Intermediation, Compensation and Tacit Collusion in Insurance Markets

Intermediation, Compensation and Tacit Collusion in Insurance Markets

Andreas RichterLudwig-Maximilians-University

Muinch

Jörg SchillerWHU – Otto Beisheim School of

Management

Uwe FochtUniversity of Hamburg

ARIA Annual Meeting

Washington 2006

2Intermediation, Compensation and Tacit Collusion in Insurance Markets

Agenda

1. Introduction

2. Model Framework

3. Market without Intermediation

4. Market with Intermediation

a) Fee-for-Advice

b) Commission

5. Collusion and Intermediation

6. Concluding Remarks


Collusive Behavior in German Commercial Insurance

In 2005, the German Federal Cartel Office imposed a 150 Million Euro fine against 17 leading commercial insurance companies.

From 1999 to 2002 insurance companies established a cartel in order to enforce higher premiums as a “reorganization measure”.

In particular, they agreed to

– Increase premiums and deductibles

– Waive premium reductions

– Unify terms and conditions

Enforcement measures for the cartel

– Insurers: Exclusion from pool solutions

– Brokers: Termination of cooperation


Main focus

Why is collusive behavior in commercial insurance a common phenomenon?

What is the specific role of an insurance broker in this context?

To what extent does the broker’s compensation affect pricing and collusive behavior of insurance companies?


Insurance market with heterogeneous risk profiles and differentiated products (Schultz, 2004).

Consumers’ risk profiles are uniformly distributed in [0,1].

Two insurers (i = 0,1) offer policies at the two extremes of

the risk profile space and compete in premiums pi.

Constant marginal costs c.

Model Framework (I)


Model Framework (II)

Willingness to pay v for consumers is sufficiently large.

→ In equilibrium the market is completely covered.

Disutility of mismatch t·, increases linearly in the distance

to the demanded product.

Two types of consumers:

– Informed consumers with fraction (0,1] are perfectly

informed about their risk profile and the premiums pi;

– Uninformed consumers with fraction (1−) only form

rational expectations regarding their risk profile and

premiums pi.


Market without Intermediation

Sequence of play:

1. Insurers simultaneously offer contracts at premiums pi.2. Consumers decide whether and where to purchase an

insurance policy.

In the symmetric subgame perfect Nash equilibrium prices and profits are

and

Both premium level and profits decline in the fraction of informed consumers.

One half of the uninformed consumers match with the wrong product

→ Resulting welfare loss:

t

cp *

2* t

t4

11


Market with Intermediation

Cost per risk analysis .

Two compensation systems are considered:- Broker is paid by the insured (fee-for-advice)- Broker is paid by the insurance company (commission)

The broker acts completely non-strategic!

The broker is endowed with an information technology which perfectly reveals the risk profile of an individual consumer.

0k


Market with Intermediation (Fee-for-Advice)

Broker‘s fee at which uninformed consumers are indifferent

If k ≤ (1/4)t holds, the broker offers risk analyses and all uninformed consumers purchase this service.

Thus, since = 1, equilibrium premiums and profits are

and

tm4

1ˆ

tcp ˆ2

ˆt


Market with Intermediation (Commission)

The risk analysis service does not cause any costs for uninformed consumers, therefore = 1.

Broker’s commission at which insurers are indifferent

Insurance companies accept offer and charge the premiums

and

The resulting insurer profit is:

th4

1~

tcp i ~ tcpu

4

5~

2~ t


Fee-for-Advice vs. Commisson System

But: In a modified model there might be incentives for a broker to match uninformed consumers with the wrong insurance company (intentional mismatch).

In both cases, due to the increased transparency on the consumer side, the insurers’ profits decrease.→ Greater incentives for collusion

From a social planner‘s point of view both remuneration systems are equivalent.


Collusion (I)

Assumption: Insurance companies jointly decide upon premium offers and the broker’s remuneration.

The coalition maximizes its joint profit subject to the broker’s participation constraint .

A commission system is superior to a fee-for-advice system.→ Prices can not be differentiated in a fee-for-advice

system.→ A fee reduces the maximum possible premium, since

0m

mtvpc 2

1max

In our model, rationing is not profitable for the cartel.


Collusion (II)

The profit maximizing premium for the cartel is:

The broker is compensated by a break even commission.

In our model, collusion does not affect social welfare (no rationing)→ There is (just) a redistribution of income.

tvpc 2

1


Concluding Remarks

In markets with uninformed consumers and heterogeneous risk profiles, intermediation has the potential to improve social welfare.

Intermediation reduces the market power as well as profits of insurance companies and increases collusion incentives.

In a competitive market both remuneration systems are equivalent.

Under collusion– a fee for advice limits the insurers‘ opportunities to extract

rents from informed consumers.– less differentiated products are offered (→ in the paper).

In our analysis we do not examine the broker’s incentive problem.


Backup


Product Differentiation

Without collusion: Insurance companies maximize profits by offering

differentiated products outside at:

Product differentiation increases consumers’ disutility of mismatching and negatively affects social welfare.

In the case of collusion: Profit maximizing product characteristics are:

In order to maximize the coalition’s joint profit, insurance companies equalize product characteristics.

4

5;

4

1

4

3;

4

1


Rationing

Rationing is only profitable, if and only if

Collusion is profitable, if and only if

→ The coalition’s joint profit under collusion is strictly higher without any rationing!

tcv

4

5

tcv

4

7

Documents

Intermediation, Compensation and Tacit Collusion in Insurance Markets