Asymptotically UMP Panel Unit Root Tests
AbstractAbstract 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.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-017.
Date of creation: 2013
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panel unit root test; Local Asymptotic Normality; limit experiment; asymptotic power envelope; information loss;
Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Longitudinal Data; Spatial Time Series
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-03-30 (All new papers)
- NEP-ECM-2013-03-30 (Econometrics)
- NEP-ETS-2013-03-30 (Econometric Time Series)
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