When can exogenous changes in beliefs generate endogenous fluctuations in rationalexpectation 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 ouranalysis is that we express the uniqueness/multiplicity condition of equilibirum pathsin terms of restrictions on five critical and economically interpretable parameters: theFrisch elasticities of the labor supply curve with respect to the real wage and to themarginal utility of wealth, the intertemporal elasticity of substitution in consumption,the elasticity of substitution between capital and labor, and the degree of increasingreturns to scale. We obtain two clear-cut conclusions: belief-driven fluctuations cannotexist in the one-sector version of the model for empirically consistent values for thesefive parameters. By contrast, belief-driven fluctuations are a robust property of thetwo-sector version of the model—with differentiated consumption and investmentgoods—, as they now emerge for a wide range of parameter values consistent withavailable empirical estimates. The key ingredients explaining these different outcomesare factor reallocation between sectors and the implied variations in the relative priceof investment, affecting the expected return on capital accumulation.