Change Matters:A Dynamic Demand for Medical Care
Jennifer L. [email protected]
Agenda:
1. Motivation
2. Literature & Contribution
3. Model
4. Empirical Tests
5. Conclusion and Future Research
22.5%
49.0%
64.1%
73.6%
80.3%
96.9%
3.1%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
Top 1% Top 5% Top 10% Top 15% Top 20% Top 50% Bottom 50%
Percent of U.S. Population
Per
cen
t o
f T
ota
l H
ealt
h C
are
Sp
end
ing
Source: Kaiser Family Foundation calculations using data from the U.S. Department of Health and Human Services,Agency for Healthcare Research and Quality, Medical Expenditure Panel Survey (MEPS), 2004.
> $13,000 < $730
Motivation
The top 5% of spenders account for nearly 50% of spending.
> 65
< 65
poorhealth
Literature & Contribution
Theoretical Literature: Willingness to Pay: Mishan (1971), Berger et.al. (1987), Murphy & Topel (2006) Human Capital: Grossman (1972), Ehrlich & Chuma (1990), Liljas (1998)
Empirical Literature: Theoretical Testing: Grossman (1972), Wagstaff (1986, 1993), VanDoorslayer (1987) Health & Wealth: Viscusi & Evans (1990), Blau & Gilleskie (2006), Finkelstein et. al. (2008) Econometrics: Newhouse et. al. (1980), Deb & Trivedi (1997), Greene (2007)
Empirical Contributions:1. Multiple equation model consistent with the theory.2. Empirical support for the significance of the change in health.3. Empirical support for the assumption that health and wealth are complements and consumption and medical care are not separable.
Theoretical Contributions:1. An explanation for the observed pattern of medical care spending.2. Model of health transition consistent with current accounting.3. Testable hypotheses about the demand for medical care.
Model: Utility
“Utility” = Consumption, Health, and the Change in Health
today
yesterday
Health gets better!
yesterday
Health gets worse.
Literature: Habit Formation -- Constantinides (1990) Adaptation -- Groot (2000), Gjerde et. al. (2005)
0, ,max ( ), ( ), ( )
T rt
Z m TLU e U Z t H t t dt
Model: Utility
1. Health State, not a flow of healthy daysGrossman (1972), Ehrlich & Chuma (1990) H
Berger et. al., (1987) “…the utility individuals derive from consumption depends on their state of health.”
( ) ( ), ( )a
RU H t U c t l t da
Murphy & Topel (2006)
2. General functional form
Change in Health
Model: Change in Health
Change in Health = Investment - Depreciation
medical careAND
current health
an amountNOT
a rate x stock
Medical literature:co-morbidities FASB # 142 (2001)
1t t t tH I H t t tI
0I
H H
0
H
H
Grossman (1972)
( ) ( ( ), ( ); ( ))I t I M t m t E t
0I
H
Old way: New way:
Multiplicative Depreciation
0
20
40
60
80
100
120
1 10 19 28 37 46 55 64 73 82 91 100
time
Hea
lth
Higher health, more negative the decline in health
Source: NYT 7/30/06
Higher health, less negative the decline in health
Model: Change in Health
Model: Change in Wealthand Endpoint Conditions
Endpoint Conditions:
( ) ( ( )) ( ) ( ) ( )R
R rR t w H t P t m t Z tt
0 min
min
0
max
(0)
( )
(0) 0
( ) 0
H H H
H T H
R R
R T
T T
Hmin and Tmax are exogenously fixed at the beginning of the planning horizon
Why do we demand medical care?
Marginal BenefitsFrom Health
= Marginal Cost ofHealth Capital
Marginal utility from health +Marginal income from health
Marginal cost of medical care +Interest rate + rate of depreciation
No inevitable disequilibrium
+ Marginal utility from the change in health x Marginal productivity of health to investment
- Marginal productivity of health to investment
Inevitable disequilibrium!Larger disequilibrium the lower the state of health
Larger disequilibrium the greater the decline in health
H
( ) ( )t H t
Benefits
H
( ) ( )t H t
Benefits
H
( )t
Benefits
H
( )t
Benefits
Marginal benefits of longevitydecrease over the lifecycle
Grossman (1972): “…even though Health capital falls over the life cycle, gross investment might increase, remain constant or decrease.”
Why do we demand more medical care?
Marginal utility from the change in health and marginal productivity of health keep benefits high.
t↓T
1'( ) (1 )ih ii i i
UH r W r
( ) ( )
(0)H H
H HR
U Uw g t r g t
RAND (2003)
Why do we demand moremedical care at the end of life?
Ehrlich & Chuma (1990)
g(T)
[ ( ) ( )]
( )
( ) ( )
( )( )
(0)
T
t
u
t
u r u du
T s r dsh
htR
g t g T e
U uw u e du
H
Time Path of Medical Care Demand
?
sgn sgn
( )
rtm Z H t H t
rt Hmt mH m t
rt rt H Rm H H H H
R
e U Z U H U H
e U Hm
re U e U U w
rp t p
Time Path for Consumption
? ? ? ?
ZH Z H Z t m
ZZ
H U U UZ
U
m
The demands for consumption and medical care are not separable.
The sign of the relationship between health and consumption, and between the demands for medical care and consumption are
empirical questions.
Summary of Theoretical Implications
1. Change matters: the change in health is a significant factor in an individual’s demand for medical care.
5. Health and wealth: health and consumption and consumption and medical care demands are not separable.
2. Price matters less over the lifecycle.
3. Quality of life matters more than longevity at the end of life.
4. The advance of medical technology increases the demand for medical care over time.
Empirical Issues
1. Consistency with the theory Gilleskie (1998)
Joint estimation of the demands for medical care and consumptionConsistency with economic restrictions
2. Unobservable health and price for medical careSingle or multiple indicator, Self-assessed health
MIMIC Van der Gaag and Wolfe (1982), Ersblad et. al. (1995)Latent Variable Bound (1999), Disney et. al. (2006)MCA Greenacre (2002) Hadley and Weidman (2006)
3. Discrete counts and unobservable heterogeneityNegative binomial, finite mixture Deb and Trivedi (1997), HHG (1984)Incidental parameters problem Greene (2007)Initial conditions problem Wooldridge (2005)
3
11
3
12
exp
exp
j
j
j i
j j j i j j j j j
mZZZ Zm ZZ Z ZH t Z Z
j
m mj Zm Zm m m m Z m m H t m m
i
Z c p c p b Budget b Change b Health Controls
m c p c p c p b Budget b Change b Health Controls
Non-linear system of equations (NLSUR)
Empirical Specification
j = hospital days (H), tests & services (TS), and general practitioner visits (GP)Controls = marital status and education Errors clustered by individual and correlated across equations
Economic Restrictions:1. Negative own-price effects (negative semi-definite Slutsky matrix)2. Symmetry in cross-price effects
1: 0jmH b The greater the decline in health, the higher the demand for
medical care.
Hypotheses:
2 : , 0Z ZHH b b The demands for health and consumption are not independent.
3: 0jZmH c The demands for medical care and consumption are not separable.
Data
Data: 14 waves (1991 – 2005) of the British Household Panel SurveyFULL sample: 119,970 person-year observationsOSM balanced panel of 40,896 observations (3,145 individuals)
0.0
2.0
4.0
6.0
8.1
De
nsity
-100 -50 0 50 100DHt
Distribution of the Change in Health
8.5e-07 aH1t 100 +----------------------------------------------------------------+ 1 + * * ***** ************** 2 | 1 | | t | ** * ******************************* s | a | l | | r | * * *********************************** e | v | o | | h | * ** * ************************************* t | l | a | e | h | * ** * ** * *********************************** * 5 +
Sel
f-re
port
ed h
ealt
h 1
= g
ood
Health Index
Self-reported Health and the Health Index
Health Index: MCA using all available data for each wave.
If the change in health matters, we should be able to see it!
Empirical Results
FULL Sample, P-values reported
coefficient unrestricted restricted unrestricted restricted unrestricted restricted unrestricted restricted
Change in Health -0.0258 -0.0285 -0.0079 -0.0109 -0.0036 -0.0042 0.0031 0.0034(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Lagged Health -0.0229 -0.0236 -0.0109 -0.0144 -0.0044 -0.0051 0.0060 0.0057(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
p(Z) -0.8754 0.0890 -2.5734 0.0385 -0.4831 -0.0012 -0.6876 -0.5723(0.159) (0.000) (0.000) (0.000) (0.000) (0.847) (0.000) (0.000)
p(HD) -1.8007 -1.6547 -0.0004 0.1071 0.1983 0.2640 0.0727 0.0890(0.000) (0.000) (0.943) (0.000) (0.000) (0.000) (0.000) (0.000)
p(TS) 0.8664 0.1071 0.0011 -0.2265 0.1685 0.0353 0.0762 0.0385(0.000) (0.000) -0.0010 (0.000) (0.000) (0.000) (0.000) (0.000)
p(GP) -0.0102 0.2640 -0.2681 0.0353 -0.4936 -0.4224 -0.0257 -0.0012(0.896) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.847)
Budget 0.0045 0.0037 0.0011 0.0017 -0.0016 -0.0016 0.0036 0.0031(0.002) (0.061) (0.001) (0.000) (0.000) (0.000) (0.000) (0.000)
Couple -0.4165 -0.3694 0.0714 0.0952 0.0276 0.0347 0.1906 0.1919(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Education 0.0030 0.0448 0.1513 0.1762 0.0232 0.0285 0.1598 0.1613(0.000) (0.505) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Constant 5.2973 4.2443 5.0689 2.1289 2.1796 1.5948 1.6182 1.4792(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Hospital Days Tests & Services General Practitioner Consumption
< 0 > 0
Robustness Results
Signs, significance and magnitudes consistent across specifications
coefficient unrestricted restricted unrestricted restricted unrestricted restricted unrestricted restricted Full OSM Full OSM
Change in Health -0.0258 -0.0285 -0.0279 -0.0287 -0.0253 -0.0268 -0.0269 -0.0255 -0.0191 -0.0259 -0.0459 -0.0526(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Lagged Health -0.0229 -0.0236 -0.0267 -0.0251 -0.0223 -0.0219 -0.0254 -0.0215 -0.0161 -0.0247 -0.0490 -0.0571(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Change in Health -0.0079 -0.0109 -0.0081 -0.0112 -0.0079 -0.0094 -0.0080 -0.0099 -0.0081 -0.0108
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Lagged Health -0.0109 -0.0144 -0.0110 -0.0147 -0.0109 -0.0130 -0.0110 -0.0135 -0.0110 -0.0144
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
unrestricted restricted unrestricted restricted Full OSM Full OSM
Change in Health -0.0036 -0.0042 -0.0043 -0.0046 -0.0205 -0.0213 -0.0292 -0.0337(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Lagged Health -0.0044 -0.0051 -0.0053 -0.0055 -0.0222 -0.0212 -0.0342 -0.0404(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
unrestricted restricted unrestricted restricted unrestricted restricted unrestricted restricted Full OSM Full OSM
Change in Health 0.0031 0.0034 0.0039 0.0037 0.0035 0.0035 0.0037 0.0038 0.0108 0.0115 0.0138 0.0150
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
Lagged Health 0.0060 0.0057 0.0057 0.0053 0.0059 0.0059 0.0055 0.0056 0.0203 0.0180 0.0211 0.0197
(0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.000)
ConsumptionRE Tobit TobitFull Sample OSM Sample Full Sample OSM Sample
Tests & Services
General Practitioner VisitsFull Sample OSM Sample Ordered LogitRE Ordered Probit
Single Equation Models
Fixed Effect NB NB
Hospital Days4 Equation Model 3 Equation Model
Full Sample OSM Sample Full Sample OSM Sample
consumption
Utility
Health
Higher Health
Lower Health
Z(H) Z(High)Z(Low)
A decline in health is associated with an increase in the marginal utility of consumption.
Health & Wealth Implications
2
0U
Z H
Holding price constant, consumption declines
Value of a “Life Year”
Murphy & Topel (2006)
Value of a Life Year
Income Consumption
ZH Z H Z t m
ZZ
H U U UZ
U
m
22.5%
49.0%
64.1%
73.6%
80.3%
96.9%
3.1%
0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
80.0%
90.0%
100.0%
Top 1% Top 5% Top 10% Top 15% Top 20% Top 50% Bottom 50%
Percent of U.S. Population
Per
cen
t o
f T
ota
l H
ealt
h C
are
Sp
end
ing
Source: Kaiser Family Foundation calculations using data from the U.S. Department of Health and Human Services,Agency for Healthcare Research and Quality, Medical Expenditure Panel Survey (MEPS), 2004.
> $13,000 < $730
Conclusion
Change Matters!We make trade-offs between health and consumption.
Econometric issues for better fit to data
Do people stay in the top 5% over time?
How are the top 5% affected by price?
What is the trade-off between quality and quantity of life?
What is the effect of medical technology?
The Wall Street Journal, December 12, 2006http://online.wsj.com/article/SB116586842161546712.html?mod=editsend
Dr. Kishnani, who led the second clinical trial, says, "What I learned from these trials is that each family has to decide when enough is enough."
How do we design a health care financing system where every family gets to make this choice?
Future Research
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