實驗八 內生解釋變量問題

實驗八內生解釋變量問題【實驗目的】掌握工具變量法、兩階段最小二乘法的使用以及內生性檢驗與過度識別約束檢驗【實驗內容】利用美國各州的數據為樣本觀測值，建立香煙需求模型（見教材138頁例4.3.4）【實驗步驟】表4.3.11995年美國48個州人均香煙消費、收入與對;香煙的課稅地區(qū)人均香煙消費Q（盒）人均收入Y（千美兀）香煙平均銷售價格P（美分/盒）香煙平均消費稅Tax（美分/盒）香煙平均的特別消費稅Taxs（美分/盒）AL101.0912.92103.9226.570.92AR111.0412.17115.1936.425.49AZ71.9513.54130.3242.876.21CA56.8616.07138.1340.039.04CO82.5816.32109.8128.870.00CT79.4720.96143.2348.568.11DE124.4716.66108.6631.500.00FL93.0715.43123.1737.996.97GA97.4714.59102.7423.620.94IA92.4013.90125.2639.375.96ID74.8512.88117.8734.125.61IL83.2716.83130.2344.627.37IN134.2614.33101.4025.924.83KS88.7514.36114.9731.505.47KY172.6512.6195.7917.725.42LA105.1812.82110.1028.874.23MA76.6218.41142.4649.216.78MD77.4717.65122.0739.375.81ME102.4713.28129.4240.037.33MI81.3915.73158.0464.968.95MN82.9516.13144.5947.249.46MO122.4514.50103.1726.900.91MS105.5811.28111.0427.567.26MT87.1612.31102.5027.560.00NC121.5414.4098.4219.033.79ND79.8112.52126.1544.627.14NE87.2714.56119.5438.065.69NH156.3416.41109.3432.150.00NJ80.3719.21133.2641.997.54NM64.6712.37115.5829.535.50NV93.5316.93135.5638.718.87NY70.8218.19145.5852.495.60OH111.3815.02108.8531.505.18OK108.6812.73111.6430.845.32OR92.1614.87124.8740.680.00PA95.6415.58115.5936.096.54RI92.6015.78147.2852.499.64SC108.0812.78100.2720.344.77地區(qū)人均香煙消費Q（盒）人均收入Y（千美兀）香煙平均銷售價格P（美分/盒）香煙平均消費稅Tax（美分/盒）香煙平均的特別消費稅Taxs（美分/盒）SD97.2213.02110.2630.844.24TN122.3214.30109.6224.288.12TX73.0814.12130.0542.657.36UT49.2712.37118.7533.145.65VA105.3916.05109.3617.395.21VT122.3314.02115.2528.875.49WA65.5315.67156.9052.8210.26WI92.4714.81132.1440.686.29WV115.5711.75109.2626.906.18WY112.2414.12104.0323.620.00資源來源：根據IntroductiontoEconometrics(2ndedition)整理。根據商品需求函數理論，對香煙的人均消費需求Q與居民的收入水平Y及香煙的銷售價格P有關；慮到在市場均衡時香煙的銷售價格也同時受香煙的需求量的影響，則Q與P之間存在著雙向因果關系，P為內生解釋變量，考慮到香煙價格中包含政府對煙草的課稅，而香煙的人均消費量本身不會直接影響政府對香煙的課稅政策，因此香煙的消費稅可能是價格的一個適當的工具變量。一、建立對數線性模型：lnQ=&o+0]lnY+P2lnP+'對原模型做回歸分析結果如下:ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:LNQMethod:LeastSquaresDate:10/28/16Time:10:56Sample:148Includedobservations:48VariableCoefficientStd.Errort-StatisticProb.C10.S40941.02263310.112070.0000LNY0.3440320.2340831.4646960.1500LNP-1.4063760.251294-5,5965260.0000R-squared0.4S2759Meandependentvar4.53S839從結果可以看出，價格確實是影響人均香煙消費的重要因素，其彈性為-1.4，特別大。懷疑P具有」生性：七J生性。。：：_.m』：：二"?：::-:-:t-:-：；-：：：二、工具變量法-"：；乙?1.--5：瀾年費稅作為P的工具變量，重新對原模型進行回歸""二把lnQlnYlnP作為一個組打開，詵擇Proc/MakeEquation/Method中的Tsls點擊確定EquationEstimationSpecificationOptionsEquBtionspecificstion.L1DependerLtv：=q-iablefoilowedbylistofregreesoreand.FDLtermE,ORanexplici+equationlikeInqCInylnpEstimationsettings；仁匕一TELS一TwcrSt色既LeqtSguarEsCT^HLSandAFJAA]Method:[咨-LeutSquare，(HLSandAjj房a-1.L5一LgwtEquarql：WL5and.ARMA.)CjfilM一GerLer：dliiedMethodofMurnenteLIML一LimitedIn￡urmationMaxiewtiLikeliTELS一TwcrSt色既LeqtSguarEsCT^HLSandAFJAA]Specification結果如下圖:(=]Equation:UISFTTTLEDSpecification結果如下圖:(=]Equation:UISFTTTLEDWorkf?[e:UNTTrLED::Untitled\在Instrumentlist中寫入工具變量，沒有工具變量的直接把解釋變量包括常數項寫上，有工具變量的就直接把工具變量寫上，如本例lnP的工具變量是tax,如下圖，點擊確定EquationEstimationEquationspecificationIlHperLdtjrLtProcObje吐PrintNameFreezeEstimateForecastStatsResidsViewDependentVariable:LNQMethod:Two-StageLeastSquaresDate:10；20/16Time:11:26Sample:148Includedobservations:48Instrumentspecification:CLNYTAXVariableCoefficientStd.Errort-StatisticProb.C10.022961.0317189.2657750.0000LNY0.2939530.2403&41.2433030.2200LNP-1.3145950.270991-4.8510720.0000R-squared0.4S1077Meandependentvar4.5S3339果。發(fā)現：吐具變量法得到的價格彈性要低于普通最小二乘借計的結

……擊注0俏每丁Sumsquaredresid1.不34獎果。乘法13.26712Durbin-Watsonstat-1.942^91P有許多州對香煙有額外的特別消費稅taxs它也可以做為p的工具變量。用tax和taxs兩個工具變量對原模型進行兩階段最小二乘回歸：皿以「時3把lnQlnYlnP作為一個組打開，選擇Proc/MakeEquation/Method中的Tsls,點擊確定，在Instrumentlist中寫入工具變量：Clnytaxtaxs點擊確定DependentVariable:LNQMethod:Two-StageLeastSquares□ate:10/23/16Time:11:38Sample:148Includedobservations:48Instrumentspecification:CLNYTAXTAXSVariableCoefficientStd.Errort-StatisticProb.C9.3936601.0585U9.34674-70.0000LNY0.23062302384761.1767340.2455LNP-1.2772760263114-4-.S544550.00000.429432Meandependentvar4.533339價格皇性進一步下降了。0.404073S.D.dependentvar0.243351四、過渡識別約束檢驗：判斷tax和taxs是否是外生變量己京-己1、用?蛭和taxs兩個工具變量對原模型進行兩階纓小二乘估計后,記錄殘差項為ete「尋嗅典e=lnQ-(9.89砸巍lnY五漩nP)-進行兩階段最小二乘后，在命令窗口：genret=resid2、再做et關于工具變量tax及taxs以及原模型外生變量lnY的普通最小二乘回歸e=a+atax+ataxs+alnY+e在命令窗口：LsetctaxtaxsInyfviewlfProcl[object![printI[Name]fFreezeI[EstimateI[Forecast![StatsIfResidslIDependentVariable:ETMethod:LeastSquaresDate:10/28/16Time:15:58Sample:148Includedobservations:48VariableCoefficientStd.Errort-StatisticProb.C-0.0657750.500136-0.1133790.9102TAX-0.0015150.003681-0.4116620.6S26TAXS0.0063670.01178S0.5400910.5919LNY0.0317110.2331140.1360320.89243、根據結果進行判斷一(1)384m；瞰2w48-0；Q07::=0.336<X°.展⑴二一3.84,即不拒絕tax和taxs作為工具變量的外生性假設S.E.ofregression0.189314-Akaikeinfocriterion-0.411162五、內生性檢驗：即判斷p是否為內生變量，?利用豪斯曼檢驗2三22：?Loglikelihood13.86790Hannan-Quinncriter.-0.3522351、構造輔助模型：lnP=#：+小ta^^.^taxs+步InY+e二：二三廿二123命令窗口：Lslnpctaxtaxslny結果如下：一ViewProcObjectPrintNameFreezeEstimateForecastStatsResidsDependentVariable:LNPMethod:LeastSquares□ate:10/28/16Time:16:21Sample:148Includedobservations:48VariableCoefTicientStd.Errort-StatisticProb.C41031530.09839241491110.0000TAX00093530.00062714.905530.0000TAXS0.0103900.0020095.4195110.0000LNY0.1002880.0397382.7250690.0092R-squared0.940297Meandependentvar4.7S1S79AdjustedR-squared0.936227S.D.dependentvar0.127790Q匚nfrahfoc-c-innAAkailzoinfnqri+臼ricn□J□AQT!

2、命令窗口genre1=resid構造輔助模型：lnQ=80+叩n7+P2lnP+P3e1+8命令窗口：LslnqcInyInpel結果如下:{=}Equation:UNTITLEDWorkfile:UNmLED::Untitled\_□X[viewProcObje吐PrintNameFreezeEstimateForecastStatsResidsDependentVariable:LNQMethod:LeastSquaresDate:10/23/16Time:16:30Sample:148Includedobservations:48VariableCoefficientStd.Errort-StatisticProb.C9.09366010315419.5374250.0000LNY0.2306230.2324901.2070350.2339L