Discrete Actions and Inverted Incentives

I remember, about a year or so back, the US weekly non-farm payroll data had shown an uptick in unemployment. Intuitively, a higher unemployment rate indicates lower economic activity, since (among other things) the average purchasing power goes down and fewer things are getting produced (since fewer people are at work). So you would expect the stock market to react to this by going down.

The exact opposite happened. The higher unemployment was greeted with a big rise in the S&P 500. I remember tweeting about it but can’t find it now. But I can find some research someone has done about this:

But here’s the kicker: the S&P500 is inversely related to the unemployment rate, and thus the market actually goes up as a response to a release of a higher than expected unemployment rate. This may seem illogical conceptually, but historical analysis and statistics show that it is true.

In the last 3 years, the unemployment rate in the United States has been surprisingly higher than expected 11 times. The result? The S&P500 went up 80% of those times within a time-frame of 90 minutes (see Fig. 2, click to enlarge the image).

The basic issue (as I see it) is that higher unemployment means lesser likelihood that the US Federal Reserve will raise interest rates. Which means lower rates for the longer foreseeable future, which translates to higher stock prices.

The kicker here is the “discrete action” on part of the Fed. Because their decision (on whether to hike rates or not) is binary, news that decreases their odds of hiking rates, even if it (the news) is bad for the market, leads the market to go up.

You can see this in action elsewhere as well. Let’s say you are the number two at a manufacturing plant, and you are not happy with the way things have been run. However, you know that with the current level of production, the company management will not bother – they only see the numbers and see that the plant is being run well, and they won’t listen to you.

However, if the production drops below a certain level, the management is certain to review the operations, at which point you will be able to make your point to them and be heard, and you will be able to hopefully better influence how the plant is run.

Normally, your incentive is in keeping production as high as possible. But now, with this discrete action (management’s review of your operations) in the picture, your incentives get reversed. It suddenly becomes rational for you to not work so hard to increase production, since lower production means higher chance of a management review.

The problem with a lot of standard economics teaching is that it abstracts away the messiness of real world “step functions” and instead uses a deceptively simple continuously increasing or decreasing demand and supply curves. And so we are conditioned to think that incentives are linear as well.

However, given the step functions inherent in everyday business (which are only made worse (steps become steeper) with discrete actions), the incentives are not linear at all, and there are points in the curve where incentives are actually inverted! And this is everywhere.

I’m writing this on a lazy Sunday morning, having postponed this for over a week, so no enthu da to make pictures and explain my point. However, I guess I’ve explained sufficiently for you to catch my pOint.

Actually – since I have an iPad with a pencil, I did make a simple sketch. Limited by my drawing (and mentally adding curves) skillsBasically normal incentives is like the red line, but the discrete action (modelled here like a negative sigmoid) means that there is a region where the overall payoff is massively downward sloping. Which means your incentives are inverted.

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