Dead shoots?

May 22, 2009 in Economics

Happily, I've only used the term "green shoots" one time in the brief history of TGR, and then only sarcastically in the title of this cartoon (which I stand by, as this post should make evident).

The term has always struck me as ridiculous, and not solely because it was first uttered at a time when it was not only false, but utterly misleading. What's worse is that the manner in which the media has pounced on the phrase has eliminated any shades of meaning, much as our eyes glaze over as reports of "billions of dollars lost" and "hundreds of thousands of jobs eliminated" come out -- we have become desensitized by the magnitude of the concept and our overexposure to it (not to mention that no matter how many times we shut our eyes and whisper, it doesn't seem to materialize).

Ultimately, the term has become synonymous with the "second derivative" argument - things are getting worse, but they are getting worse at a slower rate - green shoots sprouting! And while I don't at all equate "not-as-bad news" with "good news", I was happy to let the second derivative camp savor their banner phrase.

Until this morning.

For some reason, today I finally began to think about what "green shoots" really means: it represents the spring, rebirth and growth. It doesn't stand for a positive second derivative, but for a positive first derivative - something universally aknowledged not to be the case. I find this revelation infuriating: if we don't have a positive first derivative, representing growth, then how can there be green shoots, which also represent growth?

For those willing to continue reading, I'll illustrate what I mean with graphs that may confuse more than they educate. Shall we? Let's shall.

Follow a plant through it's life cycle: it grows in spring, flourishes in summer, withers in the fall and essentially hibernates in the winter (I don't know what the proper horticultural term is). Since I want to tie this back to derivatives and such, let's get some math involved. A simple graph of the flower's height above the ground might follow a sinusoidal curve and, courtesy of Wolfram Alpha really coming through, look like this:

Height of a flower above the ground

Here is its first derivative:

First derivative of height

And here is its second derivative:

Second derivative of height

In all these graphs, 0 is winter, 1 is spring, 2 is summer, 3 is fall, and 4 is winter again. Also, a key point is that because this is a graph of height above the ground, green shoots would be observed somewhere between 0 and 1, as the plant first emerges from the soil.

Now we need to figure out where we are in this hypothetical plant lifecycle. We know we have a negative first derivative, which puts us between 2 and 4 (summer and winter). We also have a positive second derivative - for argument's sake - which limits us to sometime after 3 (fall). So we are in the space between fall and winter; our economic "plant" is withering away, albeit at a slower pace than it was during the first cold snap.

So, IF the plant metaphor holds (and let's assume it does, for why else would we use the term "green shoots"?) and IF we are seeing the second derivative turn positive (and I'm not ready to aknowledge that, yet, but the green-shootists are) and IF the first derivative remains negative (no doubts there), we have not yet made it to spring. Only as we reach spring does the first derivative turn positive and green shoots emerge. Just to be absolutely clear: there are no green shoots yet.

(You're right, I could have spared you and written that much earlier, but I wanted to use the graphs.)

You will notice that in the winter, the plant actually retracts back into the ground, but I suppose "brown shoots" or the titular "dead shoots" doesn't quite capture the spirit of that positive second derivative. I'm sure there must be other plant metaphors, like "winter blossoms" or "the last leaves to fall", that are more appropriate.

I suggest "pushing up daisies".

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