Do negative interest rates render government debt costless? No. What about r<g? I discuss Olivier Blanchard’s presidential address and the conclusions that columnists have drawn.
For background: See this post.
Do negative interest rates render government debt costless? No. What about r<g? I discuss Olivier Blanchard’s presidential address and the conclusions that columnists have drawn.
For background: See this post.
Risk, Discounting, and Dynamic Efficiency
In the presence of risk, a comparison of the risk-free interest rate and the expected growth rate is insufficient to assess whether an economy is dynamically efficient or inefficient. Stochastic discount factors—not risk-free interest rates—enter the government’s budget constraint, even if debt is safe.
These points are made, for example, by Andrew Abel, N. Gregory Mankiw, Lawrence Summers, and Richard Zeckhauser (Assessing Dynamic Efficiency: Theory and Evidence, REStud 56(1), 1989),
the issue of dynamic efficiency can be resolved by comparing the level of investment with the cash flows generated by production after the payment of wages … dynamic efficiency cannot be assessed by comparing the safe rate of interest and the average growth rate of the capital stock, output, or any other accounting aggregate,
or Henning Bohn (The Sustainability of Budget Deficits in a Stochastic Economy, JMCB 27(1), 1995),
discounting at the safe interest rate is usually incorrect. … popular fiscal policy “indicators” like deficit levels or debt-GNP ratios may provide very little information about sustainability. … the intertemporal budget constraint imposes very few restrictions on the average primary balance.
Recent work in which these themes appear include papers by Zhengyang Jiang, Hanno Lustig, Stijn Van Nieuwerburgh, and Mindy Xiaolan (Manufacturing Risk-free Government Debt, NBER wp 27786, 2020), Robert Barro (r Minus g, NBER wp 28002, 2020), or Stan Olijslagers, Nander de Vette, and Sweder van Wijnbergen (Debt Sustainability when r−g<0: No Free Lunch after All, CEPR dp 15478, 2020).
Intergenerational Risk Sharing
With overlapping generations the way the government manages its debt has implications for intergenerational risk sharing, see for example Henning Bohn (Risk Sharing in a Stochastic Overlapping Generations Economy, mimeo, 1998), Robert Shiller (Social Security and Institutions for Intergenerational, Intragenerational, and International Risk Sharing, Carnegie-Rochester Conference on Public Policy 50, 1999), or Gabrielle Demange (On Optimality of Intergenerational Risk Sharing, Economic Theory 20(1), 2002).
Long-Run Debt Dynamics and Fiscal Space
Dmitriy Sergeyev and Neil Mehrotra (Debt Sustainability in a Low Interest World, CEPR dp 15282, 2020) offer an analysis of long-run debt dynamics under the assumption that the primary surplus systematically, and strongly responds to the debt-to-GDP ratio such that the government’s intertemporal budget constraint is necessarily satisfied:
Population growth and productivity growth have opposing effects on the debt-to-GDP ratio due to their opposing effects on the real interest rate. Lower population growth leaves the borrowing rate unchanged while directly lowering output growth, shifting the average debt-to-GDP ratio higher. By contrast, when the elasticity of intertemporal substitution is less than one, a decline in productivity growth has a more than a one-for-one effect on the real interest rate, lowering the cost of servicing the debt and thereby reducing the average debt-to-GDP ratio. To the extent that higher uncertainty accounts for low real interest rates, we find that
the variance of the log debt-to-GDP ratio unambiguously increases with higher output
uncertainty. However, uncertainty also has an effect on the mean debt-to-GDP ratio that
depends on the coefficient of relative risk aversion. Higher uncertainty lowers the real
interest rate but this effect may be outweighed by an Ito’s lemma term due to Jensen’s
inequality that works in the opposite direction.
Sergeyev and Mehrotra also consider the effects of rare disasters as well as of a maximum primary surplus which implies that debt becomes defaultable and the interest rate on debt features an endogenous risk premium, generating the possibility of a “tipping point” with a slow moving debt crises as in Guido Lorenzoni and Ivan Werning (Slow Moving Debt Crises, AER 109(9), 2019).
Ricardo Reis (The Constraint on Public Debt when r<g But g<m, mimeo, 2020) analyzes a non-stochastic framework under the assumption that the marginal product of capital, m, exceeds the growth rate, g, which in turn exceeds the risk-free interest rate, r. Reis considers the case where m is the relevant discount rate, for example because r features a liquidity premium:
there is still a meaningful government budget constraint once future surpluses and debt are discounted by the marginal product of capital.
He shows the following:
Reis concludes that most of the bubble component “has already been used.” In addition to developing a model that yields m>g>r in equilibrium he also discusses the role of inflation (stable inflation generates fiscal space because it renders debt safer and thus increases demand for debt) and inequality (more inequality increases fiscal space).
Blanchard’s Presidential Address
In his presidential address, Olivier Blanchard (Public Debt and Low Interest Rates, AER 109(4), 2019) argues that the risk-free interest rate has fallen short of average US growth rate (and similarly, in other countries). Importantly—and implicitly addressing Abel, Mankiw, Summers, Zeckhauser, and Bohn (see above)—he also argues that risk is not that much of an issue as far as the sustainability of public debt is concerned:
Jensen’s inequality is thus not an issue here. In short, if we assume that the future will be like the past (admittedly a big if), debt rollovers appear feasible. While the debt ratio may increase for some time due to adverse shocks to growth or positive shocks to the interest rate, it will eventually decrease over time. In other words, higher debt may not imply a higher fiscal cost.
Most of his formal analysis doesn’t focus on debt though. Instead he analyzes the effects of risk-free social security transfers from young to old in a stochastic OLG economy. (There are close parallels between debt and such transfers to the old that are financed by contemporaneous taxes on the young.) In a steady-state with very low interest rates higher transfers have two effects on welfare, by (i) providing an attractive substitute for savings and by (ii) reducing capital accumulation and thereby lowering wages and raising the interest rate. If the economy initially is dynamically inefficient both effects are welfare improving because (i) capital accumulation with a low return is replaced by higher yielding intergenerational transfers and (ii) lower wages and higher interest rates are attractive, starting from a situation with a low interest rate. In a stochastic economy the first channel yields welfare gains as long as the growth rate exceeds the risk-free rate, and the second channel yields welfare gains (approximately) when the growth rate exceeds the marginal product of capital. Blanchard argues
[b]e this as it may, the analysis suggests that the welfare effects of a transfer may not necessarily be adverse, or, if adverse, may not be very large.
In the corresponding case with debt there is another effect because the intergenerational transfer is not risk-free; the size of this additional effect depends on the path of the risk-free interest rates (Blanchard assumes that the debt level is stabilized which requires net tax payments by the young to reflect the contemporaneous risk-free rate). In the slightly different case where debt is increased once and then rolled over, without adjusting taxes in the future, the sustainability and welfare implications are ambiguous and critically depend on the production function:
In the linear case, debt rollovers typically do not fail [my emphasis] and welfare is increased throughout. For the generation receiving the initial transfer associated with debt issuance, the effect is clearly positive and large. For later generations, while they are, at the margin, indifferent between holding safe debt or risky capital, the inframarginal gains (from a less risky portfolio) imply slightly larger utility. But the welfare gain is small … . In the Cobb-Douglas case however, this positive effect is more than offset by the price effect, and while welfare still goes up for the first generation (by 2 percent), it is typically negative thereafter. In the case of successful debt rollovers, the average adverse welfare cost decreases as debt decreases over time. In the case of unsuccessful rollovers, the adjustment implies a larger welfare loss when it happens. If we take the Cobb-Douglas example to be more representative, are these Ponzi gambles, as Ball, Elmendorf, and Mankiw (1998) have called them, worth it from a welfare viewpoint? This clearly depends on the relative weight the policymaker puts on the utility of different generations [my emphasis].
Blanchard argues that the marginal product of capital may be smaller than commonly assumed, implying that it is more likely that the welfare effects working through (ii) are positive (those working through (i) are very likely positive). Finally, he also presents some additional potential arguments pro and con higher public debt.
Blanchard’s work has attracted substantial criticism, for instance at the January 2020 ASSA meetings (see this previous post). In a short paper presented at the meetings, Johannes Brumm, Laurence Kotlikoff, and Felix Kubler (Leveraging Posterity’s Prosperity?) point out that a negative difference between average interest and growth rates is not necessarily indicative of dynamic inefficiency (see the discussion above) and that Blanchard’s analysis disregards tax distortions as well as the welfare effects from intergenerational risk sharing (again, see above):
To see the distinction between risk-sharing and a Ponzi scheme, modify B’s two-period model to include agents working when old if they don’t randomly become disabled. Now workers face second-period asset income and labor earnings risk. The government has no safe asset in which to invest. If it borrows, invests in capital, and taxes bond holders its excess return, “safe” debt is identical to risky capital. But if the net taxes are only levied on the non-disabled, bonds become a valued risk-mitigating asset and their return can be driven far below zero. This scheme could be, and to some extend it is, implemented through progressive taxation. If, observing this gap between growth and safe rates, the government decides to institute an “efficient” Ponzi scheme with a fixed pension benefit financed on a pay-go basis by taxes on workers, net wages when young will be more variable, raising generation-specific risk and potentially producing an outcome in which no generation is better off and at least one is worse off.
Brumm, Kotlikoff, and Kubler also note that the effective interest rate at which US households are borrowing is much higher than the borrowing rate of the government; this undermines Blanchard’s approach to gauge the welfare implications. And they point out that the scheme suggested by Blanchard could harm other countries by reducing global investment.
Jasmina Hasanhodzic (Simulating the Blanchard Conjecture in a Multi-Period Life-Cycle Model) simulates a richer OLG model and rejects the Blanchard conjecture of Pareto gains due to higher transfers:
It shows that the safe rate on government debt can, on average, be far less than the economy’s growth rate without its implying that ongoing redistribution from the young to the old is Pareto improving. Indeed, in a 10-period, OLG, CGE model, whose average safe rate averages negative 2 percent on an annual basis, welfare losses to future generations resulting from the introduction of pay-go Social Security, financed with a 15 percent payroll tax, are enormous—roughly 20 percent measured as a compensating variation relative to no policy.
Relative to Blanchard’s simulations, her model implies more negative consequences of crowding out on wages, a higher tax burden from the transfer scheme, and more induced old-age consumption risk.
Michael Boskin (How, When and Why Deficits Are Dangerous) offers a broad discussion of potential weaknesses of Blanchard’s analysis. Richard Evens (Public Debt, Interest Rates, and Negative Shocks) questions Blanchard’s simulations on calibration grounds and notes that he couldn’t replicate some of Blanchard’s findings.
On his blog, John Cochrane argues along similar lines as Ricardo Reis: Even if r<g, expected primary deficits are so large that debt quotas will explode nevertheless.
Note: This post was updated several times.
Economic Journal, forthcoming, with Harris Dellas. PDF.
We study the optimal debt and investment decisions of a sovereign with private information. The separating equilibrium is characterized by a cap on the current account. A sovereign repays debt amount due that exceeds default costs in order to signal creditworthiness and smooth consumption. Accepting funding conditional on investment/reforms relaxes borrowing constraints, even when investment does not create collateral, but it depresses current consumption. The model contains the signalling elements emphasized by creditors in the Greek austerity programs and is consistent with the reduction in the loans issued by Greece and their interest rate following the 2015 election.
That’s what Daron Acemoglu and Pascual Restrepo document in an NBER working paper.
Figure 2 [below] provides a glimpse of the relevant pattern by depicting the raw correlation between the change in GDP per capita between 1990 and 2015 and the change in the ratio of the population above 50 to the population between the ages of 20 and 49. … even when we control for initial GDP per capita, initial demographic composition and differential trends by region, there is no evidence of a negative relationship between aging and GDP per capita; on the contrary, the relationship is significantly positive in many specifications.
Jointly with the Journal of Monetary Economics and the Swiss National Bank, the Study Center Gerzensee organized a conference in honor of Bob King, long-term supporter of the Study Center.
Jaume Ventura’s discussion of a paper on trade and growth by Alvarez and Lucas: PDF.
My discussion of a paper on debt and debt constraints by Bhandari, Evans, Golosov, and Sargent: PDF.
In a Resolution Foundation report, Adam Corlett examines the “Elephant Curve.” The curve shows that between 1988 and 2008 income growth in the 70th to 95th percentile range of the world income distribution was much lower than for almost all other percentiles. Since the lower middle class of rich countries is situated around the 80th percentile of the distribution the Elephant curve has been interpreted as evidence for stagnating middle class incomes in the rich countries.
Corlett emphasizes that
In his recent book Geld aus dem Nichts (Money out of Nothing), Mathias Binswanger discusses the role of banks in creating money, and money’s role in affecting the macro economy. The book is written for a non specialist audience and the arguments are often quite loose.
In the first part of the book, Binswanger describes how money mostly is created by commercial rather than central banks.
Part II provides a nice historical overview. Binswanger describes the origins of modern banking with goldsmiths first storing gold for their merchant clients, then lending some of the stored gold to third parties, and finally issuing more “receipts” than what corresponds to the gold deposits they actually accepted. From there, he argues, it was a small step to state licensed national banks like the Bank of England. On p. 120 Binswanger describes how minimum reserve requirements got out of fashion, not least because they suffered from circumvention when they were binding.
Part III lacks precision and is misguided (see also pp. 30 or 66). It covers the link between money creation and growth but confuses national accounting concepts and their relation to money and credit. Clearly, growth can occur without credit (think of an economy with just one agent to see this most directly) but Binswanger seems to dispute this point, in line with earlier writings by his father. A “model” on p. 144 does not help to clarify his views because it is orthogonal to the argument. Binswanger criticizes mainstream economics for refusing to accept the presence of long-run links between money and growth but this critique remains vain. Part IV deals with money creation and its effect on financial markets.
Part V, on reform, is sensible. Binswanger rejects proposals to move (back) to the gold standard or a 100%-money regime (or, essentially equivalent, “positive money”). His arguments against the Swiss “Vollgeld” initiative resonate with points I made here and elsewhere, including the point that it would be difficult to enforce a “Vollgeld” regime (see also p. 122). Binswanger criticizes the “Vollgeld” initiative’s vagueness concerning actual implementation of monetary policy. He ends with more limited, rather standard proposals (relating to regulation, monetary policy objectives and capital requirements) to address problems in financial markets.
In his blog, John Cochrane critically reviews arguments in favor of higher inflation in Japan.
He approves of the view that a conventional stimulus argument does not make much sense—given that Japanese growth is around potential and unemployment is low.
He does not approve of the view that inflation would be helpful by lowering (public and private) debt burdens. He doubts that an inflation induced default on outstanding debt would significantly lower taxes (rather than lead to more government spending) and that even if it did, such a default would increase the optimism of young households.
He also questions whether inflation could significantly reduce the real value of Japanese public debt (because debt maturity is short) and whether the debt burden is actually large (given near zero interest rates).
In a blog post, John Cochrane proposes step-by-step (politically unattractive) measures to increase growth:
In a Peterson Institute policy brief, Paolo Mauro and Jan Zilinsky argue that
the evidence is mixed: Those who hold a prior that fiscal adjustment is harmful for growth may find their beliefs confirmed, whereas those who believe a prior that the link is weak may find the evidence unconvincing (even aside from valid concerns about causality). To the extent that the case of Greece involves unique features beyond large fiscal adjustment, the data reveal that drawing conclusions from empirical associations that include this specific case requires caution.
A report by the White House Council of Economic Advisors surveys long-term interest rates. The “key takeaways” include:
Real and nominal interest rates in the United States have been on a steady decline since the mid-1980s. Declining interest rates are a global phenomenon. … [F]orecasters largely missed the secular decline of the last three decades.
The Ramsey growth model implies a link between labor productivity growth, per capita consumption growth and the real (inflation-adjusted) interest rate. Historically, periods of low real long-term interest rates have tended to coincide with low labor productivity growth. Projections of labor productivity growth, while imprecise, suggest 10-year real interest rates in the range of 1.5 to 3.5 per cent.
Asset-pricing models that incorporate risk suggest that the long-run nominal interest rate is the sum of expected future short-term real rates, expected future inflation rates, and a term premium. The 10-year rate in ten years that forward transactions in nominal Treasuries imply is currently 3.1 percent. Forward transactions in the market for TIPS suggest a long-term real rate just above 1.00 percent in ten years. Adding the CPI inflation rate implied by the Federal Reserve’s PCE inflation target would imply a forward nominal interest rate of 3.25 percent. The term premium in nominal Treasuries is currently estimated to be near zero, with a 2005-2014 mean of 1 percent. These components together suggest a 10-year nominal interest rate in the range of 3.1 (forward Treasuries) to 4.6 percent (based on FOMC forecasts of the long-run federal funds rate).
In a world with financially integrated national capital markets, the general level of world interest rates is determined by the equality of the global supply of saving and global investment demand. Capital markets of advanced economies are now tightly integrated while emerging market economies are becoming increasingly integrated into the global financial system. Low-income economies remain partially segmented from the global capital market. As a consequence of increasing international market integration, long-term real and nominal interest rates are increasingly moving in tandem and have declined along with U.S. rates. Nominal interest rates also tend to be correlated across countries though differences in inflation expectations can produce differences in nominal rates. In a world with uncertainty, global long-term real and nominal interest rates will include risk premiums that can reflect country-specific risk factors. Strong economic linkages, however, reinforce substantial correlation in countries’ long-term bond risk premiums.
Long-term interest rates are lower now than they were thirty years ago, reflecting an outward shift in the global supply curve of saving relative to global investment demand. It remains an open question whether the underlying factors producing current low rates are transitory, or imply long-run equilibrium long-term interest rates lower than before the financial crisis. Factors that are likely to dissipate over time—and therefore could lead to higher rates in the future—include current fiscal, monetary, and exchange rate policies; low-inflation risk as reflected in the term premium; and private-sector deleveraging in the aftermath of the global financial crisis. Factors that are more likely to persist—suggesting that low interest rates could be a long-run phenomenon—include lower forecasts of global output and productivity growth, demographic shifts, global demand for safe assets outstripping supply, and the impact of tail risks and fundamental uncertainty.
In an online book published by the Institute of Economic Affairs, Nima Sanandaji argues not only that the Scandinavian success story predates the welfare state but also that the welfare state actually undermined the success story. From the book’s summary:
Many analyses of Scandinavian countries conflate correlation with causality. It is very clear that many of the desirable features of Scandinavian societies, such as low income inequality, low levels of poverty and high levels of economic growth, predated the development of the welfare state. It is equally clear that high levels of trust also predated the era of
high government spending and taxation. All these indicators began to deteriorate after the expansion of the Scandinavian welfare states and the increase in taxes necessary to fund it.
First, before accounting for the behaviour of asset prices, we find only a weak association between goods and services price deflations and growth; the Great Depression is the main exception. In some respects, this confirms previous work. Second, the link with asset price deflations is stronger and, once these are taken into account, it further weakens the association between goods and services price deflations and growth. Finally, we find some evidence that high private debt levels have amplified the impact of property price deflations but we detect no similar link with goods and services price deflations.
On Project Syndicate, Raquel Fernández and Jonathan Portes offer four lessons from the Argentinian default in 2001 for Greece:
… if the economics are on your side, you can and should ignore politicians prophesying disaster. … a short period of political turmoil can cost surprisingly little compared to a long period of mindless pursuit of misconceived policies. But … Greece must acknowledge that its fundamental problems are of its own making. … Greece is unlikely to enjoy the breathing space provided by a commodity boom. If it is to place itself on the road to a sustainable recovery, it has no time to lose.
We shed light on the function, properties and optimal size of austerity using the standard sovereign debt model augmented to include incomplete information about credit risk. Austerity is defined as the shortfall of consumption from the level desired by a country and supported by its repayment capacity. We find that austerity serves as a tool for securing a more favorable loan package; that it is associated with over‐investment even when investment does not create collateral; and that low risk borrowers may favour more to less severe austerity. These findings imply that the amount of fresh funds obtained by a sovereign is not a reliable measure of austerity suffered; and that austerity may actually be associated with higher growth. Our analysis accommodates costly signalling for gaining credibility and also assigns a novel role to spending multipliers in the determination of optimal austerity.
European Economic Review 56(1), January 2012, with Martín Gonzalez-Eiras. PDF.
We analyze the short and long run effects of demographic ageing—increased longevity and reduced fertility—on per-capita growth. The OLG model captures direct effects, working through adjustments in the savings rate, labor supply, and capital deepening, and indirect effects, working through changes of taxes, government spending components and the retirement age in politico-economic equilibrium. Growth is driven by capital accumulation and productivity increases fueled by public investment. The closed-form solutions of the model predict taxation and the retirement age in OECD economies to increase in response to demographic ageing and per-capita growth to accelerate. If the retirement age were held constant, the growth rate in politico-economic equilibrium would essentially remain unchanged, due to a surge of social security transfers and crowding out of public investment.
(Unfortunately, the acknowledgements got lost in the publishing process.) For comments, we thank Casper van Ewijk, Enrique Kawamura, George McCandless, Alex Monge, Vincenzo Quadrini, Jaume Ventura, Fabrizio Zilibotti as well as conference and seminar participants at Banco Central de la Republica Argentina, CREI (Universidad Pompeu Fabra), EEA annual meeting, EPRU (University of Copenhagen), ESSIM, IIES (Stockholm University), Netspar, Penn State, SED annual meeting, Study Center Gerzensee, and Universidad de San Andres. Andreas Walchli provided valuable research assistance.
VoxEU, June 24, 2011, with Martin Gonzalez-Eiras. HTML.