Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

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 .

On the Impossibility of an Exact Imperfect Monitoring Folk Theorem

It is shown that, for almost every two-player game with imperfect monitoring, the conclusions of the classical folk theorem are false. So, even though these games admit a well-known approximate folk theorem, an exact folk theorem may only be obtained for a measure zero set of games. A complete characterization of the efficient equilibria of almost every such game is also given, along with an inefficiency result on the imperfect monitoring prisoner s dilemma.

Local concavifiability of preferences and determinacy of equilibrium

In this paper we consider strictly convex monotone continuous complete preorderings on R+n that are locally representable by a concave utility function. By Alexandroff 's (1939) theorem, this function is twice dífferentiable almost everywhere. We show that if the bordered hessian determinant of a concave utility representation vanishes on a null set. Then demand is countably rectifiable, that is, except for a null set of bundles, it is a countable union of c1 manifolds. This property of consumer demand is enough to guarantee that the equilibrium prices of apure exchange economy will be locally unique, for almost every endowment. We give an example of an economy satisfying these conditions but not the Katzner (1968) - Debreu (1970, 1972) smoothness conditions.

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.

On a uniform turnpike of the third kind in the Robinson-Solow-Srinivasan model

On using McKenzie’s taxonomy of optimal accumulation in the longrun, we report a “uniform turnpike” theorem of the third kind in a model original to Robinson, Solow and Srinivasan (RSS), and further studied by Stiglitz. Our results are presented in the undiscounted, discrete-time setting emphasized in the recent work of Khan-Mitra, and they rely on the importance of strictly concave felicity functions, or alternatively, on the value of a “marginal rate of transformation”, ξσ, from one period to the next not being unity. Our results, despite their specificity, contribute to the methodology of intertemporal optimization theory, as developed in economics by Ramsey, von Neumann and their followers.

Oligopolistic competition under knightian uncertainty

This artic/e applies a theorem of Nash equilibrium under uncertainty (Dow & Werlang, 1994) to the classic Coumot model of oligopolistic competition. It shows, in particular, how one can map all Coumot equilibrium (which includes the monopoly and the null solutions) with only a function of uncertainty aversion coefficients of producers. The effect of variations in these parameters over the equilibrium quantities are studied, also assuming exogenous increases in the number of matching firms in the game. The Cournot solutions under uncertainty are compared with the monopolistic one. It shows principally that there is an uncertainty aversion level in the industry such that every aversion coefficient beyond it induces firms to produce an aggregate output smaller than the monopoly output. At the end of the artic/e equilibrium solutions are specialized for Linear Demand and for Coumot duopoly. Equilibrium analysis in the symmetric case allows to identify the uncertainty aversion coefficient for the whole industry as a proportional lack of information cost which would be conveyed by market price in the perfect competition case (Lerner Index).

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.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

Environmental protection and economic growth

This paper explores the link between environmental policy and economic growth by employing an extension of the AK Growth Model. We include a state equation for renewable natural resources. We assume that the change in environmental regulations induces costs and that economic agents also derive some utility from capital stock accumulation vis-`a-vis the environment. Using the Hopf bifurcation theorem, we show that cyclical environmental policy strategies are optimal, providing theoretical support for the Environmental Kuznets Curve.

Escolha social e valores irredutíveis: uma aproximação da economia política e a ideologia

No presente paper, nós provamos que qualquer função da escolha social satisfaz o princípio da independência das alternativas irrelevantes (IIA) de Arrow se o comportamento individual é menu-dependente. Portanto, o 'Teorema da Possibilidade Geral' de Arrow não é válido quando as preferências individuais são determinadas por valores irredutíveis. Nesse contexto, qualquer instrumento de agregação que satisfaça os princípios não-ditatoriais e paretianos de unanimidade (maioria simples, por exemplo) também faz IIA. Esse poderia ser um resultado importante para a teoria da escolha social, enquanto um comportamento individual determinado por valores irredutíveis (interesse próprio, ideologia, Ética e normas sociais, por exemplo) podendo validar democracia representativa. A importância relativa de tais valores e da possibilidade de reversão da preferência determina a dinâmica da escolha social, de acordo com os princípios democráticos.

A notion of subgame perfect Nash equilibrium under knightian uncertainty

We define a subgame perfect Nash equilibrium under Knightian uncertainty for two players, by means of a recursive backward induction procedure. We prove an extension of the Zermelo-von Neumann-Kuhn Theorem for games of perfect information, i. e., that the recursive procedure generates a Nash equilibrium under uncertainty (Dow and Werlang(1994)) of the whole game. We apply the notion for two well known games: the chain store and the centipede. On the one hand, we show that subgame perfection under Knightian uncertainty explains the chain store paradox in a one shot version. On the other hand, we show that subgame perfection under uncertainty does not account for the leaving behavior observed in the centipede game. This is in contrast to Dow, Orioli and Werlang(1996) where we explain by means of Nash equilibria under uncertainty (but not subgame perfect) the experiments of McKelvey and Palfrey(1992). Finally, we show that there may be nontrivial subgame perfect equilibria under uncertainty in more complex extensive form games, as in the case of the finitely repeated prisoner's dilemma, which accounts for cooperation in early stages of the game.

Existence and uniqueness of a fixed-point for local contractions

This paper proves the existence and uniqueness of a fixed-point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed-point result can apply to study existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.

Uma resenha sobre modelos de apreçamento de derivativos

Apresento aqui uma abordagem que unifica a literatura sobre os vários modelos de apreçamento de derivativos que consiste em obter por argumentos intuitivos de não arbitragem uma Equação Diferencial Parcial(EDP) e através do método de Feynman-Kac uma solução que é representada por uma esperança condicional de um processo markoviano do preço do derivativo descontado pela taxa livre de risco. Por este resultado, temos que a esperança deve ser tomada com relação a processos que crescem à taxa livre de risco e por este motivo dizemos que a esperança é tomada em um mundo neutro ao risco(ou medida neutra ao risco). Apresento ainda como realizar uma mudança de medida pertinente que conecta o mundo real ao mundo neutro ao risco e que o elemento chave para essa mudança de medida é o preço de mercado dos fatores de risco. No caso de mercado completo o preço de mercado do fator de risco é único e no caso de mercados incompletos existe uma variedade de preços aceitáveis para os fatores de risco pelo argumento de não arbitragem. Neste último caso, os preços de mercado são geralmente escolhidos de forma a calibrar o modelo com os dados de mercado.