Let suppose an equation
Yt = a + b1Xt + b2Zt + b3Ft + e where Y is the dependent variable and X, Z and F are independent variable. If johansan cointegration shows 2 cointegrating vectors then should OLS be used to estimate the long run coefficient or OLS would be biased?
Thanks in advance.
The maximum no. of cointegration rank should be one less than the number of variables. There will be two cointegrating equations. Use VECM instead of OLS to estimated both long and short run relationship.
Thank you all. It means If i have only 1 focused equation with multiple independent variable with more than 1 cointegrating vectors, OLS would be appropriate. By using VECM, coefficients would not be interpreted. Please suggest.
The results of your unit root rests will determine whether Johansen or Bounds test approach to cointegration would be used.
Thank you Dr. Micheal. I have asked this with the assumption that Johansen test is suitable for cointegration. JUst want to know that if Johansen test sjows 2 cointegrating vectors then should we OLS for coefficients?
I would say, YES. With two cointegrating equations, there is long run relationship among the variables.
Well OLS will not be appropriate for two cointegrating vector. If you carried out the unit root test and all the variables under study were stationary at the same level or at the same order of integration say I(1). Then use VAR but if they were stationary at different level or order of integration VECM will be the appropriate technique.
Dear Dr. Ebiwonjumi, thank you very much for your response. may i ask about illness in regression model while using OLS having 2 cointegrating vector?
One of the major assumption to be satisfied before one can use OLS is the homoskedasticity which can be term as constant variance. The lack of constant variance among the variables is what led to the non stationary of the variables and this lead to the test for cointegration. Thus, the violation of any assumptions of the linear model render the use OLS in efficient in estimating the parameters of the linear model.
From the problem stated, the variables were not stationary in level that is why the author went ahead with necessary checks and test for cointegration. The use of OLS to estimate the long run relationship will produce bias coefficients. For the long run relationship use the first cointegrating equation from the cointegrating result and do the necessary adjustment . Divide the coefficients with the respective standard error to obtain the t-statistics for you to determine if a coefficient is significant or not.
Dear Dr. Havi, thank you for your response. Problem is, should we run OLS with 2 cointegrating vector or not?
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