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ECMT6007/6702: Econometric Applications Problem Set 9
发布时间：2022-11-18
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ECMT6007/6702: Econometric Applications
Problem Set 9
Semester 2 2022
Question 1. Computer Exercise: Estimating the Returns to Education
The data for this exercise nlsy13 .dta are taken from the published study by J.J. Heckman, J.L. Tobias, and E. Vytlacil (2003), ‘Simple Estimators for Treatment Parameters in a Latent-Variable Framework’, Review ofEconomics and Statistics, vol. 85, pp. 748–755. The sample is from the 1991 National Longitudinal Survey of Youth, and consists of males age 26 to 34.
(i) Run the simple regression model:
log (wage) = β0 + β1 educ + u (1)
Without controls for any other factors, what is the estimated return to another year of edu- cation? Is the return statistically significant (against a two-sided alternative at the 5% signifi- cance level?
(ii) Add to the model a quadratic in experience and a full set of regional controls for current
residence and residence at age 18:
log (wage) = β0 + β1 educ + β2 exper + β3 exper2 + β4 nc
+ β5 south + β6 west + β7 nc18 + β8 south18
+ β9 west18 + β10 urban + β11 urban18 + u (2) Report the estimation results β1 to β3 in a table. What is the 95% confidence interval for β1
(iii) A concern with estimating standard wage equations, such as (2), with the OLS estimator is omitted variable bias. Now consider CUFee – the change in university fees for students between ages 17 and 18 – as a potential instrumental variable for educ. (It has been used as an instrument in the literature because it is a related to the costs of university attendance but
is unrelated to individuals’ aptitude or ability).
Run the regression:
educ = δ0 + δ1CUFee + δ2 exper + δ3 exper2 + δ4 nc
+ δ5 south + δ6 west + δ7 nc18 + δ8 south18
+ δ9 west18 + δ10 urban + δ11 urban18 + v (3)
Keep the fitted values from this regression (in STATA use the predict command) for use in question (v) below). Is CUFee significantly related to educ at the 5% significance level (using a two-sided alternative)? What does this imply for instrument relevance?
(iv) As an additional check on the model, run the simple regression:
educ = δ0 + δ1 CUFee + v (4)
Test whether δ 1 is statistically significant at the 5% significance level (using a two-sided al- ternative). Does this have any implications for using CUFee as an instrumental variable for education? Explain your reasoning.
(v) Using the fitted value for education, e一duc, from the estimation of model (3) in (iii), estimate the following model:
log (wage) = β0 + β1 e一duc + β2 exper + β3 exper2 + β4 nc
+ β5 south + β6 west + β7 nc18 + β8 south18
+ β9 west18 + β10 urban + β11 urban18 + u (5)
Report the results for β1 to β3 in a table. What is the estimated return to education from this model?
(vi) The regression in (v) demonstrates 2SLS; however, we have not corrected the standard errors for the fact that our education variable is based on a regression. Re-estimate the model in (v) using the instrumental variables 2SLS estimator (in STATA use the ivregress 2sls command). Report the corrected standard errors for βˆ1 to βˆ3 in the table. Are they very different from the those estimated in part (v)? Discuss your answer.
(vii) From the estimates in (vi) construct the 95% confidence interval for β 1 . How does the IV confidence interval for β1 compare to that for the OLS confidence interval in part (ii)? Discuss
your answer.
(viii) The dataset is unusual in that it does contain a measure of ability (abil). One way to address
potential omitted variable bias with OLS is to include proxy variables. Use OLS to estimate the expanded model:
log (wage) = β0 + β1 educ + β2 exper + β3 exper2 + β4 nc
+ β5 south + β6 west + β7 nc18 + β8 south18
+ β9 west18 + β10 urban + β11 urban18 + β12 abil + u (6) What is the 95% confidence interval for β1 , and how does it compare to that in (ii) and (vii)?
(ix) Re-estimate the IV model by 2SLS with ability included as an extra exogenous variable. Report the 95% confidence interval for β 1 , and compare it to the answer in part (vii). Is there any important difference in the IV estimates of the return to education? Discuss your answer.
(x) Do you think the IV procedure, based on the use of CUFee as an instrumental variable, is convincing? Explain your reasoning.
Note: The nlsy13 .dta dataset can be downloaded from the course Canvas website. The dataset contains 976 observations and 14 variables. The variables correspond to:
• lwage: log (wage)
• educ: highest grade completed
• exper: years of labour market experience
• expersq : exper2
• nc: = 1 if live in north-central region (= 0 otherwise)
• south: = 1 if live in southern region (= 0 otherwise)
• west: = 1 if live in western region (= 0 otherwise)
• nc18: = 1 if live in north-central region at age 18.(= 0 otherwise)
• south18: = 1 if lived in southern region at age 18 (= 0 otherwise)
• west18: = 1 if lived in western region at age 18 (= 0 otherwise)
• urban: = 1 if live in an urban area (= 0 otherwise)
• urban18: = 1 if lived in an urban area at age 18 (= 0 otherwise)
• CUFees: change in University Student Fees between ages 18 and 17
• abil: ability measure, a general aptitude test score (not standardized)
