中級計量課后習題參考答案(第九章)

1、第九章參考答案1、表面不相關回歸的含義是，所涉及的各個回歸似乎不相關，但實際上相關。各個回歸方程分別寫出，這使得它們似乎不相關，但是它們有共同點。在本章的例子中，四個回歸中的每一個關系到一個不同的制造產業(yè)，但它們都會受到宏觀經濟條件變動（如衰退）的影響。一般來說，影響一個回歸結果的事件也很可能影響其他回歸的結果，這個事實表明，表面不相關回歸中的各回歸之間存在相關。這種相關在數(shù)學上表現(xiàn)為擾動項跨方程相關。表面不相關回歸的步驟是：（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為是固定的而不是隨機的情況下，應采用固定效應模型。如果橫截面?zhèn)€體是隨機地被選擇出來代表一個較大的總體，則采用隨機效應模型比較合適。隨機效應模型與固定效應模型一樣，允許不同橫截面種類的截距不同，但這種不同被認為是隨機的，而不是固定的。3、隨機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立的假設，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，也就是每個產業(yè)或每個橫截面種類的擾動項方差不同。5、隨機系數(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）對鋼鐵產業(yè)用OLS法估計的結果如下：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-squared0.674135    Mean dependent var10339.75Adjusted R-squared0.637928    S.D. dependent var1653.825S.E. of regression995

5、.1473    Akaike info criterion16.77522Sum squared resid17825726    Schwarz criterion16.92444Log likelihood-173.1398    Hannan-Quinn criter.16.80761F-statistic18.61879    Durbin-Watson stat0.436339Prob(F-statistic)0.00004

6、1橡膠和塑料產業(yè)：Dependent Variable: Y2Method: Least SquaresDate: 12/02/10 Time: 10:40Sample: 1980 2000Included observations: 21VariableCoefficientStd. Errort-StatisticProb.  C-49122.543331.606-14.744400.0000EMP2135.49486.70325520.213280.0000OTM22646.5571087.2842.4340990.0256R-squared0.989264 

7、;   Mean dependent var80662.43Adjusted R-squared0.988071    S.D. dependent var13744.48S.E. of regression1501.188    Akaike info criterion17.59746Sum squared resid40564183    Schwarz criterion17.74668Log likelihood-181.7734

8、60;   Hannan-Quinn criter.17.62985F-statistic829.2748    Durbin-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估計結果如下：System: SUR_YEstima

9、tion Method: Seemingly 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)28.882224.7322

10、826.1032320.0000C(3)539.5766308.85691.7470120.0892C(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-squared0.666480    Mean de

11、pendent var10339.75Adjusted R-squared0.629422    S.D. dependent var1653.825S.E. of regression1006.768    Sum squared resid18244464Durbin-Watson stat0.486554Equation: Y_XJ=C(4)+C(5)*EMP_XJ+C(6)*OTM_XJObservations: 21R-squared0.988661    Mean

12、 dependent var80662.43Adjusted R-squared0.987401    S.D. dependent var13744.48S.E. of regression1542.747    Sum squared resid42841220Durbin-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

13、=-51805.3302975+142.169865054*EMP_XJ+1822.0182034*OTM_XJ估計結果說明采用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 + 3170.25123496*OTM_GTY_XJ = -14046.4794265 + 86.7390745907*EMP_XJ + 3170.25123496*OTM_XJY_SZ = -14046.4794265 + 86.7390745907*

14、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: 11:20Sample: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84VariableCoefficientStd

15、. Errort-StatisticProb.  C-14046.483233.619-4.3438880.0000EMP?86.739072.17543439.872080.0000OTM?3170.251731.41024.3344370.0000R-squared0.953292    Mean dependent var48601.24Adjusted R-squared0.952139    S.D. dependent var26268.36S.E. of regression574

16、6.759    Akaike info criterion20.18572Sum squared resid2.68E+09    Schwarz criterion20.27254Log likelihood-844.8003    Hannan-Quinn criter.20.22062F-statistic826.5976    Durbin-Watson stat0.097683Prob(F-statistic)0.00000

17、02.變截距模型：Substituted Coefficients:=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 = -6677.56653

18、145 - 23271.5488569 + 92.1914938172*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. &#

19、160;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-squared0.986194    Mean dependent var486

20、01.24Adjusted R-squared0.985309    S.D. dependent var26268.36S.E. of regression3183.855    Akaike info criterion19.03832Sum squared resid7.91E+08    Schwarz criterion19.21195Log likelihood-793.6095    Hannan-Quinn criter

21、.19.10812F-statistic1114.371    Durbin-Watson stat0.536797Prob(F-statistic)0.0000003.變系數(shù)模型Substituted Coefficients:=Y_GT = 17035.7314082 - 13116.5513831 + 31.9999750501*EMP_GT + 722.775832436*OTM_GTY_XJ = -36005.9857126 - 13116.5513831 + 135.494779734*EMP_XJ + 2646.5568381*OTM_XJ

22、Y_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: Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 12:06Sample: 1980 2000Included observations: 21Cross-sections inc

23、luded: 4Total pool (balanced) observations: 84VariableCoefficientStd. Errort-StatisticProb.  C-13116.553127.955-4.1933320.0001_GT-EMP_GT31.9999810.274173.1146040.0026_XJ-EMP_XJ135.49488.60473415.746540.0000_SZ-EMP_SZ81.1448912.699086.3898250.0000_FZ-EMP_FZ48.967077.7079556.3527970.0000_GT-

24、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-36005.99_SZ-C-958.3302_FZ-C19928.58Effects SpecificationCross-section fixed (dummy variables)R-squared0.

25、995332    Mean dependent var48601.24Adjusted R-squared0.994618    S.D. dependent var26268.36S.E. of regression1927.023    Akaike info criterion18.09690Sum squared resid2.67E+08    Schwarz criterion18.44416Log likelihood-

26、748.0700    Hannan-Quinn criter.18.23650F-statistic1395.550    Durbin-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，繼續(xù)檢驗F1=(7.91E+08-2.67E+08)/(4-1)22.67E

27、+08/4*21-4(2+1)=23.54F(6,72)在5%的顯著性水平下查表得，23.54大于臨界值，拒絕原假設，此模型為變截距、變系數(shù)模型。但由于隨機效應的估計需要number of cross sections>number of cofes所以本題選用變截距模型來說明固定效應和隨機效應固定效應：Dependent Variable: Y?Method: Pooled Least SquaresDate: 12/04/10 Time: 12:43Sample: 1980 2000Included observations: 21Cross-sections included: 4

28、Total pool (balanced) observations: 84VariableCoefficientStd. 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-se

29、ction fixed (dummy variables)R-squared0.986194    Mean dependent var48601.24Adjusted R-squared0.985309    S.D. dependent var26268.36S.E. of regression3183.855    Akaike info criterion19.03832Sum squared resid7.91E+08    

30、Schwarz criterion19.21195Log likelihood-793.6095    Hannan-Quinn criter.19.10812F-statistic1114.371    Durbin-Watson stat0.536797Prob(F-statistic)0.000000隨機效應：Dependent Variable: Y?Method: Pooled EGLS (Cross-section random effects)Date: 12/04/10 Time: 12:44Sam

31、ple: 1980 2000Included observations: 21Cross-sections included: 4Total pool (balanced) observations: 84Swamy and Arora estimator of component variancesVariableCoefficientStd. Errort-StatisticProb.  C-22829.995723.257-3.9889850.0001EMP?91.543075.08712217.995060.0000OTM?4627.113509.17469.087

32、4770.0000Random Effects (Cross)_GT-C5179.610_XJ-C4744.613_SZ-C-3360.029_FZ-C-6564.194Effects SpecificationS.D.  Rho  Cross-section random8835.9090.8851Idiosyncratic random3183.8550.1149Weighted StatisticsR-squared0.834605    Mean dependent var3809.792Adjusted

33、R-squared0.830521    S.D. dependent var7654.781S.E. of regression3151.303    Sum squared resid8.04E+08F-statistic204.3687    Durbin-Watson stat0.521199Prob(F-statistic)0.000000Unweighted StatisticsR-squared0.947690    Me

34、an dependent var48601.24Sum squared resid3.00E+09    Durbin-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 rando

35、m effects test comparisons:VariableFixed  Random Var(Diff.) Prob. EMP?92.19149491.5430703.0358630.7098OTM?4644.3583164627.112673998.9625650.5853Hausman統(tǒng)計量的值是0.352189，說明檢驗結果不能拒絕隨機效應模型原假設，應該建立個體隨機效應模型。最終的結果為Substituted Coefficients:=Y_GT = 5179.61044307 - 22829.9870905 + 91.54

36、30698694*EMP_GT + 4627.11267304*OTM_GTY_XJ = 4744.61297148 - 22829.9870905 + 91.5430698694*EMP_XJ + 4627.11267304*OTM_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),Filenew

37、Workfile,選擇面板數(shù)據(jù)，并在右側選擇Monthly，點擊OK(2)在命令行中輸入data dvdexp income price rainfall(3)點擊Objectnewobject,選擇POOL，在彈出對話框中輸入2003,2004(4)點擊Sheet,輸入dvdexp? Income? Price? Rainfall?點擊OK(5)在彈出的對話框中輸入數(shù)據(jù)(6)在POOL窗口中點擊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,點擊確

38、定，即可得到如下回歸結果。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?-3.2049980.896944-3.5732440.0020RAINFALL?7.4621802.3972313.1128330.0057Fixed Effects (Cross)2003-C2.6073382004-C-2.607338Effects SpecificationCross-section fixed (dum