Lecture 2. Compensation and responsibility

Lecture 2. Compensation and responsibility

Erik Schokkaert (KULeuven, Department of Economics)

Structure

1. Responsibility and compensation in a quasi-linear model: optimal income redistribution in a first best setting

2. Another application: distribution mechanism (prospective financing mechanisms) in the health care sector

3. 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: (ai

R, 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 ETUS ETRS

GSS

WGSS

EIER X

EIUR

EIRR

Strengthening and relaxing EIER

GSS => WGSS => EIER => EIUR => EIRR

Strengthening and relaxing ETES

IMR => WIMR => ETES => ETUS => ETRS

Characterizations

IMR WIMR ETES ETUS ETRS

GSS X X X

WGSS X X X

EIER X X X

EIUR

EIRR

The egalitarian-equivalent solution

IMR WIMR ETES ETUS ETRS

GSS X X X EE

WGSS X X X

EIER X X X

EIUR

EIRR

pre-tax income she would earn with reference talent

uniform transfer to satisfy the budget contraint

The conditional-egalitarian solution

IMR WIMR ETES ETUS ETRS

GSS X X X EE

WGSS X X X

EIER X X X

EIUR

EIRR CE

responsibility part"guaranteed income"

CharacterizationsIMR WIMR ETES ETUS ETRS

GSS X X X X EE

WGSS X X X AEE

EIER X X X

EIUR X ACE

EIRR CE

average over all levels of talent

average over all levels of effortresponsibility part

2. Designing prospective financing schemes in the health care sector Incentive problems in health care - examples:

financing of hospitals or practices of doctors financing schemes for regions and sickness funds

Two "extreme" solutions: reimbursement of expenditures (e.g. fee for service) prospective financing

Trend towards prospective financing and benchmarking: advantage: incentives for cost control danger: incentives for risk selection

Solution? Risk adjustment

EXAMPLE 1: REGIONAL DISTRIBUTION MECHANISM

Central government

Citizen Regional authority

Local "health" tax?

Financial contribution

Subsidy

EXAMPLE 2: REGULATED COMPETITION WITH RISK ADJUSTMENT

Solidarity fund

Consumer Managed careorganisation

Premium Contribution

Solidaritycontribution

Premium subsidy

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 cost-effective 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 RA-

system? 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: total amount of premium subsidies:

ω (= )

monetary gain made on a patient i:

responsibility cut:

)a(fx ii

iii x

)a,a(fx Ri

Cii

i

i

"Cost efficiency"

NEUTRALITY: for any two individuals i and j with

consequence:

it holds that

jiCj

Ci ,aa

Rj

Ri

Cj

Ci aa,aa:j,i

ji

"Solidarity"

NO INCENTIVES FOR RISK SELECTION: for any two individuals i and j with

consequence:

it holds that

jiRj

Ri ,aa

Cj

Ci

Rj

Ri aa,aa:j,i

ji

Theorems

Proposition 1. If the medical expenditure function can be written ( ) as

then the following mechanism satisfies NIRS and NEUT:

NOTE. If , then

i)a(h)a(g)a,a(f R

iCi

Ri

Ci

k

Ck

Cii )a(g

n)a(g

n

i

ix k

Rk

Cii )a(h

n)a(g

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: egalitarian-

equivalent solutions

Keep NEUT, drop NIRS: conditional-

egalitarian 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

therefore, the estimates of the effects of the C-variables are biased, if there is correlation between C- and R-variable

)a,a(fx Ri

Cii

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 every individual has a particular health-

consumption 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 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:

)h(m)()h(w)(c iiiii

iiiiiii S)h(mT)h(wc

Pareto-principle and independenceRESPECT OF INDIVIDUAL PREFERENCES

BASE SOCIAL PREFERENCES ON INDIVIDUAL PREFERENCESIN A VICINITY OF INDIVIDUALS' CURRENT SITUATION

Pigou-Dalton condition (revised)

traditional Pigou-Dalton condition makes sense only in a unidimensional world

extension to multidimensional setting may come in conflict with the Pareto condition

cares a lot abouthealth

does not care much about health

RESTRICT APPLICATION OF PIGOU-DALTON PRINCIPLETO SITUATIONS WHERE THE TWO INDIVIDUALS HAVE THESAME PREFERENCES OR ARE BOTH AT A PERFECT HEALTHLEVEL

"FULL-HEALTH EQUIVALENT INCOMES"

In normal circumstances

Relationship with WTP?

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