Okun's law

In economics, Okun's law, named after economist Arthur Okun who proposed the relationship in 1962 (Prachowny 1993), describes a relationship between the change in the rate of unemployment and the difference between actual and potential real GDP.

Okun's law

In the United States during the period since 1965, Okun's law can be stated as saying that for every one percentage point by which the actual unemployment rate exceeds the so-called "natural" rate of unemployment, real gross domestic product is reduced by 2% to 3%. That is, unemployment above the inflation-threshold unemployment rate reduces GDP below potential output, and for every 1% excess of the natural unemployment rate, a 2% to 3% reduction in GDP is predicted. The difference between actual and potential GDP is called the GDP gap. It may be expressed as a percentage or an absolute amount.

Okun's law is more accurately called "Okun's rule of thumb" because, like Moore's law in semiconductors, it is primarily an empirical observation rather than a result derived from theory. Okun's law is approximate because factors other than employment (such as productivity) affect output. The relationship varies depending on the country and time period under consideration.

The relationship has been tested by regressing GDP or GNP growth on change in the unemployment rate. Martin Prachowny estimated about a 3% decrease in output for every 1% increase in the unemployment rate (Prachowny 1993). The magnitude of the decrease seems to be declining over time in the United States. According to Andrew Abel and Ben Bernanke, estimates based on data from more recent years give about a 2% decrease in output for every 1% increase in unemployment (Abel and Bernanke, 2005).

There are several reasons why GDP may increase or decrease more rapidly than unemployment decreases or increases. As unemployment increases,

• unemployed persons may drop out of the labor force (stop seeking work), after which they are no longer counted in unemployment statistics
• employed workers may work shorter hours
• labor productivity may decrease, perhaps because employers retain more workers than they need

One implication of Okun's law is that an increase in labor productivity together with an increase in the size of the labor force can mean that real net output grows without net unemployment rates falling (the phenomenon of "jobless growth.")

Mathematical statements of Okun's law

Okun's law may be written (Abel & Bernanke 2005) as:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\overline{Y}-Y)/\overline{Y} = c(u-\overline{u})

, where:

• Failed to parse (Missing texvc executable; please see math/README to configure.): \overline{Y}

is full-employment output

• Y is actual output
• Failed to parse (Missing texvc executable; please see math/README to configure.): \overline{u}

is the natural rate of unemployment

• u is actual unemployment rate
• c is the factor relating changes in unemployment to changes in output

In the United States since 1965 or so, the value of c has typically been around 2 or 3, as explained above.

Okun's law as shown above is difficult to use in practice because Failed to parse (Missing texvc executable; please see math/README to configure.): \overline{Y}

and Failed to parse (Missing texvc executable; please see math/README to configure.): \overline{u}

can only be estimated, not measured. A more commonly used form of Okun's law, known as the growth rate form of Okun's law, relates changes in output to changes in unemployment:

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta Y/Y = k - c \Delta u\,

, where:

• Failed to parse (Missing texvc executable; please see math/README to configure.): Y

and Failed to parse (Missing texvc executable; please see math/README to configure.): c
are as defined above

• Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta Y

is the change in actual output from one year to the next

• Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta u

is the change in actual unemployment from one year to the next

• Failed to parse (Missing texvc executable; please see math/README to configure.): k

is the average annual growth rate of full-employment output

At the present time in the United States, k is about 3% and c is about 2, so the equation may be written

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta Y/Y = 3 - 2 \Delta u\,

The graph at the top of this article illustrates the growth rate form of Okun's law, measured quarterly rather than annually.

Derivation of the growth rate form of Okun's law

We start with the first form of Okun's law:

Failed to parse (Missing texvc executable; please see math/README to configure.): (\overline{Y}-Y)/\overline{Y} = 1-Y/\overline{Y} = c(u-\overline{u})

Failed to parse (Missing texvc executable; please see math/README to configure.): -1+Y/\overline{Y} = c(\overline{u}-u)

Taking annual differences on both sides, we obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta(Y/\overline{Y}) = (Y + \Delta Y)/(\overline{Y}+ \Delta \overline{Y}) - Y/\overline{Y} = c(\Delta \overline{u}-\Delta u)

Putting both numerators over a common denominator, we obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): (\overline{Y} \Delta Y - Y \Delta \overline{Y})/(\overline{Y}(\overline{Y} + \Delta \overline{Y}))= c(\Delta \overline{u}-\Delta u)

Multiplying the left hand side by Failed to parse (Missing texvc executable; please see math/README to configure.): (\overline{Y} + \Delta \overline{Y})/Y , which is approximately equal to 1, we obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): (\overline{Y} \Delta Y - Y \Delta \overline{Y})/(\overline{Y}Y) = \Delta Y/Y - \Delta \overline{Y}/\overline{Y} \approx c(\Delta \overline{u}-\Delta u)

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta Y/Y \approx \Delta \overline{Y}/\overline{Y} + c(\Delta \overline{u}-\Delta u)

We assume that Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta \overline{u} , the change in the natural rate of unemployment, is approximately equal to 0. We also assume that Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta \overline{Y}/\overline{Y} , the growth rate of full-employment output, is approximately equal to its average value, Failed to parse (Missing texvc executable; please see math/README to configure.): k . So we finally obtain

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta Y/Y \approx k - c \Delta u

References

• Case, Karl E. & Fair, Ray C. (1999). Principles of Economics (5th ed.). Prentice-Hall. ISBN 0-13-961905-4.
• Abel, Andrew B. & Bernanke, Ben S. (2005). Macroeconomics (5th ed.). Pearson Addison Wesley. ISBN 0-321-16212-9.
• Prachowny, Martin F. J. (1993). "Okun's Law: Theoretical Foundations and Revised Estimates," The Review of Economics and Statistics, 75(2), pp. 331-336.de:Okunsches Gesetz

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