Skip to main content# Chapter 5| Welfare costs and benefits of debt and deficits

## 5.1 Debt and welfare under certainty

## 5.2 Debt and welfare under uncertainty

**Box. The effects of a transfer on welfare.**

###### Assume that people have the following utility function:15

###### Where $C_1$ is consumption when young, and $C_2$ is consumption when old, and E[U(.)] represents expected utility. Their budget constraints are given by:

######

###### When young, they receive a wage, pay the transfer $D$ to the government, and save by investing $K$ in capital. When old, they consume the proceeds from their investment and the transfer $D(1+n)(1+x)= D(1+g)$ from the government. In the first period they choose how much to save, $K$. The first order condition with respect to $K$ is given by:

###### The effects of a transfer on utility are given by:

###### They receive higher transfers in period 2 than they pay in period 1, both because there are more young than old, and because productivity is higher, and transfers increase with productivity. Thus, the presence of $(1+g)$ in the second term.

###### Using the first order condition, $X$ can be written as:

###### The riskless rate (which, in this case, is the shadow rate people would require in order to hold safe debt) satisfies:

###### Replacing in the equation above gives:

###### If $r<g$, the direct effect of a transfer (or higher debt) is to increase welfare. While the algebra is slightly different, a similar argument applies if the government issues debt rather than run a transfer scheme.

## 5.3 Fiscal policy, the ELB, and output stabilization

## 5.4 Putting the threads together.

**Box. The effects on debt and output from fiscal austerity when the effective lower bound is binding.**

###### The following quantitative example gives a sense of the trade-off between the effects of a fiscal consolidation on the debt ratio and on output when monetary policy cannot decrease the policy rate:

Assume that the debt ratio is 100%, that $(r-g)/(1+g)$ is -3%, and the primary deficit is initially 3%, so the debt ratio is constant.

Assume that, in order to decrease the debt ratio, the government increases taxes by 1% of GDP. Given the effective lower bound, the resulting decrease in demand cannot be offset by the central bank. Use a small value of the multiplier, say 1.0 (given the evidence presented in the previous section, this is a lower bound, and using a higher value would strengthen the conclusion), so the decrease in output as a result of the tax increase is 1%.

Assume an automatic stabilizer value of 0.5, so the effect of a decrease in GDP of 1% leads to a decrease in revenues of 0.5% of GDP; the net increase in taxes, and thus the improvement in the primary balance is 0.5% of GDP.

Suppose the government maintains this increase in taxes for 5 years in a row. Then, at the end of five years, the debt ratio has decreased from 100% to approximately 97.5%. If the worry was that debt was too high and exposed the country to excessive interest rate risk, note how little this long period of fiscal austerity and lower output does to decrease the interest burden if $r^*$ were to increase in the future by, say, 3%: debt service as a ratio to GDP would increase by 2.92% instead of 3%. At the same time, the welfare cost of 1% lower output and associated higher unemployment for five years, is large.

The trade-off could be even worse if we used the larger multipliers we saw in the previous section. It would also be worse if hysteresis was at work, if keeping output below potential for an extended period of time led to a decrease in potential output.32 Indeed, there may be no trade-off at all: If hysteresis is sufficiently strong, fiscal austerity may lead to a larger proportional decrease in output than in debt, and thus to a permanent increase in the debt ratio. Going beyond economic effects, it would also be worse if a long period of unemployment above the natural rate led to political unrest, and the risk of electing a populist government.

Clearly, if debt could be reduced quickly to 50% at little cost in output, this would make a substantive difference if and when the interest rate increased, but such a decrease is outside the realm of what can be realistically achieved, short of debt cancellation—which is not in the cards, and, as I have argued in Chapter 4 is simply not needed today.

**Box. The tug of war between QE and Treasury debt management**

###### Apart from the basic issue of coordination between fiscal and monetary policy, another coordination issue arises in the determination of the average maturity of the debt held by outside investors. As interest rates decreased in the past, Treasuries increased the average maturity of the public debt so as to lock in the low rates and decrease the risks of a sudden increase in short-term interest rates on interest payments. In parallel, as central banks hit the effective lower bound on the policy rate and could not decrease it further, they embarked on purchases of government (and other) securities, a policy known as quantitative easing (QE) so as to decrease the interest rate on longer maturity bonds. In doing so, they bought long maturity government bonds and issued in exchange, interest paying, zero maturity, central bank reserves.

###### The tension between the two sets of actions is obvious however. If we think of the debt of the consolidated government (Treasury plus central bank), the actions of the Treasury increased maturity, while the actions of the central bank reduced it. The net result, in terms of the maturity of the debt held by private investors has in many cases been roughly a wash. Take for example what happened during the financial crisis in the United States: Between December 2007 and July 2014, the duration of debt of the Federal government increased from 3.9 to 4.6 years. But the duration of the consolidated government debt (thus including zero maturity, interest paying central bank reserves) held by private investors actually *decreased* from 4.1 to 3.8 years (Greenwood et al. 2014 [13]).

###### Was it mostly a wash, a waste of two offsetting operations? Not completely, because as a result of both sets of operations, consolidated government debt included a larger proportion of interest paying central bank reserves, and, in contrast to government bonds, central bank reserves are not runnable, thus decreasing the risk of a run on debt. Still, it is the case that the result of these operations is that the government remains more exposed to interest rate risk than it would want.

###### The issues, looking forward, are twofold. As aggregate demand increases, should central banks phase out quantitative easing and let the Treasury manage the maturity of the debt? Indeed, one can see the choice of a higher value of $r^*$ as allowing the central bank to rely more on the policy rate and phase out its QE operations faster, letting the Treasury be in charge of debt management, and avoiding the need for coordination. And, if central banks decide to continue to rely on QE and have large balance sheets, even as policy rates become positive again, how should these be coordinated with Treasuries? 33

This chapter is about how a country's fiscal pace should be used. The fact that there is space does not mean that it should be used. Fiscal policy is about whether, when, and how to use that space.

Published onMar 30, 2022

Chapter 5| Welfare costs and benefits of debt and deficits

The chapter is organized in four sections.

Sections 1 and 2 discuss what may feel like an abstract and slightly esoteric topic, but, it turns out, a topic which is central to the discussion of fiscal policy, namely the effects of debt on welfare under certainty and then under uncertainty.

Section 1 looks at the welfare costs of debt under certainty. Public debt is widely thought of as bad, as “mortgaging the future”. The notion that higher public debt might actually be good, increase welfare (on its own, i.e. ignoring what it is used to finance) feels counterintuitive. The section reviews what we know about the answer under the assumption of certainty. The answer is that debt might indeed be good, and that the condition, under certainty, is precisely $(r-g)<0$. The section puts together the two celebrated steps of the answer. The “Golden Rule” result, due to Phelps 1961 [1], that, if $(r-g)<0$, less capital accumulation increases welfare; and the demonstration by Diamond 1965 [2] in an overlapping generation model, that, if $(r-g)<0$, issuing debt does, by decreasing capital accumulation, increase the welfare of both current and future generations. These are clearly important and intriguing results. They are however just a starting point.

A major issue is again uncertainty, the issue taken in Section 2. Under the assumption of certainty, there is only one interest rate, so the comparison between $r$ and $g$ is straightforward. But, in reality, there are many rates, reflecting their different risk characteristics. The safe rate is indeed less than the growth rate today. But the average marginal product of capital, as best as we can measure it, is substantially higher than the growth rate. Which rate matters? This is very much research in progress but, thanks to a number of recent papers, we have a better understanding of the issue. In the Diamond model for example, which focuses on finite lives as the potential source of high saving and excess capital accumulation, the relevant rate is typically a combination of the two, although with a major role for the safe rate. Going to the data suggests that the relevant rate and the growth rate are very close, making it difficult to decide empirically which side of the golden rule we actually are. In other models where, for example, the lack of insurance leads people to have high precautionary saving, potentially leading to excess capital accumulation, the answer is again that the safe rate plays a major role; in that case however, while debt is likely to help, the provision of social insurance, by getting at the source of the low $r$, may dominate debt as a way of eliminating capital overaccumulation. Overall, a prudent conclusion, given what we know, is that, in the current context, public debt may not be good, but is unlikely to be very bad—that is, to have large welfare costs; the more negative $(r-g)$, the lower the welfare costs.

Section 3 turns to the welfare benefits of debt and deficits. It focuses on the role of fiscal policy in macro stabilization, a central issue if for example monetary policy is constrained by the effective lower bound. It reviews what we know about the role of debt, spending, and taxes (and, by implication, deficits) in affecting aggregate demand: Higher debt affects wealth and thus consumption demand. Higher government spending affects aggregate demand directly, lower taxes do so by affecting consumption and investment. Multipliers, that is the effect of spending and taxes on output, have been the subject of strong controversies and a lot of recent empirical research. The section discusses what we have learned. The basic conclusion is that multipliers have the expected sign, and fiscal policy can indeed be used to affect aggregate demand.

In 1961, Phelps [1] argued the following: A market economy could accumulate too much capital. Such overaccumulation would be reflected in a simple inequality, namely $(r-g)<0$, where $r$ was the net marginal product of capital (and because Phelps was working in the context of a model with no uncertainty, $r$ was also the safe rate of interest). If this condition held, decreasing capital would actually be welfare improving.1

To understand his argument, go back to the basic national income identity (In general, we would have to include government spending, and in an open economy, exports minus imports, but the argument is simpler to present if we ignore them for the time being). Output is equal to consumption plus investment. Or equivalently, consumption is equal to output minus investment:

$\label{YCI}
C = Y - I$(1)

Assume output is equal to potential output, itself given by the production function $F(K,.)$ where the dot denotes other factors of production from labor to an index of the state of technology.

Assume that the economy is on a balanced growth path, so that $C,Y,I$ are all growing at some rate $g$. Assume that capital depreciates at rate $\delta$, so that for capital to grow at rate $g$, investment must cover both depreciation and the growth of the capital stock:

$I = (\delta + g) K$(2)

Replacing in equation ([YCI]) gives

$C = F(K,.) – (\delta+g) K$(3)

The effect of additional capital on consumption is thus given by:

$dC/dK = F_K(K,.) – (\delta+g) = (F_K(K,.)-\delta) -g$(4)

Taking the interest rate to be equal to the net marginal product of capital, $r \equiv F_K(K,.)-\delta$, the equation above becomes

$dC/dK = r-g$(5)

The relation between capital and consumption at any point along the growth path is represented in Figure 5.1. Consumption is an increasing function of capital, until $(r-g)=0$. That level of capital is called the golden rule level of capital. As we look at levels of capital higher than the golden rule level, $(r-g)$ becomes negative and consumption becomes a decreasing function of capital. The intuition is that, as the capital stock increases, depreciation (which needs to be replaced) increases linearly with capital, but the gross marginal product of capital increases at a slower pace, so that the net marginal product of capital becomes negative. Although output is higher, so much has to be put aside for investment that what is left for consumption is lower.

Suppose the economy is to the right of the golden rule, so $(r-g)<0$, and we decrease capital today, leading to more output being left for consumption.2 So long as the inequality holds3, this will lead to both more consumption today and more consumption in the future. To use the terminology used by Phelps [1], the economy is *dynamically inefficient*: both current and future generations can be made better off.

Can there really be capital overaccumulation? And why should public debt help in this case?

Diamond (1965) [2], using the same two-period overlapping model as the one we used in Chapter 4 to discuss saving and demographics, gave the answers: Even if people are fully rational and take individually optimal saving decisions, there can indeed be capital overaccumulation. If this is the case, then anything that decreases saving can, if distribution effects do not stand in the way, increase everybody’s consumption and welfare, now and in the future. Intergenerational transfers, or public debt, can play that role. The argument goes as follows:

Suppose people live for two periods, working in the first, retiring in the second. They receive a wage in the first period, save by investing in capital (so there is no separate saving/investment decision), and consume the capital and the returns from capital in the second period. Thus, the saving of the young determines the capital stock of the economy in the next period.

Suppose the economy grows on its balanced growth path, with all aggregate variables growing at rate $g$, equal to the sum of the growth rate of population (or equivalently, assuming a fixed ratio of employment to population, the rate of growth of employment), $n$, and the growth rate of productivity, $x$.4 5

The saving rate of the young determines the level of capital along the growth path. The first result the model delivers is that, while individual saving decisions are rational, there is no guarantee that these decisions imply that $r= (F_K – \delta) >g$: $(r-g)$ can be negative and there can indeed be capital overaccumulation. Put another way, a market economy, with rational individuals, can be on the wrong side of the golden rule and thus be dynamically inefficient.

The second result is that, if this is the case, transfers from the young to the old can increase welfare for all generations, current and future:

When the young save one unit, they get $(1+r)$ units when old. Now suppose that the government puts in place a transfer scheme, taking $D$ from each of the young, and giving $(1+n) D$ to each of the old within the same period (as there are $(1+n)$ young for each old), with $D$ increasing at rate $x$ over time. Think of it as a pay-as-you-go retirement system, in which the contributions from the young finance the benefits for the old, and per capita retirement contributions and benefits increase with productivity over time.

When young, people lose $D$ in income. When old they receive $D(+1) (1+n) = D(1+x)(1+n) = D(1+g)$ in income (D(+1) is the individual transfer from the young next period, and there are $(1+n)$ young workers for every old worker). If $(r-g)>0$, the transfer scheme delivers less than saving, and thus decreases their welfare. But if $(r-g)<0$ however, the transfer scheme is more attractive than saving, and increases the welfare of each generation. In this case, a pay-as-you-go retirement system can make all generations better off.

Turning from transfers to debt, debt also generates intergenerational transfers, in a slightly different way. Think of the government issuing one-period debt every period, with debt issuance increasing at rate $g$. The young who buy the debt receive $D(1+r)$ when old, and are indifferent between investing in capital or buying the debt: Both pay $r$. The issuance of debt next period is equal to $D(+1) = D(1+g)$. Thus, each period, the government gets the difference between revenues from debt issuance $D(1+g)$ and payments on debt $D(1+r)$. If $r<g$, this difference, equal to $D(g-r)$, is positive and can be redistributed to a combination of the young and the old, making them better off.

There is a limit to these two schemes, be it pay-as-you-go or debt. As debt decreases capital accumulation, it has general equilibrium effects. The wage decreases, the marginal product of capital and thus the interest rate increases. When the interest rate becomes equal to the growth rate, the economy is at the golden rule. Further debt leads to $(r-g)>0$, and debt no longer improves the welfare of all generations. The initial old gain, the others however lose. The government then has to think about the trade-off between the current old, who benefit from debt, and future generations, who face lower consumption and lose from debt. But until this threshold is reached, public debt can improve welfare for all.

These are important, intriguing, and probably to many, counterintuitive, results. They were seen as surprising but exotic outcomes until recently: Could it really be that advanced economies accumulate too much capital? Could public debt really be good for welfare, independent of what is done with it? But the fact that $r$ is now so much lower than $g$ forces us to take these questions more seriously. To give a full answer, one must look at how this analysis extends under uncertainty. This is the topic of the next section.

In contrast to the maintained assumption of Section 1, we live in a world of uncertainty, where there are many interest rates and rates of return, from rates on government bonds to the rates of return on equity and so on.

In the discussion of debt sustainability in Chapter 4, the rate that was relevant to the discussion was the rate at which the government could borrow, thus in effect the safe rate or close to it in most advanced economies. The welfare discussion in the previous section suggests however that what is important is instead the marginal product of capital, net of depreciation. And on average, this rate appears substantially higher than the average growth rate.

Figure 5.2 shows the evolution of two measures of rates of return on capital, for the United States since 1992. Both use the same measure of earnings in the numerator, namely the pre-tax earnings of U.S. non-financial corporations6. The blue line shows the ratio of earnings to the capital stock measured at replacement cost. The red line shows the ratio of earnings to the capital stock measured at market value. Which of the two is a better proxy for the marginal product of capital is not obvious: If there were no rents, then the ratio of earnings to replacement cost would be the natural measure. But part of the corporate earnings represent rents, and the value of these rents may be why the market value of capital exceeds its replacement cost, in which case using the ratio of earnings to capital at market value seems more appropriate.78 9

*Source: Figure 15, Blanchard 2019 *[4]*, extended to 2020.*

For our purposes, we do not need to choose between the two measures: The point of the figure is that either measure of the marginal product is substantially higher than the real safe rate (see Figure 3.1), and, more importantly, substantially higher than the growth rate.

This raises the obvious question: Which rate should we choose in assessing the welfare effects of debt?

To answer, think again of the Diamond economy with an underlying constant rate of growth $g$, but with fluctuations in the marginal product of capital $F_K$, leading to fluctuations around the growth path in both the marginal product of capital and in output.10 (The box below gives the basic algebra.) Return to our transfer scheme:

When the young save one unit, they get $(1+ F_K – \delta)$ units next period.

Now suppose the government puts in place a transfer scheme, taking $D$ from each the young, and giving $(1+n) D$ to each of the old, with $D$ growing at rate $x$ over time. When young, they lose $D$ in income. When old, they receive $D(+1) (1+n) = D(1+x)(1+n) = D(1+g)$ in income.

As we have seen, the average value of $(F_K – \delta)$ appears substantially higher than $g$, so it looks as if the transfer scheme (and by implication, the use of public debt) decreases the welfare of the young. But this is not right. $(F_K -\delta)$ is risky, while the transfer is riskless. Thus, we must adjust the rate of return on capital for risk. But the risk-adjusted rate of return on capital is precisely the riskless rate, $r$.11 Thus, the comparison must be between $r$ and $g$.

This would seem to lead to a striking conclusion: That, even under uncertainty, whether the effect of debt on welfare is positive still depends on a comparison between the riskless interest rate and the growth rate; and given that $(r-g)<0$, that public debt has no welfare costs, indeed has welfare benefits…12 13 This conclusion is striking and points to the deep issues raised by the very low safe rates, but it is again still only a first pass, for a number of reasons:14

$\max \; (1-\beta) U(C_1) + \beta E [U(C_2)]$(6)

$C_1 = W – D – K$(7)

$C_2 = (1+F_K – \delta) K + (1+n)(1+x) D$(8)

$-(1-\beta) U’(C_1) + \beta E [(1+F_K – \delta) U’(C_2)]=0$(9)

$X = -(1-\beta) U’(C_1) + \beta (1+g)E[ U’(C_2)]$(10)

$X = \beta ((1+g) E[U’(C_2)] – E[(1+F_K-\delta) U’(C_2)])$(11)

$(1+r) EU’(C_2) = E[(1+F_K – \delta) U’(C_2)]$(12)

$X = \beta (g-r) E [U’(C2)], \; \mbox{so if} \; r < g \; \mbox{then} \; X>0$(13)

The argument leaves aside the indirect effects of public debt. As debt is issued and displaces capital in the portfolio of the young, lower capital decreases returns to labor and increases returns to capital, and these in turn affect welfare. The implication of these indirect effects turns out to be complicated, but the conclusion is that, in general, both the safe rate and the average rate of return on capital will matter.16

In Blanchard 2019 [5], I derived an approximate formula under the assumption of a Cobb Douglas production function, which (adapted to allow for underlying growth which I had left aside in the original article) gives the condition that public debt increases welfare if $1/2 \; (r + E (F_K-\delta)) < g$, (where $E(.)$ is now an unconditional expectation) thus giving equal weights to the safe rate and the average marginal product of capital.17

Taking this approximation at face value and using a real safe rate of -0.5%, (roughly the current 10-year real rate on indexed bonds) and an average real rate of return on capital of 5.5% (roughly the average rate of return on stocks since 1992, measured by the ratio of earnings to market value) gives $1/2 \; (r + E (F_K-\delta))$ = 2.5% , close to the expected real growth rate over the next 10 years of 2%. This rough computation thus suggests that the effect of debt on welfare through the displacement of capital is probably close to zero. 18

The argument assumes that the difference between the safe rate and the expected rate of return on capital reflects investors’ rational decisions, based on their degree of risk aversion and the degree of aggregate risk associated with capital. There is however substantial controversy about whether this is the case. The issue is known as the

*equity premium puzzle*.19 The puzzle is that, given the observed limited variations in aggregate earnings, it would take an implausibly high degree of risk aversion to explain the size of the equity premium. A version of the puzzle can be seen in Figure 5.2: since 1992, the ratio of earnings to capital (at replacement cost or market value) has never been lower than the safe rate. Investors with claims to next period marginal product would have had higher returns in each year than if they held the safe asset. Various explanations have been advanced. Barro (for example Barro and Ursua 2011 [6]) has argued that rare, and thus rarely observed, macroeconomic disasters may explain the premium. If so, there may be no puzzle, just a fat tail distribution of shocks. Others have suggested behavioral explanations, for example, myopic risk aversion (Benartzi Thaler 1995 [7]); if so, one would have to see whether the argument carries through with those preferences and behavior (I have not done it).Given the difficulties in assessing what is behind the equity premium, Abel et al. [8] derived a very intuitive sufficient condition for dynamic inefficiency which does not depend on it: If, every year, gross profits exceeded gross investment, implying a positive net cash flow, then one could be confident that there was no capital overaccumulation. They applied their criterion to six major advanced economies and concluded that this condition was satisfied for every country in every year of the time period they looked at (1953 for the United States, 1960 for the others). The approach has however been revisited by Geerolf [9] who argues that, excluding land rents and entrepreneurial income from gross profits, no advanced economy actually satisfies the sufficient condition, and thus the issue of capital overaccumulation remains open.20

The overlapping generation model used to discuss the issue does not include financial frictions. These frictions exist however, and individuals face much more risk than aggregate risk. They face substantial idiosyncratic shocks that they cannot fully insure against. In this case, precautionary behavior will lead to more saving, to a lower neutral safe rate and possibly to a larger equity premium. This does not destroy the case for higher public debt to potentially increase welfare, but, in this case, public debt may not be the best tool. Providing better social insurance, and thus directly addressing the problem of missing insurance markets, is clearly a better way to do it. From a macro viewpoint (i.e. leaving aside the fact that more social insurance is likely to be welfare improving on its own), “Medicare for all” for example, even if it is fully self financing, may dominate higher debt. This point will be relevant when we discuss actual policy choices later.21

In short, the fact that $(r-g)<0$ is a strong signal that the risk adjusted return on capital is surprisingly low, and thus the welfare costs of public debt coming from the reduction in the capital stock are also low. The next section turns to potential welfare benefits

Even if monetary policy is unconstrained, fiscal policy can help reduce fluctuations. There is indeed a long tradition of letting automatic stabilizers operate, i.e. to allow for lower tax revenues and higher transfers to stimulate demand when output is unusually low: the argument is they act faster than monetary policy in affecting demand and output.22 The case for using fiscal policy is however stronger when the nominal policy rate is at the effective lower bound, or even when it is positive but low enough that monetary policy cannot offset large adverse shocks.

The question then is whether and how fiscal policy affects aggregate demand, and in turn output.23

One must distinguish between three channels: the effect of debt itself, the effect of taxes and transfers, and the effect of government spending. For those who hold the debt, public debt is part of their wealth and thus affects their consumption. Current and future taxes also affect consumption and investment. And current government spending affects demand directly.

In the two-period overlapping generation model I have used a few times in the book, the three effects are clear: The consumption of the young depends on taxes this period and expected taxes next period; the consumption of the old depends on their wealth when they become old, thus on their debt holdings, and on the taxes they pay when old; and government spending affects demand directly. In more realistic models, the effects are more intricate:24

By itself, debt is wealth for those who hold it; but it may be partly offset by the expectation of future taxes. Indeed, in the extreme case of infinitely-lived rational forward-looking individuals, for given government spending, any increase in debt is fully offset by an increase in the expected present value of taxes, and so has no effect on consumption, a result known as

*Ricardian equivalence*. But, in general, because of finite horizons or just myopia, the offset is likely to be much less than one-for-one. And, as we have seen, when $r <g$, higher debt need not require an increase in taxes later on.By itself, a decrease in taxes increases income. If the decrease in taxes is expected to extend in the future, the effect is larger. If, instead, it is expected to lead to a reversal and an increase in taxes in the future, the effect is likely to be smaller. Indeed, under the same assumption of infinitely-lived rational forward-looking individuals, and assuming no change in current and expected future government spending, the effect of the decrease in taxes today is fully offset by the expectation of higher taxes in the future, so it has no effect on consumption; this is another way of stating the Ricardian equivalence result. Again, in general, the offset is likely to be much less than one-for-one: Many households may not think about future taxes. Many also may be liquidity constrained and use the decrease in taxes to increase consumption, even if they believe that taxes will increase in the future. In short, decreases in taxes are likely to increase consumption.

By itself, an increase in government spending mechanically increases aggregate demand. To the extent however that it leads people to expect higher taxes in the future, then the direct effect may be partly offset by a decrease in consumption. Again, there is every reason to believe that the offset is limited, and that higher government spending increases aggregate demand.

These are just the first-round effects, and they trigger general equilibrium effects. The textbook example is the Keynesian multiplier, in which the initial effect of a decrease in taxes on income leads to an increase in demand, which leads to an increase in output, which leads to a further increase in income and so on. Again, the strength of the effect depends on many factors, from how many households are liquidity constrained to how open the economy is. The main factor, and the one most relevant for this discussion is the stance of monetary policy. If a fiscal expansion takes place when output is already at potential, monetary policy is likely to tighten, leading to higher interest rates, and thus a smaller effect or even no effect of the fiscal expansion on output. If a fiscal contraction takes place and—as is the case today—monetary policy is constrained by the ELB, it is likely to have a larger adverse effect on output.

The discussion makes clear that the effects of debt, taxes, and spending, depend very much on expectations as well as on monetary policy, and are likely to vary considerably across space and time. There is no such thing as “a” multiplier. Interestingly, the fiscal consolidation which took place in the wake of the Global Financial Crisis and the ELB constraints on monetary policy have led to what Ramey 2019 [10] has called a renaissance of empirical work on the effects of fiscal policy. Here are what I draw as the major conclusions:

How much does higher public debt increase aggregate demand, and in turn the neutral interest rate, $r^*$? (Recall that the neutral rate is the rate such that aggregate demand is equal to potential output. Thus, the stronger aggregate demand, the higher the neutral rate.) This is a central question: It determines in particular how much governments can increase debt until $r^*$, and by implication, $r$, becomes higher than $g$, and we return to a traditional environment where $r>g$.

It is however a difficult question to answer, for two reasons. The degree to which the effects of debt are partially offset by the anticipation of future taxes is likely to vary across time and place. For example, as we have seen, in the $(r-g)<0$ environment, higher debt may not imply future taxes later, and thus affect wealth one-for-one. And, empirically, detecting the effects of debt per se on aggregate demand and, by implication, on the neutral interest rate, is difficult given that debt moves slowly and many other factors matter more in the short run. Various estimates of the effect of debt on $r^*$ have been given, some based on a calibrated model, some based on regressions. They are summarized in Rachel and Summers (2019) [11] and range from 2 to 4 basis points for a 1% increase in the ratio of debt to GDP. Thus, Rachel and Summers argue, the increase in the debt ratio of about 60% since the early 1990s added 1.2 to 2.4% to the neutral rate. Put another way, had public debt ratios not increased, the neutral rate would be even more negative today, lower by another 1.2 to 2.4%. 25 Looking forward rather than backward, another increase in debt, by say 50% of GDP, would further increase $r^*$ by 100bp to 200bp, substantially reducing the size of the difference between $r$ and $g$, although probably not changing its sign.

For our purposes, I see the major conclusions from the recent research on tax and spending multipliers as follows:26 27 28

Based on both time series methods (typically structural vector autoregressions, called VARs) and model simulations (usually, New Keynesian dynamic stochastic general equilibrium models, called DSGEs), most estimated multipliers have the expected sign: (Plausibly exogenous) increases in taxes decrease output; (plausibly exogenous) decreases in spending decrease output.29

Surprisingly, most empirical studies find larger tax multipliers than spending multipliers. In the Ramey survey, spending multipliers range from 0.6 to 1.0.30 Tax multipliers are however typically much larger (in absolute value), ranging from -1.0 to -5.0 (!). The reason this is surprising is that, in the textbook Keynesian model, the opposite holds: In the first round, taxes affect demand through consumption, thus less than one for one, while government spending affects demand directly; the implication is that tax multipliers should be smaller than spending multipliers; this appears not to be the case, whether because of different adjustments of expectations, differences in monetary responses, or other reasons.

Of direct relevance to the current situation, given the effective lower bound constraint and the high level of debt: The multipliers appear larger when the monetary response is more limited (see Leigh et al. 2010 [12]). And they appear smaller when debt ratios are high, perhaps because people are more worried that taxes may be increased in the future, or debt may become unsustainable.

In summary: Fiscal policy can play a central role in helping keep output at potential. Higher debt increases aggregate demand. Lower taxes or higher spending also do. Multipliers are likely to vary a lot over time and space, but the bulk of the evidence is that they are different from zero, positive for spending, negative for taxes, and that they are stronger when monetary policy does not or cannot react to fiscal policy.

Real interest rates are low, debt ratios are high. In this economic environment, what do the arguments developed in the book so far imply for how fiscal policy should be designed? Let me put the various parts of the answer together: We have seen that:

The lower the neutral rate, the lower the fiscal costs of debt. Debt dynamics are more favorable; indeed as $r^*$ and by implication $r$, becomes less than $g$, governments can run (some) primary deficits while keeping their debt ratio constant.

The lower the neutral rate, the lower the welfare costs of debt. For sufficiently low neutral rates, debt may even have welfare benefits, although it is difficult to pin down the exact rate at which this happens. A reasonable working assumption is that, while neutral rates are indeed low, debt still has welfare costs, albeit limited ones.

The lower the neutral rate, the more limited is the room for monetary policy to stabilize output. In particular, if $r^*$ becomes smaller than $r_{min}$, the lowest real rate the central bank can achieve given the effective lower bound, then monetary policy can no longer maintain output at potential. Fiscal support, in the form of deficits, is needed to do so. Even if the effective lower bound is not strictly binding, the closer $r^*$ is to $r_{min}$, the less room monetary policy has to react to adverse shocks, the more fiscal support might be needed.

Putting these propositions together: The lower the neutral rate, the smaller the fiscal and welfare costs and the larger the welfare benefits of debt and deficits.

To go one step further, it is useful to think of two extreme approaches to fiscal policy:

A

*pure public finance*approach, focusing on the use of debt to smooth tax distortions or to redistribute income across generations, and ignoring the effects of policy on aggregate demand and output. It is widely believed that the levels of debt we observe today are higher than what this approach would suggest. If so, under this approach, debt should be decreased over time, and governments should be running primary surpluses.A

*pure functional finance*approach—using the terminology introduced by Abba Lerner in 1943 [3]—focusing on the macro stabilization role of fiscal policy, and ignoring the effects of policy on debt. Under this approach, if aggregate demand is weak and monetary policy is constrained, then governments should not hesitate to sustain aggregate demand and output and run primary deficits.31

We can then think of the appropriate fiscal policy as a weighted average of the pure public finance and pure functional finance approaches, with most of the weight on the pure functional finance approach and macro stabilization when the neutral rate is very low, and most of the weight on the pure public finance approach and debt reduction when the neutral rate is very high.

Start from a situation where aggregate demand is very weak, reflecting very weak private demand and a given fiscal stance. Suppose that, as a result, the neutral rate is low, indeed lower than can be achieved by the central bank given the effective lower bound: $r^*$ is less than $r_{min}$, and thus $r=r_{min} < r^*$. As monetary policy cannot set the interest rate low enough to match the neutral rate, output is lower than potential. Then, priority must be given to macro stabilization, to an increase in the budget deficit so as to return output to potential.

How large should the increase in deficits be? At a minimum, it should be such as to bring back $r^*$ back up to $r_{min}$: By doing so, it brings output back to potential, and the central bank can set the policy rate just equal to the neutral rate: $r =r_{min} = r^*$. This however leaves no room for monetary policy to react to further adverse shocks, as the effective lower bound is still strictly binding. Thus, what fiscal policy should do is aim for a higher value of $r^*$, say $r^* = r_{min} + x$ to give some room to monetary policy. How large $x$ should be depends on the trade-off between giving more room to monetary policy versus increasing the costs of debt.

Implementation could take various forms. The government could be in the lead and choose the size of the deficit. It would lead to overheating, leading the central bank to respond by increasing $r$ in line with $r^*$. Or it could take the form of a coordinated fiscal expansion/monetary contraction, with the government increasing demand and the central bank increasing the interest rate, so as to achieve potential output at the desired value of the neutral rate $r^*$.

What would obviously be the wrong fiscal policy would be to give, in this context, priority to the pure public finance approach, and embark on a fiscal consolidation in order to decrease debt. Given the assumption that, in this case, monetary policy is constrained by the effective lower bound, the effect would be a decrease in output. It would lead to a large welfare cost from lower output, and only a small welfare gain in terms of lower debt (more on this when discussing the shift to fiscal austerity in the wake of the Global Financial Crisis in the next chapter). The box below gives a sense of what the outcome for debt and output might be if such a policy were indeed to be pursued.

Note an important implication. Under this policy, if such a policy was followed, we should never observe rates lower than $r_{min}+ x$. In effect fiscal policy would set a floor for the neutral rate, standing ready to increase deficits if the neutral rate decreased below $r_{min} + x$.

Assume that private demand becomes stronger. How should fiscal policy adjust?

The same logic as the one used above suggests that, if private demand becomes stronger, the policy adjustment should take the form of delivering both some increase in the room for monetary policy and some reduction in the deficit. In other words, the increase in private demand should be partly offset by a decrease in the deficit, so as to lead to a smaller increase in aggregate demand than in private demand. And this net increase in aggregate demand should itself be offset by a monetary contraction, an increase in the policy rate, in order to maintain demand and output at potential. The outcome should be a smaller deficit, a higher neutral rate, and more room for monetary policy. Again, implementation of this combination of fiscal and monetary consolidation can take the form of fiscal policy in the lead and monetary policy reacting to avoid overheating and keep output at potential, or of coordination between the two in reaction to the movements in private demand. (Another issue of coordination between fiscal and monetary policy, namely the coordination of decisions affecting the average maturity of the debt of the consolidated government, is taken in the box below.)

As private demand increases further, the marginal benefit of increased room for monetary policy becomes smaller, the marginal cost of debt becomes larger. This implies that the fiscal offset to private demand should become stronger. Indeed, when private demand becomes very strong, and monetary policy has sufficient room to offset most adverse shocks, including fiscal consolidation, then the government can focus on the pure public finance approach, and run the surpluses it deems appropriate to reduce the debt over time, leaving monetary policy fully in charge of macro stabilization.

Assume that the debt ratio is 100%, that $(r-g)/(1+g)$ is -3%, and the primary deficit is initially 3%, so the debt ratio is constant.

Assume that, in order to decrease the debt ratio, the government increases taxes by 1% of GDP. Given the effective lower bound, the resulting decrease in demand cannot be offset by the central bank. Use a small value of the multiplier, say 1.0 (given the evidence presented in the previous section, this is a lower bound, and using a higher value would strengthen the conclusion), so the decrease in output as a result of the tax increase is 1%.

Assume an automatic stabilizer value of 0.5, so the effect of a decrease in GDP of 1% leads to a decrease in revenues of 0.5% of GDP; the net increase in taxes, and thus the improvement in the primary balance is 0.5% of GDP.

Suppose the government maintains this increase in taxes for 5 years in a row. Then, at the end of five years, the debt ratio has decreased from 100% to approximately 97.5%. If the worry was that debt was too high and exposed the country to excessive interest rate risk, note how little this long period of fiscal austerity and lower output does to decrease the interest burden if $r^*$ were to increase in the future by, say, 3%: debt service as a ratio to GDP would increase by 2.92% instead of 3%. At the same time, the welfare cost of 1% lower output and associated higher unemployment for five years, is large.

The trade-off could be even worse if we used the larger multipliers we saw in the previous section. It would also be worse if hysteresis was at work, if keeping output below potential for an extended period of time led to a decrease in potential output.32 Indeed, there may be no trade-off at all: If hysteresis is sufficiently strong, fiscal austerity may lead to a larger proportional decrease in output than in debt, and thus to a permanent increase in the debt ratio. Going beyond economic effects, it would also be worse if a long period of unemployment above the natural rate led to political unrest, and the risk of electing a populist government.

Clearly, if debt could be reduced quickly to 50% at little cost in output, this would make a substantive difference if and when the interest rate increased, but such a decrease is outside the realm of what can be realistically achieved, short of debt cancellation—which is not in the cards, and, as I have argued in Chapter 4 is simply not needed today.

That this characterization of policy is only a first pass is obvious. While the principles are clear, much more formalization and quantitative work is needed to make these recommendations operational.34 It also raises a number of issues, to which I now turn.

*Will fiscal policy actually work? Back to multipliers.*

If deficits lead to an increase in debt ratios starting from already high levels, could it be that they will not have the desired effect on aggregate demand?35 Can we be sure that multipliers will have the right sign? Could a fiscal expansion in the current context be contractionary, or a fiscal contraction be expansionary? This argument, that was made by some to argue for *expansionary fiscal austerity* after the Global Financial Crisis was that it would reassure investors that the government was committed to keep debt sustainable, that such increased investors’ confidence would lead in turn to a large decrease in spreads, to a decrease in interest rates not just for the government but for the private sector as well, all leading to an increase in aggregate demand.36 The argument cannot be rejected out of hand, and there are indeed cases in history where this confidence effect was probably at work.37 There is now wide agreement that, even if this effect was partly at work in 2009 and 2010, it was not sufficient, and fiscal austerity was unambiguously contractionary during that period.38 (more on this episode in the next chapter) In the current context, this argument, which I expect to come back soon in the conversation, also does not appear relevant. The spreads are very low already (indicating that investors are not worried about debt sustainability), and thus cannot decrease much.

*Revisiting the inflation target.*

The value of the real safe rate at the effective lower bound (which is a bound on the nominal rate, not on the real rate), $r_{min}$, depends one-for-one on expected inflation. The higher expected inflation, the lower the real safe rate at the effective lower bound, and thus the less need for fiscal deficits to sustain output. This raises the old issue of the right inflation target. The issue of the optimal rate of inflation has been long debated, but its implication for fiscal policy, namely the need to run deficits when the ELB is binding, has typically not been taken into account. That a higher inflation rate would be desirable has led to proposals for engineering a strong fiscal expansion, together with monetary policy keeping $r$ below $r^*$ for some time, so as to generate overheating and an increase in the inflation rate above the current target, perhaps leading to an upward revision of the target.39 The Biden administration stimulus plan, together with a dovish attitude by the Fed, can be seen as indeed intentionally overheating the economy, with the goal of creating, at least temporarily, higher inflation. The Fed however has not revised its target inflation up, and, so far, gives no indication of doing so (more on this in the next chapter, when discussing the effects of the Biden administration stimulus).40

*What if secular stagnation becomes worse?*

What if private demand remains so weak that, despite the central bank remaining at the ELB, the required primary deficits are so large that the debt ratio steadily increases, putting into question debt sustainability? The question is clearly relevant for Japan and its already very high debt ratios (more on this in the next chapter, when discussing Japanese fiscal policy over the last 30 years, and future prospects) and raises the issue of whether there are alternatives to fiscal deficits to sustain aggregate demand.

Some researchers have suggested relying on the Keynesian *balanced budget multiplier*, i.e. on an equal increase in spending and in taxes. The logic of the argument is that to the extent that taxes work through consumption, and given that the marginal propensity to consume is less than one, they have a less than one-for-one effect on demand, while spending affects demand directly and one-for-one. Although this works in the textbook, the empirical evidence I discussed earlier suggests that tax multipliers are actually *larger* than spending multipliers, and if so, such a balanced budget increase would most likely have perverse effects.

A more promising way is to focus on the determinants of $r^*$, and whether some of these determinants can be affected by policy. The analysis of the factors behind low $r^*$ suggest a number of leads:

On the investment side, it might be that some of the green public investment triggers a large increase in related private investment and thus a potentially large increase in demand (and in supply later on). The evidence on the spillover effects of green investment is limited, but suggestive. A study by the Council of Economic Advisors 2016 [14] concluded that the 46 billion allocated in the ARRA package passed in the United States in 2009 led to more than 150 billion in private and non federal private investment, thus a high multiplier. A study by Aldy [15] estimates that the clean energy manufacturing tax credit included in the same ARRA package, with a total tax expenditure cap of USD 2.3 billion, supported co-investment of 5.4 billion. A study by Springel 2021 [16], based on Norwegian data, finds that one dollar invested in charging stations led to four dollars in increased purchases of electric vehicles. Batini et al. [17], using a structural VAR approach, conclude that the multipliers associated with spending on renewable and fossil fuel energy investment range from 1.1 to 1.5.41 42

On the saving side, Mian et al. 2021 [18] have argued that, because the rich save proportionately more than the poor, increasing inequality in the United States since the early 1980s has contributed to higher saving and to the decrease in $r^*$. Realistically however, the decrease in inequality which would lead to significantly less saving is out of reach. I believe that in some countries, one of the most promising leads is to focus on precautionary saving. The provision of more social insurance, say an extension of Obamacare or the provision of “Medicare for all” in the United States, would be good on its own, but presumably also lead to less precautionary saving, an increase in private demand, and a lower need for budget deficits. In any case, if secular stagnation continues to dominate, these and other directions will have to be explored.