Life Cycle Responses to Health Insurance Status

Transcription

1 Life Cycle Responses to Health Insurance Status Florian Pelgrin 1, and Pascal St-Amour,3 1 EDHEC Business School University of Lausanne, Faculty of Business and Economics (HEC Lausanne) 3 Swiss Finance Institute January 5, 16 Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 1 / 9

2 Introduction Motivation Outline Exogenous changes in health insurance status: Termination of employer-provided plans at retirement. Medicare (prior to PPACA) provides guaranteed access to subsidized health insurance for 65+. Patient Protection and Affordable Care Act (PPACA, a.k.a. Obamacare). Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 / 9

3 Introduction Motivation Question asked What are life cycle effects of exogenous changes in insurance status at given point in life: on allocations (consumption, leisure, health expenditures)? on status (wealth, health)? on welfare? Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 3 / 9

4 Introduction Motivation Health insurance over the life cycle Should affect decisions at other periods of life: Health is durable good. Decisions when young have long lasting effects on future exposition to morbidity, mortality risks [Smith, 1999, Long Reach of Childhood]. Backward induction: Status and consequences of insurance when old need to be internalized when young. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 4 / 9

5 Introduction Motivation Timing of coverage important Employer-provided insurance ending at retirement: Accelerate current expenses before termination. Alters health levels longevity, sickness risks. Post-retirement coverage (e.g. Medicare): Postpone health care until coverage begins (Stockpiling). Alters health levels longevity, sickness risks. Implications: 1 Timing of coverage affects allocations, health and wealth statuses throughout life cycle. Decomposition of effects not trivial. 3 Important to understand life cycle effects of health insurance as Medicare costly, PPACA becomes operational. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 5 / 9

6 Model Economic environment Notation Timing Calendar year: y N, with y =, base year, Cohort: κ N, : t = y κ {, 1,..., T }, bounded horizon. Mortality (k = m) and morbidity (k = s) shocks generalized Bernoulli: { ɛ k with prob. exp[ λ k (H t )] t+1 = 1 with prob. 1 exp[ λ k (Shocks) (H t )] T m [, T ] = min{t : ɛ m t = 1} (Death) λ k ( ) >, falling, convex in H: Endo. mortality/morbidity risks. Diminishing returns to health-related risks control. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 6 / 9

7 Model Economic environment Health dynamics H t+1 = ( 1 δ t φ t ɛ s t+1) Ht + A t I g (H t, I t, l t ) (Health) d t = d exp[g d t], d {δ, φ} (Depreciation) A t = A exp[g A (t + κ)]. (TFP health) I g ( ) increasing, concave, health-dependent. Account for healthy leisure (moral hazard) Leibowitz [4], Sickles and Yazbeck [1998], Ehrlich and Becker [197]. Sickness ɛ s t+1 = 1 additional depreciation. -increasing deterministic and stochastic depreciation. Exogenous technological progress in A t [e.g. Hall and Jones, 7]. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 7 / 9

8 Model Economic environment Health expenditures insurance P I I OOP(I ) D ψ OOP(I ) 45 D (1 ψ) P I I Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 8 / 9

9 Model Economic environment Health expenditures insurance Notation: 1 X = 1 x=p,m (Insured), 1 M = 1 x=m (Medicare), 1 D = 1 P I t I t D t (Deductible reached), 1 R = 1 t 65 (Retired). OOPt x (I t ) = Pt I I t 1 X 1 D (1 ψ)(pt I I t D t ) Π x t = 1 X Π [1 1 M 1 R (1 π)] Pt I = P I exp[g P (t + κ)], D t = D exp[g D (t + κ)] (OOP) (Premia) (Prices) (Deduct.) Cohort effects: TFP Health production A t, Health care prices P I t Deductible D t Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 9 / 9

10 Model Economic environment Budget constraint Y x t (l t ) = 1 R Y R + (1 1 M τ)w t (1 l t ) W t+1 = [W t + Y x t (l t ) C t OOP x t (I t ) Π x t ] R f (Income) (Wealth) Conditionally deterministic. Pension income Y R (Social Security). Medicare tax τ, when applicable. Post-retirement labour income. Single risk-free asset. -dependent wages w t. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 1 / 9

11 Model Preferences and optimality Preferences Within-period utility with bequest motive: U t U(C t, l t ) + β (1 exp[ λ m (H t )]) U m (W t+1 ) = U(C t, l t ) + [β β m (H t )] U m (W t+1 ) = U t (C t, I t, l t, W t, H t ) (Preferences) where β m (H t ) β exp[ λ m (H t )] < β. Properties: U t > (strict preference for life), U m (W t+1 ) < (cost of dying), U m W U H >, (joy of giving), U CH > [Finkelstein et al., 13]. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

12 Model Preferences and optimality Preferences Value function V t = V x (W t, H t, t): V t = max {C t,i t,l t} T m t = max {C t,i t,l t} T t { T m U t + E t U t + E t s=t+1 T s=t+1 j=t β s t U s H t } = max C t,i t,l t U t + β m (H t )E t {V t+1 H t }, s 1 β m (H j ) U s H t,, (Bellman) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 1 / 9

13 Model Preferences and optimality Optimality U C,t = Value bequeathed wealth {}}{ [β β m (H t )] R f U m W,t+1 +βm (H t )E t {U C,t+1 H t } R f, U C,t OOP x I,t = βm (H t )E t {V H,t+1 H t } A t I g I,t, (1 1 M τ)w t = U l,t U C,t + I g l,t I g I,t OOP x I,t, }{{} Value OOP reduction (Consumption) (Investment) (Leisure) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

14 Model Preferences and optimality Marginal value health Solves recursion: Mortality control value Morbidity control value {}}{ V H,t = βh,t m E { t Vt+1 Ut+1 m } {}}{ H t + β m (H t )E H,t {V t+1 H t } { ] } + β m (H t )E t V H,t+1 [1 δ t φ t ɛ s t+1 + A t I g H,t H t, }{{} Durability and productive capacity value (Value health) where E H,t {V t+1 H t } = λ s H,t exp[ λ s (H t )]E t { V (Wt+1, H + t+1 ) V (W t+1, H t+1 )} H + t+1 (1 δ t) H t + A t I g (H t, I t, l t ) H t+1 H+ t+1 φ th t (1) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

15 Empirical strategy Functional forms and insurance plans Functional forms Parametrizing the model: λ m (H) = λ m + λ m 1 H ξm, (Death intensity) λ s (H) = λ s λs λs 1 + λ s 1 H ξs, (Sickness intensity) I g (H, I, l) = I η I l η l H 1 η I η l, η I, η l (, 1), (Gross investment) U(C, l) = [ µ C C 1 γ + µ l l 1 γ] 1 1 γ, µ C, µ l (, 1), (Utility) ( ) W U m 1 γ (W ) = µ m. (Bequest function) 1 γ Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

16 Empirical strategy Functional forms and insurance plans Insurance plans Exogenous insurance plans x = (x y, x o ) X = {PM, PN, NM, NN}. Diffs-in-diffs approach to identify marginal effects insurance status: Table: Insurance plans, net effects and restrictions Status: old Status: young Insured Uninsured Net effects Insured PM PN Uninsured NM NN Net effects Insured young Insured old Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

17 Empirical strategy Simulated Method of Moments Empirical strategy No analytical solutions Kinks in OOP function. Time-varying wages, productivity, prices deductibles, deterministic and stochastic depreciaiton Endogenous discounting Need numerical methods Conditional upon parametrization, parameter Θ = (Θ c, Θ e ), three phases: 1 Iteration: Solve by backward induction on value function. Simulation: Life cycle trajectories along optimal path. 3 Estimation: Iterate on parameter set Θ e Θ. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

18 Empirical strategy Data Variables Table: Data sources Data (1, 11), and explanations W Survey of Consumer Finances (SCF), Federal Reserve Bank. Financial assets held. H National Health Interview Survey (NHIS), Center for Disease Control. Selfreported health status (phstat) where Poor=.1, Fair=.85, Good=1.55, Very good=.75, Excellent=3.. S National Vital Statistics System (NVSS), Center for Disease Control. Survival rates I Medical Expenditures Survey (MEPS), ncy for Health Research and Quality. Total health services mean expenses per person with expense and distribution of expenses by source of payment. OOP Medical Expenditures Survey (MEPS), ncy for Health Research and Quality. Out-of-pocket health services mean expenses per person with expense and distribution of expenses by source of payment. l American Time Use Survey (ATUS), Bureau of Labor Statistics. Share of usual hours not worked per week, 1-uhrsworkt/4 C Consumer Expenditures Survey (CEX), Bureau of Labor Statistics. Non-durables consumption, net of health expenditures and vehicle purchases = 4*(totex4pq - healthpq - vehicle) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

19 Empirical strategy Parameters λ m λ m 1 ξ m (.1) (.6) λ s λ s 1 λ s ξ s (.161) (1.1) δ g δ φ g φ (.66) (.54) (.66) (.51) A g A η I η l µ C µ M β γ (1.85) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, / 9

20 Empirical strategy Parameters.14 Depreciation rates /(t)?(t).45 Wage rates w(t) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 / 9

21 Results Iterative results ($1,) A. Consumption between ages 6 and 65, plan PM.4. 4 Health 6 4 Wealth ($1,) C. Investment between ages 6 and 65, plan PM.1.5 B. Leisure between ages 6 and 65, plan PM Health Wealth ($1,) D. Welfare between ages 6 and 65, plan PM Health Wealth ($1,) Health E. OOP between ages 6 and 65, plan PM 6 4 Wealth ($1,).5 4 Health 6 4 Wealth ($1,) Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 1 / 9

22 Results Simulation results Population statistics Table: Data and simulated unconditional moments (age 8) Simulated Series Data PM PN NN NM Out-of-pocket, OOP Leisure, l Wealth, W Health, H Survival, S Welfare, V NaN Notes: : in 1,$, : in years. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 / 9

23 Results Simulation results Figure: Health and leisure.5 Simulated health PM Observed health A. Observed and simulated health A. Observed and simulated leisure 1 Simulated leisure PM Observed leisure B. Effects insured young..1 PM NM PN NN B. Effects insured young PM NM PN NN C. Effects insured old.4.3. PM PN NM NN C. Effects insured old.1.5 PM PN NM NN Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 3 / 9

24 Results Simulation results Figure: Investment and OOP s Simulated PM A. Simulated health investment Observed investment A. Observed and simulated OOP Simulated OOP PM Observed OOP PM NM PN NN B. Effects insured young. PM NM PN NN B. Effects insured young PM PN NM NN C. Effects insured old x C. Effects insured old PM PN NM NN Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 4 / 9

25 Results Simulation results Figure: Wealth and welfare Simulated wealth PM Observed wealth A. Observed and simulated wealth A. Simulated welfare 14 Simulated welfare PM B. Effects insured young.8.6 PM NM PN NN B. Effects insured young PM NM PN NN PM PN NM NN C. Effects insured old.8.6 PM PN NM NN C. Effects insured old Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 5 / 9

26 Results Simulation results Figure: Cohort effects.6 A. Simulated health per cohort 5 B. Simulated wealth per cohort C. Simulated leisure per cohort D. Simulated health expenditures per cohort E. Simulated welfare per cohort Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 6 / 9

27 Conclusion Conclusion Complex dynamic effects of health insurance when morbidity/mortality risks exposition is endogenous: Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 7 / 9

28 Conclusion Conclusion Can keep track with (relatively) parsimonious framework Health as human capital. Leisure and investment as inputs. Endogenous exposition to mortality/morbidity risks. Very good empirical properties: Health, wealth, OOP s, leisure, longevity. Population statistics. Life cycle statistics. Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 8 / 9

29 Conclusion Conclusion Marginal effect of insurance status: When young, conditional upon old status. When old, conditional upon young status. Main findings: Substitution: Static (leisure vs investment). Dynamic (stockpiling, leisure over life cycle,... ) Adjustment risk exposition (through precautionary health, wealth balances). Pelgrin & St-Amour (EDHEC and UNIL) Life Cycle Responses to Health Insurance January 5, 16 9 / 9