结构推理
下表是某大学1999级研究生考试分数及录取情况数据表(N=85)。定义变量X为考生考试分数;Y为考生录取为1,未录取为0;虚拟变量D1,应届生为1,非应届生为0。根据所给数据建立二元离散Logit模型与Probit模型。
YXDYXDYXDYXDYXD
1401103551033210299102731
1401003541033210297102721
1392103540033110294002670
1387003531033010293102661
1384103500032810293102631
1379003490032810292002611
1378003490032810291102600
1378003481032110291102560
1376103471032110287102520
1371003471031810286102521
1362003441031800286002451
1362103391031610282102431
1361103380030800282102420
0359103381030810282002410
0358103361030400278002391
1356103340030310275002350
0356103321030310273002320
【正确答案】解:首先,估计Logit模型。在Eviews软件中,选择“Quick/Estimate Equation”在出现的对话框中输入“Y C X D”,在“Quick/Estimate Setting”的“Methods”栏内选择“Binary”,再在新出现的选项中选择“Logit”,点击OK,可得下表所示输出结果。
Dependent Variable:Y
Method: ML-Binary Logit(Quadratic hill climbing)
Date:02/20/06 Time:21:26
Sample:185
included observations:85
Convergence achieved after 12 iterations
Covariance matrix computed using second derivatives
Variable Coefficient Std.Error z-Statistic Prob
C -242.4576 124.5183 -1.947165 0.0515
X 0.677061 0.348036 1.945380 0.0517
D1 -0.476605 2.984586 -0.159689 0.8731
Mean dependent var 0.164706 S.D. dependent var 0.373116
SE.of regression 0.122531 Akaike info criterion 0.164223
Sum squared resid 1.251316 Schwarz criterion 0.250434
Log likelihood -3.979482 Hannan-Quinn Criter 0.198900
Restr log likelihood -38.02828 Avg. log likelihood -0.046817
LR statistic(2 df) 68.09760 McFadden R-Squared 0.895355
Probability(LR stat) 1.67E-15
Obs with Dep=0 71 Total obs 85
Obs with DeP=1 14
根据输出结果可得到估计的Logit模型:
(-1.95) (1.95) (-0.16)
=0.8953 LR(2)=68.10
接下来,估计Probit模型,在上面Eviews操作步骤中的“Methods”栏内选择“Binary”后,在新出现的选项中选择“Probit”,点击OK,可得下表所示输出结果。
Dependent Variable:Y
Method: ML-Binary Logit(Quadratic hill climbing)
Date:02/20/06 Time:21:29
Sample:185
included observations:85
Convergence achieved after 11 iterations
Covariance matrix computed using second derivatives
Variable Coefficient Std.Error z-Statistic Prob
C -143.3214 69.81266 -2.052942 0.0401
X 0.400315 0.195064 2.052221 0.0401
D1 -0.247079 1.643146 -0.150369 0.8805
Mean dependent var 0.164706 S.D. dependent var 0.373116
SE.of regression 0.124527 Akaike info criterion 0.162953
Sum squared resid 1.271570 Schwarz criterion 0.249164
Log likelihood -3.925501 Hannan-Quinn Criter 0.197630
Restr log likelihood -38.02828 Avg. log likelihood -0.046182
LR statistic(2 df) 68.20556 McFadden R-Squared 0.896774
Probability(LR stat) 1.55E-15
Obs with Dep=0 71 Total obs 85
Obs with DeP=1 14
根据输出结果可得到估计的Probit模型:
(-2.05) (2.05) (-0.15)
=0.8968 LR(2)=68.21
【答案解析】