A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

A general lagrangian approach for non-concave moral hazard problems

We establish a general Lagrangian for the moral hazard problem which generalizes the well known first order approach (FOA). It requires that besides the multiplier of the first order condition, there exist multipliers for the second order condition and for the binding actions of the incentive compatibility constraint. Some examples show that our approach can be useful to treat the finite and infinite state space cases. One of the examples is solved by the second order approach. We also compare our Lagrangian with 1\1irrlees'.

Limited liability and non-responsiveness in moral hazard and adverse selection problems

This work analyses the optimal menu of contracts offered by a risk neutral principal to a risk averse agent under moral hazard, adverse selection and limited liability. There are two output levels, whose probability of occurrence are given by agent’s private information choice of effort. The agent’s cost of effort is also private information. First, we show that without assumptions on the cost function, it is not possible to guarantee that the optimal contract menu is simple, when the agent is strictly risk averse. Then, we provide sufficient conditions over the cost function under which it is optimal to offer a single contract, independently of agent’s risk aversion. Our full-pooling cases are caused by non-responsiveness, which is induced by the high cost of enforcing higher effort levels. Also, we show that limited liability generates non-responsiveness.

Solving the non-convexity problem in some shopping-time and human-capital models

Several works in the shopping-time and in the human-capital literature, due to the nonconcavity of the underlying Hamiltonian, use Örst-order conditions in dynamic optimization to characterize necessity, but not su¢ ciency, in intertemporal problems. In this work I choose one paper in each one of these two areas and show that optimality can be characterized by means of a simple aplication of Arrowís (1968) su¢ ciency theorem.

Essays on asymmetric information problems without the single-crossing property: applications to corporate finance

The objective of this dissertation is to re-examine classical issues in corporate finance, applying a new analytical tool. The single-crossing property, also called Spence-irrlees condition, is not required in the models developed here. This property has been a standard assumption in adverse selection and signaling models developed so far. The classical papers by Guesnerie and Laffont (1984) and Riley (1979) assume it. In the simplest case, for a consumer with a privately known taste, the single-crossing property states that the marginal utility of a good is monotone with respect to the taste. This assumption has an important consequence to the result of the model: the relationship between the private parameter and the quantity of the good assigned to the agent is monotone. While single crossing is a reasonable property for the utility of an ordinary consumer, this property is frequently absent in the objective function of the agents for more elaborate models. The lack of a characterization for the non-single crossing context has hindered the exploration of models that generate objective functions without this property. The first work that characterizes the optimal contract without the single-crossing property is Araújo and Moreira (2001a) and, for the competitive case, Araújo and Moreira (2001b). The main implication is that a partial separation of types may be observed. Two sets of disconnected types of agents may choose the same contract, in adverse selection problems, or signal with the same levei of signal, in signaling models.

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.

Non-asymptotic confidence bounds for the optimal value of a stochastic program

We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds for the optimal value of the problem which are essentially better than the quality of the corresponding optimal solutions. At the same time, such bounds are more reliable than “standard” confidence bounds obtained through the asymptotic approach. We also discuss bounding the optimal value of MinMax Stochastic Optimization and stochastically constrained problems. We conclude with a small simulation study illustrating the numerical behavior of the proposed bounds.