Thursday, August 20, 2015

Have interest rates actually risen?


The Council of Economic Advisors recently put out a report on the long, steady decline in long-term interest rates over the last two decades. John Cochrane called the report "excellent", and reposts the following graph:


These are government bond yields - they represent the government's cost of borrowing. Steve Williamson, however, notes that the return on government bond yields is not the same thing as the return on capital. He writes:
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...Bernanke appears to think that low real Treasury yields are associated with low rates of return on capital.
Williamson is responding to a quote by Bernanke stating that if (real) interest rates get low enough, investment will eventually be stimulated. Williamson points out the distinction between government borrowing rates and rates of return on capital in order to argue (I think) that pushing down government bond rates will not necessarily induce companies to invest.

In defense of this thesis, Williamson cites a St. Louis Fed report by Paul Gomme, B. Ravikumar, and Peter Rupert, which in turn draws on this 2011 paper by the same authors (though the data series have been updated). Gomme et al. measure what they call the "real return on capital" by dividing an income measure by a measure of book value. Here, via Williamson, is the chart of what they find:


I am not sure whether Gomme et al. are measuring the return on capital correctly here. But I am pretty sure that Williamson is making sort of an error here - or at least overlooking an important distinction. What should matter for business investment is not businesses' return on capital, but the difference between their return on capital and their cost of capital. 

That's just basic corporate finance. If your internal rate of return (basically, your return on capital) is higher than your cost of capital, you buy the capital (i.e. you invest), and you undertake the project. 

Gomme et al.'s time series - whether or not it's a good measure of the return on capital or not - is not a measure of the cost of capital. And if we're comparing government borrowing costs to business borrowing costs, we want to look at the cost of capital. 

Now, there are two basic types of capital, equity capital and debt capital. To find the cost of equity capital - which is an opportunity cost - we need a model of risk. But to find the cost of debt capital is easy - it's just the yield on corporate bonds. So here, via FRED, is the nominal yield on Aaa and Baa corporate bonds:


Here we see the same story that we saw in the CEA graph. Nominal borrowing costs for businesses have been falling more-or-less steadily since the mid-80s.

How about real rates? Here are real rates (annual, not monthly like the previous series):


Again, same exact story.

So real corporate borrowing costs have been falling more-or-less steadily for decades, just like government borrowing costs. Gomme et al.'s work on rates of return on capital does not measure a risk premium, and it does not bear on this basic story.

That does, of course, lead to a little bit of a puzzle: If Gomme et al. measure rates of return on capital correctly, then why haven't falling real costs of capital combined with rising rates of return on capital lead to a business investment boom? Even if the opportunity cost of equity capital (the equity risk premium) went up, wouldn't that just cause an investment boom, accompanies by a shift from equity financing to debt financing? For this reason, I suspect that either 1) Gomme et al. have measured the return on capital incorrectly, or 2) basic corporate finance theory doesn't capture what's going on in our economy, or 3) both. (Note: As Robert Waldmann and many others have pointed out, Gomme et al.'s series is an average rate of return, where what should matter for investment is the marginal rate. So given that, it's not even clear what kind of conclusions we could draw from Gomme et al.'s time series.)


(Fun random tidbit: While I was looking at Gomme et al.'s 2011 paper, I noticed that the 2011 abstract uses the words "A fairly basic real business cycle model". But the 2007 working paper abstract uses the words "The standard business cycle model" to refer to the same thing. Hehehe. The standard business cycle model, eh? Riiiiight...)

39 comments:

  1. Daniel Gonz√°lez4:29 PM

    A possible explanation to the paradox could be that the _average_ return on capital is high yet the _marginal_ return on capital is low. I think Williamson mentioned that distinction.

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    1. Certainly seems possible.

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    2. They are estimating return on capital by using "book value" as the measure of capital. But book value: (1) measures historical depreciated cost and (2) leaves out intangible value. Union Pacific has a price to book of 3.7, 3M is 6.9, Boeing is 11, Johnson and Johnson is almost 4 and General Electric is 2 (to pick a range of companies).

      Investing in a new venture carries risks and usually involves additional current expenses which never appear in "book value".

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    3. Yes, I heavily suspect that by leaving out intangible capital, Gomme et al. are seriously overstating the return to capital.

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  2. I think your intuition about corporate leverage may be a case of "reasoning from a price change". Low interest rates, together with high equity risk premiums, suggests that investors have low risk tolerance. All else equal, corporations would issue bonds with low interest rates, but all else can't be equal. By issuing those bonds, they increase their leverage. The same risk aversion that produces the low interest rate also punishes firms for leverage.

    For the past 50 years or so that we have good data, corporate leverage has tended to be higher when interest rates were higher, suggesting that the counterintuitive result of Modigliani Miller may be a large factor. Firms are price takers in terms of risk premiums, so the allocation to debt may mostly reflect tax benefits.....

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    1. Yep yep. This is a situation where corporate finance 101 doesn't describe the world. I'm not "reasoning from a price change" (because I think about investment quantity too), but I am leaving out huge amounts of stuff not described by basic corporate finance. Leverage constraints are one of those things...

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    2. WACC calcs and optimum capital structure topics, which certainly include leverage constraints, are part of every basic corporate finance course I've ever seen.

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    3. "Low interest rates, together with high equity risk premiums, imply......."

      Where are the high equity risk premiums? While interest rates have steadily fallen since the 1980's, equity risk premiums have been relatively steady.

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    4. http://poseidon01.ssrn.com/delivery.php?ID=509005100118098012029127107013086101062011084076070069105104086101120101072090007104001126060041109056096072069098001082088010029022075093060103013015007073072006032033078082084105083069000027107003100069025003124027101024098066064004010070114081&EXT=pdf

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    5. "The same risk aversion that produces the low interest rate also punishes firms for leverage"

      That should show up in corporate bond yields which includes a credit risk premium.

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  3. blenheim4:43 PM

    An intelligent commentator makes the same point in the comments under Williamson's blog :)

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    1. Scooped again! :-)

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    2. blenheim4:55 PM

      Great minds and all that.. (though Williamson didn't really accept the point, perhaps because I didn't state it quite as clearly as you. Maybe you and he will be able to tease things out more fully)

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  4. "Williamson points out the distinction between government borrowing rates and rates of return on capital in order to argue (I think) that pushing down government bond rates will not necessarily induce companies to invest."

    You think. I'm not arguing that at all. GRR are just measuring the rate of return on capital from the National Income Accounts. It's like measuring a wage rate, for example. So that's the rate of return that capital receives once it's in place. The investment decision of course depends on that and - as you point out (in a perhaps confusing way) - a firm could then borrow by issuing corporate bonds, invest, and that should be profitable. Not quite, course, as there's more to investment than that - the firm has to worry about what the world looks like when the investment is actually in place, and putting it in place will take some time. A legitimate question is, even though investment has grown substantially since the recession, whether it might still be puzzlingly low, given the high rate of return on capital and the low real bond yields. Maybe. But you would have to do the empirical work to figure that out.

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    1. I should add that most conventional investment theories are about arbitraging some price differential or rate of return differential. In this class is q theory - investment depends on the ratio of the market value of capital to its replacement cost. The level of stock prices might suggest that what we're seeing right now is a very large q. Thus, that could give you the same puzzle. So, in spite of your suspicious mind, you should give Gomme et al. a break.

      The idea that investment depends on more than just prices and rates of return is an old one in fact. See:

      https://ideas.repec.org/a/bin/bpeajo/v19y1988i1988-1p141-206.html

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    2. Well, whatever GRR are doing, I think it's a mistake to compare government borrowing rates with private rates of return on capital. We should compare government borrowing rates with private costs of capital, and when we do they tell the exact same story.

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    3. "...they tell the exact same story."

      What's the story though?

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    4. "it's a mistake to compare government borrowing rates with private rates of return on capital. We should compare government borrowing rates with private costs of capital"

      What does that mean? We have some rates of return that we can measure. We have some theories. Where's the mistake?

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    5. The story is that interest rates have fallen more-or-less steadily for decades now.

      Sure, we have some rates of return that we can measure. Why not compare government bond yields to the rate of growth of butternut squash? Or the rate of return to casinos on Vegas slot machines? Or the rate of return of Bridgewater's hedge funds? If you had posted graphs of any of those, and contrasted them with government bond yields, I probably also would have called it a "mistake". Though in those other cases, it would have been clear that you were just having a bit of fun, so maybe I would have used the word " joke"...

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    6. "The story is that interest rates have fallen more-or-less steadily for decades now."

      Sure. Of course there is nominal/real, different maturities, different liquidity, different types of assets in general - government debt, corporate debt, capital. These assets play different roles in the economy, and we want to understand that.

      As these things relate to investment, I'm no expert in investment theory, and neither are you. When you tell me "this is basic corporate finance," you mean that's what they taught you in corporate finance class, as a starter. That need not mean the theory you were taught was at all successful in matching the data. My impression (and this reflects my limited expertise here) is that you have to work pretty hard to get the prices (interest rates, market valuation of firms, for example) to matter in investment equations. So, "basic corporate finance theory" isn't going to fit the data very well at any time, let alone right now.

      Think about it. Why would the corporate bond rate be at all relevant for someone starting up a small business?

      In my piece, I don't really say very much, though you seem to want to say I made some kind of error. No idea what you're trying to say.

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    7. Sure. Of course there is nominal/real, different maturities, different liquidity, different types of assets in general - government debt, corporate debt, capital. These assets play different roles in the economy, and we want to understand that.

      Heh. Just in this post I looked at nominal and real, business and government. Looking at different liquidities is going to show the exact same thing, as you of course well know. Merely observing that there are many different rates of return is obviously true, but does not obviously add to this discussion... ;-)


      As these things relate to investment, I'm no expert in investment theory, and neither are you. When you tell me "this is basic corporate finance," you mean that's what they taught you in corporate finance class, as a starter. That need not mean the theory you were taught was at all successful in matching the data.

      Absolutely. As I note at the end of the post. I kind of suspect that that basic theory has major problems.

      My impression (and this reflects my limited expertise here) is that you have to work pretty hard to get the prices (interest rates, market valuation of firms, for example) to matter in investment equations. So, "basic corporate finance theory" isn't going to fit the data very well at any time, let alone right now.

      This is my impression too.

      In my piece, I don't really say very much, though you seem to want to say I made some kind of error. No idea what you're trying to say.

      Well, I just don't see the relevance of the "return on capital" from Gomme et al. for the questions you discuss in your post (Bernanke's and Summers' conjectures). Whether we want to call that an "error" or not is kind of beside the point. A non sequitur that implies an inappropriate comparison might not be an "error", but I still don't see the dang point.

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  5. I think Sumner's "Never reason from a price change" quip makes sense here. Doesn't a "great stagnation" or a permanent slowdown of technological progress explain all of this?

    If the schedule of marginal productivity of capital has fallen over the past 20 years, then we should expect the return on all capital to fall steadily. Business investment hasn't boomed because all investment has lost value, not just investment in government bonds.

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    1. Doesn't a "great stagnation" or a permanent slowdown of technological progress explain all of this?

      It might! But Gomme et al. say the return on capital has gone up, which would seem to rule out a stagnation of that sort.

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  6. Anonymous8:35 PM

    A bit on hurdle rates: https://eightateeight.wordpress.com/2015/07/23/hurdle-rates/

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  7. Why don't low interest rates translate into higher investment? You could call it one of the prime errors of mainstream macroeconomics: believing that investment is a function of interest rates. But of course it is not. Investment is a function of consumption. As every capitalist knows, when consumption is falling it makes no sense to make investments (which of course are made to cater to higher consumption in future) no matter what the interest rate.

    Which brings us to the second question. Why is the recovery after the recession so long-drawn-out? The reason is of course the fall in consumption. And why has consumption failed to respond to so many government initiatives? It is because households have lost a huge chunk of their net worth (the median household has lost 18 years) in the asset market crashes of 2007-08 and are saving more to recoup their net worth. Given that returns on savings are close to zero, it will take the median household 18 years of doubled saving rates to recover their lost net worth.

    The point therefore is to prevent asset market crashes.

    Unfortunately, the US is going through a monetary contraction now. By the beginning of next year, YoY growth of money supply (my measure) will be zero. And then the fun will start all over again.

    More details in my ebook: http://www.amazon.com/dp/B00ZX9O5XQ

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  8. What should matter for business is both the expected return on capital and cost of capital.At the optimal investment level these two things are equalised (and suboptimal investment can be mathematically be treated as optimal with distorted expectations on the return to capital. Therefore, at the margin the two concepts should be similar, barring measurement error. The cost of capital defined this way may not match market rates due to rationing and other credit standards conditions that are not captured by interest rates. In general equilibrium, you can have both a high de facto cost of capital=return to capital coexisting with a low risk-free rate due to financing constraints or taxes on capital. I'm sure Williamson is perfectly aware of this, as you should be if you pick up any standard macro textbook.

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  9. Actually if you look a bit more closely at the charts you'll see that the spread of long corporate bonds over long government bonds has widened by about 100bps since before the crisis. Not trivial and a long way from "exactly the same."

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  10. Anonymous10:15 AM

    Shouldn't there be a distinction between capital and productive capital, or does the distinction depend on the beholder? Gomme et al. only distinguish between business capital and all capital. The former is much broader than productive capital (plant and equipment, etc.), while the latter is broader still (and includes residential real estate). Yet, Gomme et al. claim that they measured the rate of return on "productive capital": "In a recent paper (Gomme, Ravikumar, and Rupert, 2011), we examined the real returns on productive capital using National Income and Product Accounts (NIPA) data." To me the distinction is relevant if it's assumed that "productive capital" is what makes labor more productive and the economy grow. By comparison, how does speculation in financial assets (including a company's own stock) make labor more productive and the economy grow? Since speculation in financial assets has increased exponentially in the past 35 years (along with the size of the financial sector), isn't there a trade-off?

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  11. The total opportunities in an economy probably follow a Zipf distribution. The best opportunities get taken first. The marginal unexploited opportunity will probably be much less profitable than the average existing business.

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  12. I actually went over and read the post by Williamson, who I think generally is koo koo, but in this case I have to say, you completely misunderstood him and wrote something totally irrelevant to anything he wrote.

    If there's a weak point in his argument it's the method of measuring return on capital he highlighted. There are plenty other methods, and this one looks like cherry picking. Also, the difference between the average and marginal return on capital deserves more than a passing mention.

    Be that as it may, all he's saying is that the presumption that government bond yields correlate with return on capital is not empirically justified, and he's absolutely right.

    Your counter, that the long-term trend in corporate bond yields is "exactly the same" as in government bond yields anyways, is 1) wrong and 2) beside the point.

    It's a shame you didn't get the point because it's actually a very important one. At least until recently productivity growth during this cycle has not been unusually weak. Corporate profitability has not been weak.

    There's no single simple explanation for that seeming contradiction, but I would mention:

    - What matters most in an economy is always in the details, never in the aggregates. When you go by aggregates you're lumping together tech megacorps like Apple and Google, which are so piled up with cash they've had to invent a new kind of hedge-fund-like corporate asset manager class, with a vast segment of small and medium business - anything too small to issue bonds - that's been starved of capital.

    - The marginal return on capital could be low even while the average return is high.

    - The cost of capital in real terms was already very low during the last cycle, due to the private financial bubble. Maximally loose monetary policy has managed to hold the real cost of capital for big corporations down at where it was in 2005-2007, but no lower. Look at the last 10 or so years in your own chart of real rates on corporate bonds: except the spike during the crisis, not much has changed. If with capital costing what it did in 2005-2007 it was pouring into real estate much more than corporate investment, there's not a lot of reason to think that with the same cost of capital corporate investment should be stimulated.

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  13. o. nate3:24 PM

    One possibility is that the downward trajectory of yields for corporate borrowers who are able to access credit may not be representative of credit availability for businesses in general. This would be similar to the situation in home mortgages, in which rates for those able to qualify are low, but restrictions to qualify for that access are high.

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  14. Anonymous3:24 PM

    "If Gomme et al. measure rates of return on capital correctly, then why haven't falling real costs of capital combined with rising rates of return on capital lead to a business investment boom? "

    It did. See fig 3 Gomme et al Economic Synopsis report linked in Noah's post.


    Fig 2 in Gomme et al's Economic Synopsis report shows that the average real return on capital was increasing from the early 1980s until the 2009/10 GR. This is in line with the increasing profit share in GDP evident since the early 1980s. This is probably explained by globalization which has driven down real wages across the globe.

    The decline in real returns on securities since the 1980s is correlated to the increase in profit share of GDP. Perhaps these two are actually related - an incipient euthanasia of the rentier effect.

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    1. Anonymous3:28 PM

      I should further add in reference to the real return of capital chart in Gomme et al that the complete term average is dragged down only by the GR slump. Prior to this it was rising.

      Henry

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    2. t did. See fig 3 Gomme et al Economic Synopsis report linked in Noah's post.

      Meh. That's gross, not net. Depreciation has gone up a lot recently, as Matt Rognlie has shown.

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    3. Anonymous2:09 AM

      Has he actually said that explicitly? He might allude to that because he talks about rapid obsolescence of high tech capital goods e.g. computers and software. Anyway, so what? Depreciation still represents expenditure about which capitalists have to make decisions based on returns. When he throws in the "you can't eat depreciation" epigram, things are getting silly. Actually, you can eat depreciation. Expenditure behind depreciation (i.e. replacement goods) goes to paying for taxes, wages, primary goods etc just as expenditure on new capital goods does.

      Henry

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  15. Anonymous3:33 PM

    I am wondering why the juxtaposition of the dolly and doggy photo to the first line of Noah's piece. Noah, are you saying this is a photo of the Council of Economic Advisors?

    Henry

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  16. This is related to average v marginal.
    I think it is important to distinguish fixed capital into residential capital (AKA houses) non residential structures and equipment (and software).

    The user cost of equipment and software is mostly depreciation. There isn't any particular reason to expect equipment investment to respond to interest rates nor is there much evidence that it ever has.

    Most of the rest of investment is residential. It is not related to the returns reported by Gomme et al -- households don't publish balance sheets or profit and loss statements. The return is partly housing services but also, in large part, expected capital gains. These have declined vastly. Or to put it another way, low current investment is almost entirely low housing investment and has nothing to do with the calculations here.

    The question becomes why aren't firms building lots of structures ? Here I guess that a lot of it is that much of non residential investment in structures is retail (shopping malls) and office parks near new housing developments. That is very much a complement to residential investment and low (given interest rates) as a result.

    But also (here really marginal v average) a lot of the profits are going to financial firms (the legend says business not non-financial business). Their marginal return to new structures is low. Another huge chunk is going to high tech. Their return to structures is low as stressed by Summers
    http://equitablegrowth.org/2015/08/20/must-read-lawrence-summers-2014-u-s-economic-prospects-secular-stagnation-hysteresis-zero-lower-bound/

    I guess the common theme is that corporate profits and investment don't have much to do with each other, so the Gomme et al meets Smith puzzle isn't so puzzling.

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  18. Anonymous12:33 PM

    Cost of debt capital is not equal to corporate bond yield. you are making assumptions about risk there (probability of default and loss given default) just like you need a model of risk to figure it out for equity.

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