Structural VARs, Deterministic and Stochastic Trends: Does Detrending Matter?

We highlight how detrending within Structural Vector Autoregressions (SVAR) is directly linked to the shock identification. Consequences of trend misspecification are investigated using a prototypical Real Business Cycle model as the Data Generating Process. Decomposing the different sources of biases in the estimated impulse response functions, we find the biases arising directly from trend misspecification are not trivial when compared to other widely studied misspecifications. Our example also illustrates how misspecifying the trend can also distort impulse response functions of even the correctly detrended variable within the SVAR system.