Unexpectedly Intriguing!
October 6, 2010

If the economy is growing at an annualized rate of 2.5% after adjusting for inflation, how much should we expect the unemployment rate to change? What if the economy grows by 5.5%? Or shrinks with a negative rate of growth of -1.5%? Better still, at what rate does the economy need to grow for enough jobs to be created to make the unemployment rate fall?

Shilling - Yr/Yr Change in Unemployment Rate as a Function of The Yr/Yr Change in Real GDP (1Q 1949 - 2Q 2010) We realized that we might be able to answer questions like these after reading John Mauldin's weekly column The Morality of Chinese Growth, which featured a chart created by Gary Shilling showing the year over year percentage change in the percentage unemployment rate as recorded by the Census Bureau's/BLS' Current Population Survey against the year-over-year percentage change in real GDP, spanning quarterly data for both from the first quarter of 1949 through the second quarter of 2010.

Looking at the data and corresponding trend line, we see that when economic growth has been low or negative, the percentage change in the unemployment rate is positive, meaning that the unemployment rate increased when measured year over year. And that's what we would expect. When the year over year GDP growth rate is solidly positive, we see that that the year over year change in the unemployment rate is negative, indicating that the unemployment rate fell with a strongly growing economy, which is also what we would expect.

The only thing that's a problem is the trend line equation, which seems to fit the data, but which really doesn't make economic sense because it's a quadratic equation. That's a problem because if we were to extend the curve to the right, we would see it begin to rise, before crossing back to indicate that we should expect the unemployment rate to rise, even if the economy were booming.

Replacing y with 0 in the trend line equation and entering it into Wolfram Alpha, we find that Shilling's trend line predicts that the unemployment rate would begin rising if economic growth ever exceeds 18.5%. And that the faster it grows above that point, the higher the unemployment rate would rise!

Yr/Yr Change in Unemployment Rate as a Function of The Yr/Yr Change in Real GDP (1Q 1949 - 2Q 2010) That just doesn't make any sense! So, we went out and got the original source data and generated a new trend line for it using ZunZun's 2-D function finding tool. Here's the option we selected, based upon its combination of mathematical simplicity (the variable x only appears once in the formula produced through ZunZun's regression analysis) and accuracy (the root mean square error of the data with respect to the curve is fairly low.)

Here, we find that instead of a parabola, the resulting trend line resembles a backwards S as it steers though the middle of all the data points. Better, instead of seeing the unemployment rate begin to rise with hugely positive rates of economic growth, it instead suggests that unemployment rates would continue to fall, which is what common sense tells us we should expect.

GDP and Unemployment Rate Data
Input Data Values
Today's Year-Over-Year GDP Growth Rate [%]
One-Year Ago's Quarterly Unemployment Rate [%]

Change in Unemployment Rate
Calculated Results Values
Year over Year Change in Unemployment Rate [%]
Expected Level of Today's Unemployment Rate [%]

And where we have a relationship like this, we can make a tool that you can use to run your own numbers! What's more, we've created a field just for the year-ago quarter's average unemployment rate so you can translate the equation's results into an actual unemployment rate!

And now we can answer all the questions we asked at the beginning of this post! For a one-year ago quarterly unemployment rate of 9.5%, if we have real year-over-year GDP growth of 2.5%, we'll see the unemployment rate climb to 10% (as the percentage change of the percentage unemployment rate is 4.7%).

If we were to see 5.5% real GDP growth, the rate of unemployment would fall from 9.5% to 8.2%, a percentage change in the unemployment rate of -13.3%. And if GDP turned negative to a real growth rate of -1.5%, we would see the unemployment rate rise to 14.3%, a year-over-year percentage increase of 50.7%.

Finally, we find we average dividing line between positive and negative changes in the unemployment rate occurs with a real GDP growth rate of 3.1%. That means in order to make the unemployment rate fall, at least on average, the real rate of GDP growth in the U.S. must be greater than 3.1%.

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