An efficient minimum distance estimator for DSGE models

Recent studies illustrate that under some conditions dynamic stochastic general equilibrium models can be expressed as structural vector autoregressive models of infinite order. Based on this mapping and the theoretical results about vector autoregressive models of infinite order this paper proposes a minimum distance estimator that: A) matches the k-period responses of the whole vector of the observable variables described by the structural model – caused after a small perturbation to the entire vector of the structural errors – with those observed in the historical data, which have been recovered through the use of a structurally identified vector autoregressive model, and B) minimises the distance between the reduced-form error covariance matrix implied by the structural model and the one estimated in the data. This estimator encompasses those in the literature, is asymptotically consistent, normally distributed and efficient. The J-type overidentifying restrictions statistic that results from this methodology can be used for the evaluation of the structural model. Finally, this study also develops the theory of the bootstrapped version of the estimator and the statistic introduced here. Monte Carlo simulation evidences based on a medium-scale DSGE model reveal very encouraging results for the proposed estimator when it is compared against modern – Bayesian maximum likelihood – and less modern – maximum likelihood and non-efficient IR matching – DSGE estimators.