Max Share identification for structural VARs in levels : there is no free lunch!

This paper examines the implications of using VARs in levels under the Max Share identification approach when variables exhibit unit or near-unit roots. We derive the asymptotic distributions of the Max Share estimator, demonstrating that it converges to a random matrix, resulting in inconsistent reduced-form impulse responses and eigenvector estimates for structural shock identification. Monte Carlo simulations highlight that VAR models in levels can exhibit significant bias and higher RMSEs at intermediate and long horizons compared to stationary representations (e.g., first-difference VARs or VECMs), particularly in the presence of multiple permanent shocks. An empirical application focusing on investment-specific technology and TFP news shocks underscores the sensitivity of results to the nonstationarity of variables and the identification order of structural shocks when using VARs in levels.