NGDP targeting and the Taylor Rule

Chris Waller pointed out to me this morning that the NGDP target is formally equivalent to a special case of the Taylor rule. (Maybe this is generally known? I don't know.)

The argument goes as follows. Let R denote the nominal interest rate. Then the NGDP target proposes a monetary policy rule of the form:

R = R* + [log(NGDP) - log(NGDP*)]

where the starred variables denote targets.  So the rule above raises the interest rate when NGDP is above target and lowers the interest rate when NGDP is below target.

Of course, NGDP = PY, so log(NGDP) = log(P) + log(Y).

Thus, we may rewrite our policy rule in the following way:

R = R* + [log(P) +log(Y) - log(P*) - log(Y*)]

Now add and subract the lagged value of log(P) from the RHS of the equation above to get:

R = R* + [log(P) - log(P-) +log(Y) - log(P*) + log(P-) - log(Y*)]

or

R = R* + A*[log(P/P-) - log(P*/P-)]  + B*[log(Y) - log(Y*)]

So the NGDP targeting rule proposes to adjust the nominal interest rate in terms of the prevailing inflation and output gaps, with weights A = B = 1.

It seems surprising that the solution A=B=1 is generically robust. But maybe it is. In many models, A>1 is required for stability. This is the so-called Taylor principle. It is also a property of learning models; see Howitt 1992.

So maybe the NGDP targeting crowd is just saying that A should be lowered and B increased? Is that it? Have to rush off to a meeting...