Midterm
Due by 3/24, 11:59PM
*Generate a Python script for your answers. You will submit your script only.
The midterm requires you to replicate the main results of Nollenberger, Rodŕıguez-Planas
and Sevilla XXXXXXXXXXOn Blackboard, you will find a pdf copy of the paper along with the dataset,
named Final sample.csv. You will re-produce Figure 1 on page 258 and Table 1 on page 260.
Below you will find further instructions to replicate these results. Note that you will not be
able to replicate their results exactly due to the fact that analysis of PISA data require some
statistical methods beyond the scope of our class. Howbeit, your results should come close to
theirs. Before start writing up your script, I urge you to read the paper carefully. It is a short
paper and will not take too much of your time.
Consider the following research questions. What explains the observed lower average math
scores of females relative to males? Are females less math oriented than males? If you were try-
ing to answer the latter question, ideally you’d like to run a randomized controlled experiment
in which, hypothetically, gender could be randomly assigned to subjects who are the same in all
other aspects. Then, one would simply compare average scores of the two groups. Since such
an experiment is not feasible, we need to resort to observational data such as PISA. However,
it is easy to find several confounding factors that explain math score and do systematically
covary with gender. Such confounders need be controlled for in linear regression models. But
problems do not end there.
Consider institutions of countries or culture. Some countries have better education systems
than others and some countries are culturally more gender-equal than others. As Nollenberge
et al XXXXXXXXXXstate “it is possible that greater gender equality leads to a reduction in the math
gender gap, ... in countries where girls perform relatively better at math, women might also be
more prepared, access better jobs, earn higher wages, and be more easily promoted and politically
empowered, leading to greater gender equality.” This is the so-called reverse causality problem.
The authors’ strategy to overcome this problem is to focus on the second-generation immi-
grants (students) who have lived in a host country since birth, and are exposed to the same
host-country institutions. These students will be exposed to the cultural beliefs of their par-
ents’ ancestry country. But note that the math test scores of these students are unlikely to
affect culture or institutions of of their parents’ ancestry country. Hence, the reverse causality
problem is unlikely to occur.
Nollenberger et al XXXXXXXXXXestimate different versions of the following specification:
PV 1MATHijkt = α1FEMALEi + α2(FEMALEi ×GGIj) + x
′
ijktβ1
+ (FEMALEi × x
′
ijkt)β2 + λj + λk + λt + δ(FEMALEi × λk) + εijkt
where PV 1MATHijkt denotes the (plausible) math test score of student i who lives in country
k at time t, and is of ancestry j. FEMALEi is an indicator equal to one if student i is a girl
and zero otherwise. GGIj is the gender equality index from student i’s country of ancestry
of j. xijkt denotes a set of control variables which will vary depending on the specification
considered. λj denotes the ancestry country dummy, λk denotes the host country dummy, and
λt denotes the PISA cohort dummy. They respectively control for time invariant country of
ancestry characteristics, time invariant host country characteristics, and individual invariant
cohort characteristics. Host country dummy is interacted with the female dummy to account
for host country educational gender gaps. The coefficient of interest is α2, which captures the
ole of cultural on gender equality in explaining gender differences in the math test scores of
second-generation immigrant girls relative to boys.
1
Below you will find the description of the main variables used in the regressions in Table 1
in Nollenberger et al. (2016).
variable description
pv1math (plausible) math test score 1
ggi gender gap index
female indicator: 1 if female, 0 otherwise
age age in years and month
diffgrade indicator: 1 if the cu
ent individual’s grade is different from the modal grade
at the children age in the host country, 0 otherwise
misced mother’s highest level of education (categorical 0 to 6)
fisced father’s highest level of education (categorical 0 to 6)
momwork indicator: 1 if mother works, 0 otherwise
dadwork indicator: 1 if father works, 0 otherwise
lgdppc log per capita GDP of the country
homepos index of cultural possessions (positive values imply higher)
pcgirls PISA index of the proportion of girls enrolled in each school
private indicator: 1 if school is private, 0 otherwise
metropolis indicator: 1 if school is a metropolitan area, 0 otherwise
ackground parents’ (both) country of birth
country host country
stweight sample weights to be used in regressions
(1) To replicate Figure 1 on page 258, you first need to calculate math gender gap values by
country of ancestry (i.e., by background). To this end, you need to regress PV 1MATH
on FEMALE dummy by background country, and save the slope estimates for the
female dummy. Then, you can generate a scatter plot where x-axis is the GGI of the
ancestry country, and y-axis is the math gender gap estimates of the ancestry country
from the regressions.
(2) To replicate Table 1 on page 260, you will estimate six different specifications. Pay
attention to the set regressors in each specification. Note that in all specifications the
dependent variables is PV 1MATH. You need to include year fixed effects (λt), ancestry
country fixed effects (λj), host country fixed effects (λk), and the interaction of female
dummy with host country fixed effects (femalei × λk) in all specifications except the
third one, where there are no ancestry country fixed effects.
References
Nollenberger, N., Rodŕıguez-Planas, N. and Sevilla, A XXXXXXXXXXThe math gender gap: The role of culture,
American Economic Review 106(5): 257–61.
2
Midterm
References
The Math Gender Gap: The Role of Culture
American Economic Association
The Math Gender Gap: The Role of Culture
Author(s): Natalia Nollenberger, Núria Rodríguez-Planas and Almudena Sevilla
Source: The American Economic Review, Vol. 106, No. 5, PAPERS AND PROCEEDINGS OF
THE One Hundred Twenty-Eighth Annual Meeting OF THE AMERICAN ECONOMIC
ASSOCIATION (MAY 2016), pp XXXXXXXXXX
Published by: American Economic Association
Stable URL: https:
www.jstor.org/stable/ XXXXXXXXXX
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American Economic Review : Papers & Proceedings 2016, 106(5): XXXXXXXXXX
http:
dx.doi.org/! XXXXXXXXXX/aer.p XXXXXXXXXX
The Math Gender Gap: The Role of Culture*
By Natalia Nollenberger, Núria Rodríguez-Planas, and Almudena Sevilla*
Using analysis across countries or states,
previous studies show that girls in more
gender-equal countries or states perform rela-
tively better than boys in math test scores (Guiso
et al. 2008; Fryer and Levitt 2010; Pope and
Sydnor XXXXXXXXXXWhile it is possible that greate
gender equality leads to a reduction in the math
gender gap, an alternative interpretation of these
findings could be that in countries where girls
perform relatively better at math, women might
also be more prepared, access better jobs, earn
higher wages, and be more easily promoted and
politically empowered - leading to greater gen-
der equality.
The cu
ent paper's contribution to this liter-
ature is twofold. First, we assess the direction
of causality using the epidemiological approach
(Fernandez XXXXXXXXXXSecond, we quantify the
effect of values and beliefs about women's role
in society transmitted from generation to genera-
tion (what we call "culture on gender equality")
versus that of a country's institutions and formal
practices on the math gender gap. In doing so,
we inform a public policy issue of first-orde
importance.
The epidemiological approach focuses on
second-generation immigrants, who have lived
in a host country since birth and are exposed to
the same host-country institutions. Crucially,
second-generation immigrants living in the
* Nollenberger: IE Business School, IE University, Calle
de María de Molina, 11-15, 28006 Madrid, Spain (e-mail:
XXXXXXXXXX); Rodríguez-Planas: Economic
Department, City University of New York (CUNY), Queens
College, Powdermaker Hall, 65-30 Kissena Boulevard,
Queens, NY XXXXXXXXXXe-mail: XXXXXXXXXX.
edu); Sevilla: School of Business and Management, Queen
Mary, University of London, Francis Bancroft Building,
Mile End Road, London El 4NS (e-mail: a.sevilla@qmul.
ac.uk). Co
esponding author: Rodríguez-Planas. The
authors declare that they have no relevant or material finan-
cial interests that relate to the research described in his paper.
tGo to http:
dx.doi.org/10.1257/aer.p XXXXXXXXXXto visit
the article page for additional materials and author disclo-
sure statement(s).
same host country are also likely to be influ-
enced by the cultural beliefs of their parents'
ancestry country. Given that math test scores of
second-generation immigrants are unlikely to
affect gender-equality measures (culture or insti-
tutions) of their parents' country of ancestry, the
problem of reverse causality is less of an issue
in our paper. In addition, with the epidemiolog-
ical approach, any country-of-ancestry variation
in the math gender gap of second-generation
immigrants in a particular host country can only
be attributed to cultural differences transmit-
ted from the immigrants' parents (or peers), as
opposed to institutional differences.
I. Data
We use data from the 2003, 2006, 2009,
and 2012 Program for International Student
Assessment (PISA), which contains a stan-
dardized (and, hence, culture-neutral) mathe-
matics assessment administered to 15-year-olds
in schools. Our sample contains 11,527
second-generation migrants from 35 different
countries of ancestry and living in 9 host coun-
tries (see online Appendix Table A.l).
On average, the gender gap in math scores
(defined as the difference in math score between
girls and boys) among second-generation
immigrants is 15.70, equivalent to 4.5 months
of schooling (see online Appendix Table A.2).
Crucially, it varies