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THE UNIVERSITY OF EDINBURGH
SCHOOL OF ECONOMICS
Essentials of Econometrics
ECNM10052
br> Exam Date: From and To: Exam Diet:
12 December 2020 13:00 – 15:00 December 2020

Please read full instructions before commencing writing
Exam paper information
• Total number of pages: 11 (including this page).
• Please answer THREE out of the four questions.
• Each question is equally weighted.
• Relevant Statistical Tables are included at the end of the paper on pages 8-11
Special instructions
• This is an open-book exam.
• You must start EACH QUESTION on a separate page. Questions must be clearly
numbered in the left margin.
• You are expected to complete this exam within the 2-hour standard exam
duration.
• You have one additional hour immediately following the exam to scan and upload
your answers to Learn.
• You must number each answer page.
• Your exam number (e.g. B123456) must be clearly written at the top of each page.
• Your answers must be clearly written in ink on lined paper.
• Answers will be subject to checks through TurnItIn.
• All work must be completed individually, without collaboration, as a standard
exam would be.
Special items
• None.
Examiners: Dr Tim Worrall (Chair), Prof. Nigar Hashimzade (External)

This examination will be marked anonymously
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PLEASE ANSWER THREE OUT OF THE FOUR QUESTIONS:


1. Earnings functions are one of the most investigated relationships in Economics. These
typically relate the logarithm of earnings to a series of explanatory variables such as
education, age, gender, among others.
i. Why, in your view, have the researchers preferred a log-linear specification over a
linear specification? What problems would this log-linear specification overcome?
ii. You are particularly interested in the relationship between earnings and age. Using
the labour force survey, you estimate two specifications, a linear and a log-linear
one. Earnings are weekly earnings measured in pounds and Age is measured in
years.
Results are reported in Table 1.


Interpret each regression carefully. Should you choose the second specification on
grounds of the higher regression R2?
iii. Research has shown that age-earning profiles typically take on an inverted U-
shape. To test this idea in your data, you add the square of age to your log-linear
regression.
Results are reported in Table 1B.

Page 3 of 12



Interpret the results again. Are there strong reasons to assume that this specification is
superior to the previous one? Why is the increase of the Age coefficient so large
relative to its value in question (ii)?
iv. To explore the age-earning profiles further, you next decide to allow the regression
line to differ for the below and above 40 years age category. Accordingly you
create a binary variable, D40age, that takes the value one for age 40 and below,
and is zero otherwise.
Estimating the earnings equation results in the following output reported in Table 1C.




Sketch both regression lines on the same graph: one for the age category 40 years and
under, and one for over 40. Does the negative sign of the coefficient on Age make
sense? Predict the ln(earnings) for a 30 year old and a 50 year old. What is the
percentage difference between these two?
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2. In the United States, approximately 25% of fatal highway crashes involve a driver who had
been drinking. Given this number, you would like to examine how effective various
government policies designed to discourage drunk driving are in reducing traffic deaths.
Specifically, you want to investigate the effect of alcohol taxes on traffic fatalities. You get
access to panel data from the United States for each of the 48 contiguous states over the
period 1982-88.
Your baseline regression is as follows:

FatalityRateit = β1BeerTaxit + uit

where i represents states and t represents years. FatalityRateit refers to the number of annual
traffic deaths per 10,000 in state i at time t. BeerTaxit refers to the a unit-tax measured in
dollars per case (inflation adjusted) in state i at time t. You estimate your baseline
regression as well as a regression that allows for time fixed effects and/or state fixed
effects. That is:
FatalityRateit = β1BeerTaxit + αi + λt + uit

where αi denotes a state fixed effect and λt denotes time fixed effects.
Table 1 below reports the OLS estimates of these models.




i. Column (1) contains the results from a regression of traffic fatalities on alcohol
taxes. Why would we not want to use the results from column (1) to inform policy
decisions with regards to improving traffic safety?
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ii. Column (2) adds in state fixed effects by using state dummy variables. Column (3)
adds time fixed effects by adding in time dummy variables. Column (4) adds in
both state and time fixed effects dummies. How many right-hand side variables are
included in each of these three regressions (not including the intercept)? Interpret
the values of the estimate of β1 in each specification. Give an example of a factor
controlled for (or captured) by the state fixed effects and the time fixed effects.
iii. Why would the standard errors given in Table 1 not be valid? What solutions do
you propose?
iv. Should we be concerned that the results in column (4) suffer from omitted variable
bias?
































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3. A very large literature has investigated whether education is a good investment or not. A
common way to study this question is to regress the logarithm of wages on completed years
of education. That is:
log(wagesi) = β0 + β1Edui + β2Femalei + ui (1)

where log(wagesi) is the logarithm of wages for individual i, Edui is the completed years of
education of individual i and Femalei is a variable that takes value 1 for women and 0 for
men. The coefficient β1 can be interpreted as a measure of the rate of return on investment in
human capital. OLS estimates suggest that this coefficient is around 8%.
i. Many researchers have worried about the fact that regression (1) suffers from
omitted variable bias because it does not control for the innate ability of
individuals. State under which conditions this would be the case.
ii. Imagine it was possible to measure individuals’ ability and it was included in
regression (1). Would the estimated coefficient on education in this new regression
go up or down? Provide an explanation using an omitted variable bias formula.
iii. Now, imagine it was not possible to measure individuals’ ability. Also, imagine
that by law students enter school in the calendar year in which they turn 6 and that
the cut-off date is December 31st. That is all children born between January 1st and
December 31 of any given year go together in the same class. Therefore those born
in January will be the oldest in the class (starting school at the age of 6 years and 8
months) and those born in December will be the youngest in the class (starting
school at the age of 5 years and 9 months). Furthermore, imagine that compulsory
schooling laws require students to remain in school only until their 16th birthday.
This implies that children born earlier in the year can leave school earlier than
those born later in the year. (i.e., can leave with less formal schooling). What are
the conditions for a valid instrument and would month of birth satisfy these
conditions?
iv. Explain how an instrumental variable regression can be described as a two stage
procedure. Also explain how it can help reduce the bias when the first OLS
assumption is violated.


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4. You are hired by the UK government and are asked to forecast the unemployment rate in
the United Kingdom, using quarterly data from 1960, first quarter, to 2010, fourth quarter.
i. The following table presents the first four autocorrelations for the UK aggregate
unemployment rate and its change for the time period 1960 (first quarter) to 2010
(fourth quarter). Explain briefly what these two sets of autocorrelations measure.


ii. You decide to estimate an AR(1) in the change in the UK unemployment rate to
forecast the aggregate unemployment rate. The result is as follows:



You also estimate an AR(1) for the change in the inflation rate and found that the
slope coefficient was 0.211 and the regression R2 was 0.04. What does the
difference in the results suggest here?
iii. The actual unemployment rate in 2010 by quarters was 4.3 percent (I quarter), 4.3
percent (II quarter), 4.2 percent (III quarter), 4.1 percent (IV quarter). What is your
forecast for the unemployment rate level in the first quarter of 2011?
iv. You want to see how sensitive your forecast is to changes in the specification.
Given that you have estimated the regression with quarterly data, you consider an
AR(4) model. You find out that there does not seem to be much difference in the
forecast of the unemployment rate level, whether you use the AR(1) or the AR(4).
Given the various information criteria (Bayes Information Criterion and Akaike
Information Criterion) and the regression R2 below, which model should you use
for forecasting?

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—— End of Examination Paper ——





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