Category Archives: Notes

Reading List on ‘Free’ or ‘Not-so-free’ Public Debt

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:

  • The debt due to a one-time primary deficit can be rolled over indefinitely and disappears asymptotically as long as r<g.
  • With permanent primary deficits that grow at the same rate as debt and output, the government’s intertemporal budget constraint features a bubble component due to r<m. This corresponds to the usual seignorage revenue measure (see p. 173 in Niepelt, Macroeconomic Analysis, 2019).
  • Suppose that from tomorrow on, the primary deficit and debt quotas are given by d and b, respectively. Then, the present value of total net revenues in the government’s budget constraint equals [- d + (m – r)*b] / (m-g). Both m>g and g>r relax the constraint, as does a lower r.
  • Along a balanced growth path, b = [- d + (m – r)*b] / (m-g) and thus, d = (g-r)*b where d is assumed to be positive. Reis argues that b cannot be larger than total assets relative to GDP. Accordingly, the deficit cannot exceed total assets times (g-r).

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.

John Cochrane about CBDC and Me

Writing about CBDC, John Cochrane makes it clear that he is in favor. He links to my work and writes

Dirk Niepelt has written a lot about CBDC theory, including reserves for all in 2015, a recent Vox-EU summary and papers,  here with Markus Brunnermeier a JME paper “CBDC coupled with central bank pass-through funding need not imply a credit crunch nor undermine financial stability,” a follow up including “The model implies annual implicit subsidies to U.S. banks of up to 0.8 percent of GDP during the period 1999-2017.”  Here  “reserves for all” “does not affect macroeconomic outcomes,”

Notions of Liquidity Trap

On Fazit, Gerald Braunberger reviews the concept of “liquidity trap.”

  • Keynes never used the term but Robertson did.
  • Hicks introduced the common notion (represented, e.g., by a flat LM curve).
  • Krugman talks about a different trap. So does Blanchard and he (incorrectly) attributes it to Keynes. So does Sinn.

Not Much Left of “Modern Monetary Theory”

Alberto Bisin (Journal of Economic Literature, December 2020) reviews Stephanie Kelton’s “The Deficit Myth: Modern Monetary Theory and the Birth of the People’s Economy:”

Never is its logical structure expressed in a direct, clear way, from head to toe. … Some of these statements are literally correct but used for incorrect or misleading implications—plays on words, effectively. They seem taken directly from the book of tricks of the Greek sophists (the ones Aristophanes makes fun of).

John Cochrane (blog post, July 2020) reviews the same book:

Skeptics have called it “magical monetary theory.” They’re right.

Dirk Niepelt (blog post/Neue Zürcher Zeitung (in German), April 2019):

The Macroeconomic Perpetuum Mobile.

The Value of Monetary Units, 1500–1914

K. Kıvanç Karaman, ¸Sevket Pamuk, Seçil Yıldırım-Karaman (2020), Money and monetary stability in Europe, 1300–1914, Journal of Monetary Economics (115).

At one extreme, the Dutch Republic depreciated its monetary unit by about 2.3 times, at the other, the Ottomans depreciated by about 25,000 times. These two numbers correspond to average annual depreciation rates of 0.2 and 2.5% respectively, with the other states falling in-between. … depreciations tended to be episodic. In particular, long periods of constant silver and gold value alternated with episodes of rapid depreciation in consecutive years. … There were also instances of one-off depreciations, but they were few, and at low rates. … monetary stability was not an elusive objective. Some states stabilized their monetary unit early. England did so by the mid-16th century, except for the fiat standard episode during the Napoleonic wars. Dutch Republic stabilized its monetary unit in the early 17th century, with very minor changes in the centuries that followed. France stabilized its monetary unit in 1795 following the fiat money experiment of the Revolution. In contrast to these western European states, in southern and eastern Europe, states continued to depreciate their monetary units until the end of the period.

Central Banks Have Accepted a Future Retail CBDC

Recent indications:

Related recent developments:

Economic Aspects of the Energy Transition

In an NBER working paper, Geoffrey Heal discusses some aspects of the energy transition to come.

On infrastructure investments:

the likely net investment required to go carbon-free is now as little as $0.179 trillion

renewable power from wind and solar PV plants is now less expensive than power from gas, coal or nuclear plants … If it were not for the intermittency of renewables, we would save money by converting to clean power.

the social benefits from stopping the CO2 emissions from coal and gas in power generation in the U.S. amount to $200bn annually, roughly an order of magnitude greater than the costs. Furthermore, these benefits will continue for ever, whereas the costs are fully paid by 2050. … As greenhouse gases are a global public bad, many of these benefits will accrue to countries other than the U.S.

Carbon taxes only delay the extraction of fossil fuels except for those fuels whose marginal extraction cost is sufficiently high such that extraction cost plus tax exceeds the cost of alternative energy sources:

the Pigouvian and Hotelling frameworks lead to rather different conclusions when it comes to thinking about the effectiveness of a carbon tax. Pigou emphasizes the impact of a tax on substitution between commodities, in this case between energy sources. Hotelling on the other hand emphasizes the impact of a tax on an exhaustible resource on the time-path of consumption of that resource.

[in the Hotelling setting] the tax either has no effect at all on the cumulative consumption of the fossil fuel, or it drives it out of the market completely.

If we want to reduce cumulative oil consumption by for example 30%, then we need a tax of about $500 per ton of CO2: if we wanted to reduce oil consumption by two thirds we would need a tax of over $600 per ton CO2.

Electricity pricing:

The marginal social cost of power from renewable sources is close to zero, as wind, solar and hydro all have essentially zero operating costs. So we would need much lower power prices to provide the correct incentives to use clean power rather than fossil fuels.

The classic response to this conundrum has been to recommend two-part tariffs, with a fixed charge or connection or membership charge recovering the fixed costs and a usage tariff covering the variable costs.

High-Skilled Immigration and Employment at Multinationals

Britta Glennon reports in an NBER working paper that the two go together.

Skilled immigration restrictions may have secondary consequences that have been largely overlooked in the immigration debate: multinational firms faced with visa constraints have an offshoring option, namely, hiring the labor they need at their foreign affiliates. If multinationals use this option, then restrictive migration policies are unlikely to have the desired effects of increasing employment of natives, but rather have the effect of offshoring jobs. Combining visa data and comprehensive data on US multinational firm activity, I find that restrictions on H-1B immigration caused foreign affiliate employment increases at the intensive and extensive margins, particularly in Canada, India, and China.

Assar Lindbeck (1930–2020)

Colleague, co-author, visionary. Assar remains a role model. He was curious, open minded, and incorruptible. He didn’t need to prove himself or that he was correct (politically and otherwise), all he wanted was to contribute and learn. He was a generalist, both in economics and beyond. He exposed nonsense and shaped policy. He will be sadly missed.

In memory of Assar Lindbeck.

First Regulated Stablecoin Retail Transaction—at Digitec?

C. Septhon reports in Modern Consensus:

The Sygnum Digital Swiss Franc (DCHF), which is pegged on a 1:1 basis with the fiat currency, was used to complete a payment for an Apple iPad at Digitec Galaxus, Switzerland’s largest online retailer. Coinify, a digital currency platform provider, enabled the sale to take place.

Sygnum is different from Tether etc. because it is a regulated bank. Accordingly, DCHF corresponds to a monitored currency board.

Financial Innovation, Central Banks, CBDC

In its annual economic report, the BIS further warms to the idea that CBDC is a key part of central banks’ response to financial innovation.

  • Central banks play a pivotal role in maintaining the safety and integrity of the payment system. They provide the solid foundation by acting as guardians of the stability of money and payments. The pandemic and resulting strain on economic activity around the world have confirmed the importance of central banks in payments.
  • Digital innovation is radically reshaping the provision of payment services. Central banks are embracing this innovation. They promote interoperability, support competition and innovation, and operate public infrastructures – all essential for easily accessible, low-cost and high-quality payment services.
  • Central banks, as critical as ever in the digital era, can themselves innovate. In particular, central bank digital currencies (CBDCs) can foster competition among private sector intermediaries, set high standards for safety and risk management, and serve as a basis for sound innovation in payments.

See this VoxEU column on Libra’s effects.

“Macroeconomic Analysis,” VoxEU, 2020

VoxEU, June 22, 2020. HTML.

Is macroeconomics useful? Of course. To make the point, academics must regain the interpretative high ground from market commentators. While it helps when policymakers understand fundamental macroeconomic concepts, it is equally important for the general public to grasp them. More, and how this relates to the new textbook, on VoxEU.

Robert Pirsig’s “Zen and the Art of Motorcycle Maintenance: An Inquiry Into Values”

Quality, not subject or object, as the elementary fabric. ἀρετή. A rehabilitation of the sophists.

Some quotes:

If the purpose of scientific method is to select from among a multitude of hypotheses, and if the number of hypotheses grows faster than experimental method can handle, then it is clear that all hypotheses can never be tested. If all hypotheses cannot be tested, then the results of any experiment are inconclusive and the entire scientific method falls short of its goal of establishing proven knowledge. …

God, I don’t want to have any more enthusiasm for big programs full of social planning for big masses of people that leave individual Quality out. These can be left alone for a while. There’s a place for them but they’ve got to be built on a foundation of Quality within the individuals involved. We’ve had that individual quality in the past, exploited as a natural resource without knowing it, and now it’s just about depleted. Everyone’s just about out if gumption. And I think it’s about time to return the rebuilding of this American resource – individual worth. There are political reactionaries who’ve been saying something close to this for years. I’m not one of them, but to the extent they’re talking about real individual worth and not just an excuse for giving more money to the rich, they’re right. We do need a return to individual integrity, self-reliance and old-fashioned gumption. We really do. …

What is good, Phaedrus, and what is not good – need we ask anyone to tell us these things?

Anthony McWatt’s discussion of Pirsig’s philosophy in Philosophy Now:

In Zen & the Art of Motorcycle Maintenance, Pirsig first explored the history of the term ‘Quality’, or what the Ancient Greeks called arête, tracing it all the way back to Plato (428-348 BCE). He concluded that the strange position of Quality in today’s West originated with Plato’s division of the human soul into its reason and emotion aspects, in his dialogue the Phaedrus. In this dialogue, Plato gave primary place to reason over emotion. Soon afterwards Aristotle was similarily emphasizing analysis over rhetoric. And as Hugh Lawson-Tancred confirms in the Introduction to his 1991 translation of Aristotle’s Rhetoric: “There are few things that are more to be deplored in Greek culture, and notably in the legacy of Plato, than the wholly forced and unnatural division between… [the] two sister studies” of rhetoric and philosophy (p.57). Eventually this division grew into the ‘subjective versus objective’ way of thinking now largely dominant in the West. So now in the West we have objectivity, reason, logic, and dialectic on the one hand; and subjectivity, emotion, imagination, intuition, and rhetoric on the other. The former terms suggest scientific respectability, while the latter are often assumed to be artistic terms, having little place in science or rationality. It is this Platonic conception of rationality that Pirsig sought to challenge by reconciling the spiritual (for example, Zen), artistic (for example, art) and scientific (for example, motorcycle maintenance) realms within the unifying paradigm of the Metaphysics of Quality. …

Plato was perhaps a little too over-confident in how usable his theory of Forms is in practice. I wonder if it ever crossed his mind that his mentor, Socrates, might have been hinting to him and the other young philosophy students in Athens that the Good and Beauty are actually indefinable? The idea of Forms was, of course, invented by Plato, not Socrates. Unfortunately, as a consequence of Plato’s thinking that reality can be basically defined, Western philosophy is in the state that it is in today: more a handmaiden of science rather than its master. Assuming that words can capture all aspects of reality is an understandable error to make at the very beginning of the Western philosophical tradition… but having said that, it was a metaphysical error avoided by East Asian philosophy. Think about Plato’s allegory of the Cave of Ignorance and escaping from it to see the Sun of the Good, then compare it with the following quote:

“Not by its rising is there light,
Not by its sinking is there darkness
Unceasing, continuous
It cannot be defined…
The image of no-thingness…
Meet it and you do not see its face
Follow it and you do not see its back.”

Dao De Jing, Laozi, Quoted in ZMM, p.253-54

If you think about it long enough, then you’ll see that there was no ‘Cave of Ignorance’ until Plato put Western culture inside its metaphysical darkness for 2,400 years!

Obituary by Paul Vitello in the New York Times:

One of Mr. Pirsig’s central ideas is that so-called ordinary experience and so-called transcendent experience are actually one and the same — and that Westerners only imagine them as separate realms because Plato, Aristotle and other early philosophers came to believe that they were.

But Plato and Aristotle were wrong, Mr. Pirsig said. Worse, the mind-body dualism, soldered into Western consciousness by the Greeks, fomented a kind of civil war of the mind — stripping rationality of its spiritual underpinnings and spirituality of its reason, and casting each into false conflict with the other.

Obituary by Michael Carlson in The Guardian.