Multipliers in a monetary union and at the ZLB

For macroeconomists

My recent post reminded me that I had earlier promised to talk about a paper by Farhi and Werning. Its an excellent and very rich paper, but this in my area which means I’m biased, so let me single out one point that should be of general interest to macroeconomists. We all should know, from Woodford for example, that in a closed economy at the zero lower bound (ZLB) the (temporary) government spending multiplier is greater than one. It is tempting to apply the same logic to a member of a monetary union, because if they are small relative to the union as a whole they too face a fixed nominal interest rate. What Farhi and Werning show is that this is incorrect, and I’ll try and explain why. (The authors also focus on this point in their paper, so the first best option is to read their paper, particularly as their intuition for the result is a little different - although I believe quite consistent - with the one I give here.)

Let me first recap on Woodford’s closed economy result. If real interest rates are constant, consumption smoothing ties current consumption to its steady state value, and the temporary increase in government spending has no impact on the steady state. So current consumption is unchanged, and we get an output multiplier of one. (I make the same point in a related two period setup here.) With intertemporal consumption, income effects really do not matter, so we can ignore them. [1] At the ZLB nominal interest rates are fixed, so any increase in output will generate some inflation, reducing real interest rates. Lower real rates will increase current consumption relative to its steady state, so the multiplier exceeds one.

Now why does the same logic not work in a monetary union? The key point is that nominal exchange rates are fixed, which implies that in steady state the price level has to return to its original level to keep competitiveness unchanged. So if inflation rises today, it must fall (relative to the base case) later. With fixed nominal rates, we now have lower real rates followed by a matching period of higher real rates. Working backwards from the steady state, we have a period of rising consumption, preceded by a period of falling consumption, with the impact effect being zero. So in a monetary union, consumption gradually falls, and then rises again, but is always below its initial and steady state level.

Neat isn’t it! Now to relate this to the real world we would want to add lots more things, and the paper does show that with credit constrained consumers the monetary union multiplier can exceed one. But this key difference between a monetary union and a closed economy remains. And of course we are assuming here that consumers realise that in a monetary union higher inflation today will be offset by lower inflation later on, a presumption which some in periphery countries in particular might want to question.

Yet if you think about the logic here, it depends crucially on prices being allowed to rise in the long run in the closed economy case. Suppose instead that the monetary authorities operated a long run price level targeting regime. Now any inflation generated by higher government spending today would require a later period in which inflation was below base to offset it. So lower real interest rates at the ZLB would be offset by higher (than steady state) real interest rates later on as the central bank reduced the price level back to target. We would get something more like the monetary union result. [2]

So the closed economy multiplier is lower with price level targeting. Of course price level targeting (or its equivalent) in itself does help at the ZLB, for exactly the same reason. At the ZLB it is generally assumed that inflation is below steady state, so real interest rates are high, which with inflation targeting just depresses consumption. But with price level targeting, low inflation today will be matched by high inflation and low real rates after the ZLB constraint is lifted, which supports current consumption. Just as price level targeting dampens the impact of a negative demand shock at the ZLB, so it dampens the impact of a positive demand shock like fiscal expansion at the ZLB. The government spending multiplier is still positive, but now below rather than above one. Fiscal stimulus at the ZLB is also beneficial because it reduces the extent inflation has to rise after the ZLB constraint has lifted under a price targeting type regime.

So this is another example of why you cannot assess the potency of fiscal policy without taking into account the monetary policy regime. The other crucial implication for Eurozone policymakers is that in standard state of the art models countercyclical fiscal policy is effective. (I also think its desirable, but I agree effectiveness is a necessary but not sufficient condition for desirability.) But of course they all know that, don’t they! 

[1] Note, however, that the multiplier of one means that human wealth has not changed anyway, because the additional output=income exactly offsets the higher tax bill.

[2] It is not exactly the same, because a monetary union involves forever fixed nominal rates: inflation falls later through competitiveness effects. In a closed economy with a price level target inflation falls, and real interest rates rise, because the central bank puts up nominal interest rates.