Technology and the Changing Family

Transcription

1 Technology and the Changing Family Jeremy Greenwood, Nezih Guner, Georgi Kocharkov and Cezar Santos UPENN; ICREA-MOVE, U. Autònoma de Barcelona and Barcelona GSE; Carlos III (Konstanz); and UPENN (Mannheim) FINET ROME June 2012

2 Introduction American households in the last 50 years 1. Decline in marriage and the rise in divorce Di erences by education levels

3 The Decline in Marriage and the Rise in Divorce Ever Married, fraction of population Marriage, < college Marriage, college Divorce, < college Divorce, college Divorced and single, fraction of ever married Year

4 Introduction American households in the last 50 years 1. Decline in marriage and the rise in divorce Di erences by education levels 2. Rise in Assortative Mating

5 The Rise in Assortative Mating Contingency Tables Husband 1960 Wife < College College < Col (0.823) (0.056) Col (0.113) (0.008) χ 2 = 40,567 corr = 0.41 n=241,488 Husband 2005 Wife < Coll Col < Col (0.450) (0.223) Col (0.218) (0.108) χ 2 = 93,446 corr = 0.52 n=347,210

6 The Rise in Assortative Mating Consider the following regression e w t = α + β t et h d j,t + γ t d j,t + ε t, j2j j2j e w t e h t 2 f0, 1g : wife s education 2 f0, 1g : husband s education d j,t : year dummies (1970, 1980, 1990, 2000, 2005)

7 The Rise in Assortative Mating Regression coefficient, β t β t 95% bounds 0.00 Year

8 Introduction American households in the last 50 years 1. Decline in marriage and the rise in divorce Di erences by education levels 2. Rise in Assortative Mating 3. Increase in Education and Labor-Force Participation (LFP) by Females

9 Increase in LFP by Females 0.8 College Female Labor-Force Participation Fraction < College Family Income Year Year

10 Education and Wages College Premium Gap Premium Gender Gap Year College Degree, % of females

11 What we do We develop a model to understand these facts Marriage and divorce di erent patterns by education rise in assortative mating Female labor supply Education All these are treated as endogenous variables

12 What we do We develop a model to understand these facts Ingridients Forces Economic and non-economic reasons for marriage Economies of scales in household consumption Home production Love Technological progress in the household sector Changing wage structure Gender wage gap College premium Growth in wages All these are taken as exogenous variables

13 What we do We develop a model to understand these facts We estimate the model Match steady state of model with data for 1960 and 2005 Decompose the e ects of di erent driving forces household technology vs. wages

14 Environment Females and males Married or single (divorced or never married) Educated (skilled) or not In nitely-lived agents with probability of death δ Agents are born with ability level a Draw from distribution A(a) in the beginning of adult life lna N(0, σ 2 a) Based on a, decide whether to get educated or not C (a) utility cost of education

15 Environment Each period singles meet other singles randomly Draw a match quality b Match quality changes over time Agents can divorce, divorced agents have to wait one period before they can match again There is a utility bonus from marrying someone who has the same education level. It does not change over time.

16 Environment One unit of time per person Housework Market work, h 2 f 0, hg Married males and singles supply h. Married females make a participation decision Utility cost k associated with female labor force participation Wages wage w e a for a male for e 2 f0, 1g wage φw e a for a female (gender gap = φ) wages change over time, both w 1 /w 0 and φ

17 Preferences Singles T s (c, n) = 1 1 ζ (c c)1 ζ + α 1 ξ n1 ξ c - market goods c - xed cost of maintaining a household n - home production

18 Preferences Couples Consumption: T m (c, n) = 1 c 1 ζ c 1 + χ 1 ζ + α 1 ξ n 1 + χ 1 ξ c is a public good subject to congestion, χ < 1 Compatibility for a couple (e, e ) M(e, e ) = µ 0 (1 e)(1 e ) {z } both non-college + µ 1 ee {z } both college Match quality b Utility cost k if wife works (constant over time)

19 Shocks Match quality b Singles Couples b N(b s, σ 2 b,s ) b 0 = (1 ρ b,m )b m + ρ b,m b + σ b,m q1 ρ b,m ε, with ε N(0, 1) Cost if wife works k k K (k)

20 Household Production n = h θd λ + (1 θ)(z h T ) λi 1/λ, 0 < λ < 1. z household s time endowment h T total market work d purchased household inputs p price of purchase household inputs household inputs and time are substitutes p declines over time

21 Singles Consider the consumption decision facing a single. This is a purely static problem. For g 2 ff, mg with ability a and educational attainment e 2 f0, 1g U g s (a, e) max c,n,d T s (c, n), subject to c = we φah pd, if g = f, w e ah pd, if g = m, and n = h θd λ + (1 θ)(1 h) λi 1/λ.

22 Married The static consumption problem for a married couple is U m m (a, e, a, e, k) max T m(c, n) h f k, c,n,d,h f 2f0,1g subject to and n = c = w e ah + w e φa hh f pd h θd λ + (1 θ)(2 h hh f ) λi 1/λ,

23 Singles DP V g s (a, e) = U g s (a, e) Z +β K Z B Z A f1 g (a, e, a, E g (a ), b, k)v g m (a, e, a, E g (a ), b, k) {z } get married +[1 1 g (a, e, a, E g (a ), b, k)]v g s (a, e) gdbs g (a )df (b)dk (k) {z } remain single dbs g (a ) endogenous distribution of singles of opposite gender E g (a ) education decision for a 1 g (a, e, a, e, b, k) indicator for a marriage V g m(a, e, a, E g (a ), b, k) value of being married

24 Education Choice V g s (a, e) - Value function, single agent At birth max fv s g (a, e) e2f0,1g ec (a)g. Decision rule e = E g (a). Cost C (a) = ε/a ω

25 Steady State S g (a) endogenous distribution of singles Z Z Z a 0 Z S g (a 0 ) = (1 δ) [1 1 g (a, E g (a), a, E g (a ), b, k)] K B A A {z } remain single ds g (a)dbs g (a )df (b)dk (k) Z Z Z a 0 Z +(1 δ) [1 1 g (a, E g (a), a, E g (a ), b, k)] K B A A {z } divorce dm g (a, a, b 1, k)dg (bjb 1 ) + δa(a 0 ) {z } replacing death

26 Estimation A Priori Information Two steady states: 1960 and 2005 Model period: 1 year Life span: 30 years Probability of survival: 1 1/30 = 0.97 Discount factor: β = Work time: h = 40/112 = 0.36 Household production: θ = 0.206, λ = McGrattan, Rogerson and Wright (1997)

27 Estimation Wages: College premium in = w 1,1960 (average ability for college men) w 0,1960 (average ability for non-college men) w 0,1960 = 1 w 1,1960 = 1.04 Increase in wages: 1.14 for non-college in w 0,2005 = 1.18 College premium in 2005: 1.76 w 1,2005 = 1.66 Gender gap estimate with Heckman correction φ 1960 = exp(eφ 1960 ) = φ 2005 = exp(eφ 2005 ) = 0.83.

28 Benchmark Economy Data and Benchmark Model Data Model Data Model Education Fem Males Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, frac

29 Benchmark Economy Data and Benchmark Model Data Model Data Model Education Fem Males Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, frac

30 Benchmark Economy Data and Benchmark Model Data Model Data Model Education Fem Males Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, frac

31 Estimated Parameters Parameters Estimated (Minimum Distance) Category Parameter Values Standard Error 95% Conf Int Preferences α = [1.170, 1.182] ξ = [2.968, 3.005] ζ = [1.806, 1.836] c= [0.046, 0.049] µ 0 = [0.057, 0.073] Ability µ 1 = [0.674, 0.993] σ a = [0.012, 0.018] Matching b s = [ 1.367, 1.056] σ b,s = [2.778, 3.025] b = 0.36 m [0.336, 0.377] σ b,m = [0.260, 0.295] Cost of Work b,m k l = [0.411, 0.569] ρ = [0.924, 0.941] Prices k h = [1.656, 2.361] p 1960 = [18.537, ] p 2005 = p 1960 e γ( ) Cost of Education γ = [0.064, 0.084] ε = [40.638, ] ω = [13.202, ]

32 Estimated Parameters Table 3: Parameters Estimated (Minimum Distance) Category Parameter Values Standard Error 95% Conf Int Preferences α = [1.170, 1.182] ξ = [2.968, 3.005] ζ = [1.806, 1.836] c= [0.046, 0.049] µ 0 = [0.057, 0.073] Ability µ 1 = [0.674, 0.993] σ a = [0.012, 0.018] Matching b s = [ 1.367, 1.056] σ b,s = [2.778, 3.025] b = 0.36 m [0.336, 0.377] σ b,m = [0.260, 0.295] Cost of Work b,m k l = [0.411, 0.569] ρ = [0.924, 0.941] Prices k h = [1.656, 2.361] p 1960 = [18.537, ] p 2005 = p 1960 e γ( ) Cost of Education γ = [0.064, 0.084] ε = [40.638, ] ω = [13.202, ]

33 Estimated Parameters Table 3: Parameters Estimated (Minimum Distance) Category Parameter Values Standard Error 95% Conf Int Preferences α = [1.170, 1.182] ξ = [2.968, 3.005] ζ = [1.806, 1.836] c= [0.046, 0.049] µ 0 = [0.057, 0.073] Ability µ 1 = [0.674, 0.993] σ a = [0.012, 0.018] Matching b s = [ 1.367, 1.056] σ b,s = [2.778, 3.025] b = 0.36 m [0.336, 0.377] σ b,m = [0.260, 0.295] Cost of Work b,m k l = [0.411, 0.569] ρ = [0.924, 0.941] Prices k h = [1.656, 2.361] p 1960 = [18.537, ] p 2005 = p 1960 e γ( ) Cost of Education γ = [0.064, 0.084] ε = [40.638, ] ω = [13.202, ]

34 Only Wages No Technological Progress in the Home (Change in Wage Structure Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

35 Only Wages No Technological Progress in the Home (Change in Wage Structure Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

36 Only Wages No Technological Progress in the Home (Change in Wage Structure Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

37 Only Wages Labor force participation of married females do not increase Indeed, for college educated women, it declines Income e ect due to higher wages Higher marriages and lower divorces in 2005 Still females get educated Insurance against being single Matching bene ts

38 Only Home Technologies No Change in Wage Structure (Technological Progress in the Home Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

39 Only Home Technologies No Change in Wage Structure (Technological Progress in the Home Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

40 Only Home Technologies No Change in Wage Structure (Technological Progress in the Home Only) Benchmark Experiment Benchmark Education Fem Males Fem Males Fem Males Marriage Fraction Sing Marr Sing Marr Sing Marr Rates < Coll Coll < Coll Coll < Coll Coll Marriage Divorce Sorting Wife Wife Wife Husband < Coll Coll < Coll Coll < Coll Coll < Coll Coll Corr, educ Participation All < Coll Coll Income, fraction

41 Only Home Technologies No increase in education No increase in assortative mating

42 Conclusions We develop an equilibrium model consistent with: a decline in marriage and a rise in divorce increasing assortative mating increasing education and female LFP Results: Technological progress in the household: increases married female LFP decline of marriage and rise of divorce Changes in the wage structure: increase education increase assortative mating.

43 Only Wages Married Female Labor-Force Participation Experiment/G.E. E ects Experiment/No G.E. E ects Benchmark Participation

44 Married DP V g m(a, e, a, e, b, k) = U g m(a, e, a, e, k) + b + M(e, e ) Z +βf B [1 g (a, e, a, e, b 0, k)v g m(a, e, a, e, b 0, k) {z } stay married +[1 1 g (a, e, a, e, b 0, k)]vs g (a, e) ]dg (b 0 jb)g {z } divorce

45 Marriage Decisions 1 g (a, e, a, e, b, k) = 1 if V g m(a, e, a, e, b, k) V g s (a, e) and Fixed point problem Vm g (a, e, a, e, b, k) Vs g (a, e )

46 Steady State S g (a) endogenous distribution of singles Z Z Z a 0 Z S g (a 0 ) = (1 δ) [1 1 g (a, E g (a), a, E g (a ), b, k)] K B A A {z } remain single ds g (a)dbs g (a )df (b)dk (k) Z Z Z a 0 Z +(1 δ) [1 1 g (a, E g (a), a, E g (a ), b, k)] K B A A {z } divorce dm g (a, a, b 1, k)dg (bjb 1 ) + δa(a 0 ) {z } replacing death

47 Steady State M g (a 0, a 0, b 0, k 0 ) = Z k 0 Z b 0 Z a 0 Z a 0 (1 δ) 1 g (a, E g (a), a, E g (a ), b, k) K B A A {z } new marriages dbs g e (a )ds g (a)df (b)dk (k) Z k 0 Z b 0 Z Z a 0 Z a 0 +(1 δ) 1 g (a, E g (a), a, E g (a ), b, k) K B B A A {z } stay married dm g (a, a, b 1, k)dg (bjb 1 )

48 Parameters Parameters A Priori information Category Parameter Values Criteria Preferences β = 0.96 (1 δ), χ = 0.70 A priori information Household Technology θ = 0.21, λ = 0.19 McGrattan et al (1997) Life span 1/δ = 30 A priori information Wages w 0,1960 = 1, w 1,1960 = 1.04 Data w 0,2005 = 1.18, w 1,2005 = 1.66 Data φ 1960 = 0.59, φ 2005 = 0.83 (gender gap) Data Hours h = 0.36 Data

49 Estimation Match a set of data moments for the 1960 and Let data represent a vector of data moments. Let M(ω) be model moments for a set of parameters ω De ne G (ω) data M(ω). Minimum distance estimation bω = arg max G (ω) 0 WG (ω), where W is some positive semi-de nite matrix. Standard errors, se ( bω) diag f [J( bω)0 WJ( bω)] 1 J( bω) 0 W ΣWJ( bω)[j( bω) 0 WJ( bω)] 10 g n where J( bω) M( bω)/ bω, Σ data 0 data, and n is the total number of observations.