An E ffi cient Impulse Response Matching Estimator for Rational Expectations Models

This paper proposes an efficient estimator for rational expectations models that consists in mapping the impulse responses from the data to the structural coefficients of the model. The data-based impulse responses are estimated by local projections, which are robust to misspecification, and provide an estimate of the impulse responses’ variance-covariance matrix. This matrix is then used to obtain the asymptotically optimal minimum chi-square estimator of the structural coefficients. We show how our method relates to existing estimation methods, including maximum likelihood, generalized method of moments, limited information impulse response matching from an estimated VAR, and minimum distance estimation from an estimated VAR. Our method only entails linear projection techniques for its implementation and can be applied broadly to systems and in other situations. As an example of its general applicability, we show how to estimate mixed autoregressive-moving average specifications. Additional Monte Carlo experiments and an application to a standard New Keynesian monetary model illustrate the many benefits of our approach. •