Nonlinearity Induced Weak Instrumentation

In regressions involving integrable functions we examine the limit properties of instrumental variable (IV) estimators that utilise integrable transformations of lagged regressors as instruments. The regressors can be either I(0) or nearly integrated (NI) processes. We show that this kind of nonlinearity in the regression function can significantly affect the relevance of the instruments. In particular, such instruments become weak when the signal of the regressor is strong, as it is in the NI case. Instruments based on integrable functions of lagged NI 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 ordinary least square (OLS) is generally superior to IV estimation in terms of mean squared error (MSE), even in the presence of endogeneity. Estimation precision is also reduced when the regressor is nonstationary.