Publication Type

Journal Article

Version

publishedVersion

Publication Date

1-2015

Abstract

We develop a method of testing linearity using power transforms of regressors, allowing for stationary processes and time trends. The linear model is a simplifying hypothesis that derives from the power transform model in three different ways, each producing its own identification problem. We call this modeling difficulty the trifold identification problem and show that it may be overcome using a test based on the quasi-likelihood ratio (QLR) statistic. More specifically, the QLR statistic may be approximated under each identification problem and the separate null approximations may be combined to produce a composite approximation that embodies the linear model hypothesis. The limit theory for the QLR test statistic depends on a Gaussian stochastic process. In the important special case of a linear time trend regressor and martingale difference errors asymptotic critical values of the test are provided. Test power is analyzed and an empirical application to crop-yield distributions is provided. The paper also considers generalizations of the Box-Cox transformation, which are associated with the QLR test statistic. (C) 2015 Elsevier B.V. All rights reserved.

Keywords

Box-Cox transform, Gaussian stochastic process, Neglected nonlinearity, Power transformation, Quasi-likelihood ratio test, Trend exponent, Trifold identification problem

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

187

Issue

1

First Page

376

Last Page

384

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2015.03.041

Publisher

Elsevier: 24 months

Additional URL

https://doi.org/10.1016/j.jeconom.2015.03.041

Download

Included in

Econometrics Commons

Share

COinS