# How much sample variation in educ is explained by parents education?

Use the data in HTV.dta to answer this equation. The data set includes information on wages ed Show more Use the data in HTV.dta to answer this equation. The data set includes information on wages education parents education and several other variables for 1230 working men in 1991. (i) What is the range of the educ variable in the sample? What percentage of men completed 12th grade but not higher grade? Do the men or their parents have on average higher levels of education. (ii) Estimate the regression model ???????? = ??0 +??1??????????????? +??2??????????????? +?? by OLS and report the results in the usual form. How much sample variation in educ is explained by parents education? Interpret the coefficient on motheduc. (iii) Add the variable abil (a measure of cognitive ability) to the regression from part (ii) and report the results in equation form. Does ability help to explain variations in education even after controlling for parents education? Explain. (iv) (Review pp. 710-712 Appendix A before answering this part) Now estimate an equation where abil appears in quadratic form: ???????? = ??0 +??1??????????????? +??2??????????????? +??3???????? +??4????????2 +?? Using the estimates ??? 3 and ??? 4 use calculus to find the value of abil call it abil* where educ is minimized. (The other coefficients and values of parents education variables have no effect; we are holding parents education fixed.) Notice that abil is measure so that negative values are permissible. You might also verify that the second derivative is positive so that you do indeed have a minimum. (v) Argue that only a small fraction of men in the sample have ability less than the value calculated in part (iv). Why is this important? (vi) Use the estimates in part (iv) to graph the relationship between the predicted education and abil. Let motheduc and fatheduc have their average values in the sample 12.18 and 12.45 respectively. Note: I recommend you try doing this using STATA or MS Excel. HTV.DES wage abil educ ne nc west south exper motheduc fatheduc brkhme14 sibs urban ne18 nc18 south18 west18 urban18 tuit17 tuit18 lwage expersq ctuit Obs: 1230 1. wage hourly wage 1991 2. abil abil. measure not standardized 3. educ highest grade completed by 1991 4. ne =1 if in northeast 1991 5. nc =1 if in nrthcntrl 1991 6. west =1 if in west 1991 7. south =1 if in south 1991 8. exper potential experience 9. motheduc highest grade mother 10. fatheduc highest grade father 11. brkhme14 =1 if broken home age 14 12. sibs number of siblings 13. urban =1 if in urban area 1991 14. ne18 =1 if in NE age 18 15. nc18 =1 if in NC age 18 16. south18 =1 if in south age 18 17. west18 =1 if in west age 18 18. urban18 =1 if in urban area age 18 19. tuit17 college tuition age 17 20. tuit18 college tuition age 18 21. lwage log(wage) 22. expersq exper^2 23. ctuit tuit18 tuit17 Show less

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