1. Educational assortative mating and income inequality in Russia
Zinchenko Daria, Lukiyanova Anna
NRU Higher School of Economics, Moscow
5th International conference
«Modern Econometric Tools and Applications» (META2018)

2. MOTIVATION DEFINITION
Assortative mating means any systematic departure from random mating.
Normally, it is positive – people tend to marry the like in terms of education, race, ethnicity, social status, etc.
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Economists are mostly interested in educational assortative mating
Stylized facts:
The proportion of couples who share the same level of schooling has been growing over the past few decades.
BUT this does not necessarily mean the change in the assortativeness of marriage. This trend reflects the rise in the share of university graduates
Income inequality has risen in many countries.
This may be (or may be not) related to the rise in assortative mating.
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3. LITERATURE LITERATURE
Measurement problems: simple measures cannot control for changes in the distribution of education attainments  more elaborated measures account for gender-specific trends in education (Eika et al., 2014, 2017; Liu, Lu, 2006; De Rose, Fraboni, 2016; Hakak, Firpo, 2017).
Main findings for:
USA(1979–2013), Norway(1980–2007) and Ireland(1973–1995)—assortative mating is positive and has been increasing over time;
UK(1973–1995), Italy(1973–2013), Brazil(1992–2014) and East Asian Countries(1950– 1990)—assortative mating is positive and has been declining over time.
LITERATURE
Impact on income inequality
Main findings for:
USA(1980–2007), Denmark(1987–2006) changes in assortative mating had weak impact on the level of household income inequality (Eika et al., 2014, Breen, Salazar, 2014; Breen, Andersen, 2011).
USA(1960–2005), Canada(1980–2005) changes in assortative mating are important for changes in income inequality (Greenwood et al., 2014; Lu et al., 2011)

4. RESEARCH QUESTION
We aim to study the structure and dynamics of educational assortative mating in Russia ( ).
How does the expansion of higher education affect the measures of educational assortative mating?
What was the impact of educational assortative mating (if any) on income inequality?
What was the importance of various factors for the time trends in income inequality, including changes in educational assortative mating and educational composition?
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5. DATA RLMS HSE: 1995–2015 We employ
household questionnaires to identify the marital status (no distinction between married and cohabitating couples);
individual questionnaires to measure education, age, incomes.
Sample restriction:
only married and cohabitating couples;
both spouses are 18+ (the official minimal marriage age in Russia);
couples with missing information on age, education, incomes and those with suspiciously large incomes were excluded;
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6. Rise in educational attainment
The increase in university education were accompanied by substantial decline in the proportion of the population without a high school diploma.
The share of highly educated women was rising faster that of men.

7. Simple measures of assortative mating
4.6 P.P.
5.8 P.P.
1.2 P.P.

8. MEASURES OF MARRIAGE ASSORTATIVENESS: THINGS BECOME MORE COMPLICATED
LOCAL measure of assortative mating (Eika et al., 2014)
𝑠 𝑖𝑗 = 𝑝( 𝑥 𝑚 =𝑖, 𝑥 𝑓 =𝑗) 𝑝( 𝑥 𝑚 =𝑖)∙𝑝( 𝑥 𝑓 =𝑗) = 𝑁 𝑖𝑗 𝑚𝑓 𝑁 𝑁 𝑖 𝑚 𝑁 𝑚 𝑁 𝑚 𝑁 ∙ 𝑁 𝑗 𝑓 𝑁 𝑓 𝑁 𝑓 𝑁 = 𝑁 𝑖𝑗 𝑚𝑓 𝑁 𝑁 𝑖 𝑚 𝑁 𝑗 𝑓
𝑤ℎ𝑒𝑟𝑒 𝑥 𝑚 =𝑖 −𝑚𝑎 𝑙𝑒 ′ 𝑠 𝑒𝑑𝑢𝑐𝑎𝑡𝑢𝑜𝑛𝑎𝑙 𝑙𝑒𝑣𝑒𝑙 𝑖;
𝑥 𝑓 =𝑗 −𝑓𝑒𝑚𝑎𝑙 𝑒 ′ 𝑠 𝑒𝑑𝑢𝑐𝑎𝑡𝑢𝑜𝑛𝑎𝑙 𝑙𝑒𝑣𝑒𝑙 𝑗;
𝑁 − 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑟𝑟𝑖𝑎ges;
𝑁 𝑖 𝑚 −𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑎𝑙𝑒𝑠 𝑤𝑖𝑡ℎ 𝑒𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 𝑙𝑒𝑣𝑒𝑙 𝑖;
𝑁 𝑗 𝑓 −𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑒𝑚𝑎𝑙𝑒𝑠 𝑤𝑖𝑡ℎ 𝑒𝑑𝑢𝑐𝑎𝑡𝑖𝑜𝑛 𝑙𝑒𝑣𝑒𝑙 𝑗.

9. LOCAL MEASURES: BY LEVEL OF EDUCATION
The Russian families are characterized by positive assortative mating.
The degree of assortative mating is the lowest among those in the middle by the level of education.
The assortative mating declines among the highly educated.
The assortative mating increases among the low educated.

10. TRENDS IN INCOME INEQUALITY
Income inequality declined over time.
Most of the reduction occurred at the ends of distribution.
The lower part of distribution contracted more rapidly than the upper part.

11. IMPACT ON INCOME INEQUALITY: METHODOLOGY (1)
In order to measure the counterfactual income inequality we use the decomposition method proposed by DiNardo et al. (1996) and extended by Eika et al. (2017).
There are three counterfactual scenarios:
impact of educational assortative mating (random mating);
changes in educational assortative mating;
changes in educational composition.
The method: this approach produces income distribution under the counterfactual scenario where the educational composition is fixed at the base year, while other variables stay at the 𝑡 year.
The reweighting function for rescaling the density function of income in 𝑡 year likes the following:
𝜓 𝑥 𝑥| 𝑡 𝑖𝑗 , 𝑡 𝑠 , 𝑡 𝑦 = 𝑑 𝐹 𝑥 ′ 𝑥| 𝑡 𝑖𝑗 =1995, 𝑡 𝑠 =𝑡 𝑑 𝐹 𝑥 𝑥| 𝑡 𝑦 =𝑡
𝑡 𝑖𝑗 −year where the educational composition is considered for estimation, 𝑡 𝑠 −year when the marital sorting parameters are measured, 𝑡 𝑦 −year in which incomes are measured.

12. Stochastic Matching Procedure
IMPACT ON INCOME INEQUALITY: METHODOLOGY (2)
𝜓 𝑥 ′ 𝑥| 𝑡 𝑖𝑗 , 𝑡 𝑠 , 𝑡 𝑦 = Ρ 𝑥 ′ 𝑡 𝑖𝑗 =1995, 𝑡 𝑠 =𝑡 Ρ 𝑥 𝑡 𝑦 =𝑡
We need to estimate Ρ 𝑥 ′ 𝑡 𝑖𝑗 =1995, 𝑡 𝑠 =𝑡 following some steps as done Eika et al. (2017).
Stochastic Matching Procedure
Draw one man from husband’s marginal distribution of education and one woman from wives' marginal distribution of education in 𝑡=1995. With probability
𝑃(𝐻𝑢𝑠𝑏𝑎𝑛𝑑=𝑖, 𝑡=1995)∙𝑃(𝑊𝑖𝑓𝑒=𝑗, 𝑡=1995)
we have a man and woman with level of education 𝑖, 𝑗.
They will get married with probability:
𝑃 ′ =𝑃(𝐻𝑢𝑠𝑏𝑎𝑛𝑑=𝑖, 𝑡=1995)∙𝑃(𝑊𝑖𝑓𝑒=𝑗, 𝑡=1995)∙ 𝑠 𝑖𝑗 (𝑡)
If they get married, we draw them from the marginal distributions of education. We repeat this steps until all husbands and wives have achieved a match.

13. IMPACT ON INCOME INEQUALITY: results (1)
Positive educational assortative mating has weak impact on income inequality.
1995
2000
2005
2010
2015
Impact in %
-1.9
-4.0
-4.4
-2.0
-4.3

14. IMPACT ON INCOME INEQUALITY: results (2)
Changes in assortative mating over time offset some of the increase in household income inequality.
Year
Impact in %
1995 –
2000
0.16
2005
0.02
2010
0.43
2015
0.18

15. IMPACT ON INCOME INEQUALITY: results (3)
Changes in the educational composition neutralize some of the increase in household income inequality.
Year
Impact in %
1995 –
2000
0.02
2005
0.34
2010
-0.22
2015
-1.27

16. conclusions
The Russian marriage market is characterized by positive assortative mating at all levels of education.
The decline of marital sorting parameter was most significant for university graduates.
At the same time assortative mating increased among the low educated.
Educational assortative mating matters very little for the distribution of household incomes.
Changes in assortative mating and in educational composition over time reduce some of the increase in household income inequality.
Изменение в уровне ассортативности и изменение в уровне образования. Учет одиночек и учет возрастной структуры.

17. Limits and future developments
Ages structure of the spouses is going to be taken into account.
The sample will be extended by including single women and men.
Изменение в уровне ассортативности и изменение в уровне образования. Учет одиночек и учет возрастной структуры.

18. Thank you
for your attention!