The Phillips curve and some further implications

CONTENTS

1. Introduction

2. Derivation of the Phillips Curve
2.1. Equilibrium of the labor-market
2.2. Function of the wage change
2.3. Some further implications
2.4. Modification of Samuelson and Solow (1960)
2.5. Popular politico-economic interpretation

3. Critics of Friedman and Phelps (1968)
3.1. Expectations-augmented Phillips curve
3.2. Interpretation of Friedman
3.3. Adjustment of the Phillips's curve in timing
3.4. Conclusion

4. Comparison of Phillips theory and some real data Appendix

References

Abstract:

The following pages consist of the derivation of the Phillips curve. Therefor I do not only speak how the curve has been developed by A. Phillips. It will be more a look back, how new modification came up by Samuelson and Solow in 1960 and some critics of Friedman and Phelpes in 1968. In the end I will compare the theory with some data from Germany.

1. Introduction

The relationship of unemployment and wages is an evergreen in both theoretical and empirical economics. A lot of economic decisions are still based on the famous work by A. Phillips that there is an inverse relationship between the rate of change of wages and the contemporaneous unemployment rate, i.e. there is a Phillips curve. This common view is grounded on the idea that wages adjust to eliminate any excess supply or demand in labor market and is supported by a huge amount of empirical work with macroeconomic data for different countries.

Phillip's model is mainly based on empirical studies of Great Britain between 1861 - 1957. He realized first that there is a conflict between stabilizing wages and achieving a low unemployment rate. By discovering that non-linear connection of the increasing of the nominal-wage and the unemployment-ratio, Phillips has found a good explanation for the data at that point of time.

Some years later the model was modified and criticized but it is still in our days a very common model for politicians for explaining unemployment.

2. Derivation of the Phillips Curve

The model is mainly based on the Keynsesian model of an aggregated competitive labormarket with the functions LS (labor supply, positive slope), LF(labor force, positive slope but more steep) and LD (labor demand).

2.1. Equilibrium of the labor-market

We reach the equilibrium level of wage W*/p (W = nominal wage, p = price-level) where LS = LD (LS* = LD*). Is Ws/p > W*/p we get some "excess supply". In the other way round is Wd/p < W*/p there exists an "excess demand" on the labor market. Assuming that p is fixed, wages change in both cases toward the equilibrium wage level. Having reached this wagelevel, there is no further tendency of changing wages. At this point the unemployment is on the natural rate, U*. It can be measured by the difference between LF and LD*.

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2.2. Function of the wage change

Now we can derive a function of the wage change , of _ and excess demand:

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In the deviation-form it looks as fellow:

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The _ indicates the responsiveness of to deviation of the changing of unemployment from U* and takes on a negative value due to the inverse relationship.

2.3. Some further implications

Here it is necessary to say that the relationship between wage change and unemployment is not symmetric for points above and below the natural rate. Furthermore we can see that there is a border to - below it will not go, no matter how high unemployment is there is a unit to the rate at which nominal wages will be reduced.

Umin however shows that there is a lower limit of unemployment: Starting from this point now, no matter how high the wages are, no additional workers can be persuaded to participate in the labor-market

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This is the Phillips curve.

Interpretation:

At a relative high level of unemployment employee will claim comparable low increasing of wages.

2.4. Modification of Samuelson and Solow (1960)

A. Samuelson and R. M. Solow worked in the 1960's again with the Phillips curve and modified it. They assumed a fixed relationship between nominal wage changes and changes of the price level. Thus they developed from the original Phillips curve, the modified Phillips curve (connection between inflation rate and unemployment ratio). They assume:

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2.5. Popular politico-economic interpretation

Economic policy-maker, who wants to achieve a low inflation rate (unemployment ratio), must accept a higher unemployment ratio (inflation rate) (the Phillips's " trade off "). The Phillips curve can be seen as a "menu " of inflation and unemployment, the politician can select from.

3. Critics of Friedman and Phelps (1968)

The connection which is represented by the Phillips curve between changes in the wage-rate and unemployment is just correct with continuous inflation expectations. If a higher inflation is expected, then also future wage agreements will be more highly; the Phillips curve shifts upward.

3.1. Expectations-augmented Phillips curve

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Now it is possible to put (1) in (2), which leads to:

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3.2. Interpretation of Friedman

The unemployment rate has the possibility to go below the natural level just if we have unexpected inflation. In the long run is the actual inflation-rate equal to the expected inflation rate:

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This leads to the conclusion that the actual unemployment ratio is equal to the natural unemployment ration and that in the same size of the inflation-rate.

So in the long run there exists no "trade-off" of inflation and unemployment.

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3.3. Adjustment of the Phillips's curve in timing

In the following figure we will start at point a. Here U is equal to U* and P* is equal to P** and that is equal to 3 %. Now we start with an expansive monetary policy. So there is a movement on the short run Phillips curve toward point b. The result is a lower unemployment ratio but a higher inflation rate; here 5 %. Now the higher inflation rate leads to a new adjustment of the expected inflation rate P**. We assume now that we have an expected inflation rate of 5 % instead of 3 %. The result is an upward shift of the Phillips curve. So the inflation-effect of the expansive monetary is increasing and the job creating effect is decreasing. In the figure this is point c.

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Furthermore the expected inflation rate is increasing and the short-run Phillips curve is shifting up. In the equilibrium it will reach point d. At this point the expected and the actual inflation rate are in equilibrium. There is no reason for further changes of the expected inflation rate.

The movement from b to d (increasing unemployment with increasing inflation at the same time) is also called "stagflation".

3.4. Conclusion

The effect of a "decreasing unemployment" by using the monetary police can just be seen in the short-run. In the long run there will be the same level of unemployment as in the short-run but a higher level of inflation.

4. Comparison of Phillips theory and some real data

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If we know have a look at same data of an industrialized nation, here for example we cannot find any Phillips curve. The connection that was found by Phillips was just true the data he had. In our day it is dangerous to base economic decisions just on his work. Source: Statistisches Bundesamt at Wiesbaden, Germany, Sonderbeitrag der Fachserie 17, row 7 page 1

The table shows the inflation-rate and unemployment-ratio from the year 1954 to 1996 (to connect the points with the right year have a look at the appendix). As we can see there is not such a connection like Phillips has found out for his kind of data. We can find high (low) unemployment at both, a high and a low inflation level. Politicians cannot choose between high unemployment or a high inflation-rate. There have to be some other mechanisms.

Even econometric studies about the wage-curve and the Phillips curve by M. Pannenberg and J. Schwarze for Germany cannot give satisfy answers.

But we have to mention that Friedman (Monetarist) and Samuleson (Keynse) are supporters of different economic theories and that the theory of Keynse is still actuall.

Appendix

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Source:

Statistisches Bundesamt Wiesbaden, Germany, Sonderbeitrag der Fachserie 17, row 7 page 1

References

Bergstrom, A. R., "Stability and inflation: a volume of essays to honour the memory of A. W. H. Phillips".

Elliott, Robert F., LABOR ECONOMICS: A Comparative Text, McGraw-Hill International (UK) Limited, 1991, 499 - 513.

"GABLER WIRTSCHAFTSLEXIKON", No. 6 P -SK 13th edition, p. 2586 -2587

Lown, Cara S. and Rich, Robert W., "Is There an Inflation Puzzle?", FRBNY ECONOMIC POLICY REVIEW / DECEMBER 1997

Pannenberg, Markus and J. Schwarze, `Phillips Curve' or `Wage Curve': Is there really a puzzle? Evidence for West Germany, German Institute for Economic Research (DIW), University of Bamberg, July 1998.

Statistisches Bundesamt Wiesbaden, Germany, Sonderbeitrag der Fachserie 17, row 7 page 1 http://www.econ.jhu.edu/People/Fonseca/HET/phillips.htm