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.

Testing the Markov property with ultra high frequency financial data

This paper develops a framework to test whether discrete-valued irregularly-spaced financial transactions data follow a subordinated Markov process. For that purpose, we consider a specific optional sampling in which a continuous-time Markov process is observed only when it crosses some discrete level. This framework is convenient for it accommodates not only the irregular spacing of transactions data, but also price discreteness. Further, it turns out that, under such an observation rule, the current price duration is independent of previous price durations given the current price realization. A simple nonparametric test then follows by examining whether this conditional independence property holds. Finally, we investigate whether or not bid-ask spreads follow Markov processes using transactions data from the New York Stock Exchange. The motivation lies on the fact that asymmetric information models of market microstructures predict that the Markov property does not hold for the bid-ask spread. The results are mixed in the sense that the Markov assumption is rejected for three out of the five stocks we have analyzed.

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.

Inattention in individual expectations

This paper investigates the expectations formation process of economic agents about inflation rate. Using the Market Expectations System of Central Bank of Brazil, we perceive that agents do not update their forecasts every period and that even agents who update disagree in their predictions. We then focus on the two most popular types of inattention models that have been discussed in the recent literature: sticky-information and noisy-information models. Estimating a hybrid model we find that, although formally fitting the Brazilian data, it happens at the cost of a much higher degree of information rigidity than observed.

Inattention in Individual Expectations

This paper investigates the expectations formation process of economic agents about infl ation rate. Using the Market Expectations System of Central Bank of Brazil, we perceive that agents do not update their forecasts every period and that even agents who update disagree in their predictions. We then focus on the two most popular types of inattention models that have been discussed in the recent literature: sticky-information and noisy-information models. Estimating a hybrid model we fi nd that, although formally fi tting the Brazilian data, it happens at the cost of a much higher degree of information rigidity than observed.

Are CGE Models still useful in economic policy making?

This paper develops background considerations to help better framing the results of a CGE exercise. Three main criticisms are usually addressed to CGE efforts. First, they are too aggregate, their conclusions failing to shed light on relevant sectors or issues. Second, they imply huge data requirements. Timeliness is frequently jeopardised by out-dated sources, benchmarks referring to realities gone by. Finally, results are meaningless, as they answer wrong or ill-posed questions. Modelling demands end up by creating a rather artificial context, where the original questions lose content. In spite of a positive outlook on the first two, crucial questions lie in the third point. After elaborating such questions, and trying to answer some, the text argues that CGE models can come closer to reality. If their use is still scarce to give way to a fruitful symbiosis between negotiations and simulation results, they remain the only available technique providing a global, inter-related way of capturing economy-wide effects of several different policies. International organisations can play a major role supporting and encouraging improvements. They are also uniquely positioned to enhance information and data sharing, as well as putting people from various origins together, to share their experiences. A serious and complex homework is however required, to correct, at least, the most dangerous present shortcomings of the technique.