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ECOM30002/90002 Econometrics 2
Group Assignment 3
Submission method: Electronically via the LMS
Weight: 7.5%
Material covered: Mainly Lectures 1–16 & Tutorials 1–8
Instructions
Group size: Minimum = 1, maximum = 4. Groups may be formed across different tutorials.
Group registration: If you plan to work in a group of 2–4 students, then you must register the
membership of your group prior to submission using the ECOM30002 A3 Group tab in the People
area on the LMS. If you plan to complete the assignment individually, you can ignore this step.
Further instructions for group registration as well as the deadline for group registration will be
announced via the LMS.
Cover page: Each assignment must include a cover page listing the full name of every member
of the group along with their student ID and the name of their tutor.
Division of marks: Equal marks will be awarded to each member of a group.
Word processing: Assignments should be submitted as fully-typed documents in PDF or Word
format. Question numbers should be clearly indicated.
Statistical output: Raw R output and/or screenshots are not acceptable. Regression output
must be presented in clearly labelled equation or table form. Figures should be presented on an
appropriate scale, labelled clearly (including axes) and with an appropriate heading. Marks may
be deducted for failure to meet any of these requirements.
Length of answers: The word limit for this assignment is 600 words. Penalties may apply for
submissions exceeding this limit by 20% or more. Concise and correct answers to questions requir-
ing interpretation/discussion will be valued over more lengthy unclear and/or off-topic attempts.
R script: You must append a complete copy of the R script that you have used to generate your
results. Your R script does not count towards the word limit.
1
Section 1: Conceptual Questions (30 marks)
(1.1) Consider a balanced panel dataset on fatalities from road traffic accidents for n = 51 US
states (including Washington D.C.), with data for each of the T = 8 years from 1990-1997.
States are indexed by i = 1, 2, . . . , n and years by t = 1, 2, . . . , T . The policy question of
interest is whether the rate of seatbelt usage has any effect on the rate of road fatalities. The
variables in the dataset are defined as follows:
FRatei,t number of road fatalities per million traffic miles
SBUsei,t seatbelt usage rate, in percent
Speed65i,t binary variable: 1 for 65 mile per hour speed limit, 0 otherwise
Speed70i,t binary variable: 1 for 70 mile per hour speed limit, 0 otherwise
BA08i,t binary variable: 1 for blood alcohol limit ≤ 0.08%, 0 otherwise
Incomei,t median per capita income, in US dollars
Agei,t mean age, in years
The following model is estimated using data only from the first and last years of the dataset:
(A) A model in differences estimated by OLS, where each variable is transformed by taking
the change in its value from 1990 to 1997 (e.g. ∆FRatei = FRatei,1997 − FRatei,1990):
∆FRatei = β0 + β1∆SBUsei + β2∆Speed65i + β3∆Speed70i
+ β4∆BA08i + β5∆ log(Incomei) + β6∆Agei + Ui
The following four models are estimated using the entire dataset:
(B) A pooled model estimated by OLS:
FRatei,t = β0 + β1SBUsei,t + β2Speed65i,t + β3Speed70i,t
+ β4BA08i,t + β5 log(Incomei,t) + β6Agei,t + Ui,t
(C) A model with state fixed effects estimated using the within estimator:
FRatei,t = αi + β1SBUsei,t + β2Speed65i,t + β3Speed70i,t
+ β4BA08i,t + β5 log(Incomei,t) + β6Agei,t + Ui,t
(D) A model with time fixed effects estimated using the within estimator:
FRatei,t = λt + β1SBUsei,t + β2Speed65i,t + β3Speed70i,t
+ β4BA08i,t + β5 log(Incomei,t) + β6Agei,t + Ui,t
(E) A model with state and time fixed effects estimated using the within estimator:
FRatei,t = αi + λt + β1SBUsei,t + β2Speed65i,t + β3Speed70i,t
+ β4BA08i,t + β5 log(Incomei,t) + β6Agei,t + Ui,t
Table 1.1 presents the coefficient estimate βˆ1 from all five models, along with its standard
error and the p-value for a two-sided test of the statistical significance of the seatbelt usage
rate. For this question, we do not concern ourselves with the issue of heteroskedasticity,
because we have not yet covered robust standard errors for panel data models.
2
Table 1.1 Estimation Results for Question 1.1
Model βˆ1 Std. Error p-value
(A) -0.008 0.004 0.085
(B) 0.014 0.002 0.000
(C) -0.007 0.001 0.000
(D) 0.015 0.002 0.000
(E) -0.004 0.001 0.008
(a.) Marks Available: 1
What is the benefit of expressing the number of road fatalities relative to mileage trav-
elled, as opposed to working with the raw number of road fatalities?
(b.) Marks Available: 5
Interpret the sign, magnitude and significance of the estimates of β1 from models (A)
and (C) using Table 1.1. Conceptually, do you expect the estimate of β1 from model
(A) to be identical to the estimate from model (C) in this case? Explain your answer.
(c.) Marks Available: 4
Explain the reasons for the difference between the estimates of β1 obtained from models
(B) and (C). Which estimate do you think is likely to be closer to the actual effect of
seatbelt usage rates on road fatalities? Explain your answer.
(d.) Marks Available: 4
Based on the information reported in Table 1.1, do you believe that state-invariant but
time-varying omitted variables generate omitted variables bias in the estimate of β1
obtained from Model (C)? Explain your answer.
(e.) Marks Available: 5
By virtue of the within transformation, the values of the state fixed effects are not
estimated in Model (C). They can, however, be estimated using an OLS regression of
FRatei,t on SBUsei,t, Speed65i,t, Speed70i,t, BA08i,t, log(Incomei,t) and Agei,t, as well as
a separate dummy variable for each state in the panel, having excluded the intercept
term.
Point estimates of the state fixed effects obtained in this way are presented as a barchart
in Figure 1.1. Briefly interpret the reported values of the state fixed effects for Wisconsin
(WI), Mississippi (MS) and North Dakota (ND). Explain why care should be taken when
interpreting the values of the state fixed effects reported in Figure 1.1.
(f.) Marks Available: 2
Below is a statement that is true for one or more of Models (A) to (E). Identify the
model or models to which this statement applies and explain your reasoning:
The estimate of β1 controls for state-invariant,
time-varying omitted variables.