Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models

Fanelli, Luca

doi:10.1016/j.jeconom.2012.04.002

Cited by 24 publications

(35 citation statements)

References 59 publications

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“…Moreover, it depends neither on extra parameters other than , nor on additional stochastic shocks other than the fundamental shocks ! t , see Lubik andSchorfheide (2003, 2004), Fanelli (2012) and Castelnuovo and Fanelli (2015). We prefer to rule out indeterminate equilibria because the occurrence of extra parameters and shocks other than fundamental shocks complicates identi…cation issues considerably.…”

Section: Structural Model State Space Representations and Assumptionsmentioning

confidence: 99%

Bootstrapping DSGE Models

2016

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This paper explores the potential of bootstrap methods in the empirical evaluation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that su¢ ce for the bootstrap Quasi-Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspeci…cation, including the case of weak identi…cation. In particular, we show that under strong identi…cation and bootstrap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identi…ed, the above result is no longer valid. Therefore, we can evaluate how close or distant is the estimated model from the case of strong identi…cation. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identi…cation. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our apprach.

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Section: Structural Model State Space Representations and Assumptionsmentioning

confidence: 99%

Bootstrapping DSGE Models

2016

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“…For values of θ s such that the matrix G ( θ s ):=

{({normalΓ}_{0}^{normalΞ} - {normalΓ}_{f} {normalΦ}_{1})}^{- 1} {normalΓ}_{f}

is unstable, i.e. λ max ( G ( θ s )) >1, the class of reduced‐form solutions associated with the New Keynesian system – becomes more involved from a dynamic standpoint (see Lubik and Schorfheide, ; Fanelli, ).…”

Section: Structural Model and Reduced Form Solutionsmentioning

confidence: 99%

“…In the special case in which ψ and

σ_{ζ}^{+}

fulfill the conditions

ψ = vec (I_{{(n_{2})}^{2}}) (\Rightarrow M (θ_{s}, ψ) = I_{3}), σ_{ζ}^{+} = 0_{6 \times 1} (\Rightarrow τ_{t} = 0_{3 \times 1} a.s. \forall t)

system – collapses to an MSV solution (McCallum, ), i.e. a reduced‐form solution which has the same time series representation as the determinate VAR solution in equation , and it is subject to the same set of cross‐equation restrictions (see Evans and Honkapohja, ; Lubik and Schorfheide, ; and Fanelli, ). This observational equivalence reflects on the properties of the testing strategy we present below.…”

Section: Structural Model and Reduced Form Solutionsmentioning

confidence: 99%

“…Therefore, the risk run by an econometrician is to confound a determinate case in which relevant propagation mechanisms are not embedded by the structural model at hand with the indeterminate scenario. In conducting their Bayesian analysis, Lubik and Schorfheide () tackle this issue by analyzing versions of a small‐scale New Keynesian model featuring different dynamic structures, while Fanelli () proposes a frequentist test of determinacy/indeterminacy that explicitly controls for the omission of propagation mechanisms from the specified system of structural Euler equations.…”

Section: Introductionmentioning

confidence: 99%

“…Importantly, in this case we cannot rule out the possibility of a Minimum State Variable (MSV) equilibrium (McCallum, ()), i.e. a solution nested within the class of indeterminate equilibria observationally equivalent to the determinate reduced form (see Evans and Honkapohja, (); Lubik and Schorfheide, (); Fanelli, ()). Notably, the non‐rejection of the CER amounts to an implicit acceptance of the hypothesis of correct specification of the New Keynesian system.…”

Section: Introductionmentioning

confidence: 99%

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Monetary Policy Indeterminacy and Identification Failures in the U.S.: Results from A Robust Test

Castelnuovo

Fanelli

2014

J of Applied Econometrics

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SummaryWe propose a novel identification‐robust test for the null hypothesis that an estimated New Keynesian model has a reduced form consistent with the unique stable solution against the alternative of sunspot‐driven multiple equilibria. Our strategy is designed to handle identification failures as well as the misspecification of the relevant propagation mechanisms. We invert a likelihood ratio test for the cross‐equation restrictions (CER) that the New Keynesian system places on its reduced‐form solution under determinacy. If the CER are not rejected, sunspot‐driven expectations can be ruled out from the model equilibrium and we accept the structural model. Otherwise, we move to a second‐step and invert an Anderson and Rubin‐type test for the orthogonality restrictions (OR) implied by the system of structural Euler equations. The hypothesis of indeterminacy and the structural model are accepted if the OR are not rejected. We investigate the finite‐sample performance of the suggested identification‐robust two‐step testing strategy by some Monte Carlo experiments and then apply it to a New Keynesian AD/AS model estimated with actual US data. In spite of some evidence of weak identification as for the ‘Great Moderation’ period, our results offer formal support to the hypothesis of a switch from indeterminacy to a scenario consistent with uniqueness occurring in the late 1970s. Our identification‐robust full‐information confidence set for the structural parameters computed on the ‘Great Moderation’ regime turns out to be more precise than the intervals previously reported in the literature through ‘limited‐information’ methods. Copyright © 2014 John Wiley & Sons, Ltd.

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Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models

Sorge

2019

Decisions Econ Finan

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Determinacy, indeterminacy and dynamic misspecification in linear rational expectations models

Abstract: This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model has a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). Under a proper set of identifica-

Cited by 24 publications

References 59 publications

Bootstrapping DSGE Models

Bootstrapping DSGE Models

Monetary Policy Indeterminacy and Identification Failures in the U.S.: Results from A Robust Test

Arbitrary initial conditions and the dimension of indeterminacy in linear rational expectations models

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