Okun's Law Explained: Unemployment, the Output Gap and a Worked Example

Okun's law is the rule of thumb that ties unemployment to output: when the unemployment rate rises above its natural rate, real GDP falls below potential output by a multiple of that excess. The common textbook form is output gap (%) = -c x (u - u*), where u is the actual unemployment rate, u* is the natural rate of unemployment, and c is the Okun coefficient, which classes usually set at about 2.

So with c = 2, every percentage point of unemployment above the natural rate goes with real GDP sitting roughly 2 percent below what the economy could sustainably produce.

What Okun's law says

The law is named after the economist Arthur Okun, who noticed that unemployment and output moved together in US data in a fairly stable ratio. It is an observed pattern, not a theorem derived from first principles. That matters for how you use it: it is a translation tool between the labor market and the output market, and the number in the middle is an estimate.

The gap form

The version most macro courses teach compares two gaps.

Output gap (%) = (Actual real GDP - Potential real GDP) / Potential real GDP x 100

Unemployment gap = Actual unemployment rate - Natural rate of unemployment

The unemployment gap is just cyclical unemployment, the part of joblessness caused by weak spending rather than by job searching or skill mismatch. Okun's law connects the two:

Output gap (%) = -c x (u - u*)

The minus sign does the important work. When unemployment is above the natural rate (a positive unemployment gap), the output gap is negative: the economy is producing less than it could. When unemployment is below the natural rate, the output gap is positive: the economy is running hot, above its sustainable level. You can compute either gap on its own with the output gap calculator and the natural rate of unemployment calculator.

The change form

Some textbooks state Okun's law in changes instead of levels. In that version, real GDP growth above the economy's normal growth rate pulls unemployment down, and growth below the normal rate pushes it up:

Change in unemployment rate = -b x (Real GDP growth - Normal growth rate)

The logic is the same. The labor force and productivity both grow over time, so output has to grow at its normal pace just to keep the unemployment rate steady. Growth slower than that leaves workers without jobs. Here b is the change-form coefficient. It is estimated separately from the gap-form coefficient c, so the two numbers need not match in real data. On an exam, use whichever version and coefficient the question gives you.

Why the coefficient is bigger than 1

A natural first guess is that 1 percent more unemployment should mean 1 percent less output. Output actually falls further, for three reasons.

1. Hours fall too. Firms cut overtime and shift workers to part time before they lay anyone off, so labor input drops by more than the headcount of unemployed people.

2. Participation falls. Some people who lose jobs stop searching and leave the labor force. They are no longer counted as unemployed, so the unemployment rate understates the lost labor.

3. Productivity dips. Firms hold on to trained staff during a slump rather than fire them and rehire later. Those workers are employed but not fully used, so output per worker sags.

Stack those effects and each point of measured cyclical unemployment stands in for a larger loss of production. The Okun's law glossary entry has a short version of this argument.

Worked example: from unemployment to lost output and back

Use these assumptions throughout: potential real GDP is $20,000 billion, the natural rate of unemployment is 4.5 percent, and the Okun coefficient is c = 2.

Part 1: unemployment rises to 7 percent

Step 1. Find cyclical unemployment. 7 - 4.5 = 2.5 percentage points.

Step 2. Apply Okun's law. Output gap = -2 x 2.5 = -5 percent.

Step 3. Convert the gap into a level of real GDP. Actual real GDP = 20,000 x (1 - 0.05) = 20,000 x 0.95 = $19,000 billion.

Step 4. Find the lost output. 20,000 - 19,000 = $1,000 billion of goods and services the economy could have produced but did not.

Check. Run the output gap formula on the answer: (19,000 - 20,000) / 20,000 x 100 = -1,000 / 20,000 x 100 = -5 percent. That matches Step 2. Dividing -5 by -2 gives back 2.5 points of cyclical unemployment, which matches Step 1.

Part 2: the economy overheats

Now suppose real GDP is 1.5 percent above potential. What unemployment rate does Okun's law imply?

Step 1. Rearrange. u - u* = output gap / (-c) = 1.5 / (-2) = -0.75 percentage points.

Step 2. Add the natural rate. u = 4.5 + (-0.75) = 3.75 percent.

Check. -2 x (3.75 - 4.5) = -2 x (-0.75) = +1.5 percent. A positive output gap goes with unemployment below the natural rate, which is the inflationary gap case.

Part 3: the change form

Assume, for this part only, that the normal growth rate is 3 percent and the change-form coefficient is b = 0.5 (equivalently 1/2). Real GDP grows just 1 percent this year, and unemployment started at 5 percent.

Step 1. Find the growth shortfall. 1 - 3 = -2 percentage points.

Step 2. Apply the change form. Change in unemployment = -0.5 x (-2) = +1 percentage point.

Step 3. New unemployment rate. 5 + 1 = 6 percent.

Check. Work backwards: a 1 point rise in unemployment divided by b = 0.5 means growth ran 2 points below normal, and 3 - 2 = 1 percent growth, which is the growth rate we started with.

Quick reference table

With a natural rate of 4.5 percent and c = 2:

Notice that the zero row is not zero unemployment. It is unemployment equal to the natural rate.

Okun's law and the natural rate of unemployment

Okun's law only works if you measure unemployment against the right baseline. That baseline is the natural rate of unemployment, the sum of frictional and structural unemployment, which is the rate the economy settles at when output equals potential. The guide to the types of unemployment separates the three kinds in detail.

Frictional and structural unemployment do not show up in Okun's law at all. A worker between jobs or retraining for a new industry is unemployed in any economy, including one at full capacity. Only cyclical unemployment, the part that comes and goes with spending, maps onto lost output. This is why "full employment" in macroeconomics means unemployment at the natural rate, not unemployment at zero, and why the output gap is zero at the natural rate.

Okun's law and the Phillips curve

Okun's law and the Phillips curve are often taught side by side because they share a variable. Okun's law links unemployment to output. The short-run Phillips curve links unemployment to inflation. Put them together and you get a chain:

Output gap -> cyclical unemployment -> inflation pressure

A negative output gap means unemployment above the natural rate, which puts the economy low and to the right on the short-run Phillips curve, where inflation tends to slow. A positive output gap means unemployment below the natural rate, which puts the economy up and to the left, where inflation tends to rise. At the natural rate, the output gap is zero and the economy sits on the long-run Phillips curve, which is vertical at that rate in the same way long-run aggregate supply is vertical at potential output. The comparison page Okun's law vs the Phillips curve walks through the two-step chain with its own numbers.

The chain also explains why bringing inflation down is costly. If a central bank tightens policy and pushes unemployment 1 point above the natural rate for a period, Okun's law says output runs about 2 percent below potential over that period (with c = 2). That lost output is the real cost of disinflation. You can trace the tradeoff between unemployment and inflation in the Phillips curve sandbox.

See it move

Make it move

The short-run and long-run Phillips curves meeting at long-run equilibrium. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Where Okun's law fits in the business cycle

During a contraction, output falls below its trend and cyclical unemployment rises, which is Okun's law seen over time. During an expansion, the gap closes and unemployment falls back toward the natural rate. The business cycle guide covers the phases and how the output gap separates the cycle from long-run growth. Long-run growth itself, the steady rise in potential output, is a separate question covered in economic growth explained. Okun's law says nothing about how fast potential output grows.

Limits of Okun's law

The coefficient is an estimate, and it moves. The value near 2 is a teaching convention. Estimates differ across countries and across periods, because they depend on how freely firms adjust hours, how strict employment protection is, and how quickly discouraged workers leave the labor force. Where firing is costly, unemployment tends to move less for a given change in output, which shows up as a larger coefficient.

Both baselines are unobserved. Neither potential GDP nor the natural rate of unemployment can be measured directly. Both are estimated, and the estimates get revised, which means the gaps you feed into Okun's law carry error before the coefficient is even applied.

The relationship can shift over the cycle. Recoveries sometimes bring output growth with only slow falls in unemployment, as firms rehire cautiously or raise productivity instead. A single fixed coefficient cannot capture that.

It is a correlation, not a cause. Okun's law does not say unemployment causes lower output or the reverse. Both usually respond to the same shift in spending. A supply shock that moves the natural rate or potential output does not break the law itself, but the gaps must then be measured against the new baselines. Measured against the old ones, the usual pairing appears to fail.

It cannot forecast on its own. Knowing the coefficient tells you how two gaps line up. It does not tell you when a recession will start or how deep it will go.

Common mistakes

• Using the total unemployment rate. Multiply only the cyclical part by the coefficient. An economy at 4.5 percent unemployment with a 4.5 percent natural rate has no output gap.
• Running the coefficient backwards. Unemployment gap times c gives the output gap. Output gap divided by c gives the unemployment gap.
• Dropping the minus sign. Unemployment above the natural rate goes with output below potential. If both gaps come out with the same sign, recheck.
• Mixing the two forms. The gap form uses levels relative to potential. The change form uses growth relative to the normal growth rate. Do not plug a growth rate into the gap form.
• Treating 2 as a fixed constant. Use the coefficient the question gives. If none is given, say you are assuming a value near 2.

Practice

Try one: potential real GDP is $12,000 billion, the natural rate is 5 percent, actual unemployment is 6.5 percent, and c = 2. Cyclical unemployment is 1.5 points, the output gap is -3 percent, and actual real GDP is 12,000 x 0.97 = $11,640 billion. Then check the unemployment side of the problem in the unemployment and inflation module.