How to Calculate Okun's Law
Okun's law: output gap (%) = −β × (u − u*). With a textbook β of 2, each point of unemployment above the natural rate means GDP about 2% below potential.
The Okun's Law formula
Calculator
Enter an output gap, an Okun coefficient and the natural rate to estimate cyclical and total unemployment.
Negative when real GDP is below potential.
An empirical estimate that varies by country and period; 2 is a common textbook value.
u − u* = −(output gap) ÷ β.
- Implied unemployment rate
- 6%
The natural rate plus cyclical unemployment.
How to calculate Okun's Law, step by step
- 1Pick the Okun coefficient. Use the β the question gives. If none is given, use 2 and say that you assumed it.
- 2From output to unemployment, divide. Cyclical unemployment = −(output gap %) ÷ β. A negative output gap gives positive cyclical unemployment.
- 3Add the natural rate if asked. The implied unemployment rate is the natural rate plus cyclical unemployment.
- 4From unemployment to output, multiply. Subtract the natural rate from the actual rate to get u − u*, then output gap (%) = −β × (u − u*).
- 5Convert to dollars if needed. Multiply the percentage gap by potential GDP to get the output shortfall or excess in dollars.
Worked example: Okun's Law
Forward: the output gap is −3% and β = 2. Cyclical unemployment = −(−3) ÷ 2 = 3 ÷ 2 = 1.5 percentage points. With a natural rate of 4.5%, the implied unemployment rate is 4.5 + 1.5 = 6.0%. Reverse: unemployment is 7.2% and the natural rate is 4.7%, so cyclical unemployment = 7.2 − 4.7 = 2.5 points. The output gap = −2 × 2.5 = −5%. If potential GDP is $25 trillion, the shortfall is 0.05 × 25 = $1.25 trillion, so actual real GDP is about 25 − 1.25 = $23.75 trillion. Check by going forward again: −(−5) ÷ 2 = 2.5 points, the cyclical unemployment you started from.
The gap version and the growth version
Okun's law comes in two forms, and questions do not always say which one they mean.
The gap version, used above, compares levels: how far output sits below potential and how far unemployment sits above its natural rate. It fits AD-AS questions about recessionary and inflationary gaps.
The growth version compares changes over a year: %ΔY ≈ g − β × Δu, where g is the growth rate of potential output and Δu is the change in the unemployment rate. With g = 3% and β = 2, a year in which unemployment rises by 1 point implies real GDP growth of about 3 − 2 × 1 = 1%. A year with unemployment flat implies growth near 3%, because output has to grow at its trend rate just to keep unemployment from rising.
Rearranged, Δu ≈ −(%ΔY − g) ÷ β. Growth of 1% against a 3% trend gives Δu ≈ −(1 − 3) ÷ 2 = +1 point. The coefficient in the growth version is estimated separately and need not equal the one in the gap version, so use whichever value the question supplies.
Why the coefficient is bigger than 1
A 1-percentage-point rise in unemployment goes with a fall in output of more than 1% because a downturn cuts more than the number of people employed. Employers shorten hours, some people stop looking for work and drop out of the labor force without being counted as unemployed, and output per worker usually dips as firms keep staff they are not fully using. Each of those trims output without raising the unemployment rate, so output moves by a multiple of unemployment.
That is also why the coefficient is an estimate rather than a fixed law. Labor market rules, how readily firms lay off workers, and the mix of industries all change the ratio, so it differs between countries and drifts over time. Treat any Okun's law answer as an approximation and say which β you used.
Okun's Law questions
What coefficient should I use for Okun's law?
Use the one the question gives. Without one, β = 2 is a common textbook choice, but it is an empirical estimate that varies by country and time period, so state the value you assumed.
Why is there a minus sign in Okun's law?
Output and unemployment move in opposite directions. When unemployment is above the natural rate, output is below potential, so a positive u − u* gives a negative output gap.
Can Okun's law give a positive output gap?
Yes. If unemployment is below the natural rate, cyclical unemployment is negative and the formula returns a positive gap, an inflationary gap. With β = 2, unemployment 0.5 points below the natural rate implies output about 1% above potential.
How does Okun's law relate to the output gap formula?
The output gap formula, (actual − potential) ÷ potential × 100, measures the gap from GDP data. Okun's law estimates the same gap from unemployment data instead, or turns a known gap into an unemployment estimate.
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