Modified two-stage least-squares estimators for the estimation of a structural vector autoregressive integrated process

We consider the estimation of a structural vector autoregressive model of nonstationary and possibly cointegrated variables without the prior knowledge of unit roots or rank of cointegration. We propose two modified two-stage least-squares estimators that are consistent and have limiting distributions that are either normal or mixed normal. Limited Monte Carlo studies are also conducted to evaluate their finite sample properties.