第9章-Multiple-Regression-教學(xué)講解課件

MultipleRegressionAnalysisP289

多元回歸分析之模型設(shè)定和數(shù)據(jù)問題

y=b0+b1x1+b2x2+...bkxk+uSpecificationandDataProblems模型設(shè)定和數(shù)據(jù)問題1MultipleRegressionAnalysisChapterOutline 本章大綱FunctionalFormmisspecification函數(shù)形式誤設(shè)-討論模型誤設(shè)的結(jié)果-P289UsingProxyvariablesforunobservedexplanatoryvariables對觀測不到的變量使用代理變量-討論用代理變量來減輕有偏性PropertiesoftheOLSUnderMeasurementError有測量誤差的OLS性質(zhì)-推導(dǎo)和解釋MissingData,NonrandomSamples,andoutliers數(shù)據(jù)缺失、非隨機(jī)樣本和離群點-討論額外的數(shù)據(jù)問題2ChapterOutline 本章大綱FunctionaFunctionalForm

函數(shù)形式Howdoweknowifwe’vegottentherightfunctionalformforourmodel?我們?nèi)绾沃滥Ｐ褪欠竦玫秸_的函數(shù)形式呢？P289:異方差的出現(xiàn)可以看成是模型的錯誤設(shè)定，但不影響有偏性和一致性，還可以通過WLS來減輕；本章討論u與xi的相關(guān)性，如果相關(guān)，稱xi為外生變量，為什么？當(dāng)被忽略的自變量為其他變量的函數(shù)時，將產(chǎn)生函數(shù)形式誤設(shè)這一問題。何謂函數(shù)形式誤設(shè)？3FunctionalForm

函數(shù)形式HowdoweFunctionalForm(continued)

函數(shù)形式（續(xù)）

First,useeconomictheorytoguideyou首先，用經(jīng)濟(jì)理論的指導(dǎo)Thinkabouttheinterpretation考慮它的解釋Doesitmakemoresenseforxtoaffectyinpercentage(uselogs)orabsoluteterms?x影響y的更合理的方式是百分比的形式（用log形式），還是絕對量的形式？Doesitmakemoresenseforthederivativeofx1tovarywithx1(quadratic)orwithx2(interactions)ortobefixed?x1的系數(shù)更合理的形式是隨x1變化（二次形式），隨x2變化（交互作用），還是固定不變？P290:2個誤設(shè)案例，一個是忽略了二次項，一個是忽略了交叉項。也可能是沒有用LOG形式；回顧第三章P85假設(shè)3不成立的幾種情況，函數(shù)形式誤設(shè)的后果P290EXP.9.1-閱讀4FunctionalForm(continued)

函數(shù)FunctionalFormMisspecification

函數(shù)形式誤設(shè)Amultipleregressionmodelsuffersfromfunctionalformmisspecificationwhenitdoesnotproperlyaccountfortherelationshipbetweenthedependentandtheobservedexplanatoryvariables.

當(dāng)一個多元回歸模型不能正確地說明被解釋變量和觀察到的解釋變量之間的關(guān)系時，此模型存在函數(shù)形式誤設(shè)問題。5FunctionalFormMisspecificatiFunctionalFormMisspecification

函數(shù)形式誤設(shè)Misspecifyingthefunctionalformofamodelcanhaveseriousconsequences.Wemayobtainbiasedorinconsistentestimatorsofthepartialeffects.誤設(shè)一個模型的函數(shù)形式可能產(chǎn)生嚴(yán)重的后果。我們得到的局部效應(yīng)的估計量可能有偏或不一致。Onewayout:toaddquadratictermsofanysignificantvariablestoamodelandtoperformajointtestofsignificance.

一種方法：向模型加入任何重要變量的二次項，進(jìn)行一個聯(lián)合顯著性檢驗。-加入二次項，對二次項系數(shù)聯(lián)合顯著性F檢驗通過時，顯示的癥狀往往是誤設(shè)，如誤將對數(shù)模型為水平模型。另外經(jīng)濟(jì)數(shù)據(jù)中，二次項可以解決大部分非線性問題-P2906FunctionalFormMisspecificatiExample:ModelingCrime

例子：對犯罪建模-P292Dependentvariable:被解釋變量：Narr86,#timesarrested,1986（1986年被捕次數(shù)）ExplanatoryVariables：解釋變量：pcnvproportionofpriorconvictions以前被定罪比例avgsen avgsentencelength,mos.平均判刑期限，單位：月tottime timeinprisonsince18,mos.18歲以來的服刑時間，單位：月Ptime86mos.inprisonduring19861986年的服刑時間，單位：月解讀：1.為什么加入二次項，因為水平項T檢驗很顯著；2.加入變量的二次項后，原先的水平變量系數(shù)變化很大；同時二次項聯(lián)合F顯著；3.二次項加入，模型的解讀變得困難，可能有更深刻的實際意義7Example:ModelingCrime

例子：對犯罪Example:ModelingCrime

例子：對犯罪建模Explanatoryvariables解釋變量Qemp86#quartersemployed,19861986年被雇傭季度數(shù)inc86 legalincome,1986,$100s1986年合法收入，單位：百美元black =1ifblack如果是黑人，black=1hispan =1ifHispanic如果是西班牙裔，hispan=1First,weregressthedependentvariablesontheindependentvariables,withoutanysquareterms.首先，我們將被解釋變量向解釋變量回歸，不包含任何平方項。8Example:ModelingCrime

例子：對犯罪

regnarr86pcnvavgsentottimeptime86qemp86inc86blackhispanSource|SSdfMSNumberofobs=2725-------------+------------------------------F(8,2716)=26.47Model|145.390104818.173763Prob>F=0.0000Residual|1864.957052716.686655763R-squared=0.0723-------------+------------------------------AdjR-squared=0.0696Total|2010.347162724.738012906RootMSE=.82865------------------------------------------------------------------------------narr86|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+----------------------------------------------------------------

pcnv|-.1332344.0403502-3.300.001-.2123546-.0541141avgsen|-.0113177.0122401-0.920.355-.0353185.0126831tottime|.0120224.00943521.270.203-.0064785.0305233

ptime86|-.0408417.008812-4.630.000-.0581206-.0235627qemp86|-.0505398.0144397-3.500.000-.0788538-.0222258

inc86|-.0014887.0003406-4.370.000-.0021566-.0008207black|.3265035.04541567.190.000.2374508.4155561hispan|.1939144.03971134.880.000.1160469.2717818_cons|.5686855.036046115.780.000.4980048.6393661------------------------------------------------------------------------------99Plottingnarr86againstpncv

繪圖：narr86關(guān)于pncv10Plottingnarr86againstpncv

繪Plottingnarr86againstinc86

繪圖：narr86關(guān)于pncv11Plottingnarr86againstinc86Plottingnarr86againstptime86

繪圖：narr86關(guān)于pncv12Plottingnarr86againstptime8

narr86Coef.Std.Err.tP>|t|[95%Conf.Interval]

pcnv.5525236.15423723.580.000.2500892.8549579

pcnvsq-.7302119.1561177-4.680.000-1.036333-.4240903avgsen-.0170216.0120539-1.410.158-.0406574.0066142tottime.011954.00928251.290.198-.0062474.0301554

ptime86.2874334.04425826.490.000.2006501.3742166

pt86sq-.0296076.0038634-7.660.000-.037183-.0220321qemp86-.0140941.0173612-0.810.417-.0481366.0199485

inc86-.0034152.0008037-4.250.000-.0049912-.0018392

inc86sq7.19e-062.56e-062.810.0052.17e-06.0000122black.292296.044836.520.000.2043916.3802004hispan.1636175.03945074.150.000.0862609.240974_cons.5046065.036835313.700.000.4323784.5768347AddingQuadratictermstosignificantVariables加入重要變量的平方項13narr86Coef.Drawbacksofaddingsquaretermstodetectfunctionalformmisspecification

取消加入平方項以檢測函數(shù)形式誤設(shè)

Theoretically,wecantestjointexclusionrestrictionstoseeifhigherordertermsorinteractionsbelongtothemodel理論上，我們作排除性約束的聯(lián)合檢驗，來看高階項和交叉項是否屬于模型。Itcanbetedioustoaddandtestextraterms.Manydegreesoffreedomsmaybeused. 加入和檢驗另外的項過程會很單調(diào)乏味且冗長。當(dāng)原模型解釋變量多時可能會消耗掉許多自由度。14DrawbacksofaddingsquareterDrawbacksofaddingsquaretermstodetectfunctionalformmisspecification

取消加入平方項以檢測函數(shù)形式誤設(shè)Somenonlinearitiescannotbepickedupbyaddingquadraticterms.Forexample,wemayfindasquaretermmatterswhenusinglogsismoreappropriate. 一些非線性關(guān)系不能通過加入二次項捕捉。例如，當(dāng)我們發(fā)現(xiàn)平方項重要時，可能對數(shù)形式更加適合。15DrawbacksofaddingsquareterRamsey’sRESETP292

Ramsey回歸設(shè)定誤差檢驗AtestoffunctionalformisRamsey’sregressionspecificationerrortest(RESET)一種函數(shù)形式的檢驗是Ramsey回歸設(shè)定誤差檢驗（RESET）。RESETaddspolynomialsintheOLSfittedvaluestotheoriginalregression.RESET在原回歸中加入OLS擬合值的多項式-沒有明確的原理指出到底要加入多少個高次方的項，但是平方和立方一般是有用的。16Ramsey’sRESETP292Ramsey’sRESET

Ramsey回歸設(shè)定誤差檢驗

Insteadofaddingfunctionsofthex’sdirectly,weaddandtestfunctionsof?我們加入并檢驗?的多次項函數(shù)，而不是直接加入x的函數(shù)。注意：如何加入函數(shù)項的？P293So,estimatey=b0+b1x1+…+bkxk+d1?2+d1?3+errorandtest所以，估計y=b0+b1x1+…+bkxk+d1?2+d1?3+error，并檢驗。H0:d1=0,d2=0,usingFstatisticorLMstatistic.H0:d1=0,d2=0，用F統(tǒng)計量或LM統(tǒng)計量。17Ramsey’sRESET

Ramsey回歸設(shè)定誤差檢驗Ramsey’sRESET

Ramsey回歸設(shè)定誤差檢驗AsignificantFstatisticsuggestssomesortoffunctionalformproblem.一個顯著的F統(tǒng)計量說明函數(shù)形式可能存在問題。ThedistributionofFisapproximatelyF2,n-k-3inlargesamplesunderthenullhypothesisandtheG-Massumptions.在零假設(shè)和G-M假定下，F(xiàn)的分布大樣本近似為F2,n-k-3分布。自由度的說明：減少了2個自由度P29318Ramsey’sRESET

Ramsey回歸設(shè)定誤差檢驗ImplementingRESETinStata

在STATA中實施RESETSTATAusescommandovtestafterregcommand.STATA在reg命令后，使用ovtest命令。?2,?3,and?4

areusedinstata.STATA使用?2,?3和?4。regnarr86pcnvavgsentottimeptime86qemp86inc86blackhispan

ovtest

RamseyRESETtestusingpowersofthefittedvaluesofnarr86RESET檢驗使用narr86擬合值的冪函數(shù)項 Ho:modelhasnoomittedvariablesF(3,2713)=4.19,Prob>F=0.005819ImplementingRESETinStata

在SImplementingRESETinStata

在STATA中實施RESETAnalternativeistospecifytheoption,rhs.一個替代的方法是指定選擇，rhsInthiscasethepowertermsofalltheexplanatoryvariablesinsteadofthefittedvaluesareusedinthetest.在這種情況下，檢驗中使用所有解釋變量的冪函數(shù)項，而不是擬合值的相應(yīng)項。ovtest,rhs RamseyRESETtestusingpowersoftheindependentvariablesRESET檢驗使用解釋變量的冪函數(shù)項Ho:modelhasnoomittedvariablesF(18,2698)=9.73Prob>F=0.000020ImplementingRESETinStata

在SCautionsinUsingRESET

使用RESET的注意事項RESETisgoodatdetectingmisspecificationsintheformofnonlinearities,notgeneralomittedvariables. RESET在探測非線性形式的函數(shù)誤設(shè)時很好用，而不是用于檢測一般的遺漏變量。Wooldridge(1995)showsthatRESEThasnopowerfordetectingomittedvariableswhenevertheyhaveexpectationsthatarelinearintheincludedindependentvariables. Wooldridge在1995年證明：當(dāng)被遺漏變量的期望值時所包含自變量的線性函數(shù)時，RESET無法探測出遺漏變量問題。P294：對RESET作用的正確評價：1.有的認(rèn)為可以檢測遺漏變量和異方差，但是Wooldridge不這樣認(rèn)為21CautionsinUsingRESET

使用RESECautioninusingofRESET

使用RESET的注意事項However,iftheomittedvariablehavenonlinearexpectationsinthedependentvariables,asignificantRESETcanindicateomitted-variableproblem. 盡管如此，如果被遺漏變量的期望是自變量的非線性形式時，一個顯著的RESET可以指出遺漏變量問題。AlsonoticethatthedrawbackoftheRESETtestiswhenthenullisrejected,RESETdoesnotsuggestwhattodointhenextstep. 也要注意到，RESET檢驗的一個缺陷是，當(dāng)零假設(shè)被拒絕后，它并不能建議我們下一步怎么做。22CautioninusingofRESET

使用REHousingPriceExample

住房價格的例子Thisexampleisusedfortwopurposes. 使用這個例子有兩個目的。First,logformscanbebetterindealingwithnonlinearitiesthenusingthelevelvariables. 首先，處理非線性問題時，log形式可能比變量原形式更好。Second,asignificantRESETmayindicatenonlineareffectofomittedvariables,likethevariable“assess”addedinlater. 其次，一個顯著的RESET可能指出被遺漏變量的非線性效應(yīng)，比如稍后加入的變量“assess”。23HousingPriceExample

住房價格的例子THousingPriceExample

住房價格的例子Dataused:hprice1.dta,variables使用數(shù)據(jù)：hprice1.dta,變量assessassessedvalue,$1000s（評估價，單位：千美元）pricehouseprice,$1000s（房價，單位：千美元）lotsizesizeoflotinsquarefeet（土地的面積，單位：平方英尺）sqrftsizeofhouseinsquarefeet（房屋的面積，單位：平方英尺）bdrmsnumberofbedrooms（臥室數(shù)）24HousingPriceExample

住房價格的例子DHousingPriceExample

住房價格的例子

P293閱讀

regpricelotsizesqrftbdrmsovtest

RamseyRESETtestusingpowersofthefittedvaluesofprice（RESET檢驗用擬合價格的冪函數(shù)項）Ho:modelhasnoomittedvariablesF(3,81)=4.26Prob>F=0.007625HousingPriceExample

住房價格的例子HousingPriceExample:thelogforms

住房價格的例子：log形式Thelogformdonotrejectthenullofnomisspecificationat5%significancelevel.Log形式的回歸在5％水平上沒有拒絕零假設(shè)：沒有函數(shù)形式誤設(shè)。--結(jié)論：第二個模型即對數(shù)模型更好一些。-P293reglpricellotsizelsqrftbdrmsovtestRamseyRESETtestusingpowersofthefittedvaluesoflprice（RESET檢驗用lprice擬合值的冪函數(shù)項）Ho:modelhasnoomittedvariablesF(3,81)=2.45Prob>F=0.069226HousingPriceExample:thelogHousingPriceExample:thelogforms

住房價格的例子：log形式reglpricelassessllotsizelsqrftbdrmsInthisstepvariablelassessisasignificantvariablewitht=6.89.這一步中，變量lassess顯著，t=6.89ovtest

RamseyRESETtestusingpowersofthefittedvaluesoflprice（RESET檢驗使用lprice擬合值的冪函數(shù)項）Ho:modelhasnoomittedvariablesF(3,80)=1.11Prob>F=0.350927HousingPriceExample:thelogHousingPriceExample:thelogforms

住房價格的例子：log形式Noticetheresultsaredifferentfromthetextbooksince?2,?3,and?4

areusedinstata,insteadof?2,?3

asinthetextbook

. 注意這里的結(jié)果和課本上不同，因為課本上使用?2,?3

，這里stata用的是?2,?3,和

?4

。Youcanreplicatethetextbookresultbyputting?2,?3

intothemainequation,anduseFtesttotesttheirjointsignificances.

你可以通過以下方法得到課本的結(jié)果：向主方程加入?2,?3

，使用F檢驗檢驗它們的聯(lián)合顯著性。28HousingPriceExample:thelogNonnestedAlternativeTests:MR

非嵌套替代模型的檢驗：MRP294

-如何檢驗非嵌套模型？二種方法：MR方法、DM方法

Whichofthefollowingmodelisbetter?下面哪一個模型更好？MizonandRichard(1986):Constructacomprehensivemodelthatcontainseachmodelasaspecialcaseandthentotesttherestrictionsthatledtoeachofthemodels.

MizonandRichard(1986):

構(gòu)造一個綜合模型，將每個模型都作為一個特殊情況包含其中，然后檢驗導(dǎo)致每個模型變的約束。注意：第6章P199曾提出用擬合優(yōu)度監(jiān)測29NonnestedAlternativeTests:MNonnestedAlternativeTests

非嵌套替代模型的檢驗Intheaboveexample,thecomprehensivemodelis在上例中，綜合模型是：

andtest

30NonnestedAlternativeTests

非嵌NonnestedAlternativeTests:DM

嵌套替代模型的檢驗：DMDavidsonandMacKinnon(1981):if(9.6)istrue,thenthefittedvaluesfrom(9.7),shouldbeinsignificantin(9.6).DavidsonandMacKinnon(1981):如果（9.6）正確，那么從（9.7）得到的擬合值在（9.6）中應(yīng)當(dāng)不顯著。注意：D-M檢驗的思路，是一個t檢驗P29431NonnestedAlternativeTests:DNonnestedAlternativeTests:DM

嵌套替代模型的檢驗：DMTotest(9.6),wefirstestimatemodel(9.7)byOLStoobtainthefittedvalues.為了檢驗（9.6），我們首先通過OLS估計模型（9.7）以得到擬合值。Putthisfittedvalueasanadditionalexplanatoryvariablein(9.6),usetstatistictotestitssignificance.將得到的擬合值作為另外的解釋變量放到（9.6）中，用t統(tǒng)計量檢驗其顯著性。32NonnestedAlternativeTests:DTheHousingPriceExample:MR

住房價格的例子：MRThecompetingmodels:競爭模型是：

(1)

reglpricebdrmscolonialassesslotsizesqrft(2)reglpricebdrmscoloniallassessllotsizelsqrft

Thecombinedregression:組合的回歸：

reglpricecolonialbdrmsassesslotsizesqrftlassessllotsizelsqrft

33TheHousingPriceExample:MR

TheHousingPriceExample:MR

住房價格的例子：MRTestingwhether(2)istherightone:檢驗（2）是否正確：testassesslotsizesqrft

F(3,79)=2.92,Prob>F=0.0392Testingwhether(1)istherightone:檢驗（1）是否正確： testlassessllotsizelsqrftF(3,79)=3.97,Prob>F=0.0108Inclusive.34TheHousingPriceExample:MR

TheHousingPriceExample:DM

住房價格的例子：DMTestingwhether(2)istherightone:檢驗（2）是否正確：reglpriceassessbdrmslotsizesqrftcolonial

predictyl,xbreglpricelassessllotsizelsqrftbdrmscolonialylThetablebelowshowthatylisaninsignificantvariable.下表顯示yl不是一個顯著的變量。35TheHousingPriceExample:DM

Source|SSdfMSNumberofobs=88-------------+------------------------------F(6,81)=48.11Model|6.2607657361.04346095Prob>F=0.0000Residual|1.7568377981.021689355R-squared=0.7809-------------+------------------------------AdjR-squared=0.7646Total|8.0176035287.092156362RootMSE=.14727

-----------------------------------------------------------------------------lprice|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+---------------------------------------------------------------lassess|.6762505.33745562.000.048.00481971.347681llotsize|-.0119247.0419541-0.280.777-.0954003.0715508lsqrft|-.1258866.1407801-0.890.374-.4059949.1542216bdrms|.0152289.0245180.620.536-.0335542.0640121colonial|.0243595.0397240.610.541-.0546788.1033977

yl|.4346309.36462431.190.237-.2908571.160119_cons|.3062863.57372220.530.595-.83524091.447813-----------------------------------------------------------------------------36Source|SS

Source|SSdfMSNumberofobs=88-------------+------------------------------F(6,81)=48.27Model|6.2654426361.04424044Prob>F=0.0000Residual|1.7521608981.021631616R-squared=0.7815-------------+------------------------------AdjR-squared=0.7653Total|8.0176035287.092156362RootMSE=.14708

----------------------------------------------------------------------------lprice|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+--------------------------------------------------------------assess|.0004822.00099150.490.628-.0014906.002455bdrms|-.0032415.0236591-0.140.891-.0503157.0438326lotsize|1.48e-061.68e-060.880.381-1.86e-064.83e-06sqrft|.0000404.00005820.690.489-.0000753.0001562colonial|.0207546.04268410.490.628-.0641735.1056826

ys|.7382357.3435822.150.035.05461531.421856_cons|1.2247571.6193960.760.452-1.9973334.446848----------------------------------------------------------------------------Testingwhether(1)istherightone檢驗（1）是否正確：37Source|SSNonnestedAlternativeTests:Comments

嵌套替代模型的檢驗：注釋Theaboveexamplefavorsthelogmodel,butitisoftenpossibletoseebothmodelsberejected,orneithermodelberejected.上面的例子偏好log模型，但可能經(jīng)常看到兩個模型都被拒絕，或，沒有一個被拒絕。38NonnestedAlternativeTests:CNonnestedAlternativeTests:Comments

嵌套替代模型的檢驗：注釋W(xué)henbotharerejectedMoreworkonspecificationneedstobedone.However,iftheeffectsofkeyindependentvariablesonyarenotverydifferent,thenitdoesnotreallymatterwhichmodelisused.

當(dāng)兩個都被拒絕需要在模型設(shè)定上花更多功夫盡管如此，如果關(guān)鍵解釋變量對y的效應(yīng)差別不是很大，那么用哪個模型關(guān)系不是很大。WhenbotharenotrejectedWecanusetheadjustedR-squaredtochoosebetweenthem.當(dāng)兩個都未被拒絕我們可以用調(diào)整過的R2在它們之間選擇。39NonnestedAlternativeTests:CProxyVariablesP295

代理變量

Whatifmodelismisspecifiedbecausenodataisavailableonanimportantxvariable?如果模型誤設(shè)是因為得不到一個重要解釋變量的數(shù)據(jù)，怎么辦？比如人的能力，是一個模糊變量，很難衡量Itmaybepossibletoavoidormitigateomittedvariablebiasbyusingaproxyvariable.可能通過使用一個代理變量避免或減輕遺漏變量偏誤。Aproxyvariableissomethingthatisrelatedtotheunobservedvariablethatwewouldliketocontrolforinouranalysis. 代理變量就是與我們在分析中試圖控制而又觀測不到的變量相關(guān)的變量。注意：引入代理變量的目的是什么？不是檢測beta3，而是為了正確獲取beta1和beta240ProxyVariablesP295ProxyVariables

代理變量-代理變量要與原始變量相關(guān)-P29641ProxyVariables

代理變量-代理變量要與原始變ProxyVariables

代理變量42ProxyVariables

代理變量42ProxyVariables

代理變量43ProxyVariables

代理變量43ProxyVariables

代理變量

P296

引入代理變量需要怎樣的條件呢？44ProxyVariables

代理變量P296ProxyVariables

代理變量P296

45ProxyVariables

代理變量P296ProxyVariables(continued)

代理變量（續(xù)）Whenthesetwoassumptionsaresatisfied,wearerunningregressionsy=(b0+b3d0)+b1x1+b2x2+b3d3x3+(u+b3v3)andhavejustredefinedintercept,errortermx3coefficient.當(dāng)這兩個假設(shè)被滿足，我們作回歸y=(b0+b3d0)+b1x1+b2x2+b3d3x3+(u+b3v3)，只要重新定義截距項，誤差項和x3系數(shù)。46ProxyVariables(continued)

代理TheIQExample.reglwageeducexpertenuremarriedsouthurbanblack

Source|SSdfMSNumberofobs=935-------------+------------------------------F(7,927)=44.75Model|41.837761975.97682312Prob>F=0.0000Residual|123.818521927.133569063R-squared=0.2526-------------+------------------------------AdjR-squared=0.2469Total|165.656283934.177362188RootMSE=.36547

----------------------------------------------------------------------------lwage|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+---------------------------------------------------------------

educ|.0654307.006250410.470.000.0531642.0776973exper|.014043.00318524.410.000.007792.020294tenure|.0117473.0024534.790.000.0069333.0165613married|.1994171.03905025.110.000.1227801.276054south|-.0909036.0262485-3.460.001-.142417-.0393903urban|.1839121.02695836.820.000.1310056.2368185

black|-.1883499.0376666-5.000.000-.2622717-.1144281_cons|5.395497.11322547.650.0005.173295.617704--------------------------------------------------------------------------

47TheIQExample.reglwageeduPlottingstandardizedIQagainstStandardizedWage

繪圖：標(biāo)準(zhǔn)化的IQ關(guān)于標(biāo)準(zhǔn)化的工資48PlottingstandardizedIQagain4949TheRegressionAddingIQ

加入IQ的回歸.reglwageeducexpertenuremarriedsouthurbanblacksdIQ

Source|SSdfMSNumberofobs=935-------------+------------------------------F(8,926)=41.27Model|43.536016185.44200202Prob>F=0.0000Residual|122.120267926.131879338R-squared=0.2628-------------+------------------------------AdjR-squared=0.2564Total|165.656283934.177362188RootMSE=.36315----------------------------------------------------------------------------lwage|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+--------------------------------------------------------------

educ|.0544106.00692857.850.000.0408133.068008exper|.0141458.00316514.470.000.0079342.0203575tenure|.0113951.00243944.670.000.0066077.0161825married|.1997644.03880255.150.000.1236134.2759154south|-.0801695.0262529-3.050.002-.1316916-.0286473urban|.1819463.02679296.790.000.1293645.2345281

black|-.1431253.0394925-3.620.000-.2206304-.0656202

sdIQ|.0535739.01492933.590.000.0242747.0828731_cons|5.536914.119208846.450.0005.3029635.770864----------------------------------------------------------------------------50TheRegressionAddingIQ

加入IQ的CautionsinUsingProxyVariables

使用代理變量注意事項

Whenassumptionsarenotsatisfiedwecannotgetconsistentestimators.Sayx3*=d0+d1x1+d2x2+d3x3+v3

Thenweareactuallyestimatingy=(b0+b3d0)+(b1+b3d1)x1+(b2+b3d2)x2+b3d3x3+(u+b3v3)Biaswilldependonsignsofb3anddj當(dāng)假設(shè)不滿足時，我們不能得到無偏、一致的估計量比如x3*=d0+d1x1+d2x2+d3x3+v3實際上，我們可以估計y=(b0+b3d0)+(b1+b3d1)x1+(b2+b3d2)x2+b3d3x3+(u+b3v3)。偏誤方向?qū)⒁蕾囉赽3

和dj的符號。51CautionsinUsingProxyVariabLaggedDependentVariables

滯后的被解釋變量

P302

Whatifthereareunobservedvariables,andyoucan’tfindreasonableproxyvariables?如果存在不可觀測的變量，并且你又找不到合理的解釋變量，怎么辦？Maybepossibletoincludealaggeddependentvariabletoaccountforomittedvariablesthatcontributetobothpastandcurrentlevelsofy 可以包含一個滯后的被解釋變量，說明同時影響過去和當(dāng)前y水平的被遺漏變量。Obviously,youmustthinkpastandcurrentyarerelatedforthistomakesense.很顯然的,我們必須認(rèn)為過去和當(dāng)前的y相關(guān)，才有意義。52LaggedDependentVariables

滯后的TheCrimeExample

犯罪的例子Variables:變量lcrmrtelog(crimerateper1000persons)（log（以1000人為單位的犯罪率））llawexpclog(lawexpenditure)（log（訴訟費(fèi)用））lcrmrt_1lcrmrtelagged（滯后的lcrmrte）unemunemploymentrate（失業(yè)率）53TheCrimeExample

犯罪的例子VariablTheCrimeExample:WithoutLaggedDependentVariable

犯罪的例子：不包含滯后的被解釋變量.reglcrmrtellawexpcunemifyear==87Source|SSdfMSNumberofobs=46-------------+------------------------------F(2,43)=1.30Model|.2719871992.1359936Prob>F=0.2824Residual|4.4899821443.104418189R-squared=0.0571-------------+------------------------------AdjR-squared=0.0133Total|4.7619693445.105821541RootMSE=.32314

----------------------------------------------------------------------------lcrmrte|Coef.Std.Err.tP>|t|[95%Conf.Interval]-------------+--------------------------------------------------------------llawexpc|.2033652.17265341.180.245-.1448236.5515539unem|-.0290032.0323387-0.900.375-.0942205.0362141_cons|3.3428991.2505272.670.011.82097215.864826----------------------------------------------------------------------------54TheCrimeExample:WithoutLagTheCrimeExample:WithLaggedDependentVariable

犯罪的例子：包含滯后的被解釋變量.reglcrmrtellawexpclcrmrt_1unem

Source|SSdfMSNumberofobs=46-------------+------------------------------F(3,42)=29.73Model|3.2373284631.07910949Prob>F=0.0000Residual|1.5246408842.036300973R-squared=0.6798-------------+------------------------------AdjR-squared=0.6570Total|4.7619693445.105821541RootMSE=.19053

----------------------------------------------------------------------------lcrmrte|Coef.Std.Err.tP>|t|[95%Conf.Interval]-----------+----------------------------------------------------------------llawexpc|-.1395764.1086412-1.280.206-.3588231.0796704lcrmrt_1|1.193923.13209859.040.000.92733711.460508unem|.008621.01951660.440.661-.0307652.0480072_cons|.0764511.82114330.090.926-1.5806831.733585----------------------------------------------------------------------------55TheCrimeExample:WithLaggedMeasurementError

測量誤差

P392

Sometimeswehavethevariablewewant,butwethinkitismeasuredwitherror有時，我們有需要的變量，但我們認(rèn)為它的測量存在誤差。Examples:Asurveyaskshow