Three kinds of unemployment coexist at every point in the cycle, and the policy response to each is different, which is the entire reason for splitting them.
Frictional, structural and cyclical unemployment
Frictional unemployment is the time it takes a worker and a job to find each other. Somebody quits, somebody graduates, somebody moves city. It is short, voluntary in character, and a sign of a functioning market: an economy with zero frictional unemployment would be one where nobody ever changed jobs. The policy response is information, meaning better matching, job portals and anything that shortens the search.
Structural unemployment is a mismatch between the skills or locations workers have and the ones employers want. A textile hub loses its industry; the workers are still there and the jobs are elsewhere, or need skills nobody has. It is long, it does not respond to demand stimulus, and it is the expensive kind. The policy response is retraining, relocation support and time.
Cyclical unemployment is the part attributable to a shortfall of aggregate demand: output below potential, so firms need fewer workers. It is the part that monetary and fiscal policy can actually address, and the part that disappears when the cycle turns.
The sum of frictional and structural unemployment is the natural rate, and an economy at its natural rate is at full employment, which is not zero unemployment and never has been. Cyclical unemployment is the observed rate minus the natural rate.
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What is Okun's law?
That identity is what makes Okun's relationship usable. Arthur Okun's 1962 finding was empirical rather than theoretical: the output gap moves with the unemployment gap in a stable, roughly linear way. In gap form,
(Y − Y*) / Y* = −c × (u − u*)
where Y* is potential output, u* is the natural rate, and c is an estimated coefficient historically near 2 for the United States. In difference form, the change in unemployment is roughly −β × (g − g*), where g is real output growth and g* is trend growth.
Both forms run in both directions. From an unemployment rate and a natural rate you get an output gap and an estimate of lost output. From a target unemployment rate you get the growth needed to reach it, which is how a forecast is checked for internal consistency.
What are the limits of Okun's law?
Two limits, both quantitative. The coefficient is not a constant: it differs across countries, and it drifts within a country as labour-market institutions change. Worked Example 4 shows that moving c from 1.6 to 2.4 on the same unemployment gap changes the estimate of lost output by $355.68 billion, which is the model risk in one parameter.
The relationship is also weak wherever the labour market absorbs shocks as underemployment rather than as unemployment, which is most of the developing world. An economy where a demand shock shows up as a farm absorbing three more family workers will not produce a clean Okun coefficient.