Tuesday, August 18, 2015

Some Real Interest Rates Are Low, But Some Others Are Not

Observed real interest rates on U.S. government debt are, by any measure, low. For example, here's the 30-day T-bill rate minus the inflation rate:
And this is the yield on 10-year TIPS:
John Cochrane has a post which references a recent Council of Economic Advisors survey on low real interest rates, which contains a useful summary of what is known about this. As well, Ben Bernanke discussed this phenomenon in his blog, and Bernanke and Larry Summers discussed what this might have to do with so-called "secular stagnation."

Some of this discussion seems to work from the assumption that the rate of return on government debt and the rate of return on capital are the same thing. For example, Bernanke shows a chart of the 5-year TIPS yield and then, in addressing what this might have to do with secular stagnation, makes this statement:
First, as I pointed out as a participant on the IMF panel at which Larry first raised the secular stagnation argument, at real interest rates persistently as low as minus 2 percent it’s hard to imagine that there would be a permanent dearth of profitable investment projects. As Larry’s uncle Paul Samuelson taught me in graduate school at MIT, if the real interest rate were expected to be negative indefinitely, almost any investment is profitable. For example, at a negative (or even zero) interest rate, it would pay to level the Rocky Mountains to save even the small amount of fuel expended by trains and cars that currently must climb steep grades. It’s therefore questionable that the economy’s equilibrium real rate can really be negative for an extended period.
So, Bernanke appears to think that low real Treasury yields are associated with low rates of return on capital. As well, Summers's arguments concerning secular stagnation seem to rely on a loanable funds theory of the real interest rate - the demand for investment (i.e. the demand for loanable funds) is low, which makes the real interest rate low. It seems clear that the real interest rate that Summers has in mind is the real rate of return on capital.

John Cochrane also discusses an idea related to low real bond yields, which he attributes to Summers:
One hypothesis that I learned from Larry Summers is that today's production function needs a lot less physical capital to produce the same productivity. A 1930s steel mill is a lot of accumulated savings. Facebook has nothing but a basketball court sized building full of 20-somethings coding while wearing headphones, and a really cool food court. The company is worth billions but it took comparatively little accumulated savings to start it up. If technology moves so that human, rather than physical capital is the heart of the K in F(K,L), productivity growth may determine interest rates in the long run, but there are lower interest rates on the transition path.
Again, this is an explanation for why the real rate of return on capital might be low.

But what if we actually go out and measure rates of return on capital? This work by Paul Gomme, B. Ravikumar, and Peter Rupert, reported in the St. Louis Fed's Economic Synopses, does that exercise. Here's their Figure 2:
So, by any of those measures, the rate of return on capital (this is average, not marginal) is as high or higher than it was before the recession. Conclusion: According to conventional measures, the rate of return on government debt is low, but the rate of return on capital is not.

In many standard economic models, there is no difference between the real interest rate faced by consumers and the marginal product of capital. But that will not be the case in models in which, for example, government debt plays some special role, for example as collateral, and therefore bears a liquidity premium. There is work by Kiyotaki and Moore that studies this type of effect, and I've worked on models in which government debt can bear liquidity premia, for example in this paper with David Andolfatto, and this paper of mine on QE. The ideas in those papers are related to Caballero's ideas on "safe asset shortages."

I think that the measurements in the work by Gomme/Ravkumar/Rupert are key to thinking about issues related to low real interest rates, so this deserves attention.


  1. How much of that "return on capital" is due to QE-facilitated revaluations of assets , which would be unlikely to spur further investment as would true demand-generated returns?

    I'm not sure the secstag argument is as dead as G/R/R seem to think it is.

    1. "How much of that "return on capital" is due to QE-facilitated revaluations of assets , which would be unlikely to spur further investment as would true demand-generated returns?"

      That's the first time I've heard that argument. You'll have to flesh that out, as on the surface I can't make any sense out of it. Bernanke, the architect of QE, certainly didn't think what he was doing would generate some kind of "false" revaluations that would not spur investment. I think he thought that, in a conventional manner, QE would lower government bond yields, spur investment, and as a result the rate of return on capital would fall.

    2. I'm just suggesting that your fig. 2 above doesn't square with this one .....


      ...which suggest to me that much of that return on capital may be a one-off from qe-boosted revaluations. Firm owners are thus wise to refrain from vigorous investment given the question about where the sales are going to come from , thus the still-alive secstag thesis.

      What Bernanke may or may not have thought is irrelevant , I would think.

    3. Also take a look at fig 3 , panel B , here :


      It's only through year-end 2012 , but at least up to then investment plans and realized investment tracks CFO-expected earnings growth , and is trending down since peaking ~2011.

  2. Interesting post Stephen. But wouldn't the low yields on corporate bonds (and/or bank lending rates to businesses) suggest that the marginal product of capital is indeed low? It seems unlikely that liquidity premia can explain either of these (particularly bank lending rates).

    1. "... low yields on corporate bonds..."

      One question would be: low relative to what? I looked at the margin between the yield on AAA corporate bonds and the yield on 10-year Treasuries, and that increased from pre-recession to post-recession. We might want to ask what the liquidity premium on a corporate bond might be. These assets don't have the same role as collateral as Treasuries or asset-backed securities, but they are certainly liquid, in that there is an active market on which these assets are traded. So, to the extent that corporate bonds are deemed safe and liquid, they substitute for other safe and liquid assets, and liquidity premia on corporate bonds therefore could have risen post-recession. Hard to answer the question, though, without doing the empirical work.

    2. Thanks for the reply.

      But isn't the relevant comparison levels, rather than spreads over treasuries? Any company cares about the difference between their marginal cost of capital (e.g. from the corporate bond market or from bank lending) and the marginal product of capital.

      If we agree that the level of interest rates in e.g. the corporate bond market are historically low, but the marginal return on investment is high, then companies would borrow and invest to arbitrage that difference. As we don't observe lots of borrowing and investment by companies with access to the corporate bond market (in historical terms) this seems to be inconsistent with your idea that a high MPK is coexisting with low market based interest rates.

      One way of reconciling this might be if some important companies don't have access to the bond market or a limited access to bank lending - but I have a sense that this sort of financial frictions story is not the one you had in mind.

      Of course: I agree that corporate bonds are liquid (though not as liquid as Treasuries). But you argue that the the rate of return on capital might actually be higher than it was before the recession (or at least, not at historical lows). But if that were true, then companies which can issue bonds at low rates should be taking advantage of them and arbitraging the difference between historically low corporate bond levels

      But shouldn't the level

    3. "If we agree that the level of interest rates in e.g. the corporate bond market are historically low, but the marginal return on investment is high, then companies would borrow and invest to arbitrage that difference."

      This arbitrage of course is not instantaneous. It takes time and resources to build plant and equipment. Any theory of investment has to take account of that in order to fit the data. You claim that we "don't observe lots of borrowing and investment," but relative to what? Investment expenditure has grown substantially since the end of the recession, though of course you might argue that the growth we have seen is inconsistent with the margin between corporate bond yields and the rate of return on capital. Of course, that margin is not the only determinant of investment. Investment decisions are forward looking by nature, so spot return differentials may be a small part of the story. Risk matters, for example. What if another financial crisis is lurking down the road?

    4. Thanks again for the reply.

      I agree that the "arbitrage" takes time - but market based interest rates have been at historical lows for many years now. It would seem odd if this were coexisting with high MPK for such a long time (the graph of APK suggests we're back to levels seen in the late 90s or mid 00s), though I suppose it's possible that companies have been pleasantly surprised for several years that we haven't had another recession.

      Perhaps your story about a fear of financial crisis (or negative "rare events") being seen as more likely is right. But if it is, it's strange that spreads have only modestly increased (as in a crisis you'd think that default risk would go up).

    5. "but market based interest rates have been at historical lows for many years now"

      Yes, there was that financial crisis event we were recovering from of course.

      "It would seem odd..."

      Basically, you have to do the empirical work to understand completely what might by "odd" and what might not. We're not going to solve this in blog comments.

      "spreads have only modestly increased"

      Which ones do you mean in this case?

  3. Apples to apples requires comparing the expected marginal return on capital to the Treasury yield. The observed average return is backward looking.

    We can't observe the expected marginal return on capital directly, but we can derive an (imperfect) indication of it. Ashwin Damodaran has a dividend discount model of the S&P500's "intrinsic value". His model uses a 2.2% terminal growth rate and puts the current index level at close to the model "fair value". S&P500 companies pay out 95% of profits as dividends and share buybacks. Since only 5% of earnings are reinvested, that 5% must have a marginal return of 44% to result in a 2.2% terminal earnings growth rate (keep in mind the model actually assumes much higher growth than that for the next five years, requiring an even higher 5-yr return on investment than the terminal one).

    This implies the market is discounting historically high marginal returns on the 5% of S&P500 earnings reinvested.

    Alternatively, one can input a lower implied return on the 5% of earnings reinvested. For the model to output the current value of the S&P500, this would require a low (by historical standards) ERP. That low implied ERP would seem to be inconsistent with the "safe asset shortage" story.

    You can find Damodaran's model here and input your own values: http://www.stern.nyu.edu/~adamodar/pc/implprem/ERPAug15.xls

    Here is the rub on a high expected marginal product: if it is high by historical standards, why is earnings reinvestment at trough levels? This implies some sort of discontinuity in the relationship between reinvestment levels and marginal returns (past 5%, they plummet).

    Away from the model itself, the common sense question is why should companies reinvest so little when average returns are so high?

    1. There's a problem in that the returns to people holding the S&P 500 don't capture what, as economists, we think is the return to capital as a factor of production. Part of what GRR's published paper is about is the radical difference in the properties of stock returns and the measured return to capital, which they get from National Income and Product Accounts data. See:


      "...why should companies reinvest so little when average returns are so high?"

      That certainly is a puzzle. We could add to this:

      2. Why are firms holding so much cash?
      3. Why are banks holding such large quantities of reserves at 0.25%?

      Possible answers: Risk - e.g. everyone's worried about the next financial crisis; everyone's waiting for something to happen, for example for the Fed to lift off. No idea whether these ideas could work or not.

    2. Another potential explanation is the increasing amounts returns generated in the so called 'winner take all' businesses. There are increasing barriers to entry with technology which could increase profits without necessarily increasing investment.

      What would be interesting is to see a cross-sectional distribution of the return to capital across businesses. My guess is that there has been a significant increase in the dispersion over time with the top getting an increasing share.

    3. Barriers to entry and monopoly. Is this a greater concern since the recession than before it? I don't know. What's it take to start up a software firm? A few geeks, some computers, and a little space to work in.

  4. I am not sure I understand why you compare interest rates (costs of debt) with return on capital. What do you mean by return on capital? Do you mean the weighted average cost of capital, or do you mean the cost of equity? Either way, I don't see why we should be surprised that the WACC/return on equity is higher than the interest rates (costs of debt).

    1. Typically, we think of capital as a factor of production that, along with labor, produces output. But, capital is also an asset. In many models that we work with, real rates of return are equated across assets (absent risk) so, for example, the real rate of return on government debt (another asset) is equal to the real rate of return available in credit markets. Of course we know that the rate of return on equity (which is not the rate of return on capital the way we're thinking about it here) tends to be higher than rates of return on debt because equity is typically riskier. That's an issue that GRR address in their paper:


      In fact the rate of return on capital, as measured from the National Income Accounts, is not so risky, as you can see in the figure.

  5. Is the BEA's capital stock measured at historical cost? We'd probably want to calculate capital returns using a marked-to-market capital stock. However, the tricky thing would be to adjust that marked-to-market capital stock for liquidity premia. If not, then we'd be committing the same sin that the sec stagnation theorists are committing; trying to draw information about returns to capital from data series that contain an embedded liquidity premium, and are therefore beset by static.

    1. For the measure that we're interested in here, I think GRR do it correctly. You take total income that can be attributed to that factor of production, and divide by the number of units of that factor of production in place at the time. In this case, then, the result is the average product of capital, or capital's average rate of return. If we're worried about explaining investment behavior, we might be concerned with capital's market value. Liquidity premia could then matter for investment, for example if the firm can issue a debt instrument to finance capital expenditure that has an attached liquidity premium, then you get more investment than if the debt instrument were illiquid. This is actually one of the roles of financial intermediaries - they make debt more liquid and therefore promote investment and capital accumulation.