Multipliers from Eurozone periphery austerity

For macroeconomists

We often see graphs relating fiscal consolidation to output growth since the Great Recession. Despite such scatter plots being very weak evidence, they appear to show that fiscal multipliers in the periphery countries like Greece have been very large indeed. At first sight this is not difficult to explain. These countries do not have their own monetary policies, and to the extent that fiscal consolidation reduces local inflation, real interest rates will rise, which increases the fiscal multiplier.

Unfortunately the basic New Keynesian (NK) model suggests this reasoning is incorrect, as Farhi and Werning show for temporary changes in government spending. While real rates might rise in the short run following a negative government spending shock, being in a monetary union ties down the long run price level in these economies. So, other things being equal, a negative government spending shock that reduces inflation now will be followed by higher inflation (compared to the no shock case) later, as the real exchange rate self-corrects. That in turn means that fiscal consolidation in the form of temporary cuts to government spending will produce a small rise in consumption for a period after the shock. (Consumption depends on the forward sum of future real interest rates, so as time progresses lower future rates dominate this sum.)

Of course that may simply mean that the basic NK model is incorrect or incomplete. As Farhi and Werning show in the same paper, with some credit constrained consumers we can get back to positive short term consumption multipliers, and therefore output multipliers greater than one. But it occurred to me, just before I was about to discuss this paper in an advanced macro graduate class, that the basic NK model could still give us what appeared to be large multipliers without such additions.

What we had in periphery countries was not just a government spending shock. In Ireland and Greece at least, that spending shock was preceded by a government debt shock. Either the government admitted to borrowing more than the official data suggested, or it had to bail out the banks. We can think of at least two types of response to a pure government debt shock. It could lead to a short sharp contraction in spending, in which case the analysis of Farhi and Werning would apply. Alternatively the government accepts that its debt will be permanently higher, and it only plans to cut spending or raise taxes to pay the interest on that additional debt.

In the latter case, assume that a significant proportion of that extra debt was owned overseas. We would have a permanent transfer from domestic to overseas citizens, and that would require a permanent depreciation in the real exchange rate. An increase in competitiveness is needed to make up for the permanently lower level of domestic demand that these transfers would produce. That in itself produces a terms of trade loss that impacts on consumption. But in addition in a monetary union, that depreciation would have to come about through a period of lower inflation, which would lead to a period in which real interest rates were higher. That in turn would decrease consumption, with the peak effect when the debt shock happened.

This is probably already written down somewhere, but it does explain why you could get apparently large multipliers in Greece and Ireland even if the simple NK model was broadly correct. What we had was a combination of a negative government spending shock and a positive government debt shock, and the latter could have led to significant falls in consumption. For these economies at least, true government spending multipliers may not be as large as they appear.

There I go again, choosing my economics to get the answer I want. Oh, wait ….

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. 

Multipliers, inflation and another response to Tyler Cowen on UK austerity

Tyler Cowen points us to a nice paper by Emmanuel Farhi and Ivan Werning on multipliers. The authors had been good enough to send me a copy earlier, so I can respond quickly. The paper contains some neat analysis, but I just want to focus on one point that Tyler mentions, which may appear counterintuitive at first, but is in fact quite a simple idea. I then want to argue against the implications for the UK that Tyler draws.

The authors focus on the ‘consumption multiplier’, which is the impact of government spending on consumption. So in a closed economy a consumption multiplier of zero is a government spending multiplier of one (there is no capital). This point is not clear from Tyler’s post.

As I have discussed before, and various papers by Eggertsson and Woodford (among others) have explored in detail, at the zero lower bound the consumption multiplier can be positive because higher output raises inflation which reduces real interest rates. The point the authors make is that the further into the future the increases in government spending are, the more powerful is this effect (as long as the zero lower bound constraint is still there). This may seem odd, but it follows simply from the properties of the New Keynesian Phillips curve.

Suppose I can increase output today or tomorrow. The New Keynesian Phillips curve basically says inflation today depends on expected inflation tomorrow and the output gap today[1]. Additional output tomorrow will raise inflation tomorrow. However it also raises inflation today because it raises expected inflation. Higher output today only raises inflation today. So for given nominal interest rates, higher output tomorrow gives me two periods of lower real interest rates, while higher output today just gives me one. A one-off addition to government spending tomorrow, because it raises output tomorrow, gives me a greater impact on real interest rates and therefore consumption than the same one-off increase in government spending today.

Does this have any new implications for the debate of UK austerity? I see things very differently from Tyler. Let’s take his initial points in turn.

1. This is where the confusion over the output and consumption multiplier comes in. Suppose we are highly uncertain about the impact fiscal or monetary policy has on inflation right now. That makes monetary policy’s impact very uncertain, but with government spending on domestic goods you get an output multiplier of one for sure.
2. Again, this is the inflation effect, where fiscal tightening reduces inflation, which at the zero lower bound raises real interest rates, leading to an appreciation. However, as Tyler notes, at the same time as 2010 austerity we also had positive inflation shocks. Furthermore, we have little idea of what caused the 2008 depreciation. So movements in the real exchange rate are not a very reliable indicator of anything.
3. I’m not quite sure what advice is being referred to here. What I would take from the timing point discussed in the paper is that you cannot ignore the impact that announcements of future austerity can have on output today. Expectations matter in macro. Those who say most of the cuts have not happened yet so they cannot explain weak UK output ignore this point. What opponents of austerity like me have been arguing for is postponing cuts until a recovery eliminates the zero lower bound constraint. Without that constraint, monetary policy can in principle completely offset the impact of any cuts on output.
4. Not guilty – indeed I have stressed how price stickiness is not the issue at the zero lower bound.
5. Again not guilty – indeed this cannot apply to anyone who uses New Keynesian theory, as the New Keynesian model is an elaboration of the RBC model.

I’ll stop there, except to make two comments. First, the conclusion that Tyler draws just does not stand up. The paper by Farhi and Werning, like much of the literature that this paper refers to, some of which I have talked about before, uses fairly standard New Keynesian models. New Keynesian models imply cuts in government spending reduce output at the zero lower bound. My discussion of this has been as transparent as I can make it. I also take great exception to the implication in (5) that I pick and choose which theory I use in order to support a particular policy position.

Second, there is a lot more that is interesting and important in the Farhi and Werning paper, particularly concerning policy in a monetary union, and I hope to talk about that in a later post.

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[1] It is not exactly the output gap in most models, but this complication is not crucial here.