The r<g Debate
Ryoichi Imai

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Fiscal Balance• Japan’s fiscal budget yielded surplus around1990 when Japan was in the economic bubble.
• After the bubble burst, Japan has suffered fiscaldeficits, which was temporarily reduced by theKoizumi cabinet in the middle of 2000s.
• The Lehman shock caused another recession,
which made the fiscal budget worse, while it has
been improved by the Abenomics.

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Is growth rate larger thaninterest rate?
• Deficit Gamble：In 1998 a Harvard economist, GregMankiw, published a paper and argued that the USgovernment could roll over a higher government
debt, because the interest rates of the US treasury
bonds have been lower than the US economy
nominal growth rate for most of the time in the past.
• In Japan, there was a debate between Takenaka,
the economy minister of the Koizumi cabinet, andProfessor Yoshikawa, a Todai economist in the early
2000s.
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The r<g debate returns• In the best-selling book of 2013, Capital in the 21stCentury, Thomas Piketty argued that r>g would be
the driving force of the increasing inequality in thecontemporary capitalist economy.
• In 2019 Olivier Blanchard, the president of theAmerican Economic Association, proposed a model
to explore the consequence of r<g.
• The MMT (Modern Monetary Theory) argues that
the US federal government should spend more toachieve full employment, and has influenced someleaders of the US Democratic Party.
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Dynamical Inefficiency• An economy with the risk-free rate lower than the output
growth rate is dynamically inefficient.
• In the dynamically inefficient economy, capital isaccumulated too much and the interest rate is too low tomaximize the welfare of all the generations.
• A slight reduction in investment associated with a slightrise in consumption will improve the welfare of all thegenerations.
• Then income transfer from young to old generations
such as the pay-as-you-go pension system will raise thewelfare of all the generations.
5What is the risk-free rate?
• The market rate is not the interest rate that thebond holders receive from the federal
government.
• Three adjustments needed– different maturities to be averaged andaggregated.
– Interest rates are taxed.
– Foreigners and public institutions areexempted from taxation on government
bonds.
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Adjusted rates differ from market rates

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Growth rates have been higher than the adjusted
interest rates except for 1980 through 2008

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The Blanchard Model• An overlapping generation model withcapital accumulation (Diamond 1965)• In the economy with no uncertainty,
income transfer from young to oldgenerations improves the welfare of allgenerations, if the economy is dynamicallyinefficient (r<g).

9Under Uncertainty• The return to hold government bonds differ from theaverage return to invest in private capital.
• Income transfer from young to old generations havethe direct income effect and the non-direct growtheffect through changes in factor price (rents andwages) and capital accumulation.
• If the average return to invest in private capital isgreater than the economy growth rate, income
transfer from young to old generations under r<g
has positive income effect and negative growtheffect.
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Income transfer• Income transfer or rolling over government
debts reduces capital accumulation andthe economy growth rate.
• If r<g, income transfer from young to oldgenerations as well as rolling over
government debts are sustainable, while
their welfare implications depend on thesubstitution elasticity between labor andcapital.
11Substitution elasticity matters• If the substitution elasticity between laborand capital is sufficiently high, capital
shortage is compensated for by morelabor inputs, and the total welfare effect ispositive.
• However, the substitution elasticity is not
so high as to compensate for capital
shortage, the total welfare effect isnegative.
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Issue more debts ?
• The Reflation advocates in Japan (or the MMTer in the US)
argue that the government should spend more to achieve
full employment.
• What if the government finances its spending by issuingmore debts?
• If labor is sufficiently substitutable for capital, rolling over
government debts is sustainable and improves the welfareof all the generations.
• If labor is not well substituted for capital, rolling over debts
is unsustainable and improves the welfare of the present
generations only, and hurts the future generations throughlower capital accumulation and lower output.
13Debt Rollover with high elasticitybetween labor and capital

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Debt Rollover with low elasticity
between labor and capital

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Debt rollover raises the welfare of all thegenerations if labor is highly substitutable to capital

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Debt rollover raises the welfare of the present generations
only, and hurts the future generations
if labor is not substitutable to capital

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Whom the governments care?
• With r<g, rolling over government debts andtransferring income to the present generations
might be unsustainable or hurt the welfare of thefuture generations through lower capital
accumulation and lower output.
• The governments optimizes its policy to target acertain weighted average of the welfare of present
and future generations.
• If the government puts more weight on the welfareof present than future generations, it might choose
debt roll over.
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The return to invest in private capital issufficiently high as Piketty claims.

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The true return to invest in private
capital might be overestimated
1. The denominator might be undervalued:
The Intangible asset is incorrectlymeasured.
2. The numerator might be overvalued: The
return to invest might not be the true
return from capital but the monopoly
rents.

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References 1• Ball, Elmendorf, Mankiw (1998), The Deficit Gamble,JCMB,– https://www.jstor.org/stable/2601125• Blanchard (2019), Public Debt and Low Interest Rates,
Presidential Lecture, AEA2019– https://www.aeaweb.org/aea/2019conference/progra
m/pdf/14020_paper_etZgfbDr.pdf• Nordhaus (2015), ARE WE APPROACHING ANECONOMIC SINGULARITY?
– https://www.nber.org/papers/w21547.pdf
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References ２• Nordhaus (2015), ARE WE APPROACHING ANECONOMIC SINGULARITY?
– https://www.nber.org/papers/w21547.pdf• Pissarides and Wallanti (2007), The Impact of TFP
Growth on Steady-State Unemployment, International
Economic Review , 48(2), pp. 607-640.
• Wasmer (2006) , General versus Specific Skills in Labor
Markets with Search Frictions and Firing Costs,
American Economic Review, Vol. 96, No. 3 (Jun., 2006),
pp. 811-831.
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