EC902/907 - Quantitative Methods: Econometrics A

Sample exam questions – Spring 2021


1. Public smoking bans In recent years, a growing awareness of the deadly effects of smoking has led most industrialized countries to enact tobacco control policies. Smoking bans may affect smoking prevalence within the population, and smoking intensity among smokers. However, to date, surprisingly little research has been done on whether people change their smoking habits as a result of smoking bans. In 2007 several German states introduced public smoking bans in the hospitality industry (bars, restaurants, and dance clubs). The following graph shows the evolution of the smoking rate over time according to survey information in those states of Germany that approved the smoking ban (lower line) and those states of Germany that by 2008 had no smoking ban (upper line).
a) Would it be appropriate to use a differences-in-differences approach in order to obtain a consistent estimate of the effect of smoking bans? Discuss briefly which assumptions need to be satisfied and whether you expect them to be satisfied in this context.
Probably yes. The crucial assumption for DID is that, in the absence of the
ban, the smoking rate would have evolved similarly in the treatment and
the control group (the so-called parallel trends assumption). The graph
suggests that the smoking rates evolved similarly in the past, which
constitutes supportive evidence (although a statistical test to verify this
would be still needed). We should also verify whether states in the
treatment group have simultaneously adopted other policies to reduce
smoking (e.g. changes in tobacco tax rates) and whether the treatment
may have somehow affected the control group (anticipation effect,
spillovers, etc.)
Common mistake: Both groups are assumed to be similar (Note: in a DID
setting they are assumed to evolve similarly, which is a less demanding
condition.) b) Imagine that you have access to a database with survey information on smoking behavior in Germany during years 2002 and 2008. This database includes information for 85,000 individuals living in treated and control states. If you use this database to estimate the impact of smoking bans on smoking behavior, at which level would you cluster your standard errors: (i) individual level, (ii) individual*year level, (iii) state level, or (iv) state*year level? Explain briefly why.
(iii) state level, acknowledging that the treatment is defined at the state
level (there might be common shocks that affect all individuals within the
state in a given year) and that there is serial correlation across time.
Note: option (iv), state*year level (e.g. Baviera-2005 would be a cluster)
would not account for serial correlation within the same state over time. c) The authors find that the smoking rate decreased by 0.4 p.p. faster in the treatment group relative to the control group, with a standard error of 0.8 p.p. Discuss the statistical and the economic magnitude of this result.
Statistical significance: The effect on the ban is not statistically
significant from zero at standard levels: using a 95% significance level,
the public smoking ban may have decreased the smoking rate by up to 2
p.p. or it may have increased it by 1.2 p.p.
Economic significance: At best, the ban may have caused a 2 p.p. decrease
in smoking rates. That would imply that approximately 8% (2/26) of
smokers quitted smoking following the introduction of the ban.
Personally I would say that, from a public health perspective, a 8%
decrease in the number of smokers may be considered like a substantial
effect, but you were allowed to disagree. In sum, we cannot discard that
the ban had an “economically” significant impact, but given the accuracy
of the estimate we are unable to draw any conclusions.


2. Does compulsory school attendance affect schooling and earnings?
(Angrist and Krueger 1991)

Using data from the 1980 census, Angrist and Krueger (1991) looked at the
relationship between educational attainment and quarter of birth for men born
from 1930 to 1959. The first figure below displays the relationship between
education and quarter of birth for men born in the 1930s. The figure clearly
shows that men born early in the calendar year tend to have lower average
schooling levels. The second figure displays average earnings by quarter of
birth for the same sample. Older cohorts tend to have higher earnings,
because earnings rise with work experience. But the figure also shows that,
on average, men born in early quarters of the year almost always earn less
than those born later in the year. Importantly, this reduced form relationship
parallels the quarter-of-birth pattern in schooling.

a) Explain briefly the rationale for the Angrist and Krueger (1991) approach.
(Why in the US people born at the beginning of the year finished less
schooling?) (5 marks)

In the US students start school the year they turn six, but they can drop out
as soon as they turn 16. As a result, students born early in the year have the
chance to drop out when they turn 16 in the beginning of the academic
year, while those ones born at the end of the year have to complete the
academic year before being allowed to drop out.

b) Would you expect the exogeneity condition to be satisfied? Provide some
example of a possible violation. (5 marks)

There might be a selection problem is some people may try to strategically
select the timing of births (e.g.: working women having kids in summer)
There might be other factors that affect the timing of births. For instance,
Buckels and Hungerman (Restat 2013) document large changes in
maternal characteristics for births throughout the year (e.g. winter births
are disproportionally realized by teenagers and the unmarried).
88 CHAPTER 4. INSTRUMENTAL VARIABLES IN ACTION
A Average Education by Quarter of Birth (first stage)
3 3
4
3 4
1
2 3
4
1
2
3
4
12 9
13
13.1
13.2
.
A. Average Education by Quarter of Birth (first stage)
2
3
4
1 2
3
4
1
2
3
4
1
2
3
4
1
2 3
4
1
2 4
1
2
1 2
12.5
12.6
12.7
12.8
.
Ye
ar
s o
f E
du
ca
tio
n
1
12.2
12.3
12.4
30 31 32 33 34 35 36 37 38 39
Year of Birth
5.94

B. Average Weekly Wage by Quarter of Birth (reduced form)
B. Average Weekly Wage by Quarter of Birth (reduced form)
3
4
3 4 3
2
3
4
3 4
3
4
3
4
3
4 2
3
4
2
45.91
5.92
5.93
ar
nin
gs
2
1
1
2 1 2 4
1
1
2
1
2
1
2
1
2
1
1
3
5.88
5.89
5.9
Lo
g W
ee
kly
E
a
5.86
5.87
30 31 32 33 34 35 36 37 38 39
Year of Birth
Figure 4.1.1: Graphical depiction of Örst stage and reduced form for IV estimates of the economic return to
schooling using quarter of birth (from Angrist and Krueger 1991).
Nonetheless, most authors tend to consider that these differences are
relatively minor.

c) Would you expect the exclusion restriction to be satisfied? Provide some
example of a possible violation. (5 marks)

There might be some minor violations. Being born at the beginning of
the year may affect individuals labor market performance through other
channels than length of education. Children born at the beginning of the
year are older than their classmates, which may affect their non-
cognitive abilities (eg Black et al. 2017). They are also older when they
take exams, leading to better educational performance (for the same
length of studies).

d) Using this empirical strategy, we learn about the impact of educational
attainment on earnings for which type of individuals? (who are the
`compliers’, in jargon) (5 marks)

Compliers are those kids who are eager to drop out. Therefore, the
instrument (month of birth) affects whether they receive the treatment or
not (years of education)
Common error (1): define compliers based on the impact of the
treatment. E.g.: compliers are kids that react to the treatment
(schooling) by gaining skills. (Note that being a complier is unrelated to
whether the treatment has an effect or not on this group (that is an
empirical question to be determined)
Common error (2): define compliers based on when they are born.


3. Should I stay or should I go (to class)?

Andrietti, D’Addazio and Velasco (2008) examine the link between
absenteeism and students’ performance using data from a Spanish university.
Initially they follow an identification strategy based on observables. Their OLS
estimates suggest that, conditional on a number of observable characteristics,
students that attend class tend to obtain better grades (betaOLS=0.11). The set
of observable characteristics includes information about students’ family
background, habits and performance in previous courses.
In order to deal with endogeneity concerns, they propose to use as
instruments for attendance (i) distance to reach campus from the student’s
house and (ii) a dummy variable that indicates if the student works.
Please reply to the following questions:

a) Discuss, for each instrument, whether the exogeneity assumption is
likely to be satisfied.

Neither instrument is likely to be exogenous. For instance, socio-
economic status might affect the area where people live and also
whether they work or not.

b) Discuss, for each instrument, whether the exclusion restriction is likely
to be satisfied. Can you think of some way to test empirically whether
this assumption is satisfied?

In both cases the exclusion restriction is not likely to hold. For instance,
distance to the university might affect not only attendance, but also time
available to study. Student who work may also have less time to study,
etc.

c) Can you please verbally characterize who are the always takers, the
never takers and the compliers in this context

The always takers (never takers) always (never) attend lectures,
independently of where they live or whether they work or not. Compliers
attend lectures only when they do not work or they live close enough.

d) The authors find that the IV estimate is equal to 0.50 (substantially
larger that the OLS estimate). Can you please provide some
reasonable explanation for the difference between IV and OLS
estimates in this particular case?

There are two possible explanations. First, note that the IV estimate is
likely to suffer a problem of weak instruments. Second, the IV estimate
identifies the LATE, while the OLS identifies the ATE.
(Note also that the omitted variable bias is likely to bias upwards the
OLS estimate, and therefore cannot explain why the IV estimate is larger
than the OLS one.)

4. The Effect of Peer Salaries In the paper “Inequality at Work: The Effect of Peer Salaries on Job Satisfaction”, David Card and co-authors study the effect of disclosing information on peers’ salaries on workers’ job satisfaction and job search intentions. They informed a randomly chosen subset of employees of the University of California about a new website listing the pay of University employees. Later on, they surveyed all campus employees, eliciting information about their use of the website, their pay and job satisfaction, and their job search intentions. Their intervention had a large impact on access to information. The fraction of people who used the website was equal to 20 percent among workers that were not informed about the existence of the website and it raises to nearly 50 percent among workers who were informed about the existence of the website. Furthermore, the intervention caused an increase in the intention to look for a new job among workers with pay below the median for their department and occupation group. In particular, individuals who received from researchers the information about the existence of the website and whose pay was below the median were 4.3 p.p. (st. error=1.8 p.p.) more likely to report that they were looking for a new job, relative to a benchmark of 21.9% in the control group. a) Imagine that we use “provision of information about the website” as an instrument for “access to information about peers’ salaries”. Propose some possible violation of the exclusion restriction.
For instance, some people may dislike learning that their salaries are
reported online. (Even if they do not check personally the website.)
Instead, the exclusion restriction would be satisfied if the people that
did not check the website somehow had not received the email at all,
for instance because it went directly to their spam folder. b) Let us assume that the exclusion restriction was satisfied. How does access to information on peers’ salaries affect the job search intentions of individuals with pay below the median? (i.e. report the IV estimate)
14.3 (=4.3/0.3) c) Quantify the share of always-takers, the share of never-takers and the share of compliers.
20%, 50%, 30%
5. Regression discontinuity design A key policy question is whether the benefits of additional medical expenditures exceed their costs. An article by Almond et al. (2010)1 studies the impact of providing extra-care to newborns. They focus on the extra-treatments received by newborns weighting less that 1,500 grams, who are typically classified by hospitals as "very low birth weight" (VLBW), and receive more treatments than newborns with slightly larger weight. For instance, the 1,500 g threshold is commonly used as a point below which diagnostic ultrasounds is used. They authors use a regression discontinuity strategy that compares health outcomes and medical treatment provision for newborns on either side of the very low birth weight threshold at 1,500 grams. As shown in the below figure, they find that newborns with birth weights just below 1,500 grams have lower one-year mortality rates than do newborns with birth weights just above this cutoff, even though mortality risk tends to decrease with birth weight. One-year mortality falls by approximately one percentage point as birth weight crosses 1,500 grams from above, which is large relative to mean infant mortality of 5.5% just above 1,500 grams.
Note: Each point represents the average mortality within one year for newborns with a certain weight. a) Explain briefly what are the key requirements that would make the RDD strategy adequate in this context.
Answer: The crucial assumption for the validity of the regression
discontinuity design is that there are no discrete changes in any relevant
variable at the threshold, other than the treatment (i.e. being labeled as
"very low birth weight"). A possible threat would be that some doctors or
parents may be able to manipulate the official weight of newborns. For
instance, it would be a problem if wealthy parents can pay doctors to classify 1 Douglas Almond, Joseph J. Doyle, Jr., Amanda E. Kowalski, Heidi Williams, Estimating Marginal Returns to Medical Care: Evidence from At-risk Newborns, The Quarterly Journal of Economics, Volume 125, Issue 2, May 2010, Pages 591–634.
their newborns as being below 1,500 so that they are entitled to receive
special treatments.
Another potential threat is the existence of other treatments based on this
threshold. Finally, RDD requires a sufficiently large mass of observations
around the threshold in order to provide estimates that are precise.

b) How would you verify the existence of manipulation of the running variable?
Answer: First, we should verify whether the density function is continuous at
the discontinuity threshold. It would be worrying if the number of newborns
with slightly less than 1,500 grams is much larger/smaller than the number
of newborns above the threshold. Second, we may want to verify that
predetermined relevant factors evolve “smoothly” with respect to the
running variable at the threshold. For instance, families with babies just
above and below the threshold should have “similar” socio-economic
characteristics, such as income or educational background.