Can you do the wrong thing and still be right? Hypothesis testing in I(2) and near-I(2) cointegrated VARs

In this paper, we investigate the small-sample performance of LR tests on long-run coefficients in the I(2) model; we focus on a comparison between I(2) and near-I(2) data, i.e. I(1) data with a second root very close to unity, and report the results of some Monte Carlo experiments. With near-I(2) data, the finite-sample properties of the tests are (i) similar to those found with genuine I(2) data, (ii) systematically superior to those of the analogous tests constructed in the I(1) model, even if the latter is, in principle, correctly specified and the former is not. Therefore, there seems to be strong support to the idea that, in practice, modelling near-I(2) data using the I(2) model may be a good idea, despite the inherent misspecification.