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Autoregressive Errors in Singular Systems of Equations

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  • Dhrymes, Phoebus J.

Abstract

We consider a system of m general linear models, where the system error vector has a singular covariance matrix owing to various “adding up” requirements and, in addition, the error vector obeys an autoregressive scheme. The paper reformulates the problem considered earlier by Berndt and Savin [8] (BS), as well as others before them; the solution, thus obtained, is far simpler, being the natural extension of a restricted least-squares-like procedure to a system of equations. This reformulation enables us to treat all parameters symmetrically, and discloses a set of conditions which is different from, and much less stringent than, that exhibited in the framework provided by BS. Finally, various extensions are discussed to (a) the case where the errors obey a stable autoregression scheme of order r; (b) the case where the errors obey a moving average scheme of order r; (c) the case of “dynamic” vector distributed lag models, that is, the case where the model is formulated as autoregressive (in the dependent variables), and moving average (in the explanatory variables), and the errors are specified to be i.i.d.

Suggested Citation

  • Dhrymes, Phoebus J., 1994. "Autoregressive Errors in Singular Systems of Equations," Econometric Theory, Cambridge University Press, vol. 10(2), pages 254-285, June.
    • Handle: RePEc:cup:etheor:v:10:y:1994:i:02:p:254-285_00
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    1. repec:ebl:ecbull:v:3:y:2005:i:54:p:1-3 is not listed on IDEAS
    2. Harry Haupt & Walter Oberhofer, 2005. "On autoregressive errors in singular systems of equations," Economics Bulletin, AccessEcon, vol. 3(54), pages 1-3.
    3. Dhrymes, Phoebus J., 1998. "Identification and Kullback information in the GLSEM," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 163-184.
    4. Gonzalo, Jesus & Lee, Tae-Hwy, 1998. "Pitfalls in testing for long run relationships," Journal of Econometrics, Elsevier, vol. 86(1), pages 129-154, June.
    5. Sansi Yang & C. Richard Shumway, 2020. "Knowledge accumulation in US agriculture: research and learning by doing," Journal of Productivity Analysis, Springer, vol. 54(2), pages 87-105, December.

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