It's a safe bet that changes in economic output have an impact on jobs, but how do economists figure out how one affects the other with any precision? Suppose we want to know how a one percentage point decline in GDP will affect the unemployment rate. Or suppose we want to know the reverse, how a change in unemployment translates into a change in output.
To answer these questions, economists use a relationship known as Okun's law, named after Arthur M. Okun who discovered it in 1962. It states that for each percentage point that output is below or above the full employment level, unemployment rises a half a percentage point. Stated another way, a one percentage point increase in unemployment translates into a two percentage point fall in output. More formally:
U - U* = -0.5(lnY - lnY*)
Where a * indicates the full employment level of output or unemployment, ln indicates the natural log and lnY - lnY* is the percentage deviation of output from its full employment level.
As an example of how to use Okun's law, suppose the government is about to implement a stimulus package, and we expect it to increase output by four percentage points over the baseline, which is the no stimulus level of output. Then, we would also expect unemployment to fall by two percentage points.
Here is a plot of Okun's law:
The chart shows the percentage change in output (horizontal axis) against the percentage change in unemployment (vertical axis) from 1960-2013 (quarterly data), with a line showing a slope of 0.5 added to illustrate the law. The fit is good, but not perfect, and hence the "law" should be treated as a rough approximation of the relationship between unemployment and output.