Working Paper: NBER ID: w23521
Authors: Francesco Bianchi; Giovanni Nicol
Abstract: We propose a novel approach to deal with the problem of indeterminacy in Linear Rational Expectations models. The method consists of augmenting the original model with a set of auxiliary exogenous equations that are used 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. As a result, the researcher can estimate the model by using standard packages without restricting the estimates to a certain area of the parameter space. We apply our method to simulated and actual data from a prototypical New-Keynesian model for both regions of the parameter space. We show that our method successfully recovers the true parameter values independent of the initial values.
Keywords: indeterminacy; linear rational expectations models; Bayesian inference; macroeconomic modeling
JEL Codes: C19; C51; C62; C63
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Augmenting the original model with additional autoregressive processes (C22) | Ensures the existence of explosive roots necessary for a determinate solution (C62) |
| The introduction of auxiliary processes (Y20) | Transforms an indeterminate model into a determinate one (C51) |
| The methodology (C90) | Allows for the estimation of the model using standard algorithms (C51) |
| The method (C90) | Leads to successful recovery of true parameter values regardless of initial values (C51) |
| The approach (Y20) | Simplifies the existing methods that require separate estimation under different conditions of determinacy and indeterminacy (C51) |
| The methodology (C90) | Can be implemented even when the boundaries of the determinacy region are unknown (C62) |