Okun's law asserts a relation between the rate of unemployment and the rate of economic growth. The higher the unemployment, the lower the growth; and the lower the unemployment, the higher the growth. Makes sense. But Okun's law is stronger than I let on: It associates a one-point change in unemployment with a two-point change in output. That's pretty specific.

A recent guest post at Econbrowser reported the testing of Okun's Law, and found that the two-to-one relation holds good. In The Myth of 'Jobless Recoveries', Laurence Ball, Daniel Leigh and Prakash Loungani write: "Fifty years after Okun’s paper, we find that this relationship fits very well, including during the Great Recession." Okun's Law, they report, is "strong and stable". They offer this graph:

Graph #1: Ball, Leigh and Loungani's Chart 2. Actual and Fitted Unemployment Rate, US, 1948Q2-2011Q4. |

There are two lines on the graph. One of the lines is the actual unemployment rate. The other is an estimate of the unemployment rate which they got by following Okun's law backward from output. The two lines are so close together they look like one line. Ball, Leigh and Loungani offer this as evidence Okun's law is strong and stable.

Ball, Leigh and Loungani say that their chart "shows the tight fit between actual unemployment and the estimate based on Okun’s Law." Statements like that catch my eye. I like to see if I can duplicate the results. Duplication tests both the selection of data and the calculation of values. It helps me understand the calc.

The "actual" unemployment rate is a time series I can find at FRED. That part is straightforward. What I have to work out is "the estimate based on Okun’s Law." Ball, Leigh and Loungani state the law clearly:

The textbook version states when U.S. output dips one percent below its potential, unemployment rises above its natural rate by about half a percentage point.

In other words,

Formula 1. |

But they say their graph shows "actual" unemployment (the UNRATE, I presume) and the "fitted unemployment rate from Okun specification". Plus, their graph looks like the UNRATE graph, with the high peak around 11 and the last peak around 10.

To get "actual" by itself, I added the Natural Rate of Unemployment to both sides:

Formula 2. |

I plotted that at FRED:

Graph #2:Actual Unemployment (blue) and the "Fitted" Number (red) |

Pretty good match. I don't like it though, because to make it match I had to use two vertical axes with different scales. Maybe that's because of the "two-to-one" thing, which I didn't consider in this graph. Couldn't figure out how to get FRED to do that. (The output values are log values. At FRED I took log values as the last step. So there was no extra step where I could multiply or divide by two.)

(Oops. I left the "times 2" out of my formulas, too.)

I thought it might work better if I left NROU with UNRATE, as in the first formula above. Went back to FRED and came up with this:

Graph #3: The Employment Gap (blue) and the Output Gap (red) Click Graph for FRED Source Page |

For the blue line I started with the actual rate of unemployment and subtracted the natural rate of unemployment. (Thus, where actual unemployment is above the natural rate, the blue line is above zero. Where actual is below the natural rate, the blue line is below zero.)

Because both unemployment series are given in percent values where 5% is presented as 5.0 rather than 0.05, I divided the result of subtraction by 100 to get the decimal value.

Finally, I multiplied by 2 because Okun's law says there is a two-to-one relation between unemployment and output.

For the red line I took potential output and divided it by "real" GDP. (Thus, where real output is below potential, the red line is high. Where real output is above potential, the red line is low.) Then I applied FRED's "natural log" transformation.

You see the result. The two lines are a good match to each other, and the graph is similar to the "Chart 2" graph. My numbers are lower, because I'm subtracting the natural rate from the actual rate. But

*both*sets of numbers are lower on this graph, and the two sets still match up well.

Is the similarity "evidence" that Okun's Law holds good? Come back tomorrow...

## 4 comments:

I guess that the thing that makes me suspicious about this is the "potential GDP". That just sounds weaselly -- What does that even mean? Is it some calculated value that is partially derived from the unemployment rate? If so then it could be that it's factoring the unrate into the graph.

With that said, it seems reasonable (maybe even obvious) to me that growth and unemployment should be (anti)correlated like that since they are both sort of measures of the health of the economy. So they should move one way when the economy is healthy and the opposite way when it's unhealthy.

The NROU is supposed to correspond to a certain (desirable) level of inflation. What then is the natural rate of inflation for full-employment - can you figure that one out? I think NROU would have to be 0, correct?

Ha Ha Jerry, your comment was in the spam buffer!!!

Yes, PGDP is partially derived from the unemployment rate. Yes it is factoring into the graph. Spoiler alert. "Come back tomorrow..."

Luke, it seems for NROU they pick a number they think will keep inflation (not prices, sadly) stable. And that NROU number, they say is "full employment".

Back in the 1960s, they picked 4% for full employment (but I don't know how they got that number).

For NROU, CBO uses NAIRU which they figure from the Phillips curve. Quite interesting, I have not worked it all out yet, but what a tangled web!

Now that is interesting, thanks Art.

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