Manuel S. Santos

Rational Asset Pricing Bubbles

This paper provides a fairly systematic study of general economic conditions under which rational asset pricing bubbles may arise in an intertemporal competitive equilibrium framework. Our main results are concerned with nonexistence of asset pricing bubbles in those economies. These results imply that the conditions under which bubbles are possible --including some well-known examples of monetary equilibria-- are relatively fragile.

A two-sector model of endogenous growth with leisure

In this paper we analyze a class of endogenous growth models with physical and human capital and with three altematives uses of time: unqualified leisure, work and education. In contrast to some other related models, we find that, even in the absence of technological extemalities, there could be multiple balanced paths. We provide a characterization of the qualitative behavior of consumption, leisure, work and education over those balanced paths, and study their transitional dynamics.

Smoothness of the Policy Function in Discrete Time Economic Models

The theory applying to dynamic programming has furnished a useful set of techniques for the analysis of many types of sequential models. This theory, however, has not yielded heretofore much information about the differentiability properties of optimal solutions. This aspect is of particular interest as regards the qualitative analysis of optimal paths, where differentiable methods are often called into play. This paper shows roughly that if the objective is twice continuously differentiable and strongly concave, then any interior optimal path is continuously differentiable with respect to the initial state. Copyright 1991 by The Econometric Society.

Analysis of a Numerical Dynamic Programming Algorithm Applied to Economic Models

In this paper, the authors develop a discretized version of the dynamic programming algorithm and study its convergence and stability properties. They show that the computed value function converges quadratically to the true value function and that the computed value function converges linearly, as the mesh size of the discretization converges to zero; further, the algorithm is stable. The authors also discuss several aspects of the implementation of their procedures as applied to some commonly studied growth models.

Accuracy of Numerical Solutions Using the Euler Equation Residuals

In this paper we derive sorne asymptotic properties on the accuracy of numerical solutions. We sIlow tIlat the approximation error of the policy function is of the same order of magnitude as the size of the Euler equation residuals. Moreover, for bounding this approximation error tIle most relevant parameters are the discount factor and the curvature of the return function. These findings provide theoretical foundations for the construction of tests that can assess the performance of alternative computational methods.

Convergence Properties of Policy Iteration

This paper analyzes asymptotic convergence properties of policy iteration in a class of stationary, infinite-horizon Markovian decision problems that arise in optimal growth theory. These problems have continuous state and control variables and must therefore be discretized in order to compute an approximate solution. The discretization may render inapplicable known convergence results for policy iteration such as those of Puterman and Brumelle [Math. Oper. Res., 4 (1979), pp. 60--69]. Under certain regularity conditions, we prove that for piecewise linear interpolation, policy iteration converges quadratically. Also, under more general conditions we establish that convergence is superlinear. We show how the constants involved in these convergence orders depend on the grid size of the discretization. These theoretical results are illustrated with numerical experiments that compare the performance of policy iteration and the method of successive approximations.

Differentiability of the Value Function without Interiority Assumptions

This paper studies first–order differentiability properties of the value function in concave dynamic programs. Motivated by economic considerations, we dispense with commonly imposed interiority assumptions. We suppose that the correspondence of feasible choices varies with the vector of state variables, and we allow the optimal solution to belong to the boundary of this correspondence. Under minimal assumptions we prove that the value function is continuously differentiable. We then discuss this result in the context of some economic models, and focuss on some examples in which our assumptions are not met and the value function is not differentiable.

NUMERICAL SIMULATION OF NONOPTIMAL DYNAMIC EQUILIBRIUM MODELS

In this article, we propose a recursive equilibrium algorithm for the numerical simulation of nonoptimal dynamic economies. This algorithm builds upon a convergent operator over an expanded set of state variables. The fixed point of this operator defines the set of all Markovian equilibria. We study approximation properties of the operator. We also apply our recursive equilibrium algorithm to various models with heterogeneous agents, incomplete financial markets, endogenous and exogenous borrowing constraints, taxes, and money.

On Non-Existence Of Markov Equilibria In Competitive-Market Economies

This paper presents some examples of regular dynamic economies with externalities and taxes that either lack existence of a Markov equilibrium or such equilibrium is not continuous. These examples pose further challenges for the analysis and computation of these economies.

Differentiability and comparative analysis in discrete-time infinite-horizon optimization

In this note I consider a family of discrete-time intertemporally separable optimization problems with unbounded horizon in which the objective is parameterized by a finite dimensional vector. Under standard assumptions, I show that optimal solutions vary smoothly with the initial state and the vector of parameters. These results provide a basic framework to develop the familiar methods of comparative analysis in a dynamic setting. Likewise, the local analysis of equilibria set out by Kehoe, Levine, and Romer [J. Econ. Theory50 (1990), 1–21] is extended here to economies with general equilibrium dynamics.