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Estimation of Dynamic Models with Error Components

T. W. Anderson and Cheng Hsiao
Journal of the American Statistical Association
Vol. 76, No. 375 (Sep., 1981), pp. 598-606
DOI: 10.2307/2287517
Stable URL: http://www.jstor.org/stable/2287517
Page Count: 9
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Estimation of Dynamic Models with Error Components
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Abstract

Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved dynamic process with initial value random. Asymptotic properties of the maximum likelihood and "covariance" estimators are obtained when T → ∞ and when N → ∞. The relationship between the pseudo and conditional maximum likelihood estimators is clarified. A simple consistent estimator that is independent of the initial conditions and the way in which T or N → ∞ is also suggested.

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