### Quantitative Economics, Volume 4, Issue 2 (July 2013)

### Frequentist inference in weakly identified dynamic stochastic general equilibrium models

*Pablo Guerron-Quintana, Atsushi Inoue, Lutz Kilian*

#### Abstract

A common problem in estimating dynamic stochastic general equilibrium models

is that the structural parameters of economic interest are only weakly identified.

As a result, classical confidence sets and Bayesian credible sets will not coincide

even asymptotically, and the mean, mode, or median of the posterior distribution

of the structural parameters can no longer be viewed as a consistent estimator. We

propose two methods of constructing confidence intervals for structural model

parameters that are asymptotically valid from a frequentist point of view regard-

less of the strength of identification. One involves inverting a likelihood ratio test

statistic, whereas the other involves inverting a Bayes factor statistic. A simula-

tion study shows that both methods have more accurate coverage than alternative

methods of inference. An empirical study of the degree of wage and price rigidi-

ties in the U.S. economy illustrates that the data may contain useful information

about structural model parameters even when these parameters are only weakly

identified.

Keywords. DSGE models, identification, inference, confidence sets, Bayes factor,

likelihood ratio.

JEL classification. C32, C52, E30, E50.

is that the structural parameters of economic interest are only weakly identified.

As a result, classical confidence sets and Bayesian credible sets will not coincide

even asymptotically, and the mean, mode, or median of the posterior distribution

of the structural parameters can no longer be viewed as a consistent estimator. We

propose two methods of constructing confidence intervals for structural model

parameters that are asymptotically valid from a frequentist point of view regard-

less of the strength of identification. One involves inverting a likelihood ratio test

statistic, whereas the other involves inverting a Bayes factor statistic. A simula-

tion study shows that both methods have more accurate coverage than alternative

methods of inference. An empirical study of the degree of wage and price rigidi-

ties in the U.S. economy illustrates that the data may contain useful information

about structural model parameters even when these parameters are only weakly

identified.

Keywords. DSGE models, identification, inference, confidence sets, Bayes factor,

likelihood ratio.

JEL classification. C32, C52, E30, E50.

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