Okun's Law Then and Now

I was curious to see if the relationship between unemployment and output has changed in recent years, so I took a very quick look at the issue through the lens of Okun's law (and used a simple textbook version of Okun's law as well). Recall that Okun's law is the negative relationship between unemployment and GDP. One way to look at this is to graph the growth of real GDP against changes in the unemployment rate. The data are quarterly, the sample period is 1948:Q2-2005:Q4,  and the changes are expressed in annual rates:

The equation for the fitted line is (GDP Growth) = 3.40 - 1.78ΔUN, not too far from the equation in, say, Mankiw's textbook where (GDP Growth) = 3 - 2ΔUN is used as a rough approximation (e.g. see page 35 in his 5th edition as well as the graph that is very similar to the one above).

The next step is to break the sample into two pieces. I chose 1982 as the break point. You will either like that or you won't, but it's what I chose for a first cut. The individual sub-sample graphs are similar to the total sample:

Here are the fitted lines for the two sub-samples:

And finally, here are the two estimated equations for the sub-samples:

(GDP Growth) = 3.73 - 1.87ΔUN for 1958:Q2-2005:Q4

(GDP Growth) = 2.99 - 1.49ΔUN for 1983:Q1-2005:Q4

The last set of results is close to (GDP Growth) = 3 - 1.5ΔUN if you like round numbers.

So what does this mean? Here are two observations:

• For the full sample, unemployment will be stable (ΔUN=0) when GDP growth is 3.4%. For the sub-samples, the figures are 3.73% for sample through 1982, and 2.99% for the sample after 1982. Thus, rate of output growth producing stable employment has fallen according to these estimates.

• For every percentage point unemployment increases in the early sample (i.e. an additional 1% increase over the last period), GDP growth falls by 1.87%. But in the later sample it falls less, by 1.49%.

I need to think through this more, but the decreased sensitivity of GDP growth to unemployment changes seems to be consistent with technological change allowing firms to replace people with machines more flexibly than in the earlier time period, with technological change allowing work to be digitized and performed elsewhere so that domestic unemployment can rise without output falling, and through the outsourcing of intermediate stages of production.

Comments

[baileyman]

Could statistical shenanigans with the unemployment rate create an interesting effect here? Would the conclusions be different looking at delta employment-population ratio rather than delta unemployment?

[Emmanuel]

Interesting theory...I'd second baileyman in thinking that looking at the changes in labor force participation against GDP would be interesting as well.

If globalization is indeed happening, we should see the slope flatten further going forward, no?

[bakho]

A change from 1.87% drop in production per 1% unemployment increase to 1.49% drop per 1% may mean that the employment that is being lost is of lower productivity than in the past. However, this is also true if low productivity jobs are being eliminated and replaced with higher productivity jobs.

I like your idea about intermediate production. For instance, to make a new car assume an automaker had paid100 employees in house $5000 to make a group of parts. Because of steel tariffs, the automaker discovers that they can buy the parts from country X for $4000. So the company lays off 100 employees, buys parts from country X and still sells the new car. We all know that there has been a huge shift in auto parts manufacture overseas

ON PAPER, the output is still the same car, although the parts are no longer produced. However, the labor of 100 employees has been replaced by purchased parts input. So you lose the parts production, which is labor intensive, but you keep the final car production which is less labor intensive. Overall, productivity is increased because the items with the high denominator are outsourced and the items with low denominator remain.

Computer parts are the same story.

In some industries, productivity increases can be huge. Steel that can be produced both in a mini-mill and one of the large dinosaur steel mills requires up to 7 times fewer workers per ton of steel in the mini-mill. Obviously, moving steel production to mini-mills is accompanied by huge productivity increases. The startup investment needed to build new facilities is the only brake on the process.

Shifts in production from lower productivity manufacturers to higher productivity manufacturers will affect the ratio.

Productivity is higher at Japanese auto plants than for domestic producers. So the announced drop in production of GM vehicles and increase in production by Toyota means that productivity will increase. Since none of the increased unemployment in this case will decrease total production, these numbers with the rest will lower the ratio of production loss to unemployment increase.

[spencer]

I suggest you try using the period of low productivity growth -- 1975 to 1995 --as one period and the time excluding this period as the other time to see what happens to the equation. Probably the easiest way to do this would be a dummy variable.

What changes the relationship is productivity, and since 1995 long term productivity growth has returned to the pre 1975 era growth rate. this implies the post 1995 trend should be similiar to the pre 1975 trend.

Bakko -- your comments about outsouring are correct if the parts are outsourced abroad, but not if they are just produced by a different firm in the same economy since productivity is measured for the entire economy, not the individual firm.

[spencer]

I've looked at productivity growth vs real gdp growth.
Ignoring the fact that gdp and ouput for the non farm business secto are not identical you see some interesting long term trend changes. From 1971 to 1974 productivity growth was 68% of real gdp growth.From 1975 to 1995 this ratio fell to 55% and since 1995 it rebounded to 82%. This implies that from 1971 to 1974 a one percentage point increase in rgdp generated a 0.3 increase in hours worked. From 1975 to 1995 it would be 0.45 but since 1995 it was only 0.2.

[bakho]

Spencer- you are correct that my comments on outsourcing only apply to outsourcing outside of the US. This is precisely what happened to steel parts and partly why Delphi is in so much trouble.

However, my other comment about GM and Toyota all refers to production within the American economy. So if GM drops production by 200,000 and Toyota increases production in Indiana by 200,000, the same number of cars are produced but with fewer workers because GM needs more worker hours to make a car than Toyota.

One of the features of the last recession was a lot of overcapacity. In general, less efficient facilities are shuttered and production shifted to the more efficient producers. Total output does not change, but workers are laid off because it takes fewer to do the same job. Basically, the unemployment denominator is increasing but there is no effect on the production numerator. Enough of these shifts with no loss in production will bring down the average production/unemployment ratio.

The question is why is that ratio lower today? Part of the answer is structural barriers to adding more efficient production units. A climate where overcapacity exists is prime for shuttering low productivity operations and running high productivity operations closer to capacity.

If there is NOT a wide gap between the least productive and most productive facilities, then the GDP to unemployment ratio should be larger than if there is a wide gap between least and most productive facilities. If there is a narrow gap, then it means that relatively high productivity facilities are closing or cutting back production. A wide gap allows low productivity facilities to take almost the entire hit, so the GDP to unemployment ratio will be lower.

BTW- the US has a LOT of low productivity manufacturing which is why so many manufacturing jobs have been lost.

[lowsmoke]

Before you get too excited about a small difference in regression coefficients, try testing to see if the difference is statistically significant. Without having access to the standard errors, I can't do the calculations, but my sense of the data is that it is highly unlikely that the coefficients were estimated precisely enought for the difference to be significant.

[Mark Thoma]

I should have added this. An F-test for the joint significance of an intercept and slope dummy (=1 after 1982) gives a p-value of 0.03621758. So, the two lines are different at the 5% level of significance.

I hadn't looked closely at the properties of the residuals (but DW is near 2 in test regression), so I didn't include the test statistic in the original post.

[lowsmoke]

It sounds like your F-test was for whether the two coefficients in a particular regression equation were significantly different from zero. But what I suggested was testing your assertion that the slope coefficients in the two regression equations differ from each other. My hunch is that the difference, 1.87 minus 1.49, is not statistically significant.

[Kash Mansori]

Mark: It might be worthwhile doing GDP growth in per capita terms. The earlier period may have a higher intercept simply because there was faster population growth during the 1950s and 60s.

[Mark Thoma]

Thanks Kash and lowsmoke, everyone elsee too - good suggestions. I will try to find time to improve the model and see how it does. One thing I want to try is to use the unemployment rate minus the natural rate [U(t)-U*(t)] rather than the change from the previous period [U(t)-U(t-1)].

While multicollinearity involving the dummies makes it hard to sort things out, I think the significance is mainly an intercept effect so changing to a per capita measure of output growth might be useful. I'm not sure how the slope measure would be impacted by using U*, though it ought to increase the variance of the RHS variable as it is the deviation from the unconditional rather than the conditional mean. If so, and if the extra varaition is associtated with movements in the per capita output measure, the significance level would be increased.

Anyway, thanks all...

[pgl]

Mark - your last comment was what I was about to say. U* has changed over time. And one of the earlier comments about U not capturing excess supply - as in the labor force participation rate debate - warms my heart. But wasn't Dr. Okun's first guess at the slope coefficient closer to three?

[Mark Thoma]

pgl - my memory is similar on the 3%. At some point, the law was changed...

[Lafayette]

Very nice, but ... conclusions, anybody?

What does it all mean in terms of advisable economic policy? Yes, growth is godliness, but beyond that ... ?

In simple terms, please, for us novitiates looking in.