We propose a novel approach to deal with the problem of indeterminacy in linear rational expectations models. The method consists of augmenting the original state space with a set of auxiliary exogenous equations to provide the adequate number of explosive roots in presence of indeterminacy. The solution in this expanded state space, if it exists, is always determinate, and is identical to the indeterminate solution of the original model. The proposed approach accommodates determinacy and any degree of indeterminacy, and it can be implemented even when the boundaries of the determinacy region are unknown. Thus, the researcher can estimate the model using standard software packages without restricting the estimates to the determinacy region. We combine our solution method with a novel hybrid Metropolis–Hastings algorithm to estimate the New–Keynesian model with rational bubbles by Galí (2021) over the period 1982:Q4–2007:Q3. We find that the data support the presence of two degrees of indeterminacy, implying that the central bank was not reacting strongly enough to the bubble component.

中文翻译：

---

线性理性预期模型中不确定性的广义方法

我们提出了一种新方法来处理线性理性预期模型中的不确定性问题。该方法包括用一组辅助外生方程增加原始状态空间，以在存在不确定性的情况下提供足够数量的爆炸根。这个扩展状态空间中的解（如果存在）始终是确定的，并且与原始模型的不确定解相同。所提出的方法适应确定性和任何程度的不确定性，即使在确定性区域的边界未知时也可以实施。因此，研究人员可以使用标准软件包来估计模型，而无需将估计值限制在确定性区域。我们将我们的解决方法与一种新颖的混合 Metropolis-Hastings 算法相结合，以估计 Galí (2021) 在 1982 年第四季度至 2007 年第三季度期间提出的具有理性泡沫的新凯恩斯模型。我们发现数据支持存在两种不确定性，这意味着央行对泡沫成分的反应不够强烈。