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.

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 Call Is Coming from Inside the House

Paul Krugman wonders why no one listens to academic economists. Almost all the economists in the IGM Survey agree that the 2009 stimulus bill successfully reduced unemployment and that its benefits outweighed its costs. So why are these questions still controversial?

One answer is that economists don’t listen to themselves. More precisely, liberal economists like Krugman who want the state to take a more active role in managing the economy, continue to teach  an economic theory that has no place for activist policy.

Let me give a concrete example.

One of Krugman’s bugaboos is the persistence of claims that expansionary monetary policy must lead to higher inflation. Even after 5-plus years of ultra-loose policy with no rising inflation in sight, we keep hearing that since so “much money has been created…, there should already be considerable inflation.” (That’s from exhibit A in DeLong’s roundup of inflationphobia.) As an empirical matter, of course, Krugman is right. But where could someone have gotten this idea that an increase in the money supply must always lead to higher inflation? Perhaps from an undergraduate economics class? Very possibly — if that class used Krugman’s textbook.

Here’s what Krugman’s International Economics says about money and inflation:

A permanent increase in the money supply causes a proportional increase in the price level’s long-run value. … we should expect the data to show a clear-cut positive association between money supplies and price levels. If real-world data did not provide strong evidence that money supplies and price levels move together in the long run, the usefulness of the theory of money demand we have developed would be in severe doubt. 


Sharp swings in inflation rates [are] accompanied by swings in growth rates of money supplies… On average, years with higher money growth also tend to be years with higher inflation. In addition, the data points cluster around the 45-degree line, along which money supplies and price levels increase in proportion. … the data confirm the strong long-run link between national money supplies and national price levels predicted by economic theory. 


Although the price levels appear to display short-run stickiness in many countries, a change in the money supply creates immediate demand and cost pressures that eventually lead to future increases in the price level. 


A permanent increase in the level of a country’s money supply ultimately results in a proportional rise in its price level but has no effect on the long-run values of the interest rate or real output. 

This last sentence is simply the claim that money is neutral in the long run, which Krugman continues to affirm on his blog. [1] The “long run” is not precisely defined here, but it is clearly not very long, since we are told that “Even year by year, there is a strong positive relation between average Latin American money supply growth and inflation.”

From the neutrality of money, a natural inference about policy is drawn:

Suppose the Fed wishes to stimulate the economy and therefore carries out an increase in the level of the U.S. money supply. … the U.S. price level is the sole variable changing in the long run along with the nominal exchange rate E$/€. … The only long-run effect of the U.S. money supply increase is to raise all dollar prices.

What is “the money supply”? In the US context, Krugman explicitly identifies it as M1, currency and checkable deposits, which (he says) is determined by the central bank. Since 2008, M1 has more than doubled in the US — an annual rate of increase of 11 percent, compared with an average of 2.5 percent over the preceding decade. Krugman’s textbook states, in  unambiguous terms, that such an acceleration of money growth will lead to a proportionate acceleration of inflation. He can hardly blame the inflation hawks for believing what he himself has taught a generation of economics students.

You might think these claims about money and inflation are unfortunate oversights, or asides from the main argument. They are not. The assumption that prices must eventually change in proportion to the central bank-determined money supply is central to the book’s four chapters on macroeconomic policy in an open economy. The entire discussion in these chapters is in terms of a version of the Dornbusch “overshooting” model. In this model, we assume that

1. Real exchange rates are fixed in the long run by purchasing power parity (PPP).
2. Interest rate differentials between countries are possible only if they are offset by expected changes in the nominal exchange rate.

Expansionary monetary policy means reducing interest rates here relative to the rest of the world. In a world of freely mobile capital, investors will hold our lower-return bonds only if they expect our nominal exchange rate to appreciate in the future. With the long-run real exchange rate pinned down by PPP, the expected future nominal exchange rate depends on expected inflation. So to determine what exchange rate today will make investors willing to holder our lower-interest bonds, we have to know how policy has changed their expectations of the future price level. Unless investors believe that changes in the money supply will translate reliably into changes in the price level, there is no way for monetary policy to operate in this model.

So  these are not throwaway lines. The more thoroughly a student understands the discussion in Krugman’s textbook, the stronger should be their belief that sustained expansionary monetary policy must be inflationary. Because if it is not, Krugman gives you no tools whatsoever to think about policy.

Let me anticipate a couple of objections:

Undergraduate textbooks don’t reflect the current state of economic theory. Sure, this is often true, for better or worse. (IS-LM has existed for decades only in the Hades of undergraduate instruction.) But it’s not much of a defense, is it? If Paul Krugman has been teaching his undergraduates economic theory that produces disastrous results when used as a guide for policy, you would think that would provoke some soul-searching on his part. But as far as I can tell, it hasn’t. But in this case I think the textbook does a good job summarizing the relevant scholarship. The textbook closely follows the model in Dornbusch’s Expectations and Exchange Rate Dynamics, which similarly depends on the assumption that the price level changes proportionately with the money supply. The Dornbusch article is among the most cited in open-economy macroeconomics and international finance, and continues to appear on international finance syllabuses in most top PhD programs.

Everything changes at the zero lower bound. Defending the textbook on the ground that it’s pre-ZLB effectively concedes that what economists were teaching before 2008 has become useless since then. (No wonder people don’t listen.) If orthodox theory as of 2007 has proved to be all wrong in the post-Lehmann world, shouldn’t that at least raise some doubts about whether it was all right pre-Lehmann? But again, that’s irrelevant here, since I am looking at the 9th Edition, published in 2011. And it does talk about the liquidity trap — not, to be sure, in the main chapters on macroeconomic policy, but in a two-page section at the end. The conclusion of that section is that while temporary increases in the money supply will be ineffective at the zero lower bond, a permanent increase will have the same effects as always: “Suppose the central bank can credibly promise to raise the money supply permanently … output will therefore expand, and the currency will depreciate.” (The accompanying diagram shows how the economy returns to full employment.) The only way such a policy might fail is if there is reason to believe that the increase in the money supply will subsequently be reversed. Just to underline the point, the further reading suggested on policy at the zero lower bound is an article by Lars Svennson that calls a permanent expansion in the money supply “the foolproof way” to escape a liquidity trap. There’s no suggestion here that the relationship between monetary policy and inflation is any less reliable at the ZLB; the only difference is that the higher inflation that must inevitably result from monetary expansion is now desirable rather than costly. This might help if Krugman were a market monetarist, and wanted to blame the whole Great Recession and slow recovery on bad policy by the Fed; but (to his credit) he isn’t and doesn’t.

Liberal Keynesian economists made a deal with the devil decades ago, when they conceded the theoretical high ground. Paul Krugman the textbook author says authoritatively that money is neutral in the long run and that a permanent increase in the money supply can only lead to inflation. Why shouldn’t people listen to him, and ignore Paul Krugman the blogger?

[1] That Krugman post also contains the following rather revealing explanation of his approach to textbook writing:

Why do AS-AD? First, you do want a quick introduction to the notion that supply shocks and demand shocks are different … and AS-AD gets you to that notion in a quick and dirty, back of the envelope way. 

Second — and this plays a surprisingly big role in my own pedagogical thinking — we do want, somewhere along the way, to get across the notion of the self-correcting economy, the notion that in the long run, we may all be dead, but that we also have a tendency to return to full employment via price flexibility. Or to put it differently, you do want somehow to make clear the notion (which even fairly Keynesian guys like me share) that money is neutral in the long run. That’s a relatively easy case to make in AS-AD; it raises all kinds of expositional problems if you replace the AD curve with a Taylor rule, which is, as I said, essentially a model of Bernanke’s mind.

This is striking for several reasons. First, Krugman wants students to believe in the “self-correcting economy,” even if this requires teaching them models that do not reflect the way professional economists think. Second, they should think that this self-correction happens through “price flexibility.” In other words, what he wants his students to look at, say, falling wages in Greece, and think that the problem must be that they have not fallen enough. That’s what “a return to full employment via price flexibility” means. Third, and most relevant for this post, this vision of self-correction-by-prices is directly linked to the idea that money is neutral in the long run — in other words, that a sustained increase in the money supply must eventually result in a proportionate increase in prices. What Krugman is saying here, in other words, is that a “surprising big” part of his thinking on pedagogy is how to inculcate the exact errors that drive him crazy in policy settings. But that’s what happens once you accept that your job as an educator is to produce ideological fables.