Polynomial Regressions and Nonsense Inference

Daniel Ventosa-Santaulària and Carlos Vladimir Rodríguez-Caballero
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Carlos Vladimir Rodríguez-Caballero: Center for Research in Econometric Analysis of Time Series (CREATES) and Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, Building 2622 (203), Aarhus V 8210, Denmark
Authors registered in the RePEc Author Service: Carlos Vladimir Rodríguez Caballero

Econometrics, 2013, vol. 1, issue 3, 1-13

Abstract: Polynomial specifications are widely used, not only in applied economics, but also in epidemiology, physics, political analysis and psychology, just to mention a few examples. In many cases, the data employed to estimate such specifications are time series that may exhibit stochastic nonstationary behavior. We extend Phillips’ results (Phillips, P. Understanding spurious regressions in econometrics. J. Econom. 1986, 33, 311–340.) by proving that an inference drawn from polynomial specifications, under stochastic nonstationarity, is misleading unless the variables cointegrate. We use a generalized polynomial specification as a vehicle to study its asymptotic and finite-sample properties. Our results, therefore, lead to a call to be cautious whenever practitioners estimate polynomial regressions.

Keywords: polynomial regression; misleading inference; integrated processes (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2013
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