by Calculated Risk on 12/06/2009 04:52:00 PM

Based on the recent trend in the employment report, the U.S. economy might start adding net payroll jobs soon. This post looks at payroll employment vs. the change in real GDP, and estimates the unemployment rate in 12 months for several growth scenarios.

Credit: This idea is from a recent research note by Jan Hatzius.

Note: This is similar to Okun's relationship between GDP and unemployment.

Click on graph for larger image.

The first graph shows the four quarter change in real GDP and the four quarter change in employment, as a percent of payroll employment (to normalize for changes in payroll over time).

The second graph shows the same data in a scatter graph.

There is a clear relationship - the higher the change in the real GDP, the larger the increase in payroll employment.

This shows that real GDP has to grow at a sustained rate of about 1% just to keep the net change in payroll jobs at zero.

A 3% increase in real GDP (over a year) would lead to about a 1.5% increase in payroll employment. With approximately 131 million payroll jobs, a 1.5% increase in payroll employment would be just under 2 million jobs over the next year - and the unemployment rate would probably remain close to 10%.

The following table summarizes several growth scenarios. The unemployment rate is from the household survey and depends on the number of people in the work force - so it cannot be calculated directly. The table uses a range of unemployment rates based on 1.6 to 2.1 million people entering the workforce over the next 12 months (a combination of population growth and discouraged workers reentering the work force).

Real GDP Growth	Percent Payroll Growth	Annual Payroll Growth (000s)	Monthly Payroll Growth (000s)	Approximate Unemployment Rate in One Year
6.0%	3.5%	4,563	380	8.0% to 8.3%
5.0%	2.8%	3,684	307	8.6% to 8.9%
4.0%	2.1%	2,806	234	9.1% to 9.4%
3.0%	1.5%	1,928	161	9.7% to 10.0%
2.0%	0.8%	1,049	87	10.3% to 10.6%
1.0%	0.1%	171	14	10.8% to 11.1%

I expect a sluggish recovery in 2010, and I think the unemployment rate will stay near 10% for the next year. Those expecting a sharp drop in the unemployment rate are clearly expecting real GDP growth of 5% or more.

Obviously higher growth rates would mean an even quicker decline in the unemployment rate, and a decline in real GDP would mean much higher unemployment rates.