Title: Identification of long-run effects in near-integrated systems
Authors: Peter Boswijk - University of Amsterdam (Netherlands) [presenting]
Abstract: It has been previously shown that inference on cointegrating coefficients is not robust to local deviations from the unit root. When unit roots are incorrectly imposed, the resulting vector error correction model is misspecified. Quasi-maximum likelihood in this misspecified model leads to asymptotically mixed normal estimators, but centered around the pseudo-true value, which is related to the concept of long-run multiplier. However, in near-integrated systems, there is no unique stationary linear combination, so that the identification of appropriate long-run effects has to be addressed. We follow a previous approach and focus on the long-run relative impulse response. A new parametrisation of the unrestricted VAR model is developed, in terms of both this long-run parameter and the largest autoregressive roots. Next, we address possibilities to make asymptotically valid inference on the long-run relative impulse response. Analogously to an earlier result, we establish that the standard implementation of the bootstrap does not deliver valid inference. Therefore, we investigate alternative versions of the bootstrap, focussing in particular on the double bootstrap.