### Abstract

We derive analytically the local asymptotic power of two pooled t-ratio tests for the presence of a unit root in a panel with fixed effects. We consider two statistics which differ according to the method used to remove the bias of the pooled OLS estimator. We show that when we bias-correct the numerator only, the resulting test has significant local power in n^{-1/4} T^{-1} neighbourhoods of the null of a panel unit root, while when the entire estimator is corrected for bias, the resulting statistic has local asymptotic power in neighbourhoods shrinking at the faster rate of n^{-1/2} T^{-1}. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1-24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153-74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416-51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework.

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

Pages (from-to) | 80-104 |

Number of pages | 25 |

Journal | Econometrics Journal |

Volume | 11 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2008 Feb 1 |

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### All Science Journal Classification (ASJC) codes

- Economics and Econometrics

### Cite this

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*Econometrics Journal*, vol. 11, no. 1, pp. 80-104. https://doi.org/10.1111/j.1368-423X.2008.00236.x

**Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects.** / Moon, Hyungsik Roger; Perron, Benoit.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotic local power of pooled t-ratio tests for unit roots in panels with fixed effects

AU - Moon, Hyungsik Roger

AU - Perron, Benoit

PY - 2008/2/1

Y1 - 2008/2/1

N2 - We derive analytically the local asymptotic power of two pooled t-ratio tests for the presence of a unit root in a panel with fixed effects. We consider two statistics which differ according to the method used to remove the bias of the pooled OLS estimator. We show that when we bias-correct the numerator only, the resulting test has significant local power in n-1/4 T-1 neighbourhoods of the null of a panel unit root, while when the entire estimator is corrected for bias, the resulting statistic has local asymptotic power in neighbourhoods shrinking at the faster rate of n-1/2 T-1. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1-24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153-74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416-51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework.

AB - We derive analytically the local asymptotic power of two pooled t-ratio tests for the presence of a unit root in a panel with fixed effects. We consider two statistics which differ according to the method used to remove the bias of the pooled OLS estimator. We show that when we bias-correct the numerator only, the resulting test has significant local power in n-1/4 T-1 neighbourhoods of the null of a panel unit root, while when the entire estimator is corrected for bias, the resulting statistic has local asymptotic power in neighbourhoods shrinking at the faster rate of n-1/2 T-1. This latter test is equivalent to the well-known pooled t test proposed by Levin et al. (2002, Journal of Econometrics 108, 1-24), and its power depends only on the mean of the local-to-unity parameters. This implies that it has the same power against homogeneous and heterogeneous alternatives with the same mean autoregressive parameter. We then compare these tests to a panel version of the Sargan-Bhargava (1983, Econometrica 51, 153-74) statistic for a unit root and the common point-optimal test of Moon et al. (2007, Journal of Econometrics 141, 416-51). Monte Carlo simulations confirm the usefulness of our local-to-unity framework.

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U2 - 10.1111/j.1368-423X.2008.00236.x

DO - 10.1111/j.1368-423X.2008.00236.x

M3 - Article

AN - SCOPUS:40149098546

VL - 11

SP - 80

EP - 104

JO - Econometrics Journal

JF - Econometrics Journal

SN - 1368-4221

IS - 1

ER -