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 ….

The trouble with macro

Diane Coyle, writing in an FT blog, says

 “There are two tribes of economists, the macro and the micro. I’m one of the latter group. We have our empirical controversies, of course – much of our applied research concerns public policy choices in areas such as education and health, so vigorous disagreement is inevitable. But I think it’s fair to say that few of the micro disagreements compare in intensity to the all-out war of words between different macroeconomists about the effects of fiscal stimulus or austerity.”

She goes on to say that it is macroeconomists’ “certainty that’s astonishing”. Her comments could be summarised as asking why macroeconomists are so sure and shrill compared to their micro colleagues.

Now it could be that there is something odd about those who choose macro rather than other types of economics, but I’m not sure I’ve noticed any character traits more evident in macro people. (But who am I to judge - an open invitation for microeconomists to comment!?) It could be something to do with the nature of the theory and empirics involved, but since macro became microfounded that seems unlikely. I think the problem is in a way much more straightforward.

I think you only need to look at the recent UK election to understand the problem. One of the central themes of the Conservative’s attack on Labour involved their alleged incompetence at running the macroeconomy when they were in power. For whatever reason, macro rather than micro policy issues become central in political debates. That makes macro unusual for various reasons.

One immediate consequence is that many beyond the tribe of macroeconomists think they can write with authority of macroeconomic issues. As a recent example of a shrill macro debate Diane cites Krugman vs Ferguson. But this is not to compare like with like. On one side you have an economics Nobel Prize winner who has made important contributions to macroeconomics, and as a result is careful about what he writes. Both data and theory are respected. On the other side … well I’ve said what I think in an earlier post.

To take another politically charged topic, I have seen plenty of debates between climate change scientists and deniers who are not scientists. Often the scientist will go into detail to get the facts straight, and say how uncertain everything is, while their opponent by contrast will be confident and clear. A scientist will not be fooled by this confidence, but many others will be. When one side argues out of conviction or ideology or political bias rather than knowledge, it is difficult for someone who does have that knowledge not to respond in kind if they want to be convincing.

There is a deeper reason for shrillness, however. The debate over austerity is not a normal academic discussion about the likely size of parameter values. Here Diane is mistaken in saying that the key issue is whether the multiplier (the size of the impact of cuts in government spending on output) is greater or less than one. In talking about UK austerity, I have typically quoted OBR figures which assume a multiplier below one, which gives me the £4000 per average household cost of UK austerity. My own best guess would be that the multiplier has been larger than one, which gives me significantly higher costs, but I have never suggested that I know with certainty what the size of the multiplier has actually been. However there has, to my knowledge, been no public debate on these terms.

Instead supporters of austerity typically want to suggest that the multiplier is close to zero. They want to suggest that sacking nurses and cutting back on flood defences will be very rapidly met by an increase in private sector labour demand and investment. Although theoretically possible via various different mechanisms, the evidence and recent experience overwhelmingly suggests this does not normally happen in the kind of situation we are currently in. For much of the time those arguing for the virtues of current austerity seem to be doing so from a position of faith or political convenience rather than evidence.

Why is it important to recognise this? Because there is a danger that microeconomists may misdiagnose the problem, and suggest that macro contains some fundamental flaw which undermines eighty years of intellectual endeavour. This provides useful cover to those who have an ideological or political agenda, and want policymakers to ignore the bits of the discipline that clearly work. Sometimes microeconomists seem to think that if only they could disassociate themselves from macro, economics would become a better and more respectable subject. That is an illusion: the ideological and political forces that cause such problems for macro are not unique to it.

So I’m not sure that academic macroeconomists suffer from an excess of certainty compared to their micro colleagues. Instead I think the trouble with macro is that it is prone to ideological and political influence: like all economics, but just more so.

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. 

Macroeconomic Theory and the Multiplier

I agree with most of what John Quiggin says in his post on fiscal multipliers, but I started having problems towards the end when he writes:

“To sum up, despite the thousands of papers published every year in the field, macroeconomic theory is incapable of giving even a qualitative answer to the most basic questions about fiscal policy[3]; at least, not one that would not elicit dissent from a substantial, and well-credentialled group of leading experts.”

The footnote reads

“[3] While writing this, I wondered what would happen if you put this question to a group of DSGE theorists as a pop quiz. I suspect most would give some variant of “the question is ill-posed” and the rest would be all over the place. But, if any DSGE theorists are reading, I’d be keen to get their views.”

OK, I have written a fair number of published DSGE papers on fiscal policy over the last decade, so here is my response. New Keynesian theory, and therefore the New Neoclassical synthesis, provides pretty clear answers to the multiplier question. I have talked about this before so I will not repeat these answers here. Macroeconomic theory is ‘all over the place’ on many issues, but this is not one of them. I would go further. If policymakers had paid more attention to theory, and less to a well known piece of empirical work, they would have been less likely to have made the mistakes they have.

The problem is not ambivalent theory, but the fact that a large section of macroeconomists choose to ignore or discount the relevant theory. Now this is actually consistent with the sentence from John Quiggin’s post that I quote above, because of the part that says ‘at least ....’. So in that sense it is a quibble. But I think it is an important quibble. There is a great deal of difference between suggesting that theory is all over the place, and saying that a large body of theory – the theory used by nearly all monetary policymakers – is pretty clear, but that a significant group of economists do not accept it.

The difference comes in the following paragraph, where he says “It really is hard for me to see how the economics profession can recover from its current rotten state, at least as regards macro..” If a large section of the profession (perhaps even a majority) subscribes to the New Neoclassical synthesis framework, and that framework is sound (if far from perfect), then we still have a problem, but one that does have solutions.

Different approaches to austerity

This is a really interesting chart from the IMF’s October 2012 Fiscal Monitor (HT Antonio Fatás). The red dots are the cyclically adjusted primary balance, the blue bars changes in government expenditure and the yellow bars changes in tax revenue.

It shows the extent of austerity (the red dots). Look how ludicrous is the idea that Greece is not trying hard enough – their current and planned fiscal contraction is literally off the scale! (Here are similar numbers from the OECD.) But what I want to focus on, which this chart clearly shows, is the tax and spend composition of austerity.

In many countries (Ireland, Spain and the UK) austerity is concentrated on the expenditure side. In some (e.g. US) it is more evenly balanced, while in a few (France in particular) it mainly takes the form of rising taxes rather than lower spending. Now how you regard this depends crucially on whether these measures are permanent or temporary (where by temporary, I mean lasting around ten years or less).

If they are permanent, then this is largely a political issue about the size of the state. Raising taxes protects the existing size of the state (taking on board any distortionary costs that permanently higher taxes may bring), while cutting spending aims to reduce the size of the state. In terms of short run demand impact - which is obviously important given the current state of demand deficiency in most countries - permanent tax and spending changes will have similar effects.[1]

On the other hand, if these measures are temporary, then in macroeconomic terms their impact will be rather different, because multipliers are different. A very broad generalisation is that theory suggests multipliers for spending cuts will be significantly higher than those for tax increases. The simple idea is that consumers will smooth the impact of income changes due to tax increases, whereas cuts in spending go straight into reducing demand. In addition, incentive effects on labour supply will be much less important if they are temporary and output is demand constrained.

We need to be careful, however, because this is a generalisation that applies to government spending on goods and services with a high domestically produced content. If the decline in government spending involves a temporary reduction in civil servants’ salaries, rather than building fewer hospitals or roads, then it is much more like a tax cut. As analysis later in the IMF’s report shows, cuts in wages make up a significant proportion of spending cuts in Portugal, but not much in the UK, where cuts in government investment are more important.

So are these austerity measures temporary or permanent? Normally governments do not say. An exception is a much remarked upon feature of the French austerity plans, which is the introduction for two years of a new top tax rate of 75% on incomes over €1m. We can be pretty sure that this is one group where the income effects of tax increases on consumption will be largely smoothed away (which is good), but where the incentive effects are the subject of debate which seems more ideological than evidence based. Of course whether such temporary tax measures will in fact be temporary is a moot point, as the Bush tax cuts in the US illustrate.

In the absence of reliable information from governments, people have to make their own assessments.  In the initial stages of a crisis, if either there is an unforeseen shock to government finances, or to the long run level of output, then it may make sense to regard any austerity as permanent. However as austerity proceeds, the goal is to get debt down from a high but sustainable level to a lower sustainable level. In these circumstances a rise in taxes (say) will be temporary, and will eventually be reversed as lower debt reduces debt interest payments and therefore taxes.

So it seems likely that a good part of current austerity plans involve temporary fiscal changes designed to reduce debt levels, and so the differences between the multipliers of tax and spending changes will apply. For countries like the UK, that have focused on spending cuts, the knock on effects on output will be relatively large, whereas for countries like France the impact of austerity may be more moderate (although still unwelcome).

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[1] Spending cuts may still have a larger impact on domestic demand because government spending tends to have a lower import content than private spending.

Multipliers: using theory and evidence in macroeconomics.

Paul Krugman and Jonathan Portes have picked up on the IMF’s recent analysis (see Box 1.1) of multipliers. The IMF (or more specifically Olivier Blanchard and Daniel Leigh) say

“... earlier analysis by the IMF staff suggests that, on average, fiscal multipliers were near 0.5 in advanced economies during the three decades leading up to 2009. If the multipliers underlying the growth forecasts were about 0.5, as this informal evidence suggests, our results indicate that multipliers have actually been in the 0.9 to 1.7 range since the Great Recession.”

Jonathan paraphrases this as the IMF saying: "Delong et. al. were right; we were wrong". They, and many others besides, underestimated the impact of austerity because multipliers were underestimated.

The point I want to pick up on is why 'Delong et. al' got it right. In most cases it was not because we had undertaken a superior analysis of the empirical evidence. Instead we were thinking about basic macroeconomic theory. In particular, we recognised that a world where nominal interest rates were fixed, either because they cannot go below the Zero Lower Bound (ZLB), or because the rate is determined for the Eurozone as a whole, is very different to a world where monetary policy is unconstrained.

One of the things I did when I recently spent a week at the European department of the IMF was talk about multipliers. What I said was a version of this post. With fixed real interest rates the starting point for the government spending multiplier in New Keynesian theory is one, and most elaborations make it larger than one. These elaborations include that austerity will reduce inflation, which with fixed nominal interest rates could mean higher real interest rates.[1]  You can then add something for hysteresis effects, or any supply side effects if the government spending is investment rather than consumption. You can also add an effect from credit constrained households which, as Paul Krugman points out, are a key feature of deleveraging. So theory suggests something significantly larger than one, which is exactly what the IMF now finds.

It would be overstating things to say that the IMF's analysis proves this theory is correct. It is just not detailed enough to be a very good test. New Keynesian theory suggests austerity achieved through temporary income tax increases will have a smaller multiplier, as I discussed here.  Tax changes that impact directly on inflation will have different impacts, as I suggest here. The IMF's analysis looks at the budget deficit as a whole, so it cannot discriminate in this way.  However New Keynesian theory does suggest that multipliers can be large, and the IMF analysis suggests they have been large.

Those of us who got it right may therefore have simply had the insight to use standard theory. Those that used multipliers of around a half for fiscal consolidation packages that leaned heavily on spending cuts seemed to discount this theory, and instead may have been following evidence that was not applicable at fixed nominal interest rates.[2] . While there is plenty wrong with New Keynesian theory, it is also important to note when it gets things right. It is also important to note an occasion where thinking about macroeconomic theory can be rather more useful than naively following the evidence of the past.

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[1] As my post made clear, government spending on domestically produced goods will have the same multiplier in an open economy. Although the multiplier will be lower because government spending will have some import content, any real interest rate effect will be larger in a flexible exchange rate open economy because it they influence the real exchange rate.

[2] Antonio Fatás argues that there were plenty of earlier empirical studies of multipliers that suggested numbers well above 0.5. In my view it makes little sense estimating multipliers that do not control for the reaction of monetary policy. 

Multiplier theory: one is the magic number

I have written a bit about multipliers, particularly of the balanced budget kind, but judging by comments some recap and elaboration may be useful. So here is why, for all government spending multipliers, one is the number to start from. To make it a bit of a challenge (for me), I’ll not use any algebra.

Any discussion has to be context specific. Imagine a two period world. The first period is demand deficient because interest rates are stuck at the zero lower bound[1], but in the (longer) second period monetary policy ensures output is fixed at some level independent of aggregate demand (i.e. its supply determined). Government spending increases in period 1 only. That is the context when these multipliers are likely to be important as a policy tool.

1) Balanced budget multiplier

To recap, for a balanced budget multiplier (BBM), here is a simple proof in terms of sector balances for a closed economy. A BBM by definition does not change the public sector’s finance balance (FB). It seems very reasonable to assume that consumers consume a proportion less than one of any change to their first period post-tax income. So if higher taxes reduced income, their consumption falls by less, so their FB moves into deficit. But as the sum of the public and private sector’s FB sums to zero, it cannot do this. So post-tax income cannot fall. Hence pre-tax income must rise to just offset the impact of higher taxes. The BBM is one.

The nice thing about this result is that it holds whatever fraction of current income is consumed (as long as it’s less than one), so it is independent of the degree of consumption smoothing. What about lower consumption in the second period? No need to worry, as monetary policy ensures demand is adequate in the second period.

Although a good place to start, allowing for an impact on expected inflation and therefore real interest rates will raise this number above one. In addition, as DeLong and Summers discuss, hysteresis effects will also raise period 2 output and income from the supply side, some of which consumers will consume in period 1. We would get similar effects if the higher government spending was in the form of useful intrastructure investment. So in this case one is the place to start, but it looks like a lower bound.

2) BBM in an open economy

I’m still seeing people claim that the BBM in an open economy is small. It could be, if the government acts foolishly. Suppose the government increases its spending entirely on defence, which in turn consists of buying a new fighter jet from an overseas country. The impact on the demand for domestic output is zero. But consumers are paying for this through higher taxes, so their spending decreases – we get a negative multiplier.

Now consider the opposite: the additional government spending involves no imported goods whatsoever. The multiplier is one. You can do the maths, but it is easy to show that this is a solution by thinking about the BBM in a closed economy. There consumption does not change, because a BBM=1 raises pre-tax income to offset higher taxes. But if consumption does not change, neither will imports, so this is also the solution in the open economy case.

What the textbooks do is apply a marginal propensity to import to total output, which implicitly assumes that the same proportion of government spending is imported as consumption spending. For most economies that is not the case, as the ‘home bias’ for government spending is much larger. Furthermore, if the government is increasing its spending with the aim of raising output, it can choose to spend it on domestically produced output rather than imports. So, a multiplier of one is again a good place to start. Allowing some import leakage will reduce the multiplier, but this could easily be offset by the real interest rate effects discussed above, particular as these would in an open economy depreciate the real exchange rate.

3) Debt financed government spending with future tax increases

Although this is the standard case, from a pedagogical point of view I think it’s better to start with the BBM, and note that it’s all the same with Ricardian Equivalence. We can then have a discussion about which are the quantitatively important reasons why Ricardian Equivalence does not hold. All these go to raise the multiplier above one. You have to add, however, some discussion about the impact that distortionary tax increases will have on output in the second period, which reduces second period output and, through consumption smoothing, the size of the first period multiplier. 

4) Debt financed government spending without tax increases

In an earlier post I queried why arguments for the expansionary impact of government spending increases always involved raising taxes at some point. For debt finance, why not assume lower government spending in the future rather than higher taxes. The advantage is that you do not need to worry about supply side tax effects. Monetary policy ensures there is no impact on output of lower government spending in the second period. Now, unlike the BBM case, we do need to make some assumptions about the degree of consumption smoothing. If you think the first period is short enough, and consumers smooth enough, such that the impact of higher income on consumption in the first period is negligible, then we have a multiplier of one again.

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[1] I assume Quantitative Easing cannot negate the ZLB problem, and that inflation targets are in place and fixed. This is not about fiscal stimulus versus NGDP targeting, but just about macro theory.

Sector Financial Balances as a Diagnostic Check

                Martin Wolf has a nice post explaining the financial crisis using sector financial balances. He rightly attributes this way of looking at things to Wynn Godley. It goes way back – I remember using them as a cross-check on forecasts in the UK Treasury in the 1970s, but it was probably Godley’s influence that helped that happen too. They are not a substitute for thinking about macroeconomic behaviour, but they can often be a very useful check on whether your thoughts (or forecasts) make sense.

                Take the example of a balanced budget temporary increase in government spending, which I used recently as a challenge to heterodox economists to come up with an alternative analysis that did not use either representative agents or rational expectations. (I’ve had plenty of responses telling me of all the defects of rational expectations, but no one has as yet given me an alternative account of the impact of this particular policy measure. As Godley is respected among heterodox economists, I thought maybe retelling my analysis using sector balances might help.)

The policy itself does not directly change the government sector’s financial balance (by definition). Theory tells us that consumers will smooth the impact of temporarily higher taxes, so their sector will move into deficit. But if we were foolish enough to think the story stopped there, thinking about financial balances tells us that has to be wrong. Consumers are in deficit, and no sector has moved into surplus. Keynesian theory then tells us what happens to put things right: output and incomes increase until the point that the consumer sector is no longer in deficit. If you think about it (and given consumption would always fall by less than post-tax income because of smoothing), this has to be the point at which income has increased by an amount equal to the tax increase i.e. a balanced budget multiplier of one. We could talk about this as a dynamic multiplier process, or we could talk about rational consumers working this out, and so not bothering to reduce their consumption in the first place.

As Martin Wolf and others have pointed out many times, thinking about financial balances also tells us the foolishness of cutting government deficits when the private sector has moved into surplus to restore their asset/liability position. In a global economy, if governments are successful in cutting deficits then the private sector surplus has to diminish. That makes the idea that nothing will happen to output as a result of deficit reduction rather improbable. With interest rates stuck at zero, real interest rates cannot move to persuade the private sector that they no longer need to correct their financial position. So the only possibility left is that output falls until they no longer want to do so. (Because of consumption smoothing higher short term income would imply a rising, not falling, private sector surplus.)

Looking at sector balances are not a substitute for thinking about behaviour, but they can and should demand that we are able to tell stories about them that make sense. Where I think criticism of the mainstream macroeconomic profession is correct is that there were not enough people telling convincing stories about why the household sector balance was evolving the way it did over the two decades before the recession. (I talk more about this here.) What was I doing? The answer is writing papers looking at the impact of fiscal policy in DSGE models, and not looking at this kind of data at all. In that sense I was definitely part of the problem, although it did kind of come in useful later on.

Consumption smoothing and the balanced budget multiplier

Only for economists

                In some of the debate following this post, and then this, there often seems to be a big distinction drawn between models based on consumption smoothing, and the old fashioned balanced budget Keynesian multiplier. Even Paul Krugman felt it necessary to say that he ‘never said a word about the balanced budget multiplier’. Now of course the models are different. However I want to suggest that in the context of fiscal expansion in a recession caused by demand deficiency, the balanced budget multiplier story can be retold in a manner consistent with consumption smoothing.

                The most basic model of consumption smoothing involves two periods. Let period 1 be a demand deficient recession, and so output is determined in a Keynesian manner by aggregate demand. Period 2, which is much longer, is Classical, and nothing changes in period 2. (If having a two period model of unequal lengths is a worry, think of period 2 as being divided into a large number of sub-periods of equal length to period 1, but where every sub-period is Classical.) We keep monetary policy neutral by assuming the real interest rate is constant. Optimising consumers will then spend a fixed proportion of their permanent income in period 1: that is consumption smoothing. Let’s call this proportion c, which could be quite small. There is no investment, and the economy is closed.

                The government now increases government spending by G in period 1 only, and taxes rise by the same amount in period 1. The ‘direct’ or ‘first round’ effect is that consumption in period 1 falls by less than G, because the impact of higher taxes on consumption is smoothed via permanent income. That is as far as I needed to go in my ‘Mistakes’ post to make the point I wanted to make. However it is obviously not the end of the story, because higher output implies higher income. What happens to output eventually (call the answer Y)? Well consumption rises/falls by Y-G times the fixed proportion c, so we solve Y=G+c(Y-G), which of course implies Y=G, a multiplier of one. This is not only the same result as given by the Keynesian balanced budget multiplier, but the mechanics are identical. Consumption does not change at all: higher period 1 income offsets the higher taxes. We do not need to worry about any knock on effects in period 2, because permanent income ends up unchanged. So the simple Keynesian balanced budget multiplier need not be considered some ancient fossil that we are forced to teach undergraduate students, but a simple expression of what consumption smoothing implies in a particular context.

                We could get to the same result using consumption smoothing alone, by noting that consumption in period two is tied down by (classical) Y and permanent G. Second period consumption and the Euler equation then fixes period 1 consumption, as real interest rates are unchanged by assumption. So any change in government spending in period 1 leads to an equal increase in output.

Woodford, in section 2 of the paper noted by Krugman and myself, does something with similarities to this, but with more elegance. My period 2 becomes the steady state, a steady state in which (given the usual assumptions) the real interest rate equals the rate of time preference. With real interest rates fixed at this value in all periods, consumption is equal in all periods, so any temporary change in government spending leads to an equal temporary change in output. We get a multiplier of one. With this benchmark, it is then intuitive to see how the multiplier will fall if real interest rates are not constant but rise. Equally, if we are at a zero lower bound, the multiplier will be greater than one because higher output generates inflation, which reduces real rates.

Now I am not trying to say here that the simple, most basic Keynesian multiplier apparatus is in any sense ‘as good as’ consumption smoothing. In fact, if I was writing an introductory macro textbook, I would start with the two period consumption model and consumption smoothing, and mention the current income Keynesian consumption function only in passing. (My reasons for doing this are explained here.) All I want to suggest is one way of reinterpreting the balanced budget multiplier that is consistent with consumption smoothing. I think it is also nice that all this stuff ends up with the same result, a multiplier of one. If someone wants to argue that the multiplier is zero they need some additional argument, and as I suggested here, I have yet to see one that seems appropriate to the current situation.