Representative models of the macroeconomy (RMs), such as DSGE models, frequently contain unobserved variables. A finite-order VAR representation in the observed variables may not exist, and therefore the impulse responses of the RMs and SVAR models may differ. We demonstrate this divergence often is: (i) not substantial; (ii) reflects the omission of stock variables from the VAR; and (iii) when the RM features I (1) variables can be ameliorated by estimating a latent-variable VECM. We show that DSGE models utilize identifying restrictions stemming from common factor dynamics reflecting statistical, not economic, assumptions. We analyze the use of measurement error, and demonstrate that it may result in unintended consequences, particularly in models featuring I (1) variables.