A Wavelet Smoothing Approach to Reducing Bias in Structural Vector Autoregressions

This study proposes a modification of the Blanchard Quah method of obtaining identification in Structural Vector Autoregressions (SVAR) using long run restrictions. Employing a discrete wavelet transform (DWT) to filter out high frequency variation, it obtains a better estimate of the long run effect matrix and substantially reduces bias when tested on a simulated dataset. This modification addresses the criticism of bias in the Blanchard Quah method due to lag truncation. By filtering the high frequency variation when estimating the long run effects matrix using ordinary least squares, I push the bias towards the high frequency region where it will not bias the estimate of the long run effects matrix. I test this method against the standard method using a monte carlo experiment utilizing a two variable real business cycle model and show much lower bias than the standard method. The modified method that I refer to as Wavelet BQ is then applied to the data used to parameterize that real business cycle model and rejects the parameterization. Next, I examine data from 4 small open economies to test Dornbush's overshooting model. Wavelet BQ shows responses for all 4 countries that are of the magnitude and shape predicted by Dornbush's overshooting model. The standard method (Standard BQ) has the right shape and direction but the effect sizes are biased upward toward 0 and about half the magnitude as the ones estimated by Wavelet BQ.