Asymptotically Uniformly Most Powerful Tests for Unit Roots in Gaussian Panels with Cross-Sectional Dependence Generated by Common Factors PDF Download
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Author: Ramon Van den Akker
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Languages : en
Pages : 0
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This paper considers testing for unit roots in Gaussian panels with crosssectional dependence generated by common factors. Within our setup we can analyze restricted versions of the two prevalent approaches in the literature, that of Moon & Perron (2004), who specify a factor model for the innovations, and the PANIC setup proposed in Bai & Ng (2004), who test common factors and idiosyncratic deviations separately for unit roots. We show that both frameworks lead to locally asymptotically normal (LAN) experiments with the same central sequence and Fisher information. Using Le Cam's theory of statistical experiments we obtain the local asymptotic power envelope for unit root tests. We show that the popular Moon & Perron (2004) and Bai & Ng (2010) tests only attain the power envelope in case there is no heterogeneity in the long-run variance of the idiosyncratic components. We develop a new test which is asymptotically uniformly most powerful irrespective of possible heterogeneity in the long-run variance of the idiosyncratic components. Monte Carlo simulations corroborate our asymptotic results and document significant gains in finite-sample power if the variances of the idiosyncratic shocks differ substantially among the cross sectional units.
Author: Ramon Van den Akker
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ISBN:
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Languages : en
Pages : 0
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Book Description
This paper considers testing for unit roots in Gaussian panels with crosssectional dependence generated by common factors. Within our setup we can analyze restricted versions of the two prevalent approaches in the literature, that of Moon & Perron (2004), who specify a factor model for the innovations, and the PANIC setup proposed in Bai & Ng (2004), who test common factors and idiosyncratic deviations separately for unit roots. We show that both frameworks lead to locally asymptotically normal (LAN) experiments with the same central sequence and Fisher information. Using Le Cam's theory of statistical experiments we obtain the local asymptotic power envelope for unit root tests. We show that the popular Moon & Perron (2004) and Bai & Ng (2010) tests only attain the power envelope in case there is no heterogeneity in the long-run variance of the idiosyncratic components. We develop a new test which is asymptotically uniformly most powerful irrespective of possible heterogeneity in the long-run variance of the idiosyncratic components. Monte Carlo simulations corroborate our asymptotic results and document significant gains in finite-sample power if the variances of the idiosyncratic shocks differ substantially among the cross sectional units.
Author: I. Gaia Becheri
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Languages : en
Pages : 0
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This paper considers panels with cross-sectional dependence generated by dynamic common factors as introduced by Bai and Ng (2004, 2010) and known as the PANIC framework. Using limit experiment theory, we derive the (asymptotic) power envelope for testing for unit roots in the PANIC framework. We obtain the local asymptotic power functions of two of the most popular "second generation" panel unit root tests: those proposed in Moon and Perron (2004) and Bai and Ng (2004, 2010). We show that: i) these tests are asymptotically equivalent, and ii) only attain the power envelope in case the long-run variances of the idiosyncratic components in the PANIC framework are homogeneous. Moreover, we propose a new test that is asymptotically UMP, i.e. whose power function attains the envelope irrespective of possible heterogeneity in the long-run variances. A Monte Carlo study demonstrates that our asymptotic results provide excellent approximations to finite-sample distributions.
Author: Hyungsik Roger Moon
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Languages : en
Pages : 0
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This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data is generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We also show that these tests have no power against the same local alternatives when it is necessary to remove deterministic components. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.
Author: I. Gaia Becheri
Publisher:
ISBN:
Category :
Languages : en
Pages : 23
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In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007) presents an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon, Perron, and Phillips (2007), a pooled GLS based-test using the Breitung and Meyer (1994) device, and a new test based on the asymptotic structure of the model, are all asymptotically UMP. Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.
Author: G. S. Maddala
Publisher: Cambridge University Press
ISBN: 9780521587822
Category : Business & Economics
Languages : en
Pages : 528
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Book Description
A comprehensive review of unit roots, cointegration and structural change from a best-selling author.
Author: I. Gaia Becheri
Publisher:
ISBN:
Category :
Languages : en
Pages : 18
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Author: David Bowman
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Category :
Languages : en
Pages : 0
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In this paper the class of admissable tests for unit roots in panel data sets of autoregressive, Gaussian time series will be partially characterized. Using this characterization, several recently suggested tests are shown to be inadmissable. Since the sufficient statistic for this testing problem is multidimensional, there is no uniformly most powerful test, however, in light of the inadmissability result, a new test is proposed that appears to do well relative to existing tests. The test is parameterized in a way that allows the choice of different directional deviations from the null hypothesis over which power is to be maximized, giving added flexibility to researchers.
Author: Graham Elliott
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
This paper derives the asymptotic power envelope for tests of a unit autoregressive root for various trend specifications and stationary Gaussian autoregressive disturbances. A family of tests is proposed, members of which are asymptotically similar under a general 1(1) null (allowing nonnormality and general dependence) and which achieve the Gaussian power envelope. One of these tests, which is asymptotically point optimal at a power of 50%, is found (numerically) to be approximately uniformly most powerful (UMP) in the case of a constant deterministic term, and approximately uniformly most powerful invariant (UMPI) in the case of a linear trend, although strictly no UMP or UMPI test exists. We also examine a modification, suggested by the expression for the power envelope, of the Dickey-Fuller (1979) t-statistic; this test is also found to be approximately UMP (constant deterministic term case) and UMPI (time trend case). The power improvement of both new tests is large: in the demeaned case, the Pitman efficiency of the proposed tests relative to the standard Dickey-Fuller t-test is 1.9 at a power of 50%. A Monte Carlo experiment indicates that both proposed tests, particularly the modified Dickey-Fuller t-test, exhibit good power and small size distortions in finite samples with dependent errors.
Author: George Kapetanios
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Feng Qu
Publisher: World Scientific
ISBN: 9811220794
Category : Business & Economics
Languages : en
Pages : 167
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Book Description
This book aims to fill the gap between panel data econometrics textbooks, and the latest development on 'big data', especially large-dimensional panel data econometrics. It introduces important research questions in large panels, including testing for cross-sectional dependence, estimation of factor-augmented panel data models, structural breaks in panels and group patterns in panels. To tackle these high dimensional issues, some techniques used in Machine Learning approaches are also illustrated. Moreover, the Monte Carlo experiments, and empirical examples are also utilised to show how to implement these new inference methods. Large-Dimensional Panel Data Econometrics: Testing, Estimation and Structural Changes also introduces new research questions and results in recent literature in this field.
