中級計量課后習(xí)題參考答案(第九章)

1、第九章參考答案1、表面不相關(guān)回歸的含義是，所涉及的各個回歸似乎不相關(guān)，但實際上相關(guān)。各個回歸方程分別寫出，這使得它們似乎不相關(guān)，但是它們有共同點(diǎn)。在本章的例子中，四個回歸中的每一個關(guān)系到一個不同的制造產(chǎn)業(yè)，但它們都會受到宏觀經(jīng)濟(jì)條件變動（如衰退）的影響。一般來說，影響一個回歸結(jié)果的事件也很可能影響其他回歸的結(jié)果，這個事實表明，表面不相關(guān)回歸中的各回歸之間存在相關(guān)。這種相關(guān)在數(shù)學(xué)上表現(xiàn)為擾動項跨方程相關(guān)。表面不相關(guān)回歸的步驟是：（1）用ols法分別估計每個方程，計算和保存回歸中得到的殘差；（2）用這些殘差來估計擾動項方差和不同回歸方程擾動項之間的協(xié)方差；（3）上一步估計的擾動項方差和協(xié)方差被用于

2、執(zhí)行廣義最小二乘法，得到各方程系數(shù)的估計值。2、在不同的橫截面種類的截距之間的差異被認(rèn)為是固定的而不是隨機(jī)的情況下，應(yīng)采用固定效應(yīng)模型。如果橫截面?zhèn)€體是隨機(jī)地被選擇出來代表一個較大的總體，則采用隨機(jī)效應(yīng)模型比較合適。隨機(jī)效應(yīng)模型與固定效應(yīng)模型一樣，允許不同橫截面種類的截距不同，但這種不同被認(rèn)為是隨機(jī)的，而不是固定的。3、隨機(jī)影響模型的擾動項不再滿足普通最小二乘法各期擾動項相互獨(dú)立的假設(shè)，擾動項的一個分量在各期都相同。4、并不總是。盡管將數(shù)據(jù)合在一起將增加自由度，但有時采用混合數(shù)據(jù)也是不合適的。如果不同橫截面種類的斜率系數(shù)不同的話，則最好是分別回歸。如果試圖通過使用斜率虛擬變量來解決不同橫截面種

3、類不同斜率系數(shù)的問題，需要假定擾動項方差為常數(shù)。而采用分別回歸，每個回歸的擾動項方差可以不同，也就是每個產(chǎn)業(yè)或每個橫截面種類的擾動項方差不同。5、隨機(jī)系數(shù)模型即每個橫截面?zhèn)€體的解釋變量對被解釋變量的影響在橫截面?zhèn)€體之間的差異的變動時隨機(jī)的。有滯后因變量做自變量的動態(tài)模型就是動態(tài)面板數(shù)據(jù)模型。6、（1）對鋼鐵產(chǎn)業(yè)用OLS法估計的結(jié)果如下：Dependent Variable: Y1Method: Least SquaresDate: 12/02/10 Time: 10:39Sample: 1980 2000Included observations: 21VariableCoefficientS

4、td. Errort-StatisticProb.C3919.1801702.6912.3017560.0335EMP131.999985.3057566.0311810.0000OTM1722.7758348.28732.0752290.0526R-squared0.674135Mean dependent var10339.75Adjusted R-squared0.637928S.D. dependent var1653.825S.E. of regression995.1473Akaike info criterion16.77522Sum squared resid17825726S

5、chwarz criterion16.92444Log likelihood-173.1398Hannan-Quinn criter.16.80761F-statistic18.61879Durbin-Watson stat0.436339Prob(F-statistic)0.000041橡膠和塑料產(chǎn)業(yè)：Dependent Variable: Y2Method: Least SquaresDate: 12/02/10 Time: 10:40Sample: 1980 2000Included observations: 21VariableCoefficientStd. Errort-Stati

6、sticProb.C-49122.543331.606-14.744400.0000EMP2135.49486.70325520.213280.0000OTM22646.5571087.2842.4340990.0256R-squared0.989264Mean dependent var80662.43Adjusted R-squared0.988071S.D. dependent var13744.48S.E. of regression1501.188Akaike info criterion17.59746Sum squared resid40564183Schwarz criteri

7、on17.74668Log likelihood-181.7734Hannan-Quinn criter.17.62985F-statistic829.2748Durbin-Watson stat1.590448Prob(F-statistic)0.000000SUR的估計：在主菜單選擇Object-New Object，在彈出的對話框中選擇System，點(diǎn)擊OK。在編輯框中輸入：y_gt=c(1)+c(2)*emp_gt+c(3)*otm_gty_xj=c(4)+c(5)*emp_xj+c(6)*otm_xj估計結(jié)果如下：System: SUR_YEstimation Method: See

8、mingly Unrelated RegressionDate: 12/04/10 Time: 10:56Sample: 1980 2000Included observations: 21Total system (balanced) observations 42Linear estimation after one-step weighting matrixCoefficientStd. Errort-StatisticProb.C(1)4967.3361497.3993.3173090.0021C(2)28.882224.7322826.1032320.0000C(3)539.5766

9、308.85691.7470120.0892C(4)-51805.333007.227-17.226950.0000C(5)142.16995.88536024.156530.0000C(6)1822.018965.58521.8869580.0673Determinant residual covariance1.22E+12Equation: Y_GT=C(1)+C(2)*EMP_GT+C(3)*OTM_GTObservations: 21R-squared0.666480Mean dependent var10339.75Adjusted R-squared0.629422S.D. de

10、pendent var1653.825S.E. of regression1006.768Sum squared resid18244464Durbin-Watson stat0.486554Equation: Y_XJ=C(4)+C(5)*EMP_XJ+C(6)*OTM_XJObservations: 21R-squared0.988661Mean dependent var80662.43Adjusted R-squared0.987401S.D. dependent var13744.48S.E. of regression1542.747Sum squared resid4284122

11、0Durbin-Watson stat1.484711SUR估計的模型如下：Substituted Coefficients:=Y_GT=4967.33600398+28.8822169308*EMP_GT+539.576580766*OTM_GTY_XJ=-51805.3302975+142.169865054*EMP_XJ+1822.0182034*OTM_XJ估計結(jié)果說明采用SUR估計得到的斜率和用OLS法估計得到的斜率相同。（2）1.混合回歸模型：Substituted Coefficients:=Y_GT = -14046.4794265 + 86.7390745907*EMP_GT

12、 + 3170.25123496*OTM_GTY_XJ = -14046.4794265 + 86.7390745907*EMP_XJ + 3170.25123496*OTM_XJY_SZ = -14046.4794265 + 86.7390745907*EMP_SZ + 3170.25123496*OTM_SZY_FZ = -14046.4794265 + 86.7390745907*EMP_FZ + 3170.25123496*OTM_FZDependent Variable: Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 11:20

13、Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84VariableCoefficientStd. Errort-StatisticProb.C-14046.483233.619-4.3438880.0000EMP?86.739072.17543439.872080.0000OTM?3170.251731.41024.3344370.0000R-squared0.953292Mean dependent var48601.24Adjus

14、ted R-squared0.952139S.D. dependent var26268.36S.E. of regression5746.759Akaike info criterion20.18572Sum squared resid2.68E+09Schwarz criterion20.27254Log likelihood-844.8003Hannan-Quinn criter.20.22062F-statistic826.5976Durbin-Watson stat0.097683Prob(F-statistic)0.0000002.變截距模型：Substituted Coeffic

15、ients:=Y_GT = 5513.35297339 - 23271.5488569 + 92.1914938172*EMP_GT + 4644.35831606*OTM_GTY_XJ = 4576.61080153 - 23271.5488569 + 92.1914938172*EMP_XJ + 4644.35831606*OTM_XJY_SZ = -3412.39724347 - 23271.5488569 + 92.1914938172*EMP_SZ + 4644.35831606*OTM_SZY_FZ = -6677.56653145 - 23271.5488569 + 92.191

16、4938172*EMP_FZ + 4644.35831606*OTM_FZDependent Variable: Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 12:03Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84VariableCoefficientStd. Errort-StatisticProb.C-23271.553783.341-6.1510580.0000EMP

17、?92.191495.37723717.144770.0000OTM?4644.358510.15469.1038250.0000Fixed Effects (Cross)_GT-C5513.353_XJ-C4576.611_SZ-C-3412.397_FZ-C-6677.567Effects SpecificationCross-section fixed (dummy variables)R-squared0.986194Mean dependent var48601.24Adjusted R-squared0.985309S.D. dependent var26268.36S.E. of

18、 regression3183.855Akaike info criterion19.03832Sum squared resid7.91E+08Schwarz criterion19.21195Log likelihood-793.6095Hannan-Quinn criter.19.10812F-statistic1114.371Durbin-Watson stat0.536797Prob(F-statistic)0.0000003.變系數(shù)模型Substituted Coefficients:=Y_GT = 17035.7314082 - 13116.5513831 + 31.999975

19、0501*EMP_GT + 722.775832436*OTM_GTY_XJ = -36005.9857126 - 13116.5513831 + 135.494779734*EMP_XJ + 2646.5568381*OTM_XJY_SZ = -958.330237755 - 13116.5513831 + 81.1448912349*EMP_SZ + 3450.40621266*OTM_SZY_FZ = 19928.5845421 - 13116.5513831 + 48.967070419*EMP_FZ + 2860.78889467*OTM_FZDependent Variable:

20、Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 12:06Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84VariableCoefficientStd. Errort-StatisticProb.C-13116.553127.955-4.1933320.0001_GT-EMP_GT31.9999810.274173.1146040.0026_XJ-EMP_XJ135.49488.

21、60473415.746540.0000_SZ-EMP_SZ81.1448912.699086.3898250.0000_FZ-EMP_FZ48.967077.7079556.3527970.0000_GT-OTM_GT722.7758674.43031.0716840.2874_XJ-OTM_XJ2646.5571395.7091.8962100.0619_SZ-OTM_SZ3450.406522.62996.6020070.0000_FZ-OTM_FZ2860.789903.49753.1663500.0023Fixed Effects (Cross)_GT-C17035.73_XJ-C-

22、36005.99_SZ-C-958.3302_FZ-C19928.58Effects SpecificationCross-section fixed (dummy variables)R-squared0.995332Mean dependent var48601.24Adjusted R-squared0.994618S.D. dependent var26268.36S.E. of regression1927.023Akaike info criterion18.09690Sum squared resid2.67E+08Schwarz criterion18.44416Log lik

23、elihood-748.0700Hannan-Quinn criter.18.23650F-statistic1395.550Durbin-Watson stat0.694607Prob(F-statistic)0.000000模型類型的檢驗過程如下：F2=(2.68E+09-2.67E+08)/(4-1)(2+1)2.67E+08/4*21-4(2+1)=72.30F(9,72)在5%的顯著性水平下查表得：72.3大于臨界值，拒絕原假設(shè)，繼續(xù)檢驗F1=(7.91E+08-2.67E+08)/(4-1)22.67E+08/4*21-4(2+1)=23.54F(6,72)在5%的顯著性水平下查表

24、得，23.54大于臨界值，拒絕原假設(shè)，此模型為變截距、變系數(shù)模型。但由于隨機(jī)效應(yīng)的估計需要number of cross sectionsnumber of cofes所以本題選用變截距模型來說明固定效應(yīng)和隨機(jī)效應(yīng)固定效應(yīng)：Dependent Variable: Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 12:43Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84Variab

25、leCoefficientStd. Errort-StatisticProb.C-23271.553783.341-6.1510580.0000EMP?92.191495.37723717.144770.0000OTM?4644.358510.15469.1038250.0000Fixed Effects (Cross)_GT-C5513.353_XJ-C4576.611_SZ-C-3412.397_FZ-C-6677.567Effects SpecificationCross-section fixed (dummy variables)R-squared0.986194Mean depen

26、dent var48601.24Adjusted R-squared0.985309S.D. dependent var26268.36S.E. of regression3183.855Akaike info criterion19.03832Sum squared resid7.91E+08Schwarz criterion19.21195Log likelihood-793.6095Hannan-Quinn criter.19.10812F-statistic1114.371Durbin-Watson stat0.536797Prob(F-statistic)0.000000隨機(jī)效應(yīng)：D

27、ependent Variable: Y?Method: Pooled EGLS (Cross-section random effects)Date: 12/04/10 Time: 12:44Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84Swamy and Arora estimator of component variancesVariableCoefficientStd. Errort-StatisticProb.C-22

28、829.995723.257-3.9889850.0001EMP?91.543075.08712217.995060.0000OTM?4627.113509.17469.0874770.0000Random Effects (Cross)_GT-C5179.610_XJ-C4744.613_SZ-C-3360.029_FZ-C-6564.194Effects SpecificationS.D.RhoCross-section random8835.9090.8851Idiosyncratic random3183.8550.1149Weighted StatisticsR-squared0.8

29、34605Mean dependent var3809.792Adjusted R-squared0.830521S.D. dependent var7654.781S.E. of regression3151.303Sum squared resid8.04E+08F-statistic204.3687Durbin-Watson stat0.521199Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.947690Mean dependent var48601.24Sum squared resid3.00E+09Durbin-

30、Watson stat0.139938Hausman檢驗：Correlated Random Effects - Hausman TestPool: POOL_YTest cross-section random effectsTest SummaryChi-Sq. StatisticChi-Sq. d.f.Prob.Cross-section random0.35218920.8385Cross-section random effects test comparisons:VariableFixedRandomVar(Diff.)Prob.EMP?92.19149491.5430703.0

31、358630.7098OTM?4644.3583164627.112673998.9625650.5853Hausman統(tǒng)計量的值是0.352189，說明檢驗結(jié)果不能拒絕隨機(jī)效應(yīng)模型原假設(shè)，應(yīng)該建立個體隨機(jī)效應(yīng)模型。最終的結(jié)果為Substituted Coefficients:=Y_GT = 5179.61044307 - 22829.9870905 + 91.5430698694*EMP_GT + 4627.11267304*OTM_GTY_XJ = 4744.61297148 - 22829.9870905 + 91.5430698694*EMP_XJ + 4627.11267304*OT

32、M_XJY_SZ = -3360.0291425 - 22829.9870905 + 91.5430698694*EMP_SZ + 4627.11267304*OTM_SZY_FZ = -6564.19427205 - 22829.9870905 + 91.5430698694*EMP_FZ + 4627.11267304*OTM_FZ7、8、(1),FilenewWorkfile,選擇面板數(shù)據(jù)，并在右側(cè)選擇Monthly，點(diǎn)擊OK(2)在命令行中輸入data dvdexp income price rainfall(3)點(diǎn)擊Objectnewobject,選擇POOL，在彈出對話框中輸入20

33、03,2004(4)點(diǎn)擊Sheet,輸入dvdexp? Income? Price? Rainfall?點(diǎn)擊OK(5)在彈出的對話框中輸入數(shù)據(jù)(6)在POOL窗口中點(diǎn)擊Proc Estimate,在Dependent variable中輸入dvdexp?,在Cross-section中選擇Fixed,在右上角輸入c income price rainfall,點(diǎn)擊確定，即可得到如下回歸結(jié)果。Dependent Variable: DVDEXP?Method: Pooled Least SquaresDate: 11/30/10 Time: 22:34Sample: 1 12Included observations: 12Cross-sections included: 2Total pool (balanced) observations: 24VariableCoefficientStd. Errort-StatisticProb.C83.4369523.822113.5025000.0024INCOME?0.0614480.0098816.2187190.0000PRICE?-3.2049980.896944-3.5732440.0