计量经济学(英文)evig.pptx

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1、Lecture OneMethodologyofEconometrics1立论？结论？立论？结论？v立论:要求给出求论的路径。v结论:要求说明结论的来源。v自以为是的东西并不见得是真v我们不是上帝！2我们的习惯是这样的吗？我们的习惯是这样的吗？v结论来自感觉（象上帝）v宏观思考（象战略家）v习惯地提出政策建议（象顾问）v得争取把一个个的大、小问题搞明白再说吧！3Mainstream Analysis ApproachesNormativeAnalysisPositiveAnalysis(empiricalanalysis)4The Writer D.N.GujarativProfessorof

2、econometricsattheMilitaryAcademyatWestPointvMasterofCommercevMBAvEditorialrefereevAuthorvVisitingProfessor5WhatisEconometricsvEmpiricalsupporttothemodelsvQuantitativeanalysisofactualeconomicphenomenavSocialscienceinwhichthetoolsofeconomictheory,mathematics,andstatisticalinferenceareappliedtotheanaly

3、sis.vPositivehelpvEconomictheory_measurements6MethodologyofEconometricsvStatementoftheoryorhypothesisvObtainingthedatavSpecificationofthemathematicalmodelvSpecificationoftheeconometricmodelvEstimationoftheparametersoftheeconometricmodelvHypothesistestingvForecastingorpredictionvUsingthemodelforcontr

4、olorpolicypurposes7Statement of Theory or HypothesisvPostulate(givesomeexamples)vStatementvNote:hypothesisisnotthesameasanassumption8Obtaining the DatavNaturevSourcesvLimitations9Types of DataTimeseriesdata:quantitative,qualitative(dummyvariable)(SATIONARY)Cross-sectionaldata:(HETEROGENEITY)Pooledda

5、ta:(Paneldata)10Sources11Accuracy of Data vNon-experimentalinnaturevRound-offsandapproximationsvNon-responsevSelectivitybiasvAggregatelevelvConfidentialityvTheresultsofresearchareonlyasgoodthequalityofthedata.12Specification of the mathematical modelvYi=b1+b2*Xi0b2sampleparameter-estimate-estimatord

6、istribution-populationparameter-populationcharacteristicsvConfirmationorrefutationofeconomictheoriesonthebasisofsampleevidencevThebasementisstatisticalinference(Hypothesistesting)20Forecasting or PredictionvHypothesisortheorybeconfirmedvKnownorpredictorvariableXvPredictthefuturevaluesofthedependent2

7、1Use of the Model for Control or Policy PurposesvControlvariableXvTargetvariableYvYi=b1+b2*XivManipulatethecontrolvariableXtoproducethedesiredlevelofthetargetvariableY22Anatomy of Classical Econometric ModelingvEconomictheoryvMathematicalmodeloftheoryvEconometricmodeloftheoryvDatavEstimationofeconom

8、etricmodelvHypothesistestingvForecastingorpredictionvUsingthemodelforcontrolorpolicypurposes23第第1章章计计量量经济经济学研究的方法学研究的方法论论4第第2-3章章基本基本统计统计概念，概率分布概念，概率分布4第第4章章估估计计与假与假设设4第第5章章双双变变量模型的基本思想量模型的基本思想4第第6章章双双变变量模型的假量模型的假设检验设检验4第第7章章多元回多元回归归：估：估计计与假与假设检验设检验4第第8章章回回归归方程的函数形式方程的函数形式4第第9章章虚虚拟变拟变量的回量的回归归模型模型4第第

9、10章章多重共多重共线线性性4第第11章章异方差性异方差性4第第12章章自相关性自相关性4第第13章章模型模型选择选择：标标准与准与检验检验4实验实验实验实验1-6624Please Give Some SuggestionsZ3-W163.COM027-62082852Thankyou.25A Review of Some Statistical ConceptsLecture Two26Sample space、Sample points、EventsvPopulationisthesetofallpossibleoutcomesofrandomexperiment(samplespace

10、)vSample pointistheeachmemberofthissamplespacevEventisasubsetofthesamplespace27Probability and Random VariablesvP(A)probability(pr;p;pro)vXrandomvariable(rv)vXthevalueofarandomvariablev0=P(A)=0,29Cumulative Distribution FunctionCDFF(X)=P(X=x)(discrete)=(continuous)30CDFofDiscreteVRPDFCDFX times of f

11、ace upf(x)(PDF)Value of X f(x)(CDF)01/16X=01/1614/16X=15/1626/16X=211/1634/16X=315/1641/16X=4131CDF11/165/1611/1615/161X234032CDFofContinuousVRPDFCDFValue of X timesf(x)PDF)Value of X timesf(x)(CDF)0=X11/16X=01/161=X24/16X=15/162=X36/16X=211/163=X44/16X=315/164=X51/16X0,symmetricalS=0orleftS2,itsvar

12、ianceis70An ExamplevGiven k1=10 and k2=8,what is theprobabilityofobtaininganFvalue(a)of3.4orgreater;(b)of5.8orgreater?vTheseprobabilitiesare(a)approximately0.05;(b)approximately0.01.71Relationships1.If the denominator df,k2,is fairly large,thefollowingrelationshipholds:2.3.Largedf,thet,chisquare,and

13、Fdistributionsapproachthenormaldistribution,thesedistributions are known as the distributionsrelatedtothenormaldistribution.72 An ExamplevLet k1=20 and k2=120.The 5 percentcritical F value for these df is 1.48Therefore,k1F=(20)*(1.48)=29.6.vFrom the chi-square distribution for 20 df,the 5 percent cr

14、itical chi-square value isabout31.41.73Lecture 3(2)Estimation and Inference74ESTIMATIONvAssumethatarandomvariableXfollowsaparticularprobabilitydistributionbutdonotknowthevalue(s)oftheparameter(s)ofthedistribution.vifXfollowsthenormaldistribution,wemaywanttoknowthevalueofitstwoparameters,namely,theme

15、anandthevariance.75Estimate the UnknownsvWehavearandomsampleofsizenfromtheknownprobabilitydistribution;vUsethesampledatatoestimatetheunknownprobabilitydistribution;(non-pa)vUsethesampledatatoestimatetheunknownparameters.(pa)76Two CategoriesPointestimationIntervalestimation.77Point EstimationvLetXbea

16、rvwithPDFf(x;),istheparameterofthedistribution(forsimplicityonlyoneunknownparameter).vAssume that we know the theoreticalPDF,suchasthetdistributiondonotknowthevalueof.wedrawarandomsample of size n from this known thisPDFandthendevelopafunctionofthesamplevalues78Estimator or Estimatevprovidesusanesti

17、mateofthetrue.is known as a statistic,or an estimator,vA particular numerical value taken by the estimator is known as an estimate.can be treated as a random variable.provides us with a rule,or formula,that tells us how we may estimate the true.79An ExamplevSamplemeanisanestimatorofthetruemeanvalue,

18、.Ifinaspecificcase=50,thisprovidesanestimateof.Theestimator obtainedisknownasapointestimatorbecauseitprovidesonlyasingle(point)estimateof.80Interval EstimationDefofintervalestimation:vweobtaintwoestimatesof,byconstructingtwoestimators1(x1,x2,xn)and2(x1,x2,xn),andsaywithsomeconfidence(i.e.,probabilit

19、y)thattheintervalbetween1and2includesthetrue.vweprovidearangeofpossiblevalueswithinwhichthetrue maylie.81Key conepts vSampling,Probability distribution,An estimator.vX is normally distributed,then thesamplemeanisalsonormallydistributedwithmean=(thetruemean)andvariance=2/n,N(,2).vprobabilityis95%82In

20、tervalEstimationvMoregenerally,inintervalestimationweconstructtwoestimatorsand,bothfunctionsofthesampleXvalues,suchthatvTheintervalisknownasa confidence interval ofsize1for,v1beingknownastheconfidence coefficient,v isknownasthelevel of significance.83An ExamplevSupposethatthedistributionofheightofme

21、ninapopulationisnormallydistributedwithmean=and=2.5.vAsampleof100mendrawnrandomlyfromthispopulationhadanaverageheightof67.Establisha95%confidenceintervalforthemeanheight(=)inthepopulationasawhole.84SolutionvAsnoted,N(,2/n),whichinthiscasebecomesN(,2.52/100).v95%confidenceintervalas66.5167.4985OLS an

22、d MLvThereareseveralmethodsofobtainingpointestimators,thebestknownbeingthemethod of Ordinary leastsquares andthe method of maximumlikelihood(ML).vThedesirablestatisticalpropertiesfallintotwocategories:small-sample,andlargesample,orasymptotic.86SmallSample PropertiesvUnbiasedness.Anestimatorissaidtob

23、ean unbiased estimator of if the expectedvalueofisequaltothetrue;thatis,vE()=0vIf this equality does not hold,then theestimatorissaidtobebiased,andthebiasiscalculatedasvBias()=E()87Minimum VariancevMinimum variance.1issaidtobeaminimum-varianceestimatorofifthevarianceof1 issmallerthanoratmostequaltot

24、hevarianceof2，whichisanyotherestimatorof。88EfficientvBest unbiased，or efficient，estimator.If1and2 are twounbiased estimators of,and are twounbiased estimators of 1，and thevarianceof1issmallerthanoratmostequaltothevarianceof2，then1isa minimumvariance unbiased，orbest unbiased，orefficient，estimator.89L

25、inearity.vAn estimatoris said to be a linearestimatorofifitisalinearfunctionofthesample observations。Thus，the samplemeandefinedas90BLUEvBest linear unbiased estimator（BLUE）。If is linear，is unbiased，and hasminimumvarianceintheclassofalllinearunbiasedestimatorsof，thenitiscalledabestlinearunbiasedestim

26、ator，orBLUEforshort。91Hypothesis TestingvEstimationandhypothesis testingconstitutethetwinbranchesofclassicalstatisticalinference.vAssumethatwehaveanrvXwithaknowPDFf(;),where is the parameter of the distribution.Having obtained a random sample of size n,we obtain the point estimator.The true is rarel

27、y known,Is the estimator “compatible”with some hypothesized value of,say,=*,?92HypothesisvIn the language of hypothesis testing=*is called the null null hypothesishypothesis and is generally denoted by Ho.The null hypothesis is tested against an alternative hypothesisalternative hypothesis,denoted b

28、y H1,which,for example,may state that*.93Simple and CompositevA simplesimple hypothesis:it specifies the value(s)of the parameter(s)of the distribution;otherwise it is called a composite composite hypothesis.vThus,if XN(,2)and we state that v Ho:=15 and=2vit is a simple hypothesis,whereas v Ho:=15 a

29、nd 2vis a composite hypothesis because here the value of is not specified.94Test the Null HypothesisvTo test the null hypothesis(i.e.to test its validity),we use the sample information to obtain what is known as the test statistic.The point estimator of the unknown parameter.Then we try to find out

30、the sampling,or probability,distribution of the test statistic and use the confidence interval or test of significance approach to test the null hypothesis.95AnExample The height(X)of men in a population.We are told that Xi N(,2)=N(,2.52)vAverage height=67 =67 n=100vLet us assume that Ho:=*=69 H1:69

31、96vCouldthesamplewith=67,theteststatistic,havecomefromthepopulationwiththemeanvalueof69?vwemaynotrejectthenullhypothesisif is“sufficientlyclose”to*;otherwisewemayrejectitinfavorofthealternativehypothesis.howdowedecidethat is“sufficientlyclose”to*?97Two Approaches(1)(1)Confidence interval Confidence

32、interval(2)(2)Test of significanceTest of significance(3)Both leading to identicalidentical conclusions in any specific application.98Confidence Interval Confidence Interval ApproachApproachvSinceXiN(,2),weknowthattheteststatisticisdistributedasv100(1)confidenceintervalforbasedonandseewhetherthiscon

33、fidenceintervalincludes=*?99vTheactualmechanicsareasfollows:sinceN(,2/n),itfollowsthatvPr(1.96Zi 1.96)=0.95100Turningtoourexample,wehavealreadyestablisheda95%confidenceintervalfor,whichis66.51 67.49Thisintervalobviouslydoesnotinclude=69.Therefore,wecanrejectthenullhypothesisthatthetrueis69witha95%co

34、nfidencecoefficient.101Region and Critical ValuesvTheconfidenceintervalthatwehaveestablishediscalledtheacceptance region.vThearea(s)outsidetheacceptanceregionis(are)calledtheregion(s)of rejectionofthenullhypothesis.(Criticalregions)vThelowerandupperlimitsoftheacceptanceregionarecalledthe critical va

35、lues.102Criterion for RejectionvLanguageofhypothesistesting,ifthehypothesizedvaluefallsinsidetheacceptanceregion,onemaynotrejectthenullhypothesis;votherwiseonemayrejectit.103Two Types of ErrorvWearelikelytocommittwotypesoferrors:(1)wemayrejectH0whenitis,infact,true;thisiscalledatypeerror.v(2)wemayno

36、trejectH0whenitis,infact,false;thisiscalledatypeerror.104vIdeally,wewouldliketominimizebothtypeandtypeerror.vButunfortunately,foranygivensamplesize,itisnotpossibletominimizeboththeerrorssimultaneously.105Level of SignificancevIntheliteraturetheprobabilityoftypeerrorisdesignatedasandiscalledthelevel

37、of significance.vTheprobabilityoftypeerrorisdesignatedas.vTheprobabilityofnotcommittingatypeerror,1,iscalledthepowerof the test.106Theclassicalapproachtohypothesistestingistofixatlevelsuchas0.01or0.05andthentrytomaximizethepowerofthetest;thatisminimize.107Confidence CoefficientvConfidencecoefficient

38、(1-)issimplyoneminustheprobabilityofcommittingatypeIerror.vA95%confidencecoefficientmeansthatwearepreparedtoacceptatthemosta5%probabilityofcommittingatypeIerror.vwedonotwanttorejectthetruehypothesisbymorethan5outof100times.108P valuevThepvalue,orexactlevelofsignificance.Insteadofpreselectingatarbitr

39、arylevels,suchas1,5,or10percent.onecanobtainthep(probability)value,orexactlevelofsignificanceofateststatistic.vThep valueisdefinedasthelowestsignificancelevelatwhichanullhypothesiscanberejected.109The Test of Significance Approachvatest(statistic)issignificant,wegenerallymeanthatwecanrejectthenullhy

40、pothesis.vtheteststatisticisregardedassignificantiftheprobabilityofourobtainingitisequaltoorlessthan,theprobabilityofcommittingatypeIerror.110SummarizetheStepsInvolvedinTestingaStatisticalHypothesisvStep1.StatethenullhypothesisHoandthealternativehypothesisH1(e.g.Ho:=69andH1:69).vStep2.Selectthetests

41、tatistic(e.g,).vStep3.Determinetheprobabilitydistributionoftheteststatistic(e.g.,N(,2/n).111vStep4.Choosethelevelofsignificance(i.e.,theprobabilityofcommittingatypeIerror).vStep5.Usingtheprobabilitydistributionoftheteststatistic,establisha100(1-)%confidenceinterval.112vIfthevalueofparameterunderthen

42、ullhypothesis(e.g,=*=69)liesinthisconfidenceregion,theregionofacceptance,donotrejectthenullhypothesis.Butifitfallsoutsidethisinterval(i.e,itfallsintotheregionofrejection),youmayrejectthenullhypothesis.vKeepinmindthatinnotrejectingorrejectinganullhypothesisyouaretakingachanceofbeingwrongpercentofthet

43、ime113Examplevif=*=69,vif=0.05,theprobabilityofobtainingaZvalueof1.96or1.96is5percent(or2.5percentineachtailofthestandardizednormaldistribution).vInourillustrativeexampleZwas8.114vZ=-8isstatisticallysignificant;thatis,werejectthenullhypothesisthatthetrue*is69.vOfcourse,wereachedthesameconclusionusin

44、gtheconfidenceintervalapproachtohypothesistesting.115Lecture FourTwovariable Regression Analysis(A)Some Basic Ideas(B)Estimation(point and interval)(C)Hypothesis Testing116Some Basic IdeasvConceptofRegressionvPopulationRegressionFunction（PRF）vSampleRegressionFunction（SRF）117Two and Multiple Regressi

45、on AnalysisThemoregeneralmultipleregressionanalysisisinmanywaysalogicalextensionofthetwo-variablecase.Sowefirstintroducethetwovariableregressionanalysis.118Regression Analysis(conditional)vIs largely concerned with estimating and/or predicting the population mean or average value of the dependent va

46、riable on the basis of the known or fixed values of the explanatory variables.vConditional distribution(probabilities,expectation,mean)119PRF and SRFvPopulationRegressionFunctionisakeyconceptunderlyingregressionanalysis.vThedisturbancetermplaysacriticalroleinestimatingthePRF.vPRFisanidealizedconcept

47、.vSampleRegressionFunctionisusedtoestimatethePRF120Income XConsumption 80.100 120 140 160 180 200Weekly family consumption expenditure Y,$5560657075Total 325121Income Xp(Y|X=Xi)80.100 120 140 160 180 200p(Y|X=Xi)1/51/51/51/51/5Conditional means of Y65122Conditional Distribution8010012014016018020050

48、100150200Consumption expenditureWeekly income123Population Regression Line(Curve)E(Y|X=Xi)8010012014016018020050101150200Conditional MeanWeekly income65149124Linear Population Regression FunctionWhereandareunknownbutfixedparametersknownastheregressioncoefficients.andarealsoknownastheinterceptandslop

49、ecoefficient.125Stochastic Specification of P R F126Sample Regression FunctionvOurtaskistoestimatethePRFonthebasisofthesampleinformation.vSampleisfluctuation.vNdifferentsampleshaveNdifferentSRFs,buttheyarenotthesame.vEstimatororstatisticissimplyaruleorformulathatisusedtoestimatethetotalparameterfrom

50、sampleinformation.127IsreadasYhatorY-capEstimatorofE(Y|Xi)Denotesthesampleresidualterm128Consumption expenditureWeekly income129The Problem of Estimation130Method of Ordinary Least Squares(OLS)vNowgivennpairsofobservationsonYandX,wewouldliketodeterminetheSRFinsuchamannerthatitisascloseaspossibletoth