Is there a mapping between target rule of the form phi.(pi) + y = 0 and reaction function of the form i = max(-ibar/(1+ibar), phip.(pi) + phiy.(y))?

For instance, for a strict inflation target, using phi = 1 in the target rule in equivalent to using phip = 1000000 & phiy = 0 in the reaction function.

Sorry I wasnâ€™t aware I could use Latex code here. My question again with readable formulas:

Is there a mapping between target rule of the form \phi \pi + y = 0 and reaction function of the form i = max\left(-\frac{\bar i}{1+\bar i}, \phi_\pi \pi + \phi_y y \right)?

For instance, a strict inflation target (\pi = 0) is equivalent to \phi \rightarrow \infty in the target rule, and can be implemented using \phi_\pi = 1000000 and \phi_y = 0 in the reaction function in Dynare.

Not that I am aware of. The first obvious issue is the zero lower bound implemented by the max operator. That would require something like a complementary slackness condition. But the big problem is that the targeting rule is a limit case of the reaction function. But you seem to be interested in a general reaction function