The Art of the Phillips Curve

The subjective details holding together one of economics’ favourite models The post The Art of the Phillips Curve appeared first on Towards Data Science.

May 12, 2025 - 20:31

Flick through any popular Macroeconomic textbook of the last 50 years and you will quickly land on a page that mentions the Phillips curve. And then another page, and then another…

For example, the Macroeconomics textbook, creatively titled “Macroeconomics” by C. Jones and part of Cambridge university’s BA Economics curriculum, references the “Phillips curve” a staggering 143 times across 67 pages, covering over 10% of the 641-page brick. It takes up more space than almost¹ all other macroeconomic models, including the “MP curve” (24 pages), the “Cobb-Douglas” production function (17 pages), the “Romer model” (42 pages), the “AS/AD framework” (51 pages), and the “DSGE models” (42 pages).

In short, the Phillips curve is a pretty big deal in modern macroeconomics.

As for the contents of those 67 pages, the vast majority comes in explaining the Phillips curve’s mathematical logic, and scientific equations. For instance, here’s a small sample from the book mentioned above:

“…In normal times, you’d expect prices in the economy to continue to rise at a rate of 5 percent, and you’d raise your prices by this same amount. However, given the weakness in your industry, you’ll probably raise prices by less than 5 percent, in an effort to increase the demand for your goods.This reasoning motivates the price-setting behavior that underlies the Phillips curve. Recall that πt ≡ (Pt+1− Pt) / Pt ; that is, the inflation rate is the percentage change in the overall price level over the coming year. Firms set the amount by which they raise their prices on the basis of their expectations of the economywide inflation rate and the state of demand for their products:

Here, πet denotes expected inflation — the inflation rate that firms think will pre-vail in the rest of the economy over the coming year…”
p. 318–9, “Macroeconomics”, fourth edition. Charles Jones.

It isn’t only used at universities. Central banks throughout the globe rely on the Phillips curve findings to explain the economy and adjust their interest rates. For example, in February 2025, when the Bank of England (BoE) reduced their interest rate to 4.5%, their explanation explicitly cited Phillips curve reasoning:

“Should there be greater or longer-lasting weakness in demand relative to supply, this could push down on inflationary pressures, warranting a less restrictive path of Bank Rate [BoE interest rate]. If there were to be more constrained supply relative to demand, this could sustain domestic price and wage pressures, consistent with a relatively tighter monetary policy path.”Bank of England’s “Monetary Policy Summary, February 2025”

That might have a bit too much economist jargon for the lay person. How about this quote from the current Chair of the Federal Reserve, Jerome Powell:

[The] persistent shortfall in inflation from our target has led some to question the traditional relationship between inflation and the unemployment rate, also known as the Phillips curve.… My view is that the data continue to show a relationship between the overall state of the labor market and the change in inflation over time. That connection has weakened over the past couple of decades, but it still persists, and I believe it continues to be meaningful for monetary policy.“The Outlook for the U.S. Economy.” April 2018. Jerome Powell, Chair of the Federal Reserve (2018-present).

This article is not about the Phillips curve you will find in macroeconomic textbooks or central bank statements, but rather the Phillips curve they intentionally leave out. The fine print details glueing all that smart physics-like reasoning together. The assumptions, the history, the revisions, and the inconvenient data. In short, the macroeconomists will give you the science of the Phillips curve, I intend to give you the art of the Phillips curve.

A Short History

The Phillips curve was, unsurprisingly, conceived by a chap called Phillips — Alban William Housego Phillips to be precise. While working at the London School of Economics in the 1950s, he studied the relationship between unemployment and inflation in the United Kingdom from 1861 to 1913. What he found was an inverse correlation: as wage inflation increased, unemployment decreased.

The original Phillips curve. Source: A. W. Phillips

For the next few years Phillips and other macroeconomic academics continued to search for empirical evidence supporting such a fascinating correlation. And they did! Phillips found that the relationship persisted when the dataset was extended to 1957. Samuelson and Solow, economists at the Massachusetts Institute of Technology (MIT), published a paper in 1960 called “Analytical aspects of anti-inflation policy”. In it they found the same relationship as Phillips had, but using U.S. data from 1934 to 1958.

But Samuelson and Solow’s paper did much more than this. They expanded Phillips’ original work by demonstrating that the relationship applied not only to unemployment and wage inflation, but also to unemployment and general price inflation, at least for the U.S. data they analysed² .

Additionally, they proposed a causal model for this correlation, a theoretical framework that gained support from the growing popularity of Keynesian economists. It can’t be overstated just how significant a leap this was from Phillips’ original work. While Phillips had merely documented a statistical relationship — similar to how ice cream sales and drowning deaths both rise in summer months (due to the hidden variable of warm weather) — Samuelson and Solow were essentially claiming that manipulating one variable could directly control the other. Using our analogy, ice cream sales regulations could be used as a policy tool to reduce drownings, or conversely, that swimming safety measures could impact the ice cream market.

Cai’s curve, the relationship between monthly sales of ice cream and drowning deaths. It’s important to keep in mind correlation does not equal causation. Chart created by the author.

Samuelson and Solow’s model was as simple as:

$$\pi = f(U) \\
f'(U)

Where:

π represents the inflation rate
U represents the unemployment rate
f is a function that describes an inverse relationship

This causal theory was a particularly powerful discovery, not only because it was so simple, requiring only two metrics, but because those two metrics were possible to measure, not like awkward inputs used in other models such as animal spirits, expectations, and marginal propensity to consume. For over a century, pesky Classical and Austrian school economists had argued that it was impossible to understand the economy from broad aggregations on the basis that there were different types of underlying unemployment and inflation that all look the same if you aggregate them. To truly understand why inflation was this level or unemployment was that level, they argued, you’d have to dig into the details, and assess the situation at a microeconomic or even individual human level. “Hogwash” said the Keynesian macroeconomists, who were not only starting to build a healthy collection of models built on aggregated metrics, but had policymakers taking note of them.

As with other Keynesian models, Samuelson and Solow encouraged policymakers to exploit the model. Stating in their 1960 paper: governments could adjust inflation and unemployment as if it were a “menu of choice”³.

For the next decade, governments began to warm to the idea that they could be the ultimate conductor of the economy, turning dials and pressing knobs in order to move their country in the direction they wanted. Throughout the 1960s, new data continued to back the Phillips curve, which lead policymakers to make bolder and bolder policy decisions based on Samuelson and Solow’s model.

The first decade after the discovery of the Phillips curve it looked like the economy was solved. Source: chart and data from USA Bureau of Labor Statistics.

For example, in 1971–1972, with support from President Nixon, Federal Reserve Chairman Arthur Burns pursued an expansionary monetary policy. This involved lowering the federal funds rate from approximately 5.5% in early 1971 to around 3.5% by mid-1972, while increasing the M1 money supply at an accelerated annual rate from 5.4% in 1970 to 8.2% by 1972. These Phillips curve-influenced policies aimed to reduce unemployment, which did fall from 5.9% in 1971 to 5.1% by late 1972. Initially, inflation remained relatively contained at 3.2% in 1972, helped by another policy Nixon had enacted of freezing wage and price controls for 90 days, creating the appearance that the Phillips curve tradeoff was working. Despite these initial successes, when Nixon’s wage and price controls were lifted, both inflation and unemployment rose simultaneously. Inflation surged to 12.3% by 1974 while unemployment increased to over 7%.

The U.S. economy was exhibiting something macroeconomists had previously thought impossible: high inflation and high unemployment occurring simultaneously — a phenomenon that came to be known as “stagflation.”

This wasn’t just a blip for a couple of years either. Data points for the whole decade of the 1970s no longer fell neatly along the Phillips curve but instead a random scattering, as if there was no correlation at all (that’s being kind, some might say there was a positive correlation between unemployment and inflation). The party was over. The elegant trade-off that had empowered governments to fine-tune economic outcomes for a decade was breaking down before policymakers’ and economists’ eyes.

The 1970s obliterated the idea of the Phillips curve as it was presented in 1960. Source: data from USA Bureau of Labor Statistics, chart created by the author.

The stagflation period essentially validated what the Classical and Austrian critics had warned about — that aggregated metrics alone couldn’t capture complex economic realities.

Or had it?

Not to be so quick to give in, the Phillips curve enthusiasts sought to find excuses for the inconvenient data.

Robert Solow, who had co-authored the influential 1960 paper with Paul Samuelson, insisted that the fundamental relationship remained valid despite the stagflation anomaly. He and other Keynesians suggested the curve had simply “shifted to the right giving a worse trade-off because of cost-push inflation” caused by the external shock of the 1973 OPEC oil crisis — not because the underlying theory was flawed. In other words, the Phillips curve wasn’t wrong, but was simply missing a small detail in its equation, what would later be coined as “supply shocks”. In mathematical terms, the equation changed to:

$$\pi = f(U) + O \\
f'(U)

Where:

π represents the inflation rate
U represents the unemployment rate
f is a function that describes an inverse relationship
Ο (the greek letter omicron, not zero) represents supply shocks

However, unfortunately for Solow and others, there was significant evidence against the supply shock view that the 1970s stagflation was solely due to OPEC’s oil price quadrupling in October 1973. Data shows that stagflation began earlier, with unemployment rising from 3.6% to 4.9% between 1968 and 1970, while inflation rose from 4.7% to 5.6% during the same period. As a result, there was going to need to be more tinkering for the Phillips curve to cheat death.

And tinkering there was.

Phillips curve enthusiasts started to look for something, anything, that could save them and their model — even if it meant getting into bed with a previous enemy.

Enter Milton Friedman and Edmund Phelps. In 1967–1968, they developed critiques of the Phillips curve. Their argument was:

The Phillips curve ignored expectations. People aren’t mechanical parts in an economic machine. They adapt. They learn. If the government consistently creates inflation to reduce unemployment, people will eventually catch on and adjust their behaviour accordingly.
The Phillips curve ignored the concept of the “natural rate” of unemployment. When unemployment falls below this natural rate, wages rise, employers raise prices, and inflation increases. Once workers realize inflation is eating their wage gains, they demand even higher wages, creating an inflationary spiral. Eventually, unemployment returns to its natural rate, but with higher inflation.
Point 1 and 2 combined means there was no permanent trade-off between unemployment and inflation, only a temporary one that would disappear once people updated their expectations.

Initially, mainstream macroeconomists largely dismissed these critiques. After all, the data still supported the Phillips curve, and governments were enjoying their newfound power to “fine-tune” the economy. Why let pesky monetarists like Friedman rain on their parade? The Keynesian establishment, firmly entrenched in academia and policy circles, had little interest in a theory that undermined their influence.

But when the 1970s happened, they reached for the nearest life raft: the expectations-augmented Phillips curve that Friedman and Phelps had proposed years earlier. At least their model was still called the “Phillips curve”.⁴

Suddenly, the once-dismissed theory became the accepted wisdom. The same economists who had scoffed at Friedman and Phelps were now explaining to policymakers that, of course, there was no long-run Phillips curve trade-off. Of course expectations matter.

This convenient pivot allowed the macroeconomics profession to save face. Again, rather than admitting the fundamental flaws in their aggregation-based approach, they could claim that the model was just missing a few more variables.

The new Phillips curve equation now looked like a real head scratcher:

$$\pi_t = \pi^e_t + f(U_t – U^*) + O \\
f'(U_t – U^*)

Where:

πₜ represents the inflation rate at time t
πᵉₜ represents the expected inflation at time t
U represents the unemployment rate at time t
U* represents the “natural” rate of unemployment
f is a function that describes an inverse relationship
Ο (omicron) represents supply shocks at time t
ₜ₋₁ represents the time previous to the current time t
λ represents the weight given to recent observed inflation when forming expectations
(1-λ) represents the weight given to previous inflation expectations when forming new expectations

By the late 1970s, the economics profession had completed its pivot. Textbooks were rewritten. Lectures were updated. The new consensus emerged: there was a short-run Phillips curve (where unexpected inflation could temporarily reduce unemployment) but no long-run trade-off. This allowed economists to maintain the basic framework of the Phillips curve while explaining away its failures. The new formula had lost its original strengths of being simple and possible to measure, however, over time these had come to be more curses than gifts. What ultimately secured the Phillips curve’s enduring influence was not these initial attributes, but their replacement: resistance to being proven wrong.

If unemployment and inflation weren’t behaving as predicted, it would be because expectations had changed or that the “natural rate” of unemployment had shifted. How do economists measure these variables? They can’t, so they infer them from… the unemployment and inflation data. A beautifully circular argument, which has resulted in no further significant changes in the model to the present day.

Pseudo-Science and Un-falsifiability

The concept of unfalsifiability was popularised by philosopher Karl Popper, who argued that the ability to be falsified is what separates scientific theories from pseudo-scientific ones. This simply means that if a theory can’t be tested in a way that might prove it wrong, it’s not scientific. That also goes for theories that bend and shift to accommodate any possible evidence against them.

If I tell you there’s a spaghetti monster living on the dark-side of the Moon, what would you think? Probably that I’m a nut job. But lets say I’m thought of as an expert in the field of monsters. I have built up a plethora of mathematical equations, scientific charts, textbooks that could build a house, and most importantly a loyal fanbase, including many of the most senior figures in government defence departments, who are keen to prepare for any alien attacks — and a bigger budget that goes along with it.

Would you genuinely still think I was a nut job? Perhaps you’ve just missed something in all the jargon. After all, there are a lot of well thought of people who believe it. You don’t want to be thought of as a nut job yourself, do you? Maybe it’s best to just go along with what the experts say.

Continuing the analogy, a team of scientists strap themselves to a rocket in an effort to find the spaghetti monster, but it’s nowhere to be seen. Surely that’s proof the spaghetti monster doesn’t exist, right? Ah, not quite, it turns out one of the many equations was missing a small variable… give the experts a moment… 1,2,3… tah da! That’s fixed the problem. It turns out the spaghetti monster is actually invisible, hence why the scientists didn’t find it.

I’m sure most of you reading that got the message long before getting to the end of that silly story — sorry, it was too much fun to write. We all know of real life scenarios where this sort of thinking happens: Freudian psychoanalysis, traditional Chinese medicine, crystal healing, chiropractics… the list goes on. Sadly, as a passionate economic thinker, I’m ashamed to say a core model of macroeconomics also belongs on that list.

The fact is, time and time again economists have been given the opportunity to reject the Phillips curve, but instead continue to give it more caveats and excuses. I am of the belief that there is no conceivable scenario which would cause mainstream macroeconomics to fundamentally leave behind the Phillips curve. As such, it is by definition un-falsifiable and therefore pseudo-science.

Continued Popularity

Hang on. This can’t be right. Academic professors, professional economists, and central bank heads are all smart people. How could they possibly be fooled in believing in a pseudo-scientific idea?

One of the clearest memories I have at university was in my second-year of my economics degree. The final lecture of the module “Macroeconomics II” was coming to a close. After a tough two hour slog sitting in a stuffy lecture hall, trying my best to keep awake, let alone focus on the dry power point slides, the lecturer switched off the presentation, and casually said something along the lines:

“…and that’s everything that we need to cover for your exam. If you feel confused as to how all this makes sense in the real world, don’t worry. No one really knows if any of these models really work.”

It was an absolute bombshell moment for me. Previously, I had thought that I was still a dumb student who just hadn’t “got it” yet. What my lecturer was saying, in other-words, is that the experts all know it’s pseudo-science.

The follow up question is, of course, why do they keep pushing these models?

I can only theorise, but I’d say it’s because it keeps them all busy. Cut out 10% of macroeconomics textbooks and what happens? 10% less content to teach, 10% reduction in research grants, 10% fewer macroeconomists. Why call out the emperor’s new clothes when you’re the emperor?

In closing, we can’t rely on experts to tell us if the Phillips curve is a sham, or indeed any experts’ theory whose reputation or livelihood depends on its validity. It is up to us to make that discovery. The snake oil salesman doesn’t sell his product because he believes in it, but because his customers do.

Endnotes

¹ The “Phillips curve” didn’t quite beat the “IS curve” on this occasion, which was mentioned on 82 pages!

² Interestingly, Samuelson and Solow would have found no curving relationship had they decided to compare general price inflation and unemployment using Phillips’ original 1861 to 1957 U.K. data, rather than their new U.S. data. Arguable, if they had, the Phillips curve might never have existed outside of a few dusty journals.

³ I find this a funny choice of words, I end up imagining a policymaker coming to the leader of the free world and saying:

“Good evening Mr. President. Did you enjoy last year’s economy? Might we endeavour to introduce some variety this year? I may prove most beneficial to one’s election prospects. Something like an increase in inflation by 1% to push down unemployment to 5%, perhaps?”

⁴ H.A. Hayek had raised issues about to the long-run Phillips curve and expectations far earlier than Friedman and Phelps. For example, he noted “the stimulating effect of inflation will … operate only so long as it has not been foreseen; as soon as it comes to be foreseen, only its continuation at an increased rate will maintain the same degree of prosperity” in his book The Constitution of Liberty, published in 1960. The reason Friedman and Phelps became so famous for their critique was not their novel insights, but their willingness to modify the Phillips curve model, rather than a total rejection.

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