第七章練習(xí)題及參考解答(第四版)計(jì)量經(jīng)濟(jì)學(xué)

第七章練習(xí)題及參考解答表中給出了1981-2015年中國城鎮(zhèn)居民人均年消費(fèi)支出(PCE)和城鎮(zhèn)居民人均可支配單位：元)收入(PDI)數(shù)據(jù)。單位：元)表1981-2015年中國城鎮(zhèn)居民消費(fèi)支出(PCE)和可支配收入(PDI)數(shù)據(jù)年度城鎮(zhèn)居民人均消費(fèi)支出PCE城鎮(zhèn)居民人均可支配收入PDI年度城鎮(zhèn)居民人均消費(fèi)支出PCE城鎮(zhèn)居民人均可支配收入PDI19811999198220001983200119842002198520031986200419872005198820061989200719902008199120091992201019932011199420121995201319962014年度城鎮(zhèn)居民人均消費(fèi)支出PCE城鎮(zhèn)居民人均可支配收入PDI年度城鎮(zhèn)居民人均消費(fèi)支出PCE城鎮(zhèn)居民人均可支配收入PDI1981199919822000198320011984200219852003198620041987200519882006198920071990200819912009199220101993201119942012199520131996201419971998估計(jì)下列模型：2015PCE=A+APDI+卩t12ttPCE二B+BPDI+BPCE+Ut12t3t—1t(1)解釋這兩個(gè)回歸模型的結(jié)果。短期和長期邊際消費(fèi)傾向(MPC)是多少分析該地區(qū)消費(fèi)同收入的關(guān)系。建立適當(dāng)?shù)姆植紲竽Ｐ?，用庫伊克變換轉(zhuǎn)換為庫伊克模型后進(jìn)行估計(jì)，并對估計(jì)結(jié)果進(jìn)行分析判斷?！揪毩?xí)題參考解答】(1)解釋這兩個(gè)回歸模型的結(jié)果。DependentVariable:PCEMethod:LeastSquaresDate:03/10/18Time:09:12Sample:19812005VariableCoefficientStd.Errort-StatisticProb.VariableCoefficientStd.Errort-StatisticProb.CIncludedobservations:25VariableCoefficientStd.Errort-StatisticProb.VariableCoefficientStd.Errort-StatisticProb.PDIPDIR-squaredAdjustedR-squared.ofregression.R-squaredAdjustedR-squared.ofregression.dependentvarAkaikeinfocriterionSumsquaredresidLoglikelihoodDurbin-WatsonstatSchwarzcriterionF-statisticProb(F-statistic)Meandependentvar收入跟消費(fèi)間有顯著關(guān)系。收入每增加1元，消費(fèi)增加元。AdjustedR-squared.ofregression.dependentvarAdjustedR-squared.ofregression.dependentvarAkaikeinfocriterionSumsquaredresidLoglikelihoodSumsquaredresidLoglikelihoodDurbin-WatsonstatSchwarzcriterionF-statisticProb(F-statistic)DependentVariable:PCEMethod:LeastSquaresDate:03/10/18Time:09:13Sample(adjusted):19822005Includedobservations:24afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CPDIPCE(-1)R-squaredMeandependentvar短期和長期邊際消費(fèi)傾向(MPC)是多少分析該地區(qū)消費(fèi)同收入的關(guān)系。短期MPC=,長期MPC==建立適當(dāng)?shù)姆植紲竽Ｐ?，用庫伊克變換轉(zhuǎn)換為庫伊克模型后進(jìn)行估計(jì)，并對估計(jì)結(jié)果進(jìn)行分析判斷。在滯后1-5期內(nèi)，根據(jù)AIC最小，選擇滯后5期，其回歸結(jié)果如下：DependentVariable:PCEMethod:LeastSquaresDate:03/10/18Time:09:25Sample(adjusted):19862005Includedobservations:20afteradjustingendpointsPDIPDI(-1)PDI(-2)PDI(-3)PDI(-4)PDI(-5)R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)當(dāng)期收入對消費(fèi)有顯著影響，但各滯后期影響并不顯著。不顯著可能是分布滯后模型直接估計(jì)時(shí)共線性造成的，也可能是真沒顯著影響。庫伊克模型估計(jì)結(jié)果見上表，PCE(-1)部分回歸結(jié)果t檢驗(yàn)不顯著。表中給出了中國1980-2016年固定資產(chǎn)投資Y與社會消費(fèi)品零售總額X的資料。取阿爾蒙多項(xiàng)式的次數(shù)m=2，運(yùn)用阿爾蒙多項(xiàng)式變換法估計(jì)以下分布滯后模型：Yt二a+BX+BX+BX+BX+BX3t-34t-4+ut0t1t-12t-2表中國1980-2016年固定資產(chǎn)投資Y與社會零售總額X數(shù)據(jù)(單位：億元)年份固定資產(chǎn)投資Y社會消費(fèi)品零售總額X年份固定資產(chǎn)投資Y社會消費(fèi)品零售總額X198019991981200019822001198320021984200319852004198620051987200619882007198920081990200919912010199220111993201219942013199520141996201519972016

練習(xí)題參考解答】直接估計(jì)結(jié)果如下：DependentVariable:YMethod:LeastSquaresDate:03/10/18Time:09:32Sample(adjusted):19842016Includedobservations:33afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.X(-1)X(-2)X(-3)X(-4)R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterion+09SchwarzcriterionF-statisticProb(F-statistic)練習(xí)題參考解答】直接估計(jì)結(jié)果如下：DependentVariable:YMethod:LeastSquaresDate:03/10/18Time:09:32Sample(adjusted):19842016Includedobservations:33afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.X(-1)X(-2)X(-3)X(-4)R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterion+09SchwarzcriterionF-statisticProb(F-statistic)使用阿爾蒙變換估計(jì)結(jié)果如下：DependentVariable:YMethod:LeastSquaresDate:03/10/18Time:09:37Sample(adjusted):19842016Includedobservations:33afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.Z0Z1Z2R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterion+09SchwarzcriterionF-statisticProb(F-statistic)根據(jù)片匕+件+a2i2可計(jì)算出B=a=00

p—a+2a+4a=2012p—tt+3tt+9tt=3012p4—tt+4tt+16tt=012直接使用軟件結(jié)果：p4—tt+4tt+16tt=012直接使用軟件結(jié)果：DependentVariable:YMethod:LeastSquaresDate:03/10/18Time:09:39Sample(adjusted):19842016Includedobservations:33afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CPDL01PDL02PDL03R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterion+09SchwarzcriterionF-statisticProb(F-statistic)LagDistributionofXiCoefficientStd.ErrorT-Statistic*|*|*|01234SumofLags利用表的數(shù)據(jù)，運(yùn)用局部調(diào)整假定或自適應(yīng)預(yù)期假定估計(jì)以下模型參數(shù)，并解釋模型的經(jīng)濟(jì)意義，探測模型擾動項(xiàng)的一階自相關(guān)性：1）設(shè)定模型Y*—tt+pX+uttt其中Y*為預(yù)期最佳值。t設(shè)定模型Y*=aX0e“ttt其中Y*為預(yù)期最佳值。t設(shè)定模型Y=a+PX*+uttt其中X*為預(yù)期最佳值。t【練習(xí)題參考解答】設(shè)定模型Y*二a+PX+uttt其中Y*為預(yù)期最佳值。tDependentVariable:YMethod:LeastSquaresDate:03/10/18Time:10:09Sample(adjusted):19812016Includedobservations:36afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CXY(-1)R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresid+09SchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)根據(jù)回歸結(jié)果，可算出h統(tǒng)計(jì)量為，明顯大于2,表明5%顯著水平下存在相關(guān)性。根據(jù)回歸數(shù)據(jù)，可算出調(diào)整系數(shù)為§二1-卩*二=這表示了局部調(diào)整的速度。卩=卩*/§二=10設(shè)定模型Y*=aXPeuttt其中Y*為預(yù)期最佳值。t假設(shè)調(diào)整方程為：InY-InY=§(InY*-InY)，則轉(zhuǎn)化為一階自回歸模型后的回歸結(jié)果tt-1tt-1

為:DependentVariable:LOG(Y)Method:LeastSquaresDate:03/10/18Time:10:11Sample(adjusted):19812016Includedobservations:36afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.VariableCoefficientStd.Errort-StatisticProb.LOG(X)LOG(Y(-1))R-squaredAdjustedR-squared.ofregressionSumsquaredresidR-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihoodDurbin-WatsonstatMeandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticProb(F-statistic)根據(jù)回歸結(jié)果，計(jì)算h統(tǒng)計(jì)量時(shí)開方部分為負(fù)，沒法計(jì)算。故沒法根據(jù)h統(tǒng)計(jì)量判斷相關(guān)性。根據(jù)回歸數(shù)據(jù)，可算出調(diào)整系數(shù)為X1-卩1*二=，這表示了局部調(diào)整的速度。設(shè)定模型Y二a+BX*+uttt其中X*為預(yù)期最佳值。tDependentVariable:YMethod:LeastSquaresDate:03/10/18Time:10:09Sample(adjusted):19812016Includedobservations:36afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CXY(-1)R-squaredXY(-1)R-squaredAdjustedR-squared.ofregressionSumsquaredresidLoglikelihood+09Meandependentvar.dependentvarAkaikeinfocriterionSchwarzcriterionF-statisticDurbin-WatsonstatProb(F-statistic)Durbin-WatsonstatProb(F-statistic)可算出調(diào)節(jié)系數(shù)為―卩1*二='這表示了預(yù)期修正的速度。卩弋=表給出中國各年末貨幣流通量Y,社會商品零售額XI、城鄉(xiāng)居民儲蓄余額X2的數(shù)據(jù)。表中國年末貨幣流通量、社會商品零售額、城鄉(xiāng)居民儲蓄余額數(shù)據(jù)（單位：億元）年份年末貨幣流通量Y社會消費(fèi)品零售總額X1城鄉(xiāng)居民儲蓄年底余額X219891990199119921993199419951996199719981999200020012002200320042005200620072008200920102011201220132014利用表中數(shù)據(jù)設(shè)定模型：Y*-a+卩X+卩X+卩t11t22ttY*=aXPiX卩2eutt1t2t其中,Y*為長期（或所需求的）貨幣流通量。試根據(jù)局部調(diào)整假設(shè),作模型變換,估計(jì)并檢驗(yàn)t參數(shù),對參數(shù)經(jīng)濟(jì)意義做出解釋?！揪毩?xí)題參考解答】SumsquaredresidSchwarzcriterionSumsquaredresidSchwarzcriterion利用表中數(shù)據(jù)設(shè)定模型：Y*=a+卩X+卩X+卩t11t22ttY*=aX卩1X卩2eut1t2t其中，Y*為長期(或所需求的)貨幣流通量。試根據(jù)局部調(diào)整假設(shè)，作模型變換，估計(jì)并檢驗(yàn)t參數(shù)，對參數(shù)經(jīng)濟(jì)意義做出解釋。假設(shè)局部調(diào)整方程為：Y—Y=S(Y*-Y)，對Y*=a+卩X+卩X+卩，可轉(zhuǎn)化為tt-1tt-1t11t22tt回歸方程：Y=Sa+(1-6)YX+p5X+6u，其回歸結(jié)果如下:tt-111t22ttDependentVariable:YMethod:LeastSquaresDate:03/10/18Time:10:03Sample(adjusted):19902014Includedobservations:25afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CY(-1)X1X2R-squaredMeandependentvarR-squared.dependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterion.ofregressionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)各回歸系數(shù)在5%顯著水平下均顯著?？伤愠稣{(diào)整系數(shù)為5=1-p*==，這表示了局部調(diào)整1的速度。假設(shè)局部調(diào)整方程為：lnY-lnY=5(lnY*-lnY)，對Y*=aXp1Xp2e《，可轉(zhuǎn)化為回tt-1tt-1t1t2t歸方程：lnY=5lna+(1-5)lnY+p5lnX+p5lnX+5u，其回歸結(jié)果如下：tt-111t22ttDependentVariable:LOG(Y)Method:LeastSquaresDate:03/10/18Time:10:04Sample(adjusted):19902014Includedobservations:25afteradjustingendpointsVariableCoefficientStd.Errort-StatisticProb.CLOG(Y(-1))LOG(X1)LOG(X2)R-squaredMeandependentvarAdjustedR-squared.dependentvar.ofregressionAkaikeinfocriterionSumsquaredresidSchwarzcriterionLoglikelihoodF-statisticDurbin-WatsonstatProb(F-statistic)根據(jù)四川省1978—2014年的消費(fèi)總額Y(億元)和收入總額X(億元)的年度資料，估計(jì)出庫伊克模型如下：f=—6.91+0.28X+0.82Yttt—1t=(—1.69)(5.89)(12.68)R2=0.97DW=1.45試回答下列問題：分布滯后系數(shù)的衰減率是多少模型中是否存在多重共線性問題請說明判斷的理由。收入對消費(fèi)的即期和長期影響乘數(shù)是多少某同學(xué)查表發(fā)現(xiàn)，在顯著性水平Q=0.05下，DW檢驗(yàn)臨界值為d=1.36ld=1.59