Free to Leave? A Welfare Analysis of Divorce Regimes

Transcription

1 Free to Leave? A Welfare Analysis of Divorce Regimes Raquel Fernández & Joyce Cheng Wong American Economic Journal: Macroeconomics 2017 Presented by Francisco Javier Rodríguez for the Macro Reading Group Universidad Carlos III de Madrid February 28, 2018 Fernández & Cheng Free to Leave? February 28, / 25

2 Introduction During the 1970s, the United States switched from mutual consent (MC) to a unilateral (U) divorce regime Research question Who benefited and who lost from the change in the divorce regime? Contributions Most of the work that studies the interplay of household formation, divorce regimes, and women s labor supply is empirical Contributions with respect to quantitative models: calibration is disciplined using key moments of the life cycle, analysis is not restricted to married couples, marriage decisions are endogenous Fernández & Cheng Free to Leave? February 28, / 25

3 Overview 1 I. The Benchmark Model 2 II. Household decisions 3 III. Parametrization 4 IV. Implications of the Calibrated Model 5 V. Welfare Analysis of Divorce Regimes 6 VI. Robustness 7 VII. Conclusion Fernández & Cheng Free to Leave? February 28, / 25

4 I. The Benchmark Model The Benchmark Model Key ingredients to understanding the welfare consequences of alternative divorce regimes: 1 Marital status is endogenous 2 Markets are imperfect: no insurance against income, marital or fertility shocks, debt is not state contingent 3 Households can save, labor supply of married and divorced women is endogenous Fernández & Cheng Free to Leave? February 28, / 25

5 I. The Benchmark Model The Benchmark Model Preliminaries Agents are born with a gender g {f, m}, endowed with a productivity parameter z 0 and a marital type z 0, live for T periods (from period 1 to t R they work and from period t R to T they are retired). Preferences and Markets Instantaneous utility function: where U g (c t, P t ; s) = c1 σ t 1 σ ψs g (k t )P t + 1 s q t c t = ĉ t e (k t ; s) Fernández & Cheng Free to Leave? February 28, / 25

6 I. The Benchmark Model The Benchmark Model Wages, Retirement Benefits, and Child Support Wages: ln y g (t, z t) = γ g + γ 1 t + γ 2 t 2 + z t; z t = ρ z z t 1 + ɛ yt, ɛ yt N (0, σ ɛ) Women who divorce receive child support payments from the father (fixed fraction of wage income). Retirement income is b s g (ȳ, ȳ ). Match Quality, Assets and Children Computational burden is reduced by assuming a permanent potential marital type. At the begining of each period, unmarried individuals draw q τ t N (µ τ u, σu). If married, qτ t evolves according to: q τ t+1 = ρqqτ t + uτ t, uτ t N (µ τ t, σu) Individials start life with zero assets, and we assume a t = ag (at). Only married women receive fertility shocks. Fernández & Cheng Free to Leave? February 28, / 25

7 I. The Benchmark Model The Benchmark Model Endogenous Marital Status: Timing and State Spaces Ω s t 1 : state space of an agent with marital status s upon entering period t (prior any resolution of uncertainty). Ω s t : state space just prior to making a marital decision Ω Mτ = {a t, z t, z Ω s t, qt, kt, χt ; r} if s = Mτ, τ {y, o} t = Ω S t = {a t, z t, z t, qt ; r} if s = S Ω D t = {a t, z t, z t, qt, χt ; r} if s = S χ t = {χ ft, χ mt } where [( χ ft = k f ) ( 1t, z 1t, k f ) ( 2t, z 2t,..., k f )] nt, z nt and χ mt = [ k m 1t, km 2t,..., ] km nt Timing for divorced and single agents Fernández & Cheng Free to Leave? February 28, / 25

8 II. Household decisions A. Marriage and Divorce The (Re)Marriage Decision ( ) ( M if EVgt M Ω s =M t Ω S t Vgt S ( ) ( s = M if EVgt M Ω s =M t Ω D t Vgt D s otherwise; s {D, S} where Ω s =S r Ω s =D t ) for both g = f, m and s = S ) for both g = f, m and s = D Ω s =M τ t = {a M t, z t, z t, q t, k t, χ t ; r}; a M t = a ft + a mt Fernández & Cheng Free to Leave? February 28, / 25

9 II. Household decisions A. Marriage and Divorce The Divorce Decision The expected value associated with divorcing: E ˆV ( ) gt D Ω s =D t Ω M t = ω t EVgt (Ω s s t Ω s =D t where Ω s =D ) + (1 ω t ) V D gt t = {at D, z t, z t, k t, χ t ; r} { at D φ r g a t if agent divorced in period t, g = f, m = otherwise a t ( Ω s =D t Ω M t ) Φ Fernández & Cheng Free to Leave? February 28, / 25

10 II. Household decisions A. Marriage and Divorce Divorce Decision Under Mutual Consent (r = MC) Divorce occurs when Case 1: For φ = 0.5, E ˆV ( ) ( ) gt D Ω s =D t Ω M t Vgt M Ω s =M t Ω M t for both g {f, m} and at least one strict equality Case 2: If the above holds for only one spouse, solve for the division φ g of marital assets such that E ˆV ( ) ( ) D g t Ω s =D t Ω M t = V M g t Ω s =M t Ω M t where g is the sex of the spouse that strictly does not want to divorce with φ = 0.5, 0 φ g 1 and E ˆV ( ) ( ) gt D Ω s =D t Ω M t > Vgt M Ω s =M t Ω M t given at D = ( ) 1 φ g a M t Divorce Decision Under Unilateral Consent (R = U) ( ) ( ) Divorce occurs when E ˆV gt D Ω s =D t Ω M t > Vgt M Ω s =M t Ω M t at φ = 0.5 for at least one g {f, m} Fernández & Cheng Free to Leave? February 28, / 25

11 II. Household decisions B. The Maximization Problems Retirement (R): t R + 1 to T Upon retirement there are no longer any shocks to income or love: VR,gt s ( ) at ; ȳ g, ȳ g = max u(c t ) + I s q t + βv s ( a R,g,t+1 at+1 ; ȳ g, ȳ g ) t+1 Working Life: t = 1 to t R Divorced women: V D ft ( Ω s =D t ) = max a t+1,p t [ c 1 σ ] [ ( )] t 1 σ ψd f (k t)p t + βe Vf s,t+1 Ω s =s t+1 Ω D t subject to ĉ t + a t+1 = Ra t + [y ft κ(k t )] P t + h(χ ft ) Fernández & Cheng Free to Leave? February 28, / 25

12 II. Household decisions B. The Maximization Problems Working Life: t = 1 to t R Single agents: V S gt ( Ω s =S t Married households: ( ) = max H M t Ω s =M t ) [ c 1 σ t λ a t+1,p t [ + β λevf s,t+1 E {s =D}Φ ] subject to [ c 1 σ ] [ ( )] t = max + βe Vg,t+1 s Ω s =s t+1 Ω S t a t+1 1 σ subject to c t + a t+1 = Ra t + y gt 1 σ ψm f (k t)p t + q t ( Ω s =s f,t+1 Ω M t ] [ c 1 σ t + (1 λ) ) + (1 λ) EV s m,t+1 ] 1 σ + qt ( Ω s =s m,t+1 Ω M t ĉ t + a t+1 = Ra t + y mt h(χ mt) + h(χ ft ) + [y ft κ(k t)] P t ) Fernández & Cheng Free to Leave? February 28, / 25

13 III. Parametrization Parametrization A. The Marriage Market: Expectations and Calibration Spousal types function as artificial agents, when it comes to implications generated by the model, the authors use onle the real agents B. Data Sources Labor statistics: waves of March CPS supplement Marital status transition statistics: marital history module of 2001 and 2004 SIPP Data to calibrate income process: PSID Fernández & Cheng Free to Leave? February 28, / 25

14 III. Parametrization Parametrization Fernández & Cheng Free to Leave? February 28, / 25

15 IV. Implications of the Calibrated Model Implications of the Calibrated Model A. Model Fit and Calibrated Parameters Fernández & Cheng Free to Leave? February 28, / 25

16 IV. Implications of the Calibrated Model Implications of the Calibrated Model A. Model Fit and Calibrated Parameters Disutility of Labor: Consumption Equivalence Fernández & Cheng Free to Leave? February 28, / 25

17 IV. Implications of the Calibrated Model Implications of the Calibrated Model A. Model Fit and Calibrated Parameters Fernández & Cheng Free to Leave? February 28, / 25

18 IV. Implications of the Calibrated Model Implications of the Calibrated Model B. Married Women s LFP Fernández & Cheng Free to Leave? February 28, / 25

19 IV. Implications of the Calibrated Model Implications of the Calibrated Model B. Married Women s LFP Fernández & Cheng Free to Leave? February 28, / 25

20 IV. Implications of the Calibrated Model Implications of the Calibrated Model B. Married Women s LFP Fernández & Cheng Free to Leave? February 28, / 25

21 V. Welfare Analysis of Divorce Regimes Welfare Analysis of Divorce Regimes A. The Impact of Divorce Regimes on Marriages and Divorce Fernández & Cheng Free to Leave? February 28, / 25

22 V. Welfare Analysis of Divorce Regimes Welfare Analysis of Divorce Regimes B. Ex Ante Welfare Fernández & Cheng Free to Leave? February 28, / 25

23 V. Welfare Analysis of Divorce Regimes Welfare Analysis of Divorce Regimes B. Ex Ante Welfare Fernández & Cheng Free to Leave? February 28, / 25

24 VI. Robustness Robustness Commitment within the household: under MC, there s equivalence between commitment assumptions, but not under U. Allowing for Pareto weights to change, LFP increases more than in benchmark model, but welfare results are very similar. Love as a private good: allow love draws and shocks to be independent across partners. Welfare gains for men and loses for women become larger. Experience, Pareto weights, asset splits, and childcare costs: similar results. Fernández & Cheng Free to Leave? February 28, / 25

25 VII. Conclusion Conclusion Quantitative life-cycle model of endogenous marital status. Imperfect capital and insurance markets, limited commitment. Gender assymetries: women s earnings are lower and women bear larger share of raising children upon divorce In the future, the model can be used as a laboratory to evaluate policy changes Fernández & Cheng Free to Leave? February 28, / 25

26 Timing for Divorced and Single Agents Endogenous Marital Status: Timing and State Spaces Fernández & Cheng Free to Leave? February 28, / 25

27 Disutility of Labor: Consumption Equivalence Parameters Calibrated Internally Fernández & Cheng Free to Leave? February 28, / 25