The RBNZ's dilemma

I've been thinking about the Reserve Bank's current predicament, and found the following framework helpful to sort out the issues in my own mind. It's a kind of IS-LM approach.

As graphed above, for any given inflation target there is a range of possible combinations of the cash rate and  the value of the Kiwi dollar that would be consistent with the target. Three illustrative combinations are shown above, for inflation targets of 1%, 2% and 3%. These combinations slope downwards to the right, reflecting the fact that a lower cash rate would require a higher NZ$ to maintain the same degree of overall monetary policy pressure on inflation, and are flattish, in that interest rates are probably the more powerful instrument, so that a relatively small change in cash rate would require a relatively large change in the NZ$.

Let's assume that there's some sort of at least short-term relationship between the cash rate and the exchange rate - it's not settled in macroeconomics (as far as I know) that there is a stable longer-term relationship, with a coefficient of known sign, between local interest rates and the exchange rate. It's plausible that there is an inverse relationship (overseas investors require higher interest rates to accept the risk of a weakening currency); one can also imagine a positive relationship (in current conditions, any currency offering even modestly higher interest rates is likely to get swamped by inflows from zero-interest-rate economies). For the sake of argument, let's assume, realistically, that at least for now higher local interest rates would lead to a higher Kiwi dollar, giving us the R$0 line in the graph below. At the RBNZ's chosen cash rate C0, the financial markets will set an exchange rate of $0.

Now let's suppose that overseas monetary policy becomes easier (as has just happened in Japan). The R$0 line shifts outwards to the right, to R$1: for any given cash rate, the Kiwi dollar is now more attractive than before, as its relative interest differentials have widened. It will appreciate, as shown in the graph below.

So here's the RBNZ's dilemma. If it keeps the cash rate at C0, monetary policy will be too tight: at the exchange rate $1 that corresponds to C0, inflation will be lower than 2%. To stay on track for 2% inflation, the RBNZ ought to cut the cash rate to C* (to get back on the P = 2% line), which will reduce the exchange rate to $*. But the new C*$* combo is a move rightwards along the P = 2% line, away from C0$0, with lower interest rates and a higher currency than before, making both of its problems (frothy housing and uncompetitive exporters) worse.

Fortunately, the Bank's got a bit of leeway: it doesn't have to keep inflation strictly at 2%. It's got a band of 1% to 3% to work with (on average aiming at a longer term average of 2%). Where the logic of things leads you to, though, is this: in current markets, the Bank will need to use this leeway, and let inflation undershoot 2% for some time.