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.

A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare

Bellman's methods for dynamic optimization constitute the present mainstream in economics. However, some results associated with optimal controI can be particularly usefuI in certain problems. The purpose of this note is presenting such an example. The value function derived in Lucas' (2000) shopping-time economy in Infiation and Welfare need not be concave, leading this author to develop numerical analyses to determine if consumer utility is in fact maximized along the balanced path constructed from the first order conditions. We use Arrow's generalization of Mangasarian's results in optimal control theory and develop sufficient conditions for the problem. The analytical conclusions and the previous numerical results are compatible .

Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

The private memory of aggregate shocks

Em economias caracterizadas por choques agregados e privados, mostramos que a alocação ótima restrita pode depender de forma não-trivial dos choques agregados. Usando versões dos modelos de Atkeson e Lucas (1992) e Mirrlees (1971) de dois períodos, é mostrado que a alocação ótima apresenta memória com relação aos choques agregados mesmo eles sendo i.i.d. e independentes dos choques individuais, quando esses últimos choques não são totalmente persistentes. O fato de os choques terem efeitos persistentes na alocação mesmo sendo informação pública, foi primeiramente apresentado em Phelan (1994). Nossas simulações numéricas indicam que esse não é um resultado pontual: existe uma relação contínua entre persistência de tipos privados e memória do choque agregado.

On endogenous cost of altruism

The paper extends the cost of altruism model, analyzed in Lisboa (1999). There are three types of agents: households, providers of a service and insurance companies. Households have uncertainty about future leveIs of income. Providers, if hired by a household, have to choose a non-observable leveI of effort, perform a diagnoses and privately learn a signal. For each signal there is a procedure that maximizes the likelihood of the household obtaining the good state of nature. Finally, insurance companies offer contracts to both providers and households. The paper provides suflicient conditions for the existence of equilibrium and shows the optimal contract induces providers to care about their income and also about the likelihood households will obtain the good state of nature, which in Lisboa (1999) was stated as altruism assumption. Equilibrium is inefficient in comparison with the standard moral hazard outcome whenever high leveIs of effort is chosen precisely due to the need to incentive providers to choose the least expensive treatment for some signals. We show, however that an equilibrium is always constrained optimal.

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.

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.

A economia política da corrupção: o escândalo do orçamento

A abertura democrática no Brasil criou um otimismo com a possibilidade do resolver seus problemas crônicos como inflação e corrupção. Foi feita uma panacéia sobre democracia; da democracia surgiriam as soluções para todos os males. Entretanto, a história recente mostra que a democracia não coincide com a eliminação da corrupção e inflação crônicas. Ao contrário, a corrupção causou danos a algumas instituições fundamentais da democracia como o Presidente e o Congresso. Infelizmente, a corrupção é muito perigosa para a democracia. Como observou Tocqueville, com sua perspicácia natural, o povo ate tolera a corrupção numa tirania, por ser um fato comum neste tipo de governo. Não obstante, em uma democracia, a corrupção e inaceitável porque pessoas comuns são eleitas para representar cidadãos, e não para trabalhar contra eles. Os últimos escândalos envolvendo corrupção no Brasil, como o caso Collor e principalmente o uso "inadequado" do orçamento nacional foram importantes porque mostraram a incapacidade da sociedade para controlar este fator de risco institucional. É interessante notar que em outros grandes casos de corrupção na América Latina, como no Gráu, Cuba, Portillo, México ou mesmo na Venezuela, durante os eufóricos anos 70, a situação econômica e até mesmo política não eram ruins. Entretanto, no Brasil, aparentemente, a corrupção política cresceu num período de crises estruturais. Infelizmente este fato tem um resultado considerável: o crescente pessimismo do homem comum sobre o futuro. Entretanto a corrupção pode ser estudada cientificamente. Pode ser vista como uma escolha racional de comportamento compelido por instituições e esquemas de incentivos. Talvez alguns resultados interessantes possam emergir deste tipo de especulação histórica e teórica sobre o comportamento corrupto. Este é o maior objetivo deste estudo.

Courts as healthcare policy-makers: the problem, the responses to the problem and problems in the responses

This article starts by analysing healthcare litigation in Brazil by means of a literature review of articles that contribute with empirical findings on this phenomenon. Based on this review, I argue that health care litigation in Brazil makes the public health system less fair and rational. In the second part of this article, I discuss the three most overarching responses to control the level of litigation and its impact on the public health system: (i) the public hearing held by the Supreme Federal Court and the criteria the court established thereafter; (ii) the recommendations by the National Council of Justice aimed at building courts’ institutional capacity; and (iii) the enactment of the Federal Law 12.401/11, which created a new health technology assessment system. I argue that latter is the best response because it keeps the substantive decisions on the allocation of healthcare resources in the institution that is in the best position to make them. Moreover, this legislation will make the decisions about provision of health treatments more explicit, making easier for courts to control the procedure and the reasons for these decisions.

Construction of facilities under asymmetric information: do constitutional constraints matter?

This paper studies construction of facilities in a federal state under asymmetric information. A country consists of two regions, each ruled by a local authority. The federal government plans to construct a facility in one of the regions. The facility generates a local value in the host region and has spillover effects in the other region. The federal government does not observe the local value because it is the local authority's private information. 80 the federal governrnent designs an incentive-compatible mechanism, specifying if the facility should be constructed and a balanced scheme of interregional transfers to finance its cost. The federal governrnent is constitutionally constrained to respect a given leveI of each region's welfare. We show that depending upon the facility's local value and the spillover effect, the governrnent faces different incentive problems. Moreover, their existence depends crucially on how stringent constitutional constraints are. Therefore, the optimal mechanism will also depend upon these three features of the model.

Multiple large shareholders in corporate governance

Large shareholders of firms with majority bIocks are often at the heIm of their companies and do not necessarily have the same interests as minority shareholders. We show that bargaining problems Ied by the presence of muItipIe controlling shareholders protect minority shareholders. The same bargaining problems, however, prevent efficient decisions. By solving this trade-off we find that i) muItipIe controlling shareholders should be present in firms with Iarge costs of diIuting minority shareholders and in firms with Iarge financing requirements, ii) an optimal ownership structure requires the presence of a dass of shareholders - the minority shareholders - with no control over corporate decisions. Evidence on the ownership structure of dose corporations in the V.S. is consistent with our model.

A economia política da corrupção: o escândalo do orçamento

A abertura democrática no Brasil criou um otimismo com a possibilidade do resolver seus problemas crônicos como inflação e corrupção. Foi feita uma panaceia sobre democracia; da democracia surgiriam as soluções para todos os males. Entretanto, a história recente mostra que a democracia não coincide com a eliminação da corrupção e inflação crônicas. Ao contrário, a corrupção causou danos a algumas instituições fundamentais da democracia como o Presidente e o Confresso. Infelizmente, a corrupção é muito perigosa para a democracia. Como observou Tocqueville, com sua perspicácia natural, o povo até tolera a corrupção numa tirania, por ser um fato comum neste tipo de governo. Não obstante, em uma democracia, a corrupção é inaceitável porque pessoas comuns são eleitas para representar cidadãos, e não para trabalhar contra eles. Os últimos escândalos envolvendo corrupção no Brasil, como o caso Collor e principalmente o uso “inadequado” do orçamento nacional foram importantes porque mostraram a incapacidade da sociedade para controlar este fator de risco institucional.. É interessante notar que em outros grandes casos de corrupção na América Latina, como no Gráu, Cuba , Portillo, México ou mesmo na Venezuela, durante os eufóricos anos 70, a situação econômica e até mesmo política não eram ruins. Entretanto, no Brasil, aparentemente, a corrupção política cresceu num período de crises estruturais. Infelizmente este fato tem um resultado considerável: o crescente pessimismo do homem comum sobre o futuro. Entretanto a corrupção pode ser estudada cientificamente. Pode ser vista como uma escolha racional de comportamento compelido por instituições e esquemas de incentivos. Talvez alguns resultados interessantes possam emergir deste tipo de especulação histórica e teórica sobre o comportamento corrupto. Este é o maior objetivo deste estudo.

Optimal Mirrleesian taxation in non-competitive labor markets

We study optimal labor income taxation in non-competitive labor markets. Firms offer screening contracts to workers who have private information about their productivity. A planner endowed with a Paretian social welfare function tries to induce allocations that maximize its objective. We provide necessary and sufficient conditions for implementation of constrained efficient allocations using tax schedules. All allocations that are implementable by a tax schedule display negative marginal tax rates for almost all workers. Not all allocations that are implementable in a competitive setting are implementable in this noncompetitive environment.

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.