Statistical analysis of cointegration vectors¶
Why this mattered¶
Johansen’s 1988 paper mattered because it turned cointegration from a largely pairwise or residual-based idea into a full system-wide statistical framework. Earlier work, especially Engle and Granger’s 1987 representation theorem and two-step method, had shown why cointegrated nonstationary series could be modeled without losing long-run equilibrium information. Johansen’s contribution was to show how cointegration vectors could be estimated and tested inside a vector autoregression using maximum likelihood and the reduced-rank structure of the error-correction form. This made the number of cointegrating relationships itself an estimable object, rather than something imposed or inferred indirectly.
The paradigm shift was practical as much as theoretical: after Johansen, researchers could analyze multiple integrated macroeconomic or financial variables as a coherent dynamic system, test for the rank of long-run relations, and estimate several cointegration vectors jointly. That opened a path for empirical work on money demand, exchange rates, term structures, purchasing power parity, and other settings where economic theory predicts long-run equilibria among variables that individually wander over time. The paper helped make vector error-correction models a standard tool in applied econometrics.
Its influence also lies in how it connected time-series econometrics to later breakthroughs in structural and empirical macroeconomics. Johansen’s likelihood-based cointegration analysis provided a disciplined way to separate long-run restrictions from short-run adjustment dynamics, which later work extended through deterministic trends, weak exogeneity, structural restrictions, and broader VECM methodology. In that sense, the paper did not merely add a test; it helped define how economists would treat nonstationarity as information about equilibrium structure rather than as a nuisance to be differenced away.
Abstract¶
(no abstract available)
Related¶
- cite → Distribution of the Estimators for Autoregressive Time Series with a Unit Root — Johansen's cointegration analysis cites Dickey-Fuller unit-root theory as the time-series foundation for testing nonstationarity.
- cite → Co-Integration and Error Correction: Representation, Estimation, and Testing — Johansen's cointegration analysis builds on Engle and Granger's claim that cointegrated nonstationary series admit an error-correction representation.
- cite ← MAXIMUM LIKELIHOOD ESTIMATION AND INFERENCE ON COINTEGRATION — WITH APPLICATIONS TO THE DEMAND FOR MONEY — Johansen and Juselius build directly on Johansen's statistical analysis of cointegration vectors to perform maximum-likelihood inference in vector autoregressions.
- cite ← Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models — Johansen's 1991 paper builds on his 1988 likelihood-based statistical analysis of cointegration vectors in vector autoregressive systems.
- enables ← Distribution of the Estimators for Autoregressive Time Series with a Unit Root — Dickey and Fuller's unit-root asymptotics supplied the nonstationary time-series foundation Johansen needed to derive likelihood tests for cointegration vectors.