The Phillips curve is an
economic model, named after
William Phillips William Phillips may refer to:
Entertainment
* William Phillips (editor) (1907–2002), American editor and co-founder of ''Partisan Review''
* William T. Phillips (1863–1937), American author
* William Phillips (director), Canadian film-make ...
hypothesizing a correlation between reduction in
unemployment
Unemployment, according to the OECD (Organisation for Economic Co-operation and Development), is people above a specified age (usually 15) not being in paid employment or self-employment but currently available for work during the refe ...
and increased rates of wage rises within an economy. While Phillips himself did not state a linked relationship between employment and
inflation
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
, this was a trivial deduction from his statistical findings.
Paul Samuelson
Paul Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he " ...
and
Robert Solow
Robert Merton Solow, GCIH (; born August 23, 1924) is an American economist whose work on the theory of economic growth culminated in the exogenous growth model named after him. He is currently Emeritus Institute Professor of Economics at th ...
made the connection explicit and subsequently
Milton Friedman
Milton Friedman (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the ...
and
Edmund Phelps put the theoretical structure in place.
While there is a short run tradeoff between unemployment and inflation, it has not been observed in the long run.
[Chang, R. (1997]
"Is Low Unemployment Inflationary?"
''Federal Reserve Bank of Atlanta Economic Review'' 1Q97:4-13 In 1967 and 1968, Friedman and Phelps asserted that the Phillips curve was only applicable in the short-run and that, in the long-run, inflationary policies would not decrease unemployment.
Friedman then correctly predicted that in the
1973–75 recession, both
inflation and unemployment would increase.
In the 2010s the slope of the Phillips curve appears to have declined and there has been controversy over the usefulness of the Phillips curve in predicting inflation. A 2022 study found that the slope of the Phillips curve is small and was small even during the early 1980s. Nonetheless, the Phillips curve remains the primary framework for understanding and forecasting inflation used in central banks.
History
William Phillips William Phillips may refer to:
Entertainment
* William Phillips (editor) (1907–2002), American editor and co-founder of ''Partisan Review''
* William T. Phillips (1863–1937), American author
* William Phillips (director), Canadian film-make ...
, a
New Zealand
New Zealand ( mi, Aotearoa ) is an island country in the southwestern Pacific Ocean. It consists of two main landmasses—the North Island () and the South Island ()—and over 700 smaller islands. It is the sixth-largest island coun ...
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''. 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 Anthony Samuelson (May 15, 1915 – December 13, 2009) was an American economist who was the first American to win the Nobel Memorial Prize in Economic Sciences. When awarding the prize in 1970, the Swedish Royal Academies stated that he " ...
and
Robert Solow
Robert Merton Solow, GCIH (; born August 23, 1924) is an American economist whose work on the theory of economic growth culminated in the exogenous growth model named after him. He is currently Emeritus Institute Professor of Economics at th ...
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 (February 27, 1867 – April 29, 1947) was an American economist, statistician, inventor, eugenicist and progressive social campaigner. He was one of the earliest American neoclassical economists, though his later work on debt de ...
had 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 ( ; sometimes Keynesianism, named after British economist John Maynard Keynes) are the various macroeconomic theories and models of how aggregate demand (total spending in the economy) strongly influences economic output an ...
policy. They could tolerate a reasonably high rate of inflation as this would lead to lower unemployment – there would be a
trade-off
A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and anot ...
between inflation and unemployment. For example,
monetary policy
Monetary policy is the policy adopted by the monetary authority of a nation to control either the interest rate payable for federal funds, very short-term borrowing (borrowing by banks from each other to meet their short-term needs) or the money s ...
and/or
fiscal policy
In economics and political science, fiscal policy is the use of government revenue collection ( taxes or tax cuts) and expenditure to influence a country's economy. The use of government revenue expenditures to influence macroeconomic variabl ...
could be used to stimulate the economy, raising
gross domestic product
Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced and sold (not resold) in a specific time period by countries. Due to its complex and subjective nature this measure is of ...
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. Economist
James Forder
James Forder (born 1964) is a British academic / economist and Tutorial Fellow in Economics at Balliol College, University of Oxford. He is editor of ''Oxford Economic Papers''. He co-authored the book "Both Sides of the Coin" along with Chris Huh ...
argues that this view is historically false and that neither economists nor governments took that view and that the 'Phillips curve myth' was an invention of the 1970s.
Since 1974, seven Nobel Prizes have been given to economists for, among other things, work critical of some variations 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
Thomas John Sargent (born July 19, 1943) is an American economist and the W.R. Berkley Professor of Economics and Business at New York University. He specializes in the fields of macroeconomics, monetary economics, and time series econometr ...
,
Christopher Sims
Christopher Albert Sims (born October 21, 1942) is an American econometrician and macroeconomist. He is currently the John J.F. Sherrerd '52 University Professor of Economics at Princeton University. Together with Thomas Sargent, he won the ...
,
Edmund Phelps,
Edward Prescott
Edward Christian Prescott (December 26, 1940 – November 6, 2022) was an American economist. He received the Nobel Memorial Prize in Economics in 2004, sharing the award with Finn E. Kydland, "for their contributions to dynamic macroeconomics: ...
,
Robert A. Mundell,
Robert E. Lucas,
Milton Friedman
Milton Friedman (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the ...
, and
F.A. Hayek.
Stagflation
In the 1970s, many countries experienced high levels of both inflation and unemployment also known as
stagflation. 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 (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the ...
. Friedman argued that the Phillips curve relationship was only a short-run phenomenon. In this he followed eight years after Samuelson and Solow
960who wrote "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 Figure 2 menu that related obtainable price and unemployment behavior will maintain its same shape in the longer run. What we do in a policy way during the next few years might cause it to shift in a definite way."
As Samuelson and Solow had argued 8 years earlier, 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
A central bank, reserve bank, or monetary authority is an institution that manages the currency and monetary policy of a country or monetary union,
and oversees their commercial banking system. In contrast to a commercial bank, a centra ...
s should not set unemployment targets below the natural rate.
[
More recent research suggests that there is a moderate trade-off between low-levels of inflation and unemployment. Work by ]George Akerlof
George Arthur Akerlof (born June 17, 1940) is an American economist and a university professor at the McCourt School of Public Policy at Georgetown University and Koshland Professor of Economics Emeritus at the University of California, Berkeley ...
, William Dickens
William T. Dickens (born December 31, 1953) is an American economist. He is a University Distinguished Professor of Economics and Social Policy at Northeastern University.
Career
Dickens was on the faculty of the University of California, Berke ...
, and George Perry, 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.
Today
Most economists no longer use the Phillips curve in its original form because it was shown to be too simplistic.[Oliver Hossfeld (2010]
"US Money Demand, Monetary Overhang, and Inflation Prediction"
''International Network for Economic Research'' working paper no. 2010.4 This can be seen in a cursory analysis of US inflation and unemployment data from 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. Modern Phillips curve models include both a short-run Phillips Curve and a long-run Phillips Curve. This is because in the short run, there is generally an inverse relationship between inflation and the unemployment rate; as illustrated in the downward sloping short-run Phillips curve. In the long run, that relationship breaks down and the economy eventually returns to the natural rate of unemployment regardless of the inflation rate.
The "short-run Phillips curve" is also called the "expectations-augmented Phillips curve", since it shifts up when inflationary expectations rise, Edmund Phelps and ]Milton Friedman
Milton Friedman (; July 31, 1912 – November 16, 2006) was an American economist and statistician who received the 1976 Nobel Memorial Prize in Economic Sciences for his research on consumption analysis, monetary history and theory and the ...
argued. In the long run, this implies that monetary policy cannot affect unemployment, which adjusts back to its " natural rate", also called the " NAIRU". The popular textbook of Blanchard
Blanchard is a French family name. It is also used as a given name. It derives from the Old French word ''blanchart'' which meant "whitish, bordering upon white". It is also an obsolete term for a white horse.
Geographical distribution
As of 2014, ...
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 dynamic stochastic general equilibrium
Dynamic stochastic general equilibrium modeling (abbreviated as DSGE, or DGE, or sometimes SDGE) is a macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-series data, as w ...
models. As Keynes mentioned: "A Government has to remember, however, that even if a tax is not prohibited it may be unprofitable, and that a medium, rather than an extreme, imposition will yield the greatest gain". In these macroeconomic model
A macroeconomic model is an analytical tool designed to describe the operation of the problems of economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such a ...
s with sticky prices, 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, Galí, and Gertler (1999), and Blanchard
Blanchard is a French family name. It is also used as a given name. It derives from the Old French word ''blanchart'' which meant "whitish, bordering upon white". It is also an obsolete term for a white horse.
Geographical distribution
As of 2014, ...
and Galí (2007).
Mathematics
There are at least two different mathematical derivations of the Phillips curve. First, there is the traditional or Keynesian
Keynesian economics ( ; sometimes Keynesianism, named after British economist John Maynard Keynes) are the various macroeconomic theories and models of how aggregate demand (total spending in the economy) strongly influences economic output an ...
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 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.
:
The "money wage rate" (''W'') is shorthand 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: 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
Abraham "Abba" Ptachya Lerner (also Abba Psachia Lerner; 28 October 1903 – 27 October 1982) was a Russian-born American-British economist.
Biography
Born in Novoselytsia, Bessarabia, Russian Empire, Lerner grew up in a Jewish family, which ...
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, ''gP''ex). This produces the expectations-augmented wage Phillips curve:
:
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 (March 5, 1918 – March 11, 2002) was an American economist who served on the Council of Economic Advisers and consulted with the Board of Governors of the Federal Reserve System, and taught at Harvard and Yale Universities. He ...
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 1 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:
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 (), 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:
Under assumption (), 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 a unit price (P) as a mark-up (M) over the unit labor cost in production measured at a standard rate of capacity utilization (say, at 90 percent use of plant and equipment) and then adds in the unit materials cost.
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 cost) + (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 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.
Price
Then, combined with the wage Phillips curve quation 1and the assumption made above about the trend behavior of money wages quation 2 this price-inflation equation gives us a simple expectations-augmented price Phillips curve:
: gP = −f(U − U*) + 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(U − U*) + λ·gPex + gUMC.
Economist Robert J. Gordon 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.)
Expectational equilibrium gives us the long-term Phillips curve. First, with λ less than unity:
:gP = /(1 − λ)�(−f(U − U*) + 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(U − U*) = gUMC.
If we further assume (as seems reasonable) that there are no long-term supply shocks, this can be simplified to become:
: −f(U − U*) = 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 of 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
In economics, aggregate supply (AS) or domestic final supply (DFS) is the total supply of goods and services that firms in a national economy plan on selling during a specific time period. It is the total amount of goods and services that fir ...
function:
:
where ''Y'' is log value of the actual output, is log value of the "natural" level of output, is a positive constant, is log value of the actual price level, and is log value of the expected price level. Lucas assumes that 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
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in m ...
, '' 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 :
:
Subtracting last year's price levels will give us inflation rates, because
:
and
:
where and are the inflation
In economics, inflation is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduct ...
and expected inflation respectively.
There is also a negative relationship between output and unemployment (as expressed by Okun's law
In economics, Okun's law is an empirically observed relationship between unemployment and losses in a country's production. It is named after Arthur Melvin Okun, who first proposed the relationship in 1962. The "gap version" states that for ever ...
). Therefore, using
:
where is a positive constant, is unemployment, and is the natural rate of unemployment or NAIRU, we arrive at the final form of the short-run Phillips curve:
:
This equation, plotting inflation rate against unemployment gives the downward-sloping curve in the diagram that characterizes the Phillips curve.
New Keynesian version
The New Keynesian Phillips curve was originally derived by Roberts in 1995, and since been used in most state-of-the-art New Keynesian DSGE models like the one of Clarida, Galí, and Gertler (2000).
:
where
:
The current expectations of next period's inflation are incorporated as