Abstract
Kormilitsina (Comput Econ 41(4): 525–555, 2013) develops a perturbation-based algorithm to solve up to the second order of approximation rational expectations models with informational subperiods (timing restrictions). It is there claimed that the restricted framework inherits equilibrium (non)uniqueness properties from its unrestricted counterpart. This comment provides an example where timing restrictions cause non-existence of dynamically stable equilibria, even though the model’s unrestricted counterpart exhibits saddle-path stability. Implications for the execution of Kormilitsina’s algorithm are discussed.
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Notes
A formal proof, which builds upon Proposition 1 in Kormilitsina (2013), is available from the authors upon request.
Equivalently, since timing restrictions force the nominal interest rate to act as a backward-looking variable, the RE model with informational subperiods fails to meet a basic rank condition which is regularly required to hold by standard solution routines, e.g. assumption 4.5 in Klein (2000).
That is, the restricted model fails to inherit the saddle-path stability property from its unrestricted counterpart whenever \(\alpha >1\), i.e. a non-zero measure subset of the model’s structural parameters.
In fact, \([f^1_{y}]_{*j}=0\) for column \(j \in [i, n_y]\) implies generic singularity of the coefficient matrix \(\Delta (f^1)_{[x',y]}\). Invertibility of the latter is exploited in Kormilitsina (2013) when constructing the RE solution to the restricted model by means of linear transformations of its unrestricted counterpart’s, irrespective of whether the autoregressive matrix in (4) is invertible or not.
References
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We wish to thank Anna Kormilitsina and Elmar Mertens for extremely helpful suggestions. Any remaining errors are our own.
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Hespeler, F., Sorge, M.M. Solving Rational Expectations Models with Informational Subperiods: A Comment. Comput Econ 53, 1649–1654 (2019). https://doi.org/10.1007/s10614-018-9829-2
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DOI: https://doi.org/10.1007/s10614-018-9829-2