Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Mar, 1987, Volume 55, Issue 2

Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model<391:ETVRPI>2.0.CO;2-X
p. 391-407

David M. Lilien, Robert F. Engle, Russell P. Robins

The expectation of the excess holding yield on a long bond is postulated to depend upon its conditional variance. Engle's (1982a) ARCH model is extended to allow the conditional variance to be a determinant of the mean and is called ARCH-M. Estimation and inference procedures are proposed and the model is applied to three interest rate data sets. In most cases the ARCH process and the time varying risk premium are highly significant. A collection of LM diagnostic tests reveals the robustness of the model to various specification changes such as alternative volatility or ARCH measures, regime changes, and interest rate formulations. The model explains and interprets the recent econometric failures of the expectations hypothesis of the term structure.

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