SIS 2008 contributed paper format

A quantile approach to assess gender differences
in financial literacy among Italian students
Un approccio quantile per valutare le differenze di genere
nell’alfabetizzazione finanziaria degli studenti Italiani
Sergio Longobardi and Margherita Maria Pagliuca
Abstract Recent data from the OECD PISA (2012) highlight that there are no
differences in financial literacy between boys and girls in all participating countries
with the exception of Italy where boys perform significantly higher. In this light, we
analyze the determinants and “dynamics” of this gap among Italian 15-year-olds
students applying some counterfactual decomposition methods. Main findings reveal
that although the majority of the gender gap is explained by differences in the
coefficients, an important role in this differential is played by the attitudes to problem
solving and the scholastic behavior.
Abstract I recenti dati dell’indagine OECD PISA 2012 mettono in evidenza che
l’Italia è l’unico Paese in cui sussistono differenze significative tra maschi e femmine
per quanto riguarda l’alfabetizzazione finanziaria. In questa ottica vengono
analizzate le determinanti e le “dinamiche” di questo gap ricorrendo alla
decomposizione di Oaxaca ed a quella di Machado-Mata. I principali risultati
rivelano che sebbene la maggior parte del gap è dovuto a differenze nel processo di
produzione delle competenze, un ruolo importante è svolto dalle attitudini al problem
solving e dal comportamento scolastico.
Key words: Financial literacy, Gender gap, Decomposition techniques, Quantile
regression
1
Sergio Longobardi, University of Naples "Parthenope"; email: [email protected]
Margherita Pagliuca, University of Naples "Parthenope"; email: [email protected]
2
Sergio Longobardi and Margherita Maria Pagliuca
1 Financial literacy and gender gap
A large body of research focuses on gender as an important determinant of financial
literacy and has documented a persistent gender gap (Hanna, Hill, and Perdue, 2010).
Lusardi and Mitchell (2008) argued that financial illiteracy is even more prevalent
among women than men while Chen and Volpe (2002) find similar gender differences
at younger ages. Understanding how and why men and women have different levels
of financial literacy is crucial to developing policies aimed at reducing the gender gap
and improving the saving and investing decisions of women. In this light we employ
the recent data on financial literacy carried out by OECD Programme for International
Students Assessment (PISA). The analysis focuses on Italian students because this is
the only country where the boys significantly outperform the girls.
2
Data and methods
PISA 2012 is the first large-scale international study to assess the financial literacy,
learned in and outside of school, of 15-year-olds nearing the end of compulsory
education. It assesses the extent to which students in 18 participating countries have
the knowledge and skills that are essential to make financial decisions and plans for
their future. It is thus able to provide a rich set of comparative data that policy makers
and other stakeholders can use to make evidence-based decisions.
On the basis of PISA data, we investigate the gender gap in Italy by comparing the
male and female financial literacy scores. Firstly, a raw estimate of this differential is
obtained by a simple Educational Production Function (EPF):
𝑦𝑖𝑗 = 𝛽0 + 𝛽1 𝐹 + 𝜖(𝑖)𝑗
where yij is the performance in financial literacy, F is a dummy variable for gender
(male=0, female=1) and e is the error component. The coefficient 𝛽1 provides a first
estimate of the size of gender gap but it does not allow to control for other factors
which influence the students’ performance. In this light, we adopt a “full” EPF in
order to obtain an adjusted estimate of gender gap, controlling for a set of (m) student
and (s) school characteristics:
𝑚
𝑠
𝑦𝑖𝑗 = 𝛽0 + 𝛽1 𝐹𝑖𝑗 + ∑ 𝛽𝑘 𝑥𝑘𝑖𝑗 + ∑ 𝛽𝑡 𝑧𝑡𝑗 + 𝜖(𝑖)𝑗
𝑘=1
𝑡=1
Subsequently, in order to investigate the gap along the entire financial literacy
distribution, a quantile regression model is employed:
𝑞
𝑄𝑞 (𝑌𝑖 |𝑋𝑖 ) = 𝛼0 + 𝛼 𝑞 𝑀𝑖 + 𝛾 𝑠 𝑋𝑖 + 𝛾 𝑠 𝑍𝑖 + 𝜀𝑖
A quantile approach to assess gender differences in financial literacy among Italian students
3
Once the educational production functions are estimated, we proceed to disentangle
the score gap between male and female into more components trough the three-fold
Oaxaca decomposition method (Oaxaca and Ransom, 1998):
′
′
′
𝐸(𝑌𝑚) − 𝐸(𝑌𝑓) = [𝐸(𝑌𝑚) − 𝐸(𝑌𝑓) ] 𝛽𝑓 + 𝐸(𝑋𝑓 ) (𝛽𝑚 − 𝛽𝑓 ) + [𝐸(𝑌𝑚) − 𝐸(𝑌𝑓) ] (𝛽𝑚 − 𝛽𝑓 )
The first component, called endowments effect, represents the share of score gap due
to different average characteristics between the two groups. The second component,
coefficients effect, is obtained as difference in the slopes and it amounts to the
proportion of score gap related to different production processes. The third summand,
called interaction or characteristics-return effect, is the residual part of the
decomposition and captures the leverage produced by both effects happening
simultaneously.
Finally, we extend this approach beyond the mean level by applying the quantile
decomposition proposed by Machado and Mata (2005). This decomposition is based
on the assumption that score differentials are explained by a non-discriminatory
coefficients vector, denoted by “*”, which is estimated in a regression that pools
together samples of both male and female. Let f((i)) be an estimator of the marginal
density of  (the financial literacy score) for the group i on the observed sample
(j(i) and f*((i)) be an estimator of the density of  on a generated sample
(j*(i), i.e. a marginal distribution implied by the model. The counterfactual
densities will be denoted by f*((1);X(0)) for the density of male score distribution if
all covariates had i=m distributions and f*((1);y(0)) for the score density for males
in only one factor y were distributed as in i=f. The analysis of changes occurred from
f((1)) to f ((0)) can be analyzed comparing: f*((1);Z(0)) with f*((0)), that is the
contribution of the quantile regression coefficients for the overall change, and f*((1))
with f*((1);Z(0)): the contribution of covariates to the changes in the score density:
𝛼(𝑓(𝜔(1)) − 𝛼(𝑓(𝜔(0)) = [𝑎(𝑓 ∗ (𝜔(1); 𝑍(0)) − 𝛼(𝑓 ∗ (𝜔(0))] +
+[𝑎(𝑓 ∗ (𝜔(1); ) − 𝛼(𝑓 ∗ (𝜔(1); 𝑍(0))] + 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙
where the first term on the right side hand is the effect due to coefficients and the
second term the effect due to covariates.
3
Main results
In the empirical analysis, we opted for a stepwise (or “incremental”) regression
approach, which is quite common in this kind of academic research. More specifically,
we started by estimating a model with only a gender dummy as explanatory variable,
then we included student-level characteristics (immigration status and the index of
socio economic status) in the Model 2. Some covariates related to attitude and
behavior are added in the Model 3. This set of variables plays an important role both
on the financial literacy performance and on gender gap. It includes: an index of ICT
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Sergio Longobardi and Margherita Maria Pagliuca
use, a variable related to openness to problem solving1, a dummy related to
perseverance2 and a variable which describes the scholastic behaviour: how many
time in the last two week the student skip a whole school day. Finally, we also control
for the schools characteristics in the Model 4.
The results of OLS regression (table 1) show that the raw gap (model 1) between male
and female students is significantly in favor of males, although it is not very high. In
the model 2, the gap rises after controlling for family background (ESCS index) and
immigrate status (from -7.905 to -8.772). This increase is probably due to better
family background of the female students and to a higher proportion of immigrants in
the male sample.
By contrast, the gender coefficient declined in magnitude and significance when the
four variables related to students’ attitudes and behavior are included (model 3). This
result confirms that factors like positive perseverance or openness to problem solving
play an important role in explaining the financial literacy (OECD 2014) and a different
endowment of these characteristics between male and female students (as
demonstrated in the subsequent decomposition analysis) could account for a large
share of the gap. Surprisingly, although many schools’ features have a significant
impact on the performance in financial literacy, they do not help to change neither the
significance nor the magnitude of gender gap.
Table 1: Results of OLS regression
Category
Student
characteristics
Students
attitudes and
behaviour
School
characteristics
Variable
Gender (1=female)
Index of economic, social and
cultural status (ESCS)
Immigrate (1=yes)
ICT Entertainment Use (index)
Student likes to solve complex
problem
Low perseverance
Skip a whole school day in the
last two weeks. (ref="0-2 times")
>2 times
Student-Teacher ratio
Quality of school physical
infrastructure
Ratio of computers and students
School location (ref:"Town")
Village or small town
City or large city
Private school (1=yes)
Mathematics Extracurr. activities
at school (ref:3 activites)
1 or 2 activites
>3 activites
Constant
Mod.1
-7.905***
Mod.2
-8.772***
24.087***
Mod.3
-7.177*
19.468***
Mod.4
-7.08*
16.001***
-22.238***
-19.486**
4.472**
-17.316*
4.752**
18.65***
15.592***
-25.389***
-23.357***
-17.165***
-17.92**
5.258***
5.495**
0.212
-3.368
0.077
-33.902***
7.796
462.304***
465.991***
473.604***
17.423***
414.88***
In addition to the OLS estimates, we employ a quantile approach to analyze the
“dynamics” of gender gaps at different percentiles of financial literacy distribution.
The quantile regression results also confirm the stronger effect of students attitudes
Students’ response to how well the statement “I like to solve complex problems” describes them.
Students’ response to how well the statement “When confronted with a problem, I give up easily”
describes them.
1
2
A quantile approach to assess gender differences in financial literacy among Italian students
5
and behavior on gender gap, furthermore it is highlighted the lower impact of school
characteristics which inclusion remains almost unchanged the difference between
males and females.
Figure 1: Analysis of gender gap (Female- Male) through quantile regression approach.
Although the Oaxaca decomposition (tab.2) suggests that the majority of the gender
gap is due to differences in coefficients rather than in characteristics, an important
share of the financial literacy gap can be attributed to differences in students’ attitudes
and behavior.
Table 2: Oaxaca threefold decomposition by group of variables.
Coef.
Std.err.
OVERALL
group_1=Male
487.469
2.130
group_2=Female
474.357
1.800
difference
13.113
2.788
endowments
3.099
1.316
coefficients
9.192
2.671
interaction
Students characteristics
Attitudes and behaviour
School characteristics
Students characteristics
Attitudes and behaviour
School characteristics
constant
Students characteristics
Attitudes and behaviour
School characteristics
0.822
ENDOWMENTS
0.092
3.096
-0.089
COEFFICIENTS
-1.181
-15.249
14.314
11.307
INTERACTION
-0.419
2.081
-0.840
z
P>z
228.850
263.590
4.700
2.350
3.440
0.000
0.000
0.000
0.019
0.001
1.268
0.650
0.517
0.546
0.859
0.691
0.170
3.600
-0.130
0.867
0.000
0.898
0.587
3.820
10.103
11.192
-2.010
-3.990
1.420
1.010
0.044
0.000
0.157
0.312
0.268
1.052
0.655
-1.560
1.980
-1.280
0.118
0.048
0.200
Some results of Oaxaca approach are confirmed by the Machado-Mata decomposition
(fig.2) but the analysis of the entire scores distribution consents to observe the
considerable heterogeneity of the endowments and returns effect at different
percentiles of distribution. Generally, we find that the gap is almost null at the low
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Sergio Longobardi and Margherita Maria Pagliuca
percentiles (see also fig.1) and it is mostly determined by higher returns of
endowments. In particular, the characteristics effect is low, and almost constant, along
the entire distribution, it explains the 25-30% of gap until the 50th percentile but it
becomes not significant in the upper tail of distribution (over 60 th percentile) where
the gap and the magnitude of the return effects increased dramatically.
Figure 2: Machado-Mata decomposition of gender gap at various percentiles of score distribution
In summary, a relevant part of gender gap is due to difference in the coefficient, i.e.
how the students “transform” their personal, familiar and school characteristics into
competences, but an important role is also played by some “attitudinal factors”.
Reinforcing these attitudes at school may thus have a positive impact on acquiring not
only core skills but also skills in financial decision making.
References
Chen, H.; Volpe, R. P.: Gender Differences in Personal Financial Literacy Among College
Students. Financ. Serv. Rev. (2002), 11:289–307.
Hanna, M. E., Hill, R. R., Perdue,G.: School of study and financial literacy. J. Econ. Econ.
Educ. Res. (2010), 11(3): 29-37.
Lusardi, A, Mitchell, O., S.: Planning and Financial Literacy: How Do Women Fare? Am.
Econ. Rev. :(2008), 98(2):413–417.
Machado, J.A.F., Mata, J.: Counterfactual Decomposition of Changes in Wage Distributions
Using Quantile Regression. J. App. Econ. (2005), 200: 445-465.
Oaxaca, R.L., Ransom, M.: Calculation of approximate variances for wage decomposition. J.
Econ. Soc. Meas. (1998), 24: 55-61.

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