Wednesday, April 27, 2011

Signaling Highlights

Please find the results of the value of education experiment here.

We studied signaling through the value of education game. In signaling games, the key parameter in the mental model are the beliefs of employers about a worker's type following each signal. In a separating equilibrium, different signals produce different beliefs. In our game, we saw that a separating equilibrium consisted of believing that grade school (or BS) were associated with low types while MBA was associated with being a high type. In that case, a low type could not gain by pretending to be a high type and, therefore, these beliefs are confirmed by actions. We also saw that one could not sustain a separating equilibrium by believing that low types choose grade school while high types choose BS or MBA. The reason is that the marginal benefit to a low type from imitating a high type and getting a BS was 100k while the marginal cost was only 80k; therefore, low types will "invade" the BS population and thereby destroy the signal.

Let us reflect on this for a moment. 20-30 years ago, an MBA was unnecessary to climb to the highest levels in business whereas now it more or less is required. What has changed over that time is undergraduate enrollments. 20-30 years ago, many people ended their education with a high school degree. Now, there are strong incentives to proceed to get an undergraduate degree and many subsidies and loans to make this affordable. In a sense, an undergraduate education is now too cheap to offer a useful signal. In our game, this signal inflation was altogether a bad thing since there were no gains to human capital from signaling. Of course, the reality is that there are some human capital gains. Nonetheless, the results of the game indicate that there is an incentive to overinvest in education purely for the signaling aspect. In other words, the problem might be too much education rather than too little.

Besides the separating equilibrium, there was also a pooling equilibrium in the game. In a pooling equilibrium, everyone is supposed to get a grade school degree. So long as employers are sufficiently skeptical about the signal value of a BS, then no type will wish to deviate. Obviously, this equilibrium is better for low types since their quality is no longer being revealed. What is more surprising is that, for the parameters of our game, it is also good for high types. While high types earn more than low types when they separate, these gains are more than burned up in the cost of the signal.

Again, it is useful to reflect on this. In effect, the signaling game is a type of coordination game based on employer beliefs. If employers believe that education contains little signal value, then this is self-reinforcing and workers are happy to go along. If, however, they believe strongly in the power of the signal, this too is self-reinforcing, and types divide by signals. In our game, the payoffs were higher in the pooling setting than in the separating setting. In effect, this is like choosing the worse outcome in a coordination game, but in a more subtle way. This suggests that policies like restricting advertising (as was the case for many years in the distilled spirits industry) can actually enhance the profits of all brands, both low-end and high-end.

1 comment:

Unknown said...

The Economist on the Game Theory of sports.