Asymptotically UMP Panel Unit Root Tests

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Abstract

Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages19
Volume2013-017
Publication statusPublished - 2013

Publication series

NameCentER Discussion Paper
Volume2013-017

Fingerprint

Panel unit root tests
Perturbation
Power envelope
Unit root tests
Optimal test
Heterogeneous panels
Cross-sectional dependence
Equality
Local power

Keywords

  • panel unit root test
  • Local Asymptotic Normality
  • limit experiment
  • asymptotic power envelope
  • information loss

Cite this

Becheri, I. G., Drost, F. C., & van den Akker, R. (2013). Asymptotically UMP Panel Unit Root Tests. (CentER Discussion Paper; Vol. 2013-017). Tilburg: Econometrics.
Becheri, I.G. ; Drost, F.C. ; van den Akker, R. / Asymptotically UMP Panel Unit Root Tests. Tilburg : Econometrics, 2013. (CentER Discussion Paper).
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title = "Asymptotically UMP Panel Unit Root Tests",
abstract = "Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.",
keywords = "panel unit root test, Local Asymptotic Normality, limit experiment, asymptotic power envelope, information loss",
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year = "2013",
language = "English",
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Becheri, IG, Drost, FC & van den Akker, R 2013 'Asymptotically UMP Panel Unit Root Tests' CentER Discussion Paper, vol. 2013-017, Econometrics, Tilburg.

Asymptotically UMP Panel Unit Root Tests. / Becheri, I.G.; Drost, F.C.; van den Akker, R.

Tilburg : Econometrics, 2013. (CentER Discussion Paper; Vol. 2013-017).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Asymptotically UMP Panel Unit Root Tests

AU - Becheri, I.G.

AU - Drost, F.C.

AU - van den Akker, R.

N1 - Pagination: 19

PY - 2013

Y1 - 2013

N2 - Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.

AB - Abstract This paper considers optimal unit root tests for a Gaussian cross-sectionally independent heterogeneous panel with incidental intercepts and heterogeneous alternatives generated by random perturbations. We derive the (asymptotic and local) power envelope for two models: an auxiliary model where both the panel units and the random perturbations are observed, and the second one, the model of main interest, for which only the panel units are observed. We show that both models are Locally Asymptotically Normal (LAN). It turns out that there is an information loss: the power envelope for the auxiliary model is above the envelope for the model of main interest. Equality only holds if the alternatives are homogeneous. Our results exactly identify in which setting the unit root test of Moon, Perron, and Phillips (2007) is asymptotically UMP and, in fact, they show it is not possible to exploit possible heterogeneity in the alternatives, confirming a conjecture of Breitung and Pesaran (2008). Moreover, we propose a new asymptotically optimal test and we extend the results to a model allowing for cross-sectional dependence.

KW - panel unit root test

KW - Local Asymptotic Normality

KW - limit experiment

KW - asymptotic power envelope

KW - information loss

M3 - Discussion paper

VL - 2013-017

T3 - CentER Discussion Paper

BT - Asymptotically UMP Panel Unit Root Tests

PB - Econometrics

CY - Tilburg

ER -

Becheri IG, Drost FC, van den Akker R. Asymptotically UMP Panel Unit Root Tests. Tilburg: Econometrics. 2013. (CentER Discussion Paper).