Sang-Wook (Stanley) Cho

Transcription

1 Beggar-thy-parents? A Lifecycle Model of Intergenerational Altruism Sang-Wook (Stanley) Cho University of New South Wales, Sydney July 2009, CEF Conference

2 Motivation & Question Since Becker (1974), several studies analyzing the size and the effect of parental transfers to children, both intervivos transfers to younger children, and bequests. Borrowing constraints may induce the parents to transfer resources to constrained children (who tend to be younger) rather than leaving it for later bequests.

3 Question We analyse intergenerational transfer of wealth in the US vs. Korea using a standard lifecycle model with different transfer motives Explore the aggregate, distributional, and welfare impact of borrowing constraint The role of borrowing constraint in accounting for cross-country differences in wealth accumulation & timing of transfer

4 Preview of results Inter-vivos transfer with altruistic motive can account for, on average, 30% of total inter-vivos transfer from parents to children in both countries (29% for US, 32% for Korea) Higher borrowing constraints (that prevent children from borrowing to smooth their consumption) tend to generate larger transfers early in life (relative to bequests). This matches the empirical evidence from Korea (a stricter constraints country) and the US.

5 Aggregate Intervivos Transfer Table: Aggregate Intervivos Transfer - US, Korea Author Source Percentage TR TR Y Altonji et al. PSID 23% $ % (1997) (1988) (received) McGarry HRS 29% $ % (1999) (1992) (gave) Kim et al. KLIPS 21% $ % (2004) (2002) (received)

6 Age-Transfer Distribution Table: Age-Transfer Distribution - US, Korea Age Groups Fraction of households receiving transfers US 29.5% 22.6% 19.1% 16.5% 11.8% Korea 26.6% 28.6% 27.3% 19.1% 13.7% Transfer as a fraction of average household income US 4.3% 5.6% 6.5% 6.7% 4.8% Korea 5.2% 14.7% 9.9% 6.2% 9.2% Transfer as a fraction of average cohort income US 5.6% 5.2% 5.2% 5.2% 3.5% Korea 13.3% 14.0% 8.3% 5.5% 7.7%

7 Evidence of Borrowing Constraint? Table: Mortgage-GDP ratio and Loan-to-value ratios - US, Korea Year Outstanding Mortgage-to-GDP Ratio US 53% 52% 54% 56% 55% Korea 10% 11% 12% 12% 13% Loan-to-value ratio US 78% 80% 80% 78% 79% Korea 25% 26% 28% 28% 33%

8 Summarizing... Age-transfer profile shows that the relative importance of transfer income is larger for Korean households, especially in the younger cohorts aged less than 40. The degree of credit constraint in Korea is larger as evidenced from the size of the mortgage market and the down-payment requirements.

9 Demographics & Technology 1 period in the model corresponds to 5 years. Agents enter working life at 25(j = 1), retire at 65(j = 9), live at most until 80(J = 12). Retired agents face mortality risk, upon death agents leave bequest, equally re-distributed to agents (aged 40-55) Final goods produced can be consumed (C), invested (I ) or spent by government (G).

10 Intergenerational Transfers INTERGENERATIONAL TRANSFERS Parents Work Retire j = 7, 8, 9 j = 10,11,12 Bequest Children Intervivos transfer j = 1, 2, 3 j = 4, 5, 6 Work Work

11 Preferences CRRA utility function U(c j ) = c1 σ j 1 σ Warm-glow bequest motive, De Nardi (2004). ϕ(q) = ϕ 1 [ 1 + q ϕ 2 ] 1 σ Intervivos transfer motivated by altruism parents care about children s utility with discount factor γ < 1.

12 Labor Productivity Exogenous age-efficiency profile ɛ j + stochastic productivity shocks y j (Markov process) First period productivity shock is inherited from parents according to a transition function Q yh. Afterwards, producvitity evolves according to transition function Q y. Total productivity given by ɛ j y j, wage rate given by ω.

13 Market Arrangements Working agents can borrow upto some fraction of current period labor income. a j+1 κ 1 ωɛ j y j j = 1,..., 9 Retired households cannot borrow. a j+1 0 j = 10,..., 12

14 Government Equal re-distribution of bequest to children in periods j = 4, 5, 6. T = j=10,11,12 j=4,5,6 q m (dx) m (dx) (1) Social security benefit b m (dx) = τ ss j=10,11,12 j=1,...,9 ωɛy m (dx) (2) Constant government expenditure from tax revenues. τ c C + τ k rk = G (3)

15 Household Recursive Problem Children (working, receiving inter-vivos transfers) j = 1, 2, 3 Children (working, receiving bequest) j = 4, 5, 6 Parent (working, giving inter-vivos transfers) j = 7, 8, 9 Parent (retired, giving bequest) j = 10, 11, 12

16 Household Recursive Problem : Parents at (j = 7, 8, 9) V (j, a, y, ã, ỹ) = max c,a,tr U(c) + γu( c) + I j=7,8βev (j + 1, a, y, ã, ỹ ) +I j=9 βv (j + 1, a ) subject to (4) (1 + τ c )c + tr + a (1 τ ss )ωɛy + (1 + r(1 τ k ))a c 0 a κ 1 ωɛy

17 Household Recursive Problem : Children at ( j = 1, 2, 3) V ( j, a, y, ã, ỹ) = max c,ã U( c) + I j=1,2 βev ( j + 1, a, y, ã, ỹ ) +I j=3 βev ( j + 1, ã, ỹ ) subject to (5) (1 + τ c ) c + ã (1 τ ss )ωɛỹ + (1 + r(1 τ k ))ã + tr c 0 ã κ 1 ωɛỹ

18 Common Parameter Definition and Values Table: Common Parameter Definition and Values Parameters Definition Values σ Risk-aversion coefficient 1.5 α Capital income share δ Depreciation rate φ 1 Bequest parameter -9.5 φ 2 Bequest parameter 11.6 b Replacement ratio 0.4 τ c Consumption tax rate 0.05 ρ Persistence of income process 0.85

19 Country-specific Parameter Definition and Values Table: Country-Specific Parameter Definition and Values Parameters US Korea κ σy τ ss 9.0% 12.4% Table: Parameters to match given set of targets Parameters Definition US Korea β Discount factor γ Pure altruism parameter

20 US Table: Summary Statistics of Benchmark Simulation - US Variable Benchmark Data Capital output ratio Transfer-to-bequest ratio Average Wealth

21 US Table: Summary Statistics of Benchmark Simulation - US Variable Benchmark Data Average flow of bequest (% of GDP) 1.6% 2.6% Transfer to (% of GDP) 0.54% 4.3% Transfer to (% of GDP) 1.94% 5.6% Transfer to (% of GDP) 2.66% 6.5% Gini (wealth)

22 Korea Table: Summary Statistics of Benchmark Simulation - Korea Variable Benchmark Data Capital output ratio Transfer-to-bequest ratio Average Wealth

23 Korea Table: Summary Statistics of Benchmark Simulation - Korea Variable Benchmark Data Average flow of bequest (% of GDP) 1.2% 1.9% Transfer to (% of GDP) 1.97% 5.2% Transfer to (% of GDP) 3.17% 14.7% Transfer to (% of GDP) 3.70% 9.9% Gini (wealth)

24 Table: Tightening Borrowing Constraint - US Parameter (κ 1 = 0.75) (κ 1 = 0.25) Capital output ratio Transfer-to-bequest ratio Average Wealth T tr tr tr Gini

25 Table: Relaxing Borrowing Constraint - Korea Parameter (κ 1 = 0.25) (κ 1 = 0.75) Capital output ratio Transfer-to-bequest ratio Average Wealth T tr tr tr Gini

26 Conclusion Life-cycle model with intergenerational linkages to study wealth transfers between parents and children. While the parents are of working age, the utility of the children s consumption enters the utility of the parents. When parents die, they leave bequests, and have an (exogenous) warm-glow utility from leaving a bequest. Higher borrowing constraints (that prevent children from borrowing to smooth their consumption) tend to generate larger transfers early in life (relative to bequests). This matches the empirical evidence from Korea (a stricter constraints country) and the US.

27 Extensions Better calibration of Korean data Incorporate two-sided altruism (children supporting elderly parents) Incorporate taxes (estate tax vs. gift tax)