The welfare cost of unpriced heterogeneity in insurance markets

• Author: Paolo Donni,Valentino Dardanoni
• Date: 01 November 2016
• Published date: 01 November 2016
• DOI: http://doi.org/10.1111/1756-2171.12164

RAND Journal of Economics

Vol.47, No. 4, Winter 2016

pp. 998–1028

The welfare cost of unpriced heterogeneity

in insurance markets

Valentino Dardanoni∗

and

Paolo Li Donni∗

We consider the welfare loss of unpriced heterogeneity in insurance markets, which results

when private information or regulatoryconstraints prevent insurance companies to set premiums

reflecting expected costs. We propose a methodology which uses survey data to measure this

welfareloss. After identifying some “types” which determine expected risk and insurance demand,

we derive the key factors defining the demand and cost functions in each market induced by these

unobservable types. These are used to quantify the efficiency costs of unpriced heterogeneity. We

apply our methods to the US Long-Term Care and Medigap insurance markets, where we find

that unpriced heterogeneity causes substantial inefficiency.

1. Introduction

In many insurance markets, private information or regulatory constraints prevent insurers

to set premiums reflecting individuals’ costs. In this context, unpriced heterogeneity refers to all

characteristics which affect insurance demand and expected claims but are not priced byinsurance

companies. Under unpriced heterogeneity, individuals pay insurance premiums which do not

reflect expected costs. Because efficiency requires that individuals should purchase insurance

if and only if their willingness to pay for the contract is greater than their expected costs, the

existence of unpriced heterogeneity implies that some individuals overbuy and some underbuy.

How largeis the resulting welfare loss? If contracts were priced conditional on individual expected

risks, or if the social planner could use appropriate observables to price heterogeneity, how large

would the welfare gain be? In this article, we propose a methodology to address these questions.

To measure welfare loss, we recover willingness-to-pay and expected costs by segmenting

the market into “types” that have costs independent of coverages.To identify these unobservable

types, we exploit as a source of external variation individual observable characteristics which

act as indicators of risk and risk preferences, but are not used by insurers to price the contract

∗Universit`

a di Palermo; valentino.dardanoni@unipa.it, paolo.lidonni@unipa.it.

Wethank the Editor (Chad Syverson), and two referees for very insightful comments. Wethank Alberto Bennardo, Alberto

Bisin, Liran Einav,Antonio Forcina, Mark Machina, Andrea Pozzi, Dan Silverman, Joel Sobel, Antonio Tesoriere.Nicola

Persico deserves special thanks for his time and encouragement.

998 C2016, The RAND Corporation.

DARDANONI AND LI DONNI / 999

(called “unused observables” by Finkelstein and Poterba,2014). If these types were contractible,

they could be segregated into separate “synthetic” markets, each with its own insurance contract.

Within each synthetic market individuals have the same expected claims, and all heterogeneity

is idiosyncratic; there would be no welfare loss from charging the same price to all customers.

The estimates of willingness-to-pay and expected costs allow us to calculate counterfactual price

changes conditional on the features of the unobserved markets, allowing prices to vary with

expected costs. The magnitude of the welfare gain that could be achieved pricing these types

depends on demand slopes and on the difference between current and counterfactual efficient

prices in each market through the usual deadweight loss triangle.

The literature on the empirical appraisal of the welfare implications of pricing insurance

contracts is recent (see Einav, Finkelstein, and Levin, 2010, for a survey). Our article is mostly

related to the articles of Einav, Finkelstein, and Cullen (2010) and Bundorf, Levin, and Mahoney

(2012).1The seminal article of Einav, Finkelstein, and Cullen (2010) studies the welfare cost of

privateinfor mation in a simple and intuitiveframework where the researcher describes preferences

for insurance and expected utilization, estimating the aggregate demand and marginal and average

cost curves. Bundorf, Levin, and Mahoney(2012) consider a str uctural model of health plan choice

taking into account unobservable health risk, which interact in the estimation of the demand and

expected cost functions, and measure the welfare gain of allowing prices to vary with expected

costs.

Our article differs from current literature in several aspects. First, compared with Einav,

Finkelstein, and Cullen (2010), we decompose the aggregate market into separate synthetic

markets. Within these markets, we find efficient prices and measure the inefficiency of the

implicit cross-subsidization—which do not emerge by looking at the aggregate market—giving

a very different perspective on the nature of the distortions created by unpriced heterogeneity. In

comparison with Bundorf, Levin, and Mahoney (2012), who model private risk as a univariate

normally distributed unobserved variable and assume idiosyncratic preference heterogeneity, we

allow for nonparametric structural heterogeneity jointly affecting both claims and preferences.

The other difference between the current article and existing ones is that we show how

our approach can be applied when the researcher uses survey data rather than firm data with

exogenous variation in prices. For our purpose, the advantage of using survey data is twofold.

First, and this is key to our approach, survey data typically contains information on individual

characteristics which act as indicators of riskiness and insurance preferences, helping to extract

systematic unobserved differences in claims and coverages. Second, survey data allow to explore

the efficiency of insurance markets with large representativesamples, enabling the study of many

cases where the researcher does not have access to appropriate firm or administrative data. On

the other hand, the most relevant limitation of our approach is precisely due to the use of survey

data, which generally do not contain information on individual insurance premiums. To sidestep

this issue, we do a calibration exercise using external information on the price elasticity of the

aggregate demand for insurance taken from recent literature. In general, the researcher may

leverage a set of credible estimates of the policy effects of interest using reasonable ranges for

this parameter.

We apply our methods to the US Long-Term Care (LTC) and Medigap insurance markets.

In both markets, we find that unpriced heterogeneity causes substantial inefficiency. In LTC

insurance we find that, conditional on insurers’ risk classification, there are two underlying

unobserved synthetic markets with large differences in insurance valuation and expected risks.

High-risk individuals are almost 2.5 times more likely to use a nursing home than low-risk ones:

we estimate that a one-dollar subsidy to the high-risk types costs the low-risk types between

1Recent articles closely related with ours are also Lustig (2011), on the efficiency of Medigap insurance and

Geruso (2013), on unpriced heterogeneity in health plan choice. These studies analyze how heterogeneous preferences

over insurance—uncorrelated with individual insurable risk—can induce, under a uniform-price setting, inefficient self-

sorting into plans.

C

The RAND Corporation 2016.