Tax cuts vs spending vs helicopters

Some people still seem unable, or maybe unwilling, to understand the basic New Keynesian (NK) model. Should it be surprising in this model that cutting taxes on wages at the Zero Lower Bound (i.e. when nominal interest rates are fixed) are contractionary? Of course not. The basic NK model contains an intertemporal consumption function that implies Ricardian Equivalence holds, so consumers save all of the extra income they get from a tax cut. But cutting taxes increases the incentive to work, thereby increasing labour supply, which through a Phillips curve decreases inflation. With a fixed nominal interest rate that implies higher real rates, which are contractionary. QED.

Now the main thing not to like here is the consumption function and Ricardian Equivalence. Empirical evidence points strongly to a significant income effect, with a marginal propensity to consume around a third rather than zero. There are good theoretical reasons why you might get this result, even with totally rational consumers. But the implication that cutting taxes will lead to some increase in labour supply seems reasonable, and that will put some downward pressure on inflation. This is why pushing ‘structural reforms’ that expand the supply side in a liquidity trap can be counterproductive in the short term. (Things are more complex when you have a fixed exchange rate.)

Now you may quite reasonably believe that in the real world a positive income effect from a tax cut will raise demand by more than any increase in supply, so inflation will rise and real rates will fall. But it remains the case that as a stimulus measure directly raising demand through higher government spending does not generate this supply side offset. That the NK model has this feature seems like a virtue to me. The only point I have to add is that because helicopter money, as traditionally envisaged, is a lump sum transfer (everyone gets an equal amount, so it is independent of wages), you do not get this offsetting supply side effect. So for that reason helicopter money is more effective as a stimulus instrument in a liquidity trap than cutting taxes on wages.

Multipliers and evidence

I should be more careful with titles. The title of this post may have misled some (including Paul Krugman) to characterise what I was saying as favouring a priori beliefs over evidence. What I was in fact talking about was different kinds of evidence.

One kind of evidence on multipliers comes from directly relating output to some fiscal variable like government spending. In much the same way we could base monetary policy on attempts to relate output or inflation directly to changes in interest rates. This is sometimes called ‘reduced form’ estimation. As I said in my post, these studies are valuable, and if they repeatedly show something different from other evidence that would be worrying. However in my experience I have found them less reliable than evidence based on looking at the structure of the economy. I discuss a personal example here, but two more recent examples where reduced form evidence has not proved robust concern the impact of debt on growth and evidence supporting expansionary austerity.

As I wrote in the recent post: “My priors come from thinking about models, or perhaps more accurately mechanisms, that have a solid empirical foundation.” Again perhaps I was remiss in not emphasising that last clause, but it is critical. Robert Waldmann did interpret what I wrote correctly, but has a more worrying (for me) charge - that my view of what specific structural empirical evidence says is tempered by modern microfounded modelling.

A good example concerns how consumers might react to a temporary increase in income. I wrote that my prior is that consumers will largely discount temporary income changes. But what exactly do I mean by ‘largely’ here? Is a marginal propensity to consume out of temporary income of, say, 0.3 large or not? As I have noted elsewhere, there is good empirical evidence to support a number of that kind, and it is possible to explain this in terms of consumers optimising in the face of uncertainty. 

But the plain vanilla intertemporal consumption model implies a marginal propensity to consume out of temporary income close to (or identical to) zero. So when I wrote “largely discount”, did I in fact temper my knowledge of the empirical evidence because of this basic (and in macro ubiquitous) theory? Or was I attempting to use a form of words which was ambiguous enough not to upset those who did have a strong attachment to the plain vanilla model, which would have been just as bad.

It would be ironic if I had been. On a number of occasions I have argued that it was unfortunate that the microfoundations revolution has completely killed (in the academic literature, if not in all central banks) the alternative of analysing aggregate models where relationships are partly justified by empirical evidence. One of my reasons for believing this to be unfortunate is that it tends to put too much weight on simple theory relative to evidence. When I wrote ‘largely discount’ was I providing an example of just this kind of thing?

If it was, it may only have been a temporary lapse. Paul thinks a multiplier of around 1.5 is reasonable (I assume at the Zero Lower Bound when there will be little or no monetary policy offset), and when I wrote this I also assumed a multiplier of 1.5. However I think the point that Robert was making is a very important one: in macro we seem generally happier falling back on what standard theory says than on what the majority of empirical evidence suggests.     

Faith in multipliers

Economists could skip to the penultimate paragraph

The multiplier is the size of any decrease in output that results from a fiscal contraction (lower government spending or higher taxes), both measured in the same units. Why am I confident that multipliers that result from temporary decreases in government spending in current conditions will be somewhere around one rather than somewhere around zero? It is not because of empirical studies that try to directly estimate multiplier sizes.

Do not get me wrong. Such studies are very important, as are meta studies that try and pull together and synthesise the large number of individual studies. However I tend to use them to either confirm or question my priors. My priors come from thinking about models, or perhaps more accurately mechanisms, that have a solid empirical foundation. Let me explain.

Some of the terminology makes more sense if we talk about an increase in government spending (for example, a new school being built), so from now on I’ll consider that. A multiplier around one means that for every school built GDP increases by the cost of that school (a multiplier of exactly one) plus or minus some private sector expenditure (hence around one). If private sector expenditure falls we talk about it being crowded out, but if private sector spending increases we can talk about that expenditure being encouraged or crowded in by the additional public spending. The first point to note is that by thinking in this way I’m focusing on aggregate demand rather than aggregate supply, which I think is appropriate in the situation we have recently been in. If, in contrast, everyone was already working as much as they could, it might be more natural to start from a multiplier of zero, because the school will have been built with labour that otherwise will have built something else. A multiplier of zero is called complete crowding out.

Will we get crowding in or crowding out? Here my starting point is to note that because the increase in government spending is temporary, any impact on pre-tax income or taxes will be relatively small relative to a consumer’s lifetime income. As a result, aggregate consumption is likely to change either way by an amount that is a lot less than the cost of the school. For similar reasons firms think long term when planning investment, so they are not going to invest that much because of a temporary increase in government spending and GDP. There is a lot more we could say here, but I want to keep it simple.

We next need to think about whether this reasoning could be upset by some change in a price that results from the extra school being built. The two key prices here are the real exchange rate and the real interest rate. My basic model of exchange rates is that they are grounded in some medium term view concerning competitiveness, plus beliefs about what might happen to short term interest rates. If the spending is temporary medium term competitiveness is largely unaffected, so what happens to real interest rates is critical. If they rise as a result of the additional employment required to build the new school, then this might lead to a real exchange rate appreciation. This will reduce the demand for domestically produced goods, and higher real interest rates will also discourage private spending directly. So what happens to interest rates is critical.

This is the second point at which actual circumstances are important. Nominal interest rates have been stuck at their Zero Lower Bound, which suggests that they would be quite likely to remain there despite any increase in employment generated by our additional school. If the additional GDP adds a bit to inflation, real interest rates might actually fall, leading to crowding in. (The point is reinforced if we reverse the sign and think about fiscal austerity - central banks will be unable to cut rates to offset austerity’s impact.)

That is where my priors come from: thinking about the structure of the economy, and situation we are in and the nature of the experiment involved. The problem for empirical studies that directly relate changes to output to changes in government spending is that they face huge difficulties in relating the data to particular circumstances and the kind of experiment involved. For example, is any increase in government spending observed in the data expected to be temporary (with relatively minor consequences for tax) or permanent (with implications for tax that could lead to complete crowding out as a result of lower consumption)? Some studies try and take account of this by focusing on shocks to spending, but that is not quite the same thing. (A new school will tend to raise GDP whether it is expected or not.) Even if the change in government spending is expected to be temporary, if any additional borrowing is paid for by cutting future spending rather than increasing taxes this will in theory make some difference.

Up until recently studies have not really controlled for monetary policy, which as we saw was crucial. This recent study from the IMF is an exception, although if you read it you will see just how difficult trying to control for monetary policy actually is. They find that monetary policy does have a large influence, which fortunately agrees with the analysis above. What some earlier studies have shown (I’ve often referenced a study by Jorda and Taylor, but here is another, and a meta analysis is here) is that multipliers tend to be larger when economies are depressed. What has not been clear is whether this is picking up a monetary policy effect (if economies are depressed, monetary policy is unlikely to try and offset the impact of any fiscal expansion), or whether it is picking up something else (for example, multipliers could be larger in a recession because more consumers are credit constrained). This IMF study, which is just based on US data and which does allow for monetary policy, finds no additional depressed economy effect. It will be interesting to see if that result proves robust to alternative treatments of monetary policy and data for other countries.         

Fiscal policy, correlations and causation

I have a sense that Paul Krugman wrote this post out of exasperation with those who cherry pick data to draw incorrect conclusions about the importance of fiscal policy. I know the feeling. Here is my version of what Paul did, using OECD data. We take growth in government consumption (G) [x axis] and GDP [y axis] for a whole bunch of countries for each year from 2010 to 2013, and plot the two variables against each other.

Paul’s point in that post was not that this positive correlation proves fiscal policy matters, but that there is a lot of variation, and so it will always be possible to find a case where G fell and GDP rose, or vice versa, but the general pattern is that the two variables are positively correlated.

I think that is as far as this should go. As Paul also said, you can quite legitimately argue that the relationship is not causal. Here is a very good argument about why it will not be. Imagine an ideal world where growth was always steady, and everything generally went according to plan, but some countries grew faster than others. If every country planned to keep the ratio of G to GDP constant, in the fast growing countries you would be likely to see high growth in both GDP and G, while in the others you would expect slower growth in both variables. What you would observe is lots of points close to a 45 degree line. This would tell you nothing about how a shock to G would influence Y. If you tried to read the 45 degree line as telling you about a G multiplier you would get implausibly large numbers.

This is not an academic point. Look at the three points involving 8% or more growth. They are for Estonia and Turkey. Growth in G in those cases happened to be quite low but positive, but no one would seriously suggest that this meant there was a huge multiplier in those countries. But these observations drag any trend line to be closer to 45 degree line. Indeed any trend line fitted to this data would come close to having that slope.

The other extreme numbers on the negative side are mainly Greece. Now there this reverse causation argument is less convincing: we know that negative growth in Greece did not cause the Greeks to reduce government spending. However the correlation there can still not be taken as causal because of another elementary econometric problem: omitted variables. Austerity did not just involve cuts in government consumption, but many other fiscal variables that will also have had a large impact on GDP.

All this is of course why people do proper econometrics on this question. Unfortunately the fact that there has been so much econometric work looking at multipliers itself creates a similar problem. Because difficulties involving omitted variables, simultaneity and other issues are difficult to solve, and because of different data sets, not all econometric work is going to come up with identical answers, and it will be possible to cherry pick among those as well.

One way of dealing with this problem is for new studies to start by replicated their predecessors where they can, as Jordà and Taylor do for example. (This is part of what David Hendry calls encompassing.) An alternative is to look at meta studies, like this recent example from Sebastian Gechert. To quote from his abstract: “We find that public spending multipliers are close to one and about 0.3 to 0.4 units larger than tax and transfer multipliers. Public investment multipliers are found to be even larger than those of spending in general by approximately 0.5 units.” Fortunately that is consistent with what theory might suggest. A subsequent meta analysis by Gechert and Rannenberg shows that multipliers are "systematically higher if the economy suffers a downturn", a result which is also key in Jordà and Taylor.   

Despite the number of econometric studies already done, I'm sure there is plenty still to do. Sharp disagreements still exist that remain unresolved, although I suspect a lot will be sorted out when the monetary regime in place is adequately controlled for. Of course we have very few recent observations of the ‘Zero Lower Bound/QE’ regime. Leaving QE to one side, what basic New Keynesian models tell us is that multipliers observed under fixed exchange rates probably act as a lower bound for ZLB multipliers, which is why what has happened in the Eurozone periphery is of some relevance to the UK, US, Japan and Eurozone as a whole. We already know enough from both theory and evidence elsewhere to suggest that at the ZLB multipliers could be large, but just how large remains unclear. However I doubt our knowledge will be improved by drawing more scatter plots. 

Eurozone fiscal policy - still not getting it

The impact of fiscal austerity on the Eurozone as a whole has been immense. In my recent Vox piece, I did a back of the envelope calculation which said that GDP in 2013 might be around 4% lower as a result of cuts in government consumption and investment alone. This seemed to accord with some model based exercises of the impact of austerity as a whole, but others gave larger numbers.

We now have another estimate, which can be thought of as a rather more thorough attempt to do what I did in the Vox article. This paper by Sebastian Gechert, Andrew Hughes Hallett and Ansgar Rannenberg uses multipliers and applies them to the fiscal changes that have occurred in the Eurozone from 2011. Apart from the later start date, the first difference compared to my back of the envelope calculation is that they include all fiscal changes, and not just government consumption and investment. As a large part of the fiscal consolidation in the Eurozone has involved reducing fiscal transfers, this is important.

The second, and more interesting, difference is that rather than pluck a multiplier out of the air, as I did, they use a meta analysis of other studies. I have previously mentioned this meta analysis by Gechert: this paper is based on a follow up by Gechert and Rannenberg. [Correction from original post.] The studies on which these meta analyses are based are not ideal from my personal point of view (more on this later), but what this second paper shows is that fiscal multipliers are larger in depressed economies. Applying these ‘meta multipliers’ to the Eurozone fiscal consolidation implies that GDP was 7.7% lower by 2013 as a result. These numbers are more in the ballpark of the Rannenberg et al paper that I have discussed before.

All these estimates point to huge losses, which monetary policy has neither been willing or able to counteract. Yet the speed at which those in charge of the Eurozone begin to realise the mistake that they have made is painfully slow. Take this recent Vox piece by Marco Buti and Nicolas Carnot. Thankfully they ignore all the Eurozone’s tortuous and sometimes contradictory rules, and just look at two numbers: a measure of ‘economic conditions’ (like the output gap), and a measure of the fiscal gap, which is the difference between the actual primary balance and what it needs to be to get debt falling gradually.

They argue that policy needs to balance the need to reduce both gaps. Looking at these two numbers, they conclude that Germany is overachieving on fiscal adjustment and has a need to increase activity, but although France and Spain also need to increase demand they have a long way to go to eliminate the fiscal gap, so this should dominate. The conclusion is that Germany should go for fiscal stimulus, but “moderate consolidation appears warranted in both France and Spain”. Overall “the Eurozone should conduct a close-to-neutral fiscal stance”.

Let’s deal with that last conclusion first. The mistake there is simple. When monetary policy is stuck at the Zero Lower Bound, it is crazy to balance the output gap with what is your main instrument for correcting that gap, which is fiscal policy. Getting the fiscal gap right is important in the longer term, but in the short term it is the means by which you get the output gap to zero. As the studies mentioned at the beginning of this post show, the current recession is the result of trying to correct the fiscal gap at completely the wrong time. The right policy is to get the output gap to zero, so interest rates can rise above the ZLB, and then you deal with the deficit. Readers of this blog and the blogs of others must be sick and tired of seeing us make this same point over and over again, but the logic has yet to get through to where it matters.

The same principles apply to countries within the Eurozone, except with an additional complication of within Eurozone competitiveness. If a country is too competitive relative to the rest of the Eurozone, it needs to run a positive output gap for a time to generate the inflation that will correct that position, and vice versa. For that reason Germany needs a large positive output gap at the moment (compared to an estimated actual negative gap), and therefore a much more expansionary fiscal policy - not because it is overachieving on debt adjustment. France and Spain now look roughly OK in terms of competitiveness relative to the average (see chart below, and assuming that entry rates in 2000 were appropriate), so there we need fiscal expansion to close the output gap.

So at both the aggregate and individual country level, the inappropriate bias towards fiscal contraction that caused huge losses in the Eurozone in the past continues to operate. Which means, unfortunately, that the needless waste of resources caused by austerity continues to get larger by the day.

Relative Unit Labour Costs, 2010=100, from OECD Economic Outlook

How much has austerity cost (so far)?

For those who think I’m exaggerating when I say the intellectual case for austerity is crumbling, have a look at Alan Taylor’s Vox column. His analysis is particularly nice because it demonstrates two key problems with some earlier research. If you ignore the endogeneity of fiscal policy, and you ignore the state of the economy, then his study (joint with Oscar Jorda) replicates the ‘expansionary austerity’ result. If you take account of these things, you get numbers much more consistent with, for example, this widely cited IMF study (although their analysis attempts to improve on that work). So (journalists please note) it is not a matter of X says this and Y says something different: if you do the analysis properly austerity is clearly contractionary in bad economic times.

Alan Taylor also uses his estimates to cost the impact of UK austerity: GDP would be 3% higher today without it. Here the the relevant chart. 

He warns that this number is “likely [to be] a biased underestimate of the effects of current UK austerity. This caveat is the zero lower bound, when fiscal multipliers are known to be much larger in both theory and evidence.” Controlling for booms and slumps makes sense for various reasons, but controlling for monetary policy is at least as important. That also means that the 3% should carry the health warning that if UK GDP had been this much higher, this might have raised inflation, which might have led the MPC to raise interest rates, by more than is implicit in their estimates. But these are all big ifs.

When I did a back of the envelope calculation of the impact of cuts in just UK government spending since 2010, I came up with GDP being around 2% lower by 2013. As this ignored the impact of tax increases (e.g. VAT) and transfer cuts, then this seems quite consistent with Alan Taylor’s 3%. So if we make that 1%, 2% and 3% for 2011, 2012 and 2013, that is a total cost of 6% of GDP so far. Gross National Income was £1,557,503 million in 2012, and there were 26.4 million households, so that gives gross income of £59,000 per household. So the 6% figure implies that austerity has cost the average UK household a total of about £3,500 over these three years. Although all governments like to give the impression that they can have a big impact on people’s prosperity, few actually do. These numbers suggest that the current UK government has managed to do so, but unfortunately by making us all poorer.