Transcript Lecture 2. Compensation and responsibility

Lecture 2. Compensation and
responsibility
Erik Schokkaert (KULeuven,
Department of Economics)
Structure
1.
2.
3.
Responsibility and compensation in a quasilinear model: optimal income redistribution
in a first best setting
Another application: distribution mechanism
(prospective financing mechanisms) in the
health care sector
From first best-solutions to social orderings
1. Responsibility and compensation in a
quasi-linear setting (BOSSERT en FLEURBAEY,
Social Choice and Welfare, 1996)
Responsibility and compensation



the responsibility cut: (aiR, aiS)
EIER (equal income for equal R): full
compensation
ETES (equal transfer for equal S): strict
compensation
An impossibility and a possibility


Th 1. In general, EIER and ETES are
incompatible.
Th. 2. If the pre-tax income function is
additively separable in C- and S-variables,
then, there is a natural solution satisfying
both EIER and ETES
How to proceed from here?
IMR
WIMR
ETES
GSS
WGSS
EIER
EIUR
EIRR
X
ETUS
ETRS
Strengthening and relaxing EIER
GSS => WGSS => EIER => EIUR => EIRR
Strengthening and relaxing ETES
IMR => WIMR => ETES => ETUS => ETRS
Characterizations
IMR
GSS
X
WGSS
X
EIER
X
EIUR
EIRR
WIMR
X
X
X
ETES
X
X
X
ETUS
ETRS
The egalitarian-equivalent solution
IMR
GSS
X
WGSS
X
EIER
X
EIUR
EIRR
WIMR
X
X
X
pre-tax income she would
earn with reference talent
ETES
X
X
X
ETUS
ETRS
EE
uniform transfer to satisfy the budget
contraint
The conditional-egalitarian solution
IMR
GSS
X
WGSS
X
EIER
X
EIUR
EIRR
CE
WIMR
X
X
X
responsibility part
ETES
X
X
X
ETUS
ETRS
EE
"guaranteed income"
Characterizations
IMR
GSS
X
WGSS
X
EIER
X
EIUR
X
EIRR
CE
WIMR
X
X
X
ACE
ETES
X
X
X
ETUS
X
AEE
ETRS
EE
average over all levels of
talent
responsibility part
average over all levels of
effort
2. Designing prospective financing
schemes in the health care sector

Incentive problems in health care - examples:



Two "extreme" solutions:



reimbursement of expenditures (e.g. fee for service)
prospective financing
Trend towards prospective financing and
benchmarking:



financing of hospitals or practices of doctors
financing schemes for regions and sickness funds
advantage: incentives for cost control
danger: incentives for risk selection
Solution? Risk adjustment
EXAMPLE 1: REGIONAL DISTRIBUTION MECHANISM
Central government
Financial
contribution
Citizen
Subsidy
Regional authority
Local "health" tax?
EXAMPLE 2: REGULATED COMPETITION WITH RISK
ADJUSTMENT
Solidarity fund
Solidarity
contribution
Premium
subsidy
Managed care
organisation
Consumer
Premium
Contribution
Basic idea



In practice: risk-adjusted premium subsidies
often derived from observed expenditures
In principle: risk-adjusted premium subsidies
based on “acceptable costs”: “costs generated in
delivering a specified basic benefits package,
containing only medically necessary and costeffective care” (Van de Ven and Ellis, 2000)
Therefore: many factors, which do have an
influence on observed expenditures, should
NOT be used for calculating the risk-adjusted
premium subsidies

QUESTIONS:


what variables should be included in the RAsystem?
how to design a prospective financing system?
Reinterpretation of the Bossert-Fleurbaey
model (Schokkaert, Dhaene, Van de Voorde, HE 1998;
Schokkaert and Van de Voorde, JHealth Econ 2004)


health care expenditures: x i  f (a i )
total amount of premium subsidies:
ω (=  i)
i

monetary gain made on a patient i:

responsibility cut:
i  i  x i
C R
x i  f (a i , a i )
"Cost efficiency"

NEUTRALITY: for any two individuals i and j
with a iC  a Cj , i   j

C
consequence: i, j : a i
it holds that
i   j
C R
 a j , ai
R
 aj
"Solidarity"

NO INCENTIVES FOR RISK SELECTION:
for any two individuals i and j with
R
ai
R
 a j , i
consequence:
it holds that

 j
i, j : a iR  a Rj , a iC  a Cj
i   j
Theorems

Proposition 1. If the medical expenditure
function can be written (i ) as
C R
C
R
f (a i , a i )  g(a i )  h(a i )
then the following mechanism satisfies NIRS
and NEUT:


C
C
i   g(a i )   g(a k )
n
nk
NOTE. If    x i , then
i
i  g(a iC ) 

R
h
(
a

k)
nk
An impossibility result

Proposition 2. If the medical expenditure
function is not additively separable in the
variables aC and aR, then NO risk adjustment
scheme can satisfy both NIRS and NEUT.
Alternative solutions?

Keep NIRS, drop NEUT: egalitarianequivalent solutions

Keep NEUT, drop NIRS: conditionalegalitarian solutions
Empirical illustration:
-
individual data for 321,111 Belgian insured
(no self-employed)
-
RIZIV-reimbursements for 1995 (medicines
are not included)
per capita reimbursed health expenditures:
38.299 BEF (949 Euros)
-
a. treatment of omitted variables

the conventional approach neglects the
effects of the R-variables in x i  f (a iC , a iR )

therefore, the estimates of the effects of the
C-variables are biased, if there is correlation
between C- and R-variable
b. non-separable specifications

introduction of multiplicative effects in the
specification:



age * loyalty to general practitioner
medical supply * disability
no longer additively separable: conditional
egalitarian approach introduces incentives for
risk selection
A general remark


it is possible to neutralize the effect of
responsibility variables for the computation of
the premium subsidies
advisable to distinguish explicitly two stages:


do the econometric work as carefully as possible
– specify the best explanatory model
set up an explicit discussion about the ethical (or
political) choices
3. From first best to social
orderings: Fleurbaey (2005)

BASIC ASSUMPTIONS:



rejection of welfarism: subjective satisfaction is
not the ultimate criterion ("responsibility for
subjective happiness")
rejection of perfectionism: preferences of the
population should be respected
reducing income inequalities is good, provided
this has no adverse consequences on health
Some notation
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every individual has a particular healthconsumption bundle zi = (hi , ci ). Perfect
health denoted by h*.
every individual i has well-defined monotonic
preferences Ri over these bundles
how to define social preferences R over
allocations z = (z1,…,zn )?
social preferences will depend on population
profile of individual preferences, hence R(R)
Feasible allocations


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every individual i is endowed with a mapping
wi (hi ), defining her income after all taxes
and transfers except health-related ones
every individual is endowed with a mapping
mi (hi ), describing how much of medical
expenses must be made in order to bring her
to health state hi
individual budget constraint:
ci  w i (h i )  Ti  mi (h i )  Si
ci  (  ) w i (h i )  (  )mi (h i )
Pareto-principle and independence
RESPECT OF INDIVIDUAL PREFERENCES
BASE SOCIAL PREFERENCES ON INDIVIDUAL PREFERENCES
IN A VICINITY OF INDIVIDUALS' CURRENT SITUATION
Pigou-Dalton condition (revised)


traditional Pigou-Dalton condition makes
sense only in a unidimensional world
not care much
cares a
lot about
extension todoes
multidimensional
setting
may
about health
health
come in conflict with the Pareto condition
RESTRICT APPLICATION OF PIGOU-DALTON PRINCIPLE
TO SITUATIONS WHERE THE TWO INDIVIDUALS HAVE THE
SAME PREFERENCES OR ARE BOTH AT A PERFECT HEALTH
LEVEL
"FULL-HEALTH EQUIVALENT INCOMES"
In normal circumstances
Relationship with WTP?


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full-health equivalent consumption = actual
consumption – "sacrifice" for better health
willingness-to-pay = "sacrifice" for better
health + productivity gain due to better health
if productivity gain = 0, then
FHEC = Actual consumption - WTP