Total 8 questions. Need to answer all these questions.
Answer all the questions. Show all numerical answers to 3 decimal places. Carry out all tests
using a 5% level of significance. You may include Stata outputs in your answers, but your
own interpretations and explanations are necessary for earning marks.
Questions
1. (4 pts) Fit an educational attainment function using your data set by regressing 𝑆 on
𝐴SVABC, 𝑆M, and 𝑆F. Interpret the regression results. Perform t tests on the coefficients of
the variables, and a F test of the explanatory power of the model.
2. (4 pts) Regress the logarithm of 𝐸ARNINGS on 𝑆, 𝐸XP, and 𝑀ALE. Interpret the regression
results. Perform t tests on the coefficients of the variables, and a F test of the explanatory
power of the model.
3. (3pts) Regress logarithm of 𝐸ARNINGS on 𝑆, 𝐸XP, 𝑀ALE, 𝐸THHISP, and 𝐸THBLACK.
Interpret the regression results and perform t tests on the coefficients.
4. (3 pts) Perform a F test of joint explanatory power of 𝐸THHISP and 𝐸THBLACK using 𝑅^2
and verify it is the same as the F statistic in your Stata output.
5. (2 pts) Relying on your findings in questions 3 and 4, are earnings subject to ethnic
discrimination?
6. (4 pts) Define a new variable as the product of 𝑀ALE and 𝑆, call it SLOPE. Regress the
logarithm of 𝐸𝐸ARNINGS on 𝑆, EXP, MALE, 𝐸𝐸THHISP, ETHBLACK, and 𝑆LOPE. 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, 𝐴SVABC, in the data set was constructed
as a weighted average of the scores of tests of arithmetic reasoning (𝐴𝐴SVABAR), word
knowledge (𝐴SVABWK), and paragraph comprehension, (𝐴SVABPC), with 𝐴SVABAR
being given double weight. Show mathematically that, when fitting the educational
attainment model based on the composite measure:
𝑆 = 𝛽1 𝛽2𝑆M 𝛽3𝑆F 𝛽4𝐴SVABC 𝑢
instead of the model based on the individual scores:
𝑆 = 𝛽1 𝛽2 𝛽3𝑆F 𝛾1𝐴𝐴SVABAR 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. (5 pts) Using the model based on the individual scores (the second model in the previous
question), test the restrictions that 𝛾1 = 𝛾2 = 𝛾3 = 0, and that 𝛾1 𝛾2 𝛾3 = 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.