Bad Logic — Or Bad Arithmetic?

In a blog post on what he calls the “Bad Logic of Fiscal Austerity”, Paul Krugman lays the following calculation before the public:krugman

Let me start with the budget arithmetic, borrowing an approach from Brad DeLong. Consider the long-run budget implications for the United States of spending $1 trillion on stimulus at a time when the economy is suffering from severe unemployment.

That sounds like a lot of money. But the US Treasury can currently issue long-term inflation-protected securities at an interest rate of 1.75%. So the long-term cost of servicing an extra trillion dollars of borrowing is $17.5 billion, or around 0.13 percent of GDP.

Yes. That’s the long-term cost of borrowing an extra trillion dollars. (Actually, the cost is even lower than Krugman says it is.) But the long term cost of spending an extra trillion dollars is somewhere in the vicinity, of, oh, about a trillion dollars, or about 7.4% of GDP.

Now you might argue that if some of that spending puts unemployed resources to work, then the true cost of spending a trillion is somewhat less than a trillion, but Krugman, at least here, does not attempt to make that argument. Nor do I expect that even Paul Krugman would dare to argue that an adjustment for unemployed resources could reduce the cost of government spending by roughly 98%.

Krugman is right when he says that borrowing is cheap. But the issue isn’t borrowing; it’s spending—and spending is expensive. It appears that like the President, Krugman wants to divert your attention from spending to borrowing so he can dismiss legitimate concerns without even acknowledging them. It’s a cheap trick. Don’t let either of them get away with it.

Edited to add: In fairness to Krugman, he appears to be imagining that the trillion is never paid back, so that the cost of spending it is simply the debt service of 17.5 billion per year forever. But his column makes it sound like the cost is a single one-time payment of 17.5 billion, which is absurd.

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15 Responses to “Bad Logic — Or Bad Arithmetic?”


  1. 1 1 Henry

    If the spending now replaces future spending, there’s no added deadweight loss. Indeed, as a Keynesian, Krugman would presumably endorse less spending in a strong economy. Whether this actually occurs is another story.

  2. 2 2 Josh

    This post makes perfect sense to me, but I wonder Steven how should one reconcile free market principles, belief in truly limited government, and the fact that even in the most laissez faire states government along usually with a central bank still controls the money supply. I don’t hear libertarians talk about money per se much. Do you think that a government that has a central bank and prints money as it pleases can also be truly as limited as you would like? What are your thoughts on how governments should manage money?

  3. 3 3 Dave

    You don’t count the spending as a cost because the fed is planning on inflating the debt away. It’s a cost to US treasury holders (who are largely foreigners) and a benefit to our economy.

  4. 4 4 Robert Wiblin

    I figure he was trying to say that we needn’t ever pay back that trillion dollars – just pay $17.5b in interest in perpetuity. I think I have a better grasp of what a trillion dollars right now is worth, than $17.5b for every year until the end of time.

  5. 5 5 AaronG

    Dave,

    Krugman was referencing the 1.75% real rate on inflation indexed bonds. There is no inlating away inflation indexed debt (short of manipulating the CPI statistics that TIPS reference). Long term (20+ years) rates on nominal bonds are over 4%, so the current cost of servicing $1 trillion of debt that can be inflated away is $40 billion per year.

    According to this chart based on estimates from Treasury, the Federal Reserve and intra-governmental holdings comprise nearly half of all US tresury securities in 2008. Given that, inflating away the nominal debt may not be such an attractive option anyway.
    http://en.wikipedia.org/wiki/File:Estimated_ownership_of_US_Treasury_securities_by_category_0608.jpg)

  6. 6 6 nobody.really

    I can’t help but read this as a semantic argument. I sense the two concepts most relevant to this discussion are opportunity cost and crowding out.

    I sense the real issue is this: What’s the (risk-adjusted) optimal use for $1 trillion? The “cost” — that is, the forgone opportunity to achieve this optimal use — is measured relative to this optimal use. Thus, to say that the cost of a $1 trillion stimulus package is $1 trillion would imply that the stimulus package will produce $1 trillion less benefit than some alternative use for the money. I’m looking forward to hearing what that alternative is.

  7. 7 7 nobody.really

    Now on to crowding out.

    One alternative use for the $1 trillion is to leave it in private hands. As an initial matter, I’d guess most of those private hands are Chinese. Given the projected growth rate for China, maybe the world would be better off if we left the $1 trillion to be spent there instead of in the US. Alternatively, maybe the growth rate in China would be even higher if the US could stimulate its economy.

    In the long run I expect future US taxpayers will pick up the bill. Do we estimate that the benefit to be achieved by future US taxpayers will be greater than the benefit to be achieved by an additional $1 trillion stimulus today?

    Today the world is faced with an unusually deep recession — which I understand to mean that we have an unusually large supply of resources standing idle. We have limited means of storing the value of all these idled resources; that which cannot be stored is wasted. In contrast, when a more normal level of economic activity resumes there will be fewer idle resources to employ, and additional economic activity will require “crowding out” existing activity. Thus, all else being equal, there is cause to believe that additional spending today would achieve greater benefits than additional spending under almost any other circumstances.

    But won’t additional government spending today crowd out additional private spending today? Perhaps — if you believe that there’s a lot of pent-up private spending waiting to occur. The fact that interest rates are low would seem to undermine this theory.

    A caveat: I write as if there is one interest rate — and for a while in the mid-2000s this almost seemed to be true. But today we’re back in the world in which different people face different interest rates for different projects. While banks advertise low interest rates, they have also tightened their lending requirements. I sense that for many people interest rates are, for practical purposes, infinite. I do not regard these people as having been crowded out of the market for capital. The banks don’t lack access to capital; they lack confidence in the borrower.

  8. 8 8 Dave

    AaronG – Given TIPS make up less than 4% of all outstanding debt, the “kill it with inflation” policy will be effective in reducing the cost to us by at least 96% (assuming of course the CPI is in no way downward biased). The rest of the cost will be borne by foreign owners.

  9. 9 9 Dave

    nobody.really – the fact that resources are left idle by the profit seeking private sector is because the costs of using them outweigh the benefits. If prices were allowed to fall to market clearing rates, this would change.

  10. 10 10 AaronG

    Dave,

    The current composition of outstanding debt isn’t the point. Krugman said we could finance $1 trillion at a cost of $17.5 billion/year, which is only true if we retain the inflation risk.

    Did you follow my link about the holders of US Treasuries? Foreigners hold less than 30% of the outstanding debt as of 2008, so inflation would not be solely born by foreigners. Social Security, for instance, would be brought to premature insolvency by high inflation.

  11. 11 11 nobody.really

    nobody.really – the fact that resources are left idle by the profit seeking private sector is because the costs of using them outweigh the benefits. If prices were allowed to fall to market clearing rates, this would change.

    That’s the laissez faire theory, anyway. But does it accurately describe the current situation? When the Fed sets the price of borrowing at basically 0% and still people aren’t borrowing, it becomes harder to believe that the problem is that capital costs just haven’t fallen to market-clearing prices yet.

    Meanwhile, governments are market participants, too. Governments consume labor and capital for roads and schools and bombs and such. Surely even the most hard-boiled penny-pincher will see the logic of spending extra to stocking up on staples while they’re on sale, assuming the sale is big enough. And we haven’t seen a sale of this magnitude since the 1930s.

    Ironically, while people discuss the prospects for long-term inflation, Dave’s response – that we’ll see more economic activity when prices fall more – suggests we’re already in a deflationary spiral. I guess government could behave more like a profit-maximizer by playing the same game, holding off on spending in anticipation that prices will fall further. Hard to say if that’s in government’s long-term interest or not, given government’s various goals.

    The fact that government has contradictory motives – getting a good deal as a consumer, and reviving the economy for the benefit of producers – would pose a problem if I imaged that government had some better ability to time markets than the rest of us do. I don’t. Because the prescription for pursuing either goal seems pretty similar — buy while prices are low – I don’t see any real conflict in policy.

  12. 12 12 Dave

    Aaron G: Your link is blank. But even with the 70% held domestically, that portion is the USA owing money to itself. If it’s inflated away, the cost to the nation as a whole is exactly offset by the benefit. It just becomes a matter of who within the nation actually bears the cost and who gets the benefit. Foreign investors would definately feel the brunt of the cost of inflation without any offset benefit to foreigners as a whole. ie all they get is a bunch of worthless loans, at least we get domestic borrowers effectievley not having to pay the loan back.

    “The current composition of outstanding debt isn’t the point. Krugman said we could finance $1 trillion at a cost of $17.5 billion/year, which is only true if we retain the inflation risk”
    – I wasn’t addressing Krugman’s statement. I was addressing the debt program as a whole. But I completely disagree that there is no inflating away inflation indexed bond. Forgetting the manipulation argument, there is huge lag effect. In an extreme case scenario, we borrow $1t in TIPs, then use it to stimulate the economy, then the next day we print a $1t note to buy the debt back. The CPI number showing 100% inflation per month doesn’t come out until a month later so the bond TIP never gets reset.

    nobody.really: I wasn’t referring to the borrowing cost of capital, I was referring to the absolute cost of capital itself. eg the banks are marking their assets to myth right now. If they were forced to liquidate a factory in Detroit for $1, hell even I might buy it (without a loan) and maybe do something with it. And with depressed wages, I might hire some people to try work something out. But instead, it sits on their books at overinflated prices being idle. If I wanted to buy it at their level, I wouldn’t have enough for staff ad infinitum.

    The government is nothing like a market player. Market players make decisions using cost/beneift analysis based on their money hoping to make a profit and fearing a loss. Governments make decisions using cost/beneift analysis based on other people’s money hoping to win more votes than they lose.

  13. 13 13 nobody.really

    I wasn’t referring to the borrowing cost of capital, I was referring to the absolute cost of capital itself. eg the banks are marking their assets to myth right now. If they were forced to liquidate a factory in Detroit for $1, hell even I might buy it (without a loan) and maybe do something with it. And with depressed wages, I might hire some people to try to work something out. But instead, it sits on their books at overinflated prices being idle. If I wanted to buy it at their level, I wouldn’t have enough for staff ad infinitum.

    A fair point, albeit not one closely related to evaluating the cost of a stimulus plan. I have a vague notion that mark-to-market policies should help the problem Mark’s describing, but I guess there is no mark-to-market remedy for sticky wages. Each worker must reconcile himself to the new market value of his labor, at whatever pace that worker can endure.

    The government is nothing like a market player. Market players make decisions using cost/beneift analysis based on their money hoping to make a profit and fearing a loss. Governments make decisions using cost/beneift analysis based on other people’s money hoping to win more votes than they lose.

    Again, this may well be true; again, this may not be relevant.

    To my mind, Landsburg criticizes Krugman for failing to correctly assess the “cost” of a stimulus plan without articulating a standard by which to evaluate that cost. Similarly, Dave criticizes government consumption without articulating a standard by which to evaluate that consumption.

    I have attempted to articulate what I regard to be a reasonable standard: Governments should respond in a manner similar to a rational consumer. That is, when the price of things government needs drops, government should seize that opportunity and buy more. Government might even respond to the wealth effect created by deflation by expanding the list of the things it chooses to consume.

    Now, some will argue that governments do not actually act in such a prudent fashion. That’s a fine argument, but it’s not a basis for criticizing government when it does engage in behavior I’d expect from a prudent consumer. Dave’s criticisms might be better directed at specific boondoggle projects to which the stimulus dollars are directed, not to the concept of a stimulus per se.

  14. 14 14 Dave

    I fail to see why you feel everything in the discussion forum needs to directly address the original post. I was merely responding to the things you were saying that I felt were misguided (though I may be too). I thought that’s how discussions open up? Your responses to mine were pointing out I wasn’t addressing the original post. I wasn’t trying to.

  15. 15 15 Michael

    Steven,

    I really think you should grow your beard back. Then we could have clash of the bearded economists!

  1. 1 There He Goes Again at Steven Landsburg | The Big Questions: Tackling the Problems of Philosophy with Ideas from Mathematics, Economics, and Physics

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