Alain Venditti

Indeterminacy in dynamic models: When Diamond meets Ramsey

In this paper, we consider an aggregate overlapping generations model with endogenous labour, consumption in both periods of life, homothetic preferences and productive external effects coming from the average capital and labour. We show that under realistic calibrations of the parameters, in particular a large enough share of first period consumption over the wage income, local indeterminacy of equilibria cannot occur with capital externalities alone but that it can occur when there are only, however small, labour externalities. More precisely, under gross substitutability, the existence of multiple equilibria requires a large enough elasticity of capital-labour substitution and a large enough elasticity of the labour supply. We also show that if labour externalities are slightly stronger and the elasticity of labour supply is larger, local indeterminacy occurs in a Cobb-Douglas economy. Finally, we show that, as a consequence of our restriction on first period consumption, a locally indeterminate steady state is generically characterized by an under-accumulation of capital. It follows therefore that while agents live over a finite number of periods, the conditions for the existence of locally indeterminate equilibria are very similar to those obtained within infinite horizon models and that from this point of view, Diamond meets Ramsey.

Intersectoral Externalities and Indeterminacy

Abstract We consider a two-sector economy with positive intersectoral external effects and nonincreasing social returns. We show that if the discount factor ρ is close to 1 then local indeterminacy may be obtained with mild market imperfections. Moreover, with additional conditions, when ρ is made smaller the steady state becomes totally unstable and quasi-periodic cycles, along which equilibrium paths are indeterminate, may appear through a Hopf bifurcation. This will be proved even if the investment good is capital intensive at the private level while this condition guarantees local determinacy in the sector specific case. Journal of Economic Literature Classification Numbers: C62, E32, O41.

Indeterminacy And The Role Of Factor Substitutability

We discuss the role of the elasticity of substitution in the local determinacy properties of a steady state or a stationary balanced growth path in a general multisector economy with CES technologies. Our main results are the following: We give some sufficient conditions for the occurrence of local indeterminacy in exogenous and endogenous growth models. We show that local indeterminacy takes place even without a capital intensity reversal from the private to the social level if the productive factors are weakly substitutable. Moreover, we show that the conditions for local indeterminacy in exogenous growth models and in endogenous growth models may be qualitatively different.

Optimal growth and cycles in overlapping generations models

SummaryThis paper investigates the dynamical properties of optimal paths in one-sector overlapping generations models without assuming that the utility function of the representative agent is separable. When the utility function is separable, the optimal growth paths monotonically converges toward the modified golden rule steady state. In the non-separable case, we show that the optimal growth path may be oscillating and optimal two-period cycles may exist. Applying these results to the model with altruism, we show that the condition of operative bequest is fully compatible with endogeneous fluctuations provided that the discount factor is close enough to one. All our results are illustrated using Cobb-Douglas utility and production functions.

Indeterminacy in discrete-time infinite-horizon models with non-linear utility and endogenous labor

Over the last decade, a large number of papers have established the fact that locally indeterminate equilibria and sunspots fluctuations may arise in infinite-horizon growth models with external effects in production. These contributions also show that there exist significant differences between one-sector and two-sector models. As initially established by Benhabib and Farmer (1994), in one-sector models local indeterminacy requires some increasing returns based on externalities coming from capital and more importantly labor, a strongly elastic labor supply, and a large enough elasticity of intertemporal substitution in consumption which may however remain within plausible intervals.

Aggregate instability under balanced-budget consumption taxes: A re-examination

We re-examine the destabilizing role of balanced-budget fiscal policy rules based on consumption taxation. Using a one-sector model with infinitely-lived households, we consider a specification of preferences derived from Jaimovich (2008) [14] and Jaimovich and Rebelo (2009) [15] which is flexible enough to encompass varying degrees of income effect. When the income effect is not too large, we show that there exists a Laffer curve, which explains the multiplicity of steady states, and that non-linear consumption taxation may destabilize the economy, promoting expectation-driven fluctuations, if the elasticity of intertemporal substitution in consumption is sufficiently larger than one and the tax rate is counter-cyclical with respect to consumption. Numerical illustrations also show that consumption taxation may be a source of instability for most OECD countries for a wide range of structural parametersʼ configurations. We finally prove the robustness of our conclusions if we consider a discrete-time setup.

Determinacy of Equilibrium in an Overlapping Generations Model with Heterogeneous Agents

We consider the determinacy of perfect foresight equilibrium near a steady state in an overlapping generations model with production and both altruistic and non altruistic agents having distinct utility functions. The proportions of each type of consumers is exogenously given. Such a model may be interpreted as both a particular case and an extension of the one considered by Muller and Woodford(1988) in which both finite and infinite lived agents coexist.

Indeterminacy and endogenous fluctuations in two-sector growth models with externalities

Abstract This paper discusses the influence of technological externalities on the dynamic properties of accumulation paths in a two-sector growth model in discrete time. Following the recent paper of Boldrin and Rustichini (1994), in which the authors study indeterminacy in a particular case, we first provide some necessary and/or sufficient conditions for the indeterminacy of equilibria in the general two-sector model. We also provide some conditions for the existence of period two cycles when equilibria are indeterminate. We prove finally that depending on the nature of externality, indeterminacy may lead to the existence of quasi-periodic paths.

Capital depreciation, factor substitutability and indeterminacy ⁄

We consider a discrete-time two-sector CES economy with sector specific external effects and partial depreciation of capital. We show that the occurrence of local indeterminacy of equilibria depends on an interplay between factor substitutability and capital depreciation. When the elasticity of substitution is less than one, local indeterminacy may occur with low depreciation of capital. When the elasticity of substitution is greater than one, local indeterminacy is more likely if the rate of depreciation is high.

Turnpike theory : Some new results on the saddle point property of equilibria and on the existence of endogenous cycles

Abstract This paper discusses the saddle point stability of equilibria and the existence of endogenous cycles in a general optimal growth model defined as a variational problem. We shall give new proofs of several turnpike theorems and generalize a condition on the indirect utility function suggested by Brock, Scheinkman, and Magill to the analysis of stability and bifurcation. Furthermore, we shall provide a characterization of the bound δ∗ beyond which the steady state may be unstable and prove that under some conventional assumptions δ∗ is the discount rate value for which a bifurcation of periodic orbits may be obtained by means of the Hopf theorem.