Existence of Bifurcation in Macroeconomic Dynamics: Grandmont was Right

Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont¡¯s conclusions within the parameter space of the Bergstrom- Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy¡¯s data, and is clearly policy relevant. In addition, initial results by Barnett and Duzhak (2006) indicate the possible existence of Hopf bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, our explanation of the relevant theory reveals that singularity bifurcation may be a common property of Euler equations models. These results further confirm Grandmont¡¯s views. Beginning with Grandmont¡¯s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters. Grandmont was right.Bifurcation, inference, dynamic general equilibrium, Pareto optimality, Hopf bifurcation, Euler equations, Leeper and Sims model, singularity bifurcation, stability.

Existence of Singularity Bifurcation in an Euler-Equations Model of the United States Economy: Grandmont was Right

Abstract: Grandmont (1985) found that the parameter space of the most classical dynamic general-equilibrium macroeconomic models are stratified into an infinite number of subsets supporting an infinite number of different kinds of dynamics, from monotonic stability at one extreme to chaos at the other extreme, and with all forms of multiperiodic dynamics between. But Grandmont provided his result with a model in which all policies are Ricardian equivalent, no frictions exist, employment is always full, competition is perfect, and all solutions are Pareto optimal. Hence he was not able to reach conclusions about the policy relevance of his dramatic discovery. As a result, Barnett and He (1999, 2001, 2002) investigated a Keynesian structural model, and found results supporting Grandmont’s conclusions within the parameter space of the Bergstrom-Wymer continuous-time dynamic macroeconometric model of the UK economy. That prototypical Keynesian model was produced from a system of second order differential equations. The model contains frictions through adjustment lags, displays reasonable dynamics fitting the UK economy’s data, and is clearly policy relevant. In addition, results by Barnett and Duzhak (2008,2009) demonstrate the existence of Hopf and flip (period doubling) bifurcation within the parameter space of recent New Keynesian models. Lucas-critique criticism of Keynesian structural models has motivated development of Euler equations models having policy-invariant deep parameters, which are invariant to policy rule changes. Hence, we continue the investigation of policy-relevant bifurcation by searching the parameter space of the best known of the Euler equations general-equilibrium macroeconometric models: the path-breaking Leeper and Sims (1994) model. We find the existence of singularity bifurcation boundaries within the parameter space. Although never before found in an economic model, singularity bifurcation may be a common property of Euler equations models, which often do not have closed form solutions. Our results further confirm Grandmont’s views. Beginning with Grandmont’s findings with a classical model, we continue to follow the path from the Bergstrom-Wymer policy-relevant Keynesian model, to New Keynesian models, and now to Euler equations macroeconomic models having deep parameters.Bifurcation; inference; dynamic general equilibrium; Pareto optimality; Hopf bifurcation; Euler equations; Leeper and Sims model; singularity bifurcation; stability

Hysteresis and Post Walrasian Economics

Macroeconomics, hysteresis The “new consensus” dsge (dynamic stochastic general equilibrium) macroeconomic model has microfoundations provided by a single representative agent. In this model shocks to the economic environment do not have any lasting effects. In reality adjustments at the micro level are made by heterogeneous agents, and the aggregation problem cannot be assumed away. In this paper we show that the discontinuous adjustments made by heterogeneous agents at the micro level mean that shocks have lasting effects, aggregate variables containing a selective, erasable memory of the shocks experienced. This hysteresis framework provides foundations for the post-Walrasian analysis of macroeconomic systems

Wealth, income, earnings and the statistical mechanics of flow systems

This paper looks at empirical data from economics regarding wealth, earnings and income, alongside a flow model for an economy based on the general Lotka-Volterra models of Levy & Solomon. The data and modelling suggest that a simple economic system might provide a tractable model for giving an exact statistical mechanical solution for an 'out of equilibrium' flow model. This might also include an exact mathematical definition of a 'dissipative structure' derived from maximum entropy considerations. This paper is primarily a qualitative discussion of how such a mathematical proof might be achieved

Computation in Economics

This is an attempt at a succinct survey, from methodological and epistemological perspectives, of the burgeoning, apparently unstructured, field of what is often – misleadingly – referred to as computational economics. We identify and characterise four frontier research fields, encompassing both micro and macro aspects of economic theory, where machine computation play crucial roles in formal modelling exercises: algorithmic behavioural economics, computable general equilibrium theory, agent based computational economics and computable economics. In some senses these four research frontiers raise, without resolving, many interesting methodological and epistemological issues in economic theorising in (alternative) mathematical modesClassical Behavioural Economics, Computable General Equilibrium theory, Agent Based Economics, Computable Economics, Computability, Constructivity, Numerical Analysis

The Impact of Monetary and Commodity Fundamentals, Macro News and Central Bank Communication on the Exchange Rate: Evidence from South Africa

This paper studies drivers of high-frequency (daily) dynamics of the South African rand vis-à-vis the dollar from January 2001 to July 2007. We find strong nonlinear effects of commodity prices, perceived country and emerging market risk premium and changes in the dollar-euro exchange rate on changes in daily returns of the rand-dollar exchange rate. We also identify a one-sided nonlinear mean reversion to the long-term monetary equilibrium. In addition we establish very short-lived effects on the exchange rate of selected macroeconomic surprises and central bank communication aimed at talking up the rand.exchange rate, nonlinearity, commodity prices, monetary model, macroeconomic news, central bank communication, South Africa

Wealth, income, earnings and the statistical mechanics of flow systems

This paper looks at empirical data from economics regarding wealth, earnings and income, alongside a flow model for an economy based on the general Lotka-Volterra models of Levy & Solomon. The data and modelling suggest that a simple economic system might provide a tractable model for giving an exact statistical mechanical solution for an 'out of equilibrium' flow model. This might also include an exact mathematical definition of a 'dissipative structure' derived from maximum entropy considerations. This paper is primarily a qualitative discussion of how such a mathematical proof might be achieved.wealth; earnings; income; entropy; lotka; volterra; dissipative

Post-crisis macrofinancial modeling: Continuous time approaches

Post-crisis macrofinancial modeling: Continuous time approache