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Non-monotone insurance contracts and their empirical consequences

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  • Araújo, Aloísio Pessoa de
  • Moreira, Humberto Ataíde

Abstract

The goal of this paper is to show the possibility of a non-monotone relation between coverage ans risk which has been considered in the literature of insurance models since the work of Rothschild and Stiglitz (1976). We present an insurance model where the insured agents have heterogeneity in risk aversion and in lenience (a prevention cost parameter). Risk aversion is described by a continuous parameter which is correlated with lenience and for the sake of simplicity, we assume perfect correlation. In the case of positive correlation, the more risk averse agent has higher cosr of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and iplies a positive correlation between overage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the SCP be broken, but also the monotonocity of contracts, i.e., the prediction that high (low) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case there are some coverage levels associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation between coverage and riskiness may have every sign (even though the ex-post correlation is always positive). Moreover, using another instrument (a proxy for riskiness), we give a testable implication to desentangle single crossing ans non single croosing under an ex-post zero correlation result: the monotonicity of coverage as a function os riskiness. Since by controlling for risk aversion (no asymmetric information), coverage is monotone function of riskiness, this also fives a test for asymmetric information. Finally, we relate this theoretical results to empirical tests in the recent literature, specially the Dionne, Gouruéroux and Vanasse (2001) work. In particular, they found an empirical evidence that seems to be compatible with asymmetric information and non single crossing in our framework. More generally, we build a hidden information model showing how omitted variables (asymmetric information) can bias the sign of the correlation of equilibrium variables conditioning on all observable variables. We show that this may be the case when the omitted variables have a non-monotonic relation with the observable ones. Moreover, because this non-dimensional does not capture this deature. Hence, our main results is to point out the importance of the SPC in testing predictions of the hidden information models.

Suggested Citation

  • Araújo, Aloísio Pessoa de & Moreira, Humberto Ataíde, 2002. "Non-monotone insurance contracts and their empirical consequences," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 512, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
  • Handle: RePEc:fgv:epgewp:512
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    Cited by:

    1. Hanming Fang & Michael P. Keane & Dan Silverman, 2008. "Sources of Advantageous Selection: Evidence from the Medigap Insurance Market," Journal of Political Economy, University of Chicago Press, vol. 116(2), pages 303-350, April.
    2. Aloisio Araujo & Luciano Castro & Humberto Moreira, 2008. "Non-monotoniticies and the all-pay auction tie-breaking rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(3), pages 407-440, June.
    3. Moreira, Humberto Ataíde & Araújo, Aloísio Pessoa de & Castro Filho, Luciano I. de, 2004. "Pure strategy equilibria of multidimensional and non-monotonic auctions," FGV/EPGE Economics Working Papers (Ensaios Economicos da EPGE) 571, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil).
    4. Marcelo de Paiva Abreu, 2003. "The political economy of economic integration in the Americas: Latin American interests," Textos para discussão 468, Department of Economics PUC-Rio (Brazil).
    5. Araujo, Aloisio & Moreira, Humberto & Tsuchida, Marcos, 2011. "Do dividend changes signal future earnings?," Journal of Financial Intermediation, Elsevier, vol. 20(1), pages 117-134, January.

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