Optimal Estimation of Cointegrated Systems with Irrelevant Instruments

Peter Phillips

No 1547, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: It has been know since Phillips and Hansen (1990) that cointegrated systems can be consistently estimated using stochastic trend instruments that are independent of the system variables. A similar phenomenon occurs with deterministically trending instruments. The present work shows that such “irrelevant” deterministic trend instruments may be systematically used to produce asymptotically efficient estimates of a cointegrated system. The approach is convenient in practice, involves only linear instrumental variables estimation, and is a straightforward one step procedure with no loss of degrees of freedom in estimation. Simulations reveal that the procedure works well in practice, having little finite sample bias and less finite sample dispersion than other popular cointegrating regression procedures such as reduced rank VAR regression, fully modified least squares, and dynamic OLS. The procedure is shown to be a form of maximum likelihood estimation where the likelihood is constructed for data projected onto the trending instruments. This “trend likelihood”” is related to the notion of the local Whittle likelihood but avoids frequency domain issues altogether. Correspondingly, the approach developed here has many potential applications beyond conventional cointegrating regression, such as the estimation of long memory and fractional cointegrating relationships.

Keywords: Asymptotic efficiency; Cointegrated system; Instrumental variables; Irrelevant instrument; Karhunen-Loeve representation; Long memory; Optimal estimation; Orthonormal basis; Trend basis; Trend likelihood (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 44 pages
Date: 2006-01
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1400
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in Journal of Econometrics (January 2014), 178(2): 210-214

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Journal Article: Optimal estimation of cointegrated systems with irrelevant instruments (2014)
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