I'm wondering how to interpret Okun’s coefficient. Say you have $y^c = -1*u^c$. This means that a 1% increase in the cyclical unemployment gap will produce a 1% decrease in the cyclical output gap. And if we had $y^c = -2*u^c$, this means that a 1% increase in the cyclical unemployment gap will produce a 2% decrease in the cyclical output gap. The “-2” regime therefore looks more contractionary.
However if we renormalize the equations we have respectively,
$u^c = -1*y^c$ [renormalized -1 case]
$u^c = -0.5*y^c$ [renormalized -2 case]
Here the -2 case looks the least contractionary, since a 1% fall in the cyclical output gap will only produce a rise of 0.5% in unemployment.
In one case a scenario is most contractionary and in the other least contractionary.
Can anyone lift my confusion?