Health and Inequality Jay H. Hong SNU Josep Pijoan-Mas CEMFI Jos - PowerPoint PPT Presentation

Health and Inequality Jay H. Hong SNU Josep Pijoan-Mas CEMFI José Víctor Ríos-Rull Penn, UCL, NBER Facing Demographic Change in a Challenging Economic Environment October 27, 2017 Institute for Fiscal Studies Work in Progress

Introduction

Motivation • Inequality (economic inequality) is one of the themes of our time. • Large body of literature documenting inequality in labor earnings, income, and wealth across countries and over time Katz, Murphy (QJE 1992); Krueger et al (RED 2010); Piketty (2014); Kuhn, Ríos-Rull (QR 2016); Khun et al (2017) • We also know of large socio-economic gradients in health outcomes • In mortality Kitagawa, Hauser (1973); Pijoan-Mas, Rios-Rull (Demography 2014); De Nardi et al (ARE 2016); Chetty et al (JAMA 2016) • In many other health outcomes Marmot et al (L 1991); Smith (JEP 1999); Bohacek, Bueren, Crespo, Mira, Pijoan-Mas (2017) ⊲ We want to compare and relate inequality in health outcomes to pure economic inequality . 1

What we do • We build measures of inequality between socio-economic groups • We use the notion of Compensated Variation to compare • We take into account – Differences in Consumption – Differences in Mortality – Differences in Health – The actions that will be taken by the disadvantaged groups to improve health and mortality when given more resources • In doing so, we develop novel ways of measuring a/ Health-related preferences b/ Health-improving technology with medical expenditures 2

The project (1) Pose a model of consumption and health choices (2) Estimate the quantitative model with over-identifying restrictions (2) Use our estimates to 1. Do welfare analysis, i.e. compare the fate of different groups given their allocations. 2. Ask what different groups would do if their resources were different and how much does welfare change. 3

Today we will (1) Discuss briefly how to compare welfare given allocations. (2) Write and calibrate a simple model of consumption and health choices • Useful to understand identification from a simple set of statistics (3) Talk about the estimation of a big quantitative model with over-identifying restrictions • Adds more realistic features ⊲ Part (3) still preliminary 4

Welfare Comparison: Compensated Variation

The Logic, Consider, dropouts and college graduates, d and c 1. Under the same preferences u ( c ) , then to make them equally happy, we have to set u ( c d ) = u ( c c ) , i.e. to give c d c d − 1 extra consumption to the d group. 2. If they have different longevities, then we have to use a u function that includes consumption and and the value of expected longevity ℓ : u ( c , ℓ ) . Then the compensated variation be the amount c d c d − 1 that solves u ( c d , ℓ d ) = u ( c c , ℓ c ) Notice that we do not change ℓ d 3. If their health differs, u has to take health and longevity into account. The compensated variation does not change health or longevity. u ( c d , ℓ d , h d ) = u ( c c , ℓ c , h c ) 4. If we estimate preferences and health maintenance technology when compensating people, they would alter their health and longevity in 5 ways we could calculate.

Stylized Model: The construction of u

Setup 1. Perpetual old: survival and health transitions age-independent 2. Complete markets: annuities and health-contingent securities (Guarantees stationarity; allows to ignore financial risks associated to health) 3. Choices: non-medical c vs medical consumption x 4. Types e differ in • resources a e • initial health distribution µ e h • health transitions Γ e hh ′ ( x ) • but not in survival probability γ h , (Pijoan-Mas, Rios-Rull, Demo 2014) 5. Instantaneous utility function depends on consumption and health u ( c , h ) = α h + χ h log c 6. Let health h ∈ { h g , h b } 6

Optimization The recursive problem � � � V e ( a , h ) = max Γ e hh ′ ( x ) V e ( a ′ h ′ , h ′ ) u ( c , h ) + β γ h x , c , a ′ h ′ h ′ � q e s.t. x + c + γ h hh ′ a ′ h ′ = a ( 1 + r ) h ′ • In equilibrium ( 1 + r ) = β − 1 and q e hh ′ = Γ e hh ′ • Standard Complete Market result (Euler equation for c ) : 1 1 c g = c ′ g , c b = c ′ χ g = χ b and b c g c b • Optimal health investment (Euler equation for x ) : � � ∂ Γ e hh g ( x ) V e ( a ′ h g , h g ) − V e ( a ′ u c ( c h , h ) = β γ h h b , h b ) ∂ x 7

Welfare comparisions • The attained value in each health state is given by � � � � V e α g + χ g log c e g = A e g χ g c e V e α b + χ b log χ b b g � � � � �� − 1 Γ e gg ( x e 1 − Γ e gg ( x e γ g 0 g ) g ) A e = where I − β Γ e bg ( x e 1 − Γ e bg ( x e 0 γ b g ) g ) • The unconditional value of the average person of type e is given by � � V e = µ e g V e 1 − µ e V e g + g b • Welfare comparision holding x constant � � � � c c g ; µ c h , Γ c [ 1 + ∆ c ] c d g ; µ d h , Γ d = V V h , γ h , α h , χ h h , γ h , α h , χ h • Welfare comparision allowing x to be chosen optimally � � � � c c g ; µ c h , Λ c , γ h , α h , χ h c d g ([ 1 + ∆ a ] a , . ); µ d h , Λ d , γ h , α h , χ h 8 V = V

Data

Link Various Sources 1. HRS gives • Health distribution at age 50 (by education type) • Health transitions (by age, health, and education type) • Survival functions (by age, health) ⊲ Obtain the objects µ e h , Γ e hh ′ ( x ∗ ) , γ h 2. PSID (1999+) gives • Non-durable consumption (by age, health, and education type) • Out of Pocket medical expenditures (by age, health, and education type) ⊲ Obtain health modifier of marginal utility χ h ( χ g = 1, χ b = 0 . 85) ⊲ Obtain health technology parameters Λ e 3. Standard data in clinical analysis • Outside estimates of the value of a statistical life (VSL) • Health Related Quality of Life (HRQL) scoring data from HRS ⊲ Obtain α g , α b 9

Measuring health objects • We use all waves in HRS, white males aged 50-88 • Health stock measured by self-rated health (2 states) • Findings 1. At age 50, college graduates are in better health than HS dropouts – µ c g = 0 . 94 – µ d g = 0 . 59 2. Large differences in survival by health • e g = 33 . 1 (life expectancy if always in good health) ⇒ γ g = 0 . 970 • e b = 19 . 3 (life expectancy if always in bad health) ⇒ γ g = 0 . 948 3. College health transitions are better • Γ c gg − Γ d gg = 0 . 056 (college are better at remaining in good health) • Γ c bg − Γ d bg = 0 . 261 (and even better at recovering good health) 10

The value of life across health states The data • The Health Utility Index Mark 3 (HUI3) is a HRQL scoring used in clinical analysis Horsman et al (2003), Feeny et al (2002), Furlong et al (1998) • Trade-off between years of life under different health conditions • From patient/individual/household surveys: no revealed preference • It measures quality of Vision, Hearing, Speech, Ambulation, Dexterity, Emotion, Cognition, Pain up to 6 levels • It aggregates them into utility values to compare years of life under different health conditions – Score of 1 reflects perfect health (all levels at its maximum) – Score of 0 reflects dead – A score of 0 . 75 means that a person values 4 years under his current health equal to 3 years in perfect health • Use HUI3 data from a subsample of 1,156 respondents in 2000 HRS 11

The value of life across health states Mapping into the model • In the data we find that – Average score for h = h g is 0 . 85 and for h = h b is 0 . 60 • Imagine an hypothetical state of perfect health ¯ h . Then, c e , ¯ u ( c e g , h g ) = 0 . 85 u (¯ h ) c e , ¯ u ( c e b , h b ) = 0 . 60 u (¯ h ) • Therefore, u ( c e b , h b ) = α g + χ g log c e g , h g ) = 0 . 85 g u ( c e α b + χ b log c e 0 . 60 b 12

Results without Endogeneous Health

Welfare differences without endogenous health Welfare of different types CG HSG HSD CG-HSG CG-HSD Cons while in Good Health $ 41,348 $ 31,817 $ 23,621 30 % 75 % Life Expectancy 30.8 28.5 25.2 2.3 5.6 Healthy Life Expectancy 27.5 22.2 14.3 5.3 13.2 Unhealthy Life Expectancy 3.3 6.3 10.9 -3.0 -7.6 Compensated variation (1 + ∆ c ) health diff: none 1.30 1.75 health diff: quantity of life 2.05 6.37 health diff: quality of life 2.05 6.63 health diff: both 3.21 24.95 13

Welfare differences Comments • Welfare differences due to quality and quantity of life are huge • Question If health is so important, why low types do not give up consumption to buy better health? • Our answer By revealed preference, it must be that out-of-pocket health spending is not too useful in improving health after age 50 14

Results with Endogeneous Health

Health technology Functional form • Assume the following functional forms: x 1 − ν g Γ e λ e gg ( x ) = 0 , g + λ 1 , g 1 − ν g x 1 − ν b Γ e λ e bg ( x ) = 0 , b + λ 1 , b 1 − ν b • This form is flexible: – it can impute all the advantage as being intrinsic to the type ( λ 1 , h = 0) (It could also be the result of different non-monetary investments, which we will ignore.) – or as being the result of having more resources ( λ e 0 , h = 0) – or somenthing in between. λ c 0 , g , λ c 0 , b , λ d 0 , g , λ d • This adds 8 parameters: ν g , ν b λ 1 , g , λ 1 , b 0 , b 15