Marji Lines

Effects of Inflation Expectations on Macroeconomic Dynamics: Extrapolative Versus Regressive Expectations

Abstract In this paper, we integrate heterogeneous inflation expectations into a simple monetary model. Guided by empirical evidence, we assume that boundedly rational agents, selecting between extrapolative and regressive forecasting rules to predict the future inflation rate, prefer rules that have produced low prediction errors in the past. We show that integrating this behavioral expectation formation process into the monetary model leads to the possibility of endogenous macroeconomic dynamics. For instance, our model replicates certain empirical regularities such as irregular growth cycles or inflation persistence. Moreover, we observe multi-stability via a Chenciner bifurcation.

Introductory Notes on the Dynamics of Linear and Linearized Systems

In the following we provide terminology and concepts which are central to understanding the dynamical behavior of nonlinear systems. The first four sections are a necessarily very brief introduction to the dynamics of linear systems, in which we concentrate on those aspects most useful for acquiring a sense of the basic behaviours characterising systems of differential and difference equations. The last four sections introduce basic notions of stability, the linear approximation and the Hartman-Grobman Theorem, the use of the Centre Manifold Theorem, local bifurcation theory.*

Local Bifurcation Theory Applied to OLG Models

In Section 1 a brief overview is given of the standard overlapping generations model as presented in Blanchard and Fischer (1989). The first step in all sections below is to develop the model structure with a minimum of functional hypotheses, followed by results under explicit forms for utility and/or production. In Section 2 the basic model is then extended to include a pay-as-you-go pension scheme and forward dynamics are determined from the backward equation of motion. In Section 3 the basic model is extended to allow for the accumulation of capital, leading to a second order relation for which fold bifurcations exist. In Section 4 a brief overview is given of a well-known OLG model in two dimensions, following Medio (1992) for which Neimark-Sacker bifurcations exist. In Section 5 an extension is given for the case of an environmental externality leading to a three dimensional system for which both fold and Neimark-Sacker bifurcations exist.

The dynamics of capital accumulation in an overlapping generations model

Abstract This paper studies capital accumulation in a slightly altered, explicit OLG model. The fundamental difference with the standard model lies in the initial conditions. If a portion of the initial allocation of the capital stock is not assigned to retirees, the framework allowing for a genuine accumulation of capital is provided. Dynamic aspects of the resulting model are analyzed, including dynamics of the quotas of capital stock, shares of total output, partial influences of parameters, the connection between the depreciation rate and capitals contribution to production, and the relation of the latter to saddle-node bifurcations and the existence of real-valued equilibria. It is demonstrated that the model is able to describe the initial phase of accumulation.