計量經(jīng)濟學(xué)第5,6,7題答案

1、第7章練習(xí)5在申請出國讀學(xué)位的16名學(xué)生中有如下GRE數(shù)量與詞匯分?jǐn)?shù)。學(xué)生編號數(shù)量成績Q詞匯成績V是否準(zhǔn)入Y1=準(zhǔn)，0=不準(zhǔn)學(xué)生編號數(shù)量成績Q詞匯成績V是否準(zhǔn)入Y1=準(zhǔn)，0=不準(zhǔn)176055019520660126003500108002500372032001167048004710630112670520155304301137807101665057001452045007800500115680590186506801165003800解：根據(jù)Eview軟件得如下表：Dependent Variable: YMethod: ML - Binary Logit (Quadratic hi

2、ll climbing)Date: 05/22/11 Time: 22:19Sample: 1 16Included observations: 16Convergence achieved after 5 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.C-11.107416.124290-1.8136650.0697Q0.0039680.0080080.4955150.6202V0.0176960.0087522.0219140

3、.0432McFadden R-squared0.468521Mean dependent var0.562500S.D. dependent var0.512348S.E. of regression0.382391Akaike info criterion1.103460Sum squared resid1.900896Schwarz criterion1.248321Log likelihood-5.827681Hannan-Quinn criter.1.110878Restr. log likelihood-10.96503LR statistic10.27469Avg. log li

4、kelihood-0.364230Prob(LR statistic)0.005873Obs with Dep=07Total obs16Obs with Dep=19于是，我們可得到Logit模型為： -1.81 0.49 2.02 ， LR(2)=10.27如果在Binary estination這一欄中選擇Probit估計方法，可得到如下表：Dependent Variable: YMethod: ML - Binary Probit (Quadratic hill climbing)Date: 05/22/11 Time: 22:25Sample: 1 16Included obser

5、vations: 16Convergence achieved after 5 iterationsCovariance matrix computed using second derivativesVariableCoefficientStd. Errorz-StatisticProb.C-6.6345423.396882-1.9531270.0508Q0.0024030.0045850.5241210.6002V0.0105320.0046932.2442990.0248McFadden R-squared0.476272Mean dependent var0.562500S.D. de

6、pendent var0.512348S.E. of regression0.381655Akaike info criterion1.092836Sum squared resid1.893588Schwarz criterion1.237696Log likelihood-5.742687Hannan-Quinn criter.1.100254Restr. log likelihood-10.96503LR statistic10.44468Avg. log likelihood-0.358918Prob(LR statistic)0.005395Obs with Dep=07Total

7、obs16Obs with Dep=19于是，我們可得到Probit模型為： -1.95 0.52 2.24 ， LR(2)=10.44第7章練習(xí)6下表列出了美國、加拿大、英國在19801999年的失業(yè)率Y以及對制造業(yè)的補償X的相關(guān)數(shù)據(jù)資料。美 國加拿大英 國年份補助失業(yè)率補助失業(yè)率補助失業(yè)率美元/小時%美元/小時%美元/小時%198055.67.1497.243.77.0198161.17.654.17.344.110.5198267.09.759.610.642.211.3198368.89.663.911.539.011.8198471.27.564.310.937.211.719857

8、5.17.263.510.239.011.2198678.57.063.39.247.811.2198780.76.268.08.460.210.3198864.05.576.07.368.38.6198986.65.384.17.067.77.2199090.85.691.57.781.76.9199195.66.8100.19.890.58.81992100.07.5100.010.6100.010.11993102.76.995.510.788.710.51994105.66.191.79.492.39.71995107.95.693.38.595.98.71996109.35.493.

9、18.795.68.21997111.44.994.48.2103.37.01998117.34.590.67.5109.86.31999123.24.991.95.7112.26.1解：1根據(jù)Eview 軟件操作得如下表：美國US：Dependent Variable: YMethod: Least SquaresDate: 05/22/11 Time: 22:38Sample: 1980 1999Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C10.568581.1389829.2789720.0

10、000X-0.0454030.012538-3.6211890.0020R-squared0.421464Mean dependent var6.545000Adjusted R-squared0.389323S.D. dependent var1.432875S.E. of regression1.119732Akaike info criterion3.158696Sum squared resid22.56840Schwarz criterion3.258269Log likelihood-29.58696Hannan-Quinn criter.3.178133F-statistic13

11、.11301Durbin-Watson stat0.797022Prob(F-statistic)0.001953根據(jù)上表可得對美國的OLS估計結(jié)果為： 9.28 -3.62 ， ， D.W.=0.797， RSS=22.57加拿大(CA)：Dependent Variable: YMethod: Least SquaresDate: 05/22/11 Time: 22:43Sample: 1980 1999Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C9.3424521.8107015.15957

12、90.0001X-0.0065800.022333-0.2946480.7716R-squared0.004800Mean dependent var8.820000Adjusted R-squared-0.050489S.D. dependent var1.600855S.E. of regression1.640770Akaike info criterion3.922848Sum squared resid48.45828Schwarz criterion4.022421Log likelihood-37.22848Hannan-Quinn criter.3.942286F-statis

13、tic0.086817Durbin-Watson stat0.578517Prob(F-statistic)0.771634同樣，根據(jù)上表可得對加拿大CA的OLS估計結(jié)果為： 5.16 -0.29 ， ， D.W.=0.579， RSS=48.46英國UK：Dependent Variable: YMethod: Least SquaresDate: 05/22/11 Time: 22:48Sample: 1980 1999Included observations: 20VariableCoefficientStd. Errort-StatisticProb.C12.554260.99023

14、412.678080.0000X-0.0465910.012777-3.6463530.0018R-squared0.424845Mean dependent var9.155000Adjusted R-squared0.392891S.D. dependent var1.916542S.E. of regression1.493315Akaike info criterion3.734513Sum squared resid40.13981Schwarz criterion3.834087Log likelihood-35.34513Hannan-Quinn criter.3.753951F

15、-statistic13.29589Durbin-Watson stat0.698064Prob(F-statistic)0.001847同樣，根據(jù)上表可得對英國UK的OLS估計結(jié)果為： 12.68 -3.65 ， ， D.W.=0.6981， RSS=40.14(2)將三個國家的數(shù)據(jù)合并成一個樣本共60個樣本點，根據(jù)Eview軟件得：OLS估計結(jié)果如下：Dependent Variable: YMethod: Least SquaresDate: 05/22/11 Time: 22:58Sample: 1980 2039Included observations: 60VariableCoe

16、fficientStd. Errort-StatisticProb.C12.149460.82026614.811610.0000X-0.0495000.009844-5.0287290.0000R-squared0.303622Mean dependent var8.173333Adjusted R-squared0.291616S.D. dependent var2.009120S.E. of regression1.690988Akaike info criterion3.921268Sum squared resid165.8475Schwarz criterion3.991079Lo

17、g likelihood-115.6380Hannan-Quinn criter.3.948575F-statistic25.28811Durbin-Watson stat0.492398Prob(F-statistic)0.000005根據(jù)上表得估計方程為： 14.81 -5.03 ， ， D.W.=0.49， RSS=165.853在Eviews軟件下，估計變截距固定影響模型得到如下結(jié)果：固定影響模型可按最小二乘虛擬變量LSDV模型估計，記D2為加拿大CA的虛擬變量；即觀測值屬于CA時取值為1，其他取值為0；記D3為英國的虛擬變量，取值規(guī)律同D2，所以，LSDV模型的OLS估計結(jié)果如下：

18、11.73 4.12 4.20 -4.33， ， D.W.=0.664， RSS=117.94美國US沒有設(shè)定虛擬變量，成為比擬的基準(zhǔn)?？梢钥闯?，該結(jié)果與上述固定效應(yīng)模型的估計結(jié)果是一致的。4為了比擬以上三個模型，需要進(jìn)行如下兩個F檢驗。首先，進(jìn)行“截距和斜率在不同的橫截面樣本點和時間上都相同的假設(shè)檢驗，相應(yīng)的F檢驗為： F(n-1)(k+1),nT-n(k+1)其中，S3為第二類模型，即合成的大樣本模型相應(yīng)的殘差平方和，S1為第一類模型，即按橫截面樣本點分別估計的各單一方程的殘差平方和。 如果接受該假設(shè)，那么選取第二類模型。如果該假設(shè)被拒絕，那么再進(jìn)行“斜率在不同的橫截面樣本點和時間上都相同，但截距不相同的假設(shè)，相應(yīng)的F檢驗為：F(n-1)k,nT-n(k+1)其中，S2為第三類模型，即固定效應(yīng)模型的相應(yīng)的殘差平方和。如果接受該假設(shè)，那么選取第三類模型。拒絕該假設(shè)，那么選取第一類模型，即按橫截面樣本點分別估計的各單一的模型方程。由上述估計結(jié)果，知： 于是， =6.64， =1.64 對于，在5%的顯著性水