In 1958, A. W. Phillips wrote a paper on Economica (London School of Economics), entitled “The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957”. Analysing data concerning money wages and unemployment rates in the UK, Phillips managed to draw a curve representing the inverse relation between these variables. It must be said that Irving Fisher had already pointed out a relationship between price levels and unemployment in his paper “A Statistical Relation between Unemployment and Price Changes”, 1926 (cleverly renamed later as “I Discovered the Phillips Curve”). The Phillips curve has evolved following other empirical studies, and is widely known nowadays, even though it has also been criticized.

In his article, Phillips drew a curve showing the inverse relation between the rate of change of money wage rates, as a percentage change per year () and the unemployment rate (U).

Two important things must be noted: the point where the curve crosses the abscissa, and the fact that the ordinate seems to work as an asymptote. The importance of the point of crossing must be highlighted (around 5,5%), since it is the rate of unemployment that an economy will have for a zero increase in the money wages. This point will be named, in further developments of the Phillips curve, Natural Rate of Unemployment and Non-Accelerating Inflation Rate of Unemployment (NAIRU). Regarding the asymptote, as the author pointed out, there was no data of higher rates of change in money wage, nor lower unemployment rates. It can be concluded that unemployment cannot be lowered beyond a certain level.

Two years later, Richard G. Lipsey would publish a paper in the same journal deepening the mathematics regarding the curve, as well as expanding Phillips’ research by doing further econometrical tests.

Also in 1960, Paul A. Samuelson and Robert M. Solow, in their “Analytical Aspects of Anti-Inflation Policy”, studied a similar relation, in this case using data from the United States. Although they used inflation (Π) instead of the rate of change in money wages, they came up with similar results. Even though the curve might seem different because of the scale used, the unemployment rate at price stability is the same as at money wage stability (around 5,5%), and there seem to be no way to lower unemployment beyond a certain level (around 1%).

It was in this paper that the Phillips curve was considered a “menu of choice” for the first time. This meant that, concerning policy making, governments would be able to choose between a low rate of unemployment with high inflation, and a higher rate of unemployment with lower inflation. However, as the authors pointed out, this menu had to be used only in the short-run, since certain policies or economic events might change the shape of the curve in the longer run.

In the mid 50s, and until the late 60s, the adaptive expectations hypothesis became popular, especially because of the works by Phillip Cagan and Milton Friedman. This hypothesis would endure almost unquestioned until the late 60s and early 70s, when economist Robert Lucas (among others) brought forward a rational expectations hypothesis, from earlier works by J. F. Muth.

The term natural rate of unemployment was introduced by Milton Friedman in 1968, in his article “The Role of Monetary Policy”, following his presidential address delivered at the annual meeting of the American Economic Association, in 1967. It is based in Knut Wicksell’ concept of “natural” rate, which defines how there will be no permanent changes in the considered variable below or above its natural level.

The natural rate of unemployment defines the level at which unemployment will remain, no matter how great the effects of monetary policy. The only way to permanently keep unemployment under its natural rate is to resort to higher and higher inflation rates, which in turn would be highly hazardous for the economy. This can be easily understood using an expectations-augmented Phillips curve.

Even though the natural rate of unemployment is usually merged in the economic literature with the term NAIRU, there are a few differences between both terms. These differences are summarized in the following grid:

The term NAIRU (non-accelerating inflation rate of unemployment) is a term first used by James Tobin in 1980, in his article “Stabilization Policy Ten Years After”. It refers to the level of unemployment at which the economy settles if monetary policy is held stable. In these terms, it can be associated to Friedman’s natural rate of unemployment.

The NAIRU is based on empirical evidence regarding inflation and unemployment. Indeed, in most countries, inflation rises when unemployment is low because of the higher demand this implies; correspondingly, inflation falls when unemployment is high. This relation explains how unemployment may be above or below the NAIRU level not only because of the effects of monetary policy, but also because other factors such as production costs or trade unions negotiation processes. The Layard-Nickell NAIRU model explains it quite simply.

Even though the term NAIRU is usually merged in the economic literature with the term natural rate of unemployment, there are a few differences between the two. These differences are summarized in the following grid:

Adaptive expectation models are ways of predicting an agent’s behaviour based on their past experiences and past expectations for that same event. They are first used by Irving Fisher in his book “The Purchasing Power of Money”, 1911, and further developed in the 1940s and 1950s, especially by Phillip Cagan in his article “The Monetary Dynamics of Hyper-Inflation”, 1956 and, most famously, by Milton Friedman in 1957, in his book “A Theory of the Consumption Function”.

Models are usually based around the following formula: 

E_t x_t+1 is our expectation (E) in year  for a variable x in the year t+1. It is based on our expectation from the year before (t-1) for variable x in our current year, and a weighted proportion of our past expectations. Remember that our expectations from last year were, in turn, based on those of the year before, so all our expectations from the first time we ever dared assume anything are contained within the equation.

λ will depend on how much we were off last year versus this year: if our predictions are proving to be volatile, we will be more likely to adjust them. It will also depend on how much groundbreaking new information we have received, rendering previous expectations useless. Basically, it depends on how much we feel we might have been off last year when we predicted things for next year.

The easiest way to know how adaptive expectations work, is to understand the expectations-augmented Phillips curve. Using also this same curve, it is also easy to understand how rational expectations work.

The expectations-augmented Phillips curve introduces adaptive expectations into the Phillips curve. These adaptive expectations, which date from Irving Fisher’s book “The Purchasing Power of Money”, 1911, were introduced into the Phillips curve by monetarists, specially Milton Friedman. Therefore, we could say that the expectations-augmented Phillips curve was first used to explain the monetarists’ view of the Phillips curve.

Adaptive expectations models led to an important shift in the perception of a government’s ability to act. Under Keynes’ money illusion, changes in nominal variables (prices, wages, etc…) were accepted by agents as real despite overall purchasing power remaining stable.

However, monetarism embraced the adaptive expectations theory to mean that people would stumble once or twice on the same stone, but not a third. In this way, if the government decided on an expansionist monetary policy, inflation would rise and unemployment would fall, based on the Phillips curve. However, a second or third time around, agents would be quick to associate higher inflation with rising salaries in a vicious circle, and adjust their behaviour accordingly based on past experiences. They would anticipate that inflation would drain their purchasing power accordingly, and monetary policy would have little effect. If we see this graphically:

Initially, unemployment and inflation are at point A. The government decides to embark on an expansionist monetary policy, which floods the markets with inexpensive credit, incentivising consumption. Expectations shift to point B along the Phillips curve: unemployment is reduced through economic stimulus with a trade off in the form of inflation. However, after a short period, agents will begin to associate expansionist policies with inflation, which means a drain on their resources, and they will push for higher wages. This will stop the consumption stimulus and also deincentivise hiring. Eventually, agents will shift their expectations curves to point C. A second time around, D will be achieved, leading more or less rapidly to point E. This is why, in the long term, inflation has little effect on unemployment and vice versa. Expansionist monetary policy will lead directly to inflation, with no permanent effect on unemployment.

In summary, monetarists sustained that the Phillips curve will hold up in the short term, but not in the long term. In the long term, the Phillips curve is completely vertical and determines the natural rate of unemployment, as Friedman puts it in his article “The role of Monetary Policy”, 1968.

Rational expectation models are those where an agent’s future predictions affect the value they assign to a variable in their current time period. In this sort of self-fulfilling prophecy, expectations become truths, and errors in forecasting future variables become random. This makes those forecasts valid, because present expectations about the future become dependent variables of future values. This model was developed and put forwards by John Muthin two articles: “Optimal Properties of Exponentially Weighted Forecasts”,1960, and “Rational Expectations and the Theory of Price Movements”, 1961 and later summarised by Peter Whittle in 1963, before becoming influential in Robert Lucas’ work in the 1970s. Particularly, Lucas developed the use of rational expectations in his article “Expectations and the Neutrality of Money”, 1972, in which he used Edmund Phelps’ island parable, though applying rational expectations, instead of adaptive expectations.

Mathematically, rational expectations can be represented as: 

Which simply means that the value of x today will be the value that we expected it to be plus a random error.

Essential to this hypothesis is the fact that individuals have perfect information and markets are perfect and tend towards equilibrium. This places us firmly back in the realm of neoclassical economics, whose main ideas where retaken by New Classical Macroeconomics.

New Classical Macroeconomics takes expectations one step further than monetarists did when using adaptive expectations. Rather than supposing that agents will learn to adjust their behaviour based on past experiences, they apply rational expectations, and directly assume that:

• All agents have sufficient working knowledge of the economy and its basic structural relationships to anticipate cause and effect;
• All agents assume that markets naturally reach an equilibrium;
• Information is perfect: market force drivers are ‘common knowledge’.

This all signals a return to the cornerstones of neoclassical economics, and although in practical terms it may be a slight stretch, it means taking the expectations-augmented Phillips curve one step further:

As New Classical Macroeconomics views it, agents are able to anticipate future events without needing to have experienced them previously. This time around, agents will anticipate expansionist monetary policies, and therefore skip point B. Agents have sufficient working knowledge of the economy and monetary policy is transparent enough for agents to directly associate a fall in interest rates with a rise in inflation. Therefore, they waste no time in asking for salary raises (the change on inflation expectations shift the curve directly to point C), and inflation rises before a drop in unemployment is ever reached. Expansionist monetary policy is not even effective in the short term. In the very short term, a small effect might exist, but only as a result of the time needed for expectations to lead to action.

The only way for monetary policy to work under these scenarios is for it to be enough of a surprise and of enough magnitude to pose an economic shock. If agents are not expecting dramatic policy, they have no time to put themselves in order. In this way, economic policy must go beyond expectations, otherwise even an inkling that the government is likely to act will lead to agents immediately counteracting policy, probably before policy is even enacted.