The Near Irrelevance of the Vertical Long-Run Phillips Curve

From a discussion about how much credit Milton Friedman deserves for changing the way that economists thought about inflation, I want to nudge the conversation in a slightly different direction, to restate a point that I made some time ago in one of my favorite posts (The Lucas Critique Revisited). But if Friedman taught us anything it is that incessant repetition of the same already obvious point can do wonders for your reputation. That’s one lesson from Milton that I am willing to take to heart, though my tolerance for hearing myself say the same darn thing over and over again is probably not as great as Friedman’s was, which to be sure is not the only way in which I fall short of him by comparison. (I am almost a foot taller than he was by the way). Speaking of being a foot taller than Friedman, I don’t usually post pictures on this blog, but here is one that I have always found rather touching. And if you don’t know who the other guy is in the picture, you have no right to call yourself an economist.

friedman_&_StiglerAt any rate, the expectations augmented, long-run Phillips Curve, as we all know, was shown by Friedman to be vertical. But what exactly does it mean for the expectations-augmented, long-run Phillips Curve to be vertical? Discussions about whether the evidence supports the proposition that the expectations-augmented, long-run Phillips Curve is vertical (including some of the comments on my recent posts) suggest that people are not clear on what “long-run” means in the context of the expectations-augmented Phillips Curve and have not really thought carefully about what empirical content is contained by the proposition that the expectations-augmented, long-run Phillips Curve is vertical.

Just to frame the discussion of the Phillips Curve, let’s talk about what the term “long-run” means in economics. What it certainly does not mean is an amount of calendar time, though I won’t deny that there are frequent attempts to correlate long-run with varying durations of calendar time. But all such attempts either completely misunderstand what the long-run actually represents, or they merely aim to provide the untutored with some illusion of concreteness in what is otherwise a completely abstract discussion. In fact, what “long run” connotes is simply a full transition from one equilibrium state to another in the context of a comparative-statics exercise.

If a change in some exogenous parameter is imposed on a pre-existing equilibrium, then the long-run represents the full transition to a new equilibrium in which all endogenous variables have fully adjusted to the parameter change. The short-run, then, refers to some intermediate adjustment to the parameter change in which some endogenous variables have been arbitrarily held fixed (presumably because of some possibly reasonable assumption that some variables are able to adjust more speedily than other variables to the posited parameter change).

Now the Phillips Curve that was discovered by A. W. Phillips in his original paper was a strictly empirical relation between observed (wage) inflation and observed unemployment. But the expectations-augmented long-run Phillips Curve is a theoretical construct. And what it represents is certainly not an observable relationship between inflation and unemployment; it rather is a locus of points of equilibrium, each point representing full adjustment of the labor market to a particular rate of inflation, where full adjustment means that the rate of inflation is fully anticipated by all economic agents in the model. So what the expectations-augmented, long-run Phillips Curve is telling us is that if we perform a series of comparative-statics exercises in which, starting from full equilibrium with the given rate of inflation fully expected, we impose on the system a parameter change in which the exogenously imposed rate of inflation is changed and deduce a new equilibrium in which the fully and universally expected rate of inflation equals the alternative exogenously imposed inflation parameter, the equilibrium rate of unemployment corresponding to the new inflation parameter will not differ from the equilibrium rate of unemployment corresponding to the original inflation parameter.

Notice, as well, that the expectations-augmented, long-run Phillips Curve is not saying that imposing a new rate of inflation on an actual economic system would lead to a new equilibrium in which there was no change in unemployment; it is merely comparing alternative equilibria of the same system with different exogenously imposed rates of inflation. To make a statement about the effect of a change in the rate of inflation on unemployment, one has to be able to specify an adjustment path in moving from one equilibrium to another. The comparative-statics method says nothing about the adjustment path; it simply compares two alternative equilibrium states and specifies the change in endogenous variable induced by the change in an exogenous parameter.

So the vertical shape of the expectations-augmented, long-run Phillips Curve tells us very little about how, in any given situation, a change in the rate of inflation would actually affect the rate of unemployment. Not only does the expectations-augmented long-run Phillips Curve fail to tell us how a real system starting from equilibrium would be affected by a change in the rate of inflation, the underlying comparative-statics exercise being unable to specify the adjustment path taken by a system once it departs from its original equilibrium state, the expectations augmented, long-run Phillips Curve is even less equipped to tell us about the adjustment to a change in the rate of inflation when a system is not even in equilibrium to begin with.

The entire discourse of the expectations-augmented, long-run Phillips Curve is completely divorced from the kinds of questions that policy makers in the real world usually have to struggle with – questions like will increasing the rate of inflation of an economy in which there is abnormally high unemployment facilitate or obstruct the adjustment process that takes the economy back to a more normal unemployment rate. The expectations-augmented, long-run Phillips Curve may not be completely irrelevant to the making of economic policy – it is good to know, for example, that if we are trying to figure out which time path of NGDP to aim for, there is no particular reason to think that a time path with a 10% rate of growth of NGDP would probably not generate a significantly lower rate of unemployment than a time path with a 5% rate of growth – but its relationship to reality is sufficiently tenuous that it is irrelevant to any discussion of policy alternatives for economies unless those economies are already close to being in equilibrium.

26 Responses to “The Near Irrelevance of the Vertical Long-Run Phillips Curve”


  1. 1 Nick Rowe January 28, 2015 at 3:16 am

    Galbraith? (He was tall and thin, and around the same age as Friedman. Plus, it would be a touching photo if it were Galbraith.)

    (But Prof! I didn’t know identifying economists from rear-view photos would be on the exam!)

    Suppose we had decided to target inflation, and were trying to decide which inflation rate to target. It seems to me it is useful to break the question up into two parts:

    1. If we were already targeting x%, and would continue to target x%, what would be the best number for x? (Call it x*). That’s the Long Run question.

    2. Given that inflation is currently y%, and y > x* (say), what are the costs of transition to x*? That’s the Short Run question.

  2. 2 robertwaldmann January 28, 2015 at 3:18 am

    I entirely agree. I think the practical and empirical irrelevance of the long run Phillips curve helps us understand how it came to be believed that old Keynesians (I am thinking Solow, Samuelson and Tobin) contested Friedman’s claim. In fact, in everything by them which I have read (which isn’t close to everything that that they wrote) they agreed with his argument and conclusion, then went on to say that it didn’t offer much guidance to policymakers or econometricians. That is, they made your point (again and again). They are considered to be very smart, but not for making that obvious but important point again and again.

    Now the fact that 4 such economists agree should convince me. But I beg to differ with all 4 (see below for qualifications). The argument relies on the assumption that there is a unique equilibrium unemployment rate. It is assumed that cyclical unemployment can’t become structural or, in modern jargon, that there is no hysteresis. The existence of a natural rate of unemployment which is also the NAIRU is an article of faith. There isn’t much evidence in this continent (Europe) for any such thing. Friedman’s obvious and convincing claim is that forecast errors can’t have the same sign indefinately. The assertion that deviations of unemployment from the natural rate are all due to forecast errors and nothing else anticipates so called new Keynesian macroeconomics and still dominates the profession. However, it was not argued or defended and has been challenged by decades of European data. Samuelson and Solow discussed this issue in their 1960 AEA talk on the Phillips curve. I’m sure Tobin discussed it a lot. But somehow hysteresis is found when economists look for it then assumed away when they advise policy makers.

    The phrase “the long run Phillips curve” has content even without the possible additional words “is vertical” or “slopes down”. The phrase asserts that there is no hysteresis. It asserts that forecasts for unemployment and inflation in the distant enough future must lie on a curve — that the set of equilibria is one dimensional. With extreme enough hysteresis the set of equilibria would be limited only because the unemployment rate must be between 0 and 100%. Such a model would be crazy, but the assertion that the set equilibria is one dimensional is an assumption not a result.

  3. 3 Nick Rowe January 28, 2015 at 3:20 am

    (I think I’m agreeing with you, BTW.)

  4. 4 Nick Rowe January 28, 2015 at 3:29 am

    Robert: OK, suppose the LR Phillips Curve is vertical, but a thick vertical line. (We can build models like that (I built one myself), but they tend to be very fragile models.) We have a natural *range* of unemployment.

    What sort of AD curve would be best if the world looked like that?

  5. 5 worldofinterest January 28, 2015 at 6:09 am

    I think this misses the point of the NAIRU, or rather, is a critique of extending it to cover events which it was never intended to reflect. Essentially, NAIRU is a statement about the effect of *nominal changes* on employment under the assumption (amongst others) that (the other) *real factors* are held constant. “The Long Run” here = a period long enough that we can assume the neutrality of money. Thus, monetary easing can lower unemployment, up to a point, but further easing simply rises the price level, rather than raising output because of real constraints.

    Clearly, real factors, such as hysteresis, war, and famine on the negative side, or improving education, legal frameworks and capital markets on the positive, can move the NAIRU.

    In the real world, probably the path of unemployment has some effect on the real factors, and we are seeing that in europe, although, until one sees evidence that we are generating demand driven inflation, we will not have any idea where the NAIRU is now, although undoubtedly its higher. But that does not take away from the NAIRU as a useful way of thinking about monetary easing and unemployment/inflation. You can ease to close output gaps, but if inflation (demand side) starts to spike then you have hit your supply side constraints, and should tighten.

  6. 6 mike tennenbaum January 28, 2015 at 6:49 am

    David:
    The “tall guy” in the picture is, of course, the late George Stigler, who once said of Milton “I wish I was as sure of anything as he is of everything”. I guess that comes with being right so often. The post is well done, though I think you underestimate the importance of Friedman’s showing that the Phillips curve, as then described, was of limited usefulness as a policy tool absent some analysis of how real world transactors form expectations re expected policy measures. As a fellow UCLA student who preceded you by a couple of years, I recall Alchian/Thompson/Leijonhofvud talking about such issues in the mid to late 1960’s (aka the UCLA glory years). On a personal note, it’s good to read your stuff…..takes me back several decades, often in agreement

  7. 7 Richard G.Lipsey January 28, 2015 at 7:06 am

    I agree with Nick Rowe and Robert Waldmann. One of the most depressing things about all this is that many (most?) first year economics text books use the long run vertical Phillips curve to assert that there is only one level of unemployment and corresponding GDP that is consistent with an equality between the expected and actual inflation rates. Yet since many countries initiated a new and successful regime in which the inflation rate is targeted to stay within a narrow band on either side of a low target rate, inflation has stayed within that band (except for a few supply side shocks) where the expected and actual inflation rates have been equal while unemployment and GDP have varied over a wide range. In this new regime all too much that is in many elementary macro texts is wrong.
    I have just finished doing the 13th edition of my UK elementary text book to take account of the new regime of successful inflation targeting and had to rewrite almost completely the whole chapter on GDP and the price level

    Richard Lipsey

  8. 8 David R. Henderson January 28, 2015 at 8:37 am

    No, Nick Rowe. It’s Stigler. They were best friends. When I applied at U. of C in early 1972 and got accepted, the brochure they sent me had this picture on it.

  9. 9 David R. Henderson January 28, 2015 at 8:39 am

    And, by the way, David Glasner, I think Nick Rowe absolutely has the right to call himself an economist.

  10. 10 David Glasner January 28, 2015 at 9:32 am

    Nick, Sorry, but you guessed wrong. Galbraith (6-8) was even taller than Friedman’s companion. It would have been touching if it were they, but the truth is that, unlike Buckley and Galbraith, Friedman and Galbraith actually disliked each other.

    I agree with how you break down the short-run and long-run questions. (Good that we’re agreeing!)

    Robert, I agree with your point about the special assumptions underlying the long-run Phillips Curve. My memory is that in a later discussion of the Phillips Curve, Friedman actually conceded the possibility of hysteresis and path dependence, and said that the point of his natural rate discussion was merely to point out that monetary policy could not reduce unemployment without eventually causing inflation and beyond that point the reduction in unemployment would only be transitory. But the natural rate hypothesis was simply too appealing a pedagogical tool to be complicated by the messiness of the real world.

    Interestingly, in Sraffa’s review of Prices and Production in which he trashed Hayek’s use of the natural rate of interest as an explanation of the business cycle, Sraffa pointed out that if the banks did reduce the market rate below the natural rate the resulting investment boom might be sufficiently great to drive down the natural rate of interest to the lower rate set by the banking system. As a matter of fact, Ludwig von Mises himself conceded that this scenario was a theoretical possibility in his original presentation of his business cycle theory in The Theory of Money and Credit.

    worldofinterest, It’s not clear to me exactly what the natural rate (or NAIRU) was intended to do. But I don’t think I have any substantive disagreement with your comment.

    Mike, Great to hear from you. Yes, Stigler is the man!

    Richard, Thanks for your comment. It’s always an honor to receive a comment from you.

    The way I think about the long-run Phillips Curve is that it is strictly a locus of alternative equilibrium states existing at a point in time. It provides no basis for assuming that a cross section or times series of actual combinations of observed unemployment and observed inflation would produce a scatter that would approximate a vertical line. The long-run Phillips Curve that Friedman wanted us to think about is a creature totally distinct and disconnected from any empirically estimated Phillips Curve.

    David, Well, now Nick knows who the guy next to Friedman is, doesn’t he? So, he’s got it made.

  11. 11 David R. Henderson January 28, 2015 at 9:41 am

    Mike, It was not Stigler who made that comment. It was Solow.
    David, Milton and Rose told me, in June 1974, that their Vermont neighbor, John Kenneth Galbraith, was also their friend. They could have been lying but, somehow, I doubt it.

  12. 12 David R. Henderson January 28, 2015 at 9:42 am

    mike tennenbaum, It was not Stigler who said that; it was Solow.
    David Glasner, Actually, Rose Friedman told me in June 1974, and Milton nodded his head in agreement, that their Vermont neighbor, John Kenneth Galbraith, was also their friend.

  13. 13 David Glasner January 28, 2015 at 9:48 am

    David, You could be right about Friedman and Galbraith, but my memory (based strictly on hearsay that I can’t even attribute to any specific person) was that Friedman was highly offended by Galbraith’s attacks on him, which tended to be rather personal. He also had no respect for Galbraith as an economist, in contrast to say people like Samuelson and Solow, whose stature as economists he readily acknowledged. I also was not sure about the quote which I remember well. I would have attributed it to Samuelson. It may have been repeated by several people. I think the quote goes back even before Friedman. It might have been said about Macaulay.

  14. 14 David R. Henderson January 28, 2015 at 9:52 am

    David, Sorry for posting almost the same thing twice. I can believe that Friedman was offended (and he should have been) by Galbraith’s attacks on him, which, as you say, WERE personal. It’s also true that Friedman had little or no respect for Galbraith as an economist. But I stand by my statement that Friedman liked Galbraith, again, unless he and Rose were lying to me. There’s no contradiction between being hurt by someone and not respecting that person professionally, on the one hand, and liking him on the other. I can speak from personal experience.

  15. 15 David Glasner January 28, 2015 at 10:17 am

    I should not have said that you could be right, which might suggest that I am not sure if I believe your personal recollection. I do believe your personal recollection. So I withdraw my earlier comment that Friedman and Galbraith disliked each other.

  16. 16 Nick Rowe January 28, 2015 at 10:54 am

    Richard Lipsey! Just the man to answer this question!

    When you read Friedman 1968, after writing your own (very good) theory of the underpinnings of the Phillips Curve, what was your impression? How much of Friedman 68 struck you as new, at the time?

    Because I think I remember you saying, at a Queens/Western PhD student mini-conference at Queens in the Winter of 78 or 79 (I was the Western student with an attitude problem), that your mistake had been to assume that nominal wages, not real wages, adjusted to excess supply or demand in local labour markets, and that science progresses as we fix our mistakes (while you gave a talk on Kuhn, I think).

  17. 17 doncoffin64 January 28, 2015 at 10:58 am

    Another point to be considered, of course, is that at any given time in the actual course of the economy, we may or may not be at an equilibrium level of anything. So even if it were correct that the long-run expectation augmented Phillips curve were vertical, if we are not starting from an equilibrium level of unemployment, the long-run adjustment of the economy to a higher rate of inflation might well be a lower level of unemployment.

  18. 18 Richard Lipsey January 28, 2015 at 12:31 pm

    Nick, When Friedman called on me at the LSE not long after I had published my Phillips curve paper, he said I should have used real wages not nominal wages as the variable to be explained. I replied to him, as I still say now: NO What workers bargain over is the money wage and it is changes in them that we need to explain. If the price level, actual or expected, influences the money wage bargain, it should be part of the explanation not part of what is explained in the wage equation. Note that the expectations- augmented Phillips curve does explain money wages not real wages and the inflation occurs on the right hand side of the wage equation not the left hand side.

    My views on what is wrong with the whole approach can be found in the paper I gave to the Economics History Society a year or so ago: “The Phillips Curve and the Tyranny of an Assumed Unique Macroeconomic Equilibrium”. It is available on Research Gate

  19. 19 Benjamin Cole January 29, 2015 at 11:17 pm

    Okay, I am just a pundit, but Tim Duy produced a graph, that I copied over at Historinhas that shows the Phillips Curve to be nearly prone in the USA. It takes about 5 percent increase Iin unemployment to cut inflation by 1 percent.
    I think the modern-day Phillips Curve shows we have little to fear from low unemployment. Indeed, see USA right now…

  20. 20 Unlearningecon January 30, 2015 at 2:26 am

    Great post, David.

    “it is irrelevant to any discussion of policy alternatives for economies unless those economies are already close to being in equilibrium.”

    Here’s another question: how do we empirically determine whether or not an economy is in equilibrium?

  21. 21 David Glasner January 30, 2015 at 5:36 am

    Don, Yes, I agree completely.

    Richard, Thanks for referencing that paper. When I get a chance I will read, and perhaps write about, it. The multiple equilibria point is very important, but I wanted to stay within the four corners of Friedman’s own discussion in questioning whether he was making a substantive as opposed to a rhetorical contribution in his 1968 paper.

    Benjamin, As usual you are a tad farther out on the extreme left wing than I feel comfortable going, but I must admit that you don’t sound all that crazy to me.

    Unlearningecon, I don’t think that there is a litmus test by which to determine when an economy is in the neighborhood of an equilibrium, because the economy never is in equilibrium. Saying that the economy is close to being in equilibrium is to speak metaphorically, not empirically. I don’t know if that helps, but that’s the best I can do. Perhaps others, maybe someone like, say, Richard Lipsey, for example, could do better.

  22. 22 richard lipsey January 30, 2015 at 6:02 am

    As the discussion turns to equilibrium and all that I thought it might be worth posting he abstract to the paper of mine about the tyranny of assumed equilibrium that I referred to earlier See below
    PS I am going on holiday today and will not be able to take part in further discussions for 3 weeks.
    ABSTRACT
    To make the argument that the behaviour of modern industrial economies since the 1990s is inconsistent with theories in which there is a unique ergodic macro equilibrium, the paper starts by reviewing both the early Keynesian theory in which there was no unique level of income to which the economy was inevitably drawn and the debate about the amount of demand pressure at which it was best of maintain the economy: high aggregate demand and some inflationary pressure or lower aggregate demand and a stable price level. It then covers the rise of the simple Phillips curve and its expectations-augmented version, which introduced into current macro theory a natural rate of unemployment (and its associated equilibrium level of national income). This rate was also a NAIRU, the only rate consistent with stable inflation. It is then argued that the current behaviour of many modern economies in which there is a credible policy to maintain a low and steady inflation rate is inconsistent with the existence of either a unique natural rate or a NAIRU but is consistent with evolutionary theory in which there is perpetual change driven by endogenous technological advance. Instead of a NAIRU evolutionary economies have a non-inflationary band of unemployment (a NAIBU) indicating a range of unemployment and income over with the inflation rate is stable. The paper concludes with the observation that the great pre-Phillips curve debates of the 1950s that assumed that there was a range within which the economy could be run with varying pressures of demand, and varying amounts of unemployment and inflationary pressure, were not as silly as they were made to seem when both Keynesian and New Classical economists accepted the assumption of a perfectly inelastic, long-run Phillips curve located at the unique equilibrium level of unemployment .

  23. 23 Nick Rowe January 30, 2015 at 9:37 am

    Richard: good answer. Thanks.

  24. 24 Benjamin Cole January 30, 2015 at 1:54 pm

    David! I am not left-wing! I am an growth-oriented market monetarist. For example, I would cut the Social Security and VA “disability” programs.
    I would crank up the money presses at the Fed big time. and I would look for ways to cut the Department of Defense in half.
    So, I am not sure I am left wing. For the next couple hours anyway until I change my mind again.

  25. 25 David Glasner February 5, 2015 at 6:23 pm

    Richard, Thanks for posting the abstract. It inspired me to write a further post on the Phillips curve.

    Benjamin, I know that you’re not really left wing, but sometimes your inflationary tendencies might lead those who don’t know better to think that you are a flaming left-winger. Anyway, I was just teasing.


  1. 1 Making Sense of the Phillips Curve | Uneasy Money Trackback on February 4, 2015 at 7:47 pm

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey's unduly neglected contributions to the attention of a wider audience.

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