Making Sense of the Phillips Curve

In a comment on my previous post about supposedly vertical long run Phillips Curve, Richard Lipsey mentioned a paper he presented a couple of years ago at the History of Economics Society Meeting: “The Phillips Curve and the Tyranny of an Assumed Unique Macro Equilibrium.” In a subsequent comment, Richard also posted the abstract to his paper. The paper provides a succinct yet fascinating overview of the evolution macroeconomists’ interpretations of the Phillips curve since Phillips published his paper almost 60 years ago.

The two key points that I take away from Richard’s discussion are the following. 1) A key microeconomic assumption underlying the Keynesian model is that over a broad range of outputs, most firms are operating under conditions of constant short-run marginal cost, because in the short run firms keep the capital labor ratio fixed, varying their usage of capital along with the amount of labor utilized. With a fixed capital-labor ration, marginal cost is flat. In the usual textbook version, the short-run marginal cost is rising because of a declining capital-labor ratio, requiring an increasing number of workers to wring out successive equal increments of output from a fixed amount of capital. Given flat marginal cost, firms respond to changes in demand by varying output but not price until they hit a capacity bottleneck.

The second point, a straightforward implication of the first, is that there are multiple equilibria for such an economy, each equilibrium corresponding to a different level of total demand, with a price level more or less determined by costs, at any rate until total output approaches the limits of its capacity.

Thus, early on, the Phillips Curve was thought to be relatively flat, with little effect on inflation unless unemployment was forced down below some very low level. The key question was how far unemployment could be pushed down before significant inflationary pressure would begin to emerge. Doctrinaire Keynesians advocated driving unemployment down as low as possible, while skeptics argued that significant inflationary pressure would begin to emerge even at higher rates of unemployment, so that a prudent policy would be to operate at a level of unemployment sufficiently high to keep inflationary pressures in check.

Lipsey allows that, in the 1960s, the view that the Phillips Curve presented a menu of alternative combinations of unemployment and inflation from which policymakers could choose did take hold, acknowledging that he himself expressed such a view in a 1965 paper (“Structural and Deficient Demand Unemployment Reconsidered” in Employment Policy and the Labor Market edited by Arthur Ross), “inflationary points on the Phillips Curve represent[ing] disequilibrium points that had to be maintained by monetary policy that perpetuated the disequilibrium by suitable increases in the rate of monetary expansion.” It was this version of the Phillips Curve that was effectively attacked by Friedman and Phelps, who replaced it with a version in which the equilibrium rate of unemployment is uniquely determined by real factors, the natural rate of unemployment, any deviation from the natural rate resulting in a series of adjustments in inflation and expected inflation that would restore the natural rate of unemployment.

Sometime in the 1960s the Phillips curve came to be thought of as providing a stable trade-off between inflation and unemployment. When Lipsey did adopt this trade-off version, as for example Lipsey (1965), inflationary points on the Phillips curve represented disequilibrium points that had to be maintained by monetary policy that perpetuated the disequilibrium by suitable increases in the rate of monetary expansion. In the new Classical interpretation that began with Edmund Phelps (1967), Milton Friedman (1968) and Lucas and Rapping (1969), each point was an equilibrium point because demands and supplies of agents were shifted from their full-information locations when they misinterpreted the price signals. There was, however, only one full-information equilibrium of income, Y*, and unemployment, U*.

The Friedman-Phelps argument was made as inflation rose significantly in the late 1960s, and the mild 1969-70 recession reduce inflation by only a smidgen, setting the stage for Nixon’s imposition of his disastrous wage and price controls in 1971 combined with a loosening of monetary policy by a compliant Arthur Burns as part of Nixon’s 1972 reelection strategy. When the hangover to the 1972 monetary binge was combined with a quadrupling of oil prices by OPEC in late 1973, the result was a simultaneous increase in inflation and unemployment – stagflation — a combination widely perceived as a decisive refutation of Keynesian theory. To cope with that theoretical conundrum, the Keynesian model was expanded to incorporate the determination of the price level by deriving an aggregate supply and aggregate demand curve in price-level/output space.

Lipsey acknowledges a crucial misstep in constructing the Aggregate Demand/Aggregate Supply framework: assuming a unique macroeconomic equilibrium, an assumption that implied the existence of a unique natural rate of unemployment. Keynesians won the battle, providing a perfectly respectable theoretical explanation for stagflation, but, in doing so, they lost the war to Friedman, paving the way for the malign ascendancy of New Classical economics, with which New Keynesian economics became an effective collaborator. Whether the collaboration was willing or unwilling is unclear and unimportant; by assuming a unique equilibrium, New Keynesians gave up the game.

I was so intent in showing that this AD-AS construction provided a simple Keynesian explanation of stagflation, contrary to the accusation of the New Classical economists that stagflation provided a conclusive refutation of Keynesian economics that I paid too little attention to the enormous importance of the new assumption introduced into Keynesian models. The addition of an expectations-augmented Philips curve, negatively sloped in the short run but vertical in the long run, produced a unique macro equilibrium that would be reached whatever macroeconomic policy was adopted.

Lipsey does not want to go back to the old Keynesian paradigm; he prefers a third approach that can be traced back to, among others, Joseph Schumpeter in which the economy is viewed “as constantly evolving under the impact of endogenously generated technological change.” Such technological change can be vaguely foreseen, but also gives rise to genuine surprises. The course of economic development is not predetermined, but path-dependent. History matters.

I suggest that the explanation of the current behaviour of inflation, output and unemployment in modern industrial economies is provided not by any EWD [equilibrium with deviations] theory but by evolutionary theories. These build on the obvious observation that technological change is continual in modern economies (decade by decade at least since 1760), but uneven (tending to come in spurts), and path dependent (because, among other reasons, knowledge is cumulative with one advance enabling another). These changes are generated endogenously by private-sector, profit-seeking agents competing in terms of new products, new processes and new forms of organisation, and by public sector activities in such places as universities and government research laboratories. They continually alter the structure of the economy, causing waves of serially correlated investment expenditure that are a major cause of cycles, as well as driving the long-term growth that continually transforms our economic, social and political structures. In their important book As Time Goes By, Freeman and Louça (2001) trace these processes as they have operated since the beginnings of the First Industrial Revolution.

A critical distinction in all such theories is between risk, which is easily handled in neoclassical economics, and uncertainty, which is largely ignored in it except to pay it lip service. In risky situations, agents with the same objective function and identical knowledge will chose the same alternative: the one that maximizes the expected value of their profits or utility. This gives rise to unique predictable behaviour of agents acting under specified conditions. In contrast in uncertain situations, two identically situated and motivated agents can, and observably do, choose different alternatives — as for example when different firms all looking for the same technological breakthrough chose different lines of R&D — and there is no way to tell in advance of knowing the results which is the better choice. Importantly, agents typically make R&D decisions under conditions of genuine uncertainty. No one knows if a direction of technological investigation will go up a blind alley or open onto a rich field of applications until funds are spend investigating the route. Sometimes trivial expenses produce results of great value while major expenses produce nothing of value. Since there is no way to decide in advance which of two alternative actions with respect to invention or innovation is the best one until the results are known, there is no unique line of behaviour that maximises agents’ expected profits. Thus agents are better understood as groping into an uncertain future in a purposeful, profit- or utility-seeking manner, rather than as maximizing their profits or utility.

This is certainly the right way to think about how economies evolve over time, but I would just add that even if one stays within the more restricted framework of Walrasian general equilibrium, there is simply no persuasive theoretical reason to assume that there is a unique equilibrium or that an economy will necessarily arrive at that equilibrium no matter how long we wait. I have discussed this point several times before most recently here. The assumption that there is a natural rate of unemployment “ground out,” as Milton Friedman put it so awkwardly, “by the Walrasian system of general equilibrium equations” simply lacks any theoretical foundation. Even in a static model in which knowledge and technology were not evolving, the natural rate of unemployment is a will o the wisp.

Because there is no unique static equilibrium in the evolutionary world in which history matters, no adjustment mechanism is required to maintain it. Instead, the constantly changing economy can exist over a wide range of income, employment and unemployment values, without behaving as it would if its inflation rate were determined by an expectations-augmented Phillips curve or any similar construct centred on unique general equilibrium values of Y and U. Thus there is no stable long-run vertical Phillips curve or aggregate supply curve.

Instead of the Phillips curve there is a band as shown in Figure 4 [See below]. Its midpoint is at the expected rate of inflation. If the central bank has a credible inflation target that it sticks to, the expected rate will be that target rate, shown as πe in the figure. The actual rate will vary around the expected rate depending on a number of influences such as changes in productivity, the price of oil and food, but not significantly on variations in U or Y. At either end of this band, there may be something closer to a conventional Phillips curve with prices and wages falling in the face of a major depression and rising in the face of a major boom financed by monetary expansion. Also, the whole band will be shifted by anything that changes the expected rate of inflation.

phillips_lipsey

Lipsey concludes as follows:

So we seem to have gone full circle from early Keynesian view in which there was no unique level of income to which the economy was inevitably drawn, through a simple Phillips curve with its implied trade off, to an expectations-augmented Phillips curve (or any of its more modern equivalents) with its associated unique level of national income, and finally back to the early non-unique Keynesian view in which policy makers had an option as to the average pressure of aggregate demand at which the economy could be operated.

“Perhaps [then] Keynesians were too hasty in following the New Classical economists in accepting the view that follows from static [and all EWD] models that stable rates of wage and price inflation are poised on the razor’s edge of a unique NAIRU and its accompanying Y*. The alternative does not require a long term Phillips curve trade off, nor does it deny the possibility of accelerating inflations of the kind that have bedevilled many third world countries. It is merely states that industrialised economies with low expected inflation rates may be less precisely responsive than current theory assumes because they are subject to many lags and inertias, and are operating in an ever-changing and uncertain world of endogenous technological change, which has no unique long term static equilibrium. If so, the economy may not be similar to the smoothly functioning mechanical world of Newtonian mechanics but rather to the imperfectly evolving world of evolutionary biology. The Phillips relation then changes from being a precise curve to being a band within which various combinations of inflation and unemployment are possible but outside of which inflation tends to accelerate or decelerate. Perhaps then the great [pre-Phillips curve] debates of the 1940s and early 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 inflation[ary 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, one-dimensional, long run Phillips curve located at a unique equilibrium Y* and NAIRU.” (Lipsey, “The Phillips Curve,” In Famous Figures and Diagrams in Economics, edited by Mark Blaug and Peter Lloyd, p. 389)

11 Responses to “Making Sense of the Phillips Curve”


  1. 1 Nick Edmonds February 5, 2015 at 3:04 am

    Nice post.

    I think the point about flat marginal costs is a good one. Economists tend to throw neat well behaved production functions into models just because they are easy to use, but don’t often stop to think about how much this might be influencing their conclusions. However, I’m not sure that flat marginal cost necessarily implies multiple equilibria. The other factor here is labour supply, so you should be able to get a single equilibrium even in a pure service economy, where you have increasing disutility of labour time.

    In more real world terms, having a flat section of the Phillips curve, requires not only level labour productivity, but also a range within which real wage aspirations are flat. It is of course quite possible that this is also the case.

  2. 2 Nick Rowe February 5, 2015 at 3:48 am

    Slightly off-topic, but that Lucas Rapping 1969 paper is just wrong IIRC. Buried in a footnote is an assumption that the nominal interest rate is constant, despite perfectly flexible P and W and fluctuations in expected inflation, which makes no sense from a GE perspective. Lucas 72 actually has a similar problem, because there’s no interest rate in the model, since currency is the only asset.

    Now to think about Lipsey’s paper.

  3. 3 Nick Rowe February 5, 2015 at 4:07 am

    David: “The second point, a straightforward implication of the first, is that there are multiple equilibria for such an economy, each equilibrium corresponding to a different level of total demand, with a price level more or less determined by costs, at any rate until total output approaches the limits of its capacity.”

    I disagree.

    For simplicity, let’s ignore capital. Labour is the only input, and MPL is a constant, so each firm has a flat MC curve. And let’s also assume that elasticity of demand is a constant, so each firm sets price as a constant markup over MC, that is independent of output. We only get multiple equilibria if the economy-wide labour supply curve is perfectly elastic with respect to the real wage over some range. With an upward-sloping labour supply curve there is a unique macro equilibrium Y* and L*.

    If we start at Y*, then increase M and Aggregate Demand, and suppose that firms initially hold P constant and increase Y and L (moving along their flat MC curves), they would find they need to increase W, given P, to be able to hire more labour. And that increase in W causes their MC curves to shift up, so they would increase P in response.

    MC can be independent of Y for each individual firm (flat MC curves), but an increasing function of Y for firms in aggregate (the flat MC curves shift up if all firms increase Y).

  4. 4 Bill Woolsey February 5, 2015 at 5:51 am

    I share Lipsey’s vision of the economy. I like the risk vs. uncertainty a lot.

    I think that this very much suggests that targeting interest rates is a terrible idea. And further, that short term real interest rates might need to be negative sometime. Coordinating saving and investment in a world of creative destruction could easily require substantial variance in short term real interest rates.

    I agree that there is no guarantee that independently adjusting price to clear each market will result in a historical process of bringing the economy into a general equilibrium. I have always thought that the fact that each price is of a good that is a substitute, complement, input or output of other goods creates more disequilibrium. But I also understand that actual earnings impact demand, and actual earnings are less than equilibrium earnings in disequilibrium.

    OK..

    Does the conclusion follow that policy makers can effectively determine the average level of aggregate demand and so aggregate employment?

    The economy is running slow, so we should increase government spending? Or is this just a claim that the central bank should vary interest rates a lot? Or maybe that looking for some fixed coefficient to predict how interest rates will impact aggregate demand is a fools errand?

    Lipsey’s approach the the macroeconomy suggests that targeting the unemployment rate or real output is a bad idea. They aren’t well defined.

    I still favor a 3 percent growth path for nominal GDP even if I fully anticipate that real GDP will not remain on a 3% growth path. Let the price level adjust.

    I don’t think the no natural tendency to get to equilibrium tells us that much at all. It seems to me that targeting the GE level of real output would be a good idea. I suppose we might believe that more or less aggregate demand would make no difference as prices and wages just cobweb about and output is less than optimal because of shortages and surpluses.

    Really, I think that Glasner’s point explains why centrally planned economies like North Korea are so much more productive than market economies. Depending on decentralized price setting just doesn’t work to coordinate the economy. Only if all the prices are set once and for all, will perfect coordination occur–at best more or less like the geniuses at the North Korean planning agency who consider all production possibilities and pick the optimum one and have have all of the plant managers follow the instructions–take the resources delivered to you, produce this output and deliver it there. It is only common sense.

    I guess I should read more of Lipsey, since I like his vision of the economy so much.. But is he really saying that the old Keynesian view of flat marginal cost curves is correct? How does that apply to creative destruction?

    Surely the old Keynesian view is very much static Unemployment rises and falls as the same old factories let workers go or hire them back according to the demand for unchanging products.

    Are we really going to say that the expanding firms producing the new products or some old product in a new way can be characterized by a horizontal marginal cost curve?

    As the wreckage of failed plans is put together in new ways, wouldn’t competition for these pieces, including workers, impact their prices?

    While I am not sure about the relatively new data we now see about quits, layoffs and hires, it certainly suggests that seeing employment as existing firms letting people go and hiring them back is not that much of the story we are trying to understand.

  5. 5 Rob Rawlings February 5, 2015 at 7:30 am

    @Nick Rowe

    On “If we start at Y*, then increase M and Aggregate Demand, and suppose that firms initially hold P constant and increase Y and L (moving along their flat MC curves), they would find they need to increase W, given P, to be able to hire more labour. And that increase in W causes their MC curves to shift up, so they would increase P in response.”

    Isn’t there an assumption in these cost+markup models (where its easy to derive multiple equilibria) that W will not rise as L increases until a point of full employment is reached and cost-push inflation starts to kick in ?

  6. 6 Kevin Donoghue February 5, 2015 at 8:35 am

    Nick: “We only get multiple equilibria if the economy-wide labour supply curve is perfectly elastic with respect to the real wage over some range.”

    If this is an Old Keynesian model we’re talking about, on my reading of it at any rate, the labour supply curve does nothing apart from telling us how much involuntary unemployment there is.

  7. 7 David Glasner February 5, 2015 at 9:36 am

    Nick Edmonds, Glad you liked it. I have not thought carefully about whether flat firm marginal costs over some range is sufficient to ensure multiple equilibria. I think the general message from the GE literature is that the necessary conditions for guaranteeing a unique equilibrium are quite strong, so there is certainly no theoretical basis for the assumption that a general-equilibrium solution, if it exists, will be unique.

    Nick Rowe, Thanks for pointing out that flaw in the Lucas Rapping paper, which I haven’t looked at for about 40 years.

    I take your point about the labor supply, but it doesn’t seem implausible to me that there is a range over which the labor supply curve is perfectly elastic. In their textbook, Alchian and Allen have discussion in which they explain how demand can cause inflation even if all firms are setting price by applying a fixed markup over their costs. So I do agree with you that my statement about a flat Phillips curve being a straightforward implication of flat marginal cost curves was too strong. On the other hand, I think it is not implausible to assume that over a range of unemployment rates, the Phillips curve could be pretty flat.

    Bill, I can’t speak for Lipsey, but I suspect that he would not recommend going back to the good old days of Keynesian aggregate demand management. That certainly would not be my recommendation. But just because we don’t want to go back to old Keynesianism doesn’t mean that we can’t look critically at some of the arguments that were used to debunk old Keynesianism. I think the natural rate of unemployment is an idea that makes sense only in a very simplistic model that doesn’t capture a lot of important and fairly obvious features of the real world. I think that NGDP level targeting is a fine idea, but I suspect that if it is ever adopted, we will not be entirely happy with its results, either.

  8. 8 Nick Rowe February 5, 2015 at 10:36 am

    Rob, Kevin, and David:

    First assume the labour supply curve is a reverse-L-shaped function of the real wage W/P. So it’s flat at some level (call it “v”) until we hit full employment at L*, and is vertical thereafter.

    If v (1-1/e), there is a unique equilibrium at L=0 (100% unemployment).

    If, by sheer fluke, v = (1-1/e) we get a range of equilibria between L=0 and L=L*.

    If instead we assume the labour supply curve is a reverse-L-shaped function of the nominal wage W, we get a standard Old Keynesian reverse-L-shaped AS curve.

  9. 9 Nick Rowe February 5, 2015 at 10:40 am

    Curses! The greater than less than signs messed up my comment! Here it is again:

    Rob, Kevin, and David:

    First assume the labour supply curve is a reverse-L-shaped function of the real wage W/P. So it’s flat at some level (call it “v”) until we hit full employment at L*, and is vertical thereafter.

    If v is less than (1-1/e), where e is the (assumed constant) elasticity of an individual firm’s demand curve, there is a unique equilibrium at L=L* (full employment).

    If v is greater than (1-1/e), there is a unique equilibrium at L=0 (100% unemployment).

    If, by sheer fluke, v = (1-1/e) we get a range of equilibria between L=0 and L=L*.

    If instead we assume the labour supply curve is a reverse-L-shaped function of the nominal wage W, we get a standard Old Keynesian reverse-L-shaped AS curve.


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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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