External sources of as-if randomness — that is, external instruments — can be used to identify the dynamic causal effects of macroeconomic shocks. One method is a one-step instrumental variables regression (local projections – IV); a more efficient two-step method involves a vector autoregression. We show that, under a restrictive instrument validity condition, the one-step method is valid even if the vector autoregression is not invertible, so comparing the two estimates provides a test of invertibility. If, however, lagged endogenous variables are needed as control variables in the one-step method, then the conditions for validity of the two methods are the same.
Stock, James H., and Mark W. Watson. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments." The Economic Journal 128.610 (May 2018): 917-948.