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Nonlinearity Induced Weak Instrumentation

2013; Taylor & Francis; Volume: 33; Issue: 5-6 Linguagem: Inglês

10.1080/07474938.2013.825181

1532-4168

Ioannis Kasparis, Peter C.B. Phillips, Tassos Magdalinos,

Market Dynamics and Volatility

Abstract 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. Keywords: Instrumental variablesIntegrable functionIntegrated processInvariance principleLocal timeMixed normalityNonlinear cointegrationStationarityUnit rootsWeak InstrumentsJEL Classification: C22C32 ACKNOWLEDGMENTS 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.