Linear identification of linear rational-expectations models by exogenous variables reconciles Lucas and Sims

  • Linear rational-expectations models (LREMs) are conventionally "forwardly" estimated as follows. Structural coefficients are restricted by economic restrictions in terms of deep parameters. For given deep parameters, structural equations are solved for "rational-expectations solution" (RES) equations that determine endogenous variables. For given vector autoregressive (VAR) equations that determine exogenous variables, RES equations reduce to reduced-form VAR equations for endogenous variables with exogenous variables (VARX). The combined endogenous-VARX and exogenous-VAR equations comprise the reduced-form overall VAR (OVAR) equations of all variables in a LREM. The sequence of specified, solved, and combined equations defines a mapping from deep parameters to OVAR coefficients that is used to forwardly estimate a LREM in terms of deep parameters. Forwardly-estimated deep parameters determine forwardly-estimated RES equations that Lucas (1976) advocated for making policy predictions in his critique of policy predictions made with reduced-form equations. Sims (1980) called economic identifying restrictions on deep parameters of forwardly-estimated LREMs "incredible", because he considered in-sample fits of forwardly-estimated OVAR equations inadequate and out-of-sample policy predictions of forwardly-estimated RES equations inaccurate. Sims (1980, 1986) instead advocated directly estimating OVAR equations restricted by statistical shrinkage restrictions and directly using the directly-estimated OVAR equations to make policy predictions. However, if assumed or predicted out-of-sample policy variables in directly-made policy predictions differ significantly from in-sample values, then, the out-of-sample policy predictions won't satisfy Lucas's critique. If directly-estimated OVAR equations are reduced-form equations of underlying RES and LREM-structural equations, then, identification 2 derived in the paper can linearly "inversely" estimate the underlying RES equations from the directly-estimated OVAR equations and the inversely-estimated RES equations can be used to make policy predictions that satisfy Lucas's critique. If Sims considered directly-estimated OVAR equations to fit in-sample data adequately (credibly) and their inversely-estimated RES equations to make accurate (credible) out-of-sample policy predictions, then, he should consider the inversely-estimated RES equations to be credible. Thus, inversely-estimated RES equations by identification 2 can reconcile Lucas's advocacy for making policy predictions with RES equations and Sims's advocacy for directly estimating OVAR equations. The paper also derives identification 1 of structural coefficients from RES coefficients that contributes mainly by showing that directly estimated reduced-form OVAR equations can have underlying LREM-structural equations.

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Author:Peter A. ZadroznyGND
Parent Title (English):Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 682
Series (Serial Number):CFS working paper series (682)
Publisher:Center for Financial Studies
Place of publication:Frankfurt, M.
Document Type:Working Paper
Year of Completion:2022
Year of first Publication:2022
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2022/12/12
Tag:cross-equation restrictions of rational expectations; factorization of matrix polynomials; reconciliation of Lucas's advocacy of rational-expectations modelling and policy predictions and Sims's advocacy of VAR modelling
Issue:October 3, 2022
Page Number:46
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
JEL-Classification:C Mathematical and Quantitative Methods / C3 Multiple or Simultaneous Equation Models / C32 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C4 Econometric and Statistical Methods: Special Topics / C43 Index Numbers and Aggregation
C Mathematical and Quantitative Methods / C5 Econometric Modeling / C53 Forecasting and Other Model Applications
C Mathematical and Quantitative Methods / C6 Mathematical Methods and Programming / C63 Computational Techniques; Simulation Modeling (Updated!)
Licence (German):License LogoDeutsches Urheberrecht