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.
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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number
5255.
Find related papers by JEL classification: C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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