Dynamic price competition in auto insurance brokerage

• DOI: http://doi.org/10.1111/1756-2171.12256
• Author: Bruno C.A. Ledo,Luis H.B. Braido
• Published date: 01 December 2018
• Date: 01 December 2018

RAND Journal of Economics

Vol.49, No. 4, Winter 2018

pp. 914–935

Dynamic price competition in auto insurance

brokerage

Luis H.B. Braido∗

and

Bruno C.A. Ledo∗∗

We analyze Brazilian data on auto insurance and document that (a) about 20% of policies are

sold without brokeragecommission; (b) over 40% are sold at the highest fee allowed; and (c) the

remaining contracts are associated with a spread-out distribution of fees. Static models cannot

rationalize these findings. We develop a dynamic model of price competition with search and

switching costs that reproduces them. We use the equilibrium structure to estimate the model

parameters and infer the brokers’expected earnings, the frequency that insurees switch brokers,

and the counterfactual effects of a price ceiling policy.

1. Introduction

This article analyzes the brokerage activity in the Brazilian auto insurance market. The

standard auto insurance policy lasts for one year.Automatic extensions are not available, and new

contracts need to be signed after expiration. Contracts are sold through certified brokers.1There

are more than 15 auto insurance companies and thousands of brokers. The typical broker runs a

small local business, but the brokerage service is also offered by bank branches and Internet firms.

Insurance companies provide software programs for brokers to compute the baseline insurance

price for each given list of observables—that is, a list of characteristics of the insuree, the insured

vehicle, and the insurance contract. Brokers add a fee to the baseline price. Brokerage fees must

not exceed a ceiling level defined by the insurance company. Ceilings vary from 15% to 50% of

∗Getulio VargasFoundation, FGV/EPGE; luis.braido@fgv.br.

∗∗University of Sao Paulo, USP/FEA-RP; brunoaurichio@gmail.com.

We are thankful for comments from Rodrigo de Losso Bueno, Marcelo Medeiros, Humberto Moreira, Mauricio Moura,

Heleno Pioner, Bernard Salani´

e, Marcelo Sant’Anna, and seminar participants at the EUI, FGV-SP,FUCAPE, IPEA-RJ,

PUC-Rio, UFRJ, USP-RP, USP-SP, and at the following meetings: Econometric Society (Malaga 2012 and Shanghai

2010), European Economic Association (Glasgow 2010), and SBE (Salvador2010). We are also grateful to Antero Alves

Neto for computing support.

1We use the term broker to refer to anyperson licensed to trade auto insurance contracts. Weignore the technical

distinction between brokersand agents. In the insurance market, brokers represent the insuree and cannot have contractual

agreements with insurance companies, whereas agents make direct selling on behalf of the carriers. They both interact

with the insuree and charge a commission. There are national and regional associations of insurance brokers working to

prevent carriers from discriminating against brokers.

914 C2018, The RAND Corporation.

BRAIDO AND LEDO / 915

the policy final price, depending on observed and unobserved characteristics of the market and

the contract.

Our data document the coexistence of policies being sold with zero and positive brokerage

fees. About 20% of the contracts are sold without any brokerage commission. Over 40% are

sold at the highest fee allowed (the ceiling level). The remaining policies are associated with

commission values that are smoothly distributed within an interval that ranges from zero to over

845 Brazilian reais (BRL), which was equivalent to approximately 422.50 US dollars in terms of

purchasing power parity (PPP-adjusted USD).

It is challenging to rationalize the economics behind this evidence. On the one hand,the mass

of zero fees suggests that the brokerage market is very competitive. On the other hand, the mass

of fees at ceiling levels suggests exactly the opposite. Moreover, our regression analysis shows

that the variability in brokerage fees is poorly related to a large set of observable characteristics,

suggesting that randomness is an important element in brokerage pricing.

We recall that mixed strategy is sometimes used to model equilibrium price dispersion that

is not related to observables—see Varian (1980), Stahl (1989), Sharkey and Sibley (1993), and

Braido (2009). We notice, however, that Nash equilibrium requires that prices in the support

of each player’s mixed strategy generate the same expected payoff, given the other players’

strategies. Therefore, the usual static games do not generate zero and positive commissions being

simultaneously played in equilibrium.

We introduce switching costs into a model of price competition with informed and unin-

formed consumers.2Costs to switch brokers generate an intertemporal value for brokerage. The

game has a symmetric stationary Nash equilibrium. Depending on the parameters of the model,

this equilibrium is either in pure or in mixed strategies. Loosely speaking, when the switching

cost is very high, the pricing strategy is degenerated, and the insurees do not change brokers over

time. Otherwise, the brokers use mixed strategies over a large set of fees.

The equilibrium mixed strategies depend on the matching status of each insuree. When

dealing with a new client, brokers are tempted to set low fees to increase the probability of

making a sale and becoming matched to the consumer for the following period. This type of

loss leading generates a mass of contracts without brokerage commission. When dealing with

a regular customer, brokers take advantage of the switching cost and only offer contracts with

positive fees. They face a tension between extracting consumer surplus and risking to lose the

customer to a competitor. Their mixed strategywill have a mass point at the highest price allowed

for that contract.

We take this symmetric stationary Nash equilibrium to data. We derive a theory-consistent

data generating distribution and use it to perform a maximum likelihood estimation of the model

parameters. Among them, we found that the brokers’ discount factor equals .95 and that the

insurees’ switching cost is 213.36 BRL (equivalent to 106.68 PPP-adjusted USD). We then use

the estimated parameters for three different analyses.

First, we compute that the brokers’ lifetime expected profit is 790.62 BRL (equivalent

to 395.31 PPP-adjusted USD) when dealing with a regular customer, and it is 577.26 BRL

(equivalent to 288.63 PPP-adjusted USD) when facing a new insuree. These are important

concepts in industrial organization. They are useful for analyzing mergers and acquisitions, as

they allow us to compute the value of a portfolio with regular customers and a stable flowof new

potential clients. They are computed here through our structural procedure, which essentially

relies on price data. Second, we predict that each insuree switches brokers with a probability

of 17.17%. This number is consistent with reports from the Brazilian Association of Insurance

Brokers (FENACOR).3Finally, weanalyze the counterfactual effects of a price ceiling policy and

find that any ceiling fee lower than 63.86 BRL (equivalent to 31.93 PPP-adjusted USD) could

2Similar to Varian(1980), this last feature accounts for search frictions on the consumer side.

3For instance, FENACOR(2013) reports that brokers retain 70%–80% of their customers.

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The RAND Corporation 2018.