Giovanni Bella

Global indeterminacy of the equilibrium in the Chamley model of endogenous growth in the vicinity of a Bogdanov–Takens bifurcation

This paper studies the dynamics implied by the Chamley (1993) model, a variant of the two-sector model with an implicit characterization of the learning function. We first show that under some “regularity” conditions regarding the learning function, the model has (a) one steady state, (b) no steady states or (c) two steady states (one saddle and one non-saddle). Moreover, via the Bogdanov–Takens theorem, we prove that for critical regions of the parameters space, the dynamics undergoes a particular global phenomenon, namely the homoclinic bifurcation. Because these findings imply the existence of a continuum of equilibrium trajectories, all departing from the same initial value of the predetermined variable, the model exhibits global indeterminacy.

Transitional Dynamics Towards Sustainability: Reconsidering the EKC Hypothesis

The Environmental Kuznets Curve (EKC) hypothesis is one of the most debated economic issues. Despite its fascinating appeal for any policy maker, neither theoretical nor certain empirical evidence has been found to clean up all doubt. The aim of this paper is to present an economy where environmental quality and polluting emissions do enter the maximisation problem, and provide a transitional dynamics analysis to pursue a new different version of the EKC, depending on the level of development finally achieved.

The double scroll chaotic attractor in the dynamics of a fixed-price IS-LM model

With the aim of exploring the conditions which determine a chaotic behavior in the long-run properties of an economic model, this paper innovates the existing Keynesian macroeconomic literature by showing that the dynamics of the well-known IS-LM model may generate a double-scroll strange attractor, for a particular set of structural parameters.

A Blueprint for Optimal Intertemporal Consumption Under Environmental Constraints: The Modified Green Golden Rule

The notion of sustainability represents the core of the theoretical and political debate on the potential conflict between economic growth and environmental quality. A clear definition of what sustainability means, although still controversial, is indeed a possible keystone to better understanding what is Environmental Economics needed for. To this end, this paper aims at providing a theoretical analysis by means of a neo-classical framework, and consequently define a modified version of the common green golden rule that an economy might follow to drive the system onto the path where both optimal intertemporal consumption and sustainable growth are finally reconciled.

Shilnikov chaos in the Lucas model of endogenous growth

This paper shows that chaotic dynamics and global indeterminacy may characterize the Lucas (1988) endogenous growth model in its local determinacy region of the parameter space. This is achieved by means of the Shilnikov (1965) theorem, which exploits the existence of a family of homoclinic orbits doubly asymptotic to the balanced growth path, when it is a saddle-focus. The economic implications of these results are also discussed.

The Poverty-Environment Trap in a Modified Romer Model with Dirtiness

The model presented in this paper describes an economy with endogenous technical change and polluting production techniques. The main question we want to address is whether the adoption of “dirty” production processes might lead to a sustainable unique steady state, or guarantee the emergence of multiple equilibria. The application of the original Bogdanov–Takens theorem allows us to characterize the regions of the parametric space where the model exhibits either a global indeterminate equilibrium or a poverty-environment trap.

A Bug's Life: Competition Among Species Towards the Environment

A model of different species competing for the same environment is presented, and possible explanations of peaceful coexistence or rather internecine conflicts are consequently derived. By means of a Lotka-Volterra dynamic system we describe the evolution of two populations (bees and locusts) that differently approach the management of those natural resources they contend for, and thus make a simple parable of todays societies playing the current environmental scenario.

Homoclinic Bifurcation and Endogenous Cycles in the Dynamic IS-LM Model

This paper contributes to the new keynesian literature by showing that stable endogenous cycles can emerge as equilibrium solutions of the traditional IS-LM model. The application of the original Bogdanov-Takens theorem allows us to determine the regions of the parametric space where the model exhibits a global indeterminate solution, and a lowgrowth trapping region, characterized by a continuum of equilibrium trajectories in the proximity of a homoclinic bifurcation.

Kaldorian Assumptions and Endogenous Fluctuations in the Dynamic Fixed-Price IS-LM Model

With the aim of better understanding the conditions which determine endogenous fluctuations at business cycle frequencies, recent literature has revived interest in the Schinasi’s variant of the dynamic, intermediate-run, IS-LM model (Schinasi 1981, 1982). Results, however, remain confined to Kaldorian-type economies, namely to those economies which present a greater-than-unity marginal propensity to spend out of income. This paper contributes to the debate by showing that, in the case of a negative interest rate sensitivity of savings, stable endogenous cycles can actually emerge as equilibrium solutions of the model also in the case of non Kaldorian-type economies. To this end, we combine the instruments of the global analysis, specifically the homoclinic bifurcation Theorem of Kopell and Howard (1975), with numerical methods.

A Search Model for Joint Implementation

The aim of this paper is to present a search model in the field of environmental economics, where so-called clean and dirty producers enter the trading market, both looking for a partner with whom to exchange the goods they are endowed with. The model derived in this paper is rather simple. Nevertheless, it is able to produce a series of interesting results and useful insights, and is conveniently used here as a framework to explain the functioning of Joint Implementation programmes for polluting emissions’ reduction.