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 .

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 contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

Approximate recursive equilibrium with minimal state space

This paper shows existence of approximate recursive equilibrium with minimal state space in an environment of incomplete markets. We prove that the approximate recursive equilibrium implements an approximate sequential equilibrium which is always close to a Magill and Quinzii equilibrium without short sales for arbitrarily small errors. This implies that the competitive equilibrium can be implemented by using forecast statistics with minimal state space provided that agents will reduce errors in their estimates in the long run. We have also developed an alternative algorithm to compute the approximate recursive equilibrium with incomplete markets and heterogeneous agents through a procedure of iterating functional equations and without using the rst order conditions of optimality.

Extreme poverty and development: the role of state in the assurance of minimal existence conditions

This paper follows the idea of Amartya Sen, Nobel Prize of economic, about the role of State in the assurance of minimal existence condition, and aim to answer how countries of Latin America (specifically Brazil) and countries of Europe (specifically United Kingdom) deal with the assurance of this minimal existence conditions. According to Amartya Sen’s view, development must be seen as a process of expanding substantive freedoms, such expansion being the primary purpose of each society and the main mean of development. Substantive freedoms can be considered as basic capabilities allocated to individuals whereby they are entitled to be architects of their own lives, providing them conditions to “live as they wish”. These basic capabilities are divided by Amartya Sen in 5 (five) kinds of substantive freedoms, but for this article’s purpose, we will consider just one of this 5 (five) kinds, specifically the Protective Safety capability. Protective Safety capability may be defined as the assurance of basic means of survival for individuals who are in extreme poverty, at risk of starvation or hypothermia, or even impending famine. Among the means available that could be used to avoid such situations are the possibility of supplemental income to the needy, distributing food and clothing to the needy, supply of energy and water, among others. But how countries deal whit this protective safety? Aiming to answer this question, we selected the problem of “fuel poverty” and how Brazil and United Kingdom solve it (if they solve), in order to assess how the solution found impacts development. The analysis and the comparison between these countries will allow an answer to the question proposed.

Semiparametric estimation and inference using doubly robust moment conditions

We study semiparametric two-step estimators which have the same structure as parametric doubly robust estimators in their second step. The key difference is that we do not impose any parametric restriction on the nuisance functions that are estimated in a first stage, but retain a fully nonparametric model instead. We call these estimators semiparametric doubly robust estimators (SDREs), and show that they possess superior theoretical and practical properties compared to generic semiparametric two-step estimators. In particular, our estimators have substantially smaller first-order bias, allow for a wider range of nonparametric first-stage estimates, rate-optimal choices of smoothing parameters and data-driven estimates thereof, and their stochastic behavior can be well-approximated by classical first-order asymptotics. SDREs exist for a wide range of parameters of interest, particularly in semiparametric missing data and causal inference models. We illustrate our method with a simulation exercise.