Non-monotone insurance contracts and their empirical consequences

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.

Financial guarantees in Brazilian life insurance and pension plans

Recently regulated Brazilian life and pension products offer a benefit structure composed of minimum guaranteed annual rate, in°ation adjustment according to a price index and participation on an investment fund performance. We present a valuation model for these products. We establish a fair condition relationship between minimum guarantees and participation rates, and explore its behavior over a space of maturities, interest rates, and also fund and price index volatilities and correlation. Besides consistency to reference models, we found that the effect of the fund volatility is conditioned to the price index volatility level and the correlation between them.

Concentração nos mercados brasileiros de seguros, previdência e capitalização

Os mercados de seguros regulados pela SUSEP apresentaram queda no número de empresas e elevação no índice de concentração de Herfindahl Hirschman. O que parece um quadro preocupante no âmbito da regulação é atenuado pela diminuição do índice de Gini e outros testes de poder de mercado que não indicam que esta queda no número de empresas tenha tido impacto sobre o nível de preços. Assim como esperado a partir da evidência internacional, a concentração é maior nos mercados de seguros de vida do que nos não-vida. Este fato tem reflexo nos preços, que apresentam patamares mais altos nos seguros de vida, indicando diferença mais substancial entre mercados.

Garantias financeiras em seguros vida e previdência: um modelo de avaliação

Recentemente, o mercado brasileiro regulamentou produtos de seguro de vida e previdência com garantia de uma remuneração mínima, a ser corrigida por um índice de preços e acrescida da participação em retorno de fundo específico de investimento. Esta tese vem dar sua contribuição no âmbito da crescente demanda pela avaliação econômico financeira destes produtos. Esta demanda é motivada não apenas pelas exigências regulatórias internacionais mas também pelas necessidades de real percepção dos riscos fincnaceiros envolvidos. Assim, é aqui proposto um modelo de precificação cuja finalidade é permitir a calibragem, dentro de uma condição definida de equilíbrio, dos parâmetros de garantias de um contrato - taxa mínima e participação. Estes são assim determinados em função não só da maturidade estabelecida, como também das expectativas relativas às variáveis de mercado, como taxas de juros, volatilidade dos ativos e índice de preços. O modelo proposto mostrou comportamento similar ao constatado num conjunto referencial de modelos. Por esta razão, sugere-se que ele é adequado, dentro das limitações colocadas, ao processo de precificação dos produtos em questão.

Non-monotone insurence contracts and their empirical consequences

The goal of t.his paper is to show the possibility of a non-monot.one relation between coverage and 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 continuou.'l 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 cost of prevention leading to a higher demand for coverage. Equivalently, the single crossing property (SCP) is valid and implies a positive correlation between coverage and risk in equilibrium. On the other hand, if the correlation between risk aversion and lenience is negative, not only may the sep be broken, but also the monotonicity of contracts, i.e., the prediction that high (Iow) risk averse types choose full (partial) insurance. In both cases riskiness is monotonic in risk aversion, but in the last case t,here are some coverage leveIs associated with two different risks (low and high), which implies that the ex-ante (with respect to the risk aversion distribution) correlation bet,ween 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 disentangle single crossing and non single crossing under an ex-post zero correlation result: the monotonicity of coverage as a function of riskiness. Since by controlling for risk aversion (no asymmetric informat, ion), coverage is a monotone function of riskiness, this also gives a test for asymmetric information. Finally, we relate this theoretical results to empirica! tests in the recent literature, specially the Dionne, Gouriéroux 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 variabIes (asymmetric information) can bias the sign of the correlation of equilibrium variabIes conditioning on ali observabIe variabIes. We show that this may be t,he case when the omitted variabIes have a non-monotonic reIation with t,he observable ones. Moreover, because this non-monotonic reIat,ion is deepIy reIated with the failure of the SCP in one-dimensional screening problems, the existing lit.erature on asymmetric information does not capture t,his feature. Hence, our main result is to point Out the importance of t,he SCP in testing predictions of the hidden information models.

Life Cycle Models, Heterogeneity of Initial Assets,and Wealth Inequality

Life cycle general equilibrium models with heterogeneous agents have a very hard time reproducing the American wealth distribution. A common assumption made in this literature is that all young adults enter the economy with no initial assets. In this article, we relax this assumption – not supported by the data - and evaluate the ability of an otherwise standard life cycle model to account for the U.S. wealth inequality. The new feature of the model is that agents enter the economy with assets drawn from an initial distribution of assets, which is estimated using a non-parametric method applied to data from the Survey of Consumer Finances. We found that heterogeneity with respect to initial wealth is key for this class of models to replicate the data. According to our results, American inequality can be explained almost entirely by the fact that some individuals are lucky enough to be born into wealth, while others are born with few or no assets.