So supposedly, the RBNZ has suggested a floating GST rate as a way of controlling inflation. Now this seems silly too me for two reasons:
1) GST is a tax, as a result this would either have to be implemented through fiscal policy (and so would not work, as governments cannot commit to just focusing on inflation), or you would have to give the Bank the right to tax (as the Bank is not elected by the people this is uncomfortable)
2) The level of GST affects the price level, so if the economy is running strongly and you prop it up, you push up the price level.
Now the first criticism is self-evident, however it is a normative problem with the scheme, implying that there might be some theoretical merit. The second criticism is positive. Now, I am not saying that changing the GST tax will cause inflation, as inflation is the rate of change in the price level. Changing the GST tax will change the price level, but not change the rate at which the price level grows, in fact increasing GST will take money out of the economy, slowing growth in the price level and thereby slowing inflation.
So a floating GST tax would slow inflation, however lets think about why we want to slow inflation. We want to reduce volatility in the price level, to give people certainty. Volatility in the price level is bad as the majority of people cannot properly hedge against it. Now by having the GST tax increase and fall we are adding volatility to the price level, causing one of the problems that monetary policy is supposed to solve. It just seems a bit silly.