计量经济学课后试验 7和17章.docx

C7.4(i)The two signs that are pretty clear are 3 0. The effect of size of graduating class is not clear. It is also unclear whether males and females have systematically different GPAs. We may think that 6 0, that is, athletes do worse than other students with comparable characteristics. But remember, we are controlling for ability to some degree with hsperc and sat.有两个系数是可以确定的，3 0（SAT考试，分数越高成绩越好）。班上的人数对colgpa的影响不明确。性别在colgpa的区别上也不明确。我们可以认为6 0 signals discrimination against minorities: a white person has a greater chance of having a loan approved, other relevant factorsfixed.如果其他的适当控制其他因素，1 0表示种族间有区别：在相关因素固定的情况下，一个白人更有可能获得贷款的批准。（ii）. reg approve whiteThe simple regression results are：approve = .708 + .201 white(.018) (.020)n = 1,989, R2 = .049.The coefficient on white means that, in the sample of 1,989 loan applications, an application submitted by a white application was 20.1% more likely to be approved than that of a nonwhite applicant. This is a practically large difference and the t statistic is about 10. (We have a large sample size, so standard errors are pretty small.)分析：white的系数说明在1989个贷款申请中，白人提交的申请被批准的可能性比非白人大20.1%。这是一个很大的区别，t=10.11，说明这个结果是显著具有统计意义的。（我们有很大的样本容量，所以标准误差非常小）（iii）. reg approve white hrat obrat loanprc unem male married dep sch cosign chist pubrec mortlat1 mortlat2 vrWhen we add the other explanatory variables as controls, we obtain 1 .129，se( 1) .020. The coefficient has fallen by some margin because we are now controlling for factors that should affect loan approval rates, and some of these clearly differ by race. (On average, white people have financial characteristics such as higher incomes and stronger credit histories that make them better loan risks.) But the race effect is still strong and very significant (t statistic 6.45).当我们加入其他解释变量作为对照，我们得到1 .129，1 .129，系数下降了一些因为我们现在控制了一些因素将会影响贷款批准率，其中一些明显具有种族差异性。（平均来说，白人们金融特性等高收入和较强的信用历史，这使得他们有更强的贷款偿还能力。）但种族的影响仍然是强有力的和非常显的（t6.45）。（iv）. gen wobrat=white*obrat. reg approve white hrat obrat loanprc unem male married dep sch cosign chist pubrec mortlat1 mortlat2 vr wobratWhen we add the interaction white*obrat to the regression, its coefficient and t statistic are about .0081 and 3.53, respectively. Therefore, there is an interactive effect: a white applicant is penalized less than a nonwhite applicant for having other obligations as a larger percent of income.当我们加入一个交互项wobrat，它的系数为0.0081，t=3.53，因此，这里有交互的影响：如果有一个大的债务收入百分比，白人申请人受罚比非白人申请人少。（v）. gen whobrat=white*(obrat-32). reg approve white hrat obrat loanprc unem male married dep sch cosign chist pubrec mortlat1 mortlat2 vr whobratThe trick should be familiar by now. Replace white*obrat with white*(obrat 32); the coefficient on white is now the race differential when obrat = 32. We obtain about .113 and se .020. So the 95% confidence interval is about .113 1.96(.020) or about .074 to .152. Clearly, this interval excludes zero, so at the average obrat there is evidence of discrimination (or, at least loan approval rates that differ by race for some other reason that is not captured by the control variables).诀窍应熟悉了。用white*（obrat-32）取代white*obrat；当obrat =32时，white的系数显示出种族差异。系数为0.113，se=0.02。因此，95%置信区间为.113 1.96(.020)，或 .074至 .152。显然，这一区间不包括零，所以obrat显著地有种族差异（或者，至少由于其他原因贷款批准率在种族上存在差异，通过控制变量没有发现的）。C7.12C17.8The file JTRAIN2.dta ontains data on a job training experiment for a group of men. Men could enter the program starting in January 1976 up through about mid-1977.The program ended in December 1977.The idea is to test whether participation in the job training program had an effect on unemployment probabilities and earnings in 1978. (i)The variable train is the job training indictor. How many men in the example participated in the job training program? What was the highest number of months a man actually participated in the program? (consider the variable mosinex). sum train if train=1. sum mosinexResults display :The number of the man in the example participated in the job training program is 185. The highest number of months a man actually participated in the program is 24.参加培训的男性为185，其中在培训中参加最久的是24个月。(ii)Run a linear regression of train on several demographic and pretraining variables:unem74,unem75,age,educ,black,hisp,and married. Are these variables jointly significant at the 5% level?. reg train unem74 unem75 age educ black hisp marriedThe F statistic for joint significance of the explanatory variables is F(7,437) = 1.43 with p-value = .19. Therefore, they are jointly insignificant at even the 5% level. Note that, even though we have estimated a linear probability model, the null hypothesis we are testing is that all slope coefficients are zero, and so there is no heteroskedasticity under H0. This means that the usual F statistic is asymptotically valid.F统计量的值为1.43，p值为0.19。因此，在5%的置信水平上联合显著。请注意，即使我们估计线性概率模型，我们测试的原假设是所有的系数为零，所以有没有 H0 下的异方差。这意味着通常 F 统计量渐近有效。 (iii)Estimate a probit version of the linear model in part(ii).Compute the likelihood ratio test for joint significance of all variables .What do you conclude?. probit train unem74 unem75 age educ black hisp marriedAfter estimating the modelby probit maximum likelihood, the likelihood ratio test for joint significance is 10.18. In a 72 distribution this gives p-value = .18, which is very similar to that obtained for the LPM in part (ii).Model：The results show：LR chi2(7) = 10.18 Prob chi2= 0.1785 It is very similar to that obtained for the LPM in part (ii).结果显示：LR chi2(7) = 10.18 Prob chi2= 0.1785，这个和第二题中LPM获得的非常相似。(iv) Run a simple regression of unem78 on train and report the results in equation form. What is the estimated effect of participating in the job training program on the probability of being unemployed in 1978? Is it statistically significant?. reg unem78 trainThe simple LPM results are：参加在职培训的在1978年失业率下降了0.111，或者说是11.1个百分点。这是很大的影响：没有参加培训的失业率为0.354，培训将失业率降低至0.243，这个差异在1%的双侧检验下是具有显著统计意义的。(v)Run a probit of unem78 on train .Does it make sense to compare the probit coefficient on train with the coefficient obtained from the linear model in part(v)?. probit unem78 trainThe estimated probit model is：Standard errors ：0.080，0.128. It does not make sense to compare the probit coefficient on train with the coefficient obtained from the linear model in part(v). Probability and LPM t statistics are essentially the same.将题目四的系数和这个模型的系数比较式没有意义的。需要注意的是，两个模型的t统计量基本上是相同的。 (vi)Find the fitted probabilities from parts(v) and (vi).Explain why they are identical.Which approach would you use to measure the effect and statistical significance of the job training program?. qui reg unem78 train. predict lhat(option xb assumed; fitted values). tabulate lhat. qui probit unem78 train. predict phat(option p assumed; Pr(unem78). tabulate phat (vii)Add all of the variables from part(ii) as additional controls to the models from parts(v) and (vi).Are the fitted probabilities now identical? What is the correlation between them? . qui reg unem78 train unem74 unem75 age educ black hisp married. predict l2hat(option xb assumed; fitted values).