Testing for Asymmetric Information in Insurance Markets: A Multivariate Ordered Regression Approach

• DOI: http://doi.org/10.1111/jori.12145
• Date: 01 March 2018
• Author: Paolo Li Donni,Valentino Dardanoni,Antonio Forcina
• Published date: 01 March 2018

©2016 The Journal of Risk and Insurance. Vol.85, No. 1, 107–125 (2018).

DOI: 10.1111/jori.12145

Testing for Asymmetric Information in

Insurance Markets: A Multivariate

Ordered Regression Approach

Valentino Dardanoni

Antonio Forcina

Paolo Li Donni

Abstract

The positive correlation (PC) test is the standardprocedure used in the empir-

ical literature to detect the existence of asymmetric information in insurance

markets. This article describes a new tool to implement an extension of the

PC test based on a new family of regression models, the multivariate ordered

logit, designed to study how the joint distribution of two or more ordered

response variables depends on exogenous covariates. Wepresent an applica-

tion of our proposed extension of the PC test to the Medigap health insurance

market in the United States. Results reveal that the risk–coverage association

is not homogeneous across coverage and risk categories, and depends on

individual socioeconomic and risk preference characteristics.

Introduction

There is a constantly growing body of empirical literature studying the existence of

asymmetric information in insurance markets (for a review, see Cohen and Spiegel-

man, 2010; Einav,Finkelstein, and Levin, 2010; Chiappori and Salani ´

e, 2015). Standard

economic theory predicts that under private information, insurance claims and cov-

erage are positively correlated; this theoretical prediction has inspired the seminal

“Positive Correlation” (PC) test by Chiappori and Salani´

e (2000). The PC test rejects

the null of the absence of asymmetric information in a given insurance market when,

conditional on consumers’ characteristics used by insurance companies to price con-

tracts, individuals with more coverage experience more of the insured risk. Chiappori

and Salani´

e (2000) provide simple empirical strategies to test this hypothesis when

both insurance coverage and risk occurrence are binary variables.

Valentino Dardanoni is at the Department of Economics, Business, and Statistics (SEAS), Uni-

versity of Palermo, Viale delle Scienze, 90128 Palermo, Italy. Dardanoni can be contacted via

e-mail: valentino.dardanoni@unipa.it. Antonio Forcina is at the Department of Economics, Fi-

nance, and Statistics, University of Perugia, Via Pascoli, 06100 Perugia, Italy. Forcina can be

contacted via e-mail: forcina@stat.unipg.it. Paolo Li Donni is at the Department of Economics,

Business, and Statistics (SEAS), University of Palermo, Vialedelle Scienze, 90128 Palermo, Italy.

Li Donni can be contacted via e-mail: paolo.lidonni@unipa.it.

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108 The Journal of Risk and Insurance

The PC test has been applied to many different insurance markets, including acute

health, long-term care, automobile, annuities, life, reverse mortgages, and crop. In

most applications, its implementation relies on a simple binary bivariate probit model,

where the null of the absence of private information is tested for absence of residual

errors correlation. Contrary to the theoretical prediction of the standard adverse se-

lection insurance model, some empirical studies have found a negative risk–coverage

correlation and referred to this phenomena as “favorable” or “advantageous” selec-

tion. In a seminal article, Finkelstein and McGarry (2006) study the long-term care

insurance market in the United States and find negative correlation between insur-

ance purchase and nursing home use. They argue this is due to the existence of two

conflicting sources of private information, namely, individuals’ actual risk and risk

attitudes. Negative risk–coverage correlation is also found by Fang, Keane, and Sil-

verman (2008), who show that individuals with supplemental health insurance tend

to spend less on medical care, with cognitive ability being one of the key sources of

advantageous selection.

When private information is multidimensional, the correlation between coverage and

risk may be arbitrary if agents differ in several characteristics (e.g., riskiness, risk

aversion, cognitive ability,or cautiousness). A numerical example of this phenomenon

is given in the “The Problem” section, Table 1.1

This article contributes to the literature (1) by providing an empirical implementation

of the PC test when multiple categorical measures of insurance and loss are involved

and (2) by modeling directly which factors affect the underlying unobserved hetero-

geneity determining the risk–coverage association. Our strategy relies on a new tool,

the multivariate ordered logit, designed to study how the joint distribution of two or

more ordered response variables depend on exogenous covariates.

To show the applicability of this approach, we study the asymmetric information in

the Medigap health insurance market in the United States. Medigap is a private health

insurance designed to cover some “gaps” in the coverage left by Medicare, which is a

public health insurance program providing coverage for all individuals aged 65 and

above in the United States. This health insurance market has received a great deal

of interest in the empirical research since contracts’ pricing is heavily regulated by

federal law (Finkelstein, 2004) and there is evidence of multidimensionality of private

information (Cutler, Finkelstein, and McGarry, 2008; Fang, Keane, and Silverman,

2008; Dardanoni and Li Donni, 2012).

The article is organized as follows. Wefirst lay down the main issues when implement-

ing the standard PC test and explain the potential advantages of our extension. We

1For a similar comment, see Chiappori and Salani´

e (2015, p. 404): “Contract choices reflect not

only relativeriskiness but also these alternative characteristics. The structure of the equilibrium

may well be mostly driven by the latter (risk aversion), leading to arbitrary correlations with

risk”; however, they also argue that perfectly competitive insurance markets in equilibrium

will exhibit positive risk–coverage correlation.