sociology 362
data exercise 2
For this exercise you will use the Wooldridge data file Cps78 85.raw. You will be doing regressions of the
form:
regress lwage educ
regress lwage exper
regress lwage educ exper
where the variables are log wage, years of schooling and years of experience. You will also need to run
some auxiliary regressions.
In the notation that follows, I sometimes will use y,sand xto stand for lwage, schooling and experience.
least-squares estimation: simple vs multiple regression
1. A researcher is interested in the effect of years of schooling (s) and labor force experience (x) on hourly
wage (lwage). Do the simple regressions lwage =f(s) and lwage =f(x). Judging from these results,
what do you conclude about the direction, magnitude, signficance of the “effects” of schooling and
experience on hourly wage?
2. The researcher wants to run a multiple regression of the form lwage =f(s, x). Is this a good idea, is it
necessary? Explain. What statistic(s) might you look at to determine this before you actually run the
regression?
3. Run the multiple regression. What does this show about the effects of schooling and experience?
What light does it cast on the results of the simple regressions? In particular:
a. Explain the change in the coefficient of sbetween the simple regression and the multiple regression.
Use Stata to generate the numbers you need to exactly and numerically account for the difference
between the simple regression coefficient of sand the partial regression coefficient, i.e., ˆ
βys −ˆ
βys.x.
b. Account for the change in the coefficient of x.
c. The partial regression coefficient of, say, schooling, ˆ
βys.x gives the “effect’ of a year of schooling on
lwage after removing from schooling (i.e., s) its linear relationship with experience. Use Stata to
demonstrate this.
d. Given the results of the multiple regression, what can be said about the bias in the estimate of the
effect of schooling on hourly wage yielded by the simple regression you started with, namely,
lwage =f(s) ?
4. Let’s think now about the changes in the standard errors of the coefficients as we move from the
simple regressions to the multiple regression. Describe these changes and explain in general terms what
accounts for them. In particular:
a. Account exactly and numerically for the change in the estimated variance and thus standard error of
the educ coefficient. Use Stata to generate the numbers you need to identify the effects on the standard
error of changes in the mean square residual and changes in the relevant variation in educ as one moves
from the simple to multiple regression.
b. Do the same for exper.
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