Phillips curve

Phillips curve

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In economics, the Phillips curve is a historical inverse relationship between the rate of unemployment
Unemployment
Unemployment , as defined by the International Labour Organization, occurs when people are without jobs and they have actively sought work within the past four weeks...

 and the rate of inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

 in an economy. Stated simply, the lower the unemployment in an economy, the higher the rate of inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

. While it has been observed that there is a stable short run tradeoff between unemployment and inflation, this has not been observed in the long run.

History



William Phillips
William Phillips (economist)
Alban William Housego "A. W." "Bill" Phillips, MBE was an influential New Zealand economist who spent most of his academic career at the London School of Economics . His best-known contribution to economics is the Phillips curve, which he first described in 1958...

, a New Zealand born economist, wrote a paper in 1958 titled The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957, which was published in the quarterly journal Economica
Economica
Economica is a peer-reviewed academic journal of economics published on behalf of the London School of Economics by Wiley-Blackwell. It was established in 1934...

. In the paper Phillips describes how he observed an inverse relationship between money wage changes and unemployment in the British economy over the period examined. Similar patterns were found in other countries and in 1960 Paul Samuelson
Paul Samuelson
Paul Anthony Samuelson was an American economist, and the first American to win the Nobel Memorial Prize in Economic Sciences. The Swedish Royal Academies stated, when awarding the prize, that he "has done more than any other contemporary economist to raise the level of scientific analysis in...

 and Robert Solow
Robert Solow
Robert Merton Solow is an American economist particularly known for his work on the theory of economic growth that culminated in the exogenous growth model named after him...

 took Phillips' work and made explicit the link between inflation and unemployment: when inflation was high, unemployment was low, and vice-versa.

In the 1920s an American economist Irving Fisher
Irving Fisher
Irving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...

 noted this kind of Phillips curve relationship. However, Phillips' original curve described the behavior of money wages.

In the years following Phillips' 1958 paper, many economists in the advanced industrial countries believed that his results showed that there was a permanently stable relationship between inflation and unemployment. One implication of this for government policy was that governments could control unemployment and inflation with a Keynesian
Keynesian economics
Keynesian economics is a school of macroeconomic thought based on the ideas of 20th-century English economist John Maynard Keynes.Keynesian economics argues that private sector decisions sometimes lead to inefficient macroeconomic outcomes and, therefore, advocates active policy responses by the...

 policy. They could tolerate a reasonably high rate of inflation as this would lead to lower unemployment – there would be a trade-off
Trade-off
A trade-off is a situation that involves losing one quality or aspect of something in return for gaining another quality or aspect...

 between inflation and unemployment. For example, monetary policy
Monetary policy
Monetary policy is the process by which the monetary authority of a country controls the supply of money, often targeting a rate of interest for the purpose of promoting economic growth and stability. The official goals usually include relatively stable prices and low unemployment...

 and/or fiscal policy
Fiscal policy
In economics and political science, fiscal policy is the use of government expenditure and revenue collection to influence the economy....

 (i.e., deficit spending
Deficit spending
Deficit spending is the amount by which a government, private company, or individual's spending exceeds income over a particular period of time, also called simply "deficit," or "budget deficit," the opposite of budget surplus....

) could be used to stimulate the economy, raising gross domestic product
Gross domestic product
Gross domestic product refers to the market value of all final goods and services produced within a country in a given period. GDP per capita is often considered an indicator of a country's standard of living....

 and lowering the unemployment rate. Moving along the Phillips curve, this would lead to a higher inflation rate, the cost of enjoying lower unemployment rates.

Before the 1960s, a leftward movement along the Phillips curve described the path of the U.S. economy. This move was not a matter of deciding to achieve low unemployment as much as an unplanned side effect of the Vietnam war
Vietnam War
The Vietnam War was a Cold War-era military conflict that occurred in Vietnam, Laos, and Cambodia from 1 November 1955 to the fall of Saigon on 30 April 1975. This war followed the First Indochina War and was fought between North Vietnam, supported by its communist allies, and the government of...

. In other countries, the economic boom was more the result of conscious policies.

Since 1974 seven Nobel Prizes have been given for work critical of the Phillips curve. Some of this criticism is based on the United States' experience during the 1970s, which had periods of high unemployment and high inflation at the same time. The authors receiving those prizes include Thomas Sargent, Christopher Sims, Edmund Phelps, Edward Prescott, Robert A. Mundell, Robert E. Lucas, Milton Friedman, and F.A. Hayek.

Stagflation



In the 1970s, many countries experienced high levels of both inflation and unemployment also known as stagflation
Stagflation
In economics, stagflation is a situation in which the inflation rate is high and the economic growth rate slows down and unemployment remains steadily high...

. Theories based on the Phillips curve suggested that this could not happen, and the curve came under a concerted attack from a group of economists headed by Milton Friedman
Milton Friedman
Milton Friedman was an American economist, statistician, academic, and author who taught at the University of Chicago for more than three decades...

.

Friedman argued that the Phillips curve relationship was only a short-run phenomenon. He argued that in the long-run, workers and employers will take inflation into account, resulting in employment contracts that increase pay at rates near anticipated inflation. Unemployment would then begin to rise back to its previous level, but now with higher inflation rates. This result implies that over the longer-run there is no trade-off between inflation and unemployment. This implication is significant for practical reasons because it implies that central bank
Central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...

s should not set employment targets above the natural rate.

More recent research has shown that there is a moderate trade-off between low-levels of inflation and unemployment. Work by George Akerlof
George Akerlof
George Arthur Akerlof is an American economist and Koshland Professor of Economics at the University of California, Berkeley. He won the 2001 Nobel Prize in Economics George Arthur Akerlof (born June 17, 1940) is an American economist and Koshland Professor of Economics at the University of...

, William Dickens, and George Perry
George Perry (American economist)
George L. Perry is an American economist specializing in macroeconomic policy. A senior fellow at the Brookings Institution since 1970, he was a founding editor, with Arthur Okun, of the Brookings Papers on Economic Activity. He received his Ph.D. from the Massachusetts Institute of Technology in...

 implies that if inflation is reduced from two to zero percent, unemployment will be permanently increased by 1.5 percent. This is because workers generally have a higher tolerance for real wage cuts than nominal ones. For example, a worker will more likely accept a wage increase of two percent when inflation is three percent, than a wage cut of one percent when the inflation rate is zero.

NAIRU and rational expectations



New theories, such as rational expectations
Rational expectations
Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in...

 and the NAIRU
NAIRU
In monetarist economics, particularly the work of Milton Friedman, on which also worked Lucas Papademos and Franco Modigliani in 1975,NAIRU is an acronym for Non-Accelerating Inflation Rate of Unemployment, and refers to a level of unemployment below which inflation rises.It is widely used in...

 (non-accelerating inflation rate of unemployment) arose to explain how stagflation
Stagflation
In economics, stagflation is a situation in which the inflation rate is high and the economic growth rate slows down and unemployment remains steadily high...

 could occur. The latter theory, also known as the "natural rate of unemployment
Natural rate of unemployment
The natural rate of unemployment is a concept of economic activity developed in particular by Milton Friedman and Edmund Phelps in the 1960s, both recipients of the Nobel prize in economics...

", distinguished between the "short-term" Phillips curve and the "long-term" one. The short-term Phillips Curve looked like a normal Phillips Curve, but shifted in the long run as expectations changed. In the long run, only a single rate of unemployment (the NAIRU or "natural" rate) was consistent with a stable inflation rate. The long-run Phillips Curve was thus vertical, so there was no trade-off between inflation and unemployment. Edmund Phelps
Edmund Phelps
Edmund Strother Phelps, Jr. is an American economist and the winner of the 2006 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. Early in his career he became renowned for his research at Yale's Cowles Foundation in the first half of the 1960s on the sources of economic growth...

 won the Nobel Prize in Economics in 2006 for this.

In the diagram, the long-run Phillips curve is the vertical red line. The NAIRU theory says that when unemployment is at the rate defined by this line, inflation will be stable. However, in the short-run policymakers will face an inflation-unemployment rate tradeoff marked by the "Initial Short-Run Phillips Curve" in the graph. Policymakers can therefore reduce the unemployment rate temporarily, moving from point A to point B through expansionary policy. However, according to the NAIRU, exploiting this short-run tradeoff will raise inflation expectations, shifting the short-run curve rightward to the "New Short-Run Phillips Curve" and moving the point of equilibrium from B to C. Thus the reduction in unemployment below the "Natural Rate" will be temporary, and lead only to higher inflation in the long run.

Since the short-run curve shifts outward due to the attempt to reduce unemployment, the expansionary policy ultimately worsens the exploitable tradeoff between unemployment and inflation. That is, it results in more inflation at each short-run unemployment rate. The name "NAIRU" arises because with actual unemployment below it, inflation accelerates, while with unemployment above it, inflation decelerates. With the actual rate equal to it, inflation is stable, neither accelerating nor decelerating. One practical use of this model was to provide an explanation for stagflation, which confounded the traditional Phillips curve.

The rational expectations theory said that expectations of inflation were equal to what actually happened, with some minor and temporary errors. This in turn suggested that the short-run period was so short that it was non-existent: any effort to reduce unemployment below the NAIRU, for example, would immediately cause inflationary expectations to rise and thus imply that the policy would fail. Unemployment would never deviate from the NAIRU except due to random and transitory mistakes in developing expectations about future inflation rates. In this perspective, any deviation of the actual unemployment rate from the NAIRU was an illusion.

However, in the 1990s in the U.S., it became increasingly clear that the NAIRU did not have a unique equilibrium and could change in unpredictable ways. In the late 1990s, the actual unemployment
Unemployment
Unemployment , as defined by the International Labour Organization, occurs when people are without jobs and they have actively sought work within the past four weeks...

 rate fell below 4 % of the labor force, much lower than almost all estimates of the NAIRU. But inflation stayed very moderate rather than accelerating. So, just as the Phillips curve had become a subject of debate, so did the NAIRU.

Furthermore, the concept of rational expectations
Rational expectations
Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in...

 had become subject to much doubt when it became clear that the main assumption of models based on it was that there exists a single (unique) equilibrium
Economic equilibrium
In economics, economic equilibrium is a state of the world where economic forces are balanced and in the absence of external influences the values of economic variables will not change. It is the point at which quantity demanded and quantity supplied are equal...

 in the economy that is set ahead of time, determined independently of demand conditions. The experience of the 1990s suggests that this assumption cannot be sustained.

The Phillips curve today


Most economists no longer use the Phillips curve in its original form because it was shown to be too simplistic. This can be seen in a cursory analysis of US inflation and unemployment data 1953-92. There is no single curve that will fit the data, but there are three rough aggregations—1955–71, 1974–84, and 1985-92—each of which shows a general, downwards slope, but at three very different levels with the shifts occurring abruptly. The data for 1953-54 and 1972-73 do not group easily, and a more formal analysis posits up to five groups/curves over the period.

But still today, modified forms of the Phillips Curve that take inflationary expectations into account remain influential. The theory goes under several names, with some variation in its details, but all modern versions distinguish between short-run and long-run effects on unemployment. The "short-run Phillips curve" is also called the "expectations-augmented Phillips curve", since it shifts up when inflationary expectations rise, Edmund Phelps
Edmund Phelps
Edmund Strother Phelps, Jr. is an American economist and the winner of the 2006 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel. Early in his career he became renowned for his research at Yale's Cowles Foundation in the first half of the 1960s on the sources of economic growth...

 and Milton Friedman
Milton Friedman
Milton Friedman was an American economist, statistician, academic, and author who taught at the University of Chicago for more than three decades...

 argued. In the long run, this implies that monetary policy cannot affect unemployment, which adjusts back to its "natural rate
Natural rate of unemployment
The natural rate of unemployment is a concept of economic activity developed in particular by Milton Friedman and Edmund Phelps in the 1960s, both recipients of the Nobel prize in economics...

", also called the "NAIRU" or "long-run Phillips curve". However, this long-run "neutrality
Neutrality of money
Neutrality of money is the idea that a change in the stock of money affects only nominal variables in the economy such as prices, wages and exchange rates, with no effect on real variables, like employment, real GDP, and real consumption....

" of monetary policy does allow for short run fluctuations and the ability of the monetary authority to temporarily decrease unemployment by increasing permanent inflation, and vice versa. Blanchard (2000, chapter 8) gives a textbook presentation of the expectations-augmented Phillips curve.

An equation like the expectations-augmented Phillips curve also appears in many recent New Keynesian
New Keynesian economics
New Keynesian economics is a school of contemporary macroeconomics that strives to provide microeconomic foundations for Keynesian economics. It developed partly as a response to criticisms of Keynesian macroeconomics by adherents of New Classical macroeconomics.Two main assumptions define the New...

 dynamic stochastic general equilibrium
Dynamic stochastic general equilibrium
Dynamic stochastic general equilibrium modeling is a branch of applied general equilibrium theory that is influential in contemporary macroeconomics...

 models. In these macroeconomic models
with sticky prices
Sticky (economics)
Sticky, in the social sciences and particularly economics, describes a situation in which a variable is resistant to change. Sticky prices are an important part of macroeconomic theory since they may be used to explain why markets might not reach equilibrium right away. Nominal wages are often said...

, there is a positive relation between the rate of inflation and the level of demand, and therefore a negative relation between the rate of inflation and the rate of unemployment. This relationship is often called the "New Keynesian Phillips curve." Like the expectations-augmented Phillips curve, the New Keynesian Phillips curve implies that increased inflation can lower unemployment temporarily, but cannot lower it permanently. Two influential papers that incorporate a New Keynesian Phillips curve are Clarida
Richard Clarida
Richard Clarida is an American economist, C. Lowell Harriss Professor of Economics and International Affairs at the School of International and Public Affairs at Columbia University and Global Strategic Advisor for PIMCO. He is notable for his contributions to dynamic stochastic general...

, Galí
Jordi Galí
Jordi Galí is a Spanish macroeconomist who is regarded as one of the main figures in New Keynesian macroeconomics today...

, and Gertler
Mark Gertler
Mark Gertler was a British painter of figure subjects, portraits and still-life.His early life and his relationship with Dora Carrington were the inspiration for Gilbert Cannan's novel Mendel. The characters of Loerke in D. H...

 (1999) and Blanchard
Olivier Blanchard
Olivier Jean Blanchard is currently the chief economist at the International Monetary Fund, a post he has held since September 1, 2008. He is also the Class of 1941 Professor of Economics at MIT, though he is currently on leave. Blanchard is one of the most cited economists in the world, according...

 and Galí
Jordi Galí
Jordi Galí is a Spanish macroeconomist who is regarded as one of the main figures in New Keynesian macroeconomics today...

 (2007).

Gordon's triangle model


Robert J. Gordon
Robert J. Gordon
Robert James "Bob" Gordon is an American economist. He is the Stanley G. Harris Professor of the Social Sciences at Northwestern University. He is known for his work on productivity, growth, the causes of unemployment, and airline economics.-Education:...

 of Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....

 has analysed the Phillips curve to produce what he calls the triangle model, in which the actual inflation rate is determined by the sum of
  1. demand pull or short-term Phillips curve inflation
    Demand pull inflation
    Demand-pull inflation is asserted to arise when aggregate demand in an economy outpaces aggregate supply. It involves inflation rising as real gross domestic product rises and unemployment falls, as the economy moves along the Phillips curve. This is commonly described as "too much money chasing...

    ,
  2. cost push or supply shocks
    Cost push inflation
    Cost-push inflation is a type of inflation caused by substantial increases in the cost of important goods or services where no suitable alternative is available.Inflation originating from increase in cost is known as cost-push inflation or supply side inflation A situation that has been often...

    , and
  3. built-in inflation
    Built-in inflation
    Built-in inflation is a type of inflation that results from past events and persists in the present.Built-in inflation is one of three major determinants of the current inflation rate. In Robert J. Gordon's triangle model of inflation, the current inflation rate equals the sum of demand-pull...

    .


The last reflects inflationary expectations and the price/wage spiral
Price/wage spiral
In macroeconomics, the price/wage spiral represents a vicious circle process in which different sides of the wage bargain try to keep up with inflation to protect real incomes. Thus, this process is one possible result of inflation...

. Supply shocks and changes in built-in inflation are the main factors shifting the short-run Phillips Curve and changing the trade-off. In this theory, it is not only inflationary expectations that can cause stagflation. For example, the steep climb of oil prices during the 1970s could have this result.

Changes in built-in inflation follow the partial-adjustment
Adaptive expectations
In economics, adaptive expectations means that people form their expectations about what will happen in the future based on what has happened in the past...

 logic behind most theories of the NAIRU:
  1. Low unemployment encourages high inflation, as with the simple Phillips curve. But if unemployment stays low and inflation stays high for a long time, as in the late 1960s in the U.S., both inflationary expectations and the price/wage spiral accelerate. This shifts the short-run Phillips curve upward and rightward, so that more inflation is seen at any given unemployment rate. (This is with shift B in the diagram.)
  2. High unemployment encourages low inflation, again as with a simple Phillips curve. But if unemployment stays high and inflation stays low for a long time, as in the early 1980s in the U.S., both inflationary expectations and the price/wage spiral slow. This shifts the short-run Phillips curve downward and leftward, so that less inflation is seen at each unemployment rate.


In between these two lies the NAIRU, where the Phillips curve does not have any inherent tendency to shift, so that the inflation rate is stable. However, there seems to be a range in the middle between "high" and "low" where built-in inflation stays stable. The ends of this "non-accelerating inflation range of unemployment rates" change over time.

Theoretical questions



The Phillips curve started as an empirical observation in search of a theoretical explanation. Specifically, the Phillips curve tried to determine whether the inflation-unemployment link was causal or simply correlational. There are several major explanations of the short-term Phillips Curve regularity.

To Milton Friedman
Milton Friedman
Milton Friedman was an American economist, statistician, academic, and author who taught at the University of Chicago for more than three decades...

 there is a short-term correlation between inflation shocks and employment. When an inflationary surprise occurs, workers are fooled into accepting lower pay because they do not see the fall in real wages right away. Firms hire them because they see the inflation as allowing higher profits for given nominal wages. This is a movement along the Phillips curve as with change A. Eventually, workers discover that real wages have fallen, so they push for higher money wages. This causes the Phillips curve to shift upward and to the right, as with B.

Some economists reject this theory because it implies that workers suffer from money illusion
Money illusion
In economics, money illusion refers to the tendency of people to think of currency in nominal, rather than real, terms. In other words, the numerical/face value of money is mistaken for its purchasing power...

. However, one of the characteristics of a modern industrial economy is that workers do not encounter their employers in an atomized and perfect market. They operate in a complex combination of imperfect markets, monopolies
Monopoly
A monopoly exists when a specific person or enterprise is the only supplier of a particular commodity...

, monopsonies
Monopsony
In economics, a monopsony is a market form in which only one buyer faces many sellers. It is an example of imperfect competition, similar to a monopoly, in which only one seller faces many buyers...

, labor unions, and other institutions. In many cases, they may lack the bargaining power
Bargaining power
Bargaining power is a concept related to the relative abilities of parties in a situation to exert influence over each other. If both parties are on an equal footing in a debate, then they will have equal bargaining power, such as in a perfectly competitive market, or between an evenly matched...

 to act on their expectations, no matter how rational they are, or their perceptions, no matter how free of money illusion they are. It is not that high inflation causes low unemployment (as in Milton Friedman's theory) as much as vice-versa: Low unemployment raises worker bargaining power, allowing them to successfully push for higher nominal wages. To protect profits, employers raise prices.

Similarly, built-in inflation is not simply a matter of subjective "inflationary expectations" but also reflects the fact that high inflation can gather momentum and continue beyond the time when it was started, due to the objective price/wage spiral.

However, other economists, like Jeffrey Herbener, argue that price is market-determined and competitive firms cannot simply raise prices. They reject the Phillips curve entirely, concluding that unemployment's influence is only a small portion of a much larger inflation picture that includes prices of raw materials, intermediate goods, cost of raising capital, worker productivity, land, and other factors.

Mathematics behind the Phillips curve


There are at least two different mathematical derivations of the Phillips curve. First, there is the traditional or Keynesian version. Then, there is the new Classical version associated with Robert E. Lucas, Jr..

The traditional Phillips curve


The original Phillips curve literature was not based on the unaided application of economic theory. Instead, it was based on empirical generalizations. After that, economists tried to develop theories that fit the data.

Money wage determination


The traditional Phillips curve story starts with a wage Phillips Curve, of the sort described by A.W. Phillips himself. This describes the rate of growth of money wages (gW). Here and below, the operator g is the equivalent of "the percentage rate of growth of" the variable that follows.
gW = gWTf(U)


The "money wage rate" (W) is short-hand for total money wage costs per production employee, including benefits and payroll taxes. The focus is on only production workers' money wages, because (as discussed below) these costs are crucial to pricing decisions by the firms.

This equation tells us that the growth of money wages rises with the trend rate of growth of money wages (indicated by the superscript "T") and falls with the unemployment rate (U). The function f is assumed to be monotonically increasing with U so that the dampening of money-wage increases by unemployment is shown by the negative sign in the equation above.

There are several possible stories behind this equation. A major one is that money wages are set by bilateral negotiations under partial bilateral monopoly
Bilateral monopoly
In a bilateral monopoly there is both a monopoly and monopsony in the same market.In such, market price and output will be determined by forces like bargaining power of both buyer and seller...

: as the unemployment rate rises, all else constant worker bargaining power falls, so that workers are less able to increase their wages in the face of employer resistance.

During the 1970s, this story had to be modified, because (as the late Abba Lerner had suggested in the 1940s) workers try to keep up with inflation. Since the 1970s, the equation has been changed to introduce the role of inflationary expectations (or the expected inflation rate, gPex). This produces the expectations-augmented wage Phillips curve:
gW = gWT - f(U) + λ*gPex.


The introduction of inflationary expectations into the equation implies that actual inflation can feed back into inflationary expectations and thus cause further inflation. The late economist James Tobin
James Tobin
James Tobin was an American economist who, in his lifetime, served on the Council of Economic Advisors and the Board of Governors of the Federal Reserve System, and taught at Harvard and Yale Universities. He developed the ideas of Keynesian economics, and advocated government intervention to...

 dubbed the last term "inflationary inertia," because in the current period, inflation exists which represents an inflationary impulse left over from the past.

It also involved much more than expectations, including the price-wage spiral. In this spiral, employers try to protect profits by raising their prices and employees try to keep up with inflation to protect their real wages. This process can feed on itself, becoming a self-fulfilling prophecy.

The parameter λ (which is presumed constant during any time period) represents the degree to which employees can gain money wage increases to keep up with expected inflation, preventing a fall in expected real wages. It is usually assumed that this parameter equals unity in the long run.

In addition, the function f was modified to introduce the idea of the Non-Accelerating Inflation Rate of Unemployment (NAIRU) or what's sometimes called the "natural" rate of unemployment or the
inflation-threshold unemployment rate:
[1] gW = gWT - f(UU*) + λ·gPex.


Here, U* is the NAIRU. As discussed below, if U < U*, inflation tends to accelerate. Similarly, if U > U*, inflation tends to slow. It is assumed that f(0) = 0, so that when U = U*, the f term drops out of the equation.

In equation [1], the roles of gWT and gPex seem to be redundant, playing much the same role. However, assuming that λ is equal to unity, it can be seen that they are not. If the trend rate of growth of money wages equals zero, then the case where U equals U* implies that gW equals expected inflation. That is, expected real wages are constant.

In any reasonable economy, however, having constant expected real wages could only be consistent with actual real wages that are constant over the long haul. This does not fit with economic experience in the U.S. or any other major industrial country. Even though real wages have not risen much in recent years, there have been important increases over the decades.

An alternative is to assume that the trend rate of growth of money wages equals the trend rate of growth of average labor productivity (Z). That is:
[2] gWT = gZT.


Under assumption [2], when U equals U* and λ equals unity, expected real wages would increase with labor productivity. This would be consistent with an economy in which actual real wages increase with labor productivity. Deviations of real-wage trends from those of labor productivity might be explained by reference to other variables in the model.

Pricing decisions


Next, there is price behavior. The standard assumption is that markets are imperfectly competitive, where most businesses have some power to set prices. So the model assumes that the average business sets prices as a mark-up (M) over unit labor costs in production measured at a standard rate of capacity utilization (say, at 90 percent use of plant and equipment) and then add in unit material costs.

The standardization involves later ignoring deviations from the trend in labor productivity. For example, assume that the growth of labor productivity is the same as that in the trend and that current productivity equals its trend value:
gZ = gZT and Z = ZT.


The markup reflects both the firm's degree of market power and the extent to which overhead costs have to be paid. Put another way, all else equal, M rises with the firm's power to set prices or with a rise of overhead costs relative to total costs.

So pricing follows this equation:
P = M × (unit labor costs) + (unit materials cost)

= M × (total production employment cost)/(quantity of output) + UMC.


UMC is unit raw materials cost (total raw materials costs divided by total output). So the equation can be can be restated as:
P = M × (production employment cost per worker)/(output per production employee) + UMC.


This equation can again be stated as:
P = M×(average money wage)/(production labor productivity) + UMC

= M×(W/Z) + UMC.


Now, assume that both the average price/cost mark-up (M) and UMC are constant. On the other hand, labor productivity grows, as before. Thus, an equation determining the price inflation rate (gP) is:
gP = gW - gZT.

The price Phillips curves


Then, combined with the wage Phillips curve [equation 1] and the assumption made above about the trend behavior of money wages [equation 2], this price-inflation equation gives us a simple expectations-augmented price Phillips curve:
gP = −f(UU*) + λ·gPex.


Some assume that we can simply add in gUMC, the rate of growth of UMC, in order to represent the role of supply shocks (of the sort that plagued the U.S. during the 1970s). This produces a standard short-term Phillips curve:
gP = −f(UU*) + λ·gPex + gUMC.


Economist Robert J. Gordon
Robert J. Gordon
Robert James "Bob" Gordon is an American economist. He is the Stanley G. Harris Professor of the Social Sciences at Northwestern University. He is known for his work on productivity, growth, the causes of unemployment, and airline economics.-Education:...

 has called this the "Triangle Model" because it explains short-run inflationary behavior by three factors: demand inflation (due to low unemployment), supply-shock inflation (gUMC), and inflationary expectations or inertial inflation.

In the long run, it is assumed, inflationary expectations catch up with and equal actual inflation so that gP = gPex. This represents the long-term equilibrium of expectations adjustment. Part of this adjustment may involve the adaptation of expectations to the experience with actual inflation. Another might involve guesses made by people in the economy based on other evidence. (The latter idea gave us the notion of so-called rational expectations
Rational expectations
Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. An alternative formulation is that rational expectations are model-consistent expectations, in...

.)

Expectational equilibrium gives us the long-term Phillips curve. First, with λ less than unity:
gP = [1/(1 − λ)]·(−f(UU*) + gUMC).


This is nothing but a steeper version of the short-run Phillips curve above. Inflation rises as unemployment falls, while this connection is stronger. That is, a low unemployment rate (less than U*) will be associated with a higher inflation rate in the long run than in the short run. This occurs because the actual higher-inflation situation seen in the short run feeds back to raise inflationary expectations, which in turn raises the inflation rate further. Similarly, at high unemployment rates (greater than U*) lead to low inflation
rates. These in turn encourage lower inflationary expectations, so that inflation itself drops again.

This logic goes further if λ is equal to unity, i.e., if workers are able to protect their wages completely from expected inflation, even in the short run. Now, the Triangle Model equation becomes:
- f(UU*) = gUMC.


If we further assume (as seems reasonable) that there are no long-term supply shocks, this can be simplified to become:
f(UU*) = 0 which implies that U = U*.


All of the assumptions imply that in the long run, there is only one possible unemployment rate, U* at any one time. This uniqueness explains why some call this unemployment rate "natural."

To truly understand and criticize the uniqueness of U*, a more sophisticated and realistic model is needed. For example, we might introduce the idea that workers in different sectors push for money wage increases that are similar to those in other sectors. Or we might make the model even more realistic. One important place to look is at the determination of the mark-up, M.

New classical version


The Phillips curve equation can be derived from the (short-run) Lucas aggregate supply function. The Lucas approach is very different from that the traditional view. Instead of starting with empirical data, he started with a classical economic model following very simple economic principles.

Start with the aggregate supply
Aggregate supply
In economics, aggregate supply is the total supply of goods and services that firms in a national economy plan on selling during a specific time period...

 function:


where Y is log value of the actual output
Output
Output is the term denoting either an exit or changes which exit a system and which activate/modify a process. It is an abstract concept, used in the modeling, system design and system exploitation.-In control theory:...

, Yn is log value of the "natural" level of output
Output
Output is the term denoting either an exit or changes which exit a system and which activate/modify a process. It is an abstract concept, used in the modeling, system design and system exploitation.-In control theory:...

, a is a positive constant, P is log value of the actual price level
Price level
A price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set...

, and Pe is log value of the expected price level
Price level
A price level is a hypothetical measure of overall prices for some set of goods and services, in a given region during a given interval, normalized relative to some base set...

. Lucas assumes that Yn has a unique value.

Note that this equation indicates that when expectations of future inflation (or, more correctly, the future price level) are totally accurate, the last term drops out, so that actual output equals the so-called "natural" level of real GDP. This means that in the Lucas aggregate supply curve, the only reason why actual real GDP should deviate from potential—and the actual unemployment rate should deviate from the "natural" rate—is because of incorrect expectations of what is going to happen with prices in the future. (The idea has been expressed first by Keynes, "General Theory," Chapter 20 section III paragraph 4).

This differs from other views of the Phillips curve, in which the failure to attain the "natural" level of output can be due to the imperfection or incompleteness of markets, the stickiness of prices, and the like. In the non-Lucas view, incorrect expectations can contribute to aggregate demand failure, but they are not the only cause. To the "new Classical" followers of Lucas, markets are presumed to be perfect and always attain equilibrium (given inflationary expectations).

We re-arrange the equation into:


Next we add unexpected exogenous shocks to the world supply v:


Subtracting last year's price levels P-1 will give us inflation rates, because


and


where π and πe are the inflation
Inflation
In economics, inflation is a rise in the general level of prices of goods and services in an economy over a period of time.When the general price level rises, each unit of currency buys fewer goods and services. Consequently, inflation also reflects an erosion in the purchasing power of money – a...

 and expected inflation respectively.

There is also a negative relationship between output and unemployment (as expressed by Okun's law
Okun's law
In economics, Okun's law is an empirically observed relationship relating unemployment to losses in a country's production first quantified by Arthur M. Okun. The "gap version" states that for every 1% increase in the unemployment rate, a country's GDP will be at an additional roughly 2% lower...

). Therefore using
where b is a positive constant, U is unemployment, and Un is the natural rate of unemployment
Natural rate of unemployment
The natural rate of unemployment is a concept of economic activity developed in particular by Milton Friedman and Edmund Phelps in the 1960s, both recipients of the Nobel prize in economics...

 or NAIRU
NAIRU
In monetarist economics, particularly the work of Milton Friedman, on which also worked Lucas Papademos and Franco Modigliani in 1975,NAIRU is an acronym for Non-Accelerating Inflation Rate of Unemployment, and refers to a level of unemployment below which inflation rises.It is widely used in...

, we arrive at the final form of the short-run Phillips curve:


This equation, plotting inflation rate π against unemployment U gives the downward-sloping curve in the diagram that characterises the Phillips curve.

Further reading


External links

  • Left critique of Phillips Curve from Dollars & Sense
    Dollars & Sense
    Dollars & Sense is a magazine dedicated to providing left-wing perspectives on economics.Published six times a year since 1974, it is edited by a collective of economists, journalists, and activists committed to the ideals of social justice and economic democracy.It was initially sponsored by the...

     magazine
  • A Critique of the Phillips Curve by Charles Oliver, Ludwig von Mises Institute
    Ludwig von Mises Institute
    The Ludwig von Mises Institute , based in Auburn, Alabama, is a libertarian academic organization engaged in research and scholarship in the fields of economics, philosophy and political economy. Its scholarship is inspired by the work of Austrian School economist Ludwig von Mises...

    , February 9, 1999 (includes the article "Who's Afraid Of A Red-Hot Economy?", Investor's Business Daily
    Investor's Business Daily
    Investor's Business Daily is a national newspaper in the United States, published Monday through Friday, that covers international business, finance, and the global economy...

    , February 9, 1999)
  • Audio speech by Jeffery Herbener at the Ludwig Von Mises Institute.