Tuesday, October 29, 2013

Functional Finance and Sound Finance


Anyone who who has been following debates on fiscal policy over the past few years will have noticed that, among those who think fiscal policy can be effective, there are two distinct camps. There is a minority who think that fiscal policy is not subject to a budget constraint; that is, that as long as a government borrows in its own currency, its existing liabilities never limit its ability to adjust taxes and spending to bring the economy to full employment. And there are the majority who think that governments are subject to a binding budget constraint; that is, that while adjusting spending and taxes can in principle be used to bring about full employment, it may be impossible or undesirable to do so when the level of government debt is already high. In this view, maintaining full employment should be left to monetary policy. Following Abba Lerner, I call the first position "functional finance" and the second position "sound finance."

I believe there are important differences between these two positions. But I also believe that these differences have not been clearly articulated, and as a result these debates between them been unproductive. It is my view that there are no important differences in terms of economic theory between the two positions. A perfect application of a functional finance policy rule and of a sound finance policy rule are indistinguishable. The difference between the camps is with respect to policy errors -- which errors are most likely, and which are most costly.

Alternative Policy Rules

The starting point is the idea of instruments, which are variables directly controlled by the policymaker; and targets, which are the variables the policymaker wants to set at some level but cannot control directly. When the target variable is not at its desired level, the policymaker adjusts one or more instruments to try to bring it there. This creates relationship between the current level of the target and the chosen level of the instrument. We call this relationship a policy rule. Both functional finance and sound finance represent policy rules in this sense. Tinbergen's Rule says that for policy rules to be successful (in the sense that all targets converge to their desired levels), there must be at least as many instruments as targets. One policy lever cannot be relied on to achieve two separate outcomes.

We have two instruments in macroeconomic policy: the government budget balance, and the central bank-controlled interest rate. What are our targets?

At first glance, full employment and price stability appear to be two separate targets. But in fact, both Lerner's functional finance and the sound finance of modern textbooks agree that inflation is the result of demand-determined expenditure departing from a technologically determined level of potential output. Less than full employment means falling inflation, or deflation; overfull employment means high or rising inflation. So full employment and price stability are not two separate targets, they are two ways of describing the same target.

Both camps agree that we can identify a unique target level of output, and they agree on what that target should be. They also agree that output rises with higher government deficits, and falls with higher interest rates. So when interest rates are too high, or budget deficits too small, we will see unemployment (and perhaps deflation); when interest rates are too low or deficits are too large, we will see inflation (and perhaps bottlenecks and rising relative prices of factors in inelastic supply).

This consensus is shown in Figure 1. The full employment locus shows all the combinations of interest rates and fiscal balances that are compatible with full employment and price stability. A fall in private demand will require a rise in the deficit and/or a fall in interest rates to maintain full employment, so it will shift the full employment locus down and to the left. Similarly, a rise in private demand will shift the locus up and to the right. But for any level of private demand, with two instruments and only one target, there are an infinite number of combinations that achieve full employment.

(It is convenient to think of the fiscal balance on the horizontal axis as the primary balance, that is, the balance net of interest payments. So we are implicitly assuming that interest payments do not raise aggregate demand. It is also convenient to think of the interest rate as the real rate, that is, net of inflation. It would be straightforward to incorporate the effects of interest payments and inflation into the story, but would not change it in any interesting way.)

The first point of disagreement is what to do at a point like a. Output is below potential, but which instrument should be used to raise it? Functional finance says, the fiscal balance: government spending should be raised (or taxes should be lowered), moving the economy to the left, until we reach the full employment locus. The modern sound-finance consensus says that the interest rate should be lowered, moving the economy downward to the full employment locus. Both agree that government should do something to raise output. The disagreement is over which instrument to use.

Whichever instrument is used to keep output at potential, there is one instrument left over for some other target. The logical candidate is the sustainability of government debt.

We've discussed the math of government debt dynamics quite a bit on this blog. (See here and here and here and here.) The important thing for our purposes is that the long-run trajectory of the debt-GDP ratio depends on the primary balance, the interest rate on government borrowing, and the growth rate of GDP. If we write the ratio of government debt to GDP as b, and the primary deficit as a share of GDP as d, then for a given deficit, the equilibrium condition is b=d* 1/(g-r), where g is the average or expected growth rate of GDP over the period of interest. So for a given debt-GDP ratio b, the primary deficit required to hold it constant is d = b(g-r). (This is all just accounting; it does not depend on any economic assumptions.) It's evident that, if we take the growth rate as exogenous, then for any given debt-GDP ratio there is a set of r, d combinations for which the debt-GDP ratio is constant. We can represent these values graphically in Figure 2. The dotted horizontal line is the growth rate. The diagonal line is the constant debt ratio locus. With a deficit or interest rate above the diagonal line, the debt-GDP ratio will rise; below, it will fall.

Note that the slope of the diagonal depends on the starting debt-GDP ratio -- the higher it is, the shallower the slope will be. With no government debt, the line is vertical at the primary balance = 0 axis. So in any period in which the economy is at a point above the debt-sustainability locus, the diagonal rotates clockwise; in any period in which the economy is below the debt-sustainability locus, the diagonal rotates counter-clockwise.

What happens if the economy is off the constant-debt locus? It depends. In the area marked A (everything above the heavy line), the debt-GDP ratio rises without limit. In B, the debt-GDP ratio rises but converges to a finite value. In C the ratio falls to a finite value. In D, the debt-GDP ratio falls to zero and the government then accumulates a positive asset position, which eventually converges to a finite fraction of GDP. Finally, in area E the debt-GDP ratio falls to zero and the government then accumulates a positive asset position that rises without limit as a share of GDP. (If you are unconvinced we can go through the math.) Since the government budget constraint is normally taken to be the condition that debt-GDP ratio not rise without limit, we can ignore the distinctions between cases B through E and regard the heavy line as the government budget constraint.

We then combine this constraint with the full employment locus to give Figure 3.

Now we have two instruments and two targets. Or rather, one and a half targets: Since there is nothing special about the current debt-GDP ratio, we don't need it to stay constant; we just need it not to go to infinity. So we don't need to be on the debt-sustainability curve, we need to be on or below it. Point b, which satisfies the budget constraint exactly, is fine, but so is anywhere on the full employment locus below and to the right of b.

The functional finance-sound finance divide is just this: Functional finance says the fiscal balance instrument should be assigned to the full employment target and the interest rate instrument should be assigned to the debt sustainability target. Sound finance says the interest rate instrument should be assigned to the full employment target and and the fiscal balance instrument should be assigned to the debt sustainability target.

Functional finance and sound finance agree that the economy should be at a point like b. If policy were executed perfectly, the economy would always be at such a point, and there would be no way of knowing which rule was being followed. Since both target should always be at their chosen levels, it would make no difference -- and be impossible to tell -- which instrument was assigned to which target. The difference between the positions only becomes apparent when policy is not executed perfectly, and the economy departs from a position of full employment with sustainable public debt.

Consider a point somewhere above b, where we are have high unemployment but the debt-GDP ratio is rising without limit. What to do? Both orthodoxy and Lernerism want to get the economy back to a point like b, but they disagree on how.

In the sound-finance view, the interest rate instrument is committed to the output target. This means we must use the fiscal balance instrument free to meet the debt sustainability condition. This is how policy is normally discussed: An unsustainable upward trajectory in the debt position requires the government balance to move  toward surplus. In this case, that means that the government must cut spending or raise taxes, despite the fact that demand is already too low. Under Lernerian functional finance, on the other hand, the fiscal balance is committed to the output target, so the rule calls for higher deficits even though the debt position is already unsustainable. It is then the responsibility of monetary policy to adjust to maintain debt sustainability.

These alternatives are shown in Figure 4. The right-hand trajectory from c to b is the orthodox path. The left-hand trajectory is the Lernerian path. Implicit in the orthodox path is the idea that deficits must be brought down first, meaning a substantial period of high unemployment and output below potential; only once debt is on a sustainable path can interest rates be reduced to move back toward full employment. While the Lernerian path says in effect: If government debt is rising out of control, the central bank should intervene to force interest rates down to a level where the debt is sustainable. Then, if the resulting liquidity raises expenditure above the full employment level, you can subsequently raise taxes or cut transfers to bring demand back down.

Orthodoxy says that budget problems must be addressed fiscally. But this is true only on the implicit assumption that the interest rate is not available as an instrument to target debt sustainability. Sound finance's policy rule is a Taylor-type rule for monetary policy, combined with a long-term government budget position that satisfies the debt-sustainability constraint at that interest rate. Functional finance's policy rule: (1) fix the interest rate at a level at or below the expected growth rate (maybe even zero); (2) adjust transfers and taxes until output is at the full employment/stable prices level. The claim that fiscal policy must be subject to a budget constraint, comes down to the claim that the central bank cannot or will not keep r sufficiently low to make the full-employment fiscal position sustainable.

Why is there such disagreement about which instrument should be assigned to which target? It seems to me that the most important argument from the sound finance side is that elected governments cannot be trusted with the instrument of discretionary fiscal policy. They will not set taxes and transfers to bring aggregate demand to the full employment level, but will choose a higher, inflationary level of demand. Only independent central banks can be trusted to bring output to its socially optimal level. In this sense, the functional finance-sound finance divide is not a debate about economic theory, but about politics and sociology.

There are also more specifically economic disagreements. The sound finance side is more confident than the functional finance side about how quickly and reliably a change in interest rates will affect output. If there is a long lag between the change in the instrument and its effect, hitting the target requires accurate prediction of the state of the economy farther into the future. The existence of the ZLB reinforces this concern, since it is really just a special case of interest-inelasticity. (The statement "output does not respond strongly to any feasible change in interest rates" is equivalent to the statement "the interest-rate change needed to achieve a strong output response is not feasible.") The functional finance side also tends to see a greater social cost in falling below full employment than rising above it, while the sound finance side tends to see the costs as symmetrical.

That is the framework. Now consider some modifications and special cases.


A natural objection to the functional finance view is that it may not be possible for the central bank to maintain interest rates low enough to keep debt sustainable. If we live in a world of high capital mobility and our government's liabilities are close substitutes for liabilities elsewhere in the world, then the private sector will not hold them if their yield is too much lower. In this case -- which is not unrealistic for small, open countries -- the interest rate ceases to be a policy variable. This is shown in Figure 5, where r* is the exogenous work interest rate.

At a point like d in the figure, the public debt is stable but output is below potential. A move toward a primary deficit would raise output but put the debt on an unsustainable path. This case is not inherently implausible -- one would need to think carefully about the concrete assumptions it embodies -- but it is important to recognize that it rules out sound finance as well as functional finance. If the interest rate is set exogenously at the world level, it cannot be used to stabilize public debt or to stabilize output. An additional instrument is needed; the exchange rate is the natural choice. Since the exchange rate cannot straightforwardly be used to achieve debt sustainability, in this case there is a natural argument to switch the assignment of fiscal policy to debt sustainability and achieve full employment via the exchange rate.

Another possibility, which has been getting increasing attention recently, is that very low interest rates are destabilizing for the financial system. (I have criticized this idea before, but I don't think it can be ruled out definitively.) Then we have another condition to satisfy, a asset price stability condition. Like the debt sustainability condition, this is asymmetrical, it doesn't have to be satisfied exactly. But this one is a floor on interest rates rather than a ceiling. The is shown in Figure 6. Here, the asset price stability constraint does not initially prevent achieving both the other targets: As in Figure 3, point b initially satisfies all the constraints, as does any other point along the full employment locus below and to the right of it, down to the dotted line.

But what if a fall in private demand shifts the full employment locus far to the left? Here there is an important difference between the sound finance and functional finance rules. The functional finance rule says that the fall in private demand requires the government budget to move toward deficit. That is, we move left from b to the new full employment locus. This may in turn require a fall in interest rates, if the higher deficits would otherwise put the public debt on an unsustainable path. But public debt sustainability never requires an interest rate below the long term growth rate. So, since it is not plausible that the minimum interest rate compatible with asset price stability condition is greater than the growth rate, the possibility of asset bubbles should not limit the application of the functional finance rule.

The sound finance rule, on the other hand, says that the response to a fall in private demand should be a reduction in the interest rate. In other words, faced with the fall in private demand shown in the figure, we should move downward from point b  to the new full employment locus. Now there is the possibility that the required interest rate is incompatible with asset price stability. (In some views, this is precisely what happened a decade ago, setting the stage for the housing bubble.) This becomes an argument for setting interest rates higher than the conventional policy rule implies, even at the cost of higher unemployment.

Formally, the ZLB is identical to the asset price stability condition: both set floors to allowable interest rates. It is curious that, while concern with the ZLB and with the destabilizing effects of low interest rates often come from opposite political positions, they are -- at least in this framework -- equivalent in their implications for policy. Both are arguments for a reliance on fiscal policy to offset fall in private demand in general, rather than waiting for the floor to be reached -- that is, for some form of functional finance.

Finally, consider the case where the fiscal balance is exogenously fixed, as shown in Figure 7. I think this is the case most critics of functional finance have in mind. If the budget authority, for whatever reason, is committed to tax and spending policies corresponding to a primary deficit, there may be no interest rate that can deliver both debt sustainability and full employment. The central bank must choose one. If it chooses debt sustainability, we have a situation known in the literature as "fiscal dominance." The central bank must increase its liabilities as needed to finance the government deficit, even if that results in aggregate demand rising to inflationary levels. This is the situation at point e.

It is important to stress that Figure 7 is not what is advocated by functional finance. There is an understandable but unfortunate confusion between the claim "deficits can be at whatever level is needed to reach full employment" and "deficits can be at whatever level you want." Functional finance says the former, not the latter. A functional finance rule would call for the government to raise taxes or cut spending at a point like e -- not to balance the budget, but to eliminate the inflation. The practical problem for functional finance supporters is to convince skeptics that such a rule will be followed by an elected government.


Advocates of functional finance say that a government that borrows in its own currency never needs to adjust its taxes or spending on account of its current deficit or accumulated debt. The fiscal balance can always be set at whatever level is needed to achieve full employment. Their sound-finance critics reply, "It's true that a deficit will raise current output. But over the long run you need a primary surplus to ensure that the government stays on its budget constraint. If the central bank is forced to monetize the debt instead, you will have runaway inflation."

The critics are correctly describing the situation in Figure 7, where it is true that the government budget position has been set without regard for debt sustainability, the central bank is monetizing the debt (this is simply another way of describing holding interest rates low enough to maintain a stable path for government liabilities), and there is uncontrolled inflation. But the inference the critics draw from this possibility -- that fiscal policy must target debt sustainability -- is not correct. The correct inference is that at least one of the two instruments must target debt sustainability, and at least one must target full employment. The problem in Figure 7 is that budget balance is being set without regard for either condition -- that is, it is in violation of both policy rules. Either the sound finance rule, or the functional finance rule, or any linear combination of the two, would ensure that the economy does not remain at a point like e but instead converges to one like b in Figure 3.

The debate between sound finance and functional finance cannot be resolved as long as they are framed in terms of what kind of rule is feasible in principle, and what outcome results when it is followed exactly. The disagreement is about what kinds of rules policymakers can be expected to adhere to in practice, and about the relative costs of different policy errors.

[This post was inspired by this talk by Brad DeLong, and by some comments by Nick Rowe which I cannot locate now.]


  1. I think there’s a fair amount of unnecessary complexity there, particularly to do with “debt sustainability”. What’s wrong with aiming for no interest yielding debt at all (as advocated by Warren Mosler and Milton Friedman)? I.e. the only liability issued by government / central bank would be money (monetary base to be exact).

    In a Mosler/Friedman scenario, the government / central bank machine would just create new money and spend it into the economy (and/or cut taxes) when stimulus was needed. And if inflation looked like getting out of control, it would do the opposite: raise taxes, rein in money and “unprint” that money.

  2. There's nothing wrong with it. I explicitly suggest the possibility when I write:

    Functional finance's policy rule: (1) fix the interest rate at a level at or below the expected growth rate (maybe even zero); (2) adjust transfers and taxes until output is at the full employment/stable prices level.

    Saying that the central bank holds the interest rate at zero permanently, and that the government issues no interest-bearing assets, are functionally equivalent statements, I think. I am just translating Mosler into more conventional economics language.

  3. My point is, what you wrote is just a restatement of what the post says. But there are contexts where the language of switching the assignment of targets and instruments communicates that idea more effectively than asking people to imagine a whole different model of government finance.

  4. IMO most analysis of debt sustainability exclude the external sector or give no attention to it.

    You mention for example that

    "So for a given debt-GDP ratio b, the primary deficit required to hold it constant is d = b(g-r). (This is all just accounting; it does not depend on any economic assumptions.) "

    While it is true that the formula has been derived by simple manipulation of mathematical expressions, it doesn't mean that it is trivial and has no economic assumptions.

    For if a nation grows, income is also growing as a result and hence imports as well. But assume exports are not growing or growing very slow. This implies a rising CAD. Because of sectoral balances, it also implies a rising budget deficit.

    Otherwise if the budget deficit is small achieving the same growth would need a rising private sector deficit (given a high CAD because of growth in income) and need a private debt led growth which will end in a crash.

    Of course to prevent this from happening would require exports to grow faster or the need for import substitutes and so on.

    So issues of fiscal sustainability is closely tied to exports, balance of payments etc.

    I wrote it up here:


    So in your quote which says "simple accounting", just means a restriction on fiscal policy to keep the fiscal deficit in check but paradoxically you assume growth which seems independent of fiscal policy.

  5. Damn. I just wrote a long comment, then lost it when the hydro died! Short version:

    Good post.

    I assume fiscal policy must be sustainable, and see the second objective as (say) getting the "right" amount of intergenerational transfers.

    If the monetary and fiscal policymakers share the same objective function, the decentralised Nash Equilibrium is always the same as if a single agent chose both fiscal and monetary policy.

    But suppose we see it as a principal-agent problem. Fiscal is principal, monetary is agent. Telling the agent to ensure the right level of AD is quantifiable and hence accountable in a way that telling an agent to ensure the right level of fiscal transfers is not?

  6. Nick-

    But that's three constraints, isn't it? and still only two instruments. We would formalize "the right level of intergenerational transfers" as a target level for the interest rate, independent of the the other two conditions. Right?

    On the other hand, if we think that the optimal interest rate fro an intergenerational equity standpoint will be less than the growth rate -- and I think there are very good reasons to believe that it will be -- then the debt sustainability condition doesn't bind, and we're good to go. But that is a functional finance outcome -- demand management will all be via fiscal policy.

    1. JW: but an economy in which r < g for all periods is dynamically inefficient. You could loosen fiscal policy and make all generations better off, by running a sustainable Ponzi scheme. Samuelson 1958.

      Sustainability puts one constraint on fiscal policy, but there are multiple intertemporal paths for the primary surplus that are sustainable.

  7. If a central bank is truly independent, then its interest rate doesn't determine the government's borrowing cost, because there's default risk. In that case monetary policy dominates. But if people figure that central banks are not that independent, then government debt is always free of default risk. When the finances are sound, monetary policy dominates. When the finances are unsound, fiscal policy dominates.

    1. You need to be clearer about what you mean by "independent." If the central bank targets the government borrowing cost, then the governing borrowing cost will be whatever rate the central bank sets. Period. Any government default risk will then show up in the spread over that rate of rates faced by private borrowers.

  8. Are we creating ad hoc targets? "right" amount of intergenerational transfer? Why not also right amount inequality, population growth, CO2 emission while we are at it? How exactly is monetary policy neutral with respect to intergenerational equity? Surely, we can construct a model in which monetary policy is not neutral--just like the toy models to show public "can" be a burden.

    1. These are questions for Nick, not me. My only point is that if you have some other rule for setting the interest rate besides debt sustainability and full employment, you can achieve it if but only if it implies an interest rate below the growth rate.

  9. Very insightful. This has been very helpful for my paper research.

  10. This is nice, and it could be easily incorporated into a principles class. Couple of thoughts:

    1, In the case of exogenous world interest rate where you re-assign the exchange rate to achieve full employment. This would presumably be achieved by changing the exchange rate until the full employment curve shifts up enough so that it crosses the debt sustainability curve at d. But then why can't exchange rate policy be also used in figure 7 to shift the FE curve down so that it crosses debt sustainability at e? In the first case you raise your E to stimulate exports, in the second you lower it to lower inflation.

    2. Of course for that to work you need an exchange rate to begin with. So Eurozone members that are not Germany are still out of luck. Also, I think it sort of begs the question of whether exchange rate really is an independent instrument (I have to think about it but the trilemma comes into play here I think)

    3. There is actually a bit of difference between the "destabilizing low interest rates" case and the ZLB case.In the former, you can have a bit of an interest rate cut even as you move towards greater deficits (the left pointing arrow in your figure). In the latter, in an analogus case of a far-left shifted FE curve, you need *rising* interest rates and greater deficits. Weird, huh?

    4. To get really weird, de-endogenize some of the constants. I think what some of the sound finance folks have in mind is something like r(b,d). Likewise, forgetting for a moment that Reinhart and Rogoff monkeyed it up, we could have g(b). Then you introduce bunch of nonlinearities. Can we get that debt sustainability curve to cross the FE curve a few more times?

  11. Correction on the ZLB - you don't have to raise interest rates unless you want to be exactly on the thick line.

  12. YouNotSneaky-

    Thanks for the comments. And yes, the idea of using something like this in the classroom was part of the motivation for writing it. Taking your points in order:

    1/2. You need an exchange rate, and the central bank needs to be able to use it as an instrument. The standard trilemma argument applies here: In a world of mobile capital, if the central bank is setting the exchange rate, it cannot also set the interest rate. That's ok in the first case -- we just leave the interest rate at the world level. But it's not ok in the fiscal dominance case, because the interest rate is needed to keep the debt ratio constant.

    Now from my point of view, the situation is actually better int he Euro zone. There, inflation means a real appreciation. So the exchange rate adjustment happens automatically -- if a country is above full employment, relative prices rise and net exports fall until it returns to the full employment level. From this point of view, an advantage of the euro framework is that it reduces the cost of excessive deficits like in Figure 7. This sounds crazy but I think there's an important element of truth to it.

    3. To me, the interesting parallel between the ZLB and "too low for too long" positions is that both, logically, imply support for assigning the fiscal instrument to full employment, and/or for a more expansionary "default" fiscal stance. But neither group seems to want to draw this conclusion.

    4. A lot of people have suggested endogenizing g. That's fine but it doesn't change anything. The point is that If you think that a lower level of b is desirable -- fo rthat reason or any other -- just draw a new debt sustainability diagonal below and to the right of the current one. Nothing in the story changes. As for endogenizing r, yes, I agree people sort of implicitly have something like that in mind. But part of the point of this exercise is to see why that is not a logically coherent position. Either the central bank sets the interest rate, or it doesn't. Whether the interest rate instrument is available is logically independent of what target it is assigned to. If the interest rate is full endogenous (and you don't have the exchange rate or some other instrument) that rules out sound finance just as much as functional finance. In that world, you can't get both price stability and a stable debt-GDP ratio via any policy rule.

  13. What kind of exchange rate policy can you have if your country is facing a fixed world *real* interest rate?

  14. Good point. If we want to be able to introduce the exchange rate as an independent instrument, then it should be nominal interest rates here, not real.

  15. Yes, in which case that graph becomes "faces a world nominal interest rate and has a currency peg". Point d is Greece. The intersection of FE and r* is where they'd be if they said 'screw austerity' (though probably not for long*). It's basically an argument for a Grexit. Otherwise, bye bye full employment.

    * (there's some additional endogeneity here. Who's gonna keep lending to the government if the debt path is unsustainable and the government promises to keep it that way? If this was a phase diagram there'd be some right-pointing arrows above the DS curve)

    1. (very late reply to this but it's important)

      By hypothesis, the central bank can determine the interest rate. So the answer is, anyone who owns financial wealth. Obviously, a debt-GDP ratio that goes to infinity is going to change the economy in all sorts of (presumably undesirable) ways, which is why we regard the debt-sustainability condition as a target for policy in the first place. But one thing it will not do, is cause interest rates to rise. interest rates are a policy variable.

      Now, you might doubt that the central bank can in fact get the rate of interest wherever it wants it. but then you have to be skeptical of the orthodox policy position as well. Taylor, Woodford, etc. all take it for granted that the central bank can achieve its desired interest rate, regardless of the preferences of asset owners.

    2. My impression is that excessive government debt causes political problems because it creates a constituency of bond holders who don't care too much whether the economy flounders or not and only care that there is not the slightest risk of inflation.
      I had a go posting about that:

      and subsequently saw that Steve R Waldman had previously had the same concern too:

  16. Thanks for this very clear explanation of finance principles. It's easier to learn with such an interactive blogs. Getting different opinions and views makes learning more fun. And that's coming from a student like me. financial services consulting

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