Wealth Accumulation, Credit Card Borrowing, and. Consumption-Income Comovement

Transcription

1 Wealth Accumulation, Credit Card Borrowing, and Consumption-Income Comovement David Laibson, Andrea Repetto, and Jeremy Tobacman Current Draft: May 2002

2 1 Self control problems People are patient in the long run, but impatient in the short run. Tomorrow we want to quit smoking, exercise, and eat carrots. Today we want our cigarette, TV, and frites.

3 Self control problems in savings. Baby boomers report median target savings rate of 15%. Actual median savings rate is 5%. 76% of household s believe they should be saving more for retirement (Public Agenda, 1997). Of those who feel that they are at a point in their lives when they should be seriously saving already, only 6% report being ahead in their saving, while 55% report being behind. Consumers report a preference for flat or rising consumption paths.

4 Further evidence: Normative value of commitment. Use whatever means possible to remove a set amount of money from your bank account each month before you have a chance to spend it. Choose excess withholding. Cut up credit cards, put them in a safe deposit box, or freeze them in a block of ice. Sixty percent of Americans say it is better to keep, rather than loosen legal restrictions on retirement plans so that people don t use the money for other things. Social Security and Roscas. Christmas Clubs (10 mil. accounts).

5 An intergenerational discount function introduced by Phelps and Pollak (1968) provides a particularly tractable waytocapturesucheffects. Salience effect (Akerlof 1992), quasi-hyperbolic discounting (Laibson, 1997), present-biased preferences (O Donoghue and Rabin, 1999), quasi-geometric discounting (Krusell and Smith 2000): 1, βδ, βδ 2, βδ 3,... U t = u(c t )+βδu(c t+1 )+βδ 2 u(c t+2 )+βδ 3 u(c t+3 )+... For exponentials: β =1 U t = u(c t )+δu(c t+1 )+δ 2 u(c t+2 )+δ 3 u(c t+3 )+... For hyperbolics: β < 1 U t = u(c t )+β h δu(c t+1 )+δ 2 u(c t+2 )+δ 3 u(c t+3 )+... i

6 Outline 1. Introduction 2. Facts 3. Model 4. Estimation Procedure 5. Results 6. Conclusion

7 2 Consumption-Savings Behavior Substantial retirement wealth accumulation (SCF) Extensive credit card borrowing (SCF, Fed, Gross and Souleles 2000, Laibson, Repetto, and Tobacman 2000) Consumption-income comovement (Hall and Mishkin 1982, many others) Anomalous retirement consumption drop (Banks et al 1998, Bernheim, Skinner, and Weinberg 1997)

8 2.1 Data Statistic m e se me % borrowing on Visa? (% Visa) borrowing / mean income (mean Visa) C-Y comovement (CY ) retirement C drop (C drop) median income wealth weighted mean income wealth (wealth)

9 Three moments on previous slide (wealth, % Visa, mean Visa) from SCF data. Correct for cohort, household demographic, and business cycle effects, so simulated and empirical hh s are analogous. Compute covariances directly. C-Y from PSID: ln(c it )=αe t 1 ln(y it )+X it β + ε it (1) Cdropfrom PSID ln(c it )=I RETIRE it γ + X it β + ε it (2)

10 3 Model We use simulation framework Institutionally rich environment, e.g., with income uncertainty and liquidity constraints Literature pioneered by Carroll (1992, 1997), Deaton (1991), and Zeldes (1989) Gourinchas and Parker (2001) use method of simulated moments (MSM) to estimate a structural model of life-cycle consumption

11 3.1 Demographics Mortality, Retirement (PSID), Dependents (PSID), HS educational group 3.2 Income from transfers and wages Y t = after-tax labor and bequest income plus govt transfers (assumed exog., calibrated from PSID) y t ln(y t ). During working life: y t = f W (t)+u t + ν W t (3) During retirement: y t = f R (t)+ν R t (4)

12 3.3 Liquid assets and non-collateralized debt X t + Y t represents liquid asset holdings at the beginning of period t. Credit limit: X t λ Ȳ t λ =.30, so average credit limit is approximately $8,000 (SCF).

13 3.4 Illiquid assets Z t represents illiquid asset holdings at age t. Z bounded below by zero. Z generates consumption flows each period of γz. Conceive of Z as having some of the properties of home equity. Disallow withdrawals from Z; Z is perfectly illiquid. Z stylized to preserve computational tractability.

14 1. House of value H, mortgageofsizem. 2. Consumption flow of γh, minus interest cost of ηm, where η = i (1 τ) π. 3. γ η = net consumption flow of γh ηm γ(h M) = γz.we ve explored different possibilities for withdrawals from Z before..

15 3.5 Dynamics Let I X t and I Z t represent net investment into assets X and Z during period t Dynamic budget constraints: X t+1 = R X (X t + It X ) Z t+1 = R Z (Z t + It Z ) C t = Y t It X It Z Interest rates: ( R X R = CC if X t + It X < 0 R if X t + It X > 0 ; RZ =1 Three assumptions for h R X, γ,r CCi : Benchmark: [1.0375, 0.05, ] Aggressive: [1.03, 0.06, 1.10] Very Aggressive: [1.02, 0.07, 1.09]

16 3.6 Time Preferences Discount function: {1, βδ, βδ 2, βδ 3,...} β = 1: standard exponential discounting case β < 1: preferences are qualitatively hyperbolic Null hypothesis: β =1 U t ({C τ } T τ=t) =u(c t )+β TX τ=t+1 δ τ u(c τ ) (5)

17 In full detail, self t has instantaneous payoff function ³ Ct +γz t 1 ρ n 1 u(c t,z t,n t )=n t t 1 ρ and continuation payoffsgivenby: β +β T +N t X i=1 T +N t X i=1 δ i ³ Π i 1 j=1 s t+j (st+i ) u(c t+i,z t+i,n t+i )... δ i ³ Π i 1 j=1 s t+j (1 st+i ) B(X t+i,z t+i ) n t is effective household size: adults+(.4)(kids) γz t represents real after-tax net consumption flow s t+1 is survival probability B( ) represents the payoff in the death state

18 3.7 Computation Dynamic problem: max I X t,iz t u(c t,z t,n t )+βδe t V t,t+1 (Λ t+1 ) s.t. Budget constraints Λ t =(X t + Y t,z t,u t )(statevariables) Functional Equation: V t 1,t (Λ t )= {s t [u(c t,z t,n t )+δe t V t,t+1 (Λ t+1 )]+(1 s t )E t B(Λ t )} Solve for eq strategies using backwards induction Simulate behavior Calculate descriptive moments of consumer behavior

19 4 Estimation Estimate parameter vector θ and evaluate models wrt data. m e = N empirical moments, VCV matrix = Ω m s (θ) = analogous simulated moments q(θ) (m s (θ) m e ) Ω 1 (m s (θ) m e ) 0,ascalarvalued loss function Minimize loss function: ˆθ = arg min θ q(θ) ˆθ is the MSM estimator. Pakes and Pollard (1989) prove asymptotic consistency and normality. Specification tests: q(ˆθ) χ 2 (N #parameters)

20 5 Results Exponential (β =1)case: ˆδ =.857 ±.005; q ³ˆδ, 1 = 512 Hyperbolic case: ( ˆβ =.661 ±.012 ˆδ =.956 ±.001 q ³ˆδ, ˆβ =75 (Benchmark case: h R X, γ,r CCi =[1.0375, 0.05, ])

21 Punchlines: β estimated significantly below 1. Reject β = 1 null hypothesis with a t-stat of 25. Specification tests reject both the exponential and thehyperbolicmodels.

22 Benchmark Exponential Hyperbolic Data Std err Model m s (ˆβ, ˆδ) m Statistic: s (1, ˆδ) ˆβ =.661 m e se me ˆδ =.857 ˆδ =.956 % Visa mean V isa CY Cdrop wealth q(ˆθ)

23 Robustness Benchmark: Aggressive: Very Aggressive: h R X, γ,r CCi =[1.0375, 0.05, ] h R X, γ,r CCi = [1.03, 0.06, 1.10] h R X, γ,r CCi = [1.02, 0.07, 1.09] Benchmark Aggressive Very Aggressive exp ˆδ (.005) (.001) (.002) q ³ˆδ, hyp hˆδ, ˆβ i [.956,.661] [.944,.815] [.932,.909] (.001), (.012) (.001), (.014) (.002), (.016) q ³ˆδ, ˆβ

24 Aggressive Exponential Hyperbolic Data Std err m s (ˆβ, ˆδ) m Statistic: s (1, ˆδ) ˆβ =.815 m e se me ˆδ =.930 ˆδ =.944 % Visa mean V isa CY Cdrop wealth q(ˆθ)

25 V. Agg. Exponential Hyperbolic Data Std err m s (ˆβ, ˆδ) m Statistic: s (1, ˆδ) ˆβ =.909 m e se me ˆδ =.923 ˆδ =.932 % Visa mean V isa CY Cdrop wealth q(ˆθ) 64 33

26 6 Conclusion Structural test using the method of simulated moments rejects the exponential discounting null. Specification tests reject both the exponential and thehyperbolicmodels. Quantitative results are sensitive to interest rate assumptions. Hyperbolic discounting does a better job of matching the available empirical evidence on consumption and savings.