John Stachurski

Chapter 5 Poverty Traps

Abstract This survey reviews models of self-reinforcing mechanisms that cause poverty to persist. Some of them examine market failure in environments where the neoclassical assumptions on markets and technology break down. Other mechanisms include institutional failure which can, by itself, perpetuate self-reinforcing poverty. A common thread in all these mechanisms is their adverse impact on the acquisition of physical or human capital, and on the adoption of modern technology. The survey also reviews recent progress in the empirical poverty trap literature.

Stability of stochastic optimal growth models: a new approach

Many economic models are now explicitly dynamic and stochastic. Their state variables evolve in line with the decisions and actions of individual economic agents. These decisions are identified in turn by imposing rationality. Depending on technology, market structure, time discount rates and other primitives, rational behavior may lead either to stability or to instability.

Stochastic Optimal Growth with Unbounded Shock

This paper considers a neoclassical optimal growth problem where the shock that perturbs the economy in each time period is potentially unbounded on the state space. Sufficient conditions for existence, uniqueness and stability of equilibria are derived in terms of the primitives of the model using new techniques from the field of perturbed dynamical systems.

Stochastic Stability in Monotone Economies

This paper extends a family of well-known stability theorems for monotone economies to a significantly larger class of models. We provide a set of general conditions for existence, uniqueness and stability of stationary distributions when monotonicity holds. The conditions in our main result are both necessary and sufficient for global stability of monotone economies that satisfy a weak mixing condition introduced in the paper. Through our analysis we develop new insights into the nature and causes of stability and instability.

Endogenous inequality and fluctuations in a two-country model

We study a two-country version of Matsuyamas [K. Matsuyama, Financial market globalization, symmetry-breaking, and endogenous inequality of nations, Econometrica 72 (2004) 853-884] world economy model. As in Matsuyamas model, symmetry-breaking can be observed, and symmetry-breaking generates endogenously determined levels of inequality. In addition, we show that when the countries differ in population size, their interaction through credit markets may lead to persistent endogenous fluctuations.

Economic dynamical systems with multiplicative noise

Abstract The paper considers random economic systems generating nonlinear time series on the positive half-ray R + . Using Lyapunov techniques, new conditions for existence, uniqueness and stability of stationary equilibria are obtained. The conditions generalize earlier results from the mathematical literature, and extend to models outside the scope of existing economic methodology. Applications to growth models with productive capital are given.

Stochastic Growth with Increasing Returns: Stability and Path Dependence

The paper demonstrates global stability in a class of stochastic overlapping generations economies with increasing returns. These results are applied to the study of path dependent dynamics. In particular, for nonlinear stochastic models it is seen that persistence of the historical state and formal ergodicity may easily coincide. A new definition of path dependence is proposed that incorporates such dynamics.

Generalized Look-Ahead Methods for Computing Stationary Densities

The look-ahead estimator is used to compute densities associated with Markov processes via simulation. We study a framework that extends the look-ahead estimator to a broader range of applications. We provide a general asymptotic theory for the estimator, where both L1 consistency and L2 asymptotic normality are established. The L2 asymptotic normality implies √n convergence rates for L2 deviation.

Introduction to macroeconomic dynamics special issue in honor of Kazuo Nishimura: Nonlinear dynamics in equilibrium models

Over the past three decades, analysis of dynamics has come to the forefront of macroeconomic theory. A key impetus for progress on this front has been the connections developed between equilibrium growth theory, on one hand, and the field of nonlinear dynamics, on the other. Kazuo Nishimuras work has been at the center of these advances, and the lines of research he initiated remain an exciting area of study for young researchers with strong technical skills.

Seeking ergodicity in dynamic economies

In estimation and calibration studies, the convergence of time series sample averages plays a central role. At the same time, a significant number of economic models do not satisfy the classical ergodicity conditions. Motivated by existing work on asymptotics of stochastic economic models, we develop a new set of results on limits of sample moments and other sample averages using an order-theoretic approach. Our results include a condition that is necessary and sufficient for convergence over a broad class of moment functions. We discuss implications, sufficient conditions and a range of economic applications.