This paper proves that the fully modified vector autoregression (FM-VAR) estimator has second-order bias effects when some roots are local to unity. These bias effects are shown to result in potentially severe size distortions in FM-VAR testing when the hypothesis involves near unit root variables. In addition, the paper reveals that with the FM-VAR method near unit roots become estimated as exact unit roots with convergence speed faster than the order of the sample size. Also this result implies problems for FM-VAR testing, as such “hyperconsistent” estimates give rise to degenerate limit distributions under the null hypothesis.I am grateful to Pentti Saikkonen, Jim Stock, Markku Lanne, Jukka Nyblom, and three referees for very helpful comments on earlier drafts. This paper is a part of the research program of the Research Unit on Economic Structures and Growth (RUESG) at the Department of Economics at the University of Helsinki. Financial support from the ASLA Fulbright, the Yrjö Jahnsson Foundation, and the Finnish Cultural Foundation is gratefully acknowledged. The usual disclaimer applies.