ECMT1020: Fit an Educational Attainment Function Using your Data set Regress S on ASVABC, SM and SF: Introduction to Econometrics Essay, UoS, Singapore

Questions

1. Fit an educational attainment function using your data set. Regress S on ASVABC, SM and SF, and interpret the regression results. Perform t tests on the coefficients of the variables in the education attainment function.

2. Perform a F test of the explanatory power of the equation you obtained in Question 1. Calculate the F statistic using R2 and verify it is the same as the F statistic in your Stata output.

3. Regress the logarithm of EARNINGS on S and EXP. Interpret the regression results, perform t tests on the coefficients and F test of the explanatory power of the model.

4. Regress logarithm of EARNINGS on S, EXP, MALE, ETHHISP and ETHBLACK. Interpret the regression results and perform t tests on the coefficients. Are earnings subject to ethnic discrimination?

5. Redo Question 4 making ETHBLACK the reference category. What are the impacts of change of reference on the interpretation of the coefficients and the statistical tests (t tests of the coefficients and F test of the model)?

6. Define a slope dummy variable as the product of MALE and S. Regress the logarithm of EARNINGS on S, EXP, ETHHISP, ETHBLACK, MALE, and the slope dummy variable. Interpret the equation and perform appropriate statistical tests (t tests of the coefficients and F test of the model). Is the effect of education on earnings different for males and females?

7. The composite measure of cognitive ability, ASVABC, in the data set was constructed as a weighted average of the scores of tests of arithmetic reasoning, ASVABAR, word knowledge, ASVABWK, and paragraph comprehension, ASVABPC, with ASVABAR being given double weight. Show mathematically that, when fitting the educational attainment function

S = β1 + β2SM + β3SF + β4ASVABC + u

instead of the model using the individual scores

S = β1 + β2SM + β3SF + γ1ASVABAR + γ2ASVABWK + γ3ASVABPC + u,

one is implicitly imposing the restrictions γ1 = 2γ2 and γ1 = 2γ3. Perform a test of these restrictions using your data set.

8. Fit a wage equation with EARNINGS as the dependent variable and S, EXP and MALE as the explanatory variables. Perform a Goldfeld-Quandt test for heteroskedasticity in the S dimension.

9. Fit a wage equation using the same specification as in Question 8. Perform a White test for heteroskedasticity.

10. Perform an OLS regression of the logarithm of hourly earnings on S, EXP, ASVABC, MALE, ETHBLACK and ETHHISP using your data set and an IV regression using SM, SF, and SIBLINGS as instruments for ASVABC. Perform a Durbin-Wu-Hausman test to evaluate whether ASVABC appears to be subject to measurement error.