Some followups on capital taxation

I’m going to move on to other things, but before I do, I thought I’d point to some very good commentary inspired by the previous post on capital taxation.

You already know that interfluidity is like a really drab version of Playboy, no one reads it for the articles, the really good stuff happens in the centerfold under the fold, in the comments.

The piece provoked smart responses on other blogs, Increasing Marginal Utility, Separating Hyperplanes, and Asymptosis. [1]

Robert Waldmann points out that glib euphemisms like “the long run” lead one to overstate the case against capital taxation even on the most sympathetic understandng of the models, that under human relevant distributions and time parameters the models can favor capital taxation. Here is his case (in a PDF he describes as “heroically constructed by Sigve Indregard”).

Here are a very few substantive comments, in response to responses:

  • Beware fallacies of composition is justifying a constant-returns-to-scale production function at a macroeconomic level. It’s an assumption that is only remotely justifiable if you are sure that your production function includes all factors of production. At a macro level, it’s obvious that you can’t scale all factors of production — see e.g. the smart discussion in comments by Merijn Knibbe, JW Mason, and Douglas Edwards regarding land. Omitting factors of production in a model may be innocuous in microeconomic contexts where their quantities are unconstrained functions of the factors that you do model. We needn’t concern ourselves about oxygen as an input to our beauty salon. But in macro production functions, it is hard to know which factors are bottlenecks to increased production, and failing to include the inputs and their constraints can render the exercises useless. It is conventional in macroeconomics to model the most significant determinant of overall production as “technology”, measured as a residual between what the factors we model predict and the growth we actually observe. That’s an elegant way of ducking the fact that we are omitting important inputs. If we are omitting important inputs, scaling up the factors we do include may be no more effective than multiplying shovels without hiring more humans to wield them.

  • There are lots of ways to get confused about the idea that savings equals investment. It’s an accounting identity, and, as always with accounting identities, there are tensions between the definitions under which the identity is true (by definition) and “common-sense” notions of the phenomena described. There are two approaches to dealing with those tensions:

    1. You can accept the formal definitions that make the accounting identity true, but be very careful to avoid “slips of the tongue” in mapping those definitions to other contexts; or
    2. You can treat those definitions as very narrowly applicable formalisms, and urge caution in the opposite direction, when reconciling the common-sense idea with the formalism.

    Steve Roth takes the second approach. I’ll take the first.

    Let’s assume that S ≡ I, and define investment to mean whatever it must mean for that identity to hold true. The S will always be equal to I. However, that does not imply that investment can be modeled as a cumulation of savings! We add to savings over time, but investment returns are complicated and sometimes negative. So we might describe ΔS ≡ ΔI as a two-term sum of new saving plus return on total investment.

    ΔS ≡ ΔI = new_savings + valuation_adjustment

    Ramsey-inspired models take the second term always to be the marginal product of capital in a production function, less a constant depreciation rate. But that is not likely to be realistic, especially if we let S ≡ I include financial savings, rather than what the models imagine, the direct deployment of an unconsumed real resource. When consumers stuff dollar bills into a mattress, it may or may not be true that the resources they thereby fail to consume get usefully deployed into production. If it is true, it must depend on the complex ability of the monetary and financial system to allocate the slack made available by nonconsumption in ways that contribute to future production. By definition, putting dollar bills in a mattress rather than spending the income may count as investment (if not offset by consumption elsewhere). But there is no guarantee that it is good investment, directly or indirectly. So, in addition to cumulation of savings, we have to think much harder than the Ramsey model does about that second term, about the dynamics of valuation changes. (For a great example, consider how the United States’ chronic current account deficits have failed to cumulate into a large negative NIIP, as pointed out today by Paul Krugman.)

    Ramsey model intuitions do fine if “bad investments” are a relatively constant fraction of total savings. Failed projects just fall into the constant depreciation rate. The key is to assume that investment returns are independent of the qunatity new savings. Unfortunately, if we allow the second, valuation term of ΔS ≡ ΔI to vary as a function of the first term, if, for example, an increased rate of savings tends to be matched by poorer aggregate investment returns, then Ramsey model logic falls out the window.

    In practice, we observe that increased rates of gross saving do correlate with poor investment returns. When the financial system is asked to allocate giant pools of money, it fucks up (and steals a lot). We have to be careful in mapping these real-world observations to modeled constructs — net investment rather than gross savings is the closest Ramsey-model referent. Net domestic saving was actually low during the housing-boom-era of malinvestment, but net investment was not so low thanks to a very large capital account surplus (those scary trade deficits). Total US S ≡ I was robust when foreign saving was included. But returns on that S ≡ I were unusally poor. If you accept the accounting definitions under which S ≡ I, you must be especially attentive to the complex dynamics of financial investment returns. You cannot just map that kind of S ≡ I to the capital term in a Ramsey model.

  • That last point was already over-mathy, but for those of you who like this sort of thing, a concise way to make much of the anti-anti-capital tax case is to observe that conventionally we often write production functions like:

    Y = F(K, AL)

    where A is a stand-in for labor-augmenting technology and is presumed to be either independent of the production process or, in the most common “endogenous growth” models, a function of cumulative capital investment. To break the Chamley-Judd result, all we have to do is write

    Y = F(K, A(w)L)

    that is, let labor-augmenting technology be in part a function of (after-tax) wages, defined either as current wages or especially as a cumulation of past wages. The choice to model A as independent of wages is rarely justified, and is not remotely obvious. It is merely conventional. Funny, the direction conventions in economics seem so frequently to tilt.

[1] If I’ve left you out, it’s because I am an idiot, not because I have judged you to be. Let me know and I’ll add you.


17 Responses to “Some followups on capital taxation”

  1. vbounded writes:

    The choice to model A as independent of wages is rarely justified, and is not remotely obvious. It is merely conventional. Funny, the direction conventions in economics seem so frequently to tilt.


    Empirically, doctrinal allegiance biases researchers as much as a financial interest.

    Hence Planck’s comment, science advances one funeral at a time.

  2. JW Mason writes:

    OT but that Krugman thing you link to is utterly infuriating.

    Not because he’s wrong. He’s right, and it’s an important point — US investment returns abroad are systematically higher than foreign investment returns in the US. So cumulative deficits are not a good guide to the net international asset position, and the net international asset position is not a good guide to net income flows.

    The thing is, Krugman teaches people NOT to think like this. He made a big point recently of boasting that his textbook frames its whole discussion of exchange rates around uncovered interest parity. What he teaches his students — with hardly any caveats — is that we should think of capital as being perfectly mobile and foreign exchange markets as always in equilibrium, so that interest differentials and exchange movements just balance out. In a world like that, the divergence between cumulative US deficits and the actual US asset position would be impossible. What he explicitly teaches his students is that exchange rate changes are offset one for one by interest rates, so that valuation changes — like the ones in the post you link to — should have no effect.

    It’s the general problem with these liberal economists. Often, they have very sensible ideas about real world economics and policy. But the conservatives they hate are just the people who take seriously the theory that they themselves teach.

  3. vlade writes:

    @vbounded: I wish it was true of econ. To me it seems much slower – mostly because econ (and other social sciences) tend to be much easier to mesh up with one’s ideology. So vlade’s adjustment of Planck’s is “econ advances one funeral of ideology at a time”.

    @Steve: For long time now I thought of I in S=I identity as true investment, with uncertain return (on aggregate). To do anything else just doesn’t make sense to me, since then you start running into the matress problem (or gold-rebury, whichever you prefer). Mind you, it took an obstinate gold-lover insisting that his gold isn’t savings thus not a loan to anyone and thus no-one’s investment.

    I agree that A is a factor of wages. I’ve commented on recent mpettis posts on China development that high wages are important part of development, as they incentivise innovation. Simplified, profits go where it’s easiest to get them, a cheap labour is cheaper (and more reliable) than innovation. Even deploying more capital is cheaper than innovation (becuse in general it’s more reliable in marginal return). Innovation is the most expensive way of increasing Y, so if you want to do it, you have make all the other ways pretty much innacesible (while maintaining competition).

    Importantly also, Y should be also rewritten from the other side, as Y=B(w)+B(C)+W, that is, what you produce has to be consumed (or wasted). B in here would be a function that transforms some expected stream of income (from wages or capital investment) to currently spendable one. W is just waste (overproduction that rots or whatever you want..). One really probably should re-write it as a time function, but that’s beyond this comment.

    Looking at it only from one side is not much better than looking at one side of the private/government accounting identity – it just doesn’t exist separately.

  4. JW Mason writes:

    On S=I:

    It is true that, with appropriate definitions, savings is identically equal to investment. And it is true that the act of stuffing cash (or gold) in the mattress is an act of savings for the person carrying it out. But it does not follow that there must therefore be a corresponding act of investment somewhere. It is just as possible that the act of stuffing cash under the mattress eventually results in an equal reduction of saving elsewhere, so that aggregate savings and investment are unchanged.

    So I do not agree that:

    By definition, putting dollar bills in a mattress rather than spending the income may count as investment

    Aggregate S=I does not mean that a change in savings at the individual level implies or produces an equivalent change in investment. Keynes gives exactly this logic int he general theory. We can have I fixed, and individual units choosing the fraction of income to save. Then S=I is maintained by variations in income.

    This is what’s left out of the post — you are interested in how the identity S=I is maintained, but you forget that income adjusts. IMO this is a much more important margin than valuation adjustments, as far as this question is concerned. The problem is not, as you suggest, that you can’t cumulate aggregate saving over time to get aggregate investment. The problem is that you can’t add up individual saving choices to get aggregate savings.

  5. Steve Roth writes:

    Thanks for linking to my post, though I kind of wish you hadn’t because it’s wrong as written. It should say:

    Private Domestic Nonfinancial (i.e. households and businesses) Saving ≠ Private Domestic Nonfinancial Investment

    *Because* other sectors exist. Sliced one way: Domestic Financial + Fed Gov + International (financial and non-). (One can argue which sector the Fed should be placed in.) And there are massive flows of funds between these sectors and the Private Domestic Nonfinancial sector.

    And: those other sectors can (do) create new financial assets, notably bank deposits, which is how the cumulative surplus from production gets monetized over time.

    The Scott Sumners and John Cochranes of this world seem to think that S=I for the “private” economy. And it’s unclear what’s included in their imagined private economy (financial? international?). Their failure to understand or address the sectoral accounting makes their S=I thinking completely muddled.

    That’s what I meant to say.

  6. […] April 4: Steve Waldman kindly links to this post, and I’m rather abashed that he does because it’s wrong as written. As pointed out by […]

  7. Steve Roth writes:

    @vlade: “it took an obstinate gold-lover insisting that his gold isn’t savings thus not a loan to anyone and thus no-one’s investment”

    I have my own notions, but I’d love to hear your explanation of how gold holdings constitute a “loan” to another party (or sector?). I think it’s an important thought.

  8. stone writes:

    I guess Henry Ford was a pioneer of the compelling argument you give about higher wages helping to build productive capacity in the form of “human capital”.

    To me the mistake of Garret Jones’s interpretation of Chamley Judd is most starkly revealed by the phenomenal increase in productive capacity after the outbreak of WWII. When WWII started, factories sprung up everywhere building battleships. New technological breakthroughs came thick and fast. That was all because demand was pushed very very hard by the need for weapons. Obviously, once demand was there, there was no impediment for expansion of productive capacity. The financial means to invest, in the productive capacity to meet that demand, sprung up endogenously in response to that demand. It didn’t require workers to do without so as to give more to the capitalists. The trade off isn’t between consumption by workers versus real investment in productive capacity by capitalists. The trade off is between a slack system with idle machines and involuntarily underemployed workers versus everything humming into action.
    When there is inadequate demand, the “investment” to cause S=I can very well be in the form of unsold inventory that perishes and goes to waste. Of course financialization is another way to slip away from a real productive economy. Financialization is actually exacerbated by disproportionate returns to a small owning class.

  9. vlade writes:

    @Steve Roth:
    not the gold itself per se – the discussion was a bit more complicated that I wrote. Basically, I was trying to show him that any deposits in banks were loans to the bank by default, and thus someone’s investment (at worst bank depositing it with a CB).

    If he buys gold with his cash, he has a lump of metal, but he gave currency to someone else who again doesn’t have much choice on what to do with it – make a loan or exchange for an asset (gold being an asset, but so is loaf of bread, gold is a just a bit more durable and has less intrinsic value). If you follow the chain all the way round, either money circulates quickly (with everyone buying assets, and the seller of the assets using it to buy another asset), or eventually it end (for a time) in a bank account creating an “investment” (investment meant in the who-knows-what-the-return will be).

    The gold bug insisted that the gold is his savings – and, to an extent it is, but no really different than an investment into any other asset (and there are even bread investors, they are called supermarkets for example). But his savings (or anyone’s spending the money) go on and eventually create a loan – because there just isn’t anything else to do with the money (caveat emptor: there is, stuff it into matress, in which case the physical money representation was converted into a physical asset. That does remove money from circulation, but in the current economy this is relatively small part and not that important I believe).

  10. stone writes:

    Isn’t “investment” (as in S=I) what is described as this in wikipaedia:
    “In economic theory or in macroeconomics, investment is the amount purchased per unit time of goods which are not consumed but are to be used for future production (i.e. capital).”
    So I suppose the inventory of bread bought by the supermarket might count but I don’t see how a bank deposit does. Isn’t “buying” a bank deposit with paper currency simply an asset swap as is buying stocks or bonds on the secondary market or a pre-existing piece of real estate. The bank deposits initially were created by the bank when the bank made a loan. When you as a customer pay in paper cash to the bank and get a bank deposit in return you are in effect buying a pre-existing bank liability on the secondary market. As such it is just inter-converting existing savings rather than making an investment in the economic sense. Same thing with buying gold to keep as a store of value. Perhaps a jeweler buying inventory of gold jewelery in order to sell it on is investing. Am I in a muddle with this?

  11. jicho bovu writes:

    I’m an engineer in training, so treat my comment as a question from a layman. Here goes?
    (couple of them)

    1 – how can u get away with treating equations that obviously vary with time, as functions of all manner of manna, and leave out “time”? of course there are the assumptions that hold true at discrete points on the curve of the equation, but to leave out time in the S = I(x,y,z,….n) is reminiscent of an introductory undergraduate class, where all sorts of assumptions have to be made for the simplified cases to be true. The author and commentors, and other prominent users of that S=I equation dont appear to dabble in introductory calculus, so what the fudge is going on?

    2 – the money-in-a-mattress and gold-mountain examples are, if S = I(x,y,z,t) where t is time, considered as investment because at t=0 they might be out of market, but at t = t(need to dip in nest), the market will be re-united with its long lost dollars. So is the “time” a variable in S=I or is it some sort of get-out-of-jail card, that users of that S=I equation flash whenever its convenient and put it away when their half-wit logic seems to describe the behavior of S=I ?

  12. stone writes:

    jicho bovu@11, I’m also a layman but I thought S and I are flows and so incorporate time within them by definition. S is money saved per unit time. I also means per unit time. Hope I have not misunderstood you or am muddling this.

  13. chown -R me writes:

    store of value. Perhaps a jeweler buying inventory of gold jewelery in order to sell it on is investing. Am I in a muddle with this?

    April 5th, 2013 at 11:26 am EDT

    jicho bovu writes:

    I’m an engineer in training, so treat my comment as a question from a layman. Here goes?
    (couple of them)

    1 – how can u get away with treating equations that obviously vary with time

    The store of value will vary with respect to time. We know which direction it varies, but not until it is too late. Have you heard that when the market melts down all dollar-denominated common stock goes in the same direction? All ¥-denominated? All £? €? The magnitude of the change varies with respect to the beta of the stock. Companies highly leveraged should have higher beta. Those with no debt but cash on hand should have low beta. Does the gold denominated ¥ have a beta? Gold denominated $? Long treasuries should have a negative beta as in November ‘008. During times of uncertainty should you diversify into some of negative plus some of positive beta? Who knows? One thing for sure :

    Things are seldom as they seem. Pectin/tapioca masquerades as yogurt-cream. Pectin/tapioca is a contrary indicator.

  14. vlade writes:

    @stone: when banks get the deposit, they tend not to extinguish the money they created – usually they just re-use it, or park somewhere in the system. If you’d extinguish the money, you’d lose whatever interest you could get on them, so they would do it only if holding short-term deposits would actually cost them money (over and above normal liquidity cost). Given that most CBs now pay interest on reserves, it doesn’t pay for banks to extinguish money. Of course, you could claim that if it ends with CB that can extinguish the money, but I’d say as long as there’s some return on the money (positive or negative), I’d class it as investment – something has to generate the return (if it’s CB paying interest on reserves, it still pays a price for what it considers macro-important service).

    Money-in-the-mattess then counts as investment in any but 0% inflation scenario.

  15. […] Some followups on capital taxation […]

  16. […] Yglesias have been debating questions of saving versus investment and paradoxen of thrift. See also JW Mason in the comments here, and Simon Wren-Lewis a while back. Cullen Roche reminds us that, even under […]

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