計量經濟學雙語教學

Econometrics計量經濟學IntroductoryEconometrics

計量經濟學導論Whenyoucanmeasurewhatyouarespeakingabout,andexpressitinnumbers,youknowsomethingaboutit;

whenyoucannotmeasureit,whenyoucannotmeasureitinnumbers,yourknowledgeisofameagerandunsatisfactorykind;itmaybethebeginningofknowledge,butyouhavescarcely,inyourthoughts,advancedtothestageofscience.

------LordKelvinOUTLINEWHAT

ISECONOMETRICS?WHY

ASEPARATEDISCIPLINE?WHO

NEEDSECONOMETRICS?HOW?

-METHODOLOGYOFECONOMETRICS2022/10/2832022/10/284

1WHATISECONOMETRICS?Econometricsmeans“economicmeasurement”butmuchbroaderthanmeasurement,ascanbeseenfromthefollowingquotations:Econometricsmaybedefinedasthequantitativeanalysisofactualeconomicphenomenabasedontheconcurrentdevelopmentoftheoryandobservation,relatedbyappropriatemethodsofinference.計量經濟學是對實際經濟現(xiàn)象的定量分析,結合適當?shù)耐茢喾椒?驗證或證偽理論和實踐之間關系的命題。1

WHATISECONOMETRICS?Econometrics,theresultofacertainoutlookontheroleofeconomics,consistsoftheapplicationofmathematicalstatisticstoeconomicdatatolendempiricalsupporttothemodelsconstructedbymathematicaleconomicsandtoobtainnumericalresults.計量經濟學是應用數(shù)理統(tǒng)計方法研究經濟問題和管理問題,以便為定性理論和數(shù)理模型提供經驗支持,并獲得數(shù)值結果的一門學科。--Econometricsmaybedefinedasthesocialscienceinwhichthetoolsofeconomictheory,mathematics,andstatisticalinferenceareappliedtotheanalysisofeconomicphenomena.--Econometricsisconcernedwiththeempiricaldeterminationofeconomiclaws.2022/10/2861

WHATISECONOMETRICS?2022/10/287

2WHYASEPARATEDISCIPLINE?Econometricsisanintegrationofeconomictheory,mathematicaleconomics,economicstatistics,andmathematicalstatistics.Thesubjectdeservestobestudiedinitsownrightforthefollowingreasons.Reason1DifferentfromPureEconomictheory

--Economictheorymakesstatementsorhypothesesthataremostlyqualitativeinnature.

--Econometrics:providesnumericalestimates,givesempiricalcontenttomosteconomictheory.

（quantitative）2022/10/288

2WHYASEPARATEDISCIPLINE?2022/10/289Reason2DifferentfromMathematicaleconomics

--Mathematicaleconomics:Mainconcernistoexpresseconomictheoryinmathematicalform(equations)withoutregardtomeasurabilityorempiricalverificationofthetheory.Y=β1+β2X

--Econometrics:Mainlyinterestedintheempiricalverificationofeconomictheory.Andthisconversionofmathematicalintoeconometricequationsrequiresagreatdealofingenuityandpracticalskill.Y=β1+β2X+u

2WHYASEPARATEDISCIPLINE?2022/10/2810Reason3DifferentfromEconomicstatistics:

--Economicstatisticsismainlyconcernedwithcollecting,processing,andpresentingeconomicdataintheformofchartsandtables.

--Econometrics:beingconcernedwithusingthecollecteddatatotesteconomictheories.

2WHYASEPARATEDISCIPLINE?Econo-metricsEconomicsStatisticsMathematicsYoudo.Manydecisionsingovernment,publicadministrationandbusinessrelyonanunderstandingofeconomicrelationshipsandalsoonquantifyingthatrelationship.2022/10/28123WhoNeedsEconometrics?Ex.1.Governmentinterestedinestimatingreturns(payoff)toeducation.Onlyworthinvestingif Benefit>costofprovision knowinghowmuchgraduatesearnrelativetonon-graduatesisoneimportantelementneededtoevaluatingthisdecision(privatereturn).Ex.2.Companiesneedtoknowwhetherandbyhowmuchincreasedadvertisingexpendituregeneratesincreasedsales.

Econometricscandoallthisandmore.2022/10/28133WhoNeedsEconometrics?2022/10/2814Howdoeconometriciansproceedintheiranalysisofaneconomicproblem?Thatis,whatistheirmethodology?--Thetraditional（orclassical）methodology,whichstilldominatesempiricalresearchineconomicsandothersocialandbehavioralsciences.4HOW?-METHODOLOGYOFECONOMETRICS2022/10/2815Traditionaleconometricmethodologyproceedsalongthefollowinglines:STEP1.Statementoftheoryorhypothesis.STEP2.Specificationofthemathematicalmodelofthetheory.STEP3.Specificationofthestatistical,oreconometricmodelSTEP4.Obtainingthedata.STEP5.Estimationoftheparametersoftheeconometricmodel.STEP6.Hypothesistesting.STEP7.Forecastingorprediction.STEP8.Usingthemodelforcontrolorpolicy.4HOW?-METHODOLOGYOFECONOMETRICS2022/10/2816step1.StatementofTheoryorHypothesisKeynesstated:Thefundamentalpsychologicallawisthatmen[women]aredisposed,asaruleandonaverage,toincreasetheirconsumptionastheirincomeincreases,butnotasmuchastheincreaseintheirincome.Inshort,Keynespostulatedthatthemarginalpropensity(naturaltendency)toconsume(MPC),therateofchangeofconsumptionforaunit(say,adollar)changeinincome,isgreaterthanzerobutlessthan1.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2817step2.SpecificationoftheMathematicalModelofConsumptionAlthoughKeynespostulatedapositiverelationshipbetweenconsumptionandincome,hedidnotspecifythepreciseformofthefunctionalrelationshipbetweenthetwo.Forsimplicity,amathematicaleconomistmightsuggestthefollowingformoftheKeynesianconsumptionfunction:Y=β1+β2X,0<β2<1(1.3.1)β1,β2:theparametersofthemodel,Y:consumption(expenditure):dependentvariable

X:income:explanatoryvariable.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2818β1:theintercept,β2:slopecoefficients.measurestheMPC.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2819step3.SpecificationoftheEconometricModelofConsumption

--Relationshipsbetweeneconomicvariablesaregenerallyinexact.--Thus,ifweweretoobtaindataonconsumptionexpenditureanddisposablei.e.,aftertaxincomeofasampleof500Americanfamilies,wewouldnotexpectall500observationstolieexactlyonthestraightlineofEq.(1.3.1)

--TheErrorReasons:inadditiontoincome,othervariablesaffectconsumptionexpenditure.Forexample,sizeoffamily,agesofthemembersinthefamily,familyreligion,etc.,arelikelytoexertsomeinfluenceonconsumption.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2820step3.SpecificationoftheEconometricModelofConsumptionToallowfortheinexactrelationshipsbetweeneconomicvariables,theeconometricianwouldmodifythedeterministicconsumptionfunction(1.3.1)asfollows:Y=β1+β2X+u(1.3.2)

u:knownasthedisturbance,orerrorterm,isarandom(stochastic)variablethathaswell-definedprobabilisticproperties.u:disturbancetermmaywellrepresentallthosefactorsthataffectconsumptionbutarenottakenintoaccountexplicitly.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2821TheeconometricconsumptionfunctionhypothesizesthatthedependentvariableY(consumption)islinearlyrelatedtotheexplanatoryvariableX(income)butthattherelationshipbetweenthetwoisnotexact;itissubjecttoindividualvariation.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2822step4.ObtainingDataToestimatetheeconometricmodelgivenin(I.3.2),thatis,toobtainthenumericalvaluesofβ1andβ2,weneeddata.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2823--TheYvariable:theaggregate(fortheeconomyasawhole)personalconsumptionexpenditure(PCE)--TheXvariable:grossdomesticproduct(GDP),ameasureofaggregateincome,--Bothmeasuredinbillionsof1992dollars,theyaremeasuredinconstant(1992)prices.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2824step5.EstimationoftheEconometricModel

thestatisticaltechniqueofregressionanalysisisthemaintoolusedtoobtaintheestimates.UsingthistechniqueandthedatagiveninTable1.1,weobtainthefollowingestimatesofβ1andβ2,namely,-184.08and0.7064.Thus,theestimatedconsumptionfunctionis:?i=-184.08+0.7064Xi(1.3.3)--Itmeansconsumptionexpenditurewentupbyabout70centsforadollar’sincreaseinrealincome.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2825step6.HypothesisTesting

KeynesexpectedtheMPCtobepositivebutlessthan1.why?Inourexample,wefoundtheMPCtobeabout0.70.ButbeforeweacceptthisfindingasconfirmationofKeynesianconsumptiontheory,wemustinquirewhetherthisestimateissufficientlybelowunitytoconvinceusthatthisisnotachanceoccurrenceorpeculiarityoftheparticulardatawehaveused.Inotherwords,is0.70statisticallylessthan1?Ifitis,itmaysupportKeynes’theory.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2826step7.ForecastingorPredictionIfthechosenmodeldoesnotrefutethehypothesisortheoryunderconsideration,wemayuseittopredictthefuturevalue(s)ofthedependentvariableYonthebasisofknownorexpectedfuturevalue(s)oftheexplanatory,orpredictor,variableX.Toillustrate,supposewewanttopredictthemeanconsumptionexpenditurefor1997.TheGDPvaluefor1997was7269.8billiondollars.PuttingthisGDPfigureontheright-handsideof(1.3.3),weobtain:Y1997=-184.0779+0.7064(7269.8)=4951.3167(1.3.4)Theactualvaluein1997was4913.5billiondollars.Theforecasterrorisabout37.82billiondollars,whichisabout0.76percentoftheactualGDPvaluefor1997.OneExample-Thewell-knownKeynesiantheoryofconsumption2022/10/2827step8.UseoftheModelforControlorPolicyPurposesSupposefurtherthegovernmentbelievesthatconsumerexpendit