SVARs in the frequency domain using a continuum of restrictions

This paper proposes a joint methodology for the identification and inference of structural vector autoregressive models in the frequency domain. We show that identifying restrictions can be written naturally as an asymptotic least squares problem (Gourieroux, Monfort and Trognon, 1985) in which there is a continuum of nonlinear estimating equations. Following Carrasco and Florens (2000), we then develop a continuum asymptotic least squares estimator (C-ALS) that exploits efficiently the continuum of estimating equations thereby allowing to obtain optimal consistent estimates of impulse responses and reliable confidence intervals. Moreover the identifying restrictions can be formally tested using an appropriate J-stat and the frequency band can be selected with a data-driven procedure. Finally, we provide some new results using Monte Carlo simulations and applications regarding the hours-productivity debate and the impact of news shocks.