Department of Economics
The University of Melbourne
ECOM30001/ECOM90001: Basic Econometrics
Semester 1, 2022
Assignment 2
Introduction
Researchers and policy makers are interested in the (statistical) relationship between a
worker’s level of education and the (hourly) wage that they receive. Consider the following
econometric model:
ln wagei = β0 + β1 educi + δXi + εi (1)
where X represents a full set of control variables that are important determinants of wages
and εi is a random error which is (approximately) normally distributed with ε ∼ N (0, σ2ε).
While it is expected that β1 > 0 such that more educated workers generally earn higher
wages (conditional upon other determinants of wages), you are ultimately interested in
magnitude of β1.
1
The data file assignment2.csv contains 2,008 observations on individuals currently aged
24-34 at the time of interview, which may be used to estimate the econometric model
(1). This data file contains the following variables
lnwage=Natural logarithm of hourly wage
educ=Years of completed education
exper=Years of labour market experience
expersq=Years of labour market experience squared
disadv=1 if live in a disadvantaged region, 0 otherwise
city=1 if live in a major city, 0 otherwise
The data file also provides some variables for these individuals ten years prior to interview:
city10= 1 if lived in a major city 10 years ago, 0 otherwise
regionj=1 if lived in region j 10 years ago, 0 otherwise, j = 1, 2, . . . 4
The data file also contains some information on the education of the individual’s parents:
meduc=Completed years of education of mother
feduc=Completed years of education of father
You will need to use the following packages to complete this assignment:
stargazer : for easily generating regression output
car : for easily conducting hypothesis tests in R
sandwich : for calculting robust standard errors in R
AER : for estimating linear models using the Instrumental Variable (IV) estimator in R
These can be installed directly in RStudio from the packages tab or by using the com-
mand install.packages() and inserting the name of the package in the brackets.
Note: You are required to complete this assignment using the R statistical software.
Please include a copy of your R script file with your assignment submission (for an
additional five (5) marks).
Please insert your full R script file as an Appendix attached to the end of your submitted
assignment. You only need to submit a single file for your assignment that contains both
your assignment answers and your R script file. Do not submit your R script file as
a separate file in Canvas.
2
a) [10 marks] Consider the following econometric model:
ln wagei = β0 + β1 educi + β2 experi + β3 expersq100i
+ β4 disadvi + β5 cityi
+ β6 city10i +
4∑
j=2
β7j regionji + εi (2)
where region1 (Region 1) is the omitted category.
Note that:
expersq100i =
expersqi
100
=
exper2i
100
i) [2 marks] What is the interpretation of the population parameter β1 in model
(2)?
ii) [2 marks] What is the interpretation of the population parameter β4 in model
(2)?
iii) [6 marks] Estimate the econometric model (2) by the method of Ordinary
Least Squares (OLS) with robust (Huber-White) standard errors. Us-
ing the car package and a 5% level of significance, test the hypothesis that
all the variables relating to the individual’s geographic location 10 years ago
are important determinants of wages. Your answer should clearly state the
null and alternative hypothesis, the distribution of the test statistic, and your
conclusion.
b) [6 marks] Consider an extended version of model (2) that includes the two (2)
variables for parental education (motheduc and fatheduc).
ln wagei = β0 + β1 educi + β2 experi + β3 expersq100i
+ β4 disadvi + β5 cityi
+ β6 city10i +
4∑
j=2
β7j regionji
+ β8 meduci + β9 feduci + εi (3)
where region1 (Region 1) is the omitted category.
Estimate the econometric model (3) by the method of Ordinary Least Squares
(OLS) with robust (Huber-White) standard errors. Using the car package
and a 5% level of significance, test the hypothesis that the parental education
variables are jointly important determinants of wages. Your answer should clearly
state the null and alternative hypothesis, the distribution of the test statistic, and
your conclusion. Note that model (2) is now the restricted model.
3
c) [4 marks] Consider the econometric model (3). Do you think the condition:
COV(educi, εi|Xi) = 0
is likely to be satisfied. Outline at least one possible reason why this condition
might not be satisfied. Clearly explain the consequences for the OLS estimator if
this condition is not satisfied.
d) [6 marks] The sample is derived from a large country with a large number of
universities, geographically dispersed across the country. Consider the following
indicator variable:
near

= 1 if, at age 14, individual lived in a local area
with a university nearby
= 0 otherwise
It is suggested that geographic proximity to a university is related to education
choices. Individuals that grew up in an area without a university face a higher cost
of education. In the presence of these higher costs, all else equal, these individuals
should acquire less education. Clearly, explain the two conditions that must be
satisfied for the variable near to be a valid instrumental variable. Do you think
these two conditions are likely to be satisfied? Clearly explain why or why not.
e) [9 marks] Clearly explain what is meant by the Weak Instruments problem. Ex-
plain the consequences for statistical inference using the Instrumental Variable es-
timator (IV) with weak instruments.
Estimate the following reduced form for educ, using the robust (Huber-White)
variance estimator:
educi = pi0 + pi1 neari + pi2 experi + pi3 expersq100i
+ pi4 disadvi + pi5 cityi
+ pi6 city10i +
4∑
j=2
pi7j regionji
+ pi8 motheduci + pi9 fatheduci + εi (4)
where region1 (Region 1) is the omitted category.
Based upon your estimation results for this reduced form, is there any evidence
that near is a weak instrument? Clearly explain why or why not.
4
f) [26 marks] Consider the structural econometric model:
ln wagei = β0 + β1 educi + β2 experi + β3 expersq100i
+ β4 disadvi + β5 cityi
+ β6 city10i +
4∑
j=2
β7j regionji
+ β8 meduci + β9 feduci + εi (5)
where region1 (Region 1) is the omitted category.
i) [1 mark] Estimate this structural model using the IV estimator with robust
(Huber-White) standard errors, treating educ as the only endogenous
variable, with near as an instrumental variable. Report the results.
ii) [6 marks] At the 5% level of significance, test the hypothesis that education
has a positive effect on labour market earnings. Your answer should clearly
state the null and alternative hypotheses, the distribution of the test statistic,
and your decision.
iii) [6 marks] Using the car package and a 5% level of significance, test the
hypothesis that all the parental education variables are jointly important de-
terminants of wages. Your answer should clearly state the null and alternative
hypothesis, the distribution of the test statistic, and your conclusion.
iv) [2 marks] Compare and contrast your estimate for β1 and its standard error
in model (5) to that obtained for model (3) in part (b), estimated using the
OLS estimator.
v) [4 marks] When COV(educi, εi|Xi) 6= 0, the OLS estimator in model (3)
will not be consistent. Moreover, provided near is a valid instrument, the IV
estimator for β1 in model (5) will provide a consistent estimator for the causal
effect of education upon labour market earnings. Comparing your estimates for
β1 using the IV estimator, with those obtained using the OLS estimator (part
b), provide and explain a possible source generating COV(educi, εi|Xi) 6= 0 in
model (3).
vi) [7 marks] Using your estimates for model (5), calculate the marginal (partial)
effect for years of labour market experience, evaluated separately for 5 years,
10 years, 15 years, 20 years, 25 years, and 30 years of labour market experi-
ence. At a 5% level of significance, test the null hypothesis that, at 5 years
of experience, an additional year of labour market experience raises average
wages by at least 3.50%, all else equal.
5