I have two cointegrated equations (each uses a different, but plausible, combination of explanatory variables) and have verified cointegration using the standard tests. Both equations are of the form below, though the vector X has different elements across each equation:
ΔYt = a + b0*ΔYt-1 + b1*ΔXt-1 + b2*(Yt-1 - b3Xt-1) + et
For the first equation, the b2 is positive (and significant). I understand that we need b2 to be less than or equal to zero for the equation to make sense in the long run since it does not converge under a positive b2.
For the second equation, b2 is negative (and significant) but every coefficient in b3 is not significant.
Hence, does this mean that a cointegrating relationship with Y and both combinations of X is really not supported by the data?
ΔYt = a + b0*ΔYt-1 + b1*ΔXt-1 + b2*(Yt-1 - b3Xt-1) + et
For the first equation, the b2 is positive (and significant). I understand that we need b2 to be less than or equal to zero for the equation to make sense in the long run since it does not converge under a positive b2.
For the second equation, b2 is negative (and significant) but every coefficient in b3 is not significant.
Hence, does this mean that a cointegrating relationship with Y and both combinations of X is really not supported by the data?
