06 May 2014

A Question for the Piketty Defenders on National Income Accounting and Interest

Capital & Interest 25 Comments

OK Kevin Donoghue manages to escape the trap I had set for Piketty, much as Luke Skywalker–nursing his mangled arm–fled Vader at the end of The Empire Strikes Back.

To refresh your memories: Piketty clearly had argued that if the “marginal productivity of capital” (and from his discussion it was clear that this was a technological state of affairs, having to do with physical facts) is zero, then the return to capital r is also zero, meaning that in any period the income flowing to capital must be zero.

So I set out to show the problem with this framework. I specified a thought experiment in which all production is “due” to labor in an economic sense, and where there is clearly no physical contribution of capital goods or other forms of wealth (such as land). Nonetheless, I showed how someone in possession of a stockpile of consumption goods in period 1 could trade them intertemporally in order to obtain a perpetual flow of real consumption, which was obviously coming out of the catch that the workers were physically producing each period.

So, in response, Kevin Donoghue gave the best reply on behalf of Piketty: “Actually I’m pretty sure Piketty would simply say: loans (whether payable in money or birds) are not net wealth. I owe you 5 birds, payable next spring; an asset in your books, a liability in mine. In aggregate, Beta = 0.”

As I said, *that’s* a defensible response. It moves us forward one step in this debate (as opposed to the people trying to argue that Piketty doesn’t think “interest” counts as income to capital, or claiming that Piketty never meant that the marginal product of capital had anything to do with the rate of return on capital).

Now I could grapple with Donoghue’s response in the terms of my thought experiment, but instead I want to turn it back to the defenders of Piketty: You show me a paradigmatic example of what would count in the national income statistics as “net interest income” flowing to the capitalists. As always with these things, try to keep the example as simple as possible; boil it down to the essence of what you think “net interest income” really is, if you’re denying that my example shows a portion of total national income going to capitalists.

(NOTE: The purists can of course bite my head off for even “playing this game.” That’s fine, you’re right that there are problems with the very idea of GDP etc. But I’m doing baby steps here. I want to show the believers in the naive productivity theory of interest that their worldview leads to internal contradictions; I don’t need to replace their whole economic framework to do that.)

25 Responses to “A Question for the Piketty Defenders on National Income Accounting and Interest”

  1. Major_Freedom says:

    In real terms:

    Capital available at the start of each period can theoretically be used up entirely in the production process for that period, such that the new capital produced and made available at the start of the next production period only replaces, and does not add to, the supply of capital.

    On the money spending side of things however, nominal aggregate profits can remain positive even with a perfectly fixed supply of money and volume of spending. This profit would be generated due to aggregate money costs never quite equalling aggregate money revenues.

    The reason for the difference is due to capitalists withdrawing dividends and interest payments from business firms, in order to spend on themselves and not the businesses. Since this spending generates revenues but not costs, this leads to profits remaining positive. Again, this can take place even as capital is not growing in real terms.

  2. Philippe says:

    “To refresh your memories: Piketty clearly had argued that if the “marginal productivity of capital” (and from his discussion it was clear that this was a technological state of affairs, having to do with physical facts) is zero, then the return to capital r is also zero, meaning that in any period the income flowing to capital must be zero.”

    What he actually says is:

    “According to the simplest economic models, assuming “pure and perfect” competition in both capital and labor markets, the rate of return on capital should be exactly equal to the “marginal productivity” of capital (that is, the additional output due to one additional unit of capital). In more complex models, which are also more realistic, the rate of return on capital also depends on the relative bargaining power of the various parties involved. Depending on the situation, it may be higher or lower than the marginal productivity of capital (especially since this quantity is not always precisely measurable).”

    *by “the simplest economic models”, he means standard mainstream neoclassical models.

  3. Kevin Donoghue says:

    Thank you for the compliment, but I don’t think Luke Skywalker would have greatly impressed the girls if all he did was check the index of a book in order to divine the author’s intent. I guess I should do it again to answer your latest question: what would count in the national income statistics as “net interest income” flowing to the capitalists? Okay, a quick search gives us this:

    To summarize, I define “national wealth” or “national capital” as the total market value of everything owned by the residents and government of a given country at a given point in time, provided that it can be traded on some market. It consists of the sum total of nonfinancial assets (land, dwellings, commercial inventory, other buildings, machinery, infrastructure, patents, and other directly owned professional assets) and financial assets (bank accounts, mutual funds, bonds, stocks, financial investments of all kinds, insurance policies, pension funds, etc.), less the total amount of financial liabilities (debt). If we look only at the assets and liabilities of private individuals, the result is private wealth or private capital. If we consider assets and liabilities held by the government and other governmental entities (such as towns, social insurance agencies, etc.), the result is public wealth or public capital.

    So I take it that Greek bonds held by Germans are Kapital, nein? But of course such assets wash out in aggregate. In the consolidated accounts of a closed economy, bonds are not wealth and hence they are not capital, these being synonyms in Piketty’s lexicon.

    • Bob Murphy says:

      Right Kevin, so give me the simplest possible example you can think of, where you agree the capitalist is earning net interest income each period.

      (Incidentally, just to be clear, there *is* net capital wealth in the original example I proposed. The capitalist starts out with 50 birds. Piketty agrees that that is capital. Now where things get tricky is then if the other workers eat those 50 birds, I imagine Piketty could say by period 2 Beta had fallen to zero.)

      But rather than try to get in the trenches on my original example, Kevin, I want you to tell me what you agree that Piketty would say is a paradigmatic example of a capitalist earning net interest income from his capital. Again, make it as simple conceptually as possible, so we can argue over the essence and not get sidetracked.

      • Kevin Donoghue says:

        Didn’t I just answer that question? A German gets paid coupons on Greek bonds. By Piketty’s definition, which I just quoted, that’s a capitalist earning net interest income from his capital.

        How can I make it simpler?

        • Bob Murphy says:

          Didn’t I just answer that question? A German gets paid coupons on Greek bonds. By Piketty’s definition, which I just quoted, that’s a capitalist earning net interest income from his capital.
          How can I make it simpler?

          OK, so in my example, let me give two more pieces of information: The guy who initially caught the 50 birds is German, and everybody else is Greek.

          Now you agree with me that I just blew up Piketty right?

          • Kevin Donoghue says:

            For a guy who has been blown up, he looks pretty healthy to me. It’s late here so I’ll sign off. Maybe in the morning you’ll be able to show us evidence of his charred remains. So that you get your lurid picture in focus, please start by deciding whether you want to show the German accounts (with positive capital), the Greek accounts (negative capital) or the world accounts (zero capital).

  4. Transformer says:

    ‘… people trying to argue that Piketty doesn’t think “interest” counts as income to capital’

    An extension of Kevin’s argument is that any interest income received by one person is just negative interest income for someone else.

    • Bob Murphy says:

      Transformer wrote:

      An extension of Kevin’s argument is that any interest income received by one person is just negative interest income for someone else.

      Right, OK, so let’s take that to its logical conclusion. Clearly Piketty thinks that *it’s possible* for capitalists to earn net interest income in an economy, right?

      But hang on–no matter who is receiving interest income, somebody else is paying it. That’s true even when MPK>0.

      So did you guys just prove that net interest income can *never* exist?

      Rather than me constantly proposing examples and you guys finding ways to say “no that doesn’t count,” I want you to show me an example that *does* count.

      Kevin tried it with the Greek/German bond thing, and I showed that I can make my example fit that paradigm. So either my example goes through, and I just proved a capitalist can earn interest income even in a world where MPK=0, or Kevin needs to change his position and give me a different example of where it “counts.”

  5. Transformer says:

    “But hang on–no matter who is receiving interest income, somebody else is paying it. That’s true even when MPK>0.”

    By his own definition it sounds like Piketty will count as income to capital only that which derives from the increased physical output as a result of the deployment of that capital.

    If I lend you 5 birds and get 6 back a year later that doesn’t count as its a transfer.

    If I build a machine that allows 5 extra birds to be caught – that counts (and r would be derived from this as a proportion of the cost of the machine, factoring in time preference)

    (Not endorsing this view – just trying to see where his views lead).

    • Bob Murphy says:

      Transformer, in contrast to some others on this thread you seem like you are actually contemplating the possibility that I might be saying something important. So let’s keep this alive. I will try to refrain from sarcasm on my end too (though I can’t promise).

      I like this:

      If I build a machine that allows 5 extra birds to be caught – that counts (and r would be derived from this as a proportion of the cost of the machine, factoring in time preference)

      That’s actually where I’m going to take this next. But I know for a fact if I give my example first–where the machines help people catch more birds per hour and yet the real interest rate is zero–then the Piketty defenders will be able to come up with some reason that my example doesn’t count.

      So can you elaborate a bit on how you would adapt my fable, so that the owner of capital earns genuine net interest income?

      • Bob Murphy says:

        Oh, and obviously with all this stuff, I’m not holding you personally on the hook: Just tell me how you think Piketty’s framework would deal with it.

      • Transformer says:

        Why do I sense a trap ? But what the heck…..

        Suppose I have a choice between going out and catching birds and building a machine that will allow more birds to be caught in the future (and that I would rent out).

        I will build the machine if the discounted present value of future expected rents is greater than my cost (in terms of current birds I could have caught and possibly leisure ).

        Assuming I build the machine I start to get interest on it when people rent if from me to increase their bird haul.

        Assume that the machine takes me a year to build and I would have caught 50 birds in that time. Its costs is equivalent to 50 present birds. Now in theory the more it adds to productivity the higher the interest rate will be. If it adds 5 birds a year in marginal product its r will be 10%, if it adds 10 birds a year its r will be 20% etc.

        Now if everyone sees that I am earning a 20% when the current interest rate is only 10% they will start making similar machines and the price will be forced down until the interest rate is the same as the rate prevailing in the market.

        The question is what is the rate prevailing in the market? I will go with what Nick posted earlier on that.

        • Transformer says:

          Obviously I’m assuming the machine lasts a long time…

        • Bob Murphy says:

          Hey Transformer,

          OK this is pretty solid. But notice what you’ve done: You have to assume that there is already a positive rate of interest, in order to show how a physically productive machine can yield the owner interest income. Do you see what I mean?

          So this is a main element of the Cambridge Capital Controversy. The UK folks were saying, “You neoclassicals are trying to make it sound like the capitalists earn interest income as the ‘return’ to the increment in output due to their physical tools etc., just like the workers earn wage income from the increment in output due to their labor. But no, that’s not correct. In order for physical capital to yield interest income, we have to independently know that the interest rate is positive. So you’re arguing in a big circle. You’re saying interest is the reward for the productivity of capital, but you’re using ‘productivity’ in a weird way where a zero interest rate means all the physical machines suddenly are not productive. This isn’t at all analogous to how economists analyze wages and labor.”

          • Transformer says:

            Wages and rents will be calculated in exactly the same way as the discounted value of the physical output they add to the final output.

            But for rents we are also interested in its rate of interest (rent / value).

            Its possible that my time preference may be such that I will still build the machine and rent it out even if the stream of future revenue is less that my cost for building the machine. (if for example I need some income when I retire and I can’t store physical birds ). In other words I may accept a negative return on my investment if I need to tie in some income in the future and that is the best I can do.

            A few comments:

            1. MPK and r are clearly different things. MPK is related to r via the price of the output added by the capital good, and by the value of the capital good itself. The relationship between thee 3 things is a dynamic one

            2. If its impossible to build machines that increase physical output then all bets are off. If you don’t count consumer loans as real income to capitalists (because hey are just transfers) then if MPK= 0, capitalist income is 0 just like Piketty says.

            3. Even if MPK = 0 then you can still have a rate-of-interest based purely on time preference and that prevail for consumer loans.

            4. It still feels intuitive that there will be a positive correlation between MPK and r. I am reassured on this point by the fact that Nick Rowe seems to support this view . I do have however a nagging doubt that while MPK and time preference combined will determine the level of output, r may be determined just by time preference once everything has been factored in.

            Need to think about it some more.

            • Bob Murphy says:

              Transformer this is great stuff. You are aware of the important subtleties. In particular, you realize that the MPK directly explains the *rental price per unit time* of a capital good, which is not at all the same thing as the percentage rate of increase in the market value of a capital good over time (including its earnings).

              I have yet to see Piketty make this distinction. You would think “return on capital” was interchangeable with “rate of interest” and “rental rate.”

              It’s true that in Piketty’s QJE paper there is a small section dealing with this stuff. For all I know his co-author put that in, because I haven’t seen any of that stuff make its way into his book discussion.

              I haven’t decided yet whether these conceptual problems affect his basic thesis. But nonetheless it’s amazing that somebody who writes a whole book on capital and income distribution is at best extremely misleading to the reader when he talks about capital and interest income.

  6. martinK says:

    Seems to me Donoghue’s reply is beside the point.

    Pikkety’s claim isn’t about whether loan’s are or aren’t wealth, it’s about where the income will go to if capital is of no use in the production process:

    In such a society, all of national income and output would go to labor.
    (http://consultingbyrpm.com/blog/2014/05/a-fleshed-out-example-showing-problems-with-piketty.html)

    As Bob’s example shows *not all* (national) income necessarily goes to labor.

  7. Kevin Donoghue says:

    All right, since Bob was kind enough to compare me to Luke Skywalker (which is presumably good, though I haven’t actually seen the movie), it’s only fair to lob a bone his way:

    http://anyoldbullshit.blogspot.ie/2014/05/piketty-and-marginal-product-of-capital.html

  8. JKH says:

    I’ll give this a wild try.

    First example:

    Capitalist catches birds and lends them. The end of period inventory consists not of birds but of bird loans. The capitalist earns bird interest. Somebody else pays bird interest. Net bird interest at the macro level is zero.

    New example:

    Capitalist produces a machine for enhanced bird catching. This machine increases the number of birds caught at the macro level compared to the first (counterfactual) example.

    GDP increases relative to the first example.

    If the machine is owned by a single capitalist, he can create a corporation to own that bird machine. The capital structure can be designed as a mix of debt and equity. The interest the capitalist earns on the debt portion will represent net macro interest when GDP is calculated according to those financial accounts using birds as the medium of account. He’s just reclassified some of his profit as interest. But that interest isn’t paid by any third party in the economy. So it becomes net macro interest according to this accounting. I think something similar happens in real world NIPA accounting.

    The capitalist may have to pay for the original capital cost of the machine with birds. But the capital cost/investment is still an incremental part of GDP. It has a current period value equal to the discounted flow of future incremental bird production. That flow allows for future profit and lagged cost recovery.

    Depreciation or not can be netted out as it occurs and accounted for in net domestic product.

    The occurrence of macro level interest in the second example is entirely a function of the mix of debt and equity put in place by the capitalist for his personal claim on the incorporated machine – where finance in this case uses birds as the medium of account and I guess as the medium of exchange.

    That was a quick and dirty attempt. May be right or wrong.

  9. Major-Freedom says:

    I don’t like examples purporting to say something about real world economies that don’t have money in them. It always seems to lead to too much unnecessary confusion. Same thing happened with the overlapping generation model.

    It is EASY to show that dollar profits can remain positive even though real profits are zero.

    All we have to do is imagine a low enough ratio of saving and investment to consumption, such that the production of new capital only succeeds in merely replacing the capital used up in production.

    Dollar profits can remain positive here.

    Aggregate money profits are a mathematical difference between aggregate money revenues and aggregate money costs. Revenues can consistenly be greater than costs because of the fact that capital owners extract dividends and interest payments from their business firms, to consume for themselves. This makes total money revenues equal to capital goods spending plus capitalist consumption spending, whereas total money costs are just capital goods spending plus wage payments.

    This positive dollar profit can take place year after year, all the while real output growth remains flat.

    There, that’s just a few paragraphs.

  10. Major-Freedom says:

    Meant to say real profit *growth* is zero.

    Not as easy as I thought I guesa.

    • Major-Freedom says:

      And forgot to include consumption from wage payments in total revenues.

      Darn. Ok, via symbols:

      Aggregate revenues = K + C,

      Where K is capital goods spending.
      Where C is consumer goods spending.

      C can be broken down into consumption by capitalists who pay wages Cc, and consumption by those who earn wages Cw.

      So

      Aggregate revenues (AR) = K + Cc + Cw

      Now,

      Aggregate costs (AC) = K + W

      Where W is wage payments.

      Thus,

      Aggregate profit (AP) = AR – AC = (K + Cc + Cw) – (K – W)

      If we assume wage earners spend all their wages on consumption (not necessary, but won’t change the result), then Cw = W.

      Thus,

      AP = Cc

      In other words, the quantity of aggregate profits is equal to the dollars spent by capitalists on their own consumption. Every other spending is associated with equal revenues and costs. Wage payments are used by wage earners to spend on consumption, but the same dollars spent on wages are a monry cost. Same thing for capital goods. Capital goods spending generates money revenues, but it also generates equal money costs. The only thing that isn’t associated with equal costs and revenues is capitalist consumption. It just generates revenues.

      Interestingly, Joan Robinson’s theory of profit is almost identical to the above.

      • Philippe says:

        the Kalecki profit equation:

        gross profits (net of taxes) = gross investment + capitalists consumption + government deficit + external (export) surplus – workers’ saving

  11. guest says:

    consultingbyrpm blog tag piketty

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