Wednesday, June 29, 2011

Fiscal Arithmetic: The Blanchard Rule

When we left off, we'd concluded that the relationship between g, the growth rate of GDP, and i, the after-tax interest rate on government debt, was central to the evolution of public debt. When g > i, any primary deficit is sustainable, in the sense that the debt-GDP ratio converges to a finite value; when i > g, no primary deficit is sustainable, and a primary surplus, while formally sustainable at a certain exact value, occupies a knife-edge. Which invites the natural question, so which is bigger, usually?

There are articles that discuss this (tho not as many as you might think). Here's a good recent article by Jamie Galbraith; I also like this one by Tony Aspromourgos, and "The Intertemporal Budget Constraint and the Sustainability of Budget Deficits" by Arestis and Sawyer. (I'm sorry, I can't find a version of it online). An earlier and more mainstream, but for our current purposes especially interesting, take is this piece by Olivier Blanchard.  Blanchard says:
If i - g were negative, the government would no longer need to generate primary surpluses to achieve sustainability. ... The government could even run permanent primary deficits of any size, and these would eventually lead to a positive but constant level of debt... Theory suggests that this case, which corresponds to what is known as 'dynamic inefficiency', cannot be excluded, and that in such a case, a government should, on welfare grounds, probably issue more debt until the pressure on interest rates made them at least equal to the growth rate.
So much depends on whether the growth rate exceeds the interest rate, or not. Well, so, does it?

The funny thing about this passage in context is that Blanchard acknowledges that over most of the postwar period, the growth rate has exceeded the interest rate. But, he says, the professional consensus is that interest rates ought to equal or exceed growth rates, so he'll stick with that assumption for the rest of the article. (There's almost a genre of economics articles that freely admit a key assumption doesn't seem to be consistently satisfied in practice, but then blithely go on assuming it. The Marshall-Lerner-Robinson condition is a favorite in this vein.) But we're not here to mock; we're here to call the Blanchard rule, the prescription that if i < g, the federal deficit ought to be higher.

Below are graphs of the growth rate and after-tax 10-year government bond rate for 10 OECD countries. Both are deflated by the CPI; the tax rate is the ratio of central government taxes to GDP. This is probably a bit high, but on the other hand the average maturity of government debt is less than 10 years in many OECD countries -- in the US it is currently around 4.7 years -- so these two biases might more or less cancel each other out, leaving the red line close to the economically relevant interest rate. Source is the OECD statistics site. I've excluded 2008-2010 since the Great Recession pulls growth rates sharply down in a (let's hope!) misleading way. The lighter black line is the growth trend.

Click them to make them bigger!

Clearly we can't exclude the relevance of the Blanchard rule; for much of the time, for many rich countries, the growth rate of GDP has exceeded the 10-year interest rate. At other times, interest has exceeded growth. What we see in most cases is a fairly stable growth rate, combined with an interest rate that jumps sharply up around 1980 and then drifts downward from somewhere in the 1990s. At some point soon, I hope, I'll produce decompositions of the change in the fiscal position into the interest rate, the growth rate, changes in taxes and expenditure induced by the growth rate, and autonomous changes in taxes and spending. I suspect the first will be the most important, and the last the least. But in the meantime, we can say just looking at these graphs that changing interest rates are an important component of fiscal dynamics, so it's wrong to think just in terms of the primary balance.

Which suggests -- coming back to the earlier debate with John Quiggin -- that if we are concerned with the long-term fiscal position, we should spend at least as much time worrying about policies that affect the interest rate on government debt relative to the growth rate, as we should about taxes relative to expenditures. And we should not assume a priori that a primary deficit is unsustainable.


  1. I confess that I cannot bring to mind the intuition behind Blanchard's "professional consensus" that the real interest rate "ought" to be higher than the growth rate, i > g.

    Surely, this "professional consensus" is not a prescriptive "ought", but, perhaps, the kind of uninformed expectation that abstract thinkers arrive at, when sufficiently detached from the concrete?

    If you could sketch a brief explanation of the meaning of this peculiar professional consensus (which I presume is a theoretical view), it would be appreciated.

  2. Interesting. Until the last 150 or so years, interest rates far exceeded growth rates everywhere in all but the short run. But since then, the reverse has been the case most of the time in many countries. You've opened several cans of worms here. Money isn't actually a real thing - nothing about it follows directly from the production of commodities by means of commodities. So there won't be a way to resolve this question independent of how we set up our national accounts.

  3. Bruce-

    The intuition is that a situation in g > i is dynamically inefficient -- steady-state consumption would be higher if investment were lower. If you think households, or a social planner, are trading off the higher overall consumption if more of output is invested, versus the preference for consumption sooner rather than later (either pure time preference or a preference for smoother consumption paths) then such a situation should not arise -- there is no reason to delay consumption if you don't end up with more of it. In this sense g > i implies "oversaving".

    Whether this situation can nonetheless arise is less obvious. With a single infinitely-lived agent it won't, but in overlapping-generations models it's not so clear. As far as I can tell, it's one of those cases where the people who focus on the question admit it it's unsettled, but it's generally assumed to be true.

  4. g > i implies "oversaving".

    but the rate of investment could be raised with the extra borrowed funds not just present consumption
    ie maximal growth is the expansion path
    where i = g

    joan robinson
    in the 50's
    suggested the pure usury rate
    the rate of pure consumer loans only transactions
    might be zero or negative

    the positive rate of return on investment
    might pull up the general rate

    the comp dynamics here is always
    a mere war between models


    seems to me the story requires both closure
    ie a global level model
    and considerable attention to price level dynamics

    most macro "growth models "
    are in real terms only
    and thus without absolute prices
    and go crazy once relative prices start shifting about

    then the boguus homgeneity of the util stream is wheeled into the for ground
    demolishing all usefulness

    utlity theory is useless outside wonderland
    except as a soporific for toy modelers

    loci classici
    frank ramsey
    johnny von n

  5. Anonymous: "So there won't be a way to resolve this question independent of how we set up our national accounts."

    Yes! The accounting convention/definition/fiction that S=I, and the associated failure to model debt (hence credit, wealth, financial assets, capital gains, or really, money) in the national accounts, are at the crux of the issue.

  6. maximal growth is the expansion path where i = g

    Not sure I understand this. Explain?

    Here's how I see it. Take a simple Solow-type growth model, with a given technology, etc. Let our representative agent's discount rate vary. As the agent prefers current consumption more strongly, i rises (since i has to equate the present value of present and future consumption) and g falls (because more of current output is consumed rather than invested.) Conversely, if the agent becomes more indifferent between current and future consumption, i falls and g rises. If the agent is perfectly indifferent between current and future consumption, you'll have i=g; to get i less than g, the agent would have to have a negative rate of discount, i.e. positively prefer future consumption to current consumption. (You could make the same argument in terms of the convexity of the utility function instead of the discount rate if you like.) Since a negative discount rate (or concave utility function, i.e. increasing marginal utility from consumption) is considered implausible, the conclusion is that i less than g implies that i and g are not at the utility-maximizing level. But g can always be higher (subject to some minimum level of consumption each period). So there's nothing in a Solow model that says maximum g occurs at g=i. What kind of model is that true of?

    joan robinson in the 50's suggested the pure usury rate the rate of pure consumer loans only transactions might be zero or negative
    the positive rate of return on investment might pull up the general rate

    Schumpeter said the exact same thing, in Business Cycles. You ever looked at that? It's a fascinating book, with a lot of surprising convergences with Keynes.

    utility theory is useless outside wonderland except as a soporific for toy modelers

    True that. You ever look at that econblog Modeled Behavior? There was a spectacularly silly post there recently that said that China was growing faster than the Golden Rule rate and that proved the disadvantage of undemocratic governments -- they don't maximize utility like ours do. You really feel like you need to pull guys like that aside and gently but firmly explain that there is no Santa Claus, there's no Easter Bunny, and there is no such thing as utility.