Health Heterogeneity and the Preferences for Consumption Growth - PowerPoint PPT Presentation

Introduction Model Estimation Data Results Composition Health Heterogeneity and the Preferences for Consumption Growth Jay H. Hong Josep Pijoan-Mas Jos´ e-V´ ıctor R´ ıos-Rull Seoul National University CEMFI, CEPR Minnesota, Mpls Fed, CAERP Colloque CIREQ Montr´ eal de macro´ economie La sant´ e et la vieillesse April 2015 , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 1 / 30

Introduction Model Estimation Data Results Composition Introduction A big question in Macroeconomics is what determines savings. – The old are special (DeNardi, French, Jones (2015), Ameriks, Briggs, Caplin, Shapiro Tonetti (2015)) – There is an increasing number of them. Two fundamental characteristics of the old – Their health worsens with age – It does so at different rate for people in different socio-economic groups Pijoan-Mas, R´ ıos-Rull (2014) ⊲ How do age and health shape preferences and consumption decisions? – Surprisingly, little work exploring effects of health on consumption , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 2 / 30

Introduction Model Estimation Data Results Composition Objective We estimate the effect of health on the marginal utility of consumption We use a model where the evolution of health is itself endogenous But we use only the consumption Euler equation to estimate structural parameters – We exploit differences in consumption growth by age, education, wealth, and health groups – We use estimates of health transitions by age, education, and wealth. – We interpret them as the outcome of optimal behavior. ⊲ Hence, we do not need to know the whole health production technology. , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 3 / 30

Introduction Model Estimation Data Results Composition Conventional wisdom The marginal utility of consumption falls when health declines Domeij, Johannesson (2006) and Scholz, Seshadri (2012) – Exploit the average joint decline of health and consumption with age ⊲ But age-consumption decline may be due to other reasons Gourinchas, Parker (2002); Aguiar, Hurst (2013) Finkelstein, Luttmer, Notowidigdo (2012) – Subjective well-being increases with health, more so for individuals with larger permanent income ⊲ But not necessarily related to consumption expenditure Koijen, Van Nieuwerburgh, Yogo (2012) – Households own too little long-term care insurance, too many annuities , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 4 / 30

Introduction Model Estimation Data Results Composition Main findings At age 65, better health gives higher marginal utility of consumption 1 – You need healthy time to enjoy life However, as individuals age, this difference narrows down 2 – Consumption expenditure also substitutes for healthy time – Hence, low health may give high marginal utility of consumption We provide some direct evidence of the age effect of health on 3 consumption composition , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 5 / 30

Introduction Model Estimation Data Results Composition Model: main elements Individuals differ in: – age ( i ), education ( e ), health ( h ), wealth ( a ), income ( s ) They choose – nonmedical expend ( c ), medical expend ( x ), health-related behaviour ( y ) Education e ∈ E = { c, h, d } is predetermined. – (potentially) different patience β e – (potentially) different income process π e,i ( s ′ | s, h ) – (potentially) maybe different health technologies Γ e,i Health stock h ∈ H evolves stochastically Γ e,i ( h ′ | h, x, y ) – different survival probability γ i ( h ) – different income process π e,i ( s ′ | s, h ) – different value of medical expenditure ε i ( h ) – different value of non-medical expenditure χ i ( h ) , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 6 / 30

Introduction Model Estimation Data Results Composition Preferences Within period utility function: − ν 0 y ν 1 − ε i ( h ) u i ( h, c, x, y ) = χ i ( h ) c 1 − σ c σ c , σ x , ν 0 , ν 1 > 0 1 − σ c x σ x χ i ( h ) regulates the health-dependence of u c – It is the object of interest. We choose not to make ν 0 health-dependent: we think of y as preventive health-behavior ε i ( h ) regulates the health-dependence of u x – In the main exercise we will ignore this part. – But extension: ε i ( h ) stochastic to address the role of medical expenditure uncertainty in consumption growth. , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 7 / 30

Introduction Model Estimation Data Results Composition The Optimization Problem The Bellman equation: � v e,i ( a, h, s ) u i ( h, c, x, y ) = max c,x,y + β e ψ i ( h ) Γ i ( h ′ | h, x, y ) π e,i ( s ′ | s, h ) E ε ′ | h ′ v e,i +1 ( a ′ , h ′ , s ′ ) � � s ′ ,h ′ c + x + a ′ = a (1 + r ) + s s.t. The model can be solved to deliver decision rules c e,i ( a, h, s ) , x e,i ( a, h, s ) , y e,i ( a, h, s ) , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 8 / 30

Introduction Model Estimation Data Results Composition The FOC ⊲ Consumption Euler equation, χ i ( h ) c − σ c = Γ i ( h ′ | h, x, y ) π e,i ( s ′ | s, h ) χ i +1 ( h ′ ) ( c ′ ) − σ c � β e ψ i ( h ) (1 + r ) s ′ ,h ′ ⊲ Optimal health expenditure χ i ( h ) c − σ c β e ψ i ( h ) x ( h ′ | h, x, y ) π e,i ( s ′ | s, h ) v e,i +1 ( s ′ , h ′ , a ′ ) � Γ i = s ′ ,h ′ ε i ( h ) − σ x x − σ x − 1 − in extension ⊲ Optimal health behavior y ( h ′ | h, x, y ) π e,i ( s ′ | s, h ) v e,i +1 ( s ′ , h ′ , a ′ ) u y = β e ψ i ( h ) � Γ i s ′ ,h ′ , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 9 / 30

Introduction Model Estimation Data Results Composition Problem: Estimating the Law of Motion for Health Need to measure effects of health investments on health evolution Γ i ( h ′ | h, x, y ) Γ i x ( h ′ | h, x, y ) Γ i y ( h ′ | h, x, y ) and and – Very hard to measure directly due to endogeneity bias (typically one finds Γ i x < 0 and Γ i y < 0 ) – In addition, a substantial part of x is not strictly health care , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 10 / 30

Introduction Model Estimation Data Results Composition Our Solution 1) Use only the Euler equation of consumption – No need to solve the full dynamic problem – No need to measure Γ i x ( h ′ | h, x, y ) and Γ i y ( h ′ | h, x, y ) 2) Replace health investments by their optimal policies – Take the law of motion for health Γ i ( h ′ | h, x, y ) – replace the x and y by their optimal policies x e,i ( a, h, s ) and y e,i ( a, h, s ) – Then, the law of motion of health is function of the state variables: h ′ | a, h, s Γ e,i � � which is easy to estimate , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 11 / 30

Introduction Model Estimation Data Results Composition Consumption growth and information about χ ( h ) Γ e,i ( h ′ | h, a ) χ i +1 ( h ′ ) � c e,i +1 ( h ′ , a ′ ) � − σ β e ψ i ( h ) (1 + r ) � = 1 χ i ( h ) c e,i ( h, a ) h ′ 1/ If health was constant ( Γ e,i diagonal), higher consumption growth for high health due to ψ i ( h ) 2/ With changing health – Changes in health affect consumption growth through χ i +1 ( h ′ ) /χ i ( h ) – If health and consumption are complements ( χ ( h g ) > χ ( h b ) ) Consumption growth higher for low health – If health and consumption are substitutes ( χ ( h g ) < χ ( h b ) ) Consumption growth higher for high health 3/ If health expenditure uncertainty differs across health types, a further reason for consumption growth differences , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 12 / 30

Introduction Model Estimation Data Results Composition The model moment conditions For each agent of type ( e, i, a, h ) : – The realised value of the Euler eqn. depends on the shock h ′ h ′ , a e,i +1 ( h, a ) � − σ � = β e (1 + r ) χ ( h ′ ) c e,i +1 � � e, i, a, h ; h ′ � � f − 1 c e,i ( h, a ) χ ( h ) – So we can rewrite the Euler equation in expectation as: � � � e, i, a, h ; h ′ , � f = E h ′ | e,i,a,h h ′ | h, a � e, i, a, h ; h ′ � ψ i ( h ) Γ e,i � � � f = 0 h ′ – Which give one moment condition for every type , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 13 / 30

Introduction Model Estimation Data Results Composition The Empirical Analog We have a discretized state space Ω ≡ E × I × A × H ( Ω is a discrete set with M elements indexed by m ) For each individual j we observe – current state ω j ∈ Ω – realized shocks tomorrow h ′ j – consumption chosen tomorrow Hence, the empirical analog of our orthogonality conditions requires to compute the average consumption growth for each type ω j , h ′ j , Hong, Pijoan-Mas, R´ ıos-Rull Health Heterogeneity and the Preferences for Consumption Growth 14 / 30