### 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.

Original language | English |
---|---|

Pages (from-to) | 376-384 |

Number of pages | 9 |

Journal | Journal of Econometrics |

Volume | 187 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 Jul 1 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Cite this

*Journal of Econometrics*,

*187*(1), 376-384. https://doi.org/10.1016/j.jeconom.2015.03.041

}

*Journal of Econometrics*, vol. 187, no. 1, pp. 376-384. https://doi.org/10.1016/j.jeconom.2015.03.041

**Testing linearity using power transforms of regressors.** / Baek, Yae In; Cho, Jin Seo; Phillips, Peter C.B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Testing linearity using power transforms of regressors

AU - Baek, Yae In

AU - Cho, Jin Seo

AU - Phillips, Peter C.B.

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84929619369&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929619369&partnerID=8YFLogxK

U2 - 10.1016/j.jeconom.2015.03.041

DO - 10.1016/j.jeconom.2015.03.041

M3 - Article

AN - SCOPUS:84929619369

VL - 187

SP - 376

EP - 384

JO - Journal of Econometrics

JF - Journal of Econometrics

SN - 0304-4076

IS - 1

ER -