Winner of the New Statesman SPERI Prize in Political Economy 2016

Monday, 21 May 2012

The Costs of Debt Finance: Jonathan versus David

                Recently David Smith of the Sunday Times and Jonathan Portes of the National Institute had a blog-spat about what a debt financed public investment programme would actually cost. Jonathan suggested that as the current interest rate on UK government indexed linked (i.e. inflation adjusted) debt was only 0.5%, £30 billion worth of investment would only cost £150 million a year. This was something like the amount the Chancellor was aiming to raise by removing VAT loopholes, including the infamous pasty tax. David responded that the value of the index linked gilt would rise with inflation, so that cost should be allowed for on an annual basis, which amounts to using a nominal, not real, interest rate. Jonathan countered that the nominal interest rate, which would be paid on debt of fixed nominal value, was not appropriate, because inflation would steadily erode the real value of nominal debt. In terms if the debate, I think Jonathan is clearly right, but I want to use the opportunity of going a little further by considering intergenerational equity, which David mentions right at the end of his post.
                Now if you or I take out a loan, we do not just think about the interest we will have to pay on that loan. We also should think about how and when we have to pay that loan back. But governments appear different, because unlike people they can continue forever, so in theory any borrowing by a government never needs to be paid back. Indeed, most of the time governments honour the debt of their predecessors.  So if the debt is an index linked gilt, the government just has to pay £150 million at today’s prices on the debt forever more. True, the nominal value of that debt will be rising, but so will the nominal value of everything else, including VAT receipts. Jonathan is right: if we spread the real cost (or burden) of financing the public investment across all future generations equally, which we can, then it’s the real interest rate that matters.
                In fact we could go further still. If the number of people in the economy is increasing, or each individual’s real income is rising, then this £150 million becomes an ever smaller share of total real income. In that specific sense, the ‘burden’ on future generations is less than on the current generation. If we really want to equalise the burden in terms of a share of income across all generations, then we should not just take off the inflation rate from the nominal interest rate, we should take off the real growth rate as well. Let’s call this ‘r-g’ for short. Now at the moment UK real growth is about zero, so this would not make any difference to Jonathan’s numbers, but in other circumstances it would reduce the cost still further.
                Now what would happen if this growth adjusted interest rate, r-g, is actually zero. We then get what seems like a magical result. Rather than raise taxes each year by £150 million, we issue £150 million worth of new index linked debt each year. You might think that paying interest by borrowing more is the road to bankruptcy, because the debt gets larger and larger. But not as a share of national income: that debt ratio would be constant if r-g=0. So £30 billion of public investment, which is about 2% of GDP, turns out not to cost anyone anything! Another way of thinking about it is that if there was a last generation, that generation would have to pay back the full 2% of their GDP, but there will never be a last generation, because governments (and government debt) can go on forever. We really do get something for nothing.
                Now, on average, r-g is positive rather than zero, so we do not get this magical result. But r-g is normally a lot smaller than the nominal interest rate. So, in terms of the conventional way that economists do these calculations, using the nominal interest rate is clearly wrong.
However, if our main concern is intergenerational equity, then this conventional approach might be a mistake, depending on the nature of the public investment. It would only be fair to all generations if the investment has benefits which rise with GDP and last forever. In that case using r-g is appropriate. If the benefits do not rise with real GDP, then using just the real interest rate would make more sense. However the benefits of most types of investment do not last forever. Suppose that the project was a new hospital that lasts for 100 years, but then falls apart completely. Tax payers in 101 years time should not have to pay for this hospital, which will no longer exist. So our assumption that the debt will never be repaid is not a very fair one on future generations if the benefits of the investment do not last forever. It is also not fair that the generation in 100 years time has to pay back the entire loan. Instead, each generation should pay some combination of interest and repayment of capital.
                The easiest way of doing this is to assume the value of the investment depreciates at some annual rate. If the benefit of the project does not automatically increase with GDP, then the appropriate cost would be the real interest rate plus this depreciation rate. It is like paying back the part of the debt each year that corresponds to the depreciated capital. In this case the cost will be higher than the real interest rate, although there is no reason why it should equal to the nominal interest rate.
                Now all this assumes that intergenerational equity is our only concern. It should not be. It should be a factor - I do not believe we can assume that the current generation will always look after that problem for us - but not necessarily the overriding factor. In the current situation, public investment is useful because it reduces involuntary unemployment. Furthermore, DeLong and Summers have shown that because of hysteresis effects in this situation, increased government spending may not cost us anything at all in the long run, even if r>g. They looked at additional government consumption, but their argument will be even stronger for government investment because of the positive supply side effects of this investment. In short, this really is the time to increase public investment, both in the UK and US, and cutting it is a very foolish thing to do.


  1. "is also not fair that the generation in 100 years time has to pay back the entire loan."

    Do they? Aren't the real costs of the principal component of the investment absorbed by the first generation? Afterall, that's the generation that consumes real resources to build that hospital (i.e., concrete, steel, labor, etc.). The supposed paying back of the principal is just an accounting exercise within a future generation, but does not cross generations.

  2. Assuming a closed economy for the sake of simplicity, I suggest there is no “burden” on future generations because while some of our children inherit the obligation to pay interest on Gilts, others inherit the right to receive interest on them. The two cancel out.

    That point actually reflects a brute physical reality, namely that a motorway built in 2012 necessarily consumes labour, concrete, steel, etc produced by the blood, sweat and tears of people in 2012 or before 2012. Steel produced in 2030 cannot be consumed in 2012: that would involve time travel.

    The only way of imposing a burden on future generations is if the money for investments is borrowed from abroad (as pointed out by R.A.Musgrave in the America Economic Review in 1939 (no relation)). Repaying a debt to foreigners depresses a country’s currency, which involves a real standard of living hit.

  3. The hospital analogy is a little constraining. Supposing we take something like the Hoover Dam, which I have written about earlier. (See Dam the Economists! at: With a correct level of maintenance, upgrading of peripheral technology, and a set-aside for eventual replacement all paid out of operating revenues, would it not be correct that the dam and successor technologies will continue to provide a benefit at no cost to future generations once the original bond issue has been repaid?

  4. There is one thing I don't understand, I beg you all to forgive me if my question is stupid: Prof. James Hamilton brought in his blog a paper that shows that historically, in the US, a grouth of 1% of GDP in government consumpton has a multiplier 0,4% in public sector GDP. He is speaking about the US and the paper does not make a correlation of this result with the grouth of military expenditures in the period (or with legs). But still, it seems reasonable to suppose that England has a somehow similar multiplier; which means that those 2% of GDP will mean a growth of "only" 0,8% in the private sector economic activity - way far from the need.

    The problem is that if you want to completely take off the effects of the current crisis in England, you will need a multiplier effect of something like 4-5% of GDP, which means that the investment has to be something between 10-12,5% of GDP. My question is whether such a thing is feasible due its efect in the public debt.

    I mean, it wuold be a huge liquid increase in public sector general debt and I don't realy know the market will react to somehting like this. On the one hand I ask myslef is something like that is not unfeasible due the market reaction while in the other hand I feel that not doing this is to act like the drunk guy that have lost his keys in a dark street and keep looking only in places where there is light. Anyone?

    1. I just would like to complement this question with a further post in tha same blog that shows that the efects of government expenditure are non-linear. It is bigger during recessions than during expansions. But what about near zero positive grouth? Does the argument goes stronger if this dynamic means that the expenditures multipliers if subject to negative returns of scale (the effect of the policy progressively tend to anul its benefit)? Does this make sense or have I got everything wrong?

  5. Now, on average, r-g is positive rather than zero, so we do not get this magical result.

    Is this an empirical result? For the U.S., r < g and also for the U.K., using long run data. Rather, for long run periods, r_inf = g where r_inf is the long term risk-free rate (and the equality is a long run average). But as government debt is financed with a mix of maturities, the weighted average maturity is less than g.

    I obtained my data for the U.S. and U.K. here:

    Another data source is to note that if r > g, the government would need to run primary surpluses that on average were greater than the primary deficits of the past in order to keep the Debt/GDP ratio from rising. But this has not been the case for either the U.S. or the U.K. in the period from the end of WW2 until the present, even though the Debt/GDP ratio is lower now for both nations than it was just after WW2. Even the rigid Maastricht treaty allows for permanent on-going deficits of 3% per annum, which would inconsistent with a stable debt to GDP ratio if r > g.

    Moving to more recent times, (c.f. from 1940-1980 interest rates were well below the growth rate. From 1980-2009, interest rates were above the growth rate, but less above it than they were below it in the preceeding period. Now, with 30 year bonds selling for about 2.84%, it is very likely that rates will be below the growth rate again.

    So where is your data is that the normal case is r > g?


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