡洛模拟
●Dotheexperimentatlab
●DoitbyExcell.=NORMINV(RAND(),0,2)
●Doitbymatlab.=NORMINV(uniform(),MU,SIGMA)
●DoitbyStata.=invnorm(uniform())
12.CentralLimitTheorem’s中心极限定理
Ifthereisalargenumberofindependentandidenticallydistributed(iid)randomvariables,then,withafewexceptions,thedistributionoftheirsumtendstobeanormaldistributionasthenumberofsuchvariablesincreasesindefinitely.
随着变量个数的无限增加,独立同分布随机变量近似服从正态分布
13.Recall
U,theerrortermrepresentstheinfluenceofallthoseforcesthataffectYbutarenotspecificallyincludedintheregressionmodelbecausetherearesomanyofthemandtheindividualeffectofanyonesuchforceonYmaybetoominor.
误差项代表了未纳入回归模型的其他所有因素的影响。
因为在这些影响中,每种因素对Y的影响都很微弱
Ifalltheseforcesarerandom,ifweletUrepresentthesumofalltheseforces,thenbyinvokingtheCLT,wecanassumethattheerrortermUfollowsthenormaldistribution.如果所有这些影响因素都是随机的,用U代表所有这些影响因素之和,那么根据中心极限定理,可以假定误差项服从正态分布。
14.Anotherpropertyofnormaldistribution另一个正态分布的性质
Anylinearfunctionofanormallydistributedvariableisitselfnormallydistributed.
正态变量的性质函数仍服从正态分布。
15.Hypothesistesting假设检验
HavingknownthedistributionofOLSestimatorsb1andb2,wecanproceedthetopicofhypothesistesting.
16.Nullhypothesis零假设
“zero〞nullhypothesisisdeliberatelychosentofindoutwhetherYisrelatedtoXalall,whichisalsocalledstrawmanhypothesis.之所以选择这样一个假设是为了确定Y是否与X有关,也称为稻草人假设。
17.Weneedsomeformaltestingprocedure
18.IfournullhypothesisisB2=0andtheputedb2=0.0013,wecanfindouttheprobabilityofobtainingsuchavaluefromtheZ,thestandardnormaldistribution.如果零假设为B2=0,计算得到b2=0.0013,那么根据标准正态分布Z,能够求得获此b2值的概率Iftheprobabilityisverysmall,wecanrejectthenullhypothesis.如果这个概率非常小,如此拒绝零假设。
Iftheprobabilityislarger,say,greaterthan10percent,wemaynotrejectthenullhypothesis.如果这概率比拟大,比如大于10%,就不拒绝零假设。
19.Wedon’tknowtheσ2
Wemustknowthetrueσ2,butwecanestimateitbyusing
20.Whatwill