Discussion of Fertility, Social Mobility and Long-Run Inequality

Transcription

1 Discussion of Fertility, Social Mobility and Long-Run Inequality by Juan Carlos Cordoba, Xiying Liu, and Marla Ripoll Ali Shourideh Wharton

2 Intergenerational Persistence There seems to be a great deal of persistence in economic outcomes wealth, earnings, schooling, etc.

3 Intergenerational Persistence There seems to be a great deal of persistence in economic outcomes wealth, earnings, schooling, etc. Is this consistent with altruism and fertility choice?

4 Intergenerational Persistence There seems to be a great deal of persistence in economic outcomes wealth, earnings, schooling, etc. Is this consistent with altruism and fertility choice? Potentially important: How much of inequality comes from being born in large families Non-altruistic motives for fertility tax policy to fix the possible externalities

5 Standard Framework Barro-Becker model of endogenous fertility (Alvarez (1999)) subject to max c1 σ 1 σ + βnε V(B /n; ω) c + λ(ω)n + B = ω + (1 + r)b

6 Standard Framework Barro-Becker model of endogenous fertility (Alvarez (1999)) subject to max c1 σ 1 σ + βnε V(B /n; ω) c + λ(ω)n + B = ω + (1 + r)b Preferences are homothetic in (n, B ): n ɛ V(B /n; ω)

7 Standard Framework Barro-Becker model of endogenous fertility (Alvarez (1999)) subject to max c1 σ 1 σ + βnε V(B /n; ω) c + λ(ω)n + B = ω + (1 + r)b Preferences are homothetic in (n, B ): n ɛ V(B /n; ω) wealth expansion paths are linear in

8 Standard Framework Barro-Becker model of endogenous fertility (Alvarez (1999)) subject to max c1 σ 1 σ + βnε V(B /n; ω) c + λ(ω)n + B = ω + (1 + r)b Preferences are homothetic in (n, B ): n ɛ V(B /n; ω) wealth expansion paths are linear in B /n is independent of b

9 Barro-Becker B n

10 Barro-Becker B ω n

11 Barro-Becker B b ω n

12 Barro-Becker B B/n: constant b ω n

13 Standard Framework Barro-Becker model of endogenous fertility (Alvarez (1999)) subject to max c1 σ 1 σ + βnε V(B /n; ω) c + λ(ω)n + B = ω + (1 + r)b Preferences are homothetic in (n, B ) wealth expansion paths are linear in B /n is independent of b persistence: inconsistent with altruism More broad definition of altruism - can be warm-glow

14 Paper Cordoba, Liu and Ripoll: non-homothetic preferences + concave costs of children non-homothetic preferences: exponential discounting: β(1 e µn )V(B /n; ω) concave costs: cost of children: λ [ (n + κ) θ κ θ] MRS between n and B decreasing in n

15 Wealth-expansion lines B b ω n

16 Paper Cordoba, Liu and Ripoll: non-homothetic preferences + concave costs of children non-homothetic preferences: exponential discounting: β(1 e µn )V(B /n; ω) concave costs: cost of children: λ [ (n + κ) θ κ θ] My discussion: Are these assumptions reasonable? Are there other ways to create persistence?

17 Utility from kids How can we identify utility from kids?

18 Utility from kids How can we identify utility from kids? BB: Frisch elasticity of fertility is constant Exp.: decreasing elasticity Hard to identify perhaps from policy changes with respect to kids (e.g., one child policy, etc.)

19 Utility from kids How can we identify utility from kids? BB: Frisch elasticity of fertility is constant Exp.: decreasing elasticity Hard to identify perhaps from policy changes with respect to kids (e.g., one child policy, etc.) Alternative identification via wealth effect: look at how changes in house prices affect fertility

20 Evidence Lovenheim and Mumford (2013)

21 Evidence Lovenheim and Mumford (2013)

22 Alternative Mechanisms

23 Standard Barro-Becker BB not qualitatively in contradiction with persistence: If ω t is AR(m) b t is AR(m) Does it work? Special case: 1 σ = ε Cast the problem in terms of dynasty aggregates C t, N t, B t : subject to max C1 σ 1 σ + βe [V(ω N + (1 + r)b ; ω ) ω] C + λ(ω)n + B = ωn + (1 + r)b Standard portfolio problem with a risk-free bond and risky asset with return: ω λ(ω)

24 Standard Barro-Becker Solution - Samuelson/Merton: B N = 1 ρ n( ω) λ(ω) ρ n ( ω) ρ n determined by the stochastic process for ω /λ(ω) Olivetti and Paserman(2014): log ω = 0.07 log ω log ω + ɛ If λ(ω) is linear: 1% increase in ω increases ω /λ(ω) by 0.09% percent Does not seem to be able to create enough persistence

25 Intergenerational Transfers The only source of persistence: bequests Many households do not leave bequests or do not have bequest motives Hurd (1987): people with children deccumulate wealth faster! Kopczuk and Lupton (2007): around a quarter of the elderly do not have bequest motive The decision to have children is at a young age: uncertainty about bequests maybe need to consider other notions of intergenerational transfers

26 Quantity-Quality Trade-off subject to max c1 σ 1 σ + βnε V(ω ; ω) c + sn + λ(ω)n = ω ω = h(s, ω) Persistence through human capital: h(s, ω) Including bequests: same issue as before

27 Q-Q + Credit Constraints subject to max c1 σ 1 σ + βnε V(B /n(1 + r) + ω ; ω) c + sn + λ(ω)n + B = b + ω ω = h(s, ω) s f(b) Increase in b allows parents to invest more in children s quality increase in b leads to a higher cost of children: quantity bequest trade-off

28 Q-Q + Credit Constraints B b b n

29 Conclusion Break lack of persistence with non-homothetic preferences: needs some validation outside the model Alternative: Quality-quantity trade-off + credit constraints