Saving and Borrowing: A Response to Klein

Matthew Klein has a characteristically thoughtful post disagreeing with my new paper on income distribution and debt. I think his post has some valid arguments, but also, from my point of view, some misunderstandings. In any case, this is the conversation we should be having.

I want to respond on the specific points Klein raises. But first, in this post, I want to clarify some background conceptual issues. In particular, I want to explain why I think it’s unhelpful to think about the issues of debt and demand in terms of saving.

Klein talks a great deal about saving in his post. Like most people writing on these issues, he treats the concepts of rising debt-income ratios, higher borrowing and lower saving as if they were interchangeable. In common parlance, the question “why have households borrowed more?” is equivalent to “why have households saved less?” And either way, the spending that raises debt and reduces saving, is also understood to contribute to aggregate demand.

This conception is laid out in Figure 1 below. These are accounting rather than causal relationships. A minus sign in the link means the relationship is negative.


We start with households’ decision to consume more or less out of their income. Implicitly, all household outlays are for consumption, or at least, this is the only flow of household spending that varies significantly. An additional dollar of household consumption spending means an additional dollar of demand for goods and services; it also means a dollar less of savings. A dollar less of savings equals a dollar more of borrowing. More borrowing obviously means higher debt, or — equivalently in this view — a higher debt-GDP ratio.

There’s nothing particularly orthodox or heterodox about this way of looking at things. You can hear the claim that a rise in the household debt-income ratio contributes more or less one for one to aggregate demand as easily from Paul Krugman as from Steve Keen. Similarly, the idea that a decline in savings rates is equivalent to an increase in borrowing is used by Marxists as well as by mainstream economists, not to mention eclectic business journalists like Klein. Of course no one actually says “we assume that household assets are fixed or nonexistent.” But implicitly that’s what you’re doing when you treat the question of what has happened to household borrowing as if it were the equivalent of what has happened to household saving.

There is nothing wrong, in principle, with thinking in terms of the logic of Figure 1, or constructing models on that basis. Social science is impossible without abstraction. It’s often useful, even necessary, to think through the implications of a small subset of the relationships between economic variables, while ignoring the rest. But when we turn to  the concrete historical changes in macroeconomic quantities like household debt and aggregate demand in the US, the ceteris paribus condition is no longer available. We can’t reason in terms of the hypothetical case where all else was equal. We have to take into account all the factors that actually did contribute to those changes.

This is one of the main points of the debt-inequality paper, and of my work with Arjun Jayadev on household debt. In reality, much of the historical variation in debt-income ratios and related variables cannot be explained in terms of the factors in Figure 1. You need something more like Figure 2.

Figure 2 shows a broader set of factors that we need to include in a historical account of household sector balances. I should emphasize, again, that this is not about cause and effect. The links shown in the diagram are accounting relationships. You cannot explain the outcomes at the bottom without the factors shown here. [1] I realize it looks like a lot of detail. But this is not complexity for complexity’s sake. All the links shown in Figure 2 are quantitatively important.

The dark black links are the same as in the previous diagram. It is still true that higher household consumption spending reduces saving and raises aggregate demand, and contributes to lower saving and higher borrowing, which in turn contributes to lower net wealth and an increase in the debt ratio. Note, though, that I’ve separated saving from balance sheet improvement. The economic saving used in the national accounts is quite different from the financial saving that results in changes in the household balance sheet.

In addition to the factors the debt-demand story of Figure 1 focuses on, we also have to consider: various actual and imputed payment flows that the national accounts attribute to the household sector, but which do not involve any money payments to or fro households (blue); the asset side of household balance sheets (gray); factors other than current spending that contribute to changes in debt-income ratios (red); and change in value of existing assets (cyan).

The blue factors are discussed in Section 5 of the debt-distribution paper. There is a much fuller discussion in a superb paper by Barry Cynamon and Steve Fazzari, which should be read by anyone who uses macroeconomic data on household income and consumption. Saving, remember, is defined as the difference between income and consumption. But as Cynamon and Fazzari point out, on the order of a quarter of both household income and consumption spending in the national accounts is accounted for by items that involve no actual money income or payments for households, and thus cannot affect household balance sheets.

These transactions include, first, payments by third parties for services used by households, mainly employer-paid premiums for health insurance and payments to healthcare providers by Medicaid and Medicare. These payments are counted as both income and consumption spending for households, exactly as if Medicare were a cash transfer program that recipients then chose to use to purchase healthcare. If we are interested in changes in household balance sheets, we must exclude these payments, since they do not involve any actual outlays by households; but they still do contribute to aggregate demand. Second, there are imputed purchases where no money really changes hands at all.  The most important of these are owners’ equivalent rent that homeowners are imputed to pay to themselves, and the imputed financial services that households are supposed to purchase (paid for with imputed interest income) when they hold bank deposits and similar assets paying less than the market interest rate. Like the third party payments, these imputed interest payments are counted as both income and expenditure for households. Owners’ equivalent rent is also added to household income, but net of mortgage interest, property taxes and maintenance costs. Finally, the national accounts treat the assets of pension and similar trust funds as if they were directly owned by households. This means that employer contributions and asset income for these funds are counted as household income (and therefore add to measured saving) while benefit payments are not.

These items make up a substantial part of household payments as recorded in the national accounts – Medicare, Medicaid and employer-paid health premiums together account for 14 percent of official household consumption; owners’ equivalent rent accounts for another 10 percent; and imputed financial services for 4 percent; while consolidating pension funds with households adds about 2 percent to household income (down from 5 percent in the 1980s). More importantly, the relative size of these components has changed substantially in the past generation, enough to substantially change the picture of household consumption and income.

Incidentally, Klein says I exclude all healthcare spending in my adjusted consumption series. This is a misunderstanding on his part. I exclude only third-party health care spending — healthcare spending by employers and the federal government. I’m not surprised he missed this point, given how counterintuitive it is that Medicare is counted as household consumption spending in the first place.

This is all shown in Figure 3 below (an improved version of the paper’s Figure 1):

The two dotted lines remove public and employer payments for healthcare, respectively, from household consumption. As you can see, the bulk of the reported increase in household consumption as a share of GDP is accounted for by healthcare spending by units other than households. The gray line then removes owners’ equivalent rent. The final, heavy black line removes imputed financial services, pension income net of benefits payments, and a few other, much smaller imputed items. What we are left with is monetary expenditure for consumption by households. The trend here is essentially flat since 1980; it is simply not the case that household consumption spending has increased as a share of GDP.

So Figure 3 is showing the contributions of the blue factors in Figure 2. Note that while these do not involve any monetary outlay by households and thus cannot affect household balance sheets or debt, they do all contribute to measured household saving.

The gray factors involve household assets. No one denies, in principle, that balance sheets have both an asset side and a liability side; but it’s striking how much this is ignored in practice, with net and gross measures used interchangeably. In the first place, we have to take into account residential investment. Purchase of new housing is considered investment, and does not reduce measured saving; but it does of course involve monetary outlay and affects household balance sheets just as consumption spending does. [2] We also have take into account net acquisition of financial assets. An increase in spending relative to income moves household balance sheets toward deficit; this may be accommodated by increased borrowing, but it can just as well be accommodated by lower net purchases of financial assets. In some cases, higher desired accumulation of financial asset can also be an autonomous factor requiring balance sheet adjustment. (This is probably more important for other sectors, especially state and local governments, than for households.) The fact that adjustment can take place on the asset as well as the liability side is another reason there is no necessary connection between saving and debt growth.

Net accumulation of financial assets affects household borrowing, but not saving or aggregate demand. Residential investment also does not reduce measured saving, but it does increase aggregate demand as well as borrowing. The red line in Figure 3 adds residential investment by households to adjusted consumption spending. Now we can see that household spending on goods and services did indeed increase during the housing bubble period – conventional wisdom is right on that point. But this was a  spike of limited duration, not the secular increase that the standard consumption figures suggest.

Again, this is not just an issue in principle; historical variation in net acquisition of assets by the household sector is comparable to variation in borrowing. The decline in observed savings rates in the 1980s, in particular, was much more reflected in slower acquisition of assets than faster growth of debt. And the sharp fall in saving immediately prior to the great recession in part reflects the decline in residential investment, which peaked in 2005 and fell rapidly thereafter.

The cyan item is capital gains, the other factor, along with net accumulation, in growth of assets and net wealth. For the debt-demand story this is not important. But in other contexts it is. As I pointed out in my Crooked Timber post on Piketty, the growth in capital relative to GDP in the US is entirely explained by capital gains on existing assets, not by the accumulation dynamics described by his formula “r > g”.

Finally, the red items in Figure 2 are factors other than current spending and income that affect the debt-income ratio. Arjun Jayadev and I call this set of factors “Fisher dynamics,” after Irving Fisher’s discussion of them in his famous paper on the Great Depression. Interest payments reduce measured saving and shift balance sheets toward deficit, just like consumption; but they don’t contribute to aggregate demand. Defaults or charge-offs reduce the outstanding stock of debt, without affecting demand or measured savings. Like capital gains, they are a change in a stock without any corresponding flow. [3] Finally, the debt-income ratio has a denominator as well as a numerator; it can be raised just as well by slower nominal income growth as by higher borrowing.

These factors are the subject of two papers you can find here and here. The bottom line is that a large part of historical changes in debt ratios — including the entire long-term increase since 1980 — are the result of the items shown in red here.

So what’s the point of all this?

First, borrowing is not the opposite of saving. Not even roughly. Matthew Klein, like most people, immediately translates rising debt into declining saving. The first half of his post is all about that. But saving and debt are very different things. True, increased consumption spending does reduce saving and increase debt, all else equal. But saving also depends on third party spending and imputed spending and income that has no effect on household balance sheets. While debt growth depends, in addition to saving, on residential investment, net acquisition of financial assets, and the rate of chargeoffs; if we are talking about the debt-income ratio, as we usually are, then it also depends on nominal income growth. And these differences matter, historically. If you are interested in debt and household expenditure, you have to look at debt and expenditure. Not saving.

Second, when we do look at expenditure by households, there is no long-term increase in consumption. Consumption spending is flat since 1980. Housing investment – which does involve outlays by households and may require debt financing – does increase in the late 1990s and early 2000s, before falling back. Yes, this investment was associated with a big rise in borrowing, and yes, this borrowing did come significantly lower in the income distribution that borrowing in most periods. (Though still almost all in the upper half.) There was a debt-financed housing bubble. But we need to be careful to distinguish this episode from the longer-term rise in household debt, which has different roots.


[1] Think of it this way: If I ask why the return on an investment was 20 percent, there is no end to causal factors you can bring in, from favorable macroeconomic conditions to a sound business plan to your investing savvy or inside knowledge. But in accounting terms, the return is always explained by the income and the capital gains over the period. If you know both those components, you know the return; if you don’t, you don’t. The relationships in the figure are the second kind of explanation.

[2] Improvement of existing housing is also counted as investment, as are brokers’ commissions and other ownership transfer costs. This kind of spending will absorb some part of the flow of mortgage financing to the household sector — including the cash-out refinancing of the bubble period — but I haven’t seen an estimate of how much.

[3] There’s a strand of heterodox macro called “stock-flow consistent modeling.” Insofar as this simply means macroeconomics that takes aggregate accounting relationships seriously, I’m very much in favor of it. Social accounting matrices (SAMs) are an important and underused tool. But it’s important not to take the name too literally — economic reality is not stock-flow consistent!


Two Papers in Progress

There are two new papers on the articles page on this site. Both are work in progress – they haven’t been submitted anywhere yet.


[I’ve taken the debt-distribution paper down. It’s being revised.]

The Evolution of State-Local Balance Sheets in the US, 1953-2013


The first paper, which I presented in January in Chicago, is a critical assessment of the idea of a close link between income distribution and household debt. The idea is that rising debt is the result of rising inequality as lower-income households borrowed to maintain rising consumption standards in the face of stagnant incomes; this debt-financed consumption was critical to supporting aggregate demand in the period before 2008. This story is often associated with Ragnuram Rajan and Mian and Sufi but is also widely embraced on the left; it’s become almost conventional wisdom among Post Keynesian and Marxist economists. In my paper, I suggest some reasons for skepticism. First, there is not necessarily a close link between rising aggregate debt ratios and higher borrowing, and even less with higher consumption. Debt ratios depend on nominal income growth and interest payments as well as new borrowing, and debt mainly finances asset ownership, not current consumption. Second, aggregate consumption spending has not, contrary to common perceptions, risen as a share of GDP; it’s essentially flat since 1980. The apparent rise in the consumption share is entirely due to the combination of higher imputed noncash expenditure, such as owners’ equivalent rent; and third party health care spending (mostly Medicare). Both of these expenditure flows are  treated as household consumption in the national accounts. But neither involves cash outlays by households, so they cannot affect household balance sheets. Third, household debt is concentrated near the top of the income distribution, not the bottom. Debt-income ratios peak between the 85th and 90th percentiles, with very low ratios in the lower half of the distribution. Most household debt is owed by the top 20 percent by income. Finally, most studies of consumption inequality find that it has risen hand-in-hand with income inequality; it appears that stagnant incomes for most households have simply meant stagnant living standards. To the extent demand has been sustained by “excess” consumption, it was more likely by the top 5 percent.

The paper as written is too polemical. I need to make the tone more neutral, tentative, exploratory. But I think the points here are important and have not been sufficiently grappled with by almost anyone claiming a strong link between debt and distribution.

The second paper is on state and local debt – I’ve blogged a bit about it here in the past few months. The paper uses budget and balance sheet data from the census of governments to make two main points. First, rising state and local government debt does not imply state and local government budget deficits. higher debt does not imply higher deficits: Debt ratios can also rise either because nominal income growth slows, or because governments are accumulating assets more rapidly. For the state and local sector as a whole, both these latter factors explain more of the rise in debt ratios than does the fiscal balance. (For variation in debt ratios across state governments, nominal income growth is not important, but asset accumulation is.) Second, despite balanced budget requirements, state and local governments do show substantial variation in fiscal balances, with the sector as a whole showing deficits and surpluses up to almost one percent of GDP. But unlike the federal government, the state and local governments accommodate fiscal imbalances entirely by varying the pace of asset accumulation. Credit-market borrowing does not seem to play any role — either in the aggregate or in individual states — in bridging gaps between current expenditure and revenue.

I will try to blog some more about both these papers in the coming days. Needless to say, comments are very welcome.

Varieties of the Phillips Curve

In this post, I first talk about a variety of ways that we can formalize the relationship between wages, inflation and productivity. Then I talk briefly about why these links matter, and finally how, in my view, we should think about the existence of a variety of different possible relationships between these variables.


My Jacobin piece on the Fed was, on a certain abstract level, about varieties of the Phillips curve. The Phillips curve is any of a family graphs with either unemployment or “real” GDP on the X axis, and either the level or the change of nominal wages or the level of prices or the level or change of inflation on the Y axis. In any of the the various permutations (some of which naturally are more common than others) this purports to show a regular relationship between aggregate demand and prices.

This apparatus is central to the standard textbook account of monetary policy transmission. In this account, a change in the amount of base money supplied by the central bank leads to a change in market interest rates. (Newer textbooks normally skip this part and assume the central bank sets “the” interest rate by some unspecified means.) The change in interest rates  leads to a change in business and/or housing investment, which results via a multiplier in a change in aggregate output. [1] The change in output then leads to a change in unemployment, as described by Okun’s law. [2] This in turn leads to a change in wages, which is passed on to prices. The Phillips curve describes the last one or two or three steps in this chain.

Here I want to focus on the wage-price link. What are the kinds of stories we can tell about the relationship between nominal wages and inflation?


The starting point is this identity:

(1) w = y + p + s

That is, the percentage change in nominal wages (w) is equal to the sum of the percentage changes in real output per worker (y; also called labor productivity), in the price level (p, or inflation) and in the labor share of output (s). [3] This is the essential context for any Phillips curve story. This should be, but isn’t, one of the basic identities in any intermediate macroeconomics textbook.

Now, let’s call the increase in “real” or inflation-adjusted wages r. [4] That gives us a second, more familiar, identity:

(2) r = w – p

The increase in real wages is equal to the increase in nominal wages less the inflation rate.

As always with these kinds of accounting identities, the question is “what adjusts”? What economic processes ensure that individual choices add up in a way consistent with the identity? [5]

Here we have five variables and two equations, so three more equations are needed for it to be determined. This means there are large number of possible closures. I can think of five that come up, explicitly or implicitly, in actual debates.

Closure 1:

First is the orthodox closure familiar from any undergraduate macroeconomics textbook.

(3a) w = pE + f(U); f’ < 0

(4a) y = y*

(5a) p = w – y

Equation 3a says that labor-market contracts between workers and employers result in nominal wage increases that reflect expected inflation (pE) plus an additional increase, or decrease, that reflects the relative bargaining power of the two sides. [6] The curve described by f is the Phillips curve, as originally formulated — a relationship between the unemployment rate and the rate of change of nominal wages. Equation 4a says that labor productivity growth is given exogenously, based on technological change. 5a says that since prices are set as a fixed markup over costs (and since there is only labor and capital in this framework) they increase at the same rate as unit labor costs — the difference between the growth of nominal wages and labor productivity.

It follows from the above that

(6a) w – p = y


(7a) s = 0

Equation 6a says that the growth rate of real wages is just equal to the growth of average labor productivity. This implies 7a — that the labor share remains constant. Again, these are not additional assumptions, they are logical implications from closing the model with 3a-5a.

This closure has a couple other implications. There is a unique level of unemployment U* such that w = y + p; only at this level of unemployment will actual inflation equal expected inflation. Assuming inflation expectations are based on inflation rates realized in the past, any departure from this level of unemployment will cause inflation to rise or fall without limit. This is the familiar non-accelerating inflation rate of unemployment, or NAIRU. [7] Also, an improvement in workers’ bargaining position, reflected in an upward shift of f(U), will do nothing to raise real wages, but will simply lead to higher inflation. Even more: If an inflation-targetting central bank is able to control the level of output, stronger bargaining power for workers will leave them worse off, since unemployment will simply rise enough to keep nominal wage growth in line with y*  and the central bank’s inflation target.

Finally, notice that while we have introduced three new equations, we have also introduced a new variable, pE, so the model is still underdetermined. This is intended. The orthodox view is that the same set of “real“ values is consistent with any constant rate of inflation, whatever that rate happens to be. It follows that a departure of the unemployment rate from U* will cause a permanent change in the inflation rate. It is sometimes suggested, not quite logically, that this is an argument in favor of making price stability the overriding goal of policy. [8]

If you pick up an undergraduate textbook by Carlin and Soskice, Krugman and Wells, or Blanchard, this is the basic structure you find. But there are other possibilities.

Closure 2: Bargaining over the wage share

A second possibility is what Anwar Shaikh calls the “classical” closure. Here we imagine the Phillips curve in terms of the change in the wage share, rather than the change in nominal wages.

(3b) s =  f(U); f’ < 0

(4b) y = y*

(5b) p = p*

Equation 3b says that the wage share rises when unemployment is low, and falls when unemployment is high. In this closure, inflation as well as labor productivity growth are fixed exogenously. So again, we imagine that low unemployment improves the bargaining position of workers relative to employers, and leads to more rapid wage growth. But now there is no assumption that prices will follow suit, so higher nominal wages instead translate into higher real wages and a higher wage share. It follows that:

(6b) w = f(U) + p + y

Or as Shaikh puts it, both productivity growth and inflation act as shift parameters for the nominal-wage Phillips curve. When we look at it this way, it’s no longer clear that there was any breakdown in the relationship during the 1970s.

If we like, we can add an additional equation making the change in unemployment a function of the wage share, writing the change in unemployment as u.

(7b) u = g(s); g’ > 0 or g’ < 0

If unemployment is a positive function of the wage share (because a lower profit share leads to lower investment and thus lower demand), then we have the classic Marxist account of the business cycle, formalized by Goodwin. But of course, we might imagine that demand is “wage-led” rather than “profit-led” and make U a negative function of the wage share — a higher wage share leads to higher consumption, higher demand, higher output and lower unemployment. Since lower unemployment will, according to 3b, lead to a still higher wage share, closing the model this way leads to explosive dynamics — or more reasonably, if we assume that g’ < 0 (or impose other constraints), to two equilibria, one with a high wage share and low unemployment, the other with high unemployment and a low wage share. This is what Marglin and Bhaduri call a “stagnationist” regime.

Let’s move on.

Closure 3: Real wage fixed.

I’ll call this the “Classical II” closure, since it seems to me that the assumption of a fixed “subsistence” wage is used by Ricardo and Malthus and, at times at least, by Marx.

(3c) w – p = 0

(4c) y = y*

(5c) p = p*

Equation 3c says that real wages are constant the change in nominal wages is just equal to the change in the price level. [9] Here again the change in prices and in labor productivity are given from outside. It follows that

(6c) s = -y

Since the real wage is fixed, increases in labor productivity reduce the wage share one for one. Similarly, falls in labor productivity will raise the wage share.

This latter, incidentally, is a feature of the simple Ricardian story about the declining rate of profit. As lower quality land if brought into use, the average productivity of labor falls, but the subsistence wage is unchanged. So the share of output going to labor, as well as to landlords’ rent, rises as the profit share goes to zero.

Closure 4:

(3d) w =  f(U); f’ < 0

(4d) y = y*

(5d) p = p*

This is the same as the second one except that now it is the nominal wage, rather than the wage share, that is set by the bargaining process. We could think of this as the naive model: nominal wages, inflation and productivity are all just whatever they are, without any regular relationships between them. (We could even go one step more naive and just set wages exogenously too.) Real wages then are determined as a residual by nominal wage growth and inflation, and the wage share is determined as a residual by real wage growth and productivity growth. Now, it’s clear that this can’t apply when we are talking about very large changes in prices — real wages can only be eroded by inflation so far.  But it’s equally clear that, for sufficiently small short-run changes, the naive closure may be the best we can do. The fact that real wages are not entirely a passive residual, does not mean they are entirely fixed; presumably there is some domain over which nominal wages are relatively fixed and their “real” purchasing power depends on what happens to the price level.

Closure 5:

One more.

(3e) w =  f(U) + a pE; f’ < 0; 0 < a < 1

(4e) y = b (w – p); 0 < b < 1

(5e) p =  c (w – y); 0 < c < 1

This is more generic. It allows for an increase in nominal wages to be distributed in some proportion between higher inflation, an increase in the wage share,  and faster productivity growth. The last possibility is some version of Verdoorn’s law. The idea that scarce labor, or equivalently rising wages, will lead to faster growth in labor productivity is perfectly admissible in an orthodox framework.  But somehow it doesn’t seem to make it into policy discussions.

In other word, lower unemployment (or a stronger bargaining position for workers more generally) will lead to an increase in the nominal wage. This will in turn increase the wage share, to the extent that it does not induce higher inflation and/or faster productivity growth:

(6e) s = (1  – b – c) w

This closure includes the first two as special cases: closure 1 if we set a = 0, b = 0, and c = 1, closure 2 if we set a = 1, b = 0, and c < 1. It’s worth framing the more general case to think clearly about the intermediate possibilities. In Shaikh’s version of the classical view, tighter labor markets are passed through entirely to a higher labor share. In the conventional view, they are passed through entirely to higher inflation. There is no reason in principle why it can’t be some to each, and some to higher productivity as well. But somehow this general case doesn’t seem to get discussed.

Here is a typical example  of the excluded middle in the conventional wisdom: “economic theory suggests that increases in labor costs in excess of productivity gains should put upward pressure on prices; hence, many models assume that prices are determined as a markup over unit labor costs.” Notice the leap from the claim that higher wages put some pressure on prices, to the claim that wage increases are fully passed through to higher prices. Or in terms of this last framework: theory suggests that b should be greater than zero, so let’s assume b is equal to one. One important consequence is to implicitly exclude the possibility of a change in the wage share.


So what do we get from this?

First, the identity itself. On one level it is obvious. But too many policy discussions — and even scholarship — talk about various forms of the Phillips curve without taking account of the logical relationship between wages, inflation, productivity and factor shares. This is not unique to this case, of course. It seems to me that scrupulous attention to accounting relationships, and to logical consistency in general, is one of the few unambiguous contributions economists make to the larger conversation with historians and other social scientists. [10]

For example: I had some back and forth with Phil Pilkington in comments and on twitter about the Jacobin piece. He made some valid points. But at one point he wrote: “Wages>inflation + productivity = trouble!” Now, wages > inflation + productivity growth just means, an increasing labor share. It’s two ways of saying the same thing. But I’m pretty sure that Phil did not intend to write that an increase in the labor share always means trouble. And if he did seriously mean that, I doubt one reader in a hundred would understand it from what he wrote.

More consequentially, austerity and liberalization are often justified by the need to prevent “real unit labor costs” from rising. What’s not obvious is that “real unit labor costs” is simply another word for the labor share. Since by definition the change real unit labor costs is just the change in nominal wages less sum of inflation and productivity growth. Felipe and Kumar make exactly this point in their critique of the use of unit labor costs as a measure of competitiveness in Europe: “unit labor costs calculated with aggregate data are no more than the economy’s labor share in total output multiplied by the price level.” As they note, one could just as well compute “unit capital costs,” whose movements would be just the opposite. But no one ever does, instead they pretend that a measure of distribution is a measure of technical efficiency.

Second, the various closures. To me the question of which behavioral relations we combine the identity with — that is, which closure we use — is not about which one is true, or best in any absolute sense. It’s about the various domains in which each applies. Probably there are periods, places, timeframes or policy contexts in which each of the five closures gives the best description of the relevant behavioral links. Economists, in my experience, spend more time working out the internal properties of formal systems than exploring rigorously where those systems apply. But a model is only useful insofar as you know where it applies, and where it doesn’t. Or as Keynes put it in a quote I’m fond of, the purpose of economics is “to provide ourselves with an organised and orderly method of thinking out particular problems” (my emphasis); it is “a way of thinking … in terms of models joined to the art of choosing models which are relevant to the contemporary world.” Or in the words of Trygve Haavelmo, as 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.

I might even go a step further. It’s not just that to use a model we need to think carefully about the domain over which it applies. It may even be that the boundaries of its domain are the most interesting thing about it. As economists, we’re used to thinking of models “from the inside” — taking the formal relationships as given and then asking what the world looks like when those relationships hold. But we should also think about them “from the outside,” because the boundaries within which those relationships hold are also part of the reality we want to understand. [11] You might think about it like laying a flat map over some curved surface. Within a given region, the curvature won’t matter, the flat map will work fine. But at some point, the divergence between trajectories in our hypothetical plane and on the actual surface will get too large to ignore. So we will want to have a variety of maps available, each of which minimizes distortions in the particular area we are traveling through — that’s Keynes’ and Haavelmo’s point. But even more than that, the points at which the map becomes unusable, are precisely how we learn about the curvature of the underlying territory.

Some good examples of this way of thinking are found in the work of Lance Taylor, which often situates a variety of model closures in various particular historical contexts. I think this kind of thinking was also very common in an older generation of development economists. A central theme of Arthur Lewis’ work, for example, could be thought of in terms of poor-country labor markets that look  like what I’ve called Closure 3 and rich-country labor markets that look like Closure 5. And of course, what’s most interesting is not the behavior of these two systems in isolation, but the way the boundary between them gets established and maintained.

To put it another way: Dialectics, which is to say science, is a process of moving between the concrete and the abstract — from specific cases to general rules, and from general rules to specific cases. As economists, we are used to grounding concrete in the abstract — to treating things that happen at particular times and places as instances of a universal law. The statement of the law is the goal, the stopping point. But we can equally well ground the abstract in the concrete — treat a general rule as a phenomenon of a particular time and place.




[1] In graduate school you then learn to forget about the existence of businesses and investment, and instead explain the effect of interest rates on current spending by a change in the optimal intertemporal path of consumption by a representative household, as described by an Euler equation. This device keeps academic macroeconomics safely quarantined from contact with discussion of real economies.

[2] In the US, Okun’s law looks something like Delta-U = 0.5(2.5 – g), where Delta-U is the change in the unemployment rate and g is inflation-adjusted growth in GDP. These parameters vary across countries but seem to be quite stable over time. In my opinion this is one of the more interesting empirical regularities in macroeconomics. I’ve blogged about it a bit in the past  and perhaps will write more in the future.

[3] To see why this must be true, write L for total employment, Z for the level of nominal GDP, Y for per-capita GDP, W for the average wage, and P for the price level. The labor share S is by definition equal to total wages divided by GDP:

S = WL / Z

Real output per worker is given by

Y = (Z/P) / L

Now combine the equations and we get W = P Y S. This is in levels, not changes. But recall that small percentage changes can be approximated by log differences. And if we take the log of both sides, writing the log of each variable in lowercase, we get w = y + p + s. For the kinds of changes we observe in these variables, the approximation will be very close.

[4] I won’t keep putting “real” in quotes. But it’s important not to uncritically accept the dominant view that nominal quantities like wages are simply reflections of underlying non-monetary magnitudes. In fact the use of “real” in this way is deeply ideological.

[5] A discovery that seems to get made over and over again, is that since an identity is true by definition, nothing needs to adjust to maintain its equality. But it certainly does not follow, as people sometimes claim, that this means you cannot use accounting identities to reason about macroeconomic outcomes. The point is that we are always using the identities along with some other — implicit or explicit — claims about the choices made by economic units.

[6] Note that it’s not necessary to use a labor supply curve here, or to make any assumption about the relationship between wages and marginal product.

[7] Often confused with Milton Friedman’s natural rate of unemployment. But in fact the concepts are completely different. In Friedman’s version, causality runs the other way, from the inflation rate to the unemployment rate. When realized inflation is different from expected inflation, in Friedman’s story, workers are deceived about the real wage they are being offered and so supply the “wrong” amount of labor.

[8] Why a permanently rising price level is inconsequential but a permanently rising inflation rate is catastrophic, is never explained. Why are real outcomes invariant to the first derivative of the price level, but not to the second derivative? We’re never told — it’s an article of faith that money is neutral and super-neutral but not super-super-neutral. And even if one accepts this, it’s not clear why we should pick a target of 2%, or any specific number. It would seem more natural to think inflation should follow a random walk, with the central bank holding it at its current level, whatever that is.

[9] We could instead use w – p = r*, with an exogenously given rate of increase in real wages. The logic would be the same. But it seems simpler and more true to the classics to use the form in 3c. And there do seem to be domains over which constant real wages are a reasonable assumption.

[10] I was just starting grad school when I read Robert Brenner’s long article on the global economy, and one of the things that jumped out at me was that he discussed the markup and the wage share as if they were two independent variables, when of course they are just two ways of describing the same thing. Using s still as the wage share, and m as the average markup of prices over wages, s = 1 / (1 + m). This is true by definition (unless there are shares other than wages or profits, but none such figure in Brenner’s analysis). The markup may reflect the degree of monopoly power in product markets while the labor share may reflect bargaining power within the firm, but these are two different explanations of the same concrete phenomenon. I like to think that this is a mistake an economist wouldn’t make.

[11] The Shaikh piece mentioned above is very good. I should add, though, the last time I spoke to Anwar, he criticized me for “talking so much about the things that have changed, rather than the things that have not” — that is, for focusing so much on capitalism’s concrete history rather than its abstract logic. This is certainly a difference between Shaikh’s brand of Marxism and whatever it is I do. But I’d like to think that both approaches are called for.


EDIT: As several people pointed out, some of the equations were referred to by the wrong numbers. Also, Equation 5a and 5e had inflation-expectation terms in them that didn’t belong. Fixed.

EDIT 2: I referred to an older generation of development economics, but I think this awareness that the territory requires various different maps, is still more common in development than in most other fields. I haven’t read Dani Rodrik’s new book, but based on reviews it sounds like it puts forward a pretty similar view of economics methodology.

The End of the Supermanager?

Everyone is talking about this new paper, Firming Up Inequality. It uses individual-level data from the Social Security Administration, matched to employers by Employer Identification Number (EIN), to decompose changes in earnings inequality into a within-firm and a between-firm component. It’s a great exercise — marred only modestly by the fact that the proprietary data means that no one can replicate it — exactly the sort of careful descriptive work I wish more economists would do.

The big finding from the paper is that all the rise in earnings inequality between 1982 and 2012 is captured by the between-firm component. There is no increase in the earnings of a person in the top 1% of the earnings distribution within a given business, and the earnings of someone at the median for that same business. The whole increase in earnings inequality over this period consists of a widening gap between the firms that pay more across the board, and the firms that pay less.

I’m not sure we want to take the results of this study at face value. Yes, we should be especially interested in empirical work that challenges our prior beliefs, but at the same time, it’s hard to square the claims here with all the other evidence of a disproportionate increase in the top pay within a given firm. Lawrence Mishel gives some good reasons for skepticism here. The fact that the whole increase is accounted for by the between-firm component, yet none by the between-industry component, is very puzzling. More generally, I wonder how reliable is the assumption that there is a one to one match between EINs and what we normally think of as employers.

That said, these findings may be pointing to something important. As a check on the plausibility of the numbers in the paper, I took a look at labor income of the top 1 percent and 0.01 percent of US households, as reported in the World Top Incomes Database. And I found something I didn’t expect: Since 2000, there’s been a sharp fall in the share of top incomes that come from wages and salaries. In 2000, according to the tax data used by Piketty and his collaborators, households in the top 0.01 percent got 61 percent of their income from wages, salaries and pensions. By 2013, that had fallen to just 33 percent. (That’s excluding capital gains; including them, the labor share of top incomes fell from 31 percent to 21 percent.) For the top 1 percent, the labor share falls from 63 percent to 56 percent, the lowest it’s been since the 1970s.

Here is the average income of the top 0.01 percent over the past 40 years in inflation-adjusted dollars, broken into three components: labor income, all other non-capital gains income, and capital gains.

Average income of top 0.01% of US households, from World Top Incomes Database. 3-year moving averages.

As you can see, the 1990s look very different from today. Between 1991 and 2000, the average labor income of a top 0.01% household rose from $2.25 million to $10 million; this was about 90 percent of the total income increase for these households. During the 1990s, rising incomes at the top really were about highly paid superstars. Since 2000, though, while average incomes of the top 0.01% have increased another 20 percent, labor income for these households has fallen by almost half, down to $5.5 million. (Labor income has also fallen for the top 1 percent, though less dramatically.) So the “Firming” results, while very interesting, are perhaps less important for the larger story of income distribution than both the authors and critics assume. The rise in income inequality since 2000 is not about earnings; the top of the distribution is no longer the working rich. I don’t think that debates about inequality have caught up with this fact.

Fifteen years ago, the representative rich person in the US was plausibly a CEO, or even an elite professional. Today, they mostly just own stuff.


Causes and Effects of Wage Growth

Over here, a huge stack of exams, sitting ungraded since… no, I can’t say, it’s too embarrassing.  There, a grant proposal that extensive experimentation has shown will not, in fact, write itself. And I still owe a response to all the responses and criticism to my Disgorge the Cash paper for Roosevelt. So naturally, I thought this morning would be a good time to sit down and ask what we can learn from comparing the path of labor costs in the Employment Cost Index compared with the ECEC.

The BLS explains the difference between the two measures:

The Employment Cost Index, or ECI, measures changes in employers’ cost of compensating workers, controlling for changes in the industrial-occupational composition of jobs. … The ECI is intended to indicate how the average compensation paid by employers would have changed over time if the industrial-occupational composition of employment had not changed… [It] controls for employment shifts across 2-digit industries and major occupations. The Employer Costs for Employee Compensation, or ECEC… is designed to measure the average cost of employee compensation. Accordingly, the ECEC is calculated by multiplying each job quote by its sample weight.

In other words, the ECI measures the change in average hourly compensation, controlling for shifts in the mix of industries and occupations. The ECEC simply measures the overall change in hourly compensation, including the effects of both changes in compensation for particular jobs, and changes in the mix of jobs.

Here are the two series for the full period both are available (1987-2014), both raw and adjusted for inflation (“real”).

What do we learn from this?

First, the two series are closely correlated. This tells us that most of the variation in compensation is driven by changes within occupations and sectors, not by shifts in employment between occupations and sectors. This is clearly true at annual frequencies but it seems to be true over longer periods as well. For instance, let’s compare the behavior of compensation in the five years since the end of the recession to the last period of strong wage growth, 1997-2004. The difference between the two periods in the average annual increase in nominal wages is almost exactly the same according to the two indexes — 2.7 points by the ECI, 2.6 points by the ECEC. In other words, slower wage growth in the recent period is entirely due to slower wages growth within particular kinds of jobs. Shifts in the composition of jobs have played no role at all.

On the face of it, the fact that almost all variation in aggregate compensation is driven by changes within employment categories, seems to favor a labor/political story of slower wage growth as opposed to a China or robots story. The most obvious versions of the latter two stories involve a disproportionate loss of high-wage jobs, whereas stories about weaker bargaining position of labor predict slower compensation growth within job categories. I wouldn’t ask this one piece of evidence to carry a lot of weight in that debate. (I think it’s stronger evidence against a skills-based explanation of slower wage growth.)

While the two series in general move together, the ECEC is more strongly cyclical. In other words, during periods of high unemployment and falling wages in general, there is also a shift in the composition of employment towards lower-paid occupations. And during booms, when unemployment is low and wages are rising in general, there is a shift in the direction of higher-paid job categories. [1] Insofar as wages and labor productivity are correlated, this cyclical shift between higher-wage and lower-wage sectors could help explain why employment is more stable than output. I’ve had the idea for a while that the Okun’s law relationship — the less than one-for-one correlation between employment and output growth — reflects not only hiring/firing costs and overhead labor, but also shifts in the composition of employment in response to demand. In other words, in addition to employment adjustment costs at the level of individual enterprises, the Okun coefficient reflects cyclically varying degrees of “disguised unemployment” in Joan Robinson’s sense. [2] This is an argument I’d like to develop properly someday, since it seems fairly obvious, potentially important and empirically tractable, and I haven’t seen anyone else make it. [3] (I’m sure someone has.)

What’s going on in the most recent year? Evidently, there has been no acceleration of wage growth for a given job, but the mix of jobs created has shifted toward higher-wage categories. This suggests that to the extent wages are rising faster, it’s not a sign of labor-market pressures. (Some guy from Deutsche Bank interprets the same divergence as support for raising rates, which it’s hard not to feel is deliberately dishonest.) As for which particular higher-wage job categories are growing more rapidly — I don’t know. And, what’s going on in 1995? That year has by far the biggest divergence between the two series. It could well be an artifact of some kind, but if not, seems important. A large fall in the ECEC relative to the ECI could be a signature of deindustrialization. I’m not exploring the question further now (those exams…) but it would be interesting to ask analogous question with some series that extends earlier. It’s likely that if we were looking at the 1970s-1980s, we would find a much larger share of variation in wage growth explained by compositional shifts.

Should we adjust for inflation? I give the “real” series here, but I am in general skeptical that there is any sense in which an ex post adjustment of money flows for inflation is more real than, say, The Real World on MTV. I am even more doubtful than usual in this case, because we are normally told to think that changes in nominal wages are the main determinant of inflation. Obviously in that case we have to think of the underlying labor-market process as determining a change in nominal wage. Still, if we do compute a “real” index, things look a little different. Real ECI rises 14 percent over the full 1987-2014 period, while real ECEC rises only 5 percent. So now we can say that about two-thirds of the increase in real wages within particular job categories over the past three decades, was offset by a shift in the composition of employment toward lower-paid job categories. (This is all in the first decade, 1987-1996, however.) This way of looking at things makes sense if we think the underlying wage-setting process, whatever it is, operates in terms of a basket of consumption goods.

This invites another question: How true is it that nominal wages move with inflation?

Conventional economics wisdom suggests we can separate wages into nominal and “real” components. This is on two not quite consistent grounds. First, we might suppose that workers and employers are implicitly negotiating contracts in terms of a fixe quantity of labor time for, on the one hand, a basket of wage goods, and on the other, a basket of produced goods (which will be traded for consumption good for the employer). This contract only incidentally happens to be stated in terms of money. The ultimate terms on which consumption goods for the workers exchange with consumption goods for the employer should not be affected by the units the trade happens to be denominated in. (In this respect the labor contract is just like any other contract.) This is the idea behind Milton Friedman’s “natural rate of unemployment” hypothesis. In Friedman’s story, causality runs strictly from inflation to unemployment. High inflation is not immediately recognized by workers, leading them to overestimate the basket of goods their wages will buy. So they work more hours than they would have chosen if they had correctly understood the situation. From this point of view, there’s no cost to low unemployment in itself; the problem is just that unemployment will only be low if high inflation has tricked workers into supply too much labor. Needless to say, this is not the way anyone in the policy world thinks about the inflation-unemployment nexus today, even if they continue to use Friedman’s natural rate language.

The alternative view is that workers and employers negotiate a money-wage, and then output prices are set as a markup over that wage. In this story, causality runs from unemployment to inflation. While Friedman thought an appropriate money-supply growth rate was the necessary and sufficient condition for stable prices, with any affect on unemployment just  collateral damage from changes in inflation, in this story keeping unemployment at an appropriate level is a requirement for stabilizing prices. This is the policy orthodoxy today.  (So while people often say that NAIRU is just another name for the natural rate of unemployment, in fact they are different concepts.) I think there are serious conceptual difficulties with the orthodox view, but we’ll save those for another time. Suffice it to say that causality is supposed to run from low unemployment, to faster nominal wage growth, to higher inflation. So the question is: Is it really the case that faster nominal wage growth is associated with higher inflation?

Wage Growth and Inflation, 1947-2014

A simple scatterplot suggests a fairly tight relationship, especially at higher levels of wage growth and inflation. But if we split the postwar period at 1985, things look very different. In the first period, there’s a close relationship — regressing inflation on nominal wage growth gives an R-squared of 0.81. (Although even then the coefficient is significantly less than 1.)

Wage Growth and Inflation, 1947-1985

Since 1985, though, the relationship is much looser, with an R-squared of 0.12. And even is that driven almost entirely by period of falling wages and prices in 2009; remove that and the correlation is essentially zero.

Wage Growth and Inflation, 1986-2014

So while it was formerly true that changes in inflation were passed one for one into changes in nominal wages, and/or changes in nominal wage growth led to similar changes in inflation, neither of those things has been true for quite a while now. In recent decades, faster nominal wage growth does not translate into higher inflation.

Obviously, a few scatterplots aren’t dispositive, but they are suggestive. So supposing that there has been a  delinking of wage growth and inflation, what conclusions might we draw? I can think of a couple.

On the one hand, maybe we shouldn’t be so dismissive of  the naive view that inflation reduces the standard of living directly, by raising the costs of consumption goods while incomes are unchanged. There seems to be an emerging conventional wisdom in this vicinity. Here for instance is Gillian Tett in the FT, endorsing the BIS view that there’s nothing wrong with falling prices as long as asset prices stay high. (Priorities.) In the view of both Keynes (in the GT; he modified it later) and Schumpeter, inflation was associated with higher nominal but lower real wages, deflation with lower nominal but higher real wages. I think this may have been true in the 19th century. It’s not impossible it could be true in the future.

On the other hand. If the mission of central banks is price stability, and if there is no reliable association between changes in wage growth and changes in inflation, then it is hard to see the argument for tightening in response to falling unemployment. You really should wait for direct evidence of rising inflation. Yet central banks are as focused on unemployment as ever.

It’s perhaps significant in this regard that the authorities in Europe are shifting away from the NAIRU (Non-Accelerating Inflation Rate of Unemployment) and increasingly talking about the NAWRU (Non-Accelerating Wage Rate of Unemployment). If the goal all along has been lower wage growth, then this is what you should expect: When the link between wages and inflation weakens, the response is not to find other tools for controlling inflation, but other arguments for controlling wages. This may be the real content of the “competitiveness” discourse. Elevating competitiveness over price stability as overarching goal of policy lets you keep pushing down wages even when inflation is already low.

Worth noting here: While the ECB’s “surrender Dorothy” letter to the Spanish government ordered them to get rid of price indexing, their justification was not, as you might expect, that indexation contributes to inflationary spirals. Rather it was that it is “a structural obstacle to the adjustment of labour costs” and “contribute to hampering competitiveness.” [4]  This is interesting. In the old days we would have said, wage indexing is bad because it won’t affect real wages, it just leads to higher inflation. But apparently in the new dispensation, we say that wage indexing is bad precisely because it does affect real wages.

[1]  This might seem to contradict the previous point but it doesn’t, it’s just that the post-2009 recovery period includes both a negative composition shift in 2008-2009, when unemployment was high, and a positive compositional shift in 2014, which cancel each other out.

[2] From A Theory of Employment: “Except under peculiar conditions, a decline in effective demand which reduces the amount of employment offered in the general run of industries will not lead to ‘unemployment’ in the sense of complete idleness, but will rather drive workers into a number of occupations [such as] selling match-boxes in the Strand, cutting brushwood in the jungles, digging potatoes on allotments which are still open to them. A decline in one sort of employment leads to an increase in another sort, and at first sight it may appear that, in such a case, a decline in effective demand does not cause unemployment at all. But the matter must be more closely examined. In all those occupations which the dismissed workers take up, their productivity is less than in the occupations that they have left.”

[3] The only piece I know of that makes the connection between demand and productivity variation across sectors is this excellent article by John Eatwell (which unfortunately doesn’t seem to be available online), but it is focused on long run variation, not cyclical.

[4] The ECB’s English is not the most felicitous, is it? The Spanish version is “contribuyen a dificultar la competitividad y el crecimiento,” which also doesn’t strike me as a phrase that a native speaker would write. Maybe it sounds better in the original German.

The Non-Accelerating What Now Rate of Inflation

The NAIRU is back. Here’s Justin Wolfers in the Times the other day:

My colleague Neil Irwin wrote about this slow wage growth as if it were bad news. I feel much more optimistic. … It is only when nominal wage growth exceeds the sum of inflation (about 2 percent) and productivity growth (about 1.5 percent) that the Fed needs to be concerned…

Read that last sentence again. What is it that would be accelerating here?

The change in the wage share is equal to the increase in average nominal wages, less inflation and the increase in labor productivity. This is just accounting. So Wolfer’s condition, that wage growth not exceed the sum of inflation and labor productivity growth is, precisely, the condition that the wage share not rise. If we take him literally — and I don’t see why we shouldn’t — then the Fed should be less concerned to raise rates when inflation is higher. Which makes no sense if the goal is to control inflation. But perfect sense if the real concern is to prevent a rise in the wage share.

Unemployment and Productivity Growth

I write here frequently about “the money view” — the idea that we need to see economic relationships as a system of money flows and money commitments, that is not reducible to the “real” production and exchange of goods and services. Seeing the money-game as a self-contained system is the first step; the next step is to ask how this system interacts with the concrete activities of production.

One way to look at this interface is through the concept of potential output, and its relationship to current expenditure, or demand. In the textbook view, there is no connection between the long-run evolution of potential output with demand. This is a natural view if you think that economic quantities have an independent material existence. First we have scarce resources, then the choice about which end to devote them to. Knut Wicksell suggests somewhere an evocative metaphor for this view of economic growth: It’s as if we had a cellar full off wine in barrels, which will improve with age. The problem of economic growth is then equivalent to choosing the optimal tradeoff between having better wine, and drinking it sooner than later. But whatever choice we make, all the wine is already there. Ramsey and Solow growth models, with their “golden rule” growth rate, are descriptions of this kind of problem. Aggregate demand doesn’t come into it.

From our point of view, on the other hand, production is a creative, social activity. Economic growth is not a matter of allowing an exiting material process to continue operating through time, but of learning how to work together in new ways. The fundamental problem is coordination, not allocation.  From this point of view, the technical conditions of production are endogenous to the organization of production, and the money payments that structure it. So it’s natural to think that aggregate expenditure could be an important factor determining the pace at which productive activity can be reorganized.

Now, whether demand actually does matter in the longer run is hotly debated point in heterodox economics. You can find very smart Post Keynesians like Steve Fazzari arguing that it does, and equally smart Marxists like Dumenil and Levy arguing that it does not. (Amitava Dutt has a good summary; Mark Setterfield has a good recent discussion of the formal issues of incorporating demand into Kaldorian growth models.) But within our framework, at least it is possible to ask the question.

Which brings me to this recent article in the Real World Economic Review. I don’t recommend the piece — it is not written in a way to inspire confidence. But it does make an interesting claim, that over the long run there is an inverse relationship between unemployment and labor productivity growth in the US, with average labor productivity growth equal to 8 minus the unemployment rate. This is consistent with the idea that demand conditions influence productivity growth, most obviously because pressures to economize on labor will be greater when labor is scarce.

A strong empirical regularity like this would be interesting, if it was real. But is it?

Here is one obvious test (a bit more sensible to me than the approach in the RWER article). The figure below shows the average US unemployment rate and real growth rate of hourly labor productivity for rolling ten-year windows.

It’s not exactly “the rule of 8” — the slope of the regression line is just a big greater than -0.5, rather than -1. But it is still a striking relationship. Ten-year periods with high growth of productivity invariably also have low unemployment rates; periods of high average unemployment are invariably also periods of slow productivity growth.

Of course these are overlapping periods, so this tells us much less than it would if they were independent observations. But the association of above-average productivity growth with below-average unemployment is indeed a historical fact, at least for the postwar US. (As it turns out, this relationship is not present in most other advanced countries — see below.) So what could it mean?

1. It might mean nothing. We really only have four periods here — two high-productivity-growth, low-unemployment periods, one in the 1950s-1960s and one in the 1990s; and two low-productivity-growth, high-unemployment periods, one in the 1970s-1980s and one in the past decade or so. It’s quite possible these two phenomena have separate causes that just happened to shake out this way. It’s also possible that a common factor is responsible for both — a new technology-induced investment boom is the obvious candidate.

2. It might be that high productivity growth leads to lower unemployment. The story here I guess would be the Fed responding to a positive supply shock. I don’t find this very plausible.

3. It might be that low unemployment, or strong demand in general, fosters faster productivity growth. This is the most interesting for our purposes. I can think of several versions of this story. First is the increasing-returns story that originally motivated Verdoorn’s law. High demand allows firms to produce further out on declining cost curves. Second, low unemployment could encourage firms to adopt more labor-saving production techniques. Third, low unemployment might associated with more rapid movement of labor from lower-productivity to higher-productivity activities. (In other words, the relationship might be due to lower visible unemployment being associated with lower disguised unemployment.) Or fourth, low unemployment might be associated with a relaxing of the constraints that normally limit productivity-boosting investment — demand itself, and also financing. In any of these stories, the figure above shows a causal relationship running from the x-axis to the y-axis.

One scatterplot of course hardly proves anything. I’m really just posing the question. Still, this one figure is enough to establish one thing: A positive relationship between unemployment and labor productivity has not been the dominant influence on either variable in the postwar US. In particular, this is strong evidence against the idea the idea of technological unemployment, beloved by everyone from Jeremy Rifkin to Lawrence Summers. (At least as far as this period is concerned — the future could be different.) To tell a story in which paid labor is progressively displaced by machines, you must have a positive relationship between labor productivity and unemployment. But historically, high unemployment has been associated with slower growth in labor productivity, not faster. So we can say with confidence that whatever has driven changes in unemployment over the past 75 years, it has not been changes in the pace at which human labor is replaced by technology.

The negative relationship between unemployment and productivity growth, whatever it means, turns out to be almost unique to the US. Of the dozen or so other countries I looked at, the only one with a similar pattern is Japan, and even there the relationship is weaker. I honestly don’t know what to make of this. But if you’re interested, the other scatterplots are below the fold.

Note: Labor productivity is based on real GDP per hour, from the BLS International Labor Comparisons project; unemployment is the harmonized unemployment rate for all persons from the OECD Main Economic Indicators database. I used these because they are (supposed to be) defined consistently across countries and were available on FRED. Because the international data covers shorter periods than the US data does, I used 8-year windows instead of 10-year windows.

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. 

Wealth Distribution and the Puzzle of Germany

There’s been some discussion recently of the new estimates from Emmanuel Saez and Gabriel Zucman of the distribution of household wealth in the US. Using the capital income reported in the tax data, and applying appropriate rates of return to different kinds of assets, they are able to estimate the distribution of household wealth holdings going back to the beginning of the income tax in 1913. They find that wealth inequality is back to the levels of the 1920s, with 40% of net worth accounted for the richest one percent of households. The bottom 50% of households have a net worth of zero.

There’s a natural reaction to see this as posing the same kind of problem as the distribution of income — only more extreme — and respond with proposals to redistribute wealth. This case is argued by the very smart Steve Roth in comments here and on his own blog. But I’m not convinced. It’s worth recalling that proposals for broadening the ranks of property-owners are more likely to come from the right. What else was Bush’s “ownership society”? Social Security privatization, if he’d been able to pull it off, would have  dramatically broadened the distribution of wealth. In general, I think the distribution of wealth has a more ambiguous relationship than the distribution of income to broader social inequality.

Case in point: Last summer, the ECB released a survey of European household wealth. And unexpectedly, the Germans turned out to be among the poorest people in Europe. The median German household reported net worth of just €50,000, compared with €100,000 in Greece, €110,000 in France, and €180,000 in Spain. The pattern is essentially the same if you look at assets rather than net worth — median household assets are lower in Germany than almost anywhere else in Europe, including the crisis countries of the Mediterranean.

At the time, this finding was mostly received in terms the familiar North-South morality tale, as one more argument for forcing austerity on the shiftless South. Not only are the thrifty Germans being asked to bail out the wastrel Mediterraneans, now it turns out the Southerners are actually richer? Why can’t they take responsibility for their own debts? No more bailouts!

No surprise there. But how do we make sense of the results themselves, given what we know about the economies of Germany and the rest of Europe? I think that understood correctly, they speak directly to the political implications of wealth distribution.

First, though: Did the survey really find what it claimed to find? The answer seems to be more or less yes, but with caveats.

Paul de Grauwe points out some distortions in the headline numbers reported by the ECB. First, this is a survey of household wealth, but, de Grauwe says, households are larger in the South than in the North. This is true, but it turns out not to make much of a difference — converting from household wealth to wealth per capita leaves the basic pattern unchanged.

Per capita wealth in selected European countries. From de Grauwe.

Second, the survey focuses on median wealth, which ignores distribution. If we look at the mean household instead of the median one, we find Germany closer to the middle of the pack — ahead of Greece, though still behind France, Italy and Spain. The difference between the two measures results from the highly unequal distribution of wealth in Germany — the most unequal in Europe, according to the ECB survey. For the poorest quintile, median net worth is ten times higher in Greece and in Italy than in Germany, and 30 times higher in Spain.

This helps answer the question of apparent low German wealth — part of the reason the median German household is wealth-poor is because household wealth is concentrated at the top. But that just raises a new puzzle. Income distribution Germany is among the most equal in Europe. Why is the distribution of wealth so much more unequal? The puzzle deepens when we see that the other European countries with high levels of wealth inequality are France, Austria, and Finland, all of which also have relatively equal income distribution.

Another distortion pointed to by De Grauwe is that the housing bubble in southern Europe had not fully deflated in 2009, when the survey was taken — home prices were still significantly higher than a decade earlier. Since Germany never had a housing boom, this tends to depress measured wealth there. This explains some of the discrepancy, but not all of it. Using current home prices, the median Spanish household has more than triple the net wealth of the median German household; with 2002 home prices, only double. But this only moves Germany up from the lowest median household wealth in Europe, to the second lowest.

The puzzle posed by the wealth survey seems to be genuine. Even correcting for home prices and household size, the median Spanish or Italian household reports substantially more net wealth than the median German one, and the median Greek household about an equal amount. Yet Germany is, by most measures, a much richer country, with median household income of €33,000, compared with €22,000, €25,000 and €26,000 in Greece, Spain and Italy respectively. Use mean wealth instead of median, and German wealth is well above Greek and about equal to Spanish, but still below Italian — even though, again, average household income is much higher in Germany than in Italy. And the discrepancy between the median and mean raises the puzzle of why German wealth distribution is so much more uneven than German income distribution.

De Grauwe suggests one more correction: look at the total stock of fixed capital in each country, rather than household wealth. Measuring capital consistently across countries is notoriously dicey, but on his estimate, Germany and the Netherlands have as much as three times the capital per head as the southern countries. So Germany is richer in real terms than the South, as we all know; the difference is just that “a large part of German wealth is not held by households and therefore must be held by the corporate sector.” Problem solved!

Except… you know, Mitt Romney was right: corporations are people, in the sense that they are owned by people. The wealth of German corporations should also show up as the wealth of the owners of German stocks, bonds, or other claims on those corporations — which means, overwhelmingly, German households. Indeed, in mainstream economic theory, the “wealth” of the corporate sector just is the wealth of the households that own it. According to de Grauwe, the per capita value of the capital stock is more than twice as large in Germany as in Spain. Yet the average financial wealth held by a German household is only 25% higher than in Spain. So as in the case of distribution, this solution to the net-wealth puzzle just creates a new puzzle: Why is a dollar of capital in a German firm worth so much less to its ultimate owners than a dollar of capital in a Spanish or Italian firm?

And this, I think, points us toward the answer, or at least toward the right question.

The question is, what is the relationship between the level of market production in an economy, and the claims on future production represented by wealth? It’s a truism — tho often forgotten — that the market production counted in GDP is only a part of all the productive activity that takes place in society. In the same way, not all market production is capitalized into assets. Wealth in an economic sense represents only those claims on future income that are exercised by virtue of a legal title that is freely transferable, and hence has a market value.

For example, imagine two otherwise similar countries, one of which makes provision for retirement income through a pay-as-you-go public pension system, and the other of which uses some form of funded pension. The two countries may have identical levels of output and income, and retirees may receive exactly the same payments in both. But because the assets held by the pension funds show up on balance sheets while the right to future public pension payments does not, the first country will have less wealth than the second one. Again, this does not imply any difference in production, or income, or who ultimately bears the cost of supporting retirees; it is simply a question of how much of those future payments are capitalized into assets.

This is just an analogy; I don’t think retirement savings are the story here. The story is about home ownership and the value of corporate stock.

First, home ownership. Only 44 percent of German households own their own homes, compared with 70-80 percent in Greece, Italy and Spain. Among both homeowners and non-homeowners considered separately, median household wealth is comparable in Germany and in the southern countries. It’s only the much higher proportion of home ownership that produces higher median wealth in the South. And this is especially true at the bottom end of the distribution — almost all the bottom quintile (by income) of German households are renters, whereas in Greece, Spain and Italy there is a large fraction of homeowners even at the lowest incomes. Furthermore, German renters have far more protections than elsewhere. As I understand it, German renters are sufficiently protected against both rent increases and loss of their lease that their occupancy of their home is not much less secure than that of home owners. These protections are, in a sense, a form of property right — they are a claim on the future flow of housing services in the same way that a title to a house would be. But with a critical difference: the protections from rent regulation can’t be sold, don’t show up on the household’s balance sheet, and do not get counted as wealth.

In short: The biggest reason that German household wealth is lower than than elsewhere is that less claims on the future output of the housing sector take the form of assets. Housing is just as commodified in Germany as elsewhere (I don’t think public housing is unusually important there). But it is less capitalized.

Home ownership is the biggest and clearest part of the story here, but it’s not the whole story. Correct for home ownership rates, use mean rather than median, and you find that German household wealth is comparable to household wealth in Italy or Spain. But given that GDP per capita is much higher in Germany, and the capital stock seems to be so much larger, why isn’t household wealth higher in Germany too?

One possible answer is that income produced in the corporate sector is also less capitalized in Germany.

In a recent paper with Zucman, Thomas Piketty suggests that the relationship between equity values and the real value of corporate assets depends on who exercises power over the corporation. Piketty and Zucman:

Investors who wish to take control of a corporation typically have to pay a large premium to obtain majority ownership. This mechanism might explain why Tobin’s Q tends to be structurally below 1. It can also provide an explanation for some of the cross-country variation… : the higher Tobin’s Q in Anglo-Saxon countries might be related to the fact that shareholders have more control over corporations than in Germany, France, and Japan. This would be consistent with the results of Gompers, Ishii and Metrick (2003), who find that firms with stronger shareholders rights have higher Tobin’s Q. Relatedly, the control rights valuation story may explain part of the rising trend in Tobin’s Q in rich countries. … the ”control right” or ”stakeholder” view of the firm can in principle explain why the market value of corporations is particularly low in Germany (where worker representatives have voting rights in corporate boards without any equity stake in the company). According to this ”stakeholder” view of the firm, the market value of corporations can be interpreted as the value for the owner, while the book value can be interpreted as the value for all stakeholders.

In other words, one reason household wealth is low in Germany is because German households exercise their claims on the business sector not via financial assets, but as workers.

The corporate sector is also relatively larger in Germany than in the southern countries, where small business remains widespread. 14 percent of Spanish households and 18 percent of Italian households report ownership of a business, compared with only 9 percent of German households. Again, this is a way in which lower wealth reflects a shift in claims on the social product from property ownership to labor.

It’s not a coincidence that Europe’s dominant economy has the least market wealth. The truth is, success in the world market has depended for a long time now on limiting dependence on asset markets, just as the most successful competitors within national economies are the giant corporations that suppress the market mechanism internally. Germany, as with late industrializers like Japan, Korea, and now China, has succeeded largely by ensuring that investment is not guided by market signals, but through active planning by banks and/or the state. There’s nothing new in the fact that greater real wealth in the sense of productive capacity goes hand hand with less wealth in the sense of claims on the social product capitalized into assets. Only in the poorest and most backward countries does a significant fraction of the claims of working people on the product take the form of asset ownership.

The world of small farmers and self-employed artisans isn’t one we can, or should, return to. Perhaps the world of homeowners managing their own retirement savings isn’t one we can, or should, preserve.

“The Labouring Classes Should Have a Taste for Comforts and Enjoyments”

McDonald’s model budget for its minimum-wage employees — along with the smug, fatuous, those-people-aren’t-like-us-dear defenses of it — has been the target of well-deserved scorn.

This kind of thing has been around forever (or at least as long as capitalism). Two hundred years ago, liberal reformers offered “Promoting Sobriety and Frugality, and an Abhorrence of Gaming”as the solution to the collapse of wages following the Napoleonic wars, and gave workers instruction on “the use of roasted wheat as a substitute for coffee.” You could make an endless list of these helpful suggestions to the poor to better manage their poverty.

To be fair, liberals today do mostly see this stuff as, at best, an effort by low-wage employers to divert attention from their own compensation policies to the personal responsibility of their workers. And at worst, when the budget help includes assistance enrolling in Medicaid or the EITC, as a way of getting the public to subsidize low-wage employment.

But there’s a nagging sense in these conversations that, disingenuous as McDonald’s is here, still, at the end of the day, frugality, living within one’s means, is a virtue; that the ability to prioritize expenses and make a budget is a useful skill to have. Against that view, here’s Ricardo on wages:

It is not to be understood that the natural price of labour, estimated even in food and necessaries, is absolutely fixed and constant. … It essentially depends on the habits and customs of the people. An English labourer would consider his wages under their natural rate, and too scanty to support a family, if they enabled him to purchase no other food than potatoes, and to live in no better habitation than a mud cabin; yet these moderate demands of nature are often deemed sufficient in countries where ‘man’s life is cheap’, and his wants easily satisfied. Many of the conveniences now enjoyed in an English cottage, would have been thought luxuries at an earlier period of our history. 

The friends of humanity cannot but wish that in all countries the labouring classes should have a taste for comforts and enjoyments, and that they should be stimulated by all legal means in their exertions to procure them. … In those countries, where the labouring classes have the fewest wants, and are contented with the cheapest food, the people are exposed to the greatest vicissitudes and miseries.

In a world where the price of labor power depends on its cost, there’s no benefit to workers from budgeting responsibly, from learning to get by on less. The less people can live on, the lower wages will be. On the other hand, to the extent that former luxuries — a decent car, some nice clothes, dinner out once in a while, whatever consumer electronics item the scolds are going on about now — come to be seen as necessities, such that it’s not worth putting up with the bullshit of a job if you still can’t afford them, then wages will have to rise enough to cover that too.

For much of the 20th century, it seemed like we had left Ricardo’s world behind. Among economists, it became a well-established stylized fact that it’s the wage share, not the real wage that is relatively fixed. To even sympathetic critics of Marx, the failure of real wages to gravitate toward a (socially determined) subsistence level looked like a major departure of modern economies from the capitalism he described.

These days, though, the world is looking more Ricardian. For the majority of workers without credentials or other shelter from the logic of the labor market, real wages look less like a technologically-fixed share of output than the minimum necessary to keep people participating in wage labor at all. In the subsistence-wage world of industrializing Britain, workers’ “frugality, discipline or acquisitive virtues brought profit to their masters rather than success to themselves.”  Conversely, in that world, which may also be our world, profligacy, waste and irresponsibility could be a kind of solidarity.

I would never presume to tell someone surviving on a minimum-wage paycheck how to live their life. I know that being poor is incredibly hard work, in a way that those of us who haven’t experienced it can hardly imagine.  But as a friend of humanity, I do worry that the biggest danger isn’t that people can’t live on the minimum wage, but that they can. In which case we’re all better off if McDonald’s employees throw the bosses’ helpful budget advice away.