Ruling out Indeterminacy: the Role of Heterogeneity

Models with externalities have become increasingly popular for studying both long-term growth and business-cycle fluctuations. Externalities can lead to indeterminacy, allowing self-fulfilling expectations to determine the equilibrium. This paper argues that the importance of indeterminacy might be overstated by the literature, as it does not recognize that heterogeneity across individuals can have a strong stabilizing effect. We illustrate this in a stylized two-sector economy with an externality by considering changes in the distribution of the individual entry costs into the two sectors. First, we find that the equilibrium is indeterminate (determinate) when the entry costs are relatively homogeneous (heterogeneous) across individuals. Our second result is that for any neighbourhood of any possible long-run outcome of the economy, there is a mean preserving spread of the entry cost distribution, such that the unique steady state lies in that neighbourhood and is saddle-path stable. This implies that the aggregate characteristics may not be informative even when there is determinacy. Thus indeterminacy is not necessary to explain the empirical fact that countries with very similar fundamentals can end up in rather different steady states.