A two-dimensional non-equilibrium dynamic model

This paper develops a non-equilibrium dynamic model (NEDyM) with Keynesian features (it allows for a disequilibrium between output and demand and it considers a constant marginal propensity to consume), but where production is undertaken under plain neoclassical conditions (a constant returns to scale production function, with the stocks of capital and labor fully employed, is assumed). The model involves only two endogenous / prognostic variables: the stock of physical capital per unit of labor and a goods inventory measure. The two-dimensional system allows for a careful analysis of local and global dynamics. Points of bifurcation and long-term cyclical motion are identified. The main conclusion is that the disequilibrium hypothesis leads to persistent fluctuations generated by intrinsic deterministic factors

Location Dynamics and Knowledge Agglomeration

A simple economic activity location rule is considered. Under this rule, one regards that location decisions depend on the presence or the absence of agglomeration economies. Considering a three-location economy, the system that is built leads, under certain conditions, to a saddle-path equilibrium, relatively to which we verify that the most interesting dynamics are associated not with the eventual convergence to the steady state (the saddle-path), that occurs only under exceptional circumstances, but with the divergence process away from the steady state. To explain the dynamics of the agglomeration economies, a knowledge variable is assumed. Returning to a two location economy one is able to assess in graphical terms the relation between distribution of knowledge and location of economic activities.location decisions, dynamic systems, knowledge, technology, agglomeration economies

Diffusion Paths: Fixed Points, Periodicity and Chaos

It is common to recognize that ideas, technology and information disseminate across the economy following some kind of diffusion pattern. Typically, the process of adopting a new piece of knowledge will be translated into an s-shaped trajectory for the adoption rate. This type of process of diffusion tends to be stable in the sense that convergence from any initial state towards the long-term scenario in which all the potential adopters enter in contact with the innovation is commonly guaranteed. Here, we introduce a mechanism under which stability of the diffusion process does not necessarily hold. When the perceived law of motion concerning the evolution of the number of potential adopters differs from the actual law of motion, and agents try to learn this law resorting to an adaptive learning rule, nonlinear long-term outcomes might emerge: the percentage of individuals accepting the innovation in the long-run may be a varying value that evolves according to some cyclical (periodic or a-periodic) pattern. The concept of nonlinear diffusion that is addressed is applied to a problem of information and monetary policy.Diffusion, Nonlinearities, Chaos, Stability, Adaptive learning, Monetary policy.

Constraints on credit, consumer behaviour and the dynamics of wealth

This note develops a simple macro model where the pattern of wealth accumulation is determined by a credit multiplier and by the way households react to short run fluctuations. In this setup, long term wealth dynamics are eventually characterized by the presence of endogenous cycles.Credit constraints; Financial development; Consumer confidence; Endogenous business cycles; Nonlinear dynamics

Entropy in the creation of knowledge: a candidate source of endogenous business cycles

Two sector growth models, with physical goods and human capital produced under distinct technologies, generally consider a process of knowledge obsolescence / depreciation that is similar to the depreciation process of physical goods. As a consequence, the long term rate of per capita growth of the main economic aggregates is constant over time. This rate can be endogenously determined (in endogenous growth models, where production is subject to constant returns) or it can be the result of exogenous forces, like technological progress or population dynamics (in neoclassical growth theory, where decreasing marginal returns prevail). In this paper, we introduce a new assumption about the generation of knowledge, which involves entropy, i.e., introducing additional knowledge to generate more knowledge becomes counterproductive after a given point. The new assumption is explored in scenarios of neoclassical and endogenous growth and it is able to justify endogenous fluctuations. Entropy in the creation of knowledge will imply that human capital does not grow steadily over time. Instead, cycles of various periodicities are observable for different degrees of entropy. Complete a-periodicity (chaos) is also found for particular values of an entropy parameter. This behaviour of the human capital variable spreads to the whole economy given that this input is used in the production of final goods and, thus, main economic aggregates time paths (i.e., the time paths of physical capital, consumption and output) will also evolve following a cyclical pattern. With this argument, we intend to give support to the view of endogenous business cycles in the growth process, which is alternative to the two mainstream views on business cycles: the RBC theory and the Keynesian interpretation.Growth theory; Endogenous business cycles; Nonlinear dynamics; Entropy; Knowledge

Space, Growth and Technology: an Integrated Dynamic Approach

Economic phenomena are interrelated. From a growth perspective, time analysis concerning the choices of present and future consumption and the choices between the allocation of scientific resources should be combined with a space analysis regarding the dissemination of economic activity through geographical locations. This paper intends to present such an integrated approach under a simple endogenous growth model. The determinants of growth are, on one hand, the decisions about how to allocate technological resources and, on the other hand, the strength with which productive activities can agglomerate in order to generate increasing returns to scale. We find that the long run steady state does not have to be a state of unchangeable geography – consumption and production conditions and technological progress not only determine long term growth but also the long term tendency for the economy to geographically concentrate or disperse.Optimal control, Economic growth, Technology, Agglomeration economies, Increasing returns

Space, growth and technology: an integrated dynamic approach

Economic phenomena are interrelated. From a growth perspective, time analysis concerning the choices of present and future consumption and the choices between the allocation of scientific resources should be combined with a space analysis regarding the dissemination of economic activity through geographical locations. This paper intends to present such an integrated approach under a simple endogenous growth model. The determinants of growth are, on one hand, the decisions about how to allocate technological resources and, on the other hand, the strength with which productive activities can agglomerate in order to generate increasing returns to scale. We find that the long run steady state does not have to be a state of unchangeable geography – consumption and production conditions and technological progress not only determine long term growth but also the long term tendency for the economy to geographically concentrate or disperse.Optimal control; Economic growth; Technology; Agglomeration economies; Increasing returns

Volatility, Heterogeneous Agents and Chaos

Agent heterogeneity has been used in recent economic literature to justify nonlinear dynamics for the time paths of aggregate economic variables. In this paper, the mechanism through which heterogeneous agents leads to chaotic motion is explained. Adding to a system with initial behavior heterogeneity an adaptive learning rule based on discrete choice theory, one is able to encounter a reasonable explanation for nonlinear motion. The adaptive learning / bounded rationality rule is not the only ingredient necessary for the absence of a long run steady state; heterogeneity must also imply that the several behavior possibilities alternate as the best behavioral choice. Only in such circumstances heterogeneity persists and an unpredictable outcome is likely to arise. The paper develops two models. The first is a generic approach that exemplifies how heterogeneity concerning the volatility of two stochastic processes may lead to chaotic motion; the second is a utility maximization setup, where the source of heterogeneity is investment decisions.Heterogeneous agents, Bounded rationality, Chaos, Volatility

Externalities in R&D: a route to endogenous fluctuations

Technological progress produces both positive and negative economy wide externalities. Although positive spillovers seem to prevail most of the times, there is evidence and logical arguments revealing that investment in R&D can exceed the corresponding socially optimal level. Taking on board the assumption that the two kinds of externalities are possible and that, therefore, one is able to define the pace of technical progress required to maximize social welfare, we develop a standard two-sector optimal growth model with externalities in the production of technology. The added assumption allows for introducing endogenous business cycles in the Walrasian growth setup. The undertaken stability analysis discusses the local properties of a difference equation two-dimensional system, identifying the occurrence of a flip bifurcation, and looks at global dynamics, through a numerical example, in order to better illustrate and describe the non linear nature of the system.Technology; Externalities; Endogenous business cycles; Two-sector growth models; Nonlinear dynamics and chaos

Stability under learning: the neo-classical growth problem

A local stability condition for the standard neo-classical Ramsey growth model is derived. The proposed setting is deterministic, defined in discrete time and expectations are formed through adaptive learning. The stability condition imposes an upper bound on the long-term value of the gain sequence.Neo-classical growth, Adaptive learning, Stability