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Résumé On étudie les propriétés dynamiques des sentiers optimaux dans un exemple du modèle à générations imbriquées à un secteur dans lequel la fonction d'utilité de l'agent représentatif est non separable. On montre dans cet exemple que le sentier optimal de croissance peut osciller et que des cycles optimaux de période deux peuvent exister. En appliquant ces résultats au modèle avec altruisme, on montre que la condition de legs positif s est parfaitement compatible avec des fluc­tuations endogènes.

Optimal growth theory studies the problem of efficient resource allocation over time, a fundamental concern of economic research. Since the 1970s, the techniques of nonlinear dynamical systems have become a vital tool in optimal growth theory, illuminating dynamics and demonstrating the possibility of endogenous economic fluctuations. Kazuo Nishimura's seminal contributions on business cycles, chaotic equilibria and indeterminacy have been central to this development, transforming our understanding of economic growth, cycles, and the relationship between them. The subjects of Kazuo's analysis remain of fundamental importance to modern economic theory.

We investigate the role of non-separable preferences on the occurrence of macroeconomic instability under a balanced-budget rule where government spending is financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of non-separable utility functions, we find that expectations-driven fluctuations easily occur when consumption and labor are Edgeworth substitutes or weak Edgeworth complements. Under these properties, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability.

Imposing some constraints on public debt is often justified regarding sustainability and stability issues. This is especially the case when the ratio of public debt over GDP is restricted to be constant. Using a Ramsey model, we show that such a constraint can however be a fundamental source of indeterminacy, and therefore, of expectation-driven fluctuations. Indeed, through the intertemporal budget constraint of the government, income taxation negatively depends on future debt, i.e. on the expected level of production. This mechanism ensures that expectations on the future tax rate may be self-fulfilling. We show that this is promoted by a larger ratio of debt over GDP.

Imposing some constraints on public debt is often justified regarding sustainability and stability issues. This is especially the case when the ratio of public debt over GDP is restricted to be constant. Using a Ramsey model, we show that such a constraint can however be a fundamental source of indeterminacy, and therefore, of expectation-driven fluctuations. Indeed, through the intertemporal budget constraint of the government, income taxation negatively depends on future debt, i.e. on the expected level of production. This mechanism ensures that expectations on the future tax rate may be self-fulfilling. We show that this is promoted by a larger ratio of debt over GDP.

We investigate the role of non-separable preferences on the occurrence of macroeconomic instability under a balanced-budget rule where government spending is financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of non-separable utility functions, we find that expectations-driven fluctuations easily occur when consumption and labor are Edgeworth substitutes or weak Edgeworth complements. Under these properties, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability.

We investigate the role of preferences in the existence of expectation-driven instability under a balanced budget rule where government spendings are financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of preferences, we find that expectation-driven fluctuations are more likely when consumption and labor are Edgeworth substitutes. Under this property, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability. Numerical simulations of the model support the conclusion that labor income taxation is a plausible source of instability in most OECD countries.

We investigate the role of preferences in the existence of expectation-driven instability under a balanced budget rule where government spendings are financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of preferences, we find that expectation-driven fluctuations are more likely when consumption and labor are Edgeworth substitutes. Under this property, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability. Numerical simulations of the model support the conclusion that labor income taxation is a plausible source of instability in most OECD countries.

We investigate the role of preferences in the existence of expectation-driven instability under a balanced budget rule where government spendings are financed by a tax on labor income. Considering a one-sector neoclassical growth model with a large class of preferences, we find that expectation-driven fluctuations are more likely when consumption and labor are Edgeworth substitutes. Under this property, an intermediate range of tax rates and a sufficiently low elasticity of intertemporal substitution in consumption lead to instability. Numerical simulations of the model support the conclusion that labor income taxation is a plausible source of instability in most OECD countries.