Working Paper: CEPR ID: DP10298
Authors: Pablo A. Guerrón-Quintana; Atsushi Inoue; Lutz Kilian
Abstract: One of the leading methods of estimating the structural parameters of DSGE models is the VAR-based impulse response matching estimator. The existing asymptotic theory for this estimator does not cover situations in which the number of impulse response parameters exceeds the number of VAR model parameters. Situations in which this order condition is violated arise routinely in applied work. We establish the consistency of the impulse response matching estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. Our methods of inference remain asymptotically valid when the order condition is satisfied, regardless of whether the usual rank condition for the application of the delta method holds. Our analysis sheds new light on the choice of the weighting matrix and covers both weakly and strongly identified DSGE model parameters. We also show that under our assumptions special care is needed to ensure the asymptotic validity of Bayesian methods of inference. A simulation study suggests that the frequentist and Bayesian point and interval estimators we propose are reasonably accurate infinite samples. We also show that using these methods may affect the substantive conclusions in empirical work.
Keywords: bootstrap; DSGE; impulse response; nonstandard asymptotics; robust inference; structural estimation; VAR; weak identification
JEL Codes: C32; C52; E30; E50
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| impulse response matching estimator (C51) | consistency under nonstandard conditions (C62) |
| optimal weighting matrix (C51) | nonstandard convergence rate and distribution (C46) |
| diagonal weighting matrix (C46) | asymptotic normality and consistent standard error estimation (C51) |
| dimensionality of impulse responses (C32) | validity of inference methods (C52) |
| identification strength of parameters (C26) | conclusions drawn from empirical analyses (D12) |