FINITE‐SAMPLE SIZES OF JOHANSEN's LIKELIHOOD RATIO TESTS FOR COINTEGRATION

FINITE‐SAMPLE SIZES OF JOHANSEN's LIKELIHOOD RATIO TESTS FOR COINTEGRATION INTRODUCTION Since the work of Engle and Granger (1987) and Granger (1986), there has been a surge of interest in cointegration analyses of equilibrium relationships between non-stationary economic variables. While non-stationary economic series can wander widely through time, economic theory often suggests that specific sets of variables should obey certain long-run equilibrium constraints. If the individual economic series are stationary only after differencing but a linear combination of their levels is stationary, then the series are said to be cointegrated. An approach to analyze cointegrated systems due to Johansen (1988, 1991) has received much attention recently. Johansen proposes a maximum likelihood (ML) method for estimating long-run equilibrium relationships or cointegrating vectors and derives likelihood ratio (LR) tests for cointegration in a Gaussian vector error correction modeL' Phillips (1991), examining the distributional properties of the ML estimator of cointegrating vectors, shows that the ML estimator is super-consistent, symmetrically distributed, and median-unbiased asymptotically, and that an optimal theory of inference applies. An issue concerns the performance of the ML cointegration analysis in finite samples. The LR tests for cointegration is derived from asymptotic results and statistical inferences in finite samples may not be appropriate. In particular, the critical values based http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Oxford Bulletin of Economics & Statistics Wiley

FINITE‐SAMPLE SIZES OF JOHANSEN's LIKELIHOOD RATIO TESTS FOR COINTEGRATION

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Publisher
Wiley
Copyright
© 1993 Blackwell Publishing Ltd
ISSN
0305-9049
eISSN
1468-0084
DOI
10.1111/j.1468-0084.1993.mp55003003.x
Publisher site
See Article on Publisher Site

Abstract

INTRODUCTION Since the work of Engle and Granger (1987) and Granger (1986), there has been a surge of interest in cointegration analyses of equilibrium relationships between non-stationary economic variables. While non-stationary economic series can wander widely through time, economic theory often suggests that specific sets of variables should obey certain long-run equilibrium constraints. If the individual economic series are stationary only after differencing but a linear combination of their levels is stationary, then the series are said to be cointegrated. An approach to analyze cointegrated systems due to Johansen (1988, 1991) has received much attention recently. Johansen proposes a maximum likelihood (ML) method for estimating long-run equilibrium relationships or cointegrating vectors and derives likelihood ratio (LR) tests for cointegration in a Gaussian vector error correction modeL' Phillips (1991), examining the distributional properties of the ML estimator of cointegrating vectors, shows that the ML estimator is super-consistent, symmetrically distributed, and median-unbiased asymptotically, and that an optimal theory of inference applies. An issue concerns the performance of the ML cointegration analysis in finite samples. The LR tests for cointegration is derived from asymptotic results and statistical inferences in finite samples may not be appropriate. In particular, the critical values based

Journal

Oxford Bulletin of Economics & StatisticsWiley

Published: Aug 1, 1993

References

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