The social-distancing recession

As you know, in the past two weeks ten million people signed up for unemployment. The typical number, before two weeks ago, was was less than a quarter-million per week. So, 10 million versus half a million. Wow... Egad! What's going to happen to the economy? How bad will the recession be?

I expect you've heard of Okun's law. Okun's law says you can tell what effect a change in unemployment will have on economic growth. So if unemployment increases by ten million people (or by 20 million, or however high it goes in the next few weeks) we can estimate how much GDP growth will slow down and how bad the recession will be. We'll look into that today.

I'll be using the "growth rate version" of Okun's law, from an old (2006) PDF from Miles Brian Cahill, at Researchgate. In the paper, Cahill looks at three time periods and figures Real GDP trend growth estimates for each:

• From 1949 to 1972: 4.09% growth
• From 1973 to 1996: 3.01% growth
• From 1997 to 2004: 3.40% growth

I will figure growth from 2010 to the last data before the big jumps in unemployment, and compare that to growth after the increase of ten million having gone unemployed.

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I started by figuring the same time periods as Cahill. My results are close to his:

• From 1949 to 1972: 4.16% growth
• From 1973 to 1996: 3.05% growth
• From 1997 to 2004: 3.45% growth

My results differ some from his. There have been revisions to the data since Cahill wrote his paper, and I think this explains the differences. My results are close enough to Cahill's that I am satisfied I got the arithmetic right. Here are my three graphs:

Graph #1

Graph #2

Graph #3

I kept the X- and Y-axis limits the same on these graphs so that the "window" is always the same size. What we see in that window changes from one graph to the next. On the third graph the cluster is much smaller than on the others. In part this is because there are only one-third as many dots on Graph #3. In part, the reduced variation is probably an effect of the "great moderation".

In the trend line equation on each graph, the number before the "x" is the "Okun's Law parameter", Cahill says. That number relates unemployment to GDP growth, and we can use it to estimate how bad our social-distancing recession might be. If the number is close to 2, it means that when the unemployment rate rises by one percentage point, GDP falls about two percentage points.

So far, all these "parameter" values are close to 2. Cahill's values are 2.2, 1.83, and 1.95. Mine are 2.15, 1.83, and 1.99. (Remember, though, that all these values are for the year 2004 or before. I'm checking my work before we compare the 2010-2019 economy to the Covid-19 economy.)

Something I didn't know: According to Cahill, the number after the "+" sign in the trend line equation gives the trend growth rate of GDP. That surprised me. But here again, the results I got are a good match to Cahill's. Because these and the parameter values all turned out close to Cahill's, I figure I got the math right.

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Another explanation of Okun's law, this from Investopedia:

Okun's law ... states that when unemployment falls by 1%, GNP rises by 3%.

When unemployment falls a certain amount, GDP rises a certain amount. That's cut and dry. They say 3%, not 2%; I'll get to that in a moment. Investopedia continues:

However, the law only holds true for the U.S. economy and only applies when the unemployment rate is between 3% and 7.5%.

That's an interesting constraint. We're looking at the US economy, and our unemployment rate has been between 3% and 7.5% since mid-2013. So I'll say the constraint is not a problem.

On the 2% versus 3% difference in the impact on GDP, Investopedia says:

In the United States, the Okun coefficient estimates that when unemployment falls by 1%, GNP will rise by 3% and GDP will rise by 2%. When unemployment rises by 1%, then GNP is expected to fall by 3% and GDP is expected to fall by 2%.

The 3% number applies to GNP, Gross National Product. Economists talked GNP back in the 1960s, when Okun came up with his law. Today, economists talk GDP, Gross Domestic Product. The change occurred in the 1990s. Cahill uses GDP in his paper. I'm using GDP in this post. The 2% number applies.

So we have an answer already. The unemployment rate in February was 3.5%. In March it went to 4.4%. The difference is almost one percent. Call it a 1% rise in unemployment. So we can expect GDP to fall by 2%. That's based on Cahill's parameter value of 2, which I duplicated, and which Investopedia confirms.

Let me put the 2% decline in context:

Graph #4: Real GDP Growth, and the HP Trend since 2002

 The red line shows a "smoothed" trend of the growth rates shown in blue. The trend line starts in 2002 just a little above the 2.0 level. It gradually falls closer to 2.0 by mid-graph. (It reaches 2.006 in 2011-2012.) And it increases ever so slightly, but visibly, in 2018 and 2019.

Call it a trend growth rate of 2%.

If we have a rise in unemployment of 1% from February to March, and if the parameter value 2 is accurate, we can expect the GDP growth rate to fall by two percentage points.

If we have an RGDP trend growth rate of 2%, as Graph #4 shows, and the growth rate slows by 2%, we end up with a growth rate of zero. By the way, this is the effect of only one month's change in unemployment. If unemployment continues to fall, we can expect RGDP growth to go below zero.

How long might it last? Not long, I think. As I said the other day, this recession is not the result of something wrong with the economy. It is the result of our response to the pandemic. A necessary response, I think. But when the pandemic eases and our response can relent, employment will rise again -- probably rapidly -- and GDP growth will rise also.

But I don't want to make guesses about what will happen with the unemployment rate. I want to look at the numbers we have on the unemployment rate, and see if I can estimate the effect of those numbers on economic growth. But first I want to check that last graph.

This next graph shows the same RGDP growth data as on #4. But this time, to figure the trend I only look at the years since 2010. The trend line here shows more increase than we saw on Graph #4:

Graph #5: Real GDP Growth, and the HP Trend since 2010

One of the funky things about the Hodrick-Prescott (HP) calculation is that adding a new value to the end of the series can cause the trend to change as much as 10 or 15 years back. I didn't change or add anything in the RGDP growth numbers shown by the blue line. The blue line is exactly the same on Graph #5 as it is on #4. But when I figured the red line on #5, I omitted the blue values from before 2010. And the red line changed as a result.

The start- and end-values for the HP line on Graph #5 are 2.04 (for 2010 Q1) and 2.51 (for 2019 Q4). Say 2.0% and 2.5%. The trend shows a gradual increase in the RGDP growth rate. So we should figure a trend rate of 2.5% for the early months of 2020 when our response to the pandemic started pushing the unemployment rate up and pulling economic growth down.

We had a 1% rise in unemployment between February and March of this year. If the Okun's law parameter is close to 2, then that one month's change in unemployment is enough that we can expect Real GDP growth to fall by two percentage points.

If recent trend growth is 2.5%, as on Graph #5, and the growth rate falls by two percentage points, we can expect economic growth to slow to around 0.5% as a result of March unemployment. Or, I should say it this way: We can expect economic growth to vary around the 0.5% level, rather than around the 2.5% level, as a result of the March unemployment.


But that is only true if the Okun's law parameter still has a value close to 2. I don't think it does. I think the parameter value is much lower now: Over the past several years unemployment fell several percentage points, but sluggish GDP growth suggests that the parameter value is low.

I'll be following up in a day or so with an estimate of what the parameter value may now be and how it may impact economic growth.

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Links:
Excel file for Graphs 1, 2, 3
Excel file for Graphs 4, 5
Note: These files contain VBA macros