Closing Down the Shop: Optimal Health and Wealth Dynamics near the End of Life

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1 Closing Down the Shop: Optimal Health and Wealth Dynamics near the End of Life Julien Hugonnier 1,4,5 Florian Pelgrin 2 Pascal St-Amour 3,4 1 École Polytechnique Fédérale de Lausanne 2 EDHEC Business School 3 University of Lausanne, Faculty of Business and Economics (HEC) 4 Swiss Finance Institute 5 CEPR Jan. 18, 2017 P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

2 Introduction Stylized facts EOL (H t, W t ) dynamics 1- Health falls, 2- death risk exposure increases, esp. poor Age 40 to to 80 Share in poor/ bad health 2 2 Drop survivors 19.3% 29.7% Notes: Health: [Banks et al., 2015, Smith, 2007, Heiss, 2011, Van Kippersluis et al., 2009], survivors [Arias, 2014]. Income decile Notes: [Bosworth et al., 2016] Longevity 1940 cohort 1 st rd th th 84.6 P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

3 Introduction Stylized facts EOL (H t, W t ) dynamics 3.a- Health expenses increase Age Notes: [De Nardi et al., 2015b] Average total expend $ last year $ Concentrated in long-term care (LTC), less curative care. LTC very income/wealth elastic normal consumption good. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

4 Introduction Stylized facts EOL (H t, W t ) dynamics 3.b- Health expenses change in composition Nursing Home Health & Hospice Drugs Professional Services Hospital (Outpatients) Hospital (Inpatients) Age Notes: Source: [De Nardi et al., 2015b, Fig. 3, p. 22]. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

5 Notes: Source: [De Nardi et al., 2015b, Fig. 3, p. 22]. agep. Total St-Amour (UNIL, Medical SFI) Expenditures, Closing Down the Shop by Expenditure NETSPAR: Jan. (top 18, 2017 panel) 4 / 25 Introduction Stylized facts EOL Hospital (H t,(outpatients) W t ) dynamics Hospital (Inpatients) 0 3.b- Health expenses change in composition Age Private Insurance Out of pocket & Uncollected liability Government: Other Government: Medicaid Government: Medicare Age

6 Introduction Stylized facts EOL (H t, W t ) dynamics 4- Wealth falls Fall by 50% last 3 years, 30% last year alone, vs 2% for survivors [De Nardi et al., 2015a, French et al., 2006]. LTC not covered by Medicare, means-testing for Medicaid. Correlated with changes in health, family composition [Poterba et al., 2015, Lee and Kim, 2008]. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

7 Introduction Research question Standard explanation Ineluctable aging process: Biological decline in health status. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

8 Introduction Research question Standard explanation Ineluctable aging process: Biological decline in health status. Mechanical increase in death risk. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

9 Introduction Research question Standard explanation Ineluctable aging process: Biological decline in health status. Mechanical increase in death risk. Expand comfort care, reduce curative care. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

10 Introduction Research question Standard explanation Ineluctable aging process: Biological decline in health status. Mechanical increase in death risk. Expand comfort care, reduce curative care. Deplete financial resources to cover expenses accidental bequests. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

11 Introduction Research question Standard explanation Ineluctable aging process: Biological decline in health status. Mechanical increase in death risk. Expand comfort care, reduce curative care. Deplete financial resources to cover expenses accidental bequests. Medicaid once depleted wealth. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

12 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

13 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

14 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

15 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

16 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

17 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. Conditions under which close down the shop near the end of life: P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

18 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. Conditions under which close down the shop near the end of life: 1 Optimal joint depletion of health, and wealth capital. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

19 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. Conditions under which close down the shop near the end of life: 1 Optimal joint depletion of health, and wealth capital. 2 Threshold after which health depletion accelerated. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

20 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. Conditions under which close down the shop near the end of life: 1 Optimal joint depletion of health, and wealth capital. 2 Threshold after which health depletion accelerated. 3 Optimal increase in death risk. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

21 Introduction Research question Main research question Joint decline in (H t, W t ) = optimal decisions, rather than inevitable? Four hypotheses: 1 Health spending affect health. 2 Health affect exposure to death risk. 3 Strict preference for life. 4 Dynamically consistent decisions by agents: Horizon = dynamic decisions, and Horizon = dynamic decisions. Conditions under which close down the shop near the end of life: 1 Optimal joint depletion of health, and wealth capital. 2 Threshold after which health depletion accelerated. 3 Optimal increase in death risk. 4 Convergence towards state where indifferent between life and death. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

22 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Health dynamics [Grossman, 1972, augmented]: dh t = ((I t /H t ) α δ) H t dt φh t dq st, H 0 > 0, P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

23 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Health dynamics [Grossman, 1972, augmented]: dh t = ((I t /H t ) α δ) H t dt φh t dq st, H 0 > 0, Poisson health shocks (sickness, death): Endogenous exposure { λ s0 k = s (sickness) λ k (H t ) = λ m0 + λ m1 Ht ξm, k = m (death) P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

24 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Health dynamics [Grossman, 1972, augmented]: dh t = ((I t /H t ) α δ) H t dt φh t dq st, H 0 > 0, Poisson health shocks (sickness, death): Endogenous exposure { λ s0 k = s (sickness) λ k (H t ) = λ m0 + λ m1 Ht ξm, k = m (death) Income: Health-dependent Y (H t ) = y 0 + βh t. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

25 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Health dynamics [Grossman, 1972, augmented]: dh t = ((I t /H t ) α δ) H t dt φh t dq st, H 0 > 0, Poisson health shocks (sickness, death): Endogenous exposure { λ s0 k = s (sickness) λ k (H t ) = λ m0 + λ m1 Ht ξm, k = m (death) Income: Health-dependent Y (H t ) = y 0 + βh t. Health shock insurance: Actuarially fair X t dm st = X t dq st X t λ s0 dt. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

26 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Health dynamics [Grossman, 1972, augmented]: dh t = ((I t /H t ) α δ) H t dt φh t dq st, H 0 > 0, Poisson health shocks (sickness, death): Endogenous exposure { λ s0 k = s (sickness) λ k (H t ) = λ m0 + λ m1 Ht ξm, k = m (death) Income: Health-dependent Y (H t ) = y 0 + βh t. Health shock insurance: Actuarially fair Wealth dynamics: X t dm st = X t dq st X t λ s0 dt. dw t = (rw t + Y t C t I t ) dt + Π t σ S (dz t + θdt) + X t dm st. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

27 Theoretical framework Economic environment Model [Hugonnier et al., 2013, RESTUD] Objectives: V (W t, H t) = sup (C,Π,X,I ) U t(c), where U t(c) = 1 {Tm>t}E t Tm where, F k (U, H, k U) = Uλ k (H) t ( f (C τ, U τ ) γσ2 τ 2U τ s k=m f (C, U) = ρu ) (((C a)/u) 1 ε /ε [ ( k U U + u(1; γ k) u u(c; γ k ) = c1 γ k 1 γ k, k = m, s. subject to health, wealth dynamics. ) F k (U τ, H τ, k U τ ) dτ, 1 + ku U ; γ k )], P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

28 Theoretical framework Admissible policies Health investment: Two components I (W, H) = KBH }{{} + I 1 H ξm N 0 (W, H) }{{} Order-0 demand Death risk hedging demand where N 0 (W, H) is net total wealth. Other solutions for X, Π. If death risk can be hedged = larger demand for health. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

29 Theoretical framework Admissible policies Health investment: Two components I (W, H) = KBH }{{} + I 1 H ξm N 0 (W, H) }{{} Order-0 demand Death risk hedging demand where N 0 (W, H) is net total wealth. Other solutions for X, Π. If death risk can be hedged = larger demand for health. Monotone increasing in W. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

30 Theoretical framework Admissible policies Health investment: Two components I (W, H) = KBH }{{} + I 1 H ξm N 0 (W, H) }{{} Order-0 demand Death risk hedging demand where N 0 (W, H) is net total wealth. Other solutions for X, Π. If death risk can be hedged = larger demand for health. Monotone increasing in W. Non-monotone in H. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

31 Theoretical framework Admissible policies Admissibility and preference for life Consumption: C (W, H) = a + [A + C 1 H ξm ] N 0 (W, H) N 0 (W, H) = W + BH + (y 0 a)/r P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

32 Theoretical framework Admissible policies Admissibility and preference for life Consumption: C (W, H) = a + [A + C 1 H ξm ] N 0 (W, H) N 0 (W, H) = W + BH + (y 0 a)/r Admissibility: C (W, H) a A = {(W, H) : N 0 (W, H) 0}, = {(W, H) : W > x(h) = (y 0 a)/r BH}, P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

33 Theoretical framework Admissible policies Admissibility and preference for life Consumption: C (W, H) = a + [A + C 1 H ξm ] N 0 (W, H) N 0 (W, H) = W + BH + (y 0 a)/r Admissibility: C (W, H) a A = {(W, H) : N 0 (W, H) 0}, = {(W, H) : W > x(h) = (y 0 a)/r BH}, Homogeneity of preferences: C a > 0 = V > 0 P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

34 Theoretical framework Admissible policies Admissibility and preference for life Consumption: C (W, H) = a + [A + C 1 H ξm ] N 0 (W, H) N 0 (W, H) = W + BH + (y 0 a)/r Admissibility: C (W, H) a A = {(W, H) : N 0 (W, H) 0}, = {(W, H) : W > x(h) = (y 0 a)/r BH}, Homogeneity of preferences: C a > 0 = V > 0 Versus welfare at death V 0 = life preferred to death. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

35 Theoretical framework Admissible policies Admissibility and preference for life Consumption: C (W, H) = a + [A + C 1 H ξm ] N 0 (W, H) N 0 (W, H) = W + BH + (y 0 a)/r Admissibility: C (W, H) a A = {(W, H) : N 0 (W, H) 0}, = {(W, H) : W > x(h) = (y 0 a)/r BH}, Homogeneity of preferences: C a > 0 = V > 0 Versus welfare at death V 0 = life preferred to death. As approach non-admissible region, become indifferent between life and death. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

36 Optimal health and wealth dynamics Endogenous mortality Expected local dynamics and depletion: Health 1 Local expected changes: E t [dh] = [I h (W, H) α }{{}}{{} δ ]Hdt, I /H δ+λ s0 φ P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

37 Optimal health and wealth dynamics Endogenous mortality Expected local dynamics and depletion: Health 1 Local expected changes: E t [dh] = [I h (W, H) α }{{}}{{} δ ]Hdt, I /H δ+λ s0 φ 2 Health depletion/accelerating regions: D H = {(W, H) A : E t [dh] < 0}, } AC = {(W, H) D H : IH h (W, H) > 0. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

38 Optimal health and wealth dynamics Endogenous mortality Expected local dynamics and depletion: Wealth 1 Local expected changes: E t [dw ] = [rw + Y (H) C (W, H) I (W, H) +Π (W, H)σ S θ] dt, P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

39 Optimal health and wealth dynamics Endogenous mortality Expected local dynamics and depletion: Wealth 1 Local expected changes: E t [dw ] = [rw + Y (H) C (W, H) I (W, H) +Π (W, H)σ S θ] dt, 2 Wealth depletion region: D W = {(W, H) A : E t [dw ] < 0}. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

40 Optimal health and wealth dynamics Endogenous mortality Sufficient conditions for Closing down: Realistic for EOL Health depletion/accelerating: High depreciation and/or low ability to generate income: β < δ 1/α, Wealth depletion: P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

41 Optimal health and wealth dynamics Endogenous mortality Sufficient conditions for Closing down: Realistic for EOL Health depletion/accelerating: High depreciation and/or low ability to generate income: β < δ 1/α, Wealth depletion: Sufficient elasticity inter-temporal substitution ε 1. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

42 Optimal health and wealth dynamics Endogenous mortality Sufficient conditions for Closing down: Realistic for EOL Health depletion/accelerating: High depreciation and/or low ability to generate income: Wealth depletion: β < δ 1/α, Sufficient elasticity inter-temporal substitution ε 1. High consumption = (γ, ρ, λ m0, γ m ) high (1 + ε) θ2 2γ < ε(ρ r) + (ε 1) λ m0 1 γ m. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

43 Optimal health and wealth dynamics Endogenous mortality Phase diagram Figure: Health and wealth dynamics P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

44 Optimal health and wealth dynamics Endogenous mortality Phase diagram Figure: Health and wealth dynamics P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

45 Optimal health and wealth dynamics Endogenous mortality Phase diagram Figure: Health and wealth dynamics P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

46 Optimal health and wealth dynamics Endogenous mortality Phase diagram Figure: Health and wealth dynamics P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

47 Optimal health and wealth dynamics Terminal illness Terminal illness: λ m (H) = λ m0, H, and λ m0, δ Main result: D H = A; AC = P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

48 Optimal health and wealth dynamics Terminal illness Terminal illness: λ m (H) = λ m0, H, and λ m0, δ Main result: D H = A; AC = P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

49 Policy Increasing base income (y 0 ) Reducing incidence of Closing Down strategies Figure: Increase in y 0 (e.g. Social Security) P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

50 Policy Increasing base income (y 0 ) Reducing incidence of Closing Down strategies Figure: Increase in y 0 (e.g. Social Security) P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

51 Empirical evaluation Econometric model Model and data Structural trivariate econometric model: I j = K 0 BH j + K m H ξm j N 0 (W j, H j ) + u Ij, Π j = (θ/(γσ S )) N 0 (W j, H j ) + u πj, Y j = y 0 + βh j + u Yj, Closed-form solutions for parameters. Additional transversality conditions. By iterative 2-step ML. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

52 Empirical evaluation Econometric model Model and data Structural trivariate econometric model: I j = K 0 BH j + K m H ξm j N 0 (W j, H j ) + u Ij, Π j = (θ/(γσ S )) N 0 (W j, H j ) + u πj, Y j = y 0 + βh j + u Yj, Closed-form solutions for parameters. Additional transversality conditions. By iterative 2-step ML. Data: HRS, 2002 Detailed info on total health spending. Focus on elders 65+, with positive wealth (9,817 obs., mean age 75.3). No consumption data. Medicare = drop optimal insurance. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

53 Results Parameters Estimated and calibrated parameters Realistic for relatively old population (75.3 years): Param. Value Param. Value Param. Value α δ φ c λ s λ m λ m ξ m y $ β µ c r c σ S 0.20 c a $ ε γ ρ c γ m 0.75 c γ s N.I. Notes: *: Estimated structural and induced parameters (standard errors in parentheses), significant at 5% level; c: calibrated parameters; $: In $M; N.I.: non-identifiable/irrelevant under the exogenous morbidity restriction. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

54 Results Parameters Conditions for depletion: All verified Parameter Value Parameter Value β δ 1/α θ 2 /γ + r A Notes: *: Estimated structural and induced parameters (standard errors in parentheses), significant at 5% level; c: calibrated parameters; $: In $M. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

55 Results Parameters Estimated and calibrated parameters Out-of-sample checks: Expected longevity l(w t, H t ) = (1/λ m0 )(1 λ m1 κ 0 H ξm t ) Level H % Pop. Exp. longev. Poor Fair Good Very good Excellent Data (2002): 74.5 (M); 79.9 (F); 77.3 (A) P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

56 Results State space partitions Estimated partitions: All in (D H, D W ) for H Fair P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

57 Results State space partitions Simulated life paths: Closing Down the Shop 4 a. Wealth (M$) b. Health c. Expected surviv. (remain. yrs) # d. Welfare # Rich Poor P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

58 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

59 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. Accelerating depletion subsets. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

60 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. Accelerating depletion subsets. Paths converging to states where indifference life/death. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

61 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. Accelerating depletion subsets. Paths converging to states where indifference life/death. Realistic sufficient theoretical conditions, verified empirically: High consumption. High depreciation and/or low ability to generate income. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

62 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. Accelerating depletion subsets. Paths converging to states where indifference life/death. Realistic sufficient theoretical conditions, verified empirically: High consumption. High depreciation and/or low ability to generate income. Consistent with stylized facts: 1 Falling health. 2 Death risk increasing. 3 Change in composition: Less curative care. 4 Falling wealth. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

63 Conclusion Concluding remarks Closing down the shop strategy: Optimal depletion of health/wealth capitals. Accelerating depletion subsets. Paths converging to states where indifference life/death. Realistic sufficient theoretical conditions, verified empirically: High consumption. High depreciation and/or low ability to generate income. Consistent with stylized facts: 1 Falling health. 2 Death risk increasing. 3 Change in composition: Less curative care. 4 Falling wealth. Applicable to incurable terminal diseases. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

64 Conclusion Normative issues Reducing incidence of closing down: 1 Feasible? Yes. Base income y 0 (e.g. Soc. Sec., min. revenues, Medicaid). Subsidized medical research δ, λ s0, φ.... but (W, H) distribution will adapt. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

65 Conclusion Normative issues Reducing incidence of closing down: 1 Feasible? Yes. Base income y 0 (e.g. Soc. Sec., min. revenues, Medicaid). Subsidized medical research δ, λ s0, φ.... but (W, H) distribution will adapt. 2 Optimal? No clear normative arguments. Myopia? No, fully endogenize effects of choices horizon. Market failure? No, optimal strategy by agents in complete markets setting. Redistribution? No, poverty endogenously determined. Against excessive/aggressive EOL therapy. In favor of rights to refuse treatment. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

66 Conclusion Arias, E. (2014). United States life tables, National Vital Statistics Report, 63(7):1 62. Banks, J., Blundell, R., Levell, P., and Smith, J. P. (2015). Life-cycle consumption patterns at older ages in the US and the UK: can medical expenditures explain the difference? IFS Working Papers W15/12, Institute for Fiscal Studies. Bosworth, B. P., Burtless, G., and Zhang, K. (2016). Later retirement, inequality in old age, and the growing gap in longevity between rich and poor. Economic Studies at Brookings, Brookings Institute. De Nardi, M., French, E., and Jones, J. B. (2015a). Savings after retirement: A survey. Working Paper 21268, National Bureau of Economic Research. De Nardi, M., French, E., Jones, J. B., and McCauley, J. (2015b). Medical spending of the U.S. elderly. P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

67 Conclusion Working Paper 21270, National Bureau of Economic Research. French, E., De Nardi, M., Jones, J. B., Baker, O., and Doctor, P. (2006). Right before the end: Asset decumulation at the end of life. Federal Reserve Bank of Chicago Economic Perspectives, 30(3):2 13. Grossman, M. (1972). On the concept of health capital and the demand for health. Journal of Political Economy, 80(2): Heiss, F. (2011). Dynamics of self-rated health and selective mortality. Empirical Economics, 40(1): Hugonnier, J., Pelgrin, F., and St-Amour, P. (2013). Health and (other) asset holdings. The Review of Economic Studies, 80(2): Lee, J. and Kim, H. (2008). P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25

68 Conclusion A longitudinal analysis of the impact of health shocks on the wealth of elders. Journal of Population Economics, 21(1): Poterba, J., Venti, S., and Wise, D. A. (2015). What determines end-of-life assets? a retrospective view. Working Paper 21682, National Bureau of Economic Research. Smith, J. P. (2007). The impact of socioeconomic status on health over the life-course. Journal of Human Resources, 42(4): Van Kippersluis, H., Van Ourti, T., O Donnell, O., and van Doorslaer, E. (2009). Health and income across the life cycle and generations in Europe. Journal of Health Economics, 28: P. St-Amour (UNIL, SFI) Closing Down the Shop NETSPAR: Jan. 18, / 25