In regressions involving integrable functions we examine the limit properties of IV estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (N I) processes. We show that this kind of nonlinearity in the regression function can signi...cantly a¤ect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the N I case. Instruments

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... on integrable functions of lagged N I regressors display long range dependence and so remain relevant even at long lags, continuing to contribute to variance reduction in IV estimation. However, simulations show that OLS is generally superior to IV estimation in terms of MSE, even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary. We thank the Editor and two referees for helpful comments on an earlier version, and Timos Papadopoulos and Dimitris Mavridis for their assistance with the simulations. Phillips acknowledges partial support from the NSF under Grant No. SES 09-56687.