# The Implications of the First Derivative for Unemployment

In short: seven long years. A few months, when everyone was getting all het up about the observation that the rate of increase in the unemployment rate (the second derivative) was decreasing–that is, more and more people were losing jobs, but more and more wasn’t growing as fast as it once was, that struck me as pretty thin gruel. Well, the implications of the first derivative–the change in unemployment–are pretty grim too. Mark Thoma:

How long will it take the unemployment rate to go back down to 5 percent? A rough estimate can be obtained by looking at the rate of decline in the unemployment rate after recent recessions…

Implication: Taking the fastest rate of decline in each case, i.e. .077 percent, .054 percent, and .052 percent, the average rate of decline in the unemployment rate over the last three recessions was .061 percent

Using this figure, and starting from an unemployment rate of 10 percent — the rate that exists today — how long would it take for the unemployment rate to get to 5 percent?

Answer: (10-5)/.061 = 81.8 months, or almost 7 years. (Getting to 6 percent would take 65.5 months, or just short of five-and-a-half years.)

Keep in mind that a five percent decrease in unemployment, once you factor an increasing population, requires around 250,000 net jobs gained every month for seven years. Without a major restructuring of the economy such that capital gains much more velocity (e.g., decreasing the prices of unproductive assets such as housing, and increasing effective wages for the middle and bottom third), I don’t see how we gain a quarter of a million jobs every month.

While I’m on this topic, this is why I can’t stand the phrase ‘stimulus’: we do not need a quick pick-me-up. There’s nothing wrong with productive infrastructure expenditures that take a little while to come online–the need for jobs will still be there for years.

An aside: The most rapid decrease Thoma discusses occurred when the U.S. was a creditor, not debtor, nation, and also had net exports. Using values closer to 0.5 seem much more realistic, barring some radical change in the U.S. economy.

1. #1 Min
December 15, 2009

“While I’m on this topic, this is why I can’t stand the phrase ‘stimulus’: we do not need a quick pick-me-up. There’s nothing wrong with productive infrastructure expenditures that take a little while to come online–the need for jobs will still be there for years.”

Good point! But the Dems need jobs to pick up next year to hold on to Congress. Not that they seem to think so.

“An aside: The most rapid decrease Thoma discusses occurred when the U.S. was a creditor, not debtor, nation, and also had net exports. Using values closer to 0.5 seem much more realistic, barring some radical change in the U.S. economy.”

Another good point! As a footnote, the U. S. went from the world’s largest creditor nation to the world’s largest debtor nation under Reagan.

2. #2 MattXIV
December 15, 2009

The question here is how return to “normal” unemployment occurs. Thoma assumes it’s a linear process, but there’s no particular reason to believe this. Indeed, the fact that higher peak unemployment correlates with faster decline in Thoma’s 3 examples suggests the relationship is specifically non-linear. Nor does the historical record agree with a linear process – in the case of the ’81-82 recession, unemployment dropped rapidly from it’s peak, reaching 7% in about a year and there seems to be an inflection point in ’85 or ’86. ’90-’91 can be seen having a similar pattern but not as pronounced as the previous one. ’00 looks plausibly linear but it also doesn’t look like it fully converged. I don’t see how you can look at that figure and arrive at linear decay at a fixed rate as a model for convergence with full employment. Sometimes it’s just best to admit that you can’t make a quantitative prediction.

3. #3 Pete Murphy
December 16, 2009

Unemployment, both in the U.S. and the world as a whole, marches ever higher because the field of economics doesn’t account for the relationship between population density and per capita consumption.

Following the beating the field of economics took over the seeming failure of Malthus’ theory, economists adamantly refuse to ever again consider the effects of population growth. If they did, they might come to understand that once an optimum population density is breached, further over-crowding begins to erode per capita consumption and, consequently, per capita employment.

And these effects of an excessive population density are actually imported when a nation like the U.S. attempts to trade freely with other nations much more densely populated – nations like China, Japan, Germany, Korea and a host of others. The result is an automatic trade deficit and loss of jobs – tantamount to economic suicide.

Using 2006 data, an in-depth analysis reveals that, of our top twenty per capita trade deficits in manufactured goods (the trade deficit divided by the population of the country in question), eighteen are with nations much more densely populated than our own. Even more revealing, if the nations of the world are divided equally around the median population density, the U.S. had a trade surplus in manufactured goods of \$17 billion with the half of nations below the median population density. With the half above the median, we had a \$480 billion deficit!

If you‘re interested in learning more about this important new economic theory, then I invite you to visit my web site at http://PeteMurphy.wordpress.com.

Pete Murphy
Author, “Five Short Blasts”

4. #4 Alex
December 18, 2009

Reminds me of what Hugo Rossi once said:

“In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection.”