ECMT1020: You will use a subset consisting of 500 observations of Educational Attainment and Wage Equations (EAWE) data set: Introduction to Econometrics Assignment, UoS, Singapore

Data Description

You will use a subset consisting of 500 observations of Educational Attainment and Wage Equations (EAWE) data set to answer the questions. The description of the data set and contained variables can be found in Appendix B on p.565–569 of the textbook (also provided in a separate pdf file).

Questions

1. (4 pts) Fit an educational attainment function using your data set by regressing 𝑆 on ASV ABC, and SM, SF. Interpret the regression results. Perform t-tests on the coefficients of the variables, and an F test of the explanatory power of the model.

2.  Regress the logarithm of EARNING on 𝑆, 𝐸xp, and MALE. Interpret the regression results. Perform t-tests on the coefficients of the variables, and an F test of the explanatory power of the model.

3. Regress logarithm of EARNING on 𝑆, 𝐸xp, and MALE, ETHHISP and ETHBLACK Interpret the regression results and perform t-tests on the coefficients.

4. Perform a F test of joint explanatory power of ETHHISP and ETHBLACK using residual sums of squares of the restricted and unrestricted models, and verify it is the same as the F statistic in your Stata output.

5. Relying on your findings in questions 3 and 4, are earnings subject to ethnic discrimination?

6.  Define a new variable as the product of EARNING on 𝑆, 𝐸xp, and MALE, ETHHISP and ETHBLACK 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? Explain.

7. (5 pts) The composite measure of cognitive ability, ASVAC, 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 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 being given double weight. Show mathematically that, when fitting the educational attainment model based on the composite measure:

S=b1+b2SM+B2SF+B4ASVABC+u
instead of the model based on the individual scores:

𝑆𝑆 = B1 + B2SM2 + B#SF + y1ASVABAR +Y2ASVABWK+ Y3ASVABPC + U

one is implicitly imposing the restrictions 𝛾𝛾1 = 2𝛾𝛾2 and 𝛾𝛾1 = 2𝛾𝛾3. Perform a test of these restrictions using your data set.

8. Using the model based on the individual scores (the second model in the previous question), test the restrictions that 𝛾𝛾1 = 𝛾𝛾2 = 𝛾𝛾3 = 0, and that 𝛾𝛾1 + 𝛾𝛾2 + 𝛾𝛾3 = 0 (note: these are two separate hypotheses). Intuitively, which of these two tests is more restrictive? Give a brief answer based on the (economic) intuition and the (statistical) results of these two tests