Accuracy of numerical solutions using the eulers 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

On the policy function in continuos time economic models

In this paper, I consider a general class of continuous-time economic models with unbounded horizon. I study the sets of conditions under which the policy function is continuous, Lipschitz continuous, and Cl differentiable. 1 also single out certain postulates which may prevent higher-order differentiability. The analysis provides, therefore, a fmn foundation to the use of dynamic programming methods in continuous time models with unbounded horizo

Consistency properties of a simulation-based estimator for dynamic processes

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the uniform convergence (a.s.) of a family of sample distributions over the domain of parameters. This uniform convergence holds under mild continuity and monotonicity conditions on the dynamic process. The estimator is applied to an asset pricing model with technology adoption. A challenge for this model is to generate the observed high volatility of stock markets along with the much lower volatility of other real economic aggregates.Comment: Published in at http://dx.doi.org/10.1214/09-AAP608 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Accuracy of numerical solutions using the eulers 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.Accuracy; Euler equation residuals; value and policy functions;

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 non-existence of asset pricing bubbles in those economies. These results imply that the conditions under which bubbles are possible inc1uding sorne well-known examples of monetary equilibria-are relatively fragile

On convergence in endogenous growth models

In this paper we analyze the rate of convergence to a balanced path in a class of endogenous growth models with physical and human capital. We show that such rate depends locally on the technological parameters of the model. but does not depend on those parameters related to preferences. These results stand in sharp contrast with those of the one-sector neoclassical growth model where both preferences and technologies determine the speed of convergence toward a steady state

Accuracy of simulations for stochastic dynamic models

This paper provides a general framework for the simulation of stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then establish that the simulated moments from numerical approximations converge to their exact values as the approximation errors of the computed solutions converge to zero. These asymptotic results are of further interest in the comparative study of dynamic solutions, model estimation, and derivation of error bounds for the simulated moments

On convergence in endogenous growth models.

In this paper we analyze the rate of convergence to a balanced path in a class of endogenous growth models with physical and human capital. We show that such rate depends locally on the technological parameters of the model. but does not depend on those parameters related to preferences. These results stand in sharp contrast with those of the one-sector neoclassical growth model where both preferences and technologies determine the speed of convergence toward a steady state.Neoclassical Growth Model; Endogenous Growth Models; Stability; Speed of Convergence;

On expenditure functions

In this paper we present complete characterizations of the expenditure function for both utility representations and preference structures. Building upon these results, we also establish under minimal assumptions duality theorems for exıpenditure functions and utility representations, and for expenditure functions and preference structures. These results generalize previous work in this area; moreover, in the case of preferences structures they apply to non-completeı preorders

Investment Rates and the Aggregate Production Function

In this paper we consider a simple version of the neoclassical growth model, and carry out an empirical analysis of the main determinants of aggregate investment across countries. More specifically, we study the effects on aggregate investment of income growth, capital income shares, the relative price of capital, and various market distortions. This exercise also sheds light into the shape of the neoclassical production function. We check these investment patterns for both OECD and non-OECD countries. We also decompose investment data into equipment and structures, and explore major factors affecting their relative pricesInvestment rates; Aggregate production function; Relative price of investment