Where Do Interest Rates Come From?

What determines the level of interest rates? It seems like a simple question, but I don’t think economics — orthodox or heterodox — has an adequate answer.

One problem is that there are many different interest rates. So we have two questions: What determines the overall level of interest rates, and what determines the spreads between different interest rates? The latter in turn we can divide into the question of differences in rates between otherwise similar loans of different lengths (term spreads), differences in rates between otherwise similar loans denominated in different currencies, and all the remaining differences, grouped together under the possibly misleading name risk spreads.

In any case, economic theory offers various answers:

1. The orthodox answer, going back to the 18th century, is that the interest rate is a price that equates the desire to save with the desire to borrow. As reformulated in the later 19th century by Bohm-Bawerk, Cassel, etc., that means: The interest rate is the price of goods today relative to goods tomorrow. The interest rate is the price that balances the gains from deferring consumption with our willingness to do so. People generally prefer consumption today to consumption in the future, and because it will be possible to produce more in the future than today, so the interest rate is (normally) positive. This is a theory of all transactions that exchange spending in one period for spending (or income) in another, not specifically a theory of the interest rate on loans.

The Wicksell variant of this, which is today’s central-bank orthodoxy, is that there is a well-defined natural interest rate in this sense but that for some reason markets get this one price wrong.

2. An equally old idea is that the interest rate is the price of money. In Hume’s writings on money and interest, for instance, he vacillates between this and the previous story. It’s not a popular view in the economics profession but it’s well-represented in the business world and among populists and monetary reformers,. In this view, money is just another input to the production process, and the interest rate is its price. A creditor, in this view, isn’t someone deferring consumption to the future, but someone who — like a landlord — receives an income thanks to control of a necessary component of the production process. A business, let’s say, that needs to maintain a certain amount of working capital in the form of money or similarly liquid assets, may need to finance it with a loan on which it pays interest. Interest payments are in effect the rental price of money, set by supply and demand like anything else. As I say, this has never been a respectable view in economic theory, but you can find it in more empirical work, like this paper by Gabriel Chodorow-Reich, where credit is described in exactly these terms as an input to current production.

3. Keynes’ liquidity-preference story in The General Theory. Here again the interest rate is the price of money. But now instead of asking how much the marginal business borrower will pay for the use of money, we ask how much the marginal wealth owner needs to be compensated to give up the liquidity of money for a less-liquid bond. The other side of the market is given by a fixed stock of bonds; evidently we are dealing with a short enough period that the flow of new borrowing can be ignored, and the bond stock treated as exogenously fixed. With no new borrowing, the link from the interest rate is liked to the real economy because it is used to discount the expected flow of profits from new investment — not by business owners themselves, but by the stock market. It’s an oddly convoluted story.

4. A more general liquidity-preference story. Jorg Bibow, in a couple of his essential articles on the Keynesian theory of liquidity preference, suggests that many of the odd features of the theory are due to Keynes’ decision to drop the sophisticated analysis of the financial system from The Treatise on Money and replace it with an assumption of an exogenously fixed money stock. (It’s striking that banks play no role in in the General Theory.) But I’m not sure how much simpler this “simplification” actually makes the story, or whether it is even logically coherent; and in any case it’s clearly inapplicable to our modern world of bank-created credit money. In principle, it should be possible to tell a more general version of the liquidity preference story, where, instead of wealth holders balancing the income from holding a bond against the liquidity from holding “money,” you have banks balancing net income against incremental illiquidity from simultaneously extending a loan and creating a deposit. I’m afraid to say I haven’t read the Treatise, so I don’t know how much you can find that story there. In any case it doesn’t seem to have been developed systematically in later theories of endogenous money, which typically assume that the supply of credit is infinitely elastic except insofar as it’s limited by regulation.

5. The interest rate is set by the central bank. This is the orthodox story when we turn to the macro textbook. It’s also the story in most heterodox writers. From Wicksell onward, the whole discussion about interest rates in a macroeconomic context is about how the central bank can keep the interest rate at the level that keeps current expenditure at the appropriate level, and what happens if it fails to do so. It is sometimes suggested that the optimal or “natural” interest rate chosen by the central bank should be the the Walrasian intertemporal exchange rate — explicitly by Hayek, Friedman and sometimes by New Keynesians like Michael Woodford, and more cautiously by Wicksell. But the question of how the central bank sets the interest rate tends to drop out of view. Formally, Woodford has the central bank set the interest rate by giving it a monopoly on lending and borrowing. This hardly describes real economies, of course, but Woodford insists that it doesn’t matter since central banks could control the interest rate by standing ready to lend or borrow unlimited amounts at thresholds just above and below their target. The quite different procedures followed by real central banks are irrelevant. [1]

A variation of this (call it 5a) is where reserve requirements bind and the central bank sets the total quantity of bank credit or money. (In a world of bind reserve requirements, these will be equivalent.) In this case, the long rate is set by the demand for credit, given the policy-determined quantity. The interbank rate is then presumably bid up to the minimum spread banks are willing to lend at. In this setting causality runs from long rates to short rates, and short rates don’t really matter.

6. The interest rate is set by convention. This is Keynes’ other theory of the interest rate, also introduced in the General Theory but more fully developed in his 1937 article “Alternative Theories of the Rate of Interest.” The idea here is that changes in interest rates imply inverse changes in the price of outstanding bonds. So from the lenders’ point of view, the expected return on a loan includes not only the yield (as adjusted for default risk), but also the capital gain or loss that will result if interest rates change while the loan is still on their books. The longer the term of the loan, the larger these capital gains or losses will be. I’ve discussed this on the blog before and may come back to it in the future, but the essential point is that if people are very confident about the future value of long rates (or at least that they will not fall below some floor) then the current rate cannot get very far from that future expected rate, no matter what short rates are doing, because as the current long rate moves away from the expected long rate expected capital gains come to dominate the current yield. Take the extreme case of a perpetuity where market participants are sure that the rate will be 5% a year from now. Suppose the short rate is initially 5% also, and falls to 0. Then the rate on the perpetuity will fall to just under 4.8% and no lower, because at that rate the nearly 5% spread over the short rate just compensates market participants for the capital loss they expect when long rates return to their normal level. (Obviously, this is not consistent with rational expectations.) These kinds of self-stabilizing conventional expectations are the reason why, as Bibow puts it, “a liquidity trap … may arise at any level of interest.” A liquidity trap is an anti-bubble, if you like.

What do we think about these different stories?

I’m confident that the first story is wrong. There is no useful sense in which the interest rate on debt contracts — either as set by markets or as target by the central bank — is the price of goods today in terms of goods tomorrow. The attempt to understand interest rates in terms of the allocation across time of scarce means to alternative ends is a dead end. Some other intellectual baggage that should overboard with the “natural” rate of interest are the “real”rate of interest, the idea of consumption loans, and the intertemporal budget constraint.

But negative criticism of orthodoxy is too easy. The real work is to make a positive case for an alternative. I don’t see a satisfactory one here.

The second and third stories depend on the existence of “money” as a distinct asset with a measurable, exogenously fixed quantity. This might be a usable assumption in some historical contexts — or it might not — but it clearly does not describe modern financial systems. Woodford is right about that.

The fifth story is clearly right with respect short rates, or at least it was until recently. But it’s incomplete. As an empirical matter, it is true that interbank rates and similar short market rates closely follow the policy rate. The question is, why? The usual answer is that the central bank is the monopoly supplier of base money, and base money is used for settlement between banks. This may be so, but it doesn’t have to be. Plenty of financial systems have existed without central banks, and banks still managed to make payments to each other somehow. And where central banks exist, they don’t always have a monopoly on interbank settlement. During the 19th century, the primary tool of monetary policy at the Bank of England was the discount rate — the discount off of face value that the bank would pay for eligible securities (usually trade credit). But if the discount rate was too high — if the bank offered too little cash for securities — private banks would stop discounting securities at the central bank, and instead find some other bank that was willing to give them cash on more favorable terms. This was the problem of “making bank rate effective,” and it was a serious concern for 19th century central banks. If they tried to raise interest rates too high, they would “lose contact with the market” as banks simply went elsewhere for liquidity.

Obviously, this isn’t a problem today — when the Fed last raised policy rates in the mid-2000s, short market rates rose right along with it. Or more dramatically, Brazil’s central bank held nominal interest rates around 20 percent for nearly a decade, while inflation averaged around 8 percent. [2] In cases like these, the central bank evidently is able to keep short rates high by limiting the supply of reserves. But why in that case doesn’t the financial system develop private substitutes for reserves? Mervyn King blandly dismisses this question by saying that “it does not matter in principle whether the disequilibrium in the money market is an aggregate net shortage or a net surplus of funds—control of prices or quantities carries across irrespective of whether the central bank is the monopoly supplier or demander of its own liabilities.” [3] Clearly, the central bank cannot be both the monopoly supplier and the monopoly demander of reserves, at least not if it wants to have any effect on the rest of the world. The relevant question — to which King offers no answer — is why there are no private substitutes for central bank reserves. Is it simply a matter of legal restrictions on interbank settlements using any other asset? But then why has this one regulatory barrier remained impassable while banks have tunneled through so many others? Anyway, going forward the question may be moot if reserves remain abundant, as they will if the Fed does not shrink its balance sheet back to pre-crisis levels. In that case, new tools will be required to make the policy rate effective.

The sixth story is the one I’m most certain of. First, because it can be stated precisely in terms of asset market equilibrium. Second, because it is consistent with what we see historically. Long term interest rates are quite stable over very long periods. Third, it’s consistent with what market participants say: It’s easy to find bond market participants saying that some rate is “too low” and won’t continue, regardless of what the Fed might think. Last, but not least from my point of view, this view is clearly articulated by Keynes and by Post Keynesians like Bibow. But while I feel sure this is part of the story, it can’t be the whole story. First, because even if a conventional level of interest rates is self-stabilizing in the long run, there are clearly forces of supply and demand in credit markets that push long rates away from this level in the short run. This is even more true if what convention sets is less a level of interest rates, than a floor. And second, because Keynes also says clearly that conventions can change, and in particular that a central bank that holds short rates outside the range bond markets consider reasonable for long enough, will be able to change the definition of reasonable. So that brings us back to the question of how it is that central banks are able to set short rates.

I think the fundamental answer lies behind door number 4. I think there should be a way of describing interest rates as the price of liquidity, where liquidity refers to the capacity to honor one’s promises, and not just to some particular asset. In this sense, the scarce resource that interest is pricing is trust. And monetary policy then is at root indistinguishable from the lender of last resort function — both are aspects of the central bank’s role of standing in as guarantor for commitments within the financial system.  You can find elements of this view in the Keynesian literature, and in earlier writers going back to Thornton 200-plus years ago. But I haven’t seen it stated systematically in way that I find satisfactory.

UPDATE: For some reason I brought up the idea of the interest rate as the price of money without mentioning the classic statement of this view by Walter Bagehot. Bagehot uses the term “price of money” or “value of money” interchangeably with “discount rate” as synonyms for the interest rate. The discussion in chapter 5 of Lombard Street is worth quoting at length:

Many persons believe that the Bank of England has some peculiar power of fixing the value of money. They see that the Bank of England varies its minimum rate of discount from time to time, and that, more or less, all other banks follow its lead, and charge much as it charges; and they are puzzled why this should be. ‘Money,’ as economists teach, ‘is a commodity, and only a commodity;’ why then, it is asked, is its value fixed in so odd a way, and not the way in which the value of all other commodities is fixed? 

There is at bottom, however, no difficulty in the matter. The value of money is settled, like that of all other commodities, by supply and demand… A very considerable holder of an article may, for a time, vitally affect its value if he lay down the minimum price which he will take, and obstinately adhere to it. This is the way in which the value of money in Lombard Street is settled. The Bank of England used to be a predominant, and is still a most important, dealer in money. It lays down the least price at which alone it will dispose of its stock, and this, for the most part, enables other dealers to obtain that price, or something near it. … 

There is, therefore, no ground for believing, as is so common, that the value of money is settled by different causes than those which affect the value of other commodities, or that the Bank of England has any despotism in that matter. It has the power of a large holder of money, and no more. Even formerly, when its monetary powers were greater and its rivals weaker, it had no absolute control. It was simply a large corporate dealer, making bids and much influencing—though in no sense compelling—other dealers thereby. 

But though the value of money is not settled in an exceptional way, there is nevertheless a peculiarity about it, as there is about many articles. It is a commodity subject to great fluctuations of value, and those fluctuations are easily produced by a slight excess or a slight deficiency of quantity. Up to a certain point money is a necessity. If a merchant has acceptances to meet to-morrow, money he must and will find today at some price or other. And it is this urgent need of the whole body of merchants which runs up the value of money so wildly and to such a height in a great panic…. 

If money were all held by the owners of it, or by banks which did not pay an interest for it, the value of money might not fall so fast. … The possessors would be under no necessity to employ it all; they might employ part at a high rate rather than all at a low rate. But in Lombard Street money is very largely held by those who do pay an interest for it, and such persons must employ it all, or almost all, for they have much to pay out with one hand, and unless they receive much with the other they will be ruined. Such persons do not so much care what is the rate of interest at which they employ their money: they can reduce the interest they pay in proportion to that which they can make. The vital point to them is to employ it at some rate… 

The fluctuations in the value of money are therefore greater than those on the value of most other commodities. At times there is an excessive pressure to borrow it, and at times an excessive pressure to lend it, and so the price is forced up and down.

The relevant point in this context is the explicit statement that the interest, or discount, rate is set by the supply and demand for money. But there are a couple other noteworthy things. First, the concept of supply and demand is one of monopolistic competition, in which lenders are not price takers, but actively trade off markup against market share. And second, that the demand for money (i.e. credit) is highly inelastic because money is needed not only or mainly to purchase goods and services, but first and foremost to meet contractual money commitments.

[1] See Perry Mehrling’s useful review. Most of the text of Woodford’s textbook can be downloaded for free here. The introduction is nontechnical and is fascinating reading if you’re interested in this stuff.

[2] Which is sort of a problem for Noah Smith’s neo-Fisherite view.

[3] in the same speech, King observes that “During the 19th century, the Bank of England devoted considerable attention to making bank rate ‘effective’.” His implication is that central banks have always been able to control interest rates. But this is somewhat misleading, from my point of view: the Bank devoted so much attention to making its rate “effective” precisely because of the occasions when it failed to do so.

Mehrling on Black on Capital

In a post last week, I suggested that an alternative to thinking of capital as quantity of means of production accumulated through past investment, is to think of it as the capitalized value of expected future profit flows. Instead of writing


α = r k

where α is the profit share of national income, r is the profit rate, and k is the capital-income ratio, we should write 
k = α / r
where r is now understood as the discount rate applied to future capital income. 
Are the two rs the same? Piketty says no: the discount rate is presumably (some) risk-free interest rate, while the return on capital is typically higher. But I’m not sure this position is logically sustainable. If there are no barriers to entry, why isn’t investment carried to the point where the return on capital falls to the interest rate? On the other hand, if there are barriers to entry, so that capital can continue to earn a return above the interest rate without being flooded by new investment with borrowed funds, then profits cannot all be attributed to measured capital; some is due to whatever privilege creates the barriers. Furthermore, in that case there will not be, even tendentially, a uniform economywide rate of profit. 
In any case, whether or not we have a coherent story of how there can be a profit rate distinct from the discount rate, it’s clearly the latter that matters for corporate equity, which is the main form of capital Piketty observes in modern economies. Verizon, to take an example at random, has current annual earnings of around $20 billion and is valued by the stock market at around $200 billion. Nobody, I hope, would interpret these numbers as meaning that Verizon has $200 billion of capital and, since the economy-wide profit rate is 10%, that capital generates $20 billion in profits. Rather, Verizon — the enterprise as a whole, its physical capital, its organization and corporate culture, its brand, its relationships with regulators, the skills and compliance (or not) of its workers — currently generates $20 billion a year of profits. And the markets — applying the economy-wide discount factor embodied in the interest rate, plus a judgement about the likely change in share of the social surplus Verizon will be able to claim in the future — assess the present value of that stream of profits from now til doomsday at $200 billion.  
Now it might so happen that the stock market capitalization of a corporation is close to the reported value of assets less liabilities — this corresponds to a Tobin’s q of 1. Verizon, with total assets of $225 billion and total liabilities of $50 billion, happens to fit this case fairly well. It might also be the case that a firm’s reported net assets, deflated by some appropriate price index, correspond to its accumulated investment; it might even also be the case that there is a stable relationship between reported net capital and earnings. But as far as market capitalization goes, it makes no difference if any of those things is true. All that matters is market expectations of future earnings, and the interest rate used to discount them.
I was thinking about this in relation to Piketty’s Capital in the 21st Century. But of course the point is hardly original. Fischer Black (of the Black-Scholes option-pricing formula) made a similar argument decades ago for thinking of capital as a claim on a discounted stream of future earnings, rather than as an accumulation of past investments. 
Here’s Perry Mehrling on Black’s view of capital:

As in Fisher, Black’s emphasis is on the market value of wealth calculated as the expected present value of future income flows, rather than on the quantity of wealth calculated as the historical accumulation of savings minus depreciation. This allows Black to treat knowledge and technology as forms of capital, since their expected effects are included when we measure capital at market value. As he says: “more effective capital is more capital” (1995a, 35). Also as in Fisher, capital grows over time without any restriction from fixed factors. 

… 

For Black, the standard aggregative neoclassical production function is inadequate because it obscures sectoral and temporal detail by attributing current output to current inputs of capital and labor, but he tries anyway to express his views in that framework in order to reach his intended audience. Most important, he accommodates the central idea of mismatch to the production function framework by introducing the idea that the “utilization” of physical capital and the “effort” of human capital can vary over time. This accommodation makes it possible to express his theory in the familiar Cobb-Douglas production function form: y = A(eh)^α(fk)^(1-α), where y is output, h and k are human and physical capital, e and f are effort and utilization, and A is a temporary shock (1995, eq. 5.3). 

It’s familiar math, but the meaning it expresses remains very far from familiar to the trained economist. For one, the labor input has been replaced by human capital so there is no fixed factor. For another, both physical and human capital are measured at market values, and so are supposed to include technological change. This means that the A coefficient is not the usual technology shift factor (the familiar “Solow residual”) but only a multiplier, indeed a kind of inverse price earnings ratio, that converts the stock of effective composite capital into a flow of composite output. In effect, and as he recognizes, Black’s production function is a reduced form, not a production function at all in the usual sense of a technical relation between inputs and outputs. What Black is after comes clearer when he groups terms and summarizes as Y=AEK (eq. 5.7), where Y is output, E is composite utilization, and K is composite capital. Here the effective capital stock is just a constant multiple of output, and vice versa. It’s just an aggregate version of Black’s conception of ideal accounting practice (1993c) wherein accountants at the level of the firm seek to report a measure of earnings that can be multiplied by a constant price- earnings ratio to get the value of the firm. 

… 

In retrospect, the most fundamental source of misunderstanding came (and comes still) from the difference between an economics and a finance vision of the nature of the economy. The classical economists habitually thought of the present as determined by the past. In Adam Smith, capital is an accumulation from the careful saving of past generations, and much of modern economics still retains this old idea of the essential scarcity of capital, and of the consequent virtue attached to parsimony. The financial point of view, by contrast, sees the present as determined by the future, or rather by our ideas about the future. Capital is less a thing than an idea about future income flows discounted back to the present, and the quantity of capital can therefore change without prior saving.

In comments, A H mentioned that Post Keynesian or structuralist economics seem much closer to the kind of analysis used by finance professionals than orthodox economics does. I think one reason is that we share what Mehrling calls the “money view” or, here, the “finance vision” of the economy. Orthodoxy sees the economy as a set of exchanges of goods; the finance vision sees  a set of contractual money payments. 
Mehrling continues:

In The Nature of Capital and Income, Irving Fisher (1906) straddled the older world view of economics and the emerging world view of finance by distinguishing physical capital goods (for which the past-determines-present view makes sense) from the value of those goods (for which the future-determines-present view makes sense). By following Fisher, Black wound up employing the same straddle. 

Piketty may be in a similarly awkward position. 

Chekhov on Data

From On Official Business:

“Tell me, old chap, how long have you been village constable in these parts?” 

“Well, must be nigh on 30 years. It was about five years after the serfs was freed that I began, so you can work it out for yourself. Since then I’ve been doing it every day. … To the treasurer’s department, to the post office, to the police inspector’s house, the magistrate, council offices, tax inspector, gentle folk, village folk, and all God-fearing Christians, I carry parcels, summonses, letters, all kinds of forms and lists. Nowadays, my good sir, there’s no end to these forms — yellow, white, red — all for writing figures on. Every squire, parson and rich farmer has to write down, ten times a year, how much he’s sown or reaped, how many bushels or hundredweight of rye he’s got, how much oats and hay, what the weather’s like, and about different sorts of insects. They please themselves what they write, of course, it’s only just forms, but I has to run around handing them sheets of paper out — and then it’s me what has to collect ‘em all in. Now, that dead gent over there. There’s no need to slit him open, you yourself know it’s a waste of time and you’ll only get your hands dirty. But you’ve had to go to the bother, sir, you’ve driven out here, all because of those forms.”

It’s a reminder that underlying every economic statistic is a concrete process of making human activity legible as quantities. One person asks another person a question, and the other answers (or doesn’t) in the context of some particular relationship between them.

People often quote  Josiah Stamp to make this point. Nice to have another option.

UPDATE: While we are talking about Chekhov, I can’t resist sharing this passage from “Rothschild’s Fiddle”:

There before him stood an ancient, spreading willow tree with a massive trunk, and a crow’s nest among its branches. … He sat down at its foot and thought of the past. On the opposite shore, where that meadow now was, there had stood in those days a wood of tall birch-trees, and that bare hill on the horizon yonder had been covered with the blue bloom of an ancient pine forest. And sailboats had plied the river then, but now all lay smooth and still, and only one little birch-tree was left on the opposite bank, a graceful young thing, like a girl, while on the river there swam only ducks and geese. It was hard to believe that boats had once sailed there. It even seemed to him that there were fewer geese now than there had been. …
He was puzzled to know why he had never once been down to the river during the last forty or fifty years of his life, or, if he had been there, why he had never paid any attention to it. The stream was fine and large; he might have fished in it and sold the fish to the merchants and the government officials and the restaurant-keeper at the station, and put the money in the bank. He might have rowed in a boat from farm to farm and played on his fiddle. People of every rank would have paid him money to hear him. He might have tried to run a boat on the river, that would have been better than making coffins. Finally, he might have raised geese, and killed them, and sent them to Moscow in the winter. Why, the down alone would have brought him ten rubles a year! But he had missed all these chances and had done nothing. What losses were here! Ah, what terrible losses! And, oh, if he had only done all these things at the same time! If he had only fished, and played the fiddle, and sailed a boat, and raised geese, what capital he would have had by now! But he had not even dreamed of doing all this; his life had gone by without profit or pleasure. It had been lost for nothing, not even a trifle. Nothing was left ahead; behind lay only losses, and such terrible losses that he shuddered to think of them. But why shouldn’t men live so as to avoid all this waste and these losses? Why, oh why, should those birch and pine forests have been felled? Why should those meadows be lying so deserted? Why did people always do exactly what they ought not to do? Why had Yakov scolded and growled and clenched his fists and hurt his wife’s feelings all his life? Why, oh why, had he frightened and insulted that Jew just now? Why did people in general always interfere with one another? What losses resulted from this! What terrible losses! If it were not for envy and anger they would get great profit from one another.

UPDATE 2: Not like anyone is reading this, but I feel obliged to point out that while I find this passage affecting, I certainly don’t endorse it or anything. What Chekhov has captured perfectly is the attitude of what we used to call, quite precisely, the petty bourgeoisie, the self-employed commodity producer. (In this case, a coffin-maker and musician.) The mixing-up of personal virtue, use-values and profit is characteristic, along with the fretting about “envy” and “interference” as the obstacles to mutual profit. If a real-life Hank Rearden were described by someone with a deep and sympathetic understanding of human nature, he might sound something like this.

Which reminds me — on a very different note, does anyone who lived in Chicago in the 1990s remember a play at the Annoyance Theater called “Ayn Rand Gives Me a Boner”? The protagonist was the world’s most insufferable micromanaging boss, a supervisor at a grocery store obsessed with perfecting the checkout process. His adversary was a man with terminal cancer using the sheer power of sympathy to take over the world. Whatever you think of the title, it was kind of brilliant.

How Not to Think about Negative Rates

Last week’s big monetary-policy news was the ECB’s decision to target a negative interest rate, in the form of an 0.25 percent tax on bank reserves. This is the first time a major central bank has announced a negative policy rate, though some smaller ones (like the Bank of Sweden) have done so in the past few years.

Whether a tax on reserves is really equivalent to a negative interest rate, and whether this change should be expected to pass through to interest rates or credit availability for private borrowers, are not easy questions. I’m not going to try to answer them now. I just want to call attention to this rather extraordinary Neil Irwin column, as an example of how unsuited mainstream discussion is to addressing these questions.  
Here’s Irwin’s explanation of what a negative interest rate means:

When a bank pays a 1 percent interest rate, it’s clear what happens: If you deposit your money at the bank, it will pay you a penny each year for every dollar you deposited. When the interest rate is negative, the money goes the other direction. … Put bluntly: Normally the banks pay you to keep your money there. Under negative rates, you pay them for the privilege.

Not mentioned here, or anywhere else in the article, is that people pay interest to banks, as well as receiving interest from them. In Irwin’s world, “you” are always a creditor, never a borrower. 
Irwin continues:

The theory is that when it becomes more costly for European banks to keep money in the E.C.B., they will have incentive to do something else with it: Lend it out to consumers or businesses, for example.

Here’s the loanable funds theory in all its stupid glory. People put their “money” into a bank, which then either holds it or lends it out. Evidently it is not a requirement to be a finance columnist for the New York Times to know anything about how bank loans actually work. 
Irwin:

Banks will most likely pass these negative interest rates on to consumers, or at least try to. They may try to do so not by explicitly charging a negative interest rate, but by paying no interest and charging a fee for account maintenance.

Note that “consumers” here means depositors. The fact that banks also make loans has escaped Irwin’s attention entirely. 
Of course, most of us are already in this situation: We don’t receive any interest rate on our transaction balances, and pay are willing to pay various charges and fees for the liquidity benefits of holding them. 
The danger of negative rates, per Irwin, is that 

It is possible that, assuming banks pass along the negative rates through either fees or explicitly charging negative interest, people will withdraw their money as cash rather than keeping it on deposit at banks. … That is one big reason that the E.C.B. and other central banks are going to be reluctant to make rates highly negative; it could result in people pulling cash out of the banking system.

Again the quantity theory in its most naive and stupid form: there is a fixed quantity of “money” out there, which is either being kept in banks — which function, in Irwin’s world, as glorified safe deposit boxes — or under mattresses. Evidently he’s never thought about why the majority of us who already face negative rates on our checking accounts continue to hold them. More fundamentally, there’s no explanation of what makes negative rates special. Bank deposits don’t, in general, finance holdings of reserves, they finance bank loans. Any kind of expansionary policy must reduce the yield on bank loans and also — if margins are constant — on deposits and other bank liabilities. Making returns to creditors the acid test of policy, as Irwin does, would seem to be an argument against expansionary monetary policy in general — which of course it is.
What’s amazing to me in this piece is that here we have an article about monetary policy that literally makes no mention of loans or borrowers. In Irwin’s world, “you” are, by definition, an owner of financial assets; no other entities exist. It’s the 180-proof distillation of the bondholder’s view of the world.
Heterodox criticism of the loanable-funds theory of interest and insistence that loans create deposits, can sometimes come across as theological, almost ritual.  Articles like this are a reminder of why we can’t let these issues slide, if we want to make any sense of the financial universe in which we live.

Three Ways of Looking at alpha = r k

Piketty’s “first law of capitalism” is the accounting identity

α = r k

where α is the share of capital income in total output, r is the average return on capital, and k is the aggregate capital-output ratio.

As accounting, this is true by definition. As economics, what kind of economic behavior does it describe? There are three ways of looking at it. 

In the standard version, the profit share is determined by a production function, which is given by technology. The profit rate r* required by capital owners is fixed by technology in combination with time preferences. In this closure, k is the endogenous, or adjusting, variable.  Investment rises or falls whenever the realized profit rate differs from the required rate, thus keeping k at the level that satisfies the equation for r  = r*

In Piketty’s version, r is fixed (somehow; the mechanism is not clear) and k is determined by savings behavior and (exogenous) growth according to his “second law of capitalism”: 


k = s/g

That leaves α to passively accommodate r and k. Capitalists get whatever the current capital stock and fixed profit rate entitle them to, and workers get whatever is left over; in effect, workers are the residual claimants in Piketty’s system. (This is the opposite of the classical view, in which wages are fixed and capitalists get the residual.)

In a third interpretation, we could say that α and r are set institutionally — α through some kind of bargaining process, or by the degree of monopoly, r perhaps by the interest rate set in the financial system. The value of the capital stock is then given by capitalizing the flow of profits α Y at the discount rate r. (Y is total output.) This interpretation is the natural one if we think of “capital” as a claim to a share of the surplus as opposed to physical means of production. 

This interpretation clearly applies to pure land, or to the market value of a particular firm. What if it applied to capital in general? Since claims on the surplus — including claims exercised through nonproduced assets like land — are not created by reserving output from consumption, aggregate savings would be a meaningless accounting construct in this case. (Or we could adopt a Hicksian view of saving in which it equals the change in net wealth by definition.) Looking at things this way also puts r > g in a different light. Suppose we think of the capital stock as a whole as something like the stock of a firm, which entitles the owners to the flow of profits from that firm. If the profits today are α Y and output is expected to grow at a rate g, what is the value of the stock today? If we discount future profits at r, then it is the sum from t=0 to t=infinity of α Y (1 + g)^t / (1 + r)^t, which works out to α Y / (rg). So if we can take the rate of return on capital as the discount rate on future profits, then r > g is implied by a finite value of the capital stock.

We shouldn’t ask what capital “really” is. It really is a quantity of money in a process of self-expansion, and it really is a mass of means of production, and it really is authority over the production process. But the particular historical questions Piketty is interested in may be better suited to thinking of capital as a claim on the social surplus than as a physical quantity of means of production. Seth Ackerman has some very interesting thoughts along these lines in his contribution to the Jacobin symposium on the book.