Expectations, beliefs and the business cycle: theoretical analysis

When can exogenous changes in beliefs generate endogenous fluctuations in rational expectation models? We analyze this question in the canonical one-sector and two-sector models of the business cycle with increasing returns to scale. A key feature of our analysis is that we express the uniqueness/multiplicity condition of equilibirum paths in terms of restrictions on five critical and economically interpretable parameters: the Frisch elasticities of the labor supply curve with respect to the real wage and to the marginal utility of wealth, the intertemporal elasticity of substitution in consumption, the elasticity of substitution between capital and labor, and the degree of increasing returns to scale. We obtain two clear-cut conclusions: belief-driven fluctuations cannot exist in the one-sector version of the model for empirically consistent values for these five parameters. By contrast, belief-driven fluctuations are a robust property of the twosector version of the model-with differentiated consumption and investment goods-, as they now emerge for a wide range of parameter values consistent with available empirical estimates. The key ingredients explaining these different outcomes are factor reallocation between sectors and the implied variations in the relative price of investment, affecting the expected return on capital accumulation.