Inflection Point ?

Unemployment is a lagging indicator.

This well-known and most basic of economic investment facts seems unknown to those on the anti-American right who are hoping for an economic disaster - hoping that the Bush-Obama effort fails to cut short the economic depression we are in - and are looking for a dark cloud (two examples) rather than green shoots [*] without offering anything other than the discredited Herbert Hoover alternative.

Unemployment does not peak and begin to fall until long after a recession, which is measured by GDP, is over. Similarly, unemployment did not start to rise in any significant way until well after this Great Recession got started about a year ago.

Last week's announcement of the latest weekly jobless claims data show continued evidence of a possible inflection point (details below the fold) in unemployment as well as the data that tell us exactly why the latest graph talked about by the bloggers above, and even on "Meet The Press" today, is utter nonsense.

Let's look at that graph to see what an inflection point is, and put our focus on the "initial value" point that represents the state of the economy before the new administration could pass, let alone implement, the stimulus plan in question. Click on the graph to see it with full resolution:


The blue curves are a report prepared by two members of the Obama transition team a few weeks before taking office. The large red dots show the quarterly average value of the seasonally adjusted unemployment rate based on phone surveys. The quarterly averages were used to construct the solid blue curve prior to Q1 2009. I also show, as smaller red dots, the monthly values. (When a monthly value falls on top of an average, I put a tiny pink dot over the red one, visible only in the full size image.) The green and pink lines are explained below in the "predictions" section.

UPDATED:
I have corrected a minor error in the green line (it should have been a bit steeper) when adding the June unemployment data to the graph. The new version, which was posted on July 2, should be used rather than this one if someone wants to use this graph or modify it further. The new graph also has an appropriate attribution on it.

It is EXTREMELY important that the Q1 2009 value of 8.07% is well above the guess of about 7.54% used in the transition team analysis, a point I highlight with a blue dot. I trust you can see that the guess they based their analysis on was really wrong, and that there is no quantitative value to the resulting predictions shown in blue. In fact, there never was any real value to those predictions.

At best, one might argue that they were only predicting that the recovery act would reduce the unemployment peak by about 1%, and do so about a year earlier than without it. At worst, one might argue that they were assuming the recovery had already started and were unaware that we are trying to fight off a depression. In between would be the position that they were hiding the true situation in an attempt to "jawbone" the economy, to avoid the sort of panic that played a major role in the development of the Great Depression.

THE DATA

It is important to realize that the unemployment data are the result of a phone survey. I was actually part of that process sometime back in the 1990s. Individuals are selected at random to join the survey population, contacted on a regular basis by phone to discern their employment status over a period of many months, and then replaced by someone new. Like any survey, those data are uncertain and fluctuate. Quarterly averages help smooth out those fluctuations.

Some data, such as weekly jobless claims, are collected from state unemployment offices and reflect a reasonably true count of what happened that week. However, in order to rush them out ASAP, the first number released is only an estimate. This past week's value will be revised next week when the new value appears.

The use of highly uncertain data in models that extrapolate into the future is extremely dangerous. A 10% error in the first point will expand into a 20% error in the next point when using equations as unstable as those in economics. This mathematics, sensitive dependence on initial conditions, is well known in the math and science community but rarely makes its way into the sort of Calculus Circus math taken by business majors - and is totally unknown to reporters and politicians.

INFLECTION POINT

An inflection point is a point were there is a change in curvature of a function like unemployment. It is a second derivative of the quantity we are looking at, which is quite different than what gets emphasized in the media.

The first derivative is the change in unemployment. If unemployment goes up, the derivative (the slope of the curve) is positive and the curve goes up. If unemployment goes down, the derivative is negative and the curve goes down.

ASIDE: The weekly jobless claims provide a window into the first derivative of unemployment *if* you know the rate of job creation and the rate at which people leave the unemployment rolls. As in late 2007, you can have 325,000 people apply for unemployment and still have almost no change in the unemployment rate.

The second derivative is the change in the change. If it is ZERO, unemployment will continue to increase every month if it was already increasing (say from 6.10% to 6.85% to 7.60% to 8.35%) - and it will stay the same if it wasn't changing (say from 4.50% to 4.50% to 4.50%) or continue to fall if it was falling. If it is POSITIVE, like it was in all of 2008, unemployment rate will curve upward - increasing in every bigger steps. If it is NEGATIVE, as shown by the light blue curve through all of 2010, the rate will curve downward - rising and then falling like a fly ball.

ASIDE: A regular rise in weekly jobs claims indicates a positive second derivative, predicting that the unemployment increase will be bigger next month than last month. A regular fall in the weekly jobs claims indicated a negative second derivative, suggesting that the unemployment increase next month will be less than the increase this month.

The green line I drew on the graph shows the unemployment curve extrapolated for ZERO curvature - a constant increase in the unemployment rate based on the two previous points. Notice that the blue point for Q1 2009 is below the green line, indicating they believed the curvature was becoming negative (recovery starting) even before the stimulus package was proposed.

The true value for Q1, pointed out with an arrow, is well above the green line. This indicates that the curvature was positive and the rate of job loss was increasing rather than increasing - indicating the acceleration of the recession into depression. [**] The higher of the two pink lines is a projection that assumes that acceleration continues unabated, while the lower of the two assumes a transition to zero curvature, where I think we are today.

THE PREDICTIONS

I think the mistake made in constructing the blue graphs shown above was in assuming that the sharp drop in new jobless claims in late December, obvious in the graph shown at the bottom of this report on new jobless claims, indicated an inflection point for unemployment. That input would lead their model to predict a Q1 2009 value that is below the straight line projection of the previous two quarters, what was shown as a green line on my diagram and discussed above.

Feeding these data into their model doesn't just change the initial point by a significant amount (it is off by more than 0.5%, a 7% error in the value), it changes the initial slope by a huge amount (from about 2.7% per year to 4.8% per year, an 80% error in the initial slope) and makes the curvature slightly negative rather than significantly positive.

I'd really like to see a re-run of their model with the true Q1 value instead of their estimate. Rather than bending at the start of 2009, the light blue "without" curve might have soared up into the low teens. For those who think this is unlikely, look at your local government and college budgets without the stimulus money. Ours are cutting jobs even with that money. It would not surprise me to learn that we would have to cut our faculty and staff by 5 to 10% starting July 1 without the stimulus money from the recovery plan.

Another Modeling Error

They also made totally unrealistic assumptions about how long it would take to pass the stimulus bill, and thus when the tax cut would show up in my paycheck, as well as when the money would show up as actual jobs. Apart from helping with staffing shortages in the unemployment offices, little of the money in our state will go to work before July 1 - which means the effects won't kick in until Q3 rather than in Q1 as they had assumed. (I think they assumed the bill would pass by the end of January.) In addition, a big chunk of the money is going to avoid layoffs rather than put unemployed people to work. The "no layoffs" happens right away, in public funded operations like our college, but the "new jobs" construction requires bids and contracts.

GOOD NEWS ?

As pointed out up at the top, the number of new claims for unemployment insurance fell again, by more than expected. Is it real? Who knows. However, the drop from the peak a few months ago suggests the rate of job loss is no longer growing, and might be falling. We really won't know for several months whether the curvature has become negative. But even if we are at an inflection point, unemployment will continue to grow until new jobless claims are balanced by those taking jobs.

If sustained, this would be a leading indicator of improvement in the economy.

But I'm not holding my breath because there are too many affordable houses sitting vacant at prices the owners think would be reasonable if it weren't for the properties heading for foreclosure. I'll let you know when I see a "sold" sign within a half mile of our house.

[*] Footnote

Anyone who watches CNBC has heard this phrase quite often, but might not know where it comes from. It is an allusion to a famous bit of dialog from the movie Being There, where the Peter Sellers character Chance (aka Chauncey Gardiner, a gardener who likes to watch TV that gets mistaken for an erudite philosopher) says "There will be growth in the spring!" - which gets (mis)interpreted as a prediction that the economy will turn around in the spring.

[**] Footnote

I use the term depression in the sense of the normal depressions that were common in the late 19th century as a result of bubbles not unlike the real-estate bubble that started this one, not in the sense of the Great Depression. I explained this in an earlier blog about the state of the economy in early January 2009.