Homework 3
Draft (updated Aug 4, 2013)
Using the March, 2000 CPS we are all familiar with.
1) We are going to reanalyze the influence of
Fill in the following Table with the relevant regression output.
Use the following style for filling in the table:
regression coefficient
(standard error)
[Tstatistic with Asterisks indicating statistical significance, if appropriate see note below table]
So, a coefficient of 3.2 with a std error of 1.5 and a resulting Tstatistic of 2.1, yielding a twotailed P of just under 0.05 would look like this:
3.2
(1.5)
[2.1*]
All models are Ordinary Least Square regression models (ie
Stata regress) predicting incwage
for adults age 2564. For the

Model 1 
Model 2 
Model 3 
Model 4 
Model 5 
Model 6 














vietnam veteran 
dummy var for vietnam veteran status 
dummy var for vietnam veteran status 
dummy var for vietnam veteran status 
dummy var for vietnam veteran status 
dummy var for vietnam veteran status 
dummy var for vietnam veteran status 
sex (specify which gender you are comparing to which) 

sex 
sex 
sex 
sex 
sex 
age 


age 
age 
age 
age 
age squared 



age squared 
age squared 
age squared 
years of education (yrsed) 




years of education 
years of education 
Your control variable 1 





1 or 2 other variables that you think are appropriate controls (explain why) 
Your control variable 2 













Constant 













Unweighted N 






Rsquare 






Fstat comparison with previous model (Soc 381) 






Adjusted Rsquare 






* P< .05
** P< .01
*** P<.001, two tailed tests
2) Questions:
a) Was there an advantage in the 1999 labor market to being a vietnam veteran? How sure are we that Vietnam veteran status made a difference in individual income in 1999? Justify your answer by reference to the filledout table above.
b) Which are the control variables that seem to make the most difference to the income contrast between Vietnam veterans and others?
c) Which model fits the best by the adjusted Rsquare?
d) How do you interpret the constant in Model 1, and how do you interpret the constant term in the subsequent models? Why is the meaning of the constant more relevant in Models 1 and 2 than in models 36 (in other words, why does the constant term correspond to the real income of a relevant subset in models 1 and 2, but not in models 36)?
e) Across these 6 models, which coefficient has the largest Tscore in absolute value (ignore the constant term)? How would you interpret the magnitude of this Tstatistic?
f) Why is the age coefficient insignificant in Model 3, but significant in Model 4? For all the models with age and agesquared, determine the age at which predicted income is highest.
g) How do you interpret the coefficient for Vietnam veteran status in Model 1, and in Model 5?
h) How do you interpret the
coefficient for years of education in Model 5? Compare the
i) Explain your choice of one or two additional control variables for Model 6. Explain the coefficients for these variables, and explain their effect (if any) on the coefficient for Vietnam veteran status.
j) Why do models 2 and 3 have adjusted Rsquare that is so similar?
k) Do women get the same income benefit from education that men get? Create a new model to answer this question, starting with model 5, and report the results and explain them. How much of an income benefit do women get for each additional year of education, and how much income benefit do men get for each additional year of education?
3) (For Soc 381 only) Use the formula (in my “notes on mean and variance” to generate the Fstatistic for the comparison of the Rsquare for each successive model (i.e. comparing model 2 to model 1, then model 3 to model 2, etc) including the degrees of freedom, the statistic, and P value of this statistic. Report as F_{ }(df1, df2)= value, (P=…). Explain the meaning of the Fstatistics, what null hypotheses are accepted or rejected.
4) (For Soc 381
only) For this problem I want you to recreate Model 5 of problem 1 above, but
with a variety of different ways of estimating the model, and with different
assumptions about the weights. In this table, enter the weights, the standard
errors, and the Tstatistics or Zscores that go with each model. For model 5d,
run the regression with the option,
vce(bootstrap, reps(100)). For Model 5e, use the stata command glm
instead of regress, and use the options, family(gaussian)
link(identity).

Model 5 
Model 5b 
Model 5c 
Model 5d 
Model 5e 
Notes: 
just as in model 1, above 
with pweight instead of aweight 
without weights 
Without weights, and with bootstrap standard errors 
without weights and with Likelihood Maximization rather than OLS 






vietnam veteran (dummy var) 





Female (dummy var) 





age 





age squared 





years of education 











Constant 











Unweighted N 





Rsquare 





4a) How do the models above differ, substantively, and in their coefficients and standard errors? Comment on the differences and similarities.
4b) If you run Model 5d a second time, do you get the same standard errors answers? Why?
4c) Model 5e and model 5c coefficients are arrived at in different ways: Model 5c, using the Stata command regress derives its results via OLS, Ordinary Least Squares. Model 5e is fit iteratively using a method of maximum likelihood. Can you guess why Model 5e and Model 5c are so similar?