Sequentially Testing Polynomial Model Hypotheses Using Power Transforms of Regressors

Jin Seo Cho (jinseocho@yonsei.ac.kr), Myung-Ho Park and Peter Phillips
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Myung-Ho Park: Korea Institute of Public Finance

No 2060, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We provide a methodology for testing a polynomial model hypothesis by extending the approach and results of Baek, Cho, and Phillips (2015; Journal of Econometrics; BCP) that tests for neglected nonlinearity using power transforms of regressors against arbitrary nonlinearity. We examine and generalize the BCP quasi-likelihood ratio test dealing with the multifold identification problem that arises under the null of the polynomial model. The approach leads to convenient asymptotic theory for inference, has omnibus power against general nonlinear alternatives, and allows estimation of an unknown polynomial degree in a model by way of sequential testing, a technique that is useful in the application of sieve approximations. Simulations show good performance in the sequential test procedure in identifying and estimating unknown polynomial order. The approach, which can be used empirically to test for misspecification, is applied to a Mincer (1958, 1974) equation using data from Card (1995). The results confirm that Mincer�s log earnings equation is easily shown to be misspecified by including nonlinear effects of experience and schooling on earnings, with some flexibility required in the respective polynomial degrees.

Keywords: QLR test; Asymptotic null distribution; Misspecification; Mincer equation; Nonlinearity; Polynomial model; Power Gaussian process; Sequential testing (search for similar items in EconPapers)
JEL-codes: C12 C18 C46 C52 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2016-07
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Published in Journal of Applied Econometrics (August 2017), 33(1): 141-159

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Related works:
Journal Article: Sequentially testing polynomial model hypotheses using power transforms of regressors (2018)
Working Paper: Sequentially Testing Polynomial Model Hypotheses using Power Transforms of Regressors (2016)
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