Tentin päivämäärä / Date of exam: 16.12.2014
Opintojakson koodi, nimi ja tentin numero / The code and the name of the course and number of the exam:
721066S Principles of Econometrics (1)
Tentaattori(t)/ Examiner(s): Sanna Huikari
Sallitut apuvälineet / The devices allowed in the exam:
x Laskin (ei graafinen/ohjelmoitava)/Calculator (not graphic, programmable) x Sanakirja/Dictionary
□ Muu materiaali, tarkennettu alla/Other material, specified below
Tenttiin vastaaminen / Please answer the questions
x suomeksi/ in Finnish
Kysymyspaperi on palautettava / Paper with exam questions must be returned:
x englanniksi/ in English
□ Kyllä/Yes
x Ei/No
1. Shortly answer or define. (8 p.)
a) Explain the difference between an estimator and an estimate. Provide an example of each.
b) What role does the law of large numbers and the central limit theorem play in econometrics?
c) The least squares assumptions in the multiple regression model.
d) Binary variable.
2. Internal and external validity (6 p.)
a) When a study is internally valid? Externally valid?
b) What kinds of threats there are to internal and external validity, and what are the consequences
if these threats occur in a study?
3. (16 p.) Each month the Bureau of Labor Statistics in the U.S. Department of Labor conducts the
“Current Population Survey” (CPS), which provides data on labor force characteristics of the
population, including the level of employment, unemployment, and earnings. Approximately
65,000 randomly selected U.S. households are surveyed each month. The data used in here is a
random sample of 7711 respondents from 2008. These data are for full-time, full-year workers,
age 25-34, with a high school diploma or B.A. as their highest degree.
Table 1 contains results from six estimated regressions. The dependent variable in regressions (1)
and (2) is average hourly earnings (AHE) and in regressions (3)-(6) its logarithmic transformation.
All estimations were made by using the heteroskedasticity-robust standard errors. The values of
standard errors are presented in the table in parentheses below the estimates. The variables are:
Name
AHE
Age
Female
Bachelor
Description
Average Hourly Earnings in $s
Age of respondent in years
1 if female; 0 if male
1 if worker has a bachelor’s degree; 0 if worker has a high school degree
Remember to validate your answers!
a) According to results from regression (1), how much do earnings increase as workers age
increases by 1 year? Is the estimated regression slope coefficient statistically significant at the
5% significance level? Does age account a large fraction of the variance in earnings across
individuals?
b) According to results from regression (2), what is the estimated effect of Age on earnings? Are the
results substantively different from the results in (1) regarding the effects of Age on AHE? Does
the regression in (1) seem to suffer from omitted variable bias?
c) Bob is a 26-year-old male worker with a high school diploma. Predict Bob’s earnings using the
estimated regression (2). Alexis is a 30-year-old female worker with a bachelor’s degree. Predict
Alexis’s earnings using the same regression (2).
d) Compare the fit of the regression (1) and (2) using the regression standard errors (SER) and the
coefficient of determination R2.
e) Are gender and education determinants of earnings according to regression (2)?
f) According to results from regression (4), if age increases from 25 to 26, how are earnings
expected to change? If age increases from 33 to 34, how are earnings expected to change?
g) What does the coefficient on the interaction term Female x Bachelor in regression (5) measure?
Alexis is a 30-year-old female worker with a bachelor’s degree. What does the regression (5)
predict for her value of ln(AHE)?
h) According to results from regression (6), is the effect of age on earnings different for men than
for women?
2
Table 1. Regression results.
(1)
(2)
AHE
0.60
(0.04)
AHE
0.585
(0.037)
(3)
(4)
(5)
(6)
ln(AHE)
0.081
(0.043)
ln(AHE)
0.081
(0.043)
ln(AHE)
0.124
(0.06)
0.00091
(0.00073)
0.00091
(0.00073)
0.0015
(0.0010)
Dependent Variable
Explanatory Variables
Age
ln(AHE)
0.027
(0.002)
Age2
Female  Age
0.088
(0.087)
Female  Age2
0.0012
(0.0015)
Bachelor  Age
Bachelor  Age2
Female

Bachelor
3.66
(0.21)
0.19
(0.01)
0.19
(0.01)
0.22
(0.02)
1.31
(1.27)
8.08
(0.21)
0.43
(0.01)
0.43
(0.01)
0.40
(0.02)
0.40
(0.01)
0.069
(0.022)
0.068
(0.021)
1.09
(0.64)
1.10
(0.63)
0.36
(0.87)
109.8
(0.00)
111.13
(0.00)
59.49
(0.00)
Female  Bachelor
Intercept


0.64
(1.08)
1.88
(0.06)
F-statistic on joint hypotheses (p-values in parentheses)
(a) F-statistic on terms
involving Age
(b) Interaction terms
with Age and Age2
10.79
(0.00)
SER
9.99
9.07
0.47
0.47
0.47
0.47
2
0.03
0.20
0.20
0.20
0.20
0.20
R
3