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 times ◮ Persons with high earnings marry others with high earnings 2 / 22
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
Not a trivial question ◮ The rich marry within their class Exacerbates inequality 3 / 22
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
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
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 or the lower tail 4 / 22
Data ◮ Taken from the Luxembourg Income Study ◮ Micro data from a total of 254 surveys covering 46 countries over 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
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
Basics ◮ Household – husband and wife ◮ Incomes Y 1 and Y 2 Household income Y = Y 1 + Y 2 ◮ Let F 1 , F 2 , and F be the associated distribution functions ◮ How does inequality in Y depend on the inequality in Y 1 and Y 2 and the association between Y 1 and Y 2 ? 7 / 22
Basics – our experiment ◮ Construct a hypothetical income distribution with random matching F r ◮ Each man matched with a random woman ◮ Repeated draws have minor effects ◮ No flocking ⇐ ⇒ F r ( y ) = F ( y ) for all y ◮ Flocking: the difference between actual and hypothetical distributions ◮ Difference: CDF, normalized Lorenz curves ◮ Also: F max and F min based on perfect positive and negative assortative mating. The boundaries implied by the income distribution of each gender 8 / 22
Basics – the theoretical answer Simulate income distributions, varying inequality and association Y 1 − Y 2 ; compute Gini coefficient .1 .08 ρ =1.0 ρ =0.8 .06 Flocking ρ =0.6 .04 ρ =0.4 .02 ρ =0.2 0 0 .2 .4 .6 .8 1 Gini men ◮ Flocking increasing in association ρ ◮ Flocking inverted U-shaped in inequality 9 / 22
Basics – the theoretical answer Simulate income distributions, varying inequality and association Y 1 − Y 2 ; compute Gini coefficient .1 ρ =1.0 .08 ρ =0.8 .06 Flocking ρ =0.6 .04 ρ =0.4 .02 ρ =0.2 0 0 .2 .4 .6 .8 1 Gini men Holds empirically: (0 . 028) G 2 (0 . 014) G 2 ( G − G r ) = − 0 . 057 (0 . 007) + 0 . 099 (0 . 029) G 1 − 0 . 082 1 + 0 . 077 (0 . 018) G 2 − 0 . 044 2 + 0 . 137 (0 . 003) ρ 9 / 22
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
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 ( u ) with random matching r ◮ Gain relative to random matching given by Λ F ( u ) = F − 1 ( u ) − F − 1 ( u ) r for 0 ≤ u ≤ 1 µ 11 / 22
Winners and losers Norway Sweden United Kingdom United States .4 .4 .4 .4 .2 .2 .2 .2 0 0 0 0 −.2 −.2 −.2 −.2 −.4 −.4 −.4 −.4 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Germany Spain France Italy .4 .4 .4 .4 .2 .2 .2 .2 0 0 0 0 −.2 −.2 −.2 −.4 −.2 −.4 −.4 −.4 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Czech republic Poland South Africa Brazil .4 .4 1.5 1.5 .2 .2 1 1 0 0 .5 .5 −.2 −.2 0 0 −.4 −.4 −.5 −.5 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent 11 / 22
Winners and losers loosers winners neutral middle Country 1 − u H u L u H − u L 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 0 8 92 South Africa 81 11 8 11 / 22
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 L r ( u ) ◮ Need to compare L and L r 12 / 22
Contributions to inequality Depicting income distributions ◮ The standard Lorenz curve Lorenz curve � u 1 L ( u ) = 1 F − 1 ( t ) dt .8 µ 0 .6 Tells too little about low .4 incomes .2 0 0 20 40 60 80 100 Percent 12 / 22
Contributions to inequality Depicting income distributions ◮ The standard Lorenz curve Lorenz curve � u 1 L ( u ) = 1 F − 1 ( t ) dt .8 µ 0 .6 Tells too little about low .4 incomes .2 ◮ The normalized Lorenz curve 0 0 20 40 60 80 100 Percent (M curve) (Aaberge, 2007) � u Normalized Lorenz curve M ( u ) = 1 F − 1 ( t ) dt 1 u µ 0 .8 � 0 if u = 0 .6 = L ( u ) if 0 < u ≤ 1 .4 u .2 0 0 20 40 60 80 100 Percent 12 / 22
Contributions to inequality Normalized Lorenz curves for pre-tax earnings Norway Sweden United Kingdom United States 1 1 1 1 .8 .8 .8 .8 .6 .6 .6 .6 .4 .4 .4 .4 .2 .2 .2 .2 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Germany Spain France Italy 1 1 1 1 .8 .8 .8 .8 .6 .6 .6 .6 .4 .4 .4 .4 .2 .2 .2 .2 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Czech republic Poland South Africa Brazil 1 1 1 1 .8 .8 .8 .8 .6 .6 .6 .6 .4 .4 .4 .4 .2 .2 .2 .2 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Solid green is observed, dashed orange hypothetical. Shaded area possible distributions between perfect Lorenz positive and negative assortative mating. 12 / 22
Contributions to inequality Flocking curves Γ L ( u ) = L r ( u ) − L ( u ) u Norway Sweden United Kingdom United States .1 .1 .1 .1 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Germany Spain France Italy .1 .1 .1 .1 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Czech republic Poland South Africa Brazil .1 .1 .1 .1 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 .02 .04 .06 .08 0 0 0 0 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 Percent Percent Percent Percent Lorenz 12 / 22
Ranking flocking curves Notation ◮ An inequality associated flocking curve is defines as Flocking curves Γ L ( u ) = L r ( u ) − L ( u ) u ◮ Following a “dual approach”, a welfare function can be defined as � 1 up ′ ( u ) L ( u ) J p ( L ) = 1 + du u 0 where p ( u ) is a weighting on quantile u (non-negative, non-increasing) ◮ One family of flocking together measures is ∆ p ( L ) = J p ( L r ) − J p ( L ) 13 / 22
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