Okun’s Law Calculator
Enter the change in unemployment, the natural rate, the Okun coefficient and actual GDP growth to see trend growth and the Okun gap.
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Okun’s Law Calculator
Our Okun’s Law Calculator links a change in the unemployment rate to economic growth. Type the change in unemployment in percentage points, the natural rate of unemployment, the Okun coefficient and the actual GDP growth rate. It returns the trend growth rate, the Okun gap (how far growth is above or below trend) and the unemployment rate that results. It is useful for macroeconomics students, teachers, analysts and anyone reading growth and jobs figures side by side.
Quick answer
Okun’s law says g − g* = −β × Δu: if unemployment rises by 0.8 points and β is 2, growth is 2 × 0.8 = 1.6 points below trend. With actual growth of 1.8%, trend growth is 1.8% + 1.6 = 3.4%.
- Δu: the change in the unemployment rate, in percentage points.
- β (Okun coefficient): how many points of growth go with each point of unemployment, often about 2.
- Okun gap: actual growth minus trend growth, −β × Δu.
- Trend growth: the growth rate that keeps unemployment steady, g + β × Δu.
What Is Okun’s Law?
Okun’s law is a rule of thumb that ties unemployment to output. When an economy grows more slowly than its trend rate, firms need fewer workers and unemployment rises. When it grows faster than trend, unemployment falls. The law is named after the American economist Arthur Okun, who measured the link in United States data in 1962.
It is an observed pattern, not a law of nature. The size of the link is summed up in one number, the Okun coefficient, which differs between countries and changes over time.
Okun’s Law Formula
This calculator uses the growth-rate version of Okun’s law:
- g: the actual GDP growth rate, in percent.
- g*: the trend (potential) growth rate, in percent.
- β: the Okun coefficient.
- Δu: the change in the unemployment rate, in percentage points.
The two results come straight from it:
g* = g + β × Δu
The natural rate of unemployment is not part of these two formulas. The calculator adds the change to it to show the unemployment rate that results: u = u* + Δu.
How to Calculate Okun’s Law
Unemployment rises by 0.8 points from a natural rate of 5%, the Okun coefficient is 2 and GDP grows by 1.8%:
= −1.6%
g* = 1.8% + 2 × 0.8
= 3.4%
- Multiply the coefficient by the change. 2 × 0.8 = 1.6.
- Flip the sign for the Okun gap. Growth is 1.6 points below trend, so the gap is −1.6%.
- Add it to actual growth for the trend rate. 1.8 + 1.6 = 3.4%.
- Add the change to the natural rate. 5 + 0.8 = 5.8% unemployment.
Trend growth is 3.4%, the Okun gap is −1.6% and the unemployment rate is 5.8%.
Okun’s Law in One Picture
The line passes through zero: when unemployment does not change, growth is on trend. Its slope is −β.
| Change in unemployment | Okun gap (β = 2) |
|---|---|
| −1 point | 2% |
| 0 points | 0% |
| 0.5 points | −1% |
| 1 point | −2% |
| 2 points | −4% |
The Okun Coefficient
The coefficient β says how many percentage points of growth go with one point of unemployment. Okun’s own 1962 estimate for the United States was about 3. Many later estimates are closer to 2, which is the usual textbook value.
| Coefficient β | Gap when Δu = 1 point |
|---|---|
| 1.5 | −1.5% |
| 2 | −2% |
| 2.5 | −2.5% |
| 3 | −3% |
The coefficient is larger than 1 because a fall in output is not met by job cuts alone. Firms also cut hours, keep some staff they do not fully need, and some people stop looking for work and leave the labor force.
Okun’s Law Examples
A recovery. Unemployment falls by 0.5 points, so enter −0.5. With β = 2 and growth of 4%:
= 1%
g* = 4% + 2 × (−0.5)
= 3%
Growth is 1 point above its trend rate of 3%. From a natural rate of 5%, unemployment ends at 4.5%.
Okun’s original coefficient. Unemployment rises by 1 point, β = 3 and growth is 0.5%:
= −3%
g* = 0.5% + 3 × 1
= 3.5%
Steady unemployment. If the change is 0, the gap is 0% and trend growth equals actual growth, whatever the coefficient.
Predicting the Change in Unemployment
The same formula can be turned round to forecast unemployment from a growth figure:
If trend growth is 3%, actual growth is 1% and β is 2:
= 1 point
Unemployment is expected to rise by 1 point. If growth were 4% against a trend of 2.5%, the change would be (2.5 − 4) ÷ 2 = −0.75, a fall of 0.75 points.
Growth Version vs Gap Version
Okun’s law is written in two common ways.
- Growth-rate version: g − g* = −β × Δu. It compares growth with trend growth over a period and uses the change in unemployment. This calculator uses it.
- Gap version: (Y − Y*) ÷ Y* = −β × (u − u*). It compares the level of output with potential output and uses the distance of unemployment from its natural rate.
The two fit together. If you read Δu as the distance of unemployment above its natural rate, the Okun gap shown here is also the output gap of the gap version, as a percent of potential output.
Limits of Okun’s Law
- The coefficient is not fixed. It differs between countries and between booms and recessions.
- Trend growth is an estimate. It cannot be observed, and estimates are revised.
- Timing. Unemployment usually reacts to growth with a delay of a few quarters.
- Other forces. Changes in hours, productivity and labor force participation can break the link for a time.
- Direction of cause. The law describes how the two move together. It does not say which one drives the other.
The result is for education and rough estimates and is not a forecast.
Key Terms
- Okun’s law
- The observed link between unemployment and output growth.
- Okun coefficient
- Points of growth that go with one point of unemployment.
- Okun gap
- Actual growth minus trend growth.
- Trend growth
- The growth rate at which unemployment stays steady.
- Natural rate
- The unemployment rate when the economy is at potential output.
- Percentage point
- The plain difference between two percentages, such as 5% to 5.8%.
How to Use the Okun’s Law Calculator
- Enter the change in unemployment. Type the change in the unemployment rate in percentage points, such as 0.8. Use a minus sign if unemployment fell.
- Enter the natural rate and the coefficient. Type the natural rate of unemployment, such as 5, and the Okun coefficient, such as 2.
- Enter actual GDP growth. Type the actual GDP growth rate as a percentage, such as 1.8.
- Read and copy the result. The trend growth rate appears as you type, with the working, the Okun gap and the unemployment rate. Press Copy to copy it, or Clear or Esc to start again.
Example: unemployment down 0.5 points, a coefficient of 2 and growth of 4% give trend growth of 3% and an Okun gap of 1%.
Who Can Use This Calculator?
Frequently Asked Questions (FAQs)
What is Okun’s law?
It is a rule of thumb that links unemployment to output: when growth is below its trend rate, unemployment rises, and when growth is above trend, unemployment falls.
What is the Okun’s law formula?
In the growth-rate version, g − g* = −β × Δu, where g is actual GDP growth, g* is trend growth, β is the Okun coefficient and Δu is the change in the unemployment rate in percentage points.
How do you calculate the Okun gap?
Multiply the Okun coefficient by the change in unemployment and flip the sign. With β = 2 and unemployment up 0.8 points, the Okun gap is −1.6%.
How do you find trend growth with Okun’s law?
Add β × Δu to actual growth. With growth of 1.8%, β = 2 and Δu = 0.8, trend growth is 1.8 + 1.6 = 3.4%.
What is a typical Okun coefficient?
About 2 is the usual textbook value. Okun’s own 1962 estimate for the United States was about 3. The value differs by country and period.
What does a negative Okun gap mean?
It means the economy grew more slowly than its trend rate, which goes with rising unemployment. A positive gap means growth above trend and falling unemployment.
What if unemployment fell?
Enter the change as a negative number, such as −0.5. The Okun gap is then positive and trend growth is lower than actual growth.
How is the natural rate of unemployment used?
It does not change trend growth or the Okun gap. The calculator adds the change in unemployment to it to show the unemployment rate that results.
Is the Okun’s Law Calculator free?
Yes. It is free to use, with no sign-up and no limit on how many times you use it.
Sources
- Wikipedia. Okun’s law.
- WallStreetMojo. Okun’s Law.
- Econlib. Arthur M. Okun.
- Wikipedia. Arthur Melvin Okun.
- Wikipedia. Output gap.
- Wikipedia. Potential output.
- Wikipedia. Natural rate of unemployment.
Try our Okun’s Law Calculator to see what a change in unemployment says about growth.