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The subtitle to this article is "Evidence that Deutsche Bank (NYSE:DB) analysts don't know calculus".

A recent article in the Wall Street Journal titled "Some Good News on Jobs: Tax Withholding Improving" seems to have installed some confidence in bulls and left bears scratching their heads. The article contained a figure showing year-on-year tax receipts. Here it is:


The brief article contains this quote:

“The tax data, which are reported daily by the US Treasury, are particularly valuable to us because they are not subject to revision. Over the past 3-4 months, the plunge in tax receipts has reversed sharply. While still down in year-on-year terms (-2.5%), the lengthening recovery in tax receipts strongly supports our view that net positive hiring is very near—probably not in the February figures (due to weather), but increasingly likely when the March jobs data are reported on April 2.”

What everyone, including Deutsche Bank, are ignoring is that this is a difference curve, in this case year-on-year difference. Year-on-year comparisons make the most sense presumably because of seasonality in tax payments to the IRS. A difference curve is basically a coarse grained derivative, i.e. large steps instead of infinitesimally small steps. For those who didn't do calculus at high school, a derivative gives you the rate of change of something, basically the change of something with respect to the change of something else. The key thing to know about derivatives is that when things become negative at a slower rate, this is manifested by an upturn in the derivative plot. This is best illustrated in the figure below where on the left some quantity is dropping and eventually levels out -- but at a level much lower than it started. On the right is the derivative of that declining plot. Looks kind of "V" shaped, doesn't it.

The chart shows why difference plots can give a false sense of what is occurring. In the example above, the "V" shaped recovery is really only saying that things have stopped getting worse.

Here is a chart of employment numbers from the Bureau of Labor Statistics [BLS].

It doesn't look good, does it. No "V" shaped up-turn in employment numbers. Hmm, hang on, what does the year-on-year change look like?

That's better! Signs of a "V" shaped recovery!

Tax receipts should be correlated with employment. Everyone agrees on this, right? In the next two charts I've overlayed the YOY employment data with the YOY tax data in the Deutsche Bank chart. I did two plots with varying opacity so that the correlation is clear to all (this is actually easy to do using Mathematica).



So the YOY employment numbers are actually pretty well correlated with the YOY tax receipts. Tax receipts appear to lag 2-4 weeks as you would expect. The thing is we know that the actual employment situation is bad yet YOY employment numbers are correlated to YOY tax receipts. The answer of course is that employment numbers seems to have stopped dropping, in other words it has stopped getting worse (for now). The same goes for the tax receipts in the Deutsche Bank chart. This isn't a "V" shaped sign. All it means is that tax receipts have almost stopped falling.

To return to the quotes at the start of the article

...the plunge in tax receipts has reversed sharply...


Well if you want to put it that way. Actually all that has happened is it has stopped getting worse.

...the lengthening recovery in tax receipts...

Sorry, tax receipts haven't recovered. You are confusing a slowdown in the decline with a recovery.

So bears can breathe a sigh of relief, bulls can return to the search for signs of a recovery, and economists can continue to plot difference curves and tout them as "V" shaped recovery signs!
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As a postscript here are charts of real and nominal social security and medicare taxes and the YOY changes of those taxes. Note that tax receipts jump sharply in January.


Disclosure: no positions

Source: Debunking 'Some Good News on Jobs: Tax Withholding Improving'