Answer Happy

You are asked to reproduce some of the results of the paper. Ashenfelther, O. and A. Krueger, "Estimates of the Economic Return to Schooling from a New Sample of Twins," American Economic Review, Vol. 84 (Dec., 1994): 1157-1173. The data used by Ashenfelter and Krueger is provided under the name: twins.dta. Refer to the article for explanations of the variables. Don't worry if your results are not exactly the same as those in the paper. They should be similar, but may not be exactly the same. This study was trying to answer what seems a simple question: By how much will another year of schooling most likely raise one's income? A difficulty in trying to estimate the causal effect of education on earnings from the effect that other variables related to education have on income. A worker's natural ability, his family background, and his innate intelligence are all possible confounding factors that must be controlled for to estimate the effect of education on income accurately. Because monozygotic twins are genetically identical and have similar family backgrounds, they are thought to provide good controls for confounding variables. Use the following commands to expand the data set and obtain one observation per twin. expand 2 sort famid by famid: gen t=_n gen lwage=lwagel if t==1 replace lwage=lwage2 if t==2 gen educ=educ1 if t==1 replace educ-educ2 if t=-2 gen male male1 if t==1 replace male male2 if t==2 gen white whitel if t==1 replace white-white2 if t==2

1. Run an OLS regression of a constant, schooling, age, age-squared, gender and racial indicators on log wages to obtain coefficients similar to those reported in Table 3, column (i). (a) Report your results. Interpret your estimate of the coefficient on education. For example, explain how much more individuals with one more year of education earn, on average. (b) Use the vce(cluster famid) option and the robust option in the regress command to adjust the standard errors. Report your results. Does the significance of the coefficients change? (c) What do the coefficients on age and age-squared imply about the life-cycle profile of earnings? 2. To help interpret whether this relationship estimated from OLS is causal, write out the omitted variables bias formula for the equation: In(w;) = a + 3S; +0Z₁ + E, (1) where w, is hourly wage, S, is schooling, and Z, is an unobserved variable related to schooling in the following way Z₁ = ASi + 1 (2) Can you interpret the relationship you find with OLS between schooling and earnings as causal? Why or why not? 3. Now create dummy variables for each level of schooling, using tab educ, gen (educdum) and run the above OLS regression with those education dummies instead of the educ variable, dropping the one for high school (educdum=4). (a) Report your results. (b) Briefly explain the difference between using the variable educ and using a bunch of dummy variables educdum's. (c) Do the estimated coefficients indicate that the effect of education on log wages is linear? 4. Now estimate a differenced equation by constructing the following variables: gen deduc-educ1-educ2 if t==1 gen dlwage=lwagel-lwage2 if t==1 gen dwhite whitel-white2 if t==1 regress dlwage deduc dwhite if t==1 (a) Why aren't we including controls for age and gender in the first difference equa- tion? (b) Report your results. Re-do the OLS, dropping the control variable dwhite. Com- pare the results to column (v) in Table 3 of the paper.