Okun's law, cointegration and gap variables

If output and unemployment are cointegrated, and we equate Okun's "potential" magnitudes with the stochastic trend or "permanent" component in output and unemployment, (both defined in terms of the Beveridge and Nelson decomposition), then Okun's coefficient can be interpreted as the cointegrating coefficient between the variables. In addition output and unemployment "gaps" can be calculated from the vector equilibrium correction model linking the two variables.