Culture, Gender, and Math

Luigi GuisoFerdinando Monte

Paola SapienzaLuigi Zingales

1

Motivation

• Under representation of women in science and engineering. Existing explanations?

• Economists: demand and supply effect. Both affected in principle by:– Environment – Biology

• Strongest argument for biology is the existence of some gender differences in cognitive abilities– Men better at

• aiming • spatial ability

– Men worse at• verbal fluency and recall

• These cognitive abilities linked to biological differences between gender.

• If they can be linked to math and reading abilities biology argument.

2

Approach

• Cognitive differences have been found consistently in all the populations (except the Inuit ).

• By contrary, environmental differences across countries are huge

• Use a large sample of comparable data across countries with different attitudes toward women to determine how much of the difference in performance is correlated with different environment

3

PISA (Program for International Student Assessment)

• 276.000 students in 40 countries tested at age 15

• In 2003, 4 tests: – math, problem solving, science, reading

• Lots of data on – Intrinsic motivation – Extrinsic motivation – Stress levels

• Tests are “culture free”

4

Math tests-1

• Scores reflect ability to apply mathematics in solving real-life problems

• Questions in math covers – “space and shape” (geometry)– “change and relationship” (algebra) – “quantity” (arithmetic)– “uncertainty” (probability)

in a range of difficulty that goes from the need of simple mathematical operations to complex thinking.

• Math scores scaled to have mean of 500 and standard deviation of 100 in the OECD students’ population.

5

Math tests-2

• PISA assigns a probability distribution to each possible response pattern in each test to describe the ability associated with that pattern.

• From this distribution, PISA draws a set of five values associated with each student. These values are called plausible values

• We use plausible values in any analysis that involves test scores.

• Any estimation procedure involves the calculation of the required statistic five times, one for each set of plausible values.

• Regression analysis.6

Do Gender Differences exists in this large international sample?

Average score: 514Average score, boys: 519.22Average score, girls: 508.69

Gender gap in mathematicsAverage: -10.53Average score: 508.53Average score, boys: 492.32Average score, girls: 525.04

Gender gap in reading

Average: 32.71

Average math score

Average reading score

7

Caveat: selection

• Not in all countries mandatory school is up to 16.• Even if it is, it is not always enforced• If dropout rate different across genders and

across countries –>bias • We drop all the observations below the country

mean in social and cultural status (where drop out rate higher)

• Our qualitative results are invariant to our way of handling selection

8

Gender Gap in Math by Country

-35

-30

-25

-20

-15

-10

-5

0

5

10

15

20

9

Measures of Women Emancipation

1) Gender gap index from the Global Competitiveness Report (WEF, 2006):

2) World Value Survey: • Average of a number of gender-related questions (e.g.,

“when job are scarce, men should have more right to a job than women”, “On the whole, men make better political leaders than women do”)

3) Participation to the labor force (UNESCO)4) Female-to-male ratio of tertiary enrollment

(UNESCO)

10

Measures of Women Emancipation

Women

Emancipation

(GGI)

Avg. all WVS Female

economic

activity rate

Women

Political

Empowerme

nt

Average 0.7 2.71 51.36 0.19

St. Deviation 0.05 0.19 9.04 0.15

Observations 37 32 39 36

Women

Emancipation

(GGI)

Avg. all WVS Female

economic

activity rate

Women Emancipation (GGI)1

Avg. all WVS0.80** 1

Female economic activity rate0.65** 0.62** 1

Women Political Empowerment0.90** 0.72** 0.40*

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Table 1

LHS: Gender difference in test score, math LHS: Gender difference in test score, reading

(I) (II) (III) (IV) (V) (VI) (VII) (VIII)

Women emancipation (GGI) 105.49*** 83.56***

(26.92) (30.43)

Avg. WVS indicators 13.21* 16.39*

(7.06) (8.46)

Female economic activity rate 0.45*** 0.34**

(0.14) (0.15)

Gross tertiary enrolment, female/male ratio 8.74* 13.61***

(4.65) (4.57)

log GDP per capita, 2003 -6.56*** 1.09 -3.12 -1.35 -2.23 0.52 -0.56 0.36

(2.40) (2.26) (1.93) (2.01) (2.71) (2.71) (2.15) (1.98)

Constant -19.62 -57.16** -2.75 -7.84 -3.02 -16.09 21.49 12.81

(20.01) (23.27) (17.72) (19.80) (22.62) (27.90) (19.80) (19.48)

Observations 37 32 39 38 37 32 39 38

R-squared 0.32 0.15 0.23 0.10 0.20 0.14 0.12 0.21

12

The high variance hypothesis

Women emancipation (GGI) 2.39±

0.81**

Avg. WVS indicators 0.14±

0.19

Female economic activity rate 0.01±

0.00**

Women Political Empowerment 0.69±

0.29*

Log GDP per capita, 2003 -0.17± 0.08± -0.08± -0.13±

0.07* 0.06 0.05 0.07

Constant 0.46± -0.69± 0.63± 1.63±

0.6 0.62 0.49 0.68*

Observations 37 32 39 36

R-squared 0.22 0.11 0.25 0.16

Ratio girls-to-boys above 99th percentile, math

13

More evidence in favor of genetic?

• What if correlations between emancipation and gender gap are explained by genetic differences across countries?

• If Iceland women are “better” than in other countries (especially vis-à-vis men).

• To rule out this hypothesis, collected information on “genetic distance” across populations of different countries (Cavalli-Sforza data

• Re-run regressions among countries with similar “genetic material”– results are substantially similar. 14

Spurious correlations?

• We control for GDP, but many other possible countries characteristics are omitted from the regression.

• Our solution: insert country dummies (that control for all the possible institutional differences) => GGI becomes collinear with fixed effects.

• Solution: Insert the interaction between gender and GGI

15

Fixed effect regressions

Student individual score, mathematics Intercept 534.92± 536.54±

2.99** 2.97**

Gender -69.87± -57.11±

21.22** 22.43*

Gender * Women emancipation (GGI) 81.54± 134.86±

30.93** 38.19**

Gender * Log GDP per capita, 2003 -5.11±

2.38*

Country fixed effects Yes Yes Individual level controls Yes Yes Observations 132,124 132,124 R-squared 0.42 0.42

16

How does women emancipation affect scores ?

1) Economic channel: higher investmentHigher payoff --NO

– more hours in homework and classes– more effort in each class

2) Psychological channel -> NO– More self confidence– Less anxiety

17

How does women emancipation affect scores ?

3) Educational channel NA– Teaching style – Discipline– Different approach to subjects

4) Sociological channel NA– Role model– Peer pressure

18

Conclusions

• We identify a strong correlation between environmental factors (women emancipation) and gender gap in mathematics.

• Where women are treated more equally, they exhibit an absolute advantage in all fields.

• Note that men do better in more gender emancipated societies, according to the data.

• We did not find any clear explanation of the mechanisms in the data.

• Geometry results19

Can We Exclude A Comparative Advantage of Men in Math?

• Analyze math sub-scores.• On average men do better in all, but

particularly in geometry (spatial ability?) • The differential gap between geometry

and arithmetic does not seem to be affected by GGI

20

Do results generalize and hold?

1. Implicit Association Test correlation with TIMMS based gender gap in mathematics and science (Nosek et al., PNAS, 2009) https://implicit.harvard.edu/implicit/Launch?study=/user/education/genderscience/genderscience.expt.xml

2. Pope and Snydor (JEP, 2009) show similar pattern in the US.

3. Hyde and Mertz, PNAS 2009 meta-study focusing mostly on profound mathematical talent (Greater Male Variability Hypothesis)

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Greater Male Variability Hypothesis

• Ellis, 1894: excess male among the mentally defective and very few female geniuses.

• With more recent data Hyde and Mertz analyze IMO, PISA, and GGI. They find a correlation btw the three measures and especially a very big variability across countries in female IMO participation.

22

Hyde and Mertz

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