Dynamic panel Anderson-Hsaio estimation with roots near unity
Dynamic panel Anderson-Hsaio estimation with roots near unity
Limit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson-Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T ) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample size n→ ∞ But when T→ ∞, either for fixed n or as n→ ∞, IV is √T consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy as n→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T )→ ∞with no restriction on the divergence rates of n and T. When the common autoregressive root p = 1+c/√T the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is √n consistent for fixed T and √nT consistent with limit distribution N (0,4) when n,T→ ∞sequentially or jointly. These results are robust for common roots of the form P = 1 +c/T γ for all γ ϵ (0,1) and joint convergence holds. Limit normality holds but the variance changes when γ = 1. When γ >1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.
253-276
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
1 April 2018
Phillips, Peter C.B.
f67573a4-fc30-484c-ad74-4bbc797d7243
Phillips, Peter C.B.
(2018)
Dynamic panel Anderson-Hsaio estimation with roots near unity.
Econometric Theory, 34 (2), .
(doi:10.1017/S0266466615000298).
Abstract
Limit theory is developed for the dynamic panel IV estimator in the presence of an autoregressive root near unity. In the unit root case, Anderson-Hsiao lagged variable instruments satisfy orthogonality conditions but are well known to be irrelevant. For a fixed time series sample size (T ) IV is inconsistent and approaches a shifted Cauchy-distributed random variate as the cross-section sample size n→ ∞ But when T→ ∞, either for fixed n or as n→ ∞, IV is √T consistent and its limit distribution is a ratio of random variables that converges to twice a standard Cauchy as n→ ∞. In this case, the usual instruments are uncorrelated with the regressor but irrelevance does not prevent consistent estimation. The same Cauchy limit theory holds sequentially and jointly as (n,T )→ ∞with no restriction on the divergence rates of n and T. When the common autoregressive root p = 1+c/√T the panel comprises a collection of mildly integrated time series. In this case, the IV estimator is √n consistent for fixed T and √nT consistent with limit distribution N (0,4) when n,T→ ∞sequentially or jointly. These results are robust for common roots of the form P = 1 +c/T γ for all γ ϵ (0,1) and joint convergence holds. Limit normality holds but the variance changes when γ = 1. When γ >1 joint convergence fails and sequential limits differ with different rates of convergence. These findings reveal the fragility of conventional Gaussian IV asymptotics to persistence in dynamic panel regressions.
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am Peter Phillips
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ET 2018 Dynamic Panel AH Limit Theory in LUR Case
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Accepted/In Press date: 16 July 2015
e-pub ahead of print date: 22 September 2015
Published date: 1 April 2018
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Local EPrints ID: 419971
URI: http://eprints.soton.ac.uk/id/eprint/419971
ISSN: 0266-4666
PURE UUID: eef6677b-7566-4e4a-b858-52dfceab82c0
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Date deposited: 25 Apr 2018 16:30
Last modified: 15 Mar 2024 19:38
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