Fall 2022
Department of Economics
Bocconi University
Via Röntgen, 1
20136 Milan
Instructors:
Pamela Giustinelli (5-E1-14)
pamela.giustinelli@unibocconi.it
Martin Fankhauser (5-E3-FM01)
martin.fankhauser@unibocconi.it
PRACTICE QUESTIONS, SET 3:
SELECTION and CAUSAL DESIGNS (IVs, DID, etc.)
DS&BA 20594, Econometrics for Big Data, Part 1 (Microeconometrics)
a
Open / Essay Questions
When answering, you are welcome to use your own words and/or notation and/or graphs. If you use
a source, please reference your source.
(1) Explain the basic ideas and difference/s behind selection on observables and selection on unobservables approaches to causal inference.
(2) Applicability of the Differences-in-Differences (DID) approach; that is, the data requirements and
identification assumptions for this approach to yield identification of the ATT.
(3) In the Angrist-Imbens-Rubin’s POF with imperfect compliance, population units can be classified (under SUTVA) into one of four mutually exclusive and exhaustive types, depending on how
feasible values of the assignment-to-treatment variable, Zi ∈ {0, 1}, map into potential treatments,
{Di (0), Di (1)} ∈ {0, 1} × {0, 1}. Define and describe each of the four types.
b
Multiple Choice Questions
For each question, select the correct answer/s.
(1) Which of the following is true of the LATE parameter?
(a) LATE is the average treatment effect in the subpopulation
POF with imperfect compliance and heterogeneous effects.
(b) LATE is the average treatment effect in the subpopulation
POF with perfect compliance and heterogeneous effects.
(c) LATE is the average treatment effect in the subpopulation
POF with perfect compliance and homogeneous effects.
(d) LATE is the average treatment effect in the subpopulation
POF with imperfect compliance and homogeneous effects.
1
of compliers within the context of a
of compliers within the context of a
of compliers within the context of a
of compliers within the context of a
(2) Which of the following is/are true of traditional instrumental variables (IV)?
(a) Under the conditions of relevance and validity, the classic IV estimator is consistent (i.e. asymptotically unbiased).
(b) Identification of ATE using classic IV requires a condition of instrumental validity, aka exclusion
restriction.
(c) The classic IV estimator is a method of moments estimator.
(d) The classic IV method is a selection on unobservables approach.
(3) Consider the following simple regression model y = β0 + β1 D + ε. The variable Z is a weak
instrument for D if...
(a)
(b)
(c)
(d)
c
there
there
there
there
is
is
is
is
a
a
a
a
high correlation between Z and D.
low correlation between Z and D.
high correlation between Z and ε.
low correlation between Z and ε.
Applied Questions
(1) Diff-in-Diff (DID). Card and Krueger (1994) evaluate the impact on employment of a law that
raised minimum wage from USD 4.25 to USD 5.05 in the state of New Jersey on April 1, 1992. The
authors survey 410 fast-food restaurants in New Jersey (NJ) and eastern Pennsylvania (PA) before and
after the rise. Card and Krueger (1994) adopt a DID approach, whereby they compare employment
growth (between before and after the rise) at stores in New Jersey versus Pennsylvania (where the
minimum wage was unchanged), to obtain estimates of the causal effect of the higher minimum wage.
(a) Consider the estimates displayed in the left panel of Table 3 in Card and Krueger (1994)’s paper,
shown in the appendix below. Focus on the estimates shown in rows 1-3 and columns (i)-(iii). Identify,
define, and interpret: (i) the before-after estimates for PA, (ii) the before-after estimates for NJ, and
(iii) the DID estimates.
(b) In the introduction of their paper, Card and Krueger (1994) build a three-points discussion to
justify their approach, reported in the appendix below. Briefly comment on each of the three points
and explain why it is important for applicability of the DID approach and for identification of the
causal effect of minimum wage on employment.
(2) Causal Inference VS. Prediction in DID Regression. Meyer et al. (1995), henceforth MVD,
studied the length of time in weeks that an injured worker receives workers’ compensation, durat. On
July 15, 1980, Kentucky raised the cap on weekly earnings covered by workers’ compensation following
an injury on the job. An increase in the cap has no effect on the benefit for low-income workers, but
it makes it less costly for a high-income worker to stay on workers’ compensation (as opposed to
returning to work). Hence, MVD take high-income workers to be the treatment group and low-income
workers the control group, where high-income workers are defined as those who were subject to the
pre-policy change cap. (That is, those for whom the cap used to be binding.) Using random samples
both before and after the policy change, MVD test whether more generous workers’ compensation
causes people to stay out of work longer (everything else equal). They start with a difference-indifference (DID) analysis, using log(durat) as the dependent variable. Let af chnge be the dummy
2
variable for observations after the policy change and highearn the dummy variable for high earners.
Using the data in INJURY, the estimated equation, with standard errors in parentheses, is:
\ =1.126 + 0.0077 af tchnge+ 0.256 highearn+ 0.191 af tchnge · highearn,
log(durat)
(0.031)
(0.0447)
(0.047)
(1)
(0.069)
with N = 5, 626 and R2 = 0.021.
(a) What is the DID effect of the increased earnings cap on the length of time on workers’ compensation for high earners? Briefly comment on its statistical significance (is it statistically different
from zero?), and its “economic” significance (is it practically large?).
(b) This is a good example of how one can get a fairly precise (and statistically significant) estimate
of the effect of a policy change even without being able to explain much of the variation in the
dependent variable (note the low R2 ). Does this make sense to you? Why yes or not?
(c) The coefficient on af chnge is small and statistically insignificant. Indeed, when af chnge is
dropped from the model, the estimated equation remains very similar to (1):
\ =1.129 + 0.253 highearn+ 0.198 af tchnge · highearn,
log(durat)
(0.022)
(0.042)
(2)
(0.052)
with N = 5, 626 and R2 = 0.021. Is this surprising? Why yes or not?
(3) Traditional IVs and LATE. Angrist and Evans (1998) study the causal effect of fertility on
the work effort of women and, in the case of married women, also of their husbands. They consider
a range of outcomes, including whether the person worked in the previous year, number of weeks
worked, average hours worked, labor income, and so on.
To address endogeneity of fertility the authors use an IV approach based on the sibling sex mix in
families with two or more children. Specifically, they use a dummy = 1 if the first two children are of
the same sex (and = 0 otherwise) as an IV for further childbearing among women with at least two
children.
(a) On a theoretical ground, do you think the sibling sex-mix dummy may be a relevant instrument
for the total number of children of women (families) with 2 or more children? Why yes/not?
Given data on some measure of work effort (Y ), total number of children (C), sibling sex
composition (Z), and other family characteristics (X) for a cross-section of women (families)
with 2 or more children, how would you test for relevance of the sex-mix instrument?
(b) On a theoretical ground, do you think the sibling sex-mix dummy may be a valid instrument for
fertility? Why yes/not?
Given the same data as in (a), how would you test for validity of the sex-mix instrument?
(c) After establishing empirically the relevance of sibling sex mix for fertility, the authors estimate
the effect of fertility on a variety of labor supply outcomes for all women, married women, and
husbands of married women. The main labor supply outcomes are:
ˆ
ˆ
ˆ
ˆ
ˆ
worked for pay = 1 if the person worked in the prior year;
weeks worked = number of weeks worked in the prior year;
hours/week = average hours worked per week in the prior year;
labor income = labor earnings in the prior year (in 1995 dollars);
...
3
Table 8 (reported in the appendix below) shows OLS and IV estimates for the three groups (all
women, married women, and husbands of married women). Clearly, fertility tends to depress
women’s work effort on average. (Though not necessarily the work effort of their husbands.)
However, the IV estimates are generally smaller in absolute value than the OLS ones and have
much larger standard errors (reported in parenthesis under the point estimates).
In a “classical” IV setting with homogenous effects, how would you rationalize the observed
difference between OLS and IV estimates? (You may focus on women, i.e. columns 1, 2, 4,
and 5. But feel free to comment on husbands as well, if you like.) How about the difference in
standard errors between OLS and IV?
(d) Now consider the possibility that the population is heterogeneous in the way in which women
(families) respond to the treatment assignment provided by the instrument. How do you interpret
the IV estimates shown in Table 8 in this case? How would you rationalize the observed difference
between OLS and IV estimates?
d
Practice with Data and Codes (Not for the Exam)
(1) Békés and Kézdi (2021)’s Case Study “Founder/family ownership and quality of
management”. In the slides on selection on observables, one example was taken from this case
study (see slide 37). The goal of the analysis is to quantify the causal effect of a binary treatment,
defined to be whether a firm is still owned by its founder/family versus not, on an outcome, represented
by management quality as measured in the World Management Survey. A short description of the
case study along with the data and the code (in Stata, R, or Python) used for the regression analysis
are available at this link. By examining the code and running it on the data, you should be able
to replicate Békés and Kézdi (2021)’s analysis in Table 21.1 shown on slide 37 of the set of slides
on selection on observables. Note that the code includes a preliminary analysis of the data (used to
prepare the data, select the analytic sample for the analysis, and describe it), as well as additional
analyses of the causal effect of founder/family ownership on quality of management using selectionon-obseravables approaches other than “conditioning via regression”. (That is, after a section on
“REGRESSIONS”, which should enable you to replicate the results shown in Table 21.1, the code
has two additional sections on “EXACT MATCHING” and “PROPENSITY SCORE MATCHING”.
These are methods I mentioned in the slides, but decided not to cover given time constraints).
(2) Békés and Kézdi (2021)’s Case Study “How does a merger between airlines affect
prices?”. Imagine you work for a competition authority, and you are tasked with evaluating the
effect of a merger between two companies that already took place, on the prices of their customers
face. This case study guides you through the steps, using transaction-level data from a few years
both before and after the merger took place, and employing Differences-in-Differences (DID). Because
this is a more complex case study than others from Békés and Kézdi (2021), I have posted a detailed
description of the case study taken from Chapter 22 of their textbook. The description should help
you understand the setting and the main results, before you try to replicate the analysis. You can find
additional information about the case study as well as the data they used and their codes (in Stata,
R, and Python) at this link.
References
Angrist, J.D. and W.N. Evans (1998), ‘Children and Their Parents’ Labor Supply: Evidence from Exogenous
Variation in Family Size’, American Economic Review 88(3), 450–477.
Békés, G. and G. Kézdi (2021), Data Analysis For Business, Economics, and Policy, Cambridge University
Press.
4
Card, D. and A.B. Krueger (1994), ‘Minimum Wage and Employment: A Case Study of the Fast-Food Industry
in New Jersey and Pennsylvania’, American Economic Review 84(4), 772–793.
Meyer, B., W. Viscusi and D.L. Durbin (1995), ‘Workers’ Compensation and Injury Duration: Evidence from
a Natural Experiment’, American Economic Review 85(3), 322–340.
e
Appendix
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