Wednesday, September 23, 2015

A Bad Optimization Problem

Roheeni Saxena writes

Economic inequality in the US has drawn attention to the attitudes and behaviors of the elite, as those who are educated in the top universities are both likely to start out wealthy and disproportionately likely to have an impact on the future of this country. To examine how this elite class would manage societal resources, the authors of a paper published in Science studied a group of Yale Law School students. 
The findings indicate that they’re more likely to make economic choices based on increasing the overall wealth of the nation rather than on increasing income equality within a nation. Thus, there’s a chance we’re selecting policymakers who are unlikely to address this issue.
Rather than anything nefarious, I think this phenomena is driven almost entirely by decisions being made using bad metrics, because good metrics are just too hard to calculate.

To make my point clearer, let $x = (x_1, ... , x_n)$ be a vector of variables quantifying the underlying real state of the economy. Maybe $x_1$ is nominal GDP, $x_2$ is inflation, $x_3$ is a 10 year yield, $x_4$ is unemployment, $x_5$ is some measure of consumption/income inequality, $x_6$ is average health outcomes, $x_7$ is average societal happiness, and so on.

The so-called elites in this study lean towards policy choices with an aggregate greater benefit to society, as measured in nominal dollars. So, for example, they may be trying to maximize the output variable $y = x_1$,  NGDP. Meanwhile, a more useful quantity to optimize might be $y = x_1 + c_2x_2 + \ldots + c_nx_n$, which incorporates all these factors with some weights $c_j$. This is much more complicated though, since you need a model which tells you how policy choices impact the full state $x$, along with variables $c_j$ quantifying how many units of $x_j$ are equal in net-beneift to a unit of $x_1$. Yikes.

Making good decisions requires good models. We don't have good models, so we make the best decisions we can, which are, of course, bad.

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