计量经济学作业

（16）表4是南开大学国际经济研究所1999级研究生考试分数及录取情况数据表（n=97）。变量SCORE：考生考试分数；变量Y：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。 样本 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Y 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 0 SCORE D1 401 401 392 387 384 379 378 378 376 371 362 362 361 359 358 356 356 355 1 0 1 0 1 0 0 0 1 0 0 1 1 1 1 1 1 1 样本 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 Y SCORE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 332 332 332 331 330 328 328 328 321 321 318 318 316 308 308 304 303 303 D1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 样本 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 Y SCORE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 275 273 273 272 267 266 263 261 260 256 252 252 245 243 242 241 239 235 D1 0 0 1 1 0 1 1 1 0 0 0 1 1 1 0 0 1 0 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 354 354 353 350 349 349 348 347 347 344 339 338 338 336 334 1 0 1 0 0 0 1 1 1 1 1 0 1 1 0 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 299 297 294 293 293 292 291 291 287 286 286 282 282 282 278 表4

1 1 0 1 1 0 1 1 1 1 0 1 1 0 85 86 87 88 89 90 91 92 93 94 95 96 97 0 0 0 0 0 0 0 0 0 0 0 0 0 232 228 219 219 214 210 204 198 189 188 182 166 123 0 1 1 1 1 1 1 0 1 1 1 1 0 0 1根据表4所给数据建立二元离散Probit模型和Logit模型，对模型拟合优度和总体显著性○

进行检验。

2利用估计的Probit模型和Logit模型进行边际影响分析。 ○

3利用估计的Probit模型和Logit模型进行预测，如果某一考生为应届生且考试分数为360○

分，则该考生被录取的概率有多大?

1解：利用Eviews构建Probit模型和Logit模型 ○

Probit模型：

Dependent Variable: Y

Method: ML - Binary Probit (Quadratic hill climbing) Date: 05/16/16 Time: 00:28 Sample: 1 97

Included observations: 97

Convergence achieved after 9 iterations

Covariance matrix computed using second derivatives

Variable C SCORE D1

McFadden R-squared S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Restr. deviance LR statistic Prob(LR statistic) Obs with Dep=0 Obs with Dep=1

Dependent Variable: Y

Method: ML - Binary Probit (Quadratic hill climbing) Date: 05/16/16 Time: 09:10 Sample: 1 97

Included observations: 97

Convergence achieved after 9 iterations

Covariance matrix computed using second derivatives

Variable C SCORE

McFadden R-squared S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Restr. deviance LR statistic Prob(LR statistic)

Coefficient -144.4560 0.402868

Std. Error 70.19813 0.196186

Coefficient -143.3214 0.400315 -0.247079

Std. Error 69.81269 0.195064 1.643147

z-Statistic -2.052941 2.052220 -0.150369

Prob. 0.0401 0.0401 0.8805 0.144330 0.116307 1.271570 -3.925501 7.851002 -40.03639 -0.040469

97

0.901952 Mean dependent var 0.353250 S.E. of regression 0.142794 Sum squared resid 0.222424 Log likelihood 0.174992 Deviance

80.07278 Restr. log likelihood 72.22178 Avg. log likelihood 0.000000

83 Total obs 14

由于D1系数显著性不高，故剔除变量D1，即是否应届生对结果无影响。

z-Statistic -2.057833 2.053503

Prob. 0.0396 0.0400 0.144330 0.116277 1.284441 -3.936702 7.873405 -40.03639 -0.040585

0.901672 Mean dependent var 0.353250 S.E. of regression 0.122406 Sum squared resid 0.175493 Log likelihood 0.143872 Deviance

80.07278 Restr. log likelihood 72.19938 Avg. log likelihood 0.000000

Obs with Dep=0 Obs with Dep=1

83 Total obs 14

97

Probit模型最终估计结果是

z= (-2.057833) (2.053503) p= (0.0396) (0.0400) LR=72.19938McFadden R-squared=0.901672

该模型LR=72.19938，它对应的P值极小，说明模型总体是显著的。模型拟合优度较高，McFadden R-squared=0.901672，说明Probit模型解释了因变量90.2%的变动。

Logit模型

Dependent Variable: Y

Method: ML - Binary Logit (Quadratic hill climbing) Date: 05/16/16 Time: 00:43 Sample: 1 97

Included observations: 97

Convergence achieved after 9 iterations

Covariance matrix computed using second derivatives

Variable C SCORE D1

McFadden R-squared S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Restr. deviance LR statistic Prob(LR statistic) Obs with Dep=0 Obs with Dep=1

Dependent Variable: Y

Coefficient -242.4576 0.677061 -0.476605

Std. Error 124.5183 0.348036 2.984586

z-Statistic -1.947165 1.945380 -0.159689

Prob. 0.0515 0.0517 0.8731 0.144330 0.115377 1.251316 -3.979482 7.958964 -40.03639 -0.041026

97

0.900603 Mean dependent var 0.353250 S.E. of regression 0.143907 Sum squared resid 0.223537 Log likelihood 0.176105 Deviance

80.07278 Restr. log likelihood 72.11382 Avg. log likelihood 0.000000

83 Total obs 14

由于D1系数显著性不高，故剔除变量D1,即是否应届生对结果无影响。

Method: ML - Binary Logit (Quadratic hill climbing) Date: 05/16/16 Time: 09:17 Sample: 1 97

Included observations: 97

Convergence achieved after 8 iterations

Covariance matrix computed using second derivatives

Variable C SCORE

McFadden R-squared S.D. dependent var Akaike info criterion Schwarz criterion Hannan-Quinn criter. Restr. deviance LR statistic Prob(LR statistic) Obs with Dep=0 Obs with Dep=1

Coefficient -243.7362 0.679441

Std. Error 125.5553 0.350489

z-Statistic -1.941266 1.938553

Prob. 0.0522 0.0526 0.144330 0.115440 1.266017 -3.992330 7.984660 -40.03639 -0.041158

97

0.900282 Mean dependent var 0.353250 S.E. of regression 0.123553 Sum squared resid 0.176640 Log likelihood 0.145019 Deviance

80.07278 Restr. log likelihood 72.08812 Avg. log likelihood 0.000000

83 Total obs 14

z= (-1.941266) (1.938553) p= (0.0522) (0.0526) LR=72.08812McFadden R-squared=0.900282

该模型LR=72.08812，它对应的P值极小，说明模型总体是显著的。模型拟合优度较高，McFadden R-squared=0.900282，说明Probit模型解释了因变量90%的变动。

2解：Probit模型和Logit模型边际影响分析对比如下表： ○变量 SCORE D1 Probit模型 回归系数 0.400315 -0.247079 平均边际影响 0.159611595 -0.0985141 回归系数 0.677061 -0.47661 Logit模型 平均边际影响 0.169244261 -0.11913648 根据上表中Probit模型边际影响结果可知，在其他条件不变的情况下，考试考试分数每增加1分，考生被录取的平均概率就增加0.159611595；如果考生是应届生，则考生被录取的平均概率就减少0.0985141。

根据上表中Logit模型边际影响结果可知，在其他条件不变的情况下，考试考试分数每增加1分，考生被录取的平均概率就增加0.169244261；如果考生是应届生，则考生被录取的平均概率就减少0.11913648。

总体而言，Probit模型的平均边际影响和Logit模型的平均边际影响相差较小。

3解：利用Eviews进行预测。 ○

则该考生被录取概率为0.59~0.85之间。

本文来源：https://www.bwwdw.com/article/ahph.html