1. For a class project, you set out to analyze the effect of educational attainment on wages. You
interview a few people and obtain the following data:
Individual Education (years) Wage ($/hr)
A 10 5
B 12 6
C 12 8
D 14 10
E 16 10
F 21 16
(a) Graph the data, with wages on the y-axis and education on the x-axis.
(b) Write down the econometric model you would use to estimate the effects of an additional
year of education on the hourly wage.
(c) What is the interpretation of the two unknown parameters to be estimated? What is
the expected sign of the coefficient of education?
2. Recall the data from Question 1, the estimated regression equation is
wi = −4.63 + 0.97EDUCi
The standard errors are 1.66 and 0.11, respectively.
(a) What is the predicted wage of an individual with a high school diploma (i.e., 12 years
of schooling)?
(b) What is the predicted wage of an individual with a bachelor’s degree (i.e., 16 years of
schooling)?
(c) Does the model exactly predict the correct wage for any individual in the sample with
12 or 16 years of schooling? Does that mean the model is not useful?
1
3. Let us consider more carefully the determinants of wages. As an initial attempt to analyze
the effects of education on wages, you estimate the univariate model:
wi = α0 + α1EDUCi + εi
However, then someone points out to that some people are just “naturally” better workers
than others, regardless of schooling. After giving it some thought, you hypothesize that IQ
is a good measure of one’s “natural” ability. Thus, you consider an alternative multivariate
regression model of the form:
wi = α
0
0 + α
0
1EDUCi + α
0
2
IQi + ε
0
i
(a) What is the interpretation of α1 and α
0
1
.
(b) If it is the case that IQ has no effect on wage (in which case the two variables would be
said to be independent), how will α1 compare to α
0
1
?
(c) If it is the case that IQ has a positive effect on wage and IQ and education are uncorrelated
with each other, how will α1 compare to α
0
1
?
(d) If it is the case that IQ has a positive effect on wage and individuals with high IQ also
attend school longer on average, will α1 = α
0
1
. How do you think α1 will compare to α
0
1
?
4. Evaluate the following claim: “Under all situations, if there are omitted variables from a
regression equation which do in fact affect the variable the researcher is trying to explain,
then resulting estimates of the parameters are biased.
