Minimum Wage Part 2: Signal Detection Theory

“There are unemployed people who would be much happier working for $5 an hour than being unemployed. If they want to work for that amount, why should the government prevent that? Isn’t having a low-paying job better than having no job at all?”

Let’s call this Standard Argument #2 against Minimum Wages. (I have talked about Standard Argument #1 in an earlier post.)

In response to Standard Argument #2, I would like you to consider that there are actually two groups of people who are impacted by minimum wage legislation:


On the one hand, there are the people who are unemployed, who would be employed at $5 per hour if that were allowed, but who now cannot get a job because their prospective employers have decided that they cannot (or will not) pay $7.50 per hour for the work that the job entails.

On the other hand, there are people who are employed at $7.50 per hour, because the company has decided that they can afford to pay that amount for the work that the job entails, but who would be only getting $5.00 per hour if the minimum wage law were not in effect.


As minimum wage increases, there will be more people in both groups. One of these is a bad thing, the other is a good thing.

In the case of the first group, it is a bad thing. More people unemployed means more people suffering. It is also worse for the system at large, because these are now people who cannot buy things and cannot contribute to the functioning of the economy overall.

In the case of the second group, it is a good thing. These are families that now can provide better for themselves and their families because of the law, than they would be able to without the law. They can buy more products and services, and the economy overall benefits.

As minimum wage keeps increasing, you assume that the cost of paying for the employees eventually becomes prohibitive: so the number of people in the first group increases faster than the number of people in the second group.  Obviously, in that scenario, one can objectively and rationally say that minimum wage is too high. The down-side outweighs the up-side.

But where is the “sweet spot,” as it were? Where is that point that minimizes the number of people in Group 1 while maximizing the number of people in Group 2?

This is not a theoretical or ideological question: this is a scientific question. This is a question that you can only answer by looking at data.

In fact, science actually has an entire framework for understanding this type of problem (in the abstract), and that is called “Signal Detection Theory.”

In standard Signal Detection Theory, you have a situation where there is something in the world that is either present or not. (It could be a signal, or it could be anything else. It could be anything from “Did the doorbell ring?” to “Is there a God?”) You, as an observer, have to try to guess, based on whatever evidence you have available, whether that thing is present or not.  You could be right, or you could be wrong. In fact, there are four possibilities:

Signal Detection ConditionsIt’s possible that the thing exists (e.g. the doorbell rang, God exists, whatever) and you correctly say that it does.

It’s possible that the thing does not exist (e.g. the doorbell did not ring, God doesn’t exist) and you correctly say that it does not.

It’s possible that the thing exists, but you say it doesn’t (they call this a “miss”).

It’s possible that the thing does not exist, but you say that it does (they call this a “false alarm”).

Let’s imagine a situation where you are repeatedly being asked to tell whether a doorbell rang. Let’s say it’s a soft doorbell, and sometimes you are not completely sure. What strategy do you use?

If you are really frightened of misses, you can simply be biased toward saying the bell rang. All you do is say “Yes, it rang!” almost every time. That way, you will have almost no misses. The trade-off is that you will have a lot of false alarms.

On the other hand, if you are terrified of false alarms, you can raise the bar really high. You can hold off and almost never say “Yes, it rang!” unless you are absolutely positively sure. That way, you will have almost no false alarms. On the other hand, you will have a lot of misses.

Somewhere in between the two, there is an “ideal spot”: there is a place where you get as few false alarms as possible while at the same time getting as few misses as possible.

This kind of set-up can also be used to look at the Minimum Wage issue.

Remember what Minimum Wage is really trying to do: it’s trying to identify the maximum wage that a company really can afford to pay for unskilled labor, even though they might prefer not to. By identifying the maximum wage that the company can afford, you maximize the benefit to the worker without “breaking” the business model of the company and putting them out of business.

In this case, a “miss” is a situation where the government says “the company can’t afford to pay that amount” but the company really can afford it. A “miss” represents the company taking advantage of the worker, under-paying the worker compared to how much they really could afford.

On the other hand, a “false alarm” is a situation where the government says “the company sure can afford to pay that!” but the company really cannot. A “false alarm” represents the company being so burdened by the minimum wage law that it actually makes it impossible for the company to function.

As minimum wage increases, the number of “misses” will decrease, and the number of “false alarms” will increase. It’s like increasing your bias to say “the bell rang!” in the doorbell experiment.  Set the bar too far in one direction, you get too much of one type of error; go too far in the other direction, you get too much of the other type of error.

Somewhere in between, there is the “correct” threshold: the threshold that minimizes both types of “error.” Somewhere in between, there is a minimum wage that leads to the least number of companies being burdened to the point of being put out of business, but also leads to the least number of employees being under-paid and taken advantage of.

The real work in this debate isn’t to crow about how some companies might be burdened or about how some employees might be taken advantage of; the real work in this debate is looking at the real data, the real numbers, and finding out the practical balance between those two.