We analyze a version of the Benhabib and Farmer [3] two-sector model with sector-specific externalities in which we consider a class of utility functions inspired from the one considered in Jaimovich and Rebelo [14] which is flexible enough to encompass varying degrees of income effect. First, we show that local indeterminacy and sunspot fluctuations occur in 2-sector models under plausible configurations regarding all structural parameters – in particular regarding the intensity of income effects. Second, we prove that there even exist some configurations for which local indeterminacy arises under any degree of income effect. More precisely, for any given size of income effect, we show that there is a non-empty range of values for the Frisch elasticity of labor and the elasticity of intertemporal substitution in consumption such that indeterminacy occurs. This contrasts with the results obtained in one-sector models in both Nishimura et al. [19], in which it is shown that indeterminacy cannot occur under either GHH and KPR preferences, and in Jaimovich [13] in which local indeterminacy only arises for intermediary income effects.
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机译：我们分析了具有特定部门外部性的Benhabib and Farmer [3]两部门模型的一种版本，其中我们考虑了一类效用函数，该函数受Jaimovich和Rebelo [14]中所考虑的那种启发，具有足够的灵活性以涵盖不同程度收入效应。首先，我们表明，在所有结构参数（尤其是收入效应强度）的合理配置下，两部门模型中发生了局部不确定性和黑子波动。其次，我们证明甚至存在某些配置，在任何程度的收入效应下，本地不确定性都会出现。更确切地说，对于任何给定的收入效应规模，我们表明劳动力的弗里施弹性和消费中的跨期替代弹性存在一个非空值范围，从而发生不确定性。这与Nishimura等人在单扇区模型中获得的结果形成了鲜明对比。 [19]，其中表明在GHH和KPR偏好下都不会发生不确定性，在Jaimovich [13]中，局部不确定性只对中间收入产生影响。
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