The inequality of equal mating Rolf Aaberge 1 Jo Thori Lind 2 Kalle - - PowerPoint PPT Presentation

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The inequality of equal mating Rolf Aaberge 1 Jo Thori Lind 2 Kalle - - PowerPoint PPT Presentation

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The inequality of equal mating Rolf Aaberge 1 Jo Thori Lind 2 Kalle Moene 2 1 Statistics Norway 2 University of Oslo January 23, 2018 1 / 22 Assortative mating Marriage within own socio-economic group has existed in all societies at all

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SLIDE 1

The inequality of equal mating

Rolf Aaberge1 Jo Thori Lind2 Kalle Moene2

1Statistics Norway 2University of Oslo

January 23, 2018

1 / 22

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SLIDE 2

Assortative mating

◮ Marriage within own socio-economic group has existed in all

societies at all times

◮ Persons with high earnings marry others with high earnings

2 / 22

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SLIDE 3

Assortative mating

◮ Marriage within own socio-economic group has existed in all

societies at all times

◮ Persons with high earnings marry others with high earnings ◮ What does this imply for the inequality between households?

2 / 22

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SLIDE 4

Not a trivial question

◮ The rich marry within their class

Exacerbates inequality

3 / 22

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SLIDE 5

Not a trivial question

◮ The rich marry within their class

Exacerbates inequality

◮ The poor marry within their class

Also exacerbates inequality, but at the bottom of the distribution

3 / 22

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SLIDE 6

Not a trivial question

◮ The rich marry within their class

Exacerbates inequality

◮ The poor marry within their class

Also exacerbates inequality, but at the bottom of the distribution

◮ Still the richest can afford non-working spouses and spouses

with low income potenial

◮ “Trophy wives” ◮ “Gold diggers”

◮ Such effect could reduce inequality

3 / 22

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SLIDE 7

Hypotesis

  • 1. Equal mating into households leads to inequality between

households

  • 2. All countries have a neutral middle where equal mating has

little effect. Most of the effect is in the tails of the income distribution

  • 3. Not random whether countries are affected most in the upper
  • r the lower tail

4 / 22

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SLIDE 8

Data

◮ Taken from the Luxembourg Income Study ◮ Micro data from a total of 254 surveys covering 46 countries

  • ver the period 1967-2013.

◮ Mostly rich (OECD) countries but recently more middle

income and transition countries

◮ We focus on husband’s and wife’s labor income

◮ Avoids issues of joint taxation and jointly determined transfers ◮ Ignores equalizing effect through taxes and transfers

◮ Including capital income has negligible effect

◮ The super rich not in the sample

◮ Disposable income is a combination of assortative mating and

welfare state arrangements

◮ Interesting, but not what we study here 5 / 22

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SLIDE 9

Data – our sample

◮ We only consider husband and wife

Other family members disregarded

◮ Keep households were both are between 25 and 61 years old ◮ Leave out households earning less than 10 % of median

income to avoid unrealistically low incomes Typically this is less than 1 % of the sample

6 / 22

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SLIDE 10

Basics

◮ Household – husband and wife ◮ Incomes Y1 and Y2

Household income Y = Y1 + Y2

◮ Let F1, F2, and F be the associated distribution functions ◮ How does inequality in Y depend on the inequality in Y1 and

Y2 and the association between Y1 and Y2?

7 / 22

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SLIDE 11

Basics – our experiment

◮ Construct a hypothetical income distribution with random

matching Fr

◮ Each man matched with a random woman ◮ Repeated draws have minor effects

◮ No flocking ⇐

⇒ Fr(y) = F(y) for all y

◮ Flocking: the difference between actual and hypothetical

distributions

◮ Difference: CDF, normalized Lorenz curves ◮ Also: Fmax and Fmin based on perfect positive and negative

assortative mating. The boundaries implied by the income distribution of each gender

8 / 22

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SLIDE 12

Basics – the theoretical answer

Simulate income distributions, varying inequality and association Y1 − Y2; compute Gini coefficient

ρ=0.2 ρ=0.4 ρ=0.6 ρ=0.8 ρ=1.0

.02 .04 .06 .08 .1 Flocking .2 .4 .6 .8 1 Gini men

◮ Flocking increasing in association ρ ◮ Flocking inverted U-shaped in inequality

9 / 22

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SLIDE 13

Basics – the theoretical answer

Simulate income distributions, varying inequality and association Y1 − Y2; compute Gini coefficient

ρ=0.2 ρ=0.4 ρ=0.6 ρ=0.8 ρ=1.0

.02 .04 .06 .08 .1 Flocking .2 .4 .6 .8 1 Gini men

Holds empirically:

(G − Gr) = −0.057

(0.007) + 0.099 (0.029)G1 −0.082 (0.028) G 2 1 + 0.077 (0.018)G2 −0.044 (0.014) G 2 2 + 0.137 (0.003)ρ

9 / 22

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SLIDE 14

Caveat

◮ We keep incomes constant when changing couple structures ◮ In reality incomes would change due to e.g. labor supply

reactions

◮ This paper studies the current distribution of income, not a

real world policy experiment

10 / 22

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SLIDE 15

Winners and losers

◮ A household with income y occupies rank u = F(y) ∈ [0, 1] ◮ A household occupying rank u gets income F −1(u),

and would have gotten F −1

r

(u) with random matching

◮ Gain relative to random matching given by

ΛF(u) = F −1(u) − F −1

r

(u) µ for 0 ≤ u ≤ 1

11 / 22

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SLIDE 16

Winners and losers

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Norway

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Sweden

−.4 −.2 .2 .4 20 40 60 80 100 Percent

United Kingdom

−.4 −.2 .2 .4 20 40 60 80 100 Percent

United States

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Germany

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Spain

−.4 −.2 .2 .4 20 40 60 80 100 Percent

France

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Italy

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Czech republic

−.4 −.2 .2 .4 20 40 60 80 100 Percent

Poland

−.5 .5 1 1.5 20 40 60 80 100 Percent

South Africa

−.5 .5 1 1.5 20 40 60 80 100 Percent

Brazil

11 / 22

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SLIDE 17

Winners and losers

loosers winners neutral middle Country uL 1 − uH uH − uL Sweden 18 13 69 Norway 19 13 68 Germany 20 12 68 United Kingdom 24 11 65 Spain 27 13 60 United States 29 12 59 Czech republic 25 16 59 Poland 30 12 58 France 31 13 56 Italy 30 14 56 Brazil 8 92 South Africa 81 11 8

11 / 22

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SLIDE 18

Contributions to inequality

◮ How large is deviation from equality at each quantile u? ◮ How much of this is given by systematic matching? ◮ Given by Lorenz curves L(u) and Lr(u) ◮ Need to compare L and Lr

12 / 22

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SLIDE 19

Contributions to inequality

Depicting income distributions

◮ The standard Lorenz curve

L(u) = 1 µ u F −1(t) dt Tells too little about low incomes

Lorenz curve

.2 .4 .6 .8 1 20 40 60 80 100 Percent

12 / 22

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SLIDE 20

Contributions to inequality

Depicting income distributions

◮ The standard Lorenz curve

L(u) = 1 µ u F −1(t) dt Tells too little about low incomes

◮ The normalized Lorenz curve

(M curve) (Aaberge, 2007) M(u) = 1 uµ u F −1(t) dt =

  • if u = 0

L(u) u

if 0 < u ≤ 1

Lorenz curve

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Normalized Lorenz curve

.2 .4 .6 .8 1 20 40 60 80 100 Percent

12 / 22

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SLIDE 21

Contributions to inequality

Normalized Lorenz curves for pre-tax earnings

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Norway

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Sweden

.2 .4 .6 .8 1 20 40 60 80 100 Percent

United Kingdom

.2 .4 .6 .8 1 20 40 60 80 100 Percent

United States

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Germany

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Spain

.2 .4 .6 .8 1 20 40 60 80 100 Percent

France

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Italy

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Czech republic

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Poland

.2 .4 .6 .8 1 20 40 60 80 100 Percent

South Africa

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Brazil

Solid green is observed, dashed orange hypothetical. Shaded area possible distributions between perfect positive and negative assortative mating. Lorenz 12 / 22

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SLIDE 22

Contributions to inequality

Flocking curves ΓL(u) = Lr (u)−L(u)

u

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Norway

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Sweden

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

United Kingdom

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

United States

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Germany

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Spain

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

France

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Italy

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Czech republic

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Poland

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

South Africa

.02 .04 .06 .08 .1 20 40 60 80 100 Percent

Brazil

Lorenz 12 / 22

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SLIDE 23

Ranking flocking curves

Notation

◮ An inequality associated flocking curve is defines as Flocking

curves ΓL(u) = Lr(u)−L(u)

u ◮ Following a “dual approach”, a welfare function can be

defined as Jp(L) = 1 + 1 up′(u)L(u) u du where p(u) is a weighting on quantile u (non-negative, non-increasing)

◮ One family of flocking together measures is

∆p(L) = Jp(Lr) − Jp(L)

13 / 22

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SLIDE 24

Ranking flocking curves

Main theoretical results

Theorem

Let ΓL1 and ΓL2 be two flocking curves. Then the following are equivalent: (i) ΓL1 first degree dominates ΓL2 i.e. ΓL1(u) ≤ ΓL2(u) for all u and strictly for some (ii) ΓL2 can be obtained from ΓL1 by a sequence of correlation increasing transfers (iii) ∆p(L1) < ∆p(L2) for all positive increasing functions p

◮ Informally, there is more flocking under L2 than under L1 ◮ Mirrors results on Lorenz dominance and inequality

measurement

13 / 22

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SLIDE 25

Ranking flocking curves

Implementation

◮ Compare a class of inequality measures under the observed

and counter factual income distribution

◮ Using a single measure does not tell the whole story

◮ Specifically we use the measures

Ck =

1

  • ukdM(u)

◮ C2 is the Gini coefficient. ◮ C1 emphasizes low incomes more and C3 high incomes more ◮ Construct differences ∆i = Ci − Cir

13 / 22

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SLIDE 26

Flocking

Visualization

For each income distribution and choice of i

◮ C Actual inequality ◮ C+ with perfect assortative mating ◮ C− with perfect inverse assortative mating ◮ Cr with random mating

C− C Cr C+

14 / 22

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SLIDE 27

C2 wage income: The Gini

2.51 3.10 2.73 2.16 2.02 3.92 4.45 3.83 3.66 3.74 4.54 4.86

Norway (2010) Sweden (2005) UK (2013) US (2013) Germany (2010) Spain (2013) France (2010) Italy (2010) Czech Rep (2010) Poland (2013) South Africa (2012) Brazil (2013)

.2 .4 .6 .8 1 Inequality C2

14 / 22

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SLIDE 28

C1 wage income: Focus on low incomes

3.77 4.34 3.59 2.42 2.64 3.70 5.08 4.20 4.66 4.03 3.30 4.40

Norway (2010) Sweden (2005) UK (2013) US (2013) Germany (2010) Spain (2013) France (2010) Italy (2010) Czech Rep (2010) Poland (2013) South Africa (2012) Brazil (2013)

.2 .4 .6 .8 1 Inequality C1

14 / 22

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SLIDE 29

C3 wage income earnings: Focus on high incomes

1.89 2.45 2.11 1.90 1.64 3.75 3.65 3.20 2.91 3.19 5.03 4.83

Norway (2010) Sweden (2005) UK (2013) US (2013) Germany (2010) Spain (2013) France (2010) Italy (2010) Czech Rep (2010) Poland (2013) South Africa (2012) Brazil (2013)

.2 .4 .6 .8 1 Inequality C3

14 / 22

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SLIDE 30

Analyzing assortative mating

Additional data

◮ Log GDP/capita (WDI) ◮ Average female labor force participation (WDI) ◮ Nordic country

NB What follows are only correlations!

15 / 22

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SLIDE 31

Assortative mating (∆i = Ci − Cir)

Earnings, Gini (1) (2) (3) (4) Inequality 0.0665** 0.0831** 0.0852*** 0.0953*** (2.66) (2.61) (3.51) (3.34) Log GDP 0.00377 0.00338 0.00361 (0.97) (1.02) (1.10) Female lab part 0.000360*** 0.000284* (2.84) (1.98) Nordic country 0.00777 (1.37) N 254 232 223 223 r2 0.147 0.164 0.232 0.255

16 / 22

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SLIDE 32

Assortative mating (∆i = Ci − Cir)

Earnings, C1 measure (1) (2) (3) (4) Inequality 0.0207 0.0475 0.0502* 0.0659** (0.71) (1.31) (1.93) (2.20) Log GDP 0.00654 0.00612* 0.00631* (1.54) (1.76) (1.85) Female lab part 0.000478*** 0.000372** (3.78) (2.68) Nordic country 0.0115* (1.79) N 254 232 223 223 r2 0.0112 0.0396 0.159 0.207

16 / 22

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SLIDE 33

Assortative mating (∆i = Ci − Cir)

Earnings, C3 measure (1) (2) (3) (4) Inequality 0.0875*** 0.0967*** 0.0983*** 0.106*** (3.80) (3.32) (4.29) (3.98) Log GDP 0.00185 0.00148 0.00167 (0.55) (0.49) (0.56) Female lab part 0.000279** 0.000222 (2.39) (1.66) Nordic country 0.00563 (1.17) N 254 232 223 223 r2 0.269 0.278 0.327 0.341

16 / 22

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SLIDE 34

Where does assortative mating take place?

∆1 vs ∆3, wage income – ranks

Austria Australia Belgium Canada Czech Rep Germany Denmark France Iceland Japan Netherlands Norway Sweden Slovak Rep. UK Switzerland China Estonia Finland Hungary Ireland Israel India Italy South Korea Luxembourg Panama Poland Serbia Slovenia Taiwan US Brazil Colombia Dominican Republic Egypt Spain Georgia Greece Guatemala Mexico Peru Paraguay Russia Uruguay South Africa

10 20 30 40 50 Rank flocking3 10 20 30 40 50 Rank flocking1

17 / 22

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SLIDE 35

Where does assortative mating take place?

The role of income

Austria Australia Belgium Canada Switzerland China Czech Rep Germany Denmark Dominican Republic Estonia France Greece Guatemala Ireland India Iceland Italy Japan South Korea Netherlands Norway Sweden Slovak Rep.

−20 −10 10 20 8 9 10 11 Log GDP

17 / 22

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SLIDE 36

Where does assortative mating take place?

Explaining the difference (1) (2) (3) (4) (5) (6) Log GDP

  • 6.956***
  • 2.273
  • 2.208
  • 16.84*
  • 3.069

(-3.00) (-0.52) (-0.49) (-1.82) (-0.64) C2 Inequality 68.19*** 40.39 39.27 101.3*** 28.45 (4.76) (1.36) (1.31) (3.01) (0.81) Female lab part

  • 0.0697

0.279 0.0255 (-0.30) (0.68) (0.09) Welfare state generosity 0.0292 (0.11) Nordic country

  • 4.938

(-1.21) N 24 46 24 24 15 24 r2 0.343 0.488 0.404 0.407 0.558 0.430

17 / 22

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SLIDE 37

Summary ... so far

◮ Intra-household sharing rules affects individual benefits of

couple formation and hence choice of spouse

◮ We present an extension of inequality measurement to

measure the inequality effects of assortative mating

◮ Nordic counties: Effect of matching at the bottom ◮ Middle income countries: Effect of matching at the top

◮ More inequality driven by assortative mating seems to be

correlated with gender equality

18 / 22

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SLIDE 38

Future work

◮ Difference wage income – disposable income:

The role of the welfare state

◮ Use Norwegian register data

◮ Mating among the super rich

◮ Evolution over time

US vs Norway

◮ Model the couple formation ◮ Labor supply?

19 / 22

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SLIDE 39

Thank you!

20 / 22

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SLIDE 40

Lorenz curves for earnings

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Norway

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Sweden

.2 .4 .6 .8 1 20 40 60 80 100 Percent

United Kingdom

.2 .4 .6 .8 1 20 40 60 80 100 Percent

United States

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Germany

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Spain

.2 .4 .6 .8 1 20 40 60 80 100 Percent

France

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Italy

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Czech republic

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Poland

.2 .4 .6 .8 1 20 40 60 80 100 Percent

South Africa

.2 .4 .6 .8 1 20 40 60 80 100 Percent

Brazil

Solid green is observed, dashed orange hypothetical. Income is pre-tax wage income, excluding zero incomes. Back 21 / 22

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SLIDE 41

Ψ, difference between Lorenz curves for wage incomes

−.1 −.05 .05 20 40 60 80 100 Percent

Norway

−.1 −.05 .05 20 40 60 80 100 Percent

Sweden

−.1 −.05 .05 20 40 60 80 100 Percent

United Kingdom

−.1 −.05 .05 20 40 60 80 100 Percent

United States

−.1 −.05 .05 20 40 60 80 100 Percent

Germany

−.1 −.05 .05 20 40 60 80 100 Percent

Spain

−.1 −.05 .05 20 40 60 80 100 Percent

France

−.1 −.05 .05 20 40 60 80 100 Percent

Italy

−.1 −.05 .05 20 40 60 80 100 Percent

Czech republic

−.1 −.05 .05 20 40 60 80 100 Percent

Poland

−.1 −.05 .05 20 40 60 80 100 Percent

South Africa

−.1 −.05 .05 20 40 60 80 100 Percent

Brazil

Back 22 / 22