Bruce E. Hansen
Johansen's Reduced Rank Estimator is GMM
Econometrics, forthcoming
Abstract:
The generalized method of moments (GMM) estimator of the reduced rank regression model is derived under the assumption of conditional homoskedasticity. We show that this GMM estimator is algebraically identical to the maximum likelihood estimator under normality developed by Johansen (1988). This includes the vector error correction model (VECM) of Engle and Granger. We also show that GMM tests for reduced rank (cointegration) are algebraically similar to the Gaussian likelihood ratio tests. This shows that normality is not necessary to motivate these estimators and tests.
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Some of the above material is based upon work supported by the National Science Foundation under Grants No. SES-9022176, SES-9120576, SBR-9412339, and SBR-9807111.
Any opinions, findings, and conclusions, or recommendations expressed in this material are those of the author(s), and do not necessarily reflect the views of the NSF.