Hello,
My dependent variable is I(0) and my independent variables are I(1) - all variables in logs. Can I still run a cointegrating regression keeping both the dependent variables in levels although they are of different order? I want to do that in order to be able to estimates elasticities. If I do that, will the @johmle still provide valid statistics for evaluating the results?
Thank you in advance for your help.
Petros
Cointegration, dependent variable of different order
Re: Cointegration, dependent variable of different order
If the dependent variable is stationary and the explanatory variables aren't, then you better hope that the explanatory variables are cointegrated (either that, or they are included in differences, but that doesn't sound like what you're doing).
If you apply @JOHMLE or CATS (CATS is probably better for this) to the collection of an I(0) y and I(1) x1 and x2, the cointegrating rank would be expected to be two: y by itself is "cointegrated" and (one hopes) x1 and x2 are.
If this is demand on the LHS and two prices on the RHS, wouldn't it make more sense to standardize the prices by some overall measure of price level to get the trend out while keeping the same relative prices at any given time period? What will happen in practice is that the cointegrating vector for x1 and x2 will attempt to get rid of the common trend, but will do so with some statistical error.
If you apply @JOHMLE or CATS (CATS is probably better for this) to the collection of an I(0) y and I(1) x1 and x2, the cointegrating rank would be expected to be two: y by itself is "cointegrated" and (one hopes) x1 and x2 are.
If this is demand on the LHS and two prices on the RHS, wouldn't it make more sense to standardize the prices by some overall measure of price level to get the trend out while keeping the same relative prices at any given time period? What will happen in practice is that the cointegrating vector for x1 and x2 will attempt to get rid of the common trend, but will do so with some statistical error.
Re: Cointegration, dependent variable of different order
Tom thank you for your answer. The price is the dependent variable, the independent variables are demand and supply variables. If I understood well your answer I should run the Johansen MLE procedure with the independent variables only and hope to get indications that they are cointegrated. If that is the case I assume I could run an OLS with the dependent I(0) and the indpendent variables I(1) without worrying that the estimated coefficients may be biased because of the spurious regression problem.
Thank you for your time.
Petros
Thank you for your time.
Petros
Re: Cointegration, dependent variable of different order
I(0) on I(1) isn't a spurious regression. That's I(1) on I(1) where even if the series are independent, the R^2 doesn't converge to zero. With I(0) on I(1), the only way to make the right side stationary (if the two series aren't cointegrated) is to give them zero coefficients. They will converge to zero, typically, very, very quickly. (The coefficients will also have non-standard distributions).