Global Indeterminacy Research Articles

Multiple equilibria and global indeterminacy in an endogenous growth model with congestible public goods

This paper extends the findings in Chen and Lee (2007) to show that the use of congestible public goods can produce both local and global indeterminacy in a two‐sector endogenous growth model with productive public services financed by income taxation. Basically, we observe the effects on growth rates by changing parameters, and compare the case of a single steady‐state with the emergence of dual steady‐states, identifying the feasible ways to avoid a possible low‐growth poverty trap. The novelty of our analysis is to detect the presence of global indeterminacy by making use of the Bogdanov‐Takens bifurcation theorem. Some examples are also provided to achieve concrete policy implications.

Global indeterminacy and equilibrium selection in a model with depletion of non-renewable resources

We use the principles of global bifurcation analysis to explore the role of fiscal policy in a model where non-renewable depletion presents stock effects. Initially, we show that fiscal policy may induce the onset of two coexisting steady states, one of which is characterized by a lower depletion rate and higher income (virtuous steady state) than the other (bad steady state). Then, we shed light on the ability of an endogenous fiscal policy to act as an equilibrium selection device. We find that when the economy is sufficiently patient and exhibits low capital returns and environmental parameters, fiscal policy can create a continuum of equilibria that leads to the virtuous steady state. In the opposite situation of an impatient economy, which has high capital returns and environmental parameters, fiscal policy can only create one perfect-foresight path (a heteroclinic trajectory) through which the economy can approach the virtuous steady state.

Growth and Public Debt: What Are the Relevant Trade‐Offs?

AbstractThe interplay between growth and public debt is addressed considering a Barro‐type (1990) endogenous growth model where public spendings are financed through taxes on income and public debt. The government has a target level of public debt relative to GDP, and the long‐run debt‐to‐GDP ratio is used as a policy parameter. We show that when debt is a large enough proportion of GDP, two distinct balanced‐growth paths (BGPs) may coexist, one being indeterminate. We exhibit two types of important trade‐offs associated with self‐fulfilling expectations. First, we show that the lowest BGP is always decreasing with respect to the debt‐to‐GDP ratio while the highest one is increasing. Second, we show that the highest BGP, which provides the highest welfare, is always locally indeterminate while the lowest is always locally determinate. Therefore, local and global indeterminacy may arise and self‐fulfilling expectations appear as a crucial ingredient to understand the impact of debt on growth, welfare, and macroeconomic fluctuations. Finally, a simple calibration exercise allows to provide an understanding of the recent experiences of many OECD countries.

Adverse selection and self-fulfilling business cycles

This paper introduces a simple adverse selection problem arising in credit markets into a standard textbook continuous-time real business cycle model. Such adverse selection generates multiple steady states and both local and global indeterminacy, and can give rise to equilibria with probabilistic jumps in credit, consumption, investment and employment driven by Markov sunspots under calibrated parameterizations and fully rational expectations. Introducing reputational effects eliminates defaults and results in a unique but still indeterminate steady state. Finally we generalize the model to firms with heterogeneous and stochastic productivity, and show that indeterminacies and sunspots persist.

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.

Periodic solutions and global indeterminacy in a model of sustainable tourism

The impact of tourism on economic growth and environmental degradation is one of the most relevant debated issues. Despite the huge strand of empirical literature on the topic, a formalized theoretical investigation of the link between tourism and sustainable economic growth is unfortunately still lacking. To this end, and in line with the literature on the tourist life-cycle hypothesis, we present an endogenous growth model to study the impact of tourism activities and natural resource use on the long run steady state. The aim is to use the principles of bifurcation theory to gain hints on the global properties of the equilibrium, and show the existence of irregular patterns, either indeterminate or chaotic, which possibly suggest the emergence of a (low growth) poverty-environment trapping region.

A Note on the Bogdanov–Takens Bifurcation in the Romer Model with Learning by Doing

This paper is aimed at describing the whole set of necessary and sufficient conditions for the emergence of multiple equilibria and global indeterminacy in the standard endogenous growth framework with learning by doing. The novelty of this paper relies on the application of the original Bogdanov–Takens bifurcation theorem, which allows us to characterize the full dynamics of the model, and determine the emergence of an unavoidable poverty trap.

A simple dynastic economy with parental time investment in children’s patience

This article explores the dynamics of a general equilibrium when an individual’s rate of time preferences is endogenous in a dynastic competitive economy. We postulate that altruistic parents allocate time to make their children patient to improve their lifetime welfare. The paper shows multiplicity and instability of the competitive equilibrium. Local and global indeterminacy emerges due to complementarity between a balanced growth rate and parental time allocation. Indeterminacy implies income and growth disparity among generations. In contrast, a balanced growth path is unique and determinate in the corresponding social optimum. A unique social optimum introduces a potential policy instrument for stabilizing a cyclical competitive equilibrium.

Environmental Ramsey Policy and Sustainable Balanced Growth

AbstractWe study the link among economic growth, renewable natural resources and environmental policy. The context is a general equilibrium model of endogenous growth and environmental policy. We examine the conditions under which sustainable growth is both feasible and optimal, where the latter takes the form of second‐best optimal environmental Ramsey policies. We also investigate the conditions for an inverted U‐shaped relation between environmental policies and sustainable growth. We show that the combination of environmental production externalities and second‐best optimal Ramsey policies can lead to both local and global indeterminacy. The introduction of environmental policy, although well‐intentioned and designed to correct for market inefficiencies, triggers an expectations coordination problem; thereby differences in environmental quality and economic growth can be explained among countries with the same fundamentals.

Nonlinear dynamics and global indeterminacy in an overlapping generations model with environmental resources

We analyse the dynamics of an economy formed of overlapping generations of individuals whose well-being depends on leisure, consumption of a private good and a free access environmental resource. The production activity of the private good deteriorates the environmental resource. Individuals may defend themselves from environmental degradation by increasing consumption of the private good, which may be perceived as a “substitute” for services provided by the environmental resource. However, the resulting increase in production and consumption of the private good generates a further increase in environmental deterioration leading economic agents to increase production and consumption of the private good itself. This substitution mechanism is clearly self-reinforcing and may fuel an undesirable economic growth process according to which an increase in consumption of the private good – and the resulting increase in Gross Domestic Product – is associated with a reduction in individuals’ well-being. The article shows the emergence of several global phenomena, and individuals’ expectations about the future evolution of the environmental quality can give rise to (local and global) indeterminacy about the growth path the economy will follow starting from a given initial position.

Rational bubbles and macroeconomic fluctuations: The (de-)stabilizing role of monetary policy

We are interested in the existence of expectation-driven fluctuations of a rational bubble and the (de-)stabilizing role of monetary policy. This paper highlights the key role of credit market imperfections at the household level to explain bubble fluctuations and exhibits the stabilizing power of monetary rules responding to asset prices. We consider an overlapping generations exchange economy where households realize a portfolio choice between money and a bubble. Money is held because of a partial cash-in-advance constraint affected by the size of the bubble. A higher value of the bubble reduces the need of cash, and thus increases the fraction of consumption purchased on credit. Under these credit market features, multiplicity of steady-states (global indeterminacy) and expectation-driven fluctuations (local indeterminacy) can occur for arbitrarily small market distortions. Investing the stabilizing role of monetary policy, we show that when the monetary policy rule responds only to expected inflation, a more active rule can be destabilizing by promoting local indeterminacy and has no impact on the multiplicity of steady states. In contrast to the previous policy, when the rule responds also to asset prices, then the monetary policy can be stabilizing and rule out the multiplicity of steady states.

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.

A simple endogenous growth model of financial intermediation with multiplicity and indeterminacy

This paper analyzes the role of financial intermediation in a simple endogenous growth model. The results suggest that multiple endogenous growth paths can exist in connection with various levels of financial development, due to the reciprocal externality between financial and real sectors. According to multiplicity, the growth effects of shocks on the technology of intermediation are opposite, depending on the balanced growth path. Furthermore, transitional dynamics is examined, and reveals that the high equilibrium is a saddle path, while the low-growth is locally stable. Therefore, the model presents local and global indeterminacy. These theoretical results support the large empirical literature on the relationship between financial development and growth which depicts conflicting impacts.

Credit market imperfection, labor supply complementarity, and output volatility

This paper argues that output volatility depends on the degree of credit market imperfection. In the early stages of financial development, agents are constrained in their borrowing ability. As a result, the individual savings, affected by the labor supply, play a dual role in the economy, having repercussions on the interest rate. On the one hand, high savings imply high investment, low marginal product of capital and thus low interest rate. On the other hand, high savings affect the agents' ability to run highly productive investment projects, which increases the interest rate. When the former effect is dominant, a dynamic complementarity between individual and aggregate labor supply arises. This leads to a local and global indeterminacy of equilibrium paths. If the borrowing constraint is relaxed, the complementarity between individual and aggregate labor supply decisions weakens, equilibrium becomes globally unique and the possibility of having aggregate fluctuations in output disappears.

Relational consumption and nonlinear dynamics in an overlapping generations model

In this paper, we show that incorporating the relational dimension into an otherwise standard OLG model and focusing on dynamic leisure externalities leads to dramatically different predictions. Here, we show that when the old perceive private and relational consumption as substitutable goods, a series of interesting dynamic outcomes—such as local indeterminacy, nonlinear phenomena (including chaotic dynamics) and even multiple equilibria with global indeterminacy—may arise. We also draw some welfare implications and relate them to the well-known “happiness paradox” arising within contemporary affluent societies.

Linear production function, externalities and indeterminacy in a capital-resource growth model

This paper investigates the equilibrium growth dynamics of an economy whose production is based on natural resources and which seeks to maximize welfare to the local community. This involves determining the optimal trajectories of consumption in the local area and the use of the environmental resource. Economic dynamics are affected by negative environmental externalities which are explicitly included as unfavourable effects in a linear production function. The analysis shows the existence of local and global indeterminacy.

Indeterminacy and nonlinear dynamics in an OLG growth model with endogenous labour supply and inherited tastes

This study analyses the dynamics of a two-dimensional overlapping generations economy with endogenous labour supply à la Reichlin (J Econ Theory 40(1):89–102, 1986) and aspirations. We show that the degree of nonlinearity of consumption externality in individual utility is responsible for the existence of either one steady state or two steady states. In addition, some interesting global dynamic properties, such as cyclical behaviour and/or global indeterminacy, emerge depending on the relative importance of aspirations in utility.

Endogenous Discounting and Global Indeterminacy

This paper innovates the literature on endogenous discounting in environmental economics, by studying the global properties of the equilibrium outside the small neighborhood of the steady state. The internalization of individual consumption in the social discount rate is rich of powerful consequences from the economic point of view, for it leads to a qualitative change in the steady state and its transitional dynamics, so that the perfect foresight equilibrium may not be unique, and thus both local and global indeterminacy can eventually emerge. The main implication for decision making is that if indeterminacy occurs, public policies become not sufficient to drive the economy towards the long-run equilibrium. In particular, we show that the onset of parametric restrictions for which both global indeterminacy in the full R3 vector field, and a quasi-periodic dynamics with trajectories wrapped around an invariant torus, may eventually emerge.

TARIFF AND EQUILIBRIUM INDETERMINACY: A GLOBAL ANALYSIS

Zhang [Tariff and Equilibrium Indeterminacy, available at http://mpra.ub.uni-muenchen.de/13099/ (2009)] shows that endogenous tariffs (or energy taxes) and endogenous labor income taxes are equivalent in generating local indeterminacy. Using methods developed by Stockman [Journal of Economic Theory 145 (2010), 1060–1085], we extend Zhang's analysis to prove that endogenous tariffs and endogenous labor income taxes are also equivalent in generating global indeterminacy (chaotic equilibria) under a balanced-budget rule. More precisely, we show that the existence of Euler equation branching in an arbitrarily small neighborhood of a steady state can imply topological chaos in the sense of Devaney. In addition, Euler equation branching occurs regardless of the local uniqueness of the equilibrium around the steady state.

Load response due to local and global indeterminacies of FRP-deck bridges

In a cellular FRP deck-on-beam bridge, the deck’s load response is influenced by the cellular frame’s local indeterminacy and by the global indeterminacy due to multiple beams at each support. Thus, the stiffness distributions for both levels of indeterminacy are important. This paper reports concentrated load tests and FE analyses (FEA) of an 8m long bridge comprising cellular FRP decking bonded to and spanning across three pretensioned concrete beams. Another specimen comprising a rigidly supported, narrow width of decking where only local strains developed under load and which enabled strain measurements near the loads on external and internal surfaces of the deck, is also presented. Loads were applied via steel plates and elastomeric pads. Pressure-sensitive films enabled deduction of pad-to-deck contact zones. The FEA used contact elements at pad–deck interfaces, solid elements for the deck and beams, and included deck material and geometry anisotropies. The bridge’s test data show a 25% asymmetry of the deck’s local longitudinal strains and rapid transverse attenuation of these strains away from the loads. The FE results – including the strain asymmetry when FRP moduli are locally altered – are comparable to the experimental data. This suggests that FEA can reliably represent indeterminacy effects for these complex structures.