I feel I ought to know the answer to this question. But I don't.

Suppose that demand this period Y(t) depends on the interest rate this period r(t), **and on the expected interest rate next period E[r(t+1)]**, and on a vector of other stuff X(t).

Y(t) = D(r(t), E[r(t+1)], X(t)) where D_{1} < 0, D_{2} < 0.

Adding the expected future interest rate seems to me to be a reasonable assumption.

The rest of the model can be a standard New Keynesian model of an inflation-targeting central bank.

There are two parallel worlds:

In the first world, the central bank sets r(t) at time t, conditional on its information I(t).

In the second world, the central bank sets r(t+1) at time t, conditional on its information I(t). Each period it makes an unconditional commitment about what interest rate it will set next period, and carries out the commitment it made the previous period.

Which central bank will be able to keep inflation closer to target? What does it depend on? Why does the real world usually look like the first world, rather than the second world?

I think that the answer probably has something to do with the exact nature of the demand function D(.), and the central bank's uncertainty about some elements in the vector X(t). But what precisely? Simple examples would be good.

[Engineers: yes, this does look like a control problem; which of the two levers is most useful for keeping demand as constant as possible? But remember that people have expectations, so it *might* not be *exactly* the same as controlling a machine.]

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