3

The Phillips Curve Becomes Vertical

There is need for much more detailed research into the relations between unemployment, wage rates, prices and productivity.

—A. W. PHILLIPS (1958)

The epigraph is the final sentence of one of the most famous papers in the history of macroeconomics, published in 1958 by A. W. Phillips (1958, 299), who was then a professor at the London School of Economics (LSE).¹ The sentence reads very modestly, as does the whole paper. Despite his astounding life story, Phillips was apparently a modest man. But his 1958 paper caused a sensation and has had profound and lasting effects on fiscal and especially monetary policy around the world.

Before Phillips

To appreciate why Phillips’s 1958 paper made such a splash, a quick review of the intellectual framework of the 1950s is useful. The Keynesian revolution had swept through much of academia by then—skipping, of course, the University of Chicago. But early Keynesian models, as exemplified by the ubiquitous IS-LM model, had no theory of inflation. Taken literally, IS-LM itself was a fixed-price model; the price level never changed. No one believed that described reality, of course. Common renderings of what might be called “crude Keynesianism” sometimes conceptualized the aggregate supply curve as approximated by a backward L: flat until the economy approached full employment (at y* in the graph), then rising almost vertically (figure 3.1).

FIGURE 3.1. The backward L-shaped aggregate supply curve.

Notice the stark empirical implication of this crude Keynesian model: expanding aggregate demand by monetary or fiscal policy does not cause inflation until you pass the kink in the aggregate supply curve at “full employment.” After that, any further increases in aggregate demand cause only inflation, with no further increments to output. If you really believed in such a naive view of the world, then either monetary or fiscal policy could be employed to boost employment, but not to reduce inflation, when the economy was operating below full employment; the opposite would be true beyond full employment. Pretty simple.

Far too simple, in fact. I doubt that anyone ever believed that the real world was that binary. All you had to do to refute the stark dichotomy depicted in figure 3.1 was open your eyes. The data on inflation, displayed in figure 3.2 for the decade of the 1950s, certainly did not support the inflation-on or inflation-off view. Inflation moved up and down. Attempts to reconcile this extremely naive theory with the facts gave rise to debates over cost-push versus demand-pull inflation, the possible importance of sectoral bottlenecks, and so on. The profession was looking, desperately you might say, for a way to integrate variable inflation into Keynesian theory.

FIGURE 3.2. The U.S. inflation rate, 1950–1959 (December-to-December Consumer Price Index).

Source: Bureau of Labor Statistics.

What Phillips Found

While he eschewed making sweeping claims, Phillips filled this intellectual gap by offering a smooth empirical curve to replace the reverse-L in figure 3.1—a curve he “fit” to British wage inflation data by what can only be called unusual methods. What would soon be named the Phillips curve showed a strong negative relationship between the rate of change of money wages and the unemployment rate in the United Kingdom over the years 1861–1913. Finding such a negative relationship was hardly a surprise. The first sentence of Phillips’s famous paper (1958, 283) was a straightforward statement: “When the demand for a commodity or service is high relative to the supply of it we expect the price to rise.” I presume that students at the LSE knew that at the time.

FIGURE 3.3. Phillips’s original curve: UK data, 1861–1913.

Source: Phillips (1958).

What was surprising in Phillips’s paper was the seeming durability and consistency of the relationship. His original curve, reproduced here as figure 3.3, was based on data from 1861 to 1913. That’s a long time span. Even more amazingly, however, the data points for the years 1948–1957 (the most recent ten years at the time) fell almost exactly on the curve Phillips had fit to the older data. Thought of as a test of postsample stability of an estimated equation, the econometrician had skipped thirty-five years of data and then estimated almost exactly the same equation. Remarkable. No wonder Phillips’s paper attracted so much attention.

It did not take long to notice that it was a quick hop, step, and jump from an equation for nominal wage increases to an equation for price increases. The Phillips curve thus “closed” the Keynesian model by providing the missing equation for inflation. Notably, however, Phillips’s original wage equation included no inflation term whatsoever. Think about that. He was seeking a statistical explanation for the rate of change of nominal wages, and yet he omitted inflation as a determinant. From a modern perspective, that seems incredible. And Phillips did not just forget about inflation; he mentioned it and dismissed its importance: “It will be argued here … that cost of living adjustments will have little or no effect on the rate of change of money wage rates” (Phillips 1958, 283). Really?

Two years later, Phillips’s LSE colleague, Richard Lipsey (1960),² remedied this omission by estimating a coefficient of 0.37 on inflation in a Phillips curve of the form

wt = α πt + f (Ut) + εt, (1)

where Wt is the rate of change of nominal wages, f(U) is a nonlinear function of the unemployment rate, π_t is the inflation rate, and ε_t is a stochastic error term. When Lipsey estimated that same equation over more modern (at the time) data rather than 1861–1913, his estimate of α rose to 0.76 (with standard error 0.08). Lipsey probably never imagined how important that estimated parameter would subsequently become.

That same year, Paul Samuelson and Robert Solow (1960) brought the Philips curve to America in a paper presented at the December 1959 meetings of the American Economic Association. Their august professional status alone guaranteed that their paper would garner a great deal of attention. And it did.

Using inflation on the vertical axis rather than the rate of change of nominal wages, Samuelson and Solow (1960) sketched what they called a “modified Phillips curve for the US.” Perhaps most noteworthy and consistent with the discussion in their paper, they captioned that figure as follows: “This shows the menu of choice between different degrees of unemployment and price stability, as roughly estimated from the last twenty-five years of American data” (192). Roughly estimated, indeed. The Samuelson-Solow Phillips curve was a freehand sketch, not an econometric estimate. While I was writing this book, Solow recalled to me in private correspondence that neither he nor Samuelson had a computer at the time! Yes, and that was at MIT.

A. W. “Bill” Phillips (1914–1975)

Engineer Turned Economist

Bill Phillips is, of course, most famous for discovering what came to be called the Phillips curve. (He did not give it that name himself!) But his life before economics is little short of remarkable.³

Phillips was born on a farm in New Zealand, left high school at the age of fifteen to become an electrical engineering apprentice, and six years later moved to Australia, where he bounced around for about two years holding jobs as diverse as electrician at a gold mine and crocodile hunter. In 1937, he set off on the long journey to England, part of which was via the Trans-Siberian Railway. Once in London, he qualified as an electrical engineer. But when World War II war came, he joined the Royal Air Force. While traveling to Java by sea in 1942, Phillips’s ship was attacked by enemy aircraft, and his bravery handling a machine gun later earned him his Member of the Order of the British Empire award. Not many economists ever did that!

Unfortunately, Phillips was captured by the Japanese in Java. During his three and a half years in prisoner-of-war camps, he built and operated a clandestine radio, learned Chinese from fellow prisoners, and developed the bad nicotine habit that probably contributed to his early death.

Returning to England in 1946, Phillips enrolled at the LSE for a sociology degree but quickly developed an interest in economics and in Keynesian theory in particular. Seeing the analogy between economic flows and hydraulic ones, he built a machine in which water literally flowed through clear plastic tubes to depict the Keynesian circular flow of income and expenditure. The machine was a sensation at the LSE, graced the school’s basement for years, and was later put on display in London’s Science Museum. It now resides at the Reserve Bank of New Zealand.

Phillips joined the LSE faculty in 1950, and his rise was meteoric by the standards of the day: to professor by 1958. That was also the year in which he published his famous paper, “The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957.” The rest, as they say, is history.

In 1967, Phillips moved back to Australia to assume a chair at the Australian National University in Canberra. But in 1969, he suffered a stroke and retired to Auckland, where he died in his native land in 1975.

Interpreting the Phillips curve as a “menu of choice” became the central intellectual frame after the Samuelson-Solow article, at least among Keynesians. Policy makers could choose, say, a combination of high inflation and low unemployment or a combination of low inflation and high unemployment. Pretty soon, the conventional wisdom held that liberal Democrats preferred to ride up the Phillips curve toward lower unemployment and higher inflation, while conservative Republicans preferred to ride down the Phillips curve toward lower inflation and higher unemployment. Indeed, that became a hallmark distinguishing liberal from conservative macroeconomists.

If you read Samuelson and Solow carefully, however, they hedged their bet: “All of our discussion has been phrased in short-run terms, dealing with what might happen in the next few years. It would be wrong, though, to think that our … menu that relates obtainable price and unemployment behavior will maintain its same shape in the longer run” (1960, 193). But lest you think they correctly anticipated what would happen over the next ten to fifteen years, the esteemed pair did not pin these possible shifts of the Phillips curve mainly on changes in expected inflation. Others subsequently did so, however.

Milton Friedman’s presidential address to the American Economic Association in December 1967 received the most attention—immediately. He argued that the menu of choices allegedly offered by a negatively sloped Phillips curve was a mirage because it ignored the evolution of expected inflation. Once you took the adjustment of inflationary expectations into account, he argued, the only level of unemployment sustainable in the long run was its “natural rate,” which was “the level that would be ground out by the Walrasian system of general equilibrium equations” (Friedman 1968, 8). Most important, the natural rate of unemployment was impervious to monetary policy. (Friedman didn’t think or write much about fiscal policy.)

The mechanism was straightforward. If monetary policy pushed the unemployment rate (U) below its natural rate (U*), both inflation (π) and the rate of increase of money wages would start rising. If firms caught on to what was happening before workers did (his general presumption), then prices would rise faster than wages, so real wages would fall. Lower real wage costs would, in turn, motivate firms to boost employment, thereby pushing U below U* in the short run. Over time, however, workers would catch on, real wages would rise back to their equilibrium levels, firms would have no extra incentives to hire, and U would return to U*. The true menu of long-run choices, Friedman argued, consisted of the unique unemployment rate, U*, coupled with any rate of inflation policy makers chose. To wit, the long-run Phillips curve was vertical.

Edmund Phelps (1967, 1968) developed a similar though more formal model in which both firms and workers were fooled by inflation at first, leading to transitorily higher employment. But both eventually caught on, leading to a conclusion identical to Friedman’s: there is no trade-off in the long run. Given what was to come later, it is worth pointing out that neither Friedman’s verbal analysis nor Phelps’s equation-laden model embodied what would soon be called rational expectations. Rather, each of them viewed expectations as lagging behind reality but eventually catching up—something approximating adaptive expectations. During the transition period when U was below U*, π^e would systematically lag behind π, which was rising. Robert Lucas and others would subsequently argue that such lagging, and therefore biased, expectations were not “rational.” But in 1968, hardly anyone was thinking that way.⁴

As Robert Gordon pointed out decades later, the timing of Friedman’s presidential address and Phelps’s two papers “was impeccable and even uncanny” (2011, 16). The Kennedy-Johnson tax cuts followed by the Vietnam War buildup had pushed unemployment well below any reasonable estimate of the natural rate, and inflation rose throughout the 1960s—just as the Friedman-Phelps model had predicted (figure 3.4). Thus, the new natural rate theory both enhanced the charge that Keynesian demand-management policies were inflationary and buttressed the claim that monetarism provided a better, or at least less inflationary, policy frame.

Keynesian “theory” was wounded though, as it turned out, not mortally. As Solow reflected decades later, “Maybe a patchwork of ideas like eclectic American Keynesianism, held together partly by duct tape, is always at a disadvantage compared with a monolithic doctrine that has an answer for everything, and the same answer for everything” (2018, 424). But back to the Phillips curve—and the duct tape.

To incorporate the Friedman-Phelps analysis into the Phillips curve (1) above, add a (presumably negative) constant (because price inflation runs below wage inflation) and, much more important, replace actual inflation on the right-hand side by expected inflation to get

FIGURE 3.4. The U.S. inflation rate, 1961–1970 (December-to-December Consumer Price Index).

Source: Bureau of Labor Statistics.

$${\text{π}}_t=\theta +\alpha {\text{π}}_t^e+f(U_t)+{\epsilon }_t.$$(2)

In equilibrium ${\pi }_t={\pi }_t^e$, so equation (2) reduces to

(1 − α) π_t = θ + f (U_t),

which defines a negative relationship between π and U, to wit, a long-run sloping Phillips curve of the sort that Samuelson and Solow (1960) had depicted. If α = 1, however, you get 0 = θ + f(U_t) instead, which defines a unique equilibrium level of unemployment, Friedman’s natural rate, and a vertical long-run Phillips curve. Hence, empirical attention started to focus on estimating the parameter α. Was it equal to or less than 1?

Remember, Lipsey (1960) had estimated α to be less than 1; so did a number of papers that came after his. For example, the first in what was destined to become a long series of Phillips curve estimates by Robert Gordon (1970) estimated α to be only 0.45.5 Lipsey and Gordon were not alone in estimating α < 1. I entered graduate school in the fall of 1967, first at the LSE (the former home of Phillips) and then at MIT (the home of Samuelson and Solow). The view in such places at the time, I well remember, was that while Friedman and Phelps had made convincing theoretical cases that α should be equal to 1, the empirical evidence virtually screamed out that α < 1. It was one of those stark cases in which theory and empirics clashed sharply. As Groucho Marx memorably asked, “Who are ya gonna believe, me or your own eyes?” The view at MIT, as I recall, was go with your own eyes.

Meanwhile, a young economist at the University of Pennsylvania named Thomas Sargent (1971), a subsequent Nobel Prize winner, was demonstrating—in a beautiful five-page paper that was underappreciated at the time—that the debate over the estimated parameter α was beside the point. His argument, based on an early use of rational expectations, was this. It had become common econometric practice to proxy the unobservable expected inflation rate in (2) by a distributed lag of past actual inflation rates. Thus, people were actually estimating Phillips curve equations of the form

$${\text{π}}_t={\text{π}}_t^e+\theta +f(U_t)+{\epsilon }_t.$$(3)

and the standard test of verticality-in-the-long-run was whether the sum Σα_j was 1.0 or less than 1.0. Every empirical estimate said less.

Sargent explained why this test is irrelevant under rational expectations. To illustrate his argument, suppose the true model is

πt = ${\pi }_t^e$ + θ + f (Ut)+ εt . (4)

Since a coefficient of 1.0 sits in front of expected inflation, the implied long-run Phillips curve is vertical, just as Friedman and Phelps insisted. But suppose the stochastic process generating inflation is, say,

πt = ρπt − 1 + ut., (5)

with ρ < 1. (This simple version has just one lag; Sargent’s argument was more general.) Under rational expectations, (5) implies that ${\pi }_t^e=\rho {\pi }_{t-1}$. Substituting this into (4) yields

πt = ρπt − 1 + θ + f (Ut) + εt, (6)

with ρ < 1, which is what an econometrician using the distributed lag methodology would estimate. Equation (6) looks like a long-run sloping Phillips curve because ρ < 1. But it’s a mirage. The ρ in (6) is not the coefficient on ${\pi }_t^e$ in (4), which is 1.0. Rather, it’s the autoregressive parameter describing how inflation evolves in (5). If that parameter changes, the estimated coefficient in a Phillips curve such as (6) will change as well.⁶

As mentioned, Sargent’s important point was not absorbed right away. People kept on estimating equations that looked like (3) and testing whether Σα_j = 1 or Σα_j < 1. As time went by, however, and inflation rose, the theory and the empirical evidence came into better alignment. Already in his 1972 Brookings paper, which made no mention of Sargent’s then-recent paper, Gordon (1972) estimated a nonlinear α coefficient, finding that α rose as expected inflation rose, reaching about 1.0 when expected inflation was 7 percent. (CPI inflation was 3.4 percent in 1972 and 8.9 percent in 1973.) So, by about 1972 or 1973, the empirical debate over the verticality of the long-run Phillips curve was all but over. It was vertical both in theory and in the data. Keynesians and monetarists (and economists who would soon be called “new classicals”) agreed on that. It was a clear triumph of theory over (flawed) empirics.

As academic economists rushed to embrace rational expectations, it was soon noticed that even the short-run Phillips curve should be vertical under rational expectations (Sargent and Wallace 1975). Look back at equation (4). Under rational expectations, π_t will differ from ${\pi }_t^e$ only by a random expectational error, which must have zero mean and be independent of ${\pi }_t^e$. Putting that idea into (4) brings us right back to 0 = θ + f (U_t), that is, to a vertical Phillips curve at U*. But this time verticality obtains even in the short run. That stunning implication of rational expectations was revolutionary at the time. It was also wildly at variance with observed reality. So, while academic economists doted on it, real-world policy makers never paid it much attention (more on this in chapter 6).

Another problem with the rational expectations revolution went virtually unnoticed. Lucas’s (1976) famous econometric policy critique held, correctly, that observed empirical relationships—such as ${\pi }_t^e=\sum {\alpha }_j{\pi }_{t-j}$ could change if policy reactions changed. As just mentioned, Sargent’s (1971) important point, which predated the critique by five years, was an apposite example. But could is not will, and change does not necessarily connote change by a large amount. In the rush to revolutionize macroeconomics and, in the process, destroy Keynesianism, no one, it seemed, paused to ask whether the Lucas critique was empirically important in the context of the Phillips curve.

Well, almost no one. In a 1988 paper that garnered virtually no attention,⁷ I estimated a series of Sargent-style autoregressions of the form

π_t = Σα_jπ_{t − j} + u_t

for U.S. inflation over the period 1955:2 to 1987:4 (Blinder 1988). I then tested for the presence of a statistically significant break in this inflation-forecasting equation at the ends of 1970, 1971, 1972, and 1973—just when inflation was rising. The estimated F statistics ranged from 0.2 to 0.9, none of them coming remotely close to statistical significance. What that means is that, Lucas notwithstanding, the best-fitting autoregression for U.S. inflation remained reasonably stable through the early 1970s even though inflation itself did not. Sargent (1971) was right in principle, of course. So was Lucas (1976). But at least in this application, the Lucas critique appeared not to be quantitatively important.

Yet the old-fashioned Phillips curve did indeed fall apart later in the 1970s. Why? It was not for Lucas-Sargent reasons. It happened instead because severe adverse supply shocks wracked the United States and other economies. Adding supply-shock variables—food and energy shocks—patched the Phillips curve up quickly. But that’s a story for chapter 5.

The important point for present purposes is that by about 1972 the strong consensus among macroeconomists was that neither monetary nor conventional forms of fiscal policy had permanent effects on employment or output.⁸ There was a short-run trade-off between inflation and unemployment but no long-run trade-off. In practice, this meant that policy makers could shorten recessions and make them shallower, but at the cost of leaving the inflation rate permanently higher. Thought of a bit differently, expansionary monetary or fiscal policies could put the economy on a short-term “sugar high.” But the sugar would dissolve, leaving inflation somewhat higher in its wake. That quickly became the canonical view in academia, and it still is. It also seems to have been the view embraced by President Richard Nixon and his handpicked Federal Reserve Chair, Arthur Burns, as we shall see in the next chapter.

Chapter Summary

A. W. Phillips discovered his famous curve in 1958 in much the same way that Alexander Fleming had discovered penicillin thirty years earlier—serendipitously. But the curve stood up for decades and had profound effects on the way monetary and fiscal policy were conceptualized. Intellectually, the Phillips curve provided the missing link in the old-fashioned Keynesian model, the so-called inflation equation. In terms of policy, the curve was thought at first to offer decision makers a menu of choices for where the economy could sit in inflation-unemployment space.

But Milton Friedman and Edmund Phelps argued persuasively that there could be no such menu in the long run. On basic theoretical grounds, money had to be neutral in the long run regardless of what estimated Phillips curves of the day seemed to say. Within a few years, empirically estimated Phillips curves using lagged inflation as proxies for expected inflation were agreeing with Friedman and Phelps’s theoretical proposition, although Sargent had argued that the coefficients on lagged inflation were irrelevant anyway. In any case, practical macroeconomic thinking soon congealed around the idea that policy makers could trade more inflation for less unemployment in the short run but not in the long run. That view remains largely intact today, although even a short-run Phillips curve is hard to find in U.S. data since the late 1990s.

______________

. This chapter contains a few simple equations. Readers who are allergic to equations can skip over them and read the accompanying prose.

. Lipsey (1960), unlike Phillips, estimated the Phillips curve by conventional econometric methods. He also found a less striking fit than Phillips did.

. Much of this profile is based on Barr (2004).

. Lucas was just beginning to. See Lucas and Rapping (1969).

. In those days it was common to estimate a price equation with the rate of change of money wages on the right-hand side and a separate wage equation with expected inflation on the right-hand side. The reduced form of that two-equation system resembled (2). In his paper, Gordon (1970) used long-term interest rates to develop a statistical proxy for expected inflation.

. This was an early application of what would later become known as the Lucas critique. See chapter 6.

. At this writing, Google Scholar records only 273 citations to Blinder (1988).

. By “conventional forms” I mean to allow for permanent incentive effects from, say, changes in marginal tax rates. Such possibilities were well known at the time, even though the term supply-side economics had not yet been coined.