I. E-G uses OLS to estimate a cointegrating equation assuming that one variable is endogenous and the regressors are exogenous.
(a) This does not allow for the possible endogeneity of regressors.
• leading to endogeneity bias especially in small sample, cov(x,u) doesn't equal to 0
• indicating cointegration when no relationship exists
(b) Specifying which variable is the dependent variable in the cointegrating equation (which variable is normalised upon)
• can affect inference regarding the existence of an equilibrium relation, in small samples.
Johansen procedure:
(a) Potentially allows all variables specified in the cointegrating equation to be endogenous,
(b) Does not specify which variable(s) is dependent or independent, prior to testing.
II. E-G assumes a single cointegrating vector so cannot identify possible multiple equilibria among the variables. Hence, it is strictly only valid for cointegrating equations involving two variables.
Johansen procedure can identify multiple equilibria among systems with more than two variables.
III. E-G fails to account for short run dynamics when estimating the long run relation. It may cause inaccuracy of estimation and critical values of standard hypothesis tests becoming inappropriate in small samples, for example, because of autocorrelation.
Johansen procedure tests for, and estimates, the cointegrating vectors simultaneously with the short run dynamics. Indeed, the lag length can be chosen to remove evident autocorrelation.
IV. E-G ADF test for cointegration has low power: it tends to reject cointegration when it exists too often.
Shintani (1994) finds that the Johansen procedure has greater power than E-G (1987) in testing for cointegration.
Johansen procedure addresses the above shortcomings of E-G using a VAR in ECM
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[em01][em01]
[biggrin]谢谢诶 啊[biggrin]
