COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1872 Non-linearity Induced Weak Instrumentation Ioannis Kasparis, Peter C.B. Phillips and Tassos Magdalinos September 2012 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 (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 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. |
