The Interest Rate, the Interest Rate, and Secular Stagnation

In the previous post, I argued that the term "interest rate" is used to refer to two basically unrelated prices: The exchange rate between similar goods at different periods, and the yield on a credit-market instrument. Why does this distinction matter for secular stagnation?

Because if you think the "natural rate of interest," in the sense of the credit-market rate that brings aggregate expenditure to a desired level in some real-world economic situation, should be the time-substitution rate that would exist in a model that somehow corresponds to that situation, when the two are in fact unrelated -- well then, you are going to end up with a lot of irrelevant and misleading intuitions about what that rate should be.

In general, I do think the secular stagnation conversation is a real step forward. So it's a bit frustrating, in this context, to see Krugman speculating about the "natural rate" in terms of a Samuelson-consumption loan model, without realizing that the "interest rate" in that model is the intertemporal substitution rate, and has nothing to do with the Wicksellian natural rate. This was the exact confusion introduced by Hayek, which Sraffa tore to pieces in his review, and which Keynes went to great efforts to avoid in General Theory. It would be one thing if Krugman said, "OK, in this case Hayek was right and Keynes was wrong." But in fact, I am sure, he has no idea that he is just reinventing the anti-Keynesian position in the debates of 75 years ago.

The Wicksellian natural rate is the credit-market rate that, in current conditions, would bring aggregate expenditure to the level desired by whoever is setting monetary policy. Whether or not there is a level of expenditure that we can reliably associate with "full employment" or "potential output" is a question for another day. The important point for now is "in current conditions." The level of interest-sensitive expenditure that will bring GDP to the level desired by policymakers depends on everything else that affects desired expenditure -- the government fiscal position, the distribution of income, trade propensities -- and, importantly, the current level of income itself. Once the positive feedback between income and expenditure has been allowed to take hold, it will take a larger change in the interest rate to return the economy to its former position than it would have taken to keep it there in the first place.

There's no harm in the term "natural rate of interest" if you understand it to mean "the credit market interest rate that policymakers should target to get the economy to the state they think it should be in, from the state it in now."And in fact, that is how working central bankers do understand it. But if you understand "natural rate" to refer to some fundamental parameter of the economy, you will end up hopelessly confused. It is nonsense to say that "We need more government spending because the natural rate is low," or "we have high unemployment because the natural rate is low." If G were bigger, or if unemployment weren't high, there would be a different natural rate. But when you don't distinguish between the credit-market rate and time-substitution rate, this confusion is unavoidable.

Keynes understood clearly that it makes no sense to speak of the "natural rate of interest" as a fundamental characteristic of an economy, independent of the current state of aggregate demand:

In my Treatise on Money I defined what purported to be a unique rate of interest, which I called the natural rate of interest — namely, the rate of interest which, in the terminology of my Treatise, preserved equality between the rate of saving (as there defined) and the rate of investment. I believed this to be a development and clarification of Wicksell’s “natural rate of interest”, which was, according to him, the rate which would preserve the stability if some, not quite clearly specified, price-level. 

I had, however, overlooked the fact that in any given society there is, on this definition, a different natural rate of interest for each hypothetical level of employment. And, similarly, for every rate of interest there is a level of employment for which that rate is the “natural” rate, in the sense that the system will be in equilibrium with that rate of interest and that level of employment. Thus it was a mistake to speak of the natural rate of interest or to suggest that the above definition would yield a unique value for the rate of interest irrespective of the level of employment. I had not then understood that, in certain conditions, the system could be in equilibrium with less than full employment. 

I am now no longer of the opinion that the concept of a “natural” rate of interest, which previously seemed to me a most promising idea, has anything very useful or significant to contribute to our analysis. It is merely the rate of interest which will preserve the status quo; and, in general, we have no predominant interest in the status quo as such.

EDIT: In response to Nick Edmonds in comments, I've tried to restate the argument of these posts in simpler and hopefully clearer terms:

Step 1 is to recognize that in a model like Samuelson's, "interest rate" just means any contract that allows you to make a payment today and receive a flow of income in the future. It would be the exact same model, capturing the exact same features of the economy, if we wrote "profit rate" or "house price-to-rent ratio" instead of "interest rate." Any valid intuition the model gives us, applies to ALL asset yields, not just to the the credit-instrument yields that we call "interest rates" in every day life.

Step 2 is to think about the other factors that enter into real-world asset yields, besides the intertemporal exchange rate Samuelson is interested in -- risk, liquidity, carrying costs and depreciation, and expected capital gains. Since all real-world asset yields incorporate at least one of these factors, none correspond exactly to Samuelson's intertemporal interest rate.

Step 3 is to realize that not only are credit-instrument yields not exactly the Samuelson "interest rate," they aren't even approximately it. The great majority of credit market transactions we see in real economies are not exchanges of present income for future income, but exchanges of two different claims on future income. So the intertemporal interest rate enters on both sides and cancels out.

At that point, we have established that the "interest rate" the monetary authority is targeting is not the "interest rate" Samuelson is writing about.

Step 4 is then to ask, what does it mean to say that some particular credit-market interest rate is the "natural" one? That is where the dependence on fiscal policy, income distribution, etc. come in. But those factors are not part of the argument for why the credit-market rate is not even approximately the intertemporal rate.

The Interest Rate and the Interest Rate

We will return to secular stagnation. But we need to clear some ground first. What is an interest rate?

Imagine you are in a position to acquire a claim on a series of payments  in the future. Since an asset is just anything that promises a stream of payments in the future, we will say you are thinking of buying of an asset. What will you look at to make your decision?

First is the size of the payments you will receive, as a fraction of what you pay today. We will call that the yield of the asset, or y. Against that we have to set the risk that the payments may be different from expected or not occur at all; we will call the amount you reduce your expected yield to account for this risk r. If you have to make regular payments beyond the purchase of the asset to receive income from it (perhaps taxes, or the costs of operating the asset if it is a capital good) then we also must subtract these carrying costs c. In addition, the asset may lose value over time, in which case we have to subtract the depreciation rate d. (In the case of an asset that only lasts one period -- a loan to be paid back in full the next period, say -- d will be equal to one.) On the other hand, owning an asset can have benefits beyond the yield. In particular, an asset can be sold or used as collateral. If this is easy to do, ownership of the asset allows you to make payments now, without having to waiting for its yield in the future. We call the value of the asset for making unexpected payments its liquidity premium, l. The market value of long-lasting assets may also change over time; assuming resale is possible, these market value changes will produce a capital gain g (positive or negative), which must be added to the return. Finally, you may place a lower value on the payments from the asset simply because they take place in the future; this might be because your needs now are more urgent than you expect them to be then, or simply because you prefer income in the present to income in the future. Either way, we have to subtract this pure time-substitution rate i.

So the value of an asset costing one unit (of whatever numeraire) will be 1 + y - r - c - d + l + g - i. In equilibrium, you should be just indifferent between purchasing and not purchasing this asset, so we can write:

1 + y - r - c - d + l + g - i = 1, or

(1) y = r + c + d - l - g + i

So far, there is nothing controversial.

In formal economics, from Bohm-Bawerk through Cassel, Fisher and Samuelson to today's standard models, the practice is to simplify this relationship by assuming that we can safely ignore most of these terms. Risk, carrying costs and depreciation can be netted out of yields, capital gains must be zero on average, and liquidity is assumed not to matter or just ignored. So then we have:

(2) y = i

In these models, it doesn't matter if we use the term "interest rate" to mean y or to mean i, since they are always the same.

This assumption is appropriate for a world where there is only one kind of asset -- a risk-free contract that exchanges one good in the present for 1 + i goods in the future. There's nothing wrong with exploring what the value of i would be in such a world under various assumptions.

The problem arises when we carry equation (2) over to the real world and apply it to the yield of some particular asset. On the one hand, the yield of every existing asset reflects some or all of the other terms. And on the other hand, every contract that involves payments in more than one period -- which is to say, every asset -- equally incorporates i. If we are looking for the "interest rate" of economic theory in the economic world we observe around us, we could just as well pick the rent-home price ratio, or the profit rate, or the deflation rate, or the ratio of the college wage premium to tuition costs. These are just the yields of a house, of a share of the capital stock, of cash and of a college degree respectively. All of these are a ratio of expected future payments to present cost, and should reflect i to exactly the same extent as the yield of a bond does. Yet in everyday language, it is the yield of the bond that we call "interest", even though it has no closer connection to the interest rate of theory than any of these other yields do.

This point was first made, as far as I know, by Sraffa in his review of Hayek's Prices and Production. It was developed by Keynes, and stated clearly in chapters 13 and 17 of the General Theory.

For Keynes, there is an additional problem. The price we observe as an "interest rate" in credit markets is not even the y of the bond, which would be i modified by risk, expected capital gains and liquidity. That is because bonds do not trade against baskets of goods. They trade against money. When we see a bond being sold with a particular yield, we are not observing the exchange rate between a basket of goods equivalent to the bond's value today and baskets of goods equivalent to its yield in the future. We are observing the exchange rate between the bond today and a quantity of money today. That's what actually gets exchanged. So in equilibrium the price of the bond is what equates the expected returns on the two assets:

(3) y_B - r_B + l_B + g_B - i = l_M - i

(Neither bonds nor money depreciate or have carrying costs, and money has no risk. If our numeraire is money then money also cannot experience capital gains. If our numeraire was a basket of goods instead, then we would subtract expected inflation from both sides.)

What we see is that i appears on both sides, so it cancels out. The yield of the bond is given by:

(4) y_B  = r_B - g_B + (l_M - l_B)

The yield of the bond -- the thing that in conventional usage we call the "interest rate" -- depends on the risk of the bond, the expected price change of the bond, and the liquidity premium of money compared with the bond. Holding money today, and holding a bond today, are both means to enable you to make purchases in the future. So the intertemporal substitution rate i does not affect the bond yield.

(We might ask whether the arbitrage exists that would allow us to speak of a general rate of time-substitution i in real economies at all. But for present purposes we can ignore that question and focus on the fact that even if there is such a rate, it does not show up in the yields we normally call "interest rates".)

This is the argument as Keynes makes it. It might seem decisive. But monetarists would reject it on the grounds that nobody in fact holds money as a store of value, so equation (3) does not apply. The bond-money market is not in equilibrium, because there is zero demand for money beyond that needed for current transactions at any price. (The corollary of this is the familiar monetarist claim that any change in the stock of  money must result in a proportionate change in the value of transactions, which at full employment means a proportionate rise in the price level.) From the other side, endogenous money theorists might assert that the money supply is infinitely elastic for any credit-market interest rate, so l_M is endogenous and equation (4) is underdetermined.

As criticisms of the specific form of Keynes' argument, these are valid objections. But if we take a more realistic view of credit markets, we come to the same conclusion: the yield on a credit instrument (call this the "credit interest rate") has no relationship to the intertemporal substitution rate of theory (call this the "intertemporal interest rate.")

Suppose you are buying a house, which you will pay for by taking out a mortgage equal to the value of the house. For simplicity we will assume an amortizing mortgage, so you make the same payment each period. We can also assume the value of housing services you receive from the house will also be the same each period. (In reality it might rise or fall, but an expectation that the house will get better over time is obviously not required for the transaction to take place.) So if the purchase is worth making at all, then it will result in a positive income to you in every period. There is no intertemporal substitution on your side. From the bank's point of view, extending the mortgage means simultaneously creating an asset -- their loan to you -- and a liability -- the newly created deposit you use to pay for the house. If the loan is worth making at all, then the expected payments from the mortgage exceed the expected default losses and other costs in every period. And the deposits are newly created, so no one associated with the bank has to forego any other expenditure in the present. There is no intertemporal substation on the bank's side either.

(It is worth noting that there are no net lenders or net borrowers in this scenario. Both sides have added an asset and a liability of equal value. The language of net lenders and net borrowers is carried over from models with consumption loans at the intertemporal interest rate. It is not relevant to the credit interest rate.)

If these transactions are income-positive for all periods for both sides, why aren't they carried to infinity? One reason is that the yields for the home purchaser fall as more homes are purchased. In general, you will not value the housing services from a second home, or the additional housing services of a home that costs twice as much, as much as you value the housing services of the home you are buying now. But this only tells us that for any given interest rate there is a volume of mortgages at which the market will clear. It doesn't tell us which of those mortgage volume-interest rate pairs we will actually see.

The answer is on the liquidity side. Buying a house makes you less liquid -- it means you have less flexibility if you decide you'd like to move elsewhere, or if you need to reduce your housing costs because of unexpected fall in income or rise in other expenses. You also have a higher debt-income ratio, which may make it harder for you to borrow in the future. The loan also makes the bank less liquid -- since its asset-capital ratio is now higher, there are more states of the world in which a fall in income would require it to sell assets or issue new liabilities to meet its scheduled commitments, which might be costly or, in a crisis, impossible. So the volume of mortgages rises until the excess of housing service value over debt service costs make taking out a mortgage just worth the incremental illiquidity for the marginal household, and where the excess of mortgage yield over funding costs makes issuing a new mortgage just worth the incremental illiquidity for the marginal bank.

Monetary policy affects the volume of these kinds of transactions by operating on the l terms. Normally, it does so by changing the quantity of liquid assets available to the financial system (and perhaps directly to the nonfinancial private sector as well). In this way the central bank makes banks (and perhaps households and businesses) more or less willing to accept the incremental illiquidity of a new loan contract. Monetary policy has nothing to do with substitution between expenditure in the present period and expenditure in some future period. Rather, it affects the terms of substitution between more and less liquid claims on income in the same future period.

Note that changing the quantity of liquid assets is not the only way the central bank can affect the liquidity premium. Banking regulation, lender of last resort operations and bailouts also change the liquidity premium, by chaining the subjective costs of bank balance sheet expansion. An expansion of the reserves available to the banking system makes it cheaper for banks to acquire a cushion to protect themselves against the possibility of an unexpected fall in income. This will make them more willing to hold relatively illiquid assets like mortgages. But a belief that the Fed will take emergency action prevent a bank from failing in the event of an unexpected fall in income also increases its willingness to hold assets like mortgages. And it does so by the same channel -- reducing the liquidity premium. In this sense, there is no difference in principle between monetary policy and the central bank's role as bank supervisor and lender of last resort. This is easy to understand once you think of "the interest rate" as the price of liquidity, but impossible to see when you think of "the interest rate" as the price of time substitution.

It is not only the central bank that changes the liquidity premium. If mortgages become more liquid -- for instance through the development of a regular market in securitized mortgages -- that reduces the liquidity cost of mortgage lending, exactly as looser monetary policy would.

The irrelevance of the time-substitution rate i to the credit-market interest rate y_B becomes clear when you compare observed interest rates with other prices that also should incorporate i. Courtesy of commenter rsj at Worthwhile Canadian Initiative, here's one example: the Baa bond rate vs. the land price-rent ratio for residential property.

Both of these series are the ratio of one year's payment from an asset, to the present value of all future payments. So they have an equal claim to be the "interest rate" of theory. But as we can see, none of the variation in credit-market interest rates (y_B, in my terms) show up in the price-rent ratio. Since variation in the time-substituion rate i should affect both ratios equally, this implies that none of the variation in credit-market interest rates is driven by changes in the time-substitution interest rate. The two "interest rates" have nothing to do with each other.


(Continued here.)


EDIT: Doesn't it seem strange that I first assert that mortgages do not incorporate the intertemporal interest rate, then use the house price-rent ratio as an example of a price that should incorporate that rate? One reason to do this is to test the counterfactual claim that interest rates do, after all, incorporate Samuelson's interest rate i. If i were important in both series, they should move together; if they don't, it might be important in one, or in neither.

But beyond that, I think housing purchases do have an important intertemporal component, in a way that loan contracts do not. That's because (with certain important exceptions we are all aware of) houses are not normally purchased entirely on credit. A substantial fraction of the price is paid is upfront. In effect, most house purchases are two separate transactions bundled together: A credit transaction (for, say, 80 percent of the house value) in which both parties expect positive income in all periods, at the cost of less liquid balance sheets; and a conceptually separate cash transaction (for, say, 20 percent) in which the buyer foregoes present expenditure in return for a stream of housing services in the future. Because house purchases must clear both of these markets, they incorporate i in way that loans do not. But note, i enters into house prices only to the extent that the credit-market interest rate does not. The more important the credit-market interest rate is in a given housing purchase, the less important the intertemporal interest rate is.

This is true in general, I think. Credit markets are not a means of trading off the present against the future. They are a means of avoiding tradeoffs between the present and the future.

Secular Stagnation, Progress in Economics

It's the topic of the moment. Our starting point is this Paul Krugman post, occasioned by this talk by Lawrence Summers.

There are two ways to understand "secular stagnation." One is that the growth rate of income and output will be slower in the future. The other is that there will be a systematic tendency for aggregate demand to fall short of the economy's potential output. It's the second claim that we are interested in.

For Krugman, the decisive fact about secular stagnation is that it implies a need for persistently negative interest rates. That achieved, there is no implication that growth rates or employment need to be lower in the future than in the past. He  is imagining a situation where current levels of employment and growth rates are maintained, but with permanently lower interest rates.

We could also imagine a situation where full employment was maintained by permanently higher public spending, rather than lower interest rates. Or we could imagine a situation where nothing closed the gap and output fell consistently short of potential. What matters is that aggregate expenditure by the private sector tends to fall short of the economy's potential output, by a growing margin. For reasons I will explain down the road, I think this is a better way of stating the position than a negative "natural rate" of interest.

I think this conversation is a step forward for mainstream macroeconomic thought. There are further steps still to take. In this post I describe what, for me, are the positive elements of this new conversation. In subsequent posts, I will talk about the right way of analyzing these questions more systematically -- in terms of a Harrod-type growth model -- and  about the wrong way -- in terms of the natural rate of interest.


The positive content of "secular stagnation"

1. Output is determined by demand.

The determination of total output by total expenditure is such a familiar part of the macroeconomics curriculum that we forget how subversive it is. It denies the logic of scarcity that is the basis of economic analysis and economic morality. Since Mandeville's Fable of the Bees, it's been recognized that if aggregate expenditure determines aggregate income, then, as Krugman says, "vice is virtue and virtue is vice."

A great deal of the history of macroeconomics over the past 75 years can be thought of as various efforts to expunge, exorcize or neutralize the idea of demand-determined income, or at least to safely quarantine it form the rest of economic theory. One of the most successful quarantine strategies was to recast demand constraints on aggregate output as excess demand for money, or equivalently as the wrong interest rate. What distinguished real economies from the competitive equilibrium of Jevons or Walras was the lack of a reliable aggregate demand "thermostat". But if a central bank or other authority set that one price or that one quantity correctly, economic questions could again be reduced to allocation of scarce means to alternative ends, via markets. Both Hayek and Friedman explicitly defined the "natural rate" of interest, which monetary policy should maintain, as the rate that would exist in a Walrasian barter economy. In postwar and modern New Keynesian mainstream economics, the natural rate is defined as the market interest rate that produces full employment and stable prices, without (I think) explicit reference to the intertemporal exchange rate that is called the interest rate in models of barter economies. But he equivalence is still there implicitly, and is the source of a great deal of confusion.

I will return to the question of what connection there is, if any, between the interest rates we observe in the world around us, and what a paper like Samuelson 1958 refers to as the "interest rate." The important thing for present purposes is:

Mainstream economic theory deals with the problems raised when expenditure determines output, by assuming that the monetary authority sets an interest rate such that expenditure just equals potential output. If such a policy is followed successfully, the economy behaves as if it were productive capacity that determined output. Then, specifically Keynesian problems can be ignored by everyone except the monetary-policy technicians. One of the positive things about the secular stagnation conversation, from my point of view, is that it lets Keynes back out of this box.

That said, he is only partway out. Even if it's acknowledged that setting the right interest rate does not solve the problem of aggregate demand as easily as previously believed, the problem is still framed in terms of the interest rate.


2. Demand normally falls short of potential

Another strategy to limit the subversive impact of Keynes has been to consign him to the sublunary domain of the short run, with the eternal world of long run growth still classical. (It's a notable -- and to me irritating -- feature of macroeconomics textbooks that the sections on growth seem to get longer over time, and to move to the front of the book.) But if deviations from full employment are persistent, we can't assume they cancel out and ignore them when evaluating an economy's long-run trajectory.

One of the most interesting parts of the Summers talk came when he said, "It is a central pillar of both classical models and Keynesian models, that it is all about fluctuations, fluctuations around a given mean." (He means New Keynesian models here, not what I would consider the authentic Keynes.) "So what you need to do is have less volatility." He introduces the idea of secular stagnation explicitly as an alternative to this view that demand matters only for the short run. (And he forthrightly acknowledges that Stanley Fischer, his MIT professor who he is there to praise, taught that demand is strictly a short-run phenomenon.) The real content of secular stagnation, for Summers, is not slower growth itself, but the possibility that the same factors that can cause aggregate expenditure to fall short of the economy's potential output can matter in the long run as well as in the short run.

Now for Summers and Krugman, there still exists a fundamentals-determined potential growth rate, and historically the level of activity did fluctuate around it in the past. Only in this new era of secular stagnation, do we have to consider the dynamics of an economy where aggregate demand plays a role in long-term growth. From my point of view, it's less clear that anything has changed in the behavior of the economy. "Secular stagnation" is only acknowledging what has always been true. The notion of potential output was never well defined. Labor supply and technology, the supposed fundamentals, are strongly influenced by the level of capacity utilization. As I've discussed before, once you allow for Verdoorn's Law and hysteresis, it makes no sense to talk about the economy's "potential growth rate," even in principle. I hope the conversation may be moving in that direction. Once you've acknowledged that the classical allocation-of-scarce-means-to-alternative-ends model of growth doesn't apply in present circumstances, it's easier to take the next step and abandon it entirely.


3. Bubbles are functional

One widely-noted claim in the Summers talk is that asset bubbles have been a necessary concomitant of full employment in the US since the 1980s. Before the real estate bubble there was the tech bubble, and before that there was the commercial real estate bubble we remember as the S&L crisis. Without them, the problem of secular stagnation might have posed itself much earlier.

This claim can be understood in several different, but not mutually exclusive, senses. It may be (1) interest rates sufficiently low to produce full employment, are also low enough to provoke a bubble. It may be (2) asset bubbles are an important channel by which monetary policy affects real activity. Or it may be (3) bubbles are a substitute for the required negative interest rates. I am not sure which of these claims Summers intends. All three are plausible, but it is still important to distinguish them. In particular, the first two imply that if interest rates could fall enough to restore full employment, we would have even more bubbles -- in the first case, as an unintended side effect of the low rates, in the second, as the channel through which they would work. The third claim implies that if interest rates could fall enough to restore full employment, it would be possible to do more to restrain bubbles.

An important subcase of (1) comes when there is a minimum return that owners of money capital can accept. As Keynes said (in a passage I'm fond of quoting),

The most stable, and the least easily shifted, element in our contemporary economy has been hitherto, and may prove to be in future, the minimum rate of interest acceptable to the generality of wealth-owners.[2] If a tolerable level of employment requires a rate of interest much below the average rates which ruled in the nineteenth century, it is most doubtful whether it can be achieved merely by manipulating the quantity of money.  Cf. the nineteenth-century saying, quoted by Bagehot, that “John Bull can stand many things, but he cannot stand 2 per cent.”

If this is true, then asking owners of money wealth to accept rates of 2 percent, or perhaps much less, will face political resistance. More important for our purposes, it will create an inclination to believe the sales pitch for any asset that offers an acceptable return.

Randy Wray says that Summers is carrying water here for his own reputation and his masters in Finance. The case for bubbles as necessary for full employment justifies his past support for financial deregulation, and helps make the case against any new regulation in the future. That may be true. But I still think he is onto something important. There's a long-standing criticism of market-based finance that it puts an excessive premium on liquidity and discourages investment in long-lived assets. A systematic overestimate of the returns from fixed assets might be needed to offset the systematic overestimate of the costs of illiquidity.

Another reason I like this part of Summers' talk is that it moves us toward recognizing the fundamental symmetry between between monetary policy conventionally defined, lender of last resort operations and bank regulations. These are different ways of making the balance sheets of the financial sector more or less liquid. The recent shift from talking about monetary policy setting the money stock to talking about setting interest interest rates was in a certain sense a step toward realism, since there is nothing in modern economies that corresponds to a quantity of money. But it was also a step toward greater abstraction, since it leaves it unclear what is the relationship between the central bank and the banking system that allows the central bank to set the terms of private credit transactions. Self-interested as it may be, Summers call for regulatory forbearance here is an intellectual step forward. It moves us toward thinking of what central banks do neither in terms of money, nor in terms of interest rates, but in terms of liquidity.

Finally, note that in Ben Bernanke's analysis of how monetary policy affects output, asset prices are an important channel. That is an argument for version (2) of the bubbles claim.


4. High interest rates are not coming back

For Summers and Krugman, the problem is still defined in terms of a negative "natural rate" of interest. (To my mind, this is the biggest flaw in their analysis.) So much of the practical discussion comes down to how you convince or compel wealth owners to hold assets with negative yields. One solution is to move to permanently higher inflation rates. (Krugman, to his credit, recognizes that this option will only be available when or if something else raises aggregate demand enough to push against supply constraints.) I am somewhat skeptical that capitalist enterprises in their current form can function well with significantly higher inflation. The entire complex of budget and invoicing practices assumes that over some short period -- a month, a quarter, even a year -- prices can be treated as constant. Maybe this is an easy problem to solve, but maybe not. Anyway, it would be an interesting experiment to find out!

More directly relevant is the acknowledgement that interest rates below growth rates may be a permanent feature of the economic environment for the foreseeable future. This has important implications for debt dynamics (both public and private), as we've discussed extensively on this blog. I give Krugman credit for saying that with i < g, it is impossible for debt to spiral out of control; a deficit of any level, maintained forever, will only ever cause the debt-GDP ratio to converge to some finite level. (I also give him credit for acknowledging that this is a change in his views.) This has the important practical effect of knocking another leg out from the case for austerity. It's been a source of great frustration for me to see so many liberal, "Keynesian" economists follow every argument for stimulus with a pious invocation of the need for long-term deficit reduction. If people no longer feel compelled to bow before that shrine, that is progress.

On a more abstract level, the possibility of sub-g or sub-zero interest rates helps break down the quarantining of Keynes discussed above. Mainstream economists engage in a kind of doublethink about the interest rate. In the context of short-run stabilization, it is set by the central bank. But in other contexts, it is set by time preferences and technological tradeoff between current and future goods. I don't think there was ever any coherent way to reconcile these positions. As I will explain in a following post, the term "interest rate" in these two contexts is being used to refer to two distinct and basically unrelated prices. (This was the upshot of the Sraffa-Hayek debate.) But as long as the interest rate observed in the world (call it the "finance" interest rate) behaved similarly enough to the interest rate in the models (the "time-substitution" interest rate), it was possible to ignore this contradiction without too much embarrassment.

There is no plausible way that the "time substitution" interest rate can be negative. So the secular stagnation conversation is helping reestablish the point -- made by Keynes in chapter 17 of the General Theory, but largely forgotten -- that the interest rates we observe in the world are something different. And in particular, it is no longer defensible to treat the interest rate as somehow exogenous to discussions about aggregate demand and fiscal policy. When I was debating fiscal policy with John Quiggin, he made the case for treating debt sustainability as a binding constraint by noting that there are long periods historically when interest rates were higher than growth rates. It never occurred to him that it makes no sense to talk about the level of interest rates as an objective fact, independent of the demand conditions that make expansionary fiscal policy desirable. I don't mean to pick on John -- at the time it wasn't clear to me either.

Finally, on the topic of low interest forever, I liked Krugman's scorn for the rights of interest-recipients:

How dare anyone suggest that virtuous individuals, people who are prudent and save for the future, face expropriation? How can you suggest steadily eroding their savings either through inflation or through negative interest rates? It’s tyranny!
But in a liquidity trap saving may be a personal virtue, but it’s a social vice. And in an economy facing secular stagnation, this isn’t just a temporary state of affairs, it’s the norm. Assuring people that they can get a positive rate of return on safe assets means promising them something the market doesn’t want to deliver – it’s like farm price supports, except for rentiers.

It's a nice line, only slightly spoiled by the part about "what the market wants to deliver." The idea that it is immoral to deprive the owners of money wealth of their accustomed returns is widespread and deeply rooted. I think it lies behind many seemingly positive economic claims. If this conversation develops, I expect we will see more open assertions of the moral entitlement of the rentiers.

Functional Finance and Sound Finance

Introduction

Anyone who who has been following debates on fiscal policy over the past few years will have noticed that, among those who think fiscal policy can be effective, there are two distinct camps. There is a minority who think that fiscal policy is not subject to a budget constraint; that is, that as long as a government borrows in its own currency, its existing liabilities never limit its ability to adjust taxes and spending to bring the economy to full employment. And there are the majority who think that governments are subject to a binding budget constraint; that is, that while adjusting spending and taxes can in principle be used to bring about full employment, it may be impossible or undesirable to do so when the level of government debt is already high. In this view, maintaining full employment should be left to monetary policy. Following Abba Lerner, I call the first position "functional finance" and the second position "sound finance."

I believe there are important differences between these two positions. But I also believe that these differences have not been clearly articulated, and as a result these debates between them been unproductive. It is my view that there are no important differences in terms of economic theory between the two positions. A perfect application of a functional finance policy rule and of a sound finance policy rule are indistinguishable. The difference between the camps is with respect to policy errors -- which errors are most likely, and which are most costly.


Alternative Policy Rules

The starting point is the idea of instruments, which are variables directly controlled by the policymaker; and targets, which are the variables the policymaker wants to set at some level but cannot control directly. When the target variable is not at its desired level, the policymaker adjusts one or more instruments to try to bring it there. This creates relationship between the current level of the target and the chosen level of the instrument. We call this relationship a policy rule. Both functional finance and sound finance represent policy rules in this sense. Tinbergen's Rule says that for policy rules to be successful (in the sense that all targets converge to their desired levels), there must be at least as many instruments as targets. One policy lever cannot be relied on to achieve two separate outcomes.

We have two instruments in macroeconomic policy: the government budget balance, and the central bank-controlled interest rate. What are our targets?

At first glance, full employment and price stability appear to be two separate targets. But in fact, both Lerner's functional finance and the sound finance of modern textbooks agree that inflation is the result of demand-determined expenditure departing from a technologically determined level of potential output. Less than full employment means falling inflation, or deflation; overfull employment means high or rising inflation. So full employment and price stability are not two separate targets, they are two ways of describing the same target.

Both camps agree that we can identify a unique target level of output, and they agree on what that target should be. They also agree that output rises with higher government deficits, and falls with higher interest rates. So when interest rates are too high, or budget deficits too small, we will see unemployment (and perhaps deflation); when interest rates are too low or deficits are too large, we will see inflation (and perhaps bottlenecks and rising relative prices of factors in inelastic supply).

This consensus is shown in Figure 1. The full employment locus shows all the combinations of interest rates and fiscal balances that are compatible with full employment and price stability. A fall in private demand will require a rise in the deficit and/or a fall in interest rates to maintain full employment, so it will shift the full employment locus down and to the left. Similarly, a rise in private demand will shift the locus up and to the right. But for any level of private demand, with two instruments and only one target, there are an infinite number of combinations that achieve full employment.

(It is convenient to think of the fiscal balance on the horizontal axis as the primary balance, that is, the balance net of interest payments. So we are implicitly assuming that interest payments do not raise aggregate demand. It is also convenient to think of the interest rate as the real rate, that is, net of inflation. It would be straightforward to incorporate the effects of interest payments and inflation into the story, but would not change it in any interesting way.)

The first point of disagreement is what to do at a point like a. Output is below potential, but which instrument should be used to raise it? Functional finance says, the fiscal balance: government spending should be raised (or taxes should be lowered), moving the economy to the left, until we reach the full employment locus. The modern sound-finance consensus says that the interest rate should be lowered, moving the economy downward to the full employment locus. Both agree that government should do something to raise output. The disagreement is over which instrument to use.

Whichever instrument is used to keep output at potential, there is one instrument left over for some other target. The logical candidate is the sustainability of government debt.

We've discussed the math of government debt dynamics quite a bit on this blog. (See here and here and here and here.) The important thing for our purposes is that the long-run trajectory of the debt-GDP ratio depends on the primary balance, the interest rate on government borrowing, and the growth rate of GDP. If we write the ratio of government debt to GDP as b, and the primary deficit as a share of GDP as d, then for a given deficit, the equilibrium condition is b=d* 1/(g-r), where g is the average or expected growth rate of GDP over the period of interest. So for a given debt-GDP ratio b, the primary deficit required to hold it constant is d = b(g-r). (This is all just accounting; it does not depend on any economic assumptions.) It's evident that, if we take the growth rate as exogenous, then for any given debt-GDP ratio there is a set of r, d combinations for which the debt-GDP ratio is constant. We can represent these values graphically in Figure 2. The dotted horizontal line is the growth rate. The diagonal line is the constant debt ratio locus. With a deficit or interest rate above the diagonal line, the debt-GDP ratio will rise; below, it will fall.



Note that the slope of the diagonal depends on the starting debt-GDP ratio -- the higher it is, the shallower the slope will be. With no government debt, the line is vertical at the primary balance = 0 axis. So in any period in which the economy is at a point above the debt-sustainability locus, the diagonal rotates clockwise; in any period in which the economy is below the debt-sustainability locus, the diagonal rotates counter-clockwise.

What happens if the economy is off the constant-debt locus? It depends. In the area marked A (everything above the heavy line), the debt-GDP ratio rises without limit. In B, the debt-GDP ratio rises but converges to a finite value. In C the ratio falls to a finite value. In D, the debt-GDP ratio falls to zero and the government then accumulates a positive asset position, which eventually converges to a finite fraction of GDP. Finally, in area E the debt-GDP ratio falls to zero and the government then accumulates a positive asset position that rises without limit as a share of GDP. (If you are unconvinced we can go through the math.) Since the government budget constraint is normally taken to be the condition that debt-GDP ratio not rise without limit, we can ignore the distinctions between cases B through E and regard the heavy line as the government budget constraint.

We then combine this constraint with the full employment locus to give Figure 3.



Now we have two instruments and two targets. Or rather, one and a half targets: Since there is nothing special about the current debt-GDP ratio, we don't need it to stay constant; we just need it not to go to infinity. So we don't need to be on the debt-sustainability curve, we need to be on or below it. Point b, which satisfies the budget constraint exactly, is fine, but so is anywhere on the full employment locus below and to the right of b.

The functional finance-sound finance divide is just this: Functional finance says the fiscal balance instrument should be assigned to the full employment target and the interest rate instrument should be assigned to the debt sustainability target. Sound finance says the interest rate instrument should be assigned to the full employment target and and the fiscal balance instrument should be assigned to the debt sustainability target.

Functional finance and sound finance agree that the economy should be at a point like b. If policy were executed perfectly, the economy would always be at such a point, and there would be no way of knowing which rule was being followed. Since both target should always be at their chosen levels, it would make no difference -- and be impossible to tell -- which instrument was assigned to which target. The difference between the positions only becomes apparent when policy is not executed perfectly, and the economy departs from a position of full employment with sustainable public debt.

Consider a point somewhere above b, where we are have high unemployment but the debt-GDP ratio is rising without limit. What to do? Both orthodoxy and Lernerism want to get the economy back to a point like b, but they disagree on how.

In the sound-finance view, the interest rate instrument is committed to the output target. This means we must use the fiscal balance instrument free to meet the debt sustainability condition. This is how policy is normally discussed: An unsustainable upward trajectory in the debt position requires the government balance to move  toward surplus. In this case, that means that the government must cut spending or raise taxes, despite the fact that demand is already too low. Under Lernerian functional finance, on the other hand, the fiscal balance is committed to the output target, so the rule calls for higher deficits even though the debt position is already unsustainable. It is then the responsibility of monetary policy to adjust to maintain debt sustainability.

These alternatives are shown in Figure 4. The right-hand trajectory from c to b is the orthodox path. The left-hand trajectory is the Lernerian path. Implicit in the orthodox path is the idea that deficits must be brought down first, meaning a substantial period of high unemployment and output below potential; only once debt is on a sustainable path can interest rates be reduced to move back toward full employment. While the Lernerian path says in effect: If government debt is rising out of control, the central bank should intervene to force interest rates down to a level where the debt is sustainable. Then, if the resulting liquidity raises expenditure above the full employment level, you can subsequently raise taxes or cut transfers to bring demand back down.



Orthodoxy says that budget problems must be addressed fiscally. But this is true only on the implicit assumption that the interest rate is not available as an instrument to target debt sustainability. Sound finance's policy rule is a Taylor-type rule for monetary policy, combined with a long-term government budget position that satisfies the debt-sustainability constraint at that interest rate. Functional finance's policy rule: (1) fix the interest rate at a level at or below the expected growth rate (maybe even zero); (2) adjust transfers and taxes until output is at the full employment/stable prices level. The claim that fiscal policy must be subject to a budget constraint, comes down to the claim that the central bank cannot or will not keep r sufficiently low to make the full-employment fiscal position sustainable.

Why is there such disagreement about which instrument should be assigned to which target? It seems to me that the most important argument from the sound finance side is that elected governments cannot be trusted with the instrument of discretionary fiscal policy. They will not set taxes and transfers to bring aggregate demand to the full employment level, but will choose a higher, inflationary level of demand. Only independent central banks can be trusted to bring output to its socially optimal level. In this sense, the functional finance-sound finance divide is not a debate about economic theory, but about politics and sociology.

There are also more specifically economic disagreements. The sound finance side is more confident than the functional finance side about how quickly and reliably a change in interest rates will affect output. If there is a long lag between the change in the instrument and its effect, hitting the target requires accurate prediction of the state of the economy farther into the future. The existence of the ZLB reinforces this concern, since it is really just a special case of interest-inelasticity. (The statement "output does not respond strongly to any feasible change in interest rates" is equivalent to the statement "the interest-rate change needed to achieve a strong output response is not feasible.") The functional finance side also tends to see a greater social cost in falling below full employment than rising above it, while the sound finance side tends to see the costs as symmetrical.

That is the framework. Now consider some modifications and special cases.


Extensions

A natural objection to the functional finance view is that it may not be possible for the central bank to maintain interest rates low enough to keep debt sustainable. If we live in a world of high capital mobility and our government's liabilities are close substitutes for liabilities elsewhere in the world, then the private sector will not hold them if their yield is too much lower. In this case -- which is not unrealistic for small, open countries -- the interest rate ceases to be a policy variable. This is shown in Figure 5, where r* is the exogenous work interest rate.



At a point like d in the figure, the public debt is stable but output is below potential. A move toward a primary deficit would raise output but put the debt on an unsustainable path. This case is not inherently implausible -- one would need to think carefully about the concrete assumptions it embodies -- but it is important to recognize that it rules out sound finance as well as functional finance. If the interest rate is set exogenously at the world level, it cannot be used to stabilize public debt or to stabilize output. An additional instrument is needed; the exchange rate is the natural choice. Since the exchange rate cannot straightforwardly be used to achieve debt sustainability, in this case there is a natural argument to switch the assignment of fiscal policy to debt sustainability and achieve full employment via the exchange rate.

Another possibility, which has been getting increasing attention recently, is that very low interest rates are destabilizing for the financial system. (I have criticized this idea before, but I don't think it can be ruled out definitively.) Then we have another condition to satisfy, a asset price stability condition. Like the debt sustainability condition, this is asymmetrical, it doesn't have to be satisfied exactly. But this one is a floor on interest rates rather than a ceiling. The is shown in Figure 6. Here, the asset price stability constraint does not initially prevent achieving both the other targets: As in Figure 3, point b initially satisfies all the constraints, as does any other point along the full employment locus below and to the right of it, down to the dotted line.


But what if a fall in private demand shifts the full employment locus far to the left? Here there is an important difference between the sound finance and functional finance rules. The functional finance rule says that the fall in private demand requires the government budget to move toward deficit. That is, we move left from b to the new full employment locus. This may in turn require a fall in interest rates, if the higher deficits would otherwise put the public debt on an unsustainable path. But public debt sustainability never requires an interest rate below the long term growth rate. So, since it is not plausible that the minimum interest rate compatible with asset price stability condition is greater than the growth rate, the possibility of asset bubbles should not limit the application of the functional finance rule.

The sound finance rule, on the other hand, says that the response to a fall in private demand should be a reduction in the interest rate. In other words, faced with the fall in private demand shown in the figure, we should move downward from point b  to the new full employment locus. Now there is the possibility that the required interest rate is incompatible with asset price stability. (In some views, this is precisely what happened a decade ago, setting the stage for the housing bubble.) This becomes an argument for setting interest rates higher than the conventional policy rule implies, even at the cost of higher unemployment.

Formally, the ZLB is identical to the asset price stability condition: both set floors to allowable interest rates. It is curious that, while concern with the ZLB and with the destabilizing effects of low interest rates often come from opposite political positions, they are -- at least in this framework -- equivalent in their implications for policy. Both are arguments for a reliance on fiscal policy to offset fall in private demand in general, rather than waiting for the floor to be reached -- that is, for some form of functional finance.

Finally, consider the case where the fiscal balance is exogenously fixed, as shown in Figure 7. I think this is the case most critics of functional finance have in mind. If the budget authority, for whatever reason, is committed to tax and spending policies corresponding to a primary deficit, there may be no interest rate that can deliver both debt sustainability and full employment. The central bank must choose one. If it chooses debt sustainability, we have a situation known in the literature as "fiscal dominance." The central bank must increase its liabilities as needed to finance the government deficit, even if that results in aggregate demand rising to inflationary levels. This is the situation at point e.



It is important to stress that Figure 7 is not what is advocated by functional finance. There is an understandable but unfortunate confusion between the claim "deficits can be at whatever level is needed to reach full employment" and "deficits can be at whatever level you want." Functional finance says the former, not the latter. A functional finance rule would call for the government to raise taxes or cut spending at a point like e -- not to balance the budget, but to eliminate the inflation. The practical problem for functional finance supporters is to convince skeptics that such a rule will be followed by an elected government.


Conclusion

Advocates of functional finance say that a government that borrows in its own currency never needs to adjust its taxes or spending on account of its current deficit or accumulated debt. The fiscal balance can always be set at whatever level is needed to achieve full employment. Their sound-finance critics reply, "It's true that a deficit will raise current output. But over the long run you need a primary surplus to ensure that the government stays on its budget constraint. If the central bank is forced to monetize the debt instead, you will have runaway inflation."

The critics are correctly describing the situation in Figure 7, where it is true that the government budget position has been set without regard for debt sustainability, the central bank is monetizing the debt (this is simply another way of describing holding interest rates low enough to maintain a stable path for government liabilities), and there is uncontrolled inflation. But the inference the critics draw from this possibility -- that fiscal policy must target debt sustainability -- is not correct. The correct inference is that at least one of the two instruments must target debt sustainability, and at least one must target full employment. The problem in Figure 7 is that budget balance is being set without regard for either condition -- that is, it is in violation of both policy rules. Either the sound finance rule, or the functional finance rule, or any linear combination of the two, would ensure that the economy does not remain at a point like e but instead converges to one like b in Figure 3.

The debate between sound finance and functional finance cannot be resolved as long as they are framed in terms of what kind of rule is feasible in principle, and what outcome results when it is followed exactly. The disagreement is about what kinds of rules policymakers can be expected to adhere to in practice, and about the relative costs of different policy errors.


[This post was inspired by this talk by Brad DeLong, and by some comments by Nick Rowe which I cannot locate now.]

Shorter Economics Profession

1. Economics is the study of the allocation of scarce resources.

2. The most important topic in economics is growth.

3. Growth has nothing to do with the allocation of scarce resources.

(Inspired by this and this...)

The Puzzle of Profits

Part II of Capital begins with a puzzle: In markets, commodities are supposed to trade only for other commodities of equal value, yet somehow capitalists end up with more value than they start with.

In the world of simple exchange, money is just a convenience for enabling the exchange of commodities: C-M-C is easier to arrange than C-C. But profit-making business is different: the sequence there is M-C-M'. The capitalist enters the market and buys some commodities for a certain sum of money. Later, he sells some commodities, and has a larger sum of money. This increase -- from M to M' -- is the whole point of being capitalist. But in a world of free market exchange, how can it exist?

Let's put some obvious misunderstandings out of the way. There's nothing mysterious about the fact that people can accomplish things with tools and previously acquired materials that they would be unable to with unaided labor. The problem is not that "capital," in the sense of a stock of tools and materials, is productive in this sense. To the extent that what appears as "profit" in the national accounts is just the cost of replacing worn-out tools and materials, there's no puzzle. [1]

The mystery is, how can someone enter the market with money and, after some series of exchanges, exit with more money? In the sequence M-C-M', how can M' be greater than M? How can the mere possession of money seemingly allow one to acquire more money, seemingly without end?

Before trying to understand Marx's answer, let's consider how non-Marxist economists answer this question.

1. Truck and barter. The most popular answer, among both classical and modern economists, is that the M-C-M' sequence does not exist. All economic activity is aimed at consumption, market exchange is only intended to acquire specific use-values; when you think you see M-C-M you're really looking at part of some C-M-C sequence(s). The classical economists are full of blunt statements that the only possible end of exchange is consumption. In today's economics we find this assumption in the form of the "transversality condition" that says that wealth must go to zero as time goes to infinity. That's right, it is an axiom in modern economics that accumulation cannot be a goal in itself. Or in the words of Simon Wren-Lewis (my new go-to source for the unexamined conventional wisdom of economists): "It would be stupid to accumulate infinite wealth." Well OK then!

2. You earned it. Another answer is that the capitalist brings some additional unmeasured commodity to the production process. They are providing not just money M but also management ability, risk-bearing capacity, etc. In this view, if we correctly measured inputs, we would find that  M'=M. In its most blatantly apologetic form this is effectively skewered by comrades Ackerman and Beggs in the current Jacobin. For unincorporated businesses, it is true, it is not straightforward to distinguish between profits proper and the wages of managerial labor, but that can't account for profits in general, or for the skewed distribution of income across households. If anything, much of what is reported as managerial salaries should probably be called profits. This is a point made in different ways by Piketty and Saez  and Dumenil and Levy; you can also find it offered as straightforward business advice.

3. It was the pictures that got small. The other main classical answer is that profit is the reward for "abstinence" (Senior) or "waiting" (Cassel). (I guess this is also the theory of Bohm-Bawerk and the other Austrians, but I admit I don't know much about that stuff.) It appears today as a discount rate on future consumption. This invites the same question as the first answer: Is capitalist accumulation really motivated by future consumption? It also invites a second question: In what sense is a good tomorrow less valuable than the same good today? Is the utility derived from a glass of wine in 2013 really less than the utility derived from the same glass consumed in 2012,or 2010, or 1995? (So far this has not been my experience.) The logically consistent answer, if you want to defend profit as the return to waiting, is to say Yes. The capital owner's pure time preference then represents an objective inferiority of output at a later date compared with the same output at an earlier date.

This is a logically consistent answer to the profits puzzle, and it could even be true with the right assumptions about the probability of an extinction-event asteroid impact/Khmer Rouge takeover/zombie apocalypse. With a sufficiently high estimate of the probability of some such contingency, M' is really equal to M when discounted appropriately; capitalists aren't really gaining anything when you take into account their odds of being eaten by zombies and/or suffocated by plastic bag, before they get to enjoy their profits. [2]  But I don't think anyone wants to really own this point of view -- to hold it consistently you must believe that economic activity becomes objectively less able to satisfy human needs as time goes by. [3]

4. Oops, underpaid again. We can take the same "profit as reward for waiting" idea, but instead of seeing a pure time preference as consistent with rational behavior, as modern economists (somehow) do, instead interpret it like the classical economists (including Cassel, whose fascinating Nature and Necessity of Interest I just read), as a psychological or sociological phenomenon. Consumption in the future is objectively identical to the same consumption today, but people for some reason fail to assign it the same subjective value it the same. Either they suffer from a lack of "telescopic facility," or, in Cassel's (and Leijonhufvud's) more sophisticated formulation, the discount rate is a reflection of the human life expectancy: People are not motivated to provide for their descendants beyond their children, and future generations are not around to bargain for themselves. Either way, the outcome is that exchange does not happen at value -- production is systematically organized around a higher valuation of goods today than goods tomorrow, even though their actual capacity to provide for satisfaction of human needs is the same. Which implies that workers -- who provide labor today for a good tomorrow -- are systematically underpaid.

5. Property is theft. The last and simplest possibility is that profits are always just rents. Capitalists and workers start out as just "agents" with their respective "endowments." By whatever accident of circumstances, the former just end up underpaying the latter. Maybe they are better informed.

We could develop all these points further -- and will, I hope, in the future. But I want to move on to (my idea of) Marx's answer to the puzzle.

One other thing to clear up first: profit versus interest. Both refer to money tomorrow you receive by virtue of possessing money today. The difference is that in the case of profit, you must purchase and sell commodities in between. What is the relationship between these two forms of income? For someone like Cassel, interest has priority; profit is a derived form combining interest with income from managerial skill and/or a rent. For Marx on the other hand, and also for Smith, Ricardo, etc., profit is the primitive and interest is the derived form; interest is redistribution of profits already earned in production. (Smith: "The interest of money is always a derivative revenue, which, if it is not paid from the profit which is made by the use of the money, must be paid from some other source of revenue.") In other words, are profits an addition to interest, or is interest as a subtraction from profit? For Marx, the latter. The fundamental question is how money profits can arise through exchange of commodities. [4]

Marx gives his answer in chapter four: The capitalist purchases labor-power at its value, but gets the results of the labor expended by that labor-power. The latter exceeds the former. In other words, people are capable of producing more than it takes to reproduce themselves, and that increment is captured by the capitalist. In four hours, you can produce what you need to live on. The next four or six or eight or twelve hours, you are working for The Man.

This is the answer, as Marx gives it. Labor power is paid for at its value. But having purchased labor power, the capitalist now has access to living labor, which can produce more than the the cost of its own reproduction.

I think this is right. But it's not really a satisfactory answer, is it? It's formally correct. But what does it mean?

One way of fleshing it out is to ask: Why is it even possible that labor can produce more than the reproduction-costs of labor power? Think of Ricardo's world. Profits are positive because we have not yet reached the steady state -- there are still natural resources available whose more intensive use will yield a surplus beyond the cost of the labor and capital required to use them. The capitalist captures that surplus because capital has the short side of both markets -- there is currently excess land going unutilized, and excess labor going unutilized. [5]

Another way: There is something in the production process other than exchange, but which is captured via exchange.

I want to think of it this way: Humanity does have the ability to increase social value of output, or in other words the aggregate capacity to satisfy human needs from nature does in general grow over time. This "growth" happens through our collective creative interchange with nature -- it is about pushing into the unknown, a process of discovery -- it is not captured beforehand in the market values of commodities.

In a proper market, you cannot exchange a good in your possession for a good with a greater value, that is, with a greater capacity to satisfy human needs in general. (Your own particular needs, yes.) But you can, through creative activity, through a development of your own potential, increase the general level of satisfaction of human needs. The capitalist by buying labor power at its value, is able to capture this creative increment and call it their private property.

Our potential is realized through a creative interchange with nature. It's not known in advance. What can we do, what can't we do -- we only learn by trying. We push against the world, and discover how the world pushes back, in so doing understand it better and find how it can be reshaped to better suit our needs. Individually or collectively, it's a process of active discovery.

You as a person can exchange the various things you are in possession of, including your labor power, for other things of equal value. (Though for different use values, which are more desired by you.) But you will also discover, through a process of active learning and struggle, what you are capable of, what are the limits of your powers, what creative work you can do that you cannot fully conceive of now.

Through the process of education, you don't just acquire something that you understood clearly at the outset. You transform yourself and learn things you didn't even know you didn't know. When you do creative work you don't know what the finished product will be until you've finished it. I still -- and I hope for the rest of my life -- find myself reading economics and having those aha moments where you say, "oh that's what this debate is all about, I never got it before!" And science and technology above all involve the discovery of new possibilities through a process of active pushing against the limits of our knowledge of the world.

The results of these active process of self-development and exploration form use-values, but they are not commodities. They were not produced for exchange. They were not even known of before they came into being. But while they are not themselves commodities, they are attached to commodities, they cannot be realized except through existing commodities. I may produce in myself, through this process of self-testing, a capacity for musical performance, let's say. But I cannot realize this capacity without, at least, a sufficient claim on my own time, and probably also concrete use-values in the form of an instrument, an appropriate performance space, etc., and also some claim on the time of others. In this case one can imagine acquiring these things individually, but many -- increasingly over time -- processes of self-discovery are inherently collective. Science and technology especially. So specifically a discovery that allows cheaper production of an existing commodity, or the creation of a new commodity with new use-values, can only become become concrete in the hands of those who control the process of production of commodities. By purchasing labor power -- in the market, at its value -- capitalists gain control of the production process. They are thus able to claim the fruits of humanity's collective self-discovery and interchange with nature as their own private property.

In some cases, this is quite literal. Recall Smith's argument that one of the great advantages of the division of labor is that it allows specialized workers to discover improved ways of carrying out their tasks. "A great part of the machines made use of in those manufactures in which labour is most subdivided, were originally the inventions of common workmen, who, being each of them employed in some very simple operation, naturally turned their thoughts towards finding out easier and readier methods of performing it." Who do you think gained the surplus from these inventions? This still happens. Read any good account of work under capitalism, like Barbara Garson's classic books All the Livelong Day and The Electronic Sweatshop. You'll find people actively struggling to do their jobs better -- the customer service representative who wants to get the caller to the person who can actually solve their problem, the bookshelf installer who wants it to fit in the room just right. The results of these struggles are realized as profits for their employers. But these are exceptional. The normal case today is the large-scale collective process of discovery, which is then privately appropriated. Every new technology draws on a vast history of publicly-available scientific work -- sometimes we see this directly as with biomedical research, but even when it's not so obvious it's still there. Every Hollywood movie draws on a vast collective project of storytelling, a general collective effort to imbue certain symbols with meaning. Again see this most directly in the movies that draw on folktales and other public-domain work, but it's true generically.

It is this vast collective effort at transformation of nature and ourselves that allows the value of output to be greater than the value of what existed before it. Without it, we would eventually reach the classical steady state where the exercise of labor could produce no more than the value of the labor power that yielded it. So when Marx says the source of profits is the fact that labor can produce more than the value of labor power, lying behind this is the fact that, due to humanity's collective creative efforts, we are continuing to find new ways to shape the world to our use.

Capital is coordination before it is tangible means of production. Initially (logically and historically) the capitalist simply occupies a strategic point in exchange between independent producers thanks to the possession of liquid wealth; but as the extension of the division of labor requires more detailed coordination between the separate producers, the capitalist takes over a more direct role in managing production itself. "That a capitalist should command on the field of production, is now as indispensable as that a general should command on the field of battle."

There is another way of looking at this: in terms of the extension of cooperation and the division of labor, which is realized in and through capitalist production, but in principle is independent of it. I'll take this up in a following post.


[1] Marx makes this point clearly in his critique of the Gotha program.  Elimination of surplus as such cannot be a goal of socialism.

[2] It would seem that we have enough evidence to rule out a sufficiently high probability of world-ending catastrophe to explain observed interest rates, assuming the minimum possible return on accumulated wealth is zero. But of course in some conceivable circumstances it could be negative -- that's why I include the Khmer Rouge takeover, where your chance of summary execution is presumably positively related to your accumulated wealth. Also, maybe we have reason to think that  catastrophe is more likely in the future than we would naively infer from the past. It would be funny if someone tried to explain interest rates in terms of the doomsday argument.

[3] There has been a lot of discussion of appropriate social discount rates in the context of climate change. But nobody in that debate, as far as I can tell, takes the logical next step of arguing that excessively high discount rates imply a comprehensive market failure, not just with respect to climate change. There is not a special social discount rate for climate, there is an appropriate social discount rate for all future costs and benefits. If market interest rates are not the right tool for weighing current costs against future benefits for climate, they are not the right guide for anything, including the market activities where they currently govern.

[4] Yes, interest exists independently of profits from production, and indeed is much older. Marx recognizes this. But capitalism is not generalized usury.

[5]  And substitution between factors is impossible -- Marx's "iron law of proportions" -- or at least limited.

Cavafy on the Debt Ceiling

What are we waiting for, assembled in the forum?

            The barbarians are due here today.

Why isn’t anything happening in the senate?
Why do the senators sit there without legislating?

            Because the barbarians are coming today.
            What laws can the senators make now?
            Once the barbarians are here, they’ll do the legislating.

Why did our emperor get up so early,
and why is he sitting at the city’s main gate
on his throne, in state, wearing the crown?

            Because the barbarians are coming today
            and the emperor is waiting to receive their leader.
            He has even prepared a scroll to give him,
            replete with titles, with imposing names.

Why have our two consuls and praetors come out today
wearing their embroidered, their scarlet togas?
Why have they put on bracelets with so many amethysts,
and rings sparkling with magnificent emeralds?
Why are they carrying elegant canes
beautifully worked in silver and gold?

            Because the barbarians are coming today
            and things like that dazzle the barbarians.

Why don’t our distinguished orators come forward as usual
to make their speeches, say what they have to say?

            Because the barbarians are coming today
            and they’re bored by rhetoric and public speaking.

Why this sudden restlessness, this confusion?
(How serious people’s faces have become.)
Why are the streets and squares emptying so rapidly,
everyone going home so lost in thought?

            Because night has fallen and the barbarians have not come.
            And some who have just returned from the border say
            there are no barbarians any longer.

And now, what’s going to happen to us without barbarians?
They were, those people, a kind of solution. 

Default and the Dollar

Government shutdown, debt ceiling deadline just around the corner. Were you watching this show when it was first on, in the summer of 2011? People were predicting that even the possibility of a technical default (which almost happened), or credit-rating downgrade (which did happen, on Aug. 11) should lead to a sharp rise in US interest rates and a fall in the dollar. Neither of these things took place. There were some interesting discussions why not, which are worth revisiting now.

Here is something I wrote at the time:

How is it possible that a downgrade in federal debt could increase demand for it? One obvious reason is that it could increase the political pressure for austerity, making lower growth more likely, and owners of financial assets might recognize this.
But there's another explanation, which is the that federal debt is a kind of Giffen good. This Baseline Scenario post makes one version of the argument. Here's my version. 

Wealthholders choose their portfolio to maximize risk-adjusted return, but subject to a survival constraint such that expected probability of returns at each future time t falling below some floor is subjectively zero (less than epsilon, we can say.) The existence of this kind of floor is one of the central things that distinguishes the Minskyan view of the world. (Minsky would talk here about cashflows rather than returns, but the logic is the same.) 

Now suppose the riskiness of the portfolio increases. Then to keep the distribution of returns from crossing the floor, investors need to shift toward lower-risk assets. This is true even if the increased riskiness of the portfolio came from the lower risk assets themselves. 

Here's another way of looking at it, more in the spirit of Holmstrom and Tirole. Making a risky/illiquid investment requires holding a greater quantity of money-like assets to ensure a zero (or less than epsilon) probability of the investment pulling you below your survival constraint. In effect, this lowers the return on the investment, since the total return has to be calculated on the cost of the asset itself plus the cushion of money-like assets you need to purchase along with it. If safe assets are less safe, you have to hold more of them to cushion the same risky asset. This means that an increase in the riskiness of safe assets implies a shift in demand toward safe assets and away from risky ones.

I also wrote this, about the appreciation of the dollar following the downgrade:

There was a very interesting piece from the BIS recently about why a fall in the price of US assets may be associated with an appreciation of the dollar. (It's the McCauley chapter in the linked document.) They argue that many purchasers of dollar assets wanted the asset, not the foreign-exchange risk, so they hedged it by simultaneously selling the dollar forward, or otherwise issuing a dollar liability of equal value to the asset. But this means if the value of the US asset declines, they are overhedged, they now have a short position in the dollar. To get rid of that foreign-exchange risk they have to liquidate the dollar liability, which means buying dollars. 

If this sort of hedging were universal, it would have somewhat counterintuitive implications for the exchange rate. Changes in demand for dollar assets would then have no effect on the value of the dollar. And changes in the dollar value of US assets would induce opposite-signed changes in the value of the dollar. According to the BIS, this kind of hedging is very common among European investors in US assets, but not at all common among US purchasers of foreign assets -- for US purchasers, the foreign-exchange risk is part of the asset, not something they want to get rid of.

I don't see any reason to have a strong prior that hedging the forex risk cannot be common among purchasers of foreign assets. If it is common, this sort of "perverse" movement of exchange rates in response to asset-price changes is not just possible, but predictable. And if the hedging is asymmetric, as the BIS study suggests, then we would expect a global rise in asset prices to lead to a decline in the value of the dollar, and a global fall in asset prices to lead to a rise in the price of the dollar.  

Going a step beyond the BIS study, I think there's a sociological element here. Actual portfolio choices are very seldom made by the ultimate owners, they're made by intermediaries who are typically specialists of some kind. Now if, let's say, European purchasers of US equities are largely made by intermediaries, who specialize in equities (domestic and foreign), then they're going to want to hedge the forex risk -- that's not what they have the expertise to manage. Whereas if US purchases of European equities are largely made by intermediaries who specialize in European or in general foreign assets (equities and otherwise) then they are not going to want to hedge the forex risk, managing it is part of how they get their returns. And I think this question is going to depend on the specific kinds of financial institutions that have developed historically in each place, you can't deduce it from any underlying tastes or endowments.  

But in any case I think we have to accept that it's perfectly possible for a decline in the value of US assets to lead to a rise in the value of the dollar, even if it seems implausible at first glance.

Exchange Rates and Trade Flows in Asia

A bit more on shifting trade flows following the 1997 Asian Crisis.

Enno Schroeder, whose decomposition  of European trade flows I've mentioned here before, was kind enough to do a similar exercise for the four Asian crisis countries. His results are here; below I present them in graphical form below.

The conventional story, as we all know, is that relative prices drive trade flows. The Asian countries, in this view, moved from deficits to surpluses after 1997 because abandoning their currency pegs and devaluing made their exports cheaper and their imports more expensive. I've been suggesting a different story: Relative prices were relatively unimportant in the post-1997 move to surpluses, with the improved trade balance mostly or entirely a matter of lower imports resulting from the deep fall in income in the crisis. Looking at the picture in more detail suggests a more complex but in some ways even stronger version of my earlier story.

Some context: Suppose a country reduces its total import bill. As a matter of accounting, this reduction can be broken up into some mix of lower total quantity of goods bought, a smaller fraction of those goods being imports, and a lower price of the imported goods. Similarly for exports, any increase can be broken up into higher incomes in a country's export markets, a greater market share there for our exports, and higher export prices. So the overall trade balance -- here expressed as the ratio of total export value to total import value -- can be decomposed into the change in relative expenditure growth, the expenditure switch between the home country's goods and the rest of the world's; and the change in the relative price of home goods compared with foreign ones. (Note that relative price presumably affects trade volumes, but it also affects trade value directly -- for given trade volumes, if a country's imports are more expensive it will spend more on imports.) The cumulative contribution of each of these components is shown in the figures below, along with the nominal exchange rate. (The exchange rate is the nominal rate for July of each year, from the BIS.)

The heavy black line is the actual trade balance. Again, since the balance here is expressed as the ratio of exports to imports, a value of 1 means balanced trade. The other three solid lines show the cumulative contributions of each component to the changes in trade flows after 1996; the values represent how the trade ratio would have changed from that factor alone. Yellow is expenditure switch, from the rest of the world's goods to the home country's; this includes both home country switch from imports to domestic goods, and foreign country shift toward the home country's exports. Green is income growth in the country's trade partners relative to the home country. The solid red line is the terms of trade. The dotted red line shows the cumulative change in the nominal exchange rate; this isn't directly a contribution to the change in trade flows, but it's useful to know how closely the change in the terms of trade tracks the exchange rate.

It's convenient to think of the difference between the black line and the green line as the change in competitiveness.

The immediate effect of a devaluation is to make the home country's goods cheaper in the rest of the world, and the rest of the world's goods more expensive in the home country. The direct effect of this is to move the trade balance further toward deficit -- a descending red line in the figures below. But in the conventional story, the change in price leads to a more than proportionate change in quantity -- a rise in exports and/or a fall in imports -- so that the overall trade balance improves. This should show up here as a rise in the yellow line steeper than the fall in the red one. Income growth doesn't really come into the conventional story, so the green line should be flat.

This is not what we see. Even in terms of this simple decomposition, the post-crisis experience of each of the four Asian NICs was different, but none of them fit the standard story. Devaluations don't reliably translate into changes in the terms of trade, and changes in the terms of trade don't reliably translate into changes in trade flows. The income-trade balance link, on the other hand, looks quite reliable. In terms of the debate taking place elsewhere in econ blog land, this is a case where "hydraulic Keynesianism" looks pretty good.

Thailand is the clearest picture.

In the 1997 devaluation, the baht lost about a third of its value; the fall in the terms of trade -- the price of Thai exports relative to imports -- was less than proportionate, but still substantial. You can see this in the red lines at the bottom. But there was no expenditure switch at all. The flat yellow line shows that expenditure on foreign goods out of a given Thai income, and expenditure on Thai goods out of a given income elsewhere, did not change at all in the ten years after the crisis. (More precisely, expenditure in Thailand shifted toward domestic goods, while Thailand lost ground in its export markets; the two effects approximately canceled out.) Given that Thai goods were getting cheaper relative to foreign goods, the lack of net expenditure switch toward Thai goods should have led to deeper deficits. The only reason Thailand moved from deficit to surplus, is the decline in expenditure in Thailand relative to expenditure in its trading partners. The close match between the black and the green line in the figure, means that essentially the whole change in Thailand's trade balance is explained by the change in relative growth rates; there was no net switch toward Thai goods from foreign goods.


Indonesia is in some ways even a starker example:

Here we see a very deep devaluation, but again only a moderate change in the terms of trade, and an even smaller response of trade volumes. As in Thailand, the trade balance basically tracks relative income growth. The difference between these two cases is where the devaluation-trade flows link fails. In Thailand, the devaluation did reduce the price of exports relative to imports, but demand was not price-elastic enough for the change in prices to improve the trade balance. (In other words, the Marshall-Lerner-Robinson condition appears not to have been satisfied.) In Indonesia, the even larger devaluation -- the rupiah lost almost 80 percent of its value -- failed to change relative prices of traded goods, so demand elasticities did not come into play. This is partly because of high inflation in Indonesia following the devaluation, but not entirely - the rupiah fell by nearly half in real terms. But there was no change in the price of Indonesia's exports relative to its imports. If you want an example of a devaluation not working, this is a good one.


Korea, by contrast, looks superficially like the devaluation success story.

As I mentioned in the previous post, Korea was the only one of these countries where export growth in the decade after 1997 was as fast as in the decade before. And as the figure here shows, there was a substantial shift expenditure toward Korean goods following the crisis; alone among the four countries, Korea achieved its immediate post-crisis improvement in trade balance mainly through favorable expenditure switch rather than solely through a fall in income (though that contributed too.) But over time, Korea's terms of trade continued to deteriorate, without any further favorable expenditure switch; meanwhile, Korean growth slowed relative to its trade partners. By 2007, expenditure shares were back at 1997 levels; to the extent that Korea's trade balance was more favorable, it was only because spending was lower relative to its trade partners. Of course the surpluses it had run in the meantime had allowed the accumulation of substantial foreign exchange reserves. But if the goal is to use a lower exchange rate to achieve a permanent shift in trade balances, Korea post-1997 cannot be considered a success.

I should emphasize here: Slower relative expenditure growth in Korea does not mean slow growth in absolute terms. In fact, Korea (and, to varying degrees, the other three) did enjoy strong post-crisis recoveries. But because by far the largest trading partner for these countries is China -- taking about 25% of their exports -- even fairly strong growth translated into low relative growth. In other words, rapid growth in China implied growing exports in the NICs even in the absence of any competitiveness gains.


Finally, the one country that did achieve a lasting improvement in competitiveness, Malaysia.

In the immediate crisis period, Malaysia looks like Thailand and Indonesia: A deep devaluation fails to pass through to the relative prices of traded goods, and there is no expenditure switching; instead, the entire burden of raising the trade balance falls on slower growth in domestic expenditure. In the case of Malaysia, domestic expenditure fell by an astonishing 28 percent in 1997, a collapse in economic activity that has few precedents -- neither the US in the 1930s nor any Euro-crisis country comes close. But in the case of Malaysia, unlike the other three countries, growth subsequently accelerated relative to its trade partners, reflected in the downward sloping green line; at the same time, there was a continued expenditure switch in favor of Malaysian goods, reflected in the upward slope of the yellow line. What's especially striking about this competitiveness success story is that the favorable expenditure switch happened despite a rising price of of Malaysia's exports relative to its imports.

To continue with this analysis properly, one would want to disaggregate imports and exports by sector or industry. And would want to study, for each country, the institutional and legal changes that influenced trade flows in the decade after 1997. But failing that, it's at least worth understanding what the aggregate numbers are saying. It seems to me that they are saying this:

Even a very deep devaluation, as in Indonesia, is not guaranteed to change the relative prices of a country's imports and exports.

Even if a devaluation is passed through to relative prices, as in Thailand, price elasticities may not be large enough to produce a favorable change in the trade balance.

Even if a devaluation moves relative prices, and demand is price-elastic enough for the price change to move the trade balance in the right direction, as in Korea, a short-term improvement in competitiveness may not persist.

When countries do achieve a long-term improvement in competitiveness, like Malaysia, they don't necessarily do so through a relative cheapening of exports compared to imports. On the contrary: If the Marshall-Lerner condition is not satisfied, then a relative increase in the price of a country's exports will raise export earnings. In the case of Malaysia, improved terms of trade (that is, a rise in the price of its exports relative to its imports) account for about half the long-run improvement in its trade balance.

The Asian precedent does not make a Greek (or Spanish, or Portuguese, or Irish) devaluation look like an obviously good idea.

----

One other thing, if even real exchange rate changes are not passed through to traded-good prices in the destination country, then they must be showing up as changes in exporter profit margins. This shifts the focus from demand responses to supply responses, which I would argue are  more institutionally mediated. As you can tell if you've read this far, I am sympathetic to the "elasticity-pessimist" strand of Post Keynesian thought. But on the other side Robert Blecker has a strong argument for a strong effect of exchange rate changes, focusing on the role of export-industry profits in financing investment. Blecker's paper, in my opinion, is more convincing the straightforward "prices matter" view of exchange rate changes. But it also suggests a certain asymmetry: low profits induce exit from tradable sectors, especially for countries with Anglo-American market-based financial systems, more reliably than high profits encourage entry.


UPDATE: The fact that even large exchange rate changes produce relatively small movements in the relative prices of traded goods is well-known in the empirical trade literature. See for example here. I should have made this clearer.