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ECMT6007/6702: Econometric Applications Problem Set 8
发布时间：2022-11-18
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ECMT6007/6702: Econometric Applications
Problem Set 8
Semester 2 2022
Question 1.
Let grad be a dummy variable for whether a student-athlete at a large university graduates within 5 years of initial enrolment. Let hsATAR be the student’s high school ATAR rank, and let study be the number of hours spent per week in an organised study workshop. Suppose that, using data on a sample of 420 student-athletes, the following logit model estimates are obtained:
P (grad = 1—|hsATAR, study) = Λ (−1.17 + 1.9 hsATAR + 0.073 study)
where Λ (z) = exp (z) / [1 + exp (z)] is the logit function. Holding hsATAR fixed at 0.75;
(i) Calculate the estimated difference in graduation probability for someone who spent 10 hours per week in the study workshop and someone who spent 5 hours per week?
(ii) What is the difference in the graduation probability for someone who spends 0 hours in the
study workshop compared to someone who spent 5 hours per week?
Question 2. Computer Exercise: Women in the labour force
We will use the data in mroz11 .dta for this exercise. This dataset has been analysed in many studies of married women’s labour supply decision. The binary variable inlf equal to 1 if the woman is in the labour force, and is 0 otherwise. The human capital model, based on standard microeconomic theory, provides a framework for studying labour supply choices.
(i) Estimate the Linear Probability Model (LPM):
P (inlf = 1 | x) = β0 + β1 nwifeinc + β2 educ + β3 exper
+ β4 expersq + β5 age + β6 kidslt6 + β7 kidsge6 + u (1)
and report the results (coefficient estimates, usual standard errors, and R2) in a table.
(ii) What is the interpretation of β2 ? Is the estimated value of β2 practically (i.e. economically) significant?
(iii) Estimate the Probit model of the determinants of P (inlf = 1 | x):
(
+ β4 expersq + β5 age + β6 kidslt6 + β7 kidsge6) (2)
and report the results (coefficient estimates, standard errors, 
2 , and LLF) alongside the LPM estimates.
(iv) What is the interpretation of β2 in this model? Is it comparable to the estimate for the LPM in (1)?
(v) What is the average value in the sample for P (in—lf=1 | x) based on the estimation of (2)? [Hint: in STATA, use the command margins, grand]
(vi) Compute the marginal effects for the explanatory variables in the Probit model (2), and report them, along with their associated standard error, in the table of results.
(vii) What is the interpretation of the marginal effect for educ from the Probit model? Is this
marginal effect statistically significant at the 1% level? Is the value of the marginal effect comparable to that for the LPM? Explain.
(viii) Test whether the number of infant and older children is statistically significant in determining
women’s labour force participation using a 1% significance level. That is, use the Likelihood Ratio Test to test the null hypothesis H0 : β6 = 0, β7 = 0.
Note: The mroz11 .dta dataset can be downloaded from the course Canvas website. The dataset has 753 observations and 10 variables. The variables correspond to:
• inlf : = 1 if in the labour force (0 otherwise)
• nwifeinc: non-labour income
• educ: years of formal education
• exper: years of actual labour market experience
• expersq : = exper2
• age: age in years
• kidslt6: numbers of kids aged less than 6 years
• kidsge6: number of kids aged 6-18 years
• unem: unemployment rate in local area of residence
• lnwage: log(wage)
