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. 

Demand and Competitiveness: Germany and the EU

I put up a post the other day about Enno Schroder’s excellent work on accounting for changes in trade flows. Based on the comments, there’s some confusion about the methodology. That’s not surprising: It’s not complicated, but it’s also not a familiar way of looking at this stuff, either within or outside the economics profession. Maybe a numerical example will help?

Let’s consider two trading partners, in this case Germany and the rest of the EU. (Among other things, having just two partners avoids the whole weighting issue.) The first line of the table below shows total demand in each — that is, all private consumption, government consumption, and investment — in billions of euros. (As usual, this is final demand — transfers and intermediate goods are excluded.) So, for instance, in the year 2000 all spending by households, firms and governments in Germany totaled 2.04 trillion euros. The next two lines show the part of that expenditure that went to imports — from the rest of the EU for Germany, from Germany for the rest of the EU, and from the rest of the world for both. The final two lines of each panel then show the share of total expenditure in each place that went to German and rest-of-EU goods respectively. The table looks at 2000 and 2009, a period of growing surpluses for Germany.

2000 2009
Germany Demand 2,041 2,258
Imports from EU 340 429
Imports from Rest of World 198 235
Germany Share 74% 71%
EU ex-Germany Share 17% 19%
EU ex-Germany Demand 9,179 11,633
Imports from Germany 387 501
Imports from Rest of World 795 998
Germany Share 4% 4%
EU ex-Germany Share 87% 87%
Ratio, Germany-EU Exports to Imports 1.14 1.17
EU Surplus, Percent of German GDP 2.27 3.02

So what do we see? In 2000, 74 cents out of every euro spent in Germany went for German goods and services, and 17 cents for goods and services from the rest of the EU. Nine years later, 71 cents out of each German euro went to German stuff, and 19 cents to stuff from the rest of the EU. German households, businesses and government agencies were buying more from the rest of Europe, and less from their own country. Meanwhile, the rest of Europe was spending 4 cents out of every euro on goods and services from Germany — exactly the same fraction in 2009 as in 2000.

If Germans were buying more from the rest of the EU, and non-German Europeans were buying the same amount from Germany, how could it be that the German trade surplus with the rest of Europe increased? And by nearly one percent of German GDP, a significant amount? The answer is that total expenditure was rising much faster in the rest of Europe — by 2.7 percent a year, compared with 1.1 percent a year in Germany. This is what it means to say that the growing German surplus is entirely accounted for by demand, and that Germany actually lost competitiveness over this period.

Again, these are not estimates, they are the actual numbers as reported by EuroStat. It is simply a matter of historical fact that Germans spent more of their income on goods from the rest of the EU, and less on German goods, in 2009 than in 2000, and that the rest of the EU spent the same fraction of its income on German goods in the two years. Obviously, this does not rule out the possibility that German goods were becoming cheaper relative to the rest of Europe’s, if you postulate some other factor that would have reduced Germany’s exports without a growing cost advantage. (This is not so easy, since Germany’s exports are the sort of high-end manufactures which usually have a high income elasticity, i.e. for which demand is expected to rise over time.) And it is also compatible with a story where German export prices fell, but export demand is price-inelastic, so that lower prices did nothing to raise export earnings. But it is absolutely not compatible with a simple story where the most important driver of German trade imbalances is changing relative prices. For that story to work, the main factor in Germany’s growing surpluses would have to have been expenditure switching from other countries’ goods to Germany’s. And that didn’t happen.

NOTE: This my table, not Enno’s. The data is from Eurostat, while he uses the Penn World Tables, and he does not look at intra-European trade specifically.

UPDATE: There’s another question, which no one asked but which you should always try to answer: Why does it matter? The truth is, a big reason I care about this is that I’m curious how capitalist economies work, and this stuff seems to shed some light on that, in terms of both the specific content  and the methodology. But more specifically:

First, seeing trade flows as driven by income as well as price fits better with a vision of economy that has many different possible states of rest. It fits better with a vision of economies evolving in historical time, rather than gravitating toward an equilibrium which is both natural and optimal. In this particular case, there is no reason to suppose that the relative growth rates consistent with full employment in each country are also the relative growth rates consistent with balanced trade. A world in which trade flows respond mainly to relative prices is a world where macropolicy doesn’t pose any fundamentally different challenges in an open economy than in a closed one. Whatever mechanisms operated to ensure full employment continue to do so, and then the exchange rate adjusts to keep trade flows balanced (or appropriately unbalanced, for a country with a good reason to export or import capital.) Whereas when the main relationship is between income and trade, they cannot vary independently.

Second, there are important implications for policy. Krugman keeps saying that Germany needs higher relative prices, i.e., higher inflation. Even leaving aside the political difficulties with such a program, it makes sense on its own terms only if there is a fixed pool of European demand. To say that the only way you can have an adequate level of demand in Greece is for prices to fall relative to Germany, is to accept, on a European or global level, the structural theory of unemployment that Krugman rejects so firmly (and rightly) for the US. By contrast if competitiveness didn’t cause the problem, we shouldn’t assume competitiveness is involved in the solution. The historical evidence suggests that more rapid income growth in Germany will be sufficient to move its current account back to balance. The implications for domestic demand in Germany are the opposite in this case as in the relative-prices case: Fixing the current account problem means more jobs and orders for German workers and firms, not  higher inflation in Germany. [1]

So if you buy this story, you should be more pessimistic about a Greek exit from the euro — since there’s less reason to think that flexible exchange rates will lead to balanced trade — but more optimistic about a solution within the euro.

I don’t understand why, for economists like Krugman and Dean Baker, Keynesianism always seems to stop at the water’s edge. Why does their analysis of international trade always implicitly [2] assume a world economy continually at full capacity, where a demand shortfall in one country or region implies excess demand somewhere else? They know perfectly well that the question of unemployment in one country cannot be reduced to the question of who is getting paid too much; why do they forget it as soon as exchange rates come into the picture? Perhaps it’s for the same reasons — whatever they are — that so many economists who support all kinds of domestic regulation are ardent supporters of free trade, even though that’s just laissez-faire at the global level. In the particular case of Krugman, I think part of the problem is that his own scholarly work is in trade. So when the conversation turns to trade he loses one of the biggest assets he brings to discussions of domestic policy — a willingness to forget all the “progress” in economic theory over the past 30 or 40 years.

[1] A more reasonable version of the higher-prices-in-Germany claim is that Germany must be willing to accept higher inflation in order to raise demand. In some times and places this could certainly be true. But I don’t think it is for Germany, given the evident slack in labor markets implied by stagnant wages. And in any case that’s not what Krugman is saying — for him, higher inflation is the solution, not an unfortunate side effect.

[2] Or sometimes explicitly — e.g. this post has Germany sitting on a vertical aggregate supply curve.

The Case of Keen

(Warning: To anyone reading this who’s not immersed in the debates of the econo blogosphere, this post will fully live up the blog’s subtitle.)

One of the big things this past week was Krugman’s criticism of Steve Keen. This was a Big Deal, since it is, sadly, rare for someone of Krugman’s stature to engage with anyone in the heterodox world. Unfortunately it wasn’t a productive exchange; no real information was exchanged, and neither side, IMveryHO, covered themselves in glory. For anyone interested in what’s wrong with Krugman’s side, there’s a good discussion in the comments to this Nick Rowe post. Here I am going to focus on Keen.

Keen’s most recent paper is here; it gives the clearest statement of his view that I’ve seen. As I see it, there are two parts to it. First, he argues that a tradition running from Minsky back to Keynes and Schumpeter (and, I would add, Wicksell and on back to the “caps” in 17th century Sweden) sees money as endogenously created by the banking system, rather than exogenously set by central banks (or, earlier, by the supply of gold). This means that banks can lend to borrowers without a prior decision by anyone to save, which in turn means that changes in the terms on which banks extend credit are an important source of fluctuations in aggregate demand that drive movements in output and prices. With all this, I am in perfect agreement.

But then he tries to formalize these ideas. And about the best thing you can say about his formalization is that it uses terms in such an idiosyncratic way that communication is all but impossible. I know I’m not the only one who’s found Keen’s stuff a bit like the novel Untitled in Martin Amis’ The Information, which literally cannot be read. But let’s make an attempt. Here are what seem to be the two key elements.

Keen repeatedly says that “aggregate demand is income plus change in debt.” There are many variations on this through his writing, he evidently regards it as a central contribution. But what does it mean? To a non-economist, it appears to be a challenge to another, presumably orthodox, view that aggregate demand is equal to income. But if you are an economist you know that there is no such view, whether neoclassical, Keynesian or radical.

What economist do believe, across the spectrum, is that total expenditure = total output = total income, or Y = Z = C + I + G + X – M. Given the way our national accounts are set up, this is an identity. The question, as always, is which way causality runs. The term “aggregate demand” is shorthand for the argument that causality runs from aggregate expenditure to aggregate income, whereas pre-Keynesian orthodoxy held that causality ran strictly from income to expenditure. (It’s worth noting that in this debate Krugman is solidly with Keen — and me — on the Keynesian side.) But there isn’t any separate variable called “aggregate demand”; AD is just another name for aggregate expenditure insofar as it determines output. Nobody ever says that AD is equal to income; what they typically say is that AD is a function of income, along with other variables such as interest rates, wealth, and changes in sentiment. (People do say that income is equal to AD, but that is a very different claim, and it’s true by definition.)

I can imagine various more or less sensible things Keen might have meant by the statement, but it feels kind of silly to speculate. As written it makes no sense at all.

The second formalism is Keen’s equation, which he gives the jawbreaker of a name “the Walras-Schumpeter-Minsky’s Law”:

Y(t) + dD/dt = GDP(t) + NAT(t).

Y is income, D is debt, and NAT is net asset turnover. This last is defined as “the price index for assets P, times their quantity Q, times the annual turnover T expressed as a fraction of the number of assets, T<1: NAT = P*Q*T.”

And now we really run into problems.

First of all, is this an accounting identity, or a behavioral equation? Does it hold exactly by definition, or does it describe an empirical regularity that holds only approximately? This is the most basic thing you need to know about any equation in economics, but Keen, as far as I can tell, doesn’t say.

Second, in the national accounts and every economic tradition that I’m aware of, aggregate income Y is identically equal to GDP. They’re just two ways of representing the same quantity. So it seems that Keen is using “income” in some idiosyncratic way that he never specifies. Alternatively, and more in the spirit of Minsky and Schumpeter, perhaps he is thinking of Y as anticipated or current-period income, and GDP as realized or next-period income. But again, it’s not much use to speculate about what Keen might have meant.

The next problem is units. GDP and presumably Y are flows over a specified period (a year or a quarter); they are in units of dollars. dD/dt is an instantaneous rate of flow; it is in units of dollars per unit time. And NAT, as defined, is the product of two indexes times a fraction, so it is a dimensionless number. Well, you can’t add variables with different units. That is just algebra. So again, whatever Keen has in mind, it is something other than what he wrote. And while it’s easy enough to replace dD/dt with delta-D over the period that GDP is being measured, I really have no idea what to do with the NAT term.[1]

It doesn’t help that at no point in the paper — or in any of his other stuff that I’ve seen — does he give any values for Y or NAT. He has lots of graphs of debt, output, employment, etc., showing — to the surprise of no one — that these cyclical variables are correlated. But since Y and NAT don’t figure in any of them, it’s not clear what work the Walras-Schumpeter-Minsky’s Law is supposed to be doing. Again, if his point is that endogenous changes in credit supply are important to business cycles, I’m with him 100%. (Though so are, it’s worth noting, some perfectly orthodox New Keynesians.) But if your idea is just that there is some important connection between A and B and C, the equation A = B + C is not a good way of saying it.

Honestly, it sometimes feels as though Steve Keen read a bunch of Minsky and Schumpeter and realized that the pace of credit creation plays a big part in the evolution of GDP. So he decided to theorize that relationship by writing, credit squiggly GDP. And when you try to find out what exactly is meant by squiggly, what you get are speeches about how orthodox economics ignores the role of the banking system.

Keen is taken seriously by serious people. He’s presenting this paper at the big INET conference in Berlin next week. It’s not OK that he writes in a way that makes it impossible to understand or evaluate his ideas. For better or worse, we in the world of unconventional economics cannot rely on the usual professional gatekeepers. So we have a special duty to police each other’s work, not of course for ideology, but for meeting basic standards of logic and evidence. There are very important arguments in Schumpeter, Minsky, etc. about the role of the financial system in capitalism, which mainstream economics has downplayed, just as Keen says. And he may well have something important to add to those arguments. But until he writes in a language spoken by people other than himself, there’s no way to know.

[1] Not to mention the odd stipulation that T < 0. Why is it impossible for the average turnover time of assets to be less than a year? Or does he really mean the fraction of assets that change hands at least once? What possible economic meaning could that have?

EDIT: I’m a bit unhappy about this post. It’s too harsh on Keen. As Steve Randy Waldman suggests in comments, there probably is a valid insight in there, if one can just get past his opaque terminology. (Altho that’s all the more reason for him to stop speaking in idiolect…) More importantly, posting this critique of Keen makes it seem like I am on Krugman’s side, when his contributions to the debate have been every bit as bad in their own way — as lucid as Keen is impenetrable, but also just embarassingly wrong, at least form where I’m sitting. This post by Michael Stephens Randy Wray at the Levy Institute blog does a good job laying out the issues. I agree with everything he says, I think.

EDIT 2:… and now here’s Keen saying that

Krugman’s part of the economic establishment, which for thirty or forty years has got away with arguing that you can model a capitalist economy as if it had no banks in it, no money, and no debt… You just don’t have a model of capitalism if you don’t include those components. 

I’m also unhappy with that. Krugman (and New Keynesians/monetarists in general) are very specifically modeling an economy with money, but without banks. I agree with Keen that you do need to think about the financial system to understand macro dynamics, but you can’t make the case for that if you can’t correctly describe the position you are arguing against. I don’t think we will make intellectual progress without being more careful about this stuff.

What Adjusts?

More teaching: We’re starting on the open economy now. Exchange rates, trade, international finance, the balance of payments. So one of the first things you have to explain, is the definition of real and nominal exchange rates:

e_R = e_N P*/P 

where P and P* are the home and foreign price levels respectively, and the exchange rate e is defined as the price of foreign exchange (so an appreciation means that e falls and a depreciation means that it rises).

This is a useful definition to know — though of course it’s not as straightforward as it seems, since as we’ve discussed before there are various possibles Ps, and once we are dealing with more than two countries we have to decide how to weight them, with different statistical agencies using different weightings. But set all that aside. What I want to talk about now, is what a nice little example this equation offers of a structuralist perspective on the economy.

 As given above, the equation is an accounting identity. It’s always exactly true, simply because that’s how we’ve defined the real exchange rate. As an accounting identity, it doesn’t in itself say anything about causation. But that doesn’t mean it’s vaacuous. After all, we picked this particular definition because we think it is associated with some causal story. [1] The question is, what story? And that’s where things get interesting.

Since we have one equation, we should have one endogenous (or dependent) variable. But which one, depends on the context.

If we are telling a story about exchange rate determination, we might think that the endogenous variable is e_N. If price levels are determined by the evolution of aggregate supply and demand (or the growth of the money stock, if you prefer) in each country, and if arbitrage in the goods market enforces something like Purchasing Power Parity (PPP), then the nominal exchange rate will have to adjust to keep the real price of a comparable basket of goods from diverging across countries.

On the other hand, we might not think PPP holds, at least in the short run, and we might think that the nominal exchange rate cannot adjust freely. (A fixed exchange rate is the obvious reason, but it’s also possible that the forex markets could push the nominal exchange rate to some arbitrary level.) In that case, it’s the real exchange rate that is endogenous, so we can see changes in the price of comparable goods in one country relative to another. This is implicitly the causal structure that people have in mind when they argue that China is pursuing a mercantilist strategy by pegging its nominal exchange rate, that devaluation would improve current account balances in the European periphery, or that the US could benefit from a lower (nominal) dollar. Here the causal story runs from e_N to e_R.

Alternatively, maybe the price level is endogenous. This is less intuitive, but there’s at least one important story where it’s the case. Anti-inflation programs in a number of countries, especially in Latin America, have made use of a fixed exchange rate as a “nominal anchor.” The idea here is that in a small open economy, especially where high inflation has led to widespread use of a foreign currency as the unit of account, the real exchange rate is effectively fixed. So if the nominal exchange rate can also be effectively fixed, then, like it or not, the domestic price level P will have to be fixed as well. Here’s Jeffrey Sachs on the Bolivian stabilization:

The sudden end of a 60,000 percent inflation seems almost miraculous… Thomas Sargent (1986) argued that such a dramatic change in price inflation results from a sudden and drastic change in the public’s expectations of future government policies… I suggest, in distinction to Sargent, that the Bolivian experience highlights a different and far simpler explanation of the very rapid end of hyperinflations. By August 1985,… prices were set either explicitly or implicitly in dollars, with transactions continuing to take place in peso notes, at prices determined by the dollar prices converted at the spot exchange rate. Therefore, by stabilizing the exchange rate, domestic inflation could be made to revert immediately to the US dollar inflation rate. 

So here the causal story runs from e_N to P.

In the three cases so far, we implicitly assume that P* is fixed, or at least exogenous. This makes sense; since a single country is much smaller than the world as a whole, we don’t expect anything it does to affect the world price level much. So the last logical possibility, P* as the endogenous variable, might seem to lack a corresponding real world story. But an individual countries is not always so much smaller than the world as a whole, at least not if the individual country is the United States. It’s legitimate to ask whether a change in our price level or exchange rate might not show up as as inflation or deflation elsewhere. This is particularly likely if we are focusing on a bilateral relationship. For instance, it might well be that a devaluation of the dollar relative to the renminbi would simply (or mostly) produce corresponding deflation [2] in China, leaving the real exchange rate unchanged.

Here, of course, we have only one equation. But if we interpret it causally, that is already a model, and the question of “what adjusts?” can be rephrased as the choice between alternative model closures. With multiple-equation models, that choice gets trickier — and it can be tricky enough with one equation.

In my opinion, sensitivity to alternative model closures is at the heart of structuralist economics, and is the great methodological innovation of Keynes. The specific application that defines the General Theory is the model closure that endogenizes aggregate income — the interest rate, which was supposed to equilibrate savings and investment, is pinned down by the supply and demand of liquidity, so total income is what adjusts — but there’s a more general methodological principle. “Thinking like an economist,” that awful phrase, should mean being able to choose among different stories — different model closures — based on the historical context and your own interests. It should mean being able look at a complex social reality and judge which logical relationships represent the aspects of it you’re currently interested in, and which accounting identities are most relevant to the story you want to tell. Or as Keynes put it, economics should be thought of as

a branch of logic, a way of thinking … in terms of models, joined to the art of choosing models which are relevant to the contemporary world. … [The goal is] not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems.

Much of mainstream macroeconomics assumes there is a “true” model of the world. Connected to this, there’s an insistence — shared even by a lot of heterodox macro — on regarding some variables as being strictly exogenous and others as strictly endogenous, so that in every story causality runs the same way. In the canonical story, tastes, technology and endowments (one can’t help hearing: by the Creator) are perfectly fixed, and everything else is perfectly adjustable. [3]

Better to follow Keynes, and think about models as more or less useful for clarifying the logic of particular stories.

EDIT: Of course not everyone who recognizes the methodological distinction I’m making here agrees that the eclecticism of structuralism is an advantage. Here is my teacher Peter Skott (with Ben Zipperer):

The `heterodox’ tradition in macroeconomics contains a wide range of models. Kaleckian models treat the utilization rate as an accommodating variable, both in the short and the long run. Goodwin’s celebrated formalization of Marx, by contrast, take the utilization rate as fixed and looks at the interaction between employment and distribution. Distribution is also central to Kaldorian and Robinsonian theories which, like Goodwin, endogenize the profit share and take the utilization rate as structurally determined in the long run but, like the Kaleckians, view short-run variations in utilization as an intrinsic part of the cycle. The differences in these and other areas are important, and this diversity of views on core issues is no cause for celebration.

EDIT 2: Trygve Haavelmo, quoted by Leijonhufvud:

There is no reason why the form of a realistic model (the form of its equations) should be the same under all values of its variables. We must face the fact that the form of the model may have to be regarded as a function of the values of the variables involved. This will usually be the case if the values of some of the variables affect the basic conditions of choice under which the behavior equations in the model are derived.

That’s what I’m talking about. There is no “true” model of the economy. The behavioral relationships change depending where we are in economic space.

Also, Bruce Wilder has a long and characteristically thoughtful comment below. I don’t agree with everything he says — it seems a little too hopeless about the possibility of useful formal analysis even in principle — but it’s very worth reading.

[1] “Accounting identities don’t tell causal stories” is a bit like “correlation doesn’t imply causation.”Both statements are true in principle, but the cases we’re interested in are precisely the cases where we have some reason to believe that it’s not true. And for both statements, the converse does not hold. A causal story that violates accounting identities, or for which there is no corresponding correlation, has a problem.

[2] Or lower real wages, the same thing in this context.

[3] Or you sometimes get a hierarchy of “fast” and “slow” variables, where the fast ones are supposed to fully adjust before the slow ones change at all.

What’s the Matter with (Quasi-)Monetarism?

Let’s start from the top.

What is monetarism? As I see it, it’s a set of three claims. (1) There is a stable relationship between base money and the economically-relevant stock of money. [1] That is, there’s a stable relationship between outside money and inside money. (2) There is a stable velocity of money, so we can interpret the equation of exchange MV = PY (or MV = PT) as a behavioral relationship and not just an accounting identity. Since the first claim says that M is set exogenously by the monetary authority, causality in the equation runs from left to right. And (3), the LM aggregate supply curve is shaped like a backward L, so that changes in PY show up entire in Y when the economy is below capacity, and entirely in changes in P when it is at capacity.

In other words, (1) the central bank can control the supply of money; (2) the supply of money determines the level of nominal output; and (3) there is a single strictly optimal level of nominal output, without any tradeoffs. The implication is that monetary policy should be guided by a simple rule, that the money supply should grow at a fixed rate equal to (what we think is) the growth rate of potential output. Which is indeed, exactly what Friedman and other monetarists said.

You can relax (3) if you want — most monetarists would probably agree that in practice, disinflation is going to involve a period of depressed output. (Altho on the other hand, I’m pretty sure that when monetarism was officially adopted as the doctrine of the bank of England under Thatcher, it was claimed that slowing the growth of the money supply would control inflation without affecting growth at all. And the hedge-monetarism you run into today, that insists the huge growth in base money over the past few years could show up as hyperinflation without warning, seems to be implicitly assuming a backward-L shaped LM AS curve as well.) But basically, that’s the monetarist package.

So what’s wrong with this story? Here’s what:

The red line is base money, the blue line is broad money (M2), and the green line is nominal GDP. The monetarist story is that red moves blue, and blue moves green. Between 1990 and 2008, this story isn’t glaringly incompatible with the evidence. But since then? It’s clear that the money multiplier, as we normally talk about it, no longer has any economic reality. There might still be tools out there to control the money supply. But changing the stock of base money — the instrument of central banks, at least in theory, since the early 20th century — is no longer one of them. Monetary policy as we knew it is dead. The divergence between the blue and green lines is less dramatic in this graph, but if anything it’s even more damning. While output and prices lurched downward in the great Recession, the money supply just kept chugging along. Milton Friedman’s idea that stable growth of the money supply is a sufficient condition for stable growth of nominal GDP looks pretty definitively refuted.

So that’s monetarism, and what’s the matter with it. How about quasi-monetarism? What’s the difference from the unprefixed kind?

Some people would say, There is no difference. Quasi-monetarist is just what we call a New Keynesian who’s taken off his Keynes mask and admitted he was a Friedmanite all along. And let’s be honest, that’s sort of true. But it’s like one of those episodes in religious history where at some point the disciples have to acknowledge that, ok, the prophecies don’t seem to have exactly worked out. Which means we have to figure out what they really meant.

In this case, the core commitment is the idea that if PY is too low (we’re experiencing a recession and/or deflation) that means M is too low; if PY is too high (we’re experiencing inflation) that means M is too high. In other words, when we talk about insufficient aggregate demand, what we’re really talking about is just excess demand for money. And therefore, when we talk about policies to boost demand, we’re really just talking about policies to boost the money stock. (Nick Rowe, as usual, is admirably straightforward on this point.) But how to reconcile this with the graph above? You just have to replace some material entities with spiritual ones: The true M, or V, or both, is not visible to mortal eyes. Let’s say that velocity is exogenous but not stable. Then there is still a unique path of M that would guarantee both full employment and stable prices, but it can’t be characterized as a simple growth rate as Friedman hoped. Alternatively, maybe the problem is that the monetary authority can only control M clumsily, and can’t directly observe how far off it is. (This is the DeLong version of quasi-monetarism. The assets that count as M are always changing.) Then, there may still be the One True Growth Rate of M just as Friedman promised, but the monetary authority can’t reliably implement it. Or sublunary M and V could both depart from their platonic ideals. In any case, the answer is clear: Since it’s hard to get MV right, your rule should be to target a steady growth rate of PY (nominal GDP). Which is, indeed, exactly what the quasi-monetarists say. [2]

So what’s the alternative? I’ve been arguing that one alternative is to think of recessions as coordination failures, which could happen even in an economy without money. I’m honestly not sure if that’s going to turn out to be a productive direction to go in, or not. But in terms of the monetarist framework, the alternative is clear. Say that V is not only unstable, but endogenous. Specifically, say that it varies inversely with M. In this case, it remains true — as it must; it’s an accounting identity — that MV = PY. But nonetheless there is nothing you can do to M, that will affect P or Y. (This situation, by the way, is what Keynes meant by a liquidity trap. It wasn’t about the zero lower bound.)

This, I think, is what we actually observe, not just right now, but in general. “The” interest rate is the price of liquidity, that is, the price of money. [3] And what kinds of activity are sensitive to interest rates? Well, uh … none of them. None, anyway, except for housing. When an economic unit is deciding on the division of its income between currently-produced goods and services vs. money, the price at which they exchange just doesn’t seem to be much of a consideration. (Again, except — and it’s an important exception — when the decision takes the form of purchasing housing services from either an existing home, or a new one.) Which means that changes in M don’t have any good channel to produce changes in P or Y. In general, increases or decreases in M will just result in pro rata decreases or increases in V. Yes, it may be formally true that insufficient demand for goods equals excess demand for money; but it doesn’t matter if there’s no well-defined money demand function. A traditional Keynesian expenditure function (Z = A + cY) cannot be usefully simplified, as the quasi-monetarists would like, by thinking of it as a problem of maximizing the flow of consumption subject to some real balance constraint.

So, monetarism made some strong predictions. Quasi-monetarism admits that those predictions don’t hold up, but argues that the monetarist model is still the right one, we just can’t observe the variables in it as directly as early monetarists hoped. On some level, they may be right! But at some point, when the model gets too loosely coupled with reality, you’ll want to stop using it. Even if, in some sense, it isn’t wrong.

Which is all to say that, even if I can’t find a way to disprove it analytically, I just can’t accept the idea that the question of aggregate demand can be usefully reduced to the question of the supply of money.

[1] The simplest form of the first claim would be that the money multiplier is equal to one: Outside money is all the money there is. Something like this was supposed to be true under the gold standard, tho as the great Robert Triffin points out, it wasn’t really. Over at Windyanabasis, rsj claims that Krugman, a closet quasi-monetarist, implicitly makes this assumption.

[2] In practice, despite the tone of this post, I’m not entirely sure they’re wrong. More generally, Nick Rowe’s clear and thorough posts on this set of questions are essential reading.

[3] I’ve learned from  Bob Pollin never to write that phrase without the quotes. There are lots of interest rates, and it matters.

Net and Gross, or What We Can and Cannot Learn from Balance Sheets

One of the less acknowledged of the secret sins of economists, it seems to me, is the failure to distinguish between net and gross quantities, or to treat the net numbers if they were all that mattered. Case in point, the issue of deleveraging, where the good guys — the anti-austerians — are trying to get an accounting-identity argument to do more work than it it’s capable of. A good example is this post from Peter Dorman (which Krugman liked), which points out that in a closed economy one agent’s debt is always another agent’s asset, and total consumption must equal total income. So the only way that one agent can reduce its net liabilities is for another’s to increase, just as the only way some agents can spend less than their income is for others to spend more. In this sense increased public debt is just the flipside of private-sector deleveraging; arguments that the public sector should reduce its debt along with the private sector are incoherent. QED, right? Except, this argument proves too much. It’s true that one agent’s net financial position can’t improve unless another’s gets worse. But the same accounting logic also means that financial claims across the whole economy always sum to zero. Total net worth is always equal to the sum of tangible assets, no matter what happens on the financial side. [1] So it’s not clear what leveraging and develeraging could even mean in these terms. So, since the words evidently do mean something, it seems they’re not being used in those terms. It seems to me that when people talk about (de)leveraging, they are almost always talking about gross financial claims, not net, relative to income. A unit that adds $1,000 in debt and acquires a financial asset valued at $1,000 is more leveraged than it was before. And in this gross sense, it is perfectly possible for the public and private sector to simultaneously deleverage. Consider the following very simple economy, with just two agents:

Income Assets Liabilities Net Worth
A 1 4 3 1
B 1 5 2 3
Total 2 9 5 4
Income Assets Liabilities Net Worth
A 1 3 2 1
B 1 4 1 3
Total 2 7 3 4

The transition from T1 to T2 involves simultaneous deleveraging — in the economically meaningful sense — by both the agents in the economy, and no national accounting identities are violated. What would this look like in practice? To some extent, it could simply mean netting out offsetting financial claims, but that only really works within the financial sector; nonfinancial actors don’t generally hold financial assets and liabilities at the same time without some good institutional reason. (A firm may both receive and extend trade credit, but those two lines on the balance sheet can’t be netted out unless we want to go back to a cash-on-the-barrelhead economy. A typical middle-class household has both retirement savings and a mortgage and student-loan debt; both the borrowing and saving are sufficiently subsidized and tax-favored that it makes sense to add to the IRA rather than paying off the debt. [2]) To the extent that this kind of deleveraging does take place within the nonfinancial sector, it requires that units reduce their gross saving, i.e. their acquisition of financial assets — a suggestion that will seem even more paradoxical to conventional wisdom than the claim that private-sector deleveraging requires increased public debt. [3] But there’s another approach. Most borrowing by households and nonfinancial firms and households is undertaken to finance the acquisition of a tangible asset — in the table above, we should really divide the assets column into tangible assets and financial assets. For the low net worth units, most assets are tangible; for middle-class households, the house is by far the biggest asset, while property, plant and equipment is generally the biggest item on the asset side of a nonfinancial firm’s balance sheet. So the most natural way for the private sector and the public sector to deleverage is through a transfer of tangible assets from debtor to creditor units, combined with the extinction of the debts associated with the assets. This is, in essence, what privatization of public assets is supposed to do, when the IMF imposes it as part of a structural adjustment program. And more to the point, it’s what the foreclosure process, in its herky-jerky way, is doing in the housing market. At the end of the road, there’s a lot less mortgage debt — and a lot more big suburban landlords. [4] And the private sector has reduced its leverage, without any increase in the public sector’s. (Of course, we could just extinguish the debt and skip the asset-transfer part. But that default could be a means of deleveraging is one of those thoughts you’re not allowed to have.) Now, all this said, I completely agree with Dorman’s conclusion, that reducing public debt would hinder rather than help deleveraging. (Or rather, what he thinks is his conclusion; the real logic of his argument is that nothing can help or hinder deleveraging, since — like motion — it does not exist.) But the reason has nothing to do with balance sheets. It is because I believe that fiscal consolidation will reduce aggregate income — the denominator in leverage. I reckon Dorman (and Krugman) would agree. But this an empirical claim, not one that can be deduced from national accounting identities.
[1] Or the sum of tangible assets and base money, if you don’t treat the latter as a liability of the government. This is a question that gets people remarkably worked up, but it’s not important to this argument. (Or to any other, as far as I can tell.) [2] Actually I suspect many middle-class households are saving more than is rational — they’re acquiring financial assets when paying down debt would have a higher return. But anyone who knows me knows how comically unsuited I am to have opinions on anyone else’s personal finances. [3] Reducing debt and and expenditure simultaneously doesn’t help, since one unit’s expenditure is another’s income. For financial deleveraging to work, people really do have to save less. [4] Who might or might not end up being the banks themselves.