ECMT6002: Econometric Applications
School of Economics, University of Sydney
Semester 1, 2021
– Submit your typed answers to this assignment question on Canvas in a single
PDF file, by the beginning of class (6pm - Sydney time) on Monday, 10 May.
Attach a copy of your computer output (e.g. your STATA log) at the end of your
answers (as an appendix, not in a separate file).
– Please set the PDF file name as ECMT6002A2-SID, or ECMT6702A2-SID (for
students who take ECMT6702).
– Answer the question by yourself. Make sure you read, understood and comply with
the University of Sydney Academic Honesty in Coursework Policy 2015 and the
Academic Honesty Procedures 2016.
– Note: for hypothesis testing, present the complete hypothesis test, including null
and alternative hypotheses, test statistics and its distribution under the null, deci-
sion rule and conclusion.
1. We want to study whether and how a stronger presence of students affects rental rates.
Use the data in RENTAL for this assignment, which includes rental prices and other
variables for 64 college towns in the US for the years 1980 and 1990. The panel data
model with unobserved effects is:
log(rentit) = β0 + δ0y90t + β1log(popit) + β2log(avgincit) + β3pctstuit + αi + eit (1)
where pop is city population, avginc is average income, and pctstu is student population
as a percentage of city population (during the school semesters). (αi + eit) is the error
term, where αi is the unobserved heterogeneity, and eit represents idiosyncratic errors.
(a) Based on model (1), how do you interpret δ0, and why it should be included?
(b) Estimate model (1) by pooled OLS (POLS), and report the estimation results in
the usual format (that is, the estimated equation with standard errors in brackets
under the corresponding estimates). Are the standard errors valid? Explain briefly.
(c) Apply the first difference (FD) estimator to (1), and report the estimation results
in the usual format. Are the standard errors (without the robust option) valid?
(d) Now apply the fixed effect (FE) estimator to (1), and report the estimation results
in the usual format. How do the estimates and standard errors compare to those
(e) Apply the random effects (RE) estimator to (1), and report the estimation results
in the usual format.
(f) Put the results of all estimators above (POLS, FD, FE, and RE estimators) into
a table, one column for an estimator, with standard errors in brackets under the
corresponding estimates. If αi is a fixed effect, which estimators in the table are
consistent, and which are inconsistent? Explain briefly.
(g) Run the Wu-Hausman’s test to compare the FE to RE estimates. Remember to
state the null hypothesis and the alternative, the test statistics and its distribution
under the null, decision rule and conclusion. What can we learn from the test?
(h) Given the results by the POLS, FD, FE, RE estimators, and the test result in (g),
which estimator will you prefer? Provide brief arguments for your choice.
(i) Given the estimator you prefer in (h), how does the relative size of the student
population affect rental prices?
(j) We are concerned that the variable, avginc, could be endogenous (as the rental
revenue from students would boost the local average income). If we use the variable
enroll as the instrumental variable (IV) for avginc, what conditions must enroll
satisfy in order to be a valid IV? If a condition can be tested with the data, perform
the test (just run and report the test result).
Note: 10 points for each part, 100 in total.