In this R1 I wish to critique two arguments I often see in Gender Wage Gap threads, because they are related to same point.

First is when people claim that there, logically, cannot be a gender wage gap, because then firms would fire men and hire only women. This arbitrage will eliminate anything preventing wages from equaling marginal productivity (and therefore reflecting value added to the business).

Second is when people link to an audit study and act like that’s enough to prove discriminatory gap (it isn’t)

Both of these mistakes have the same root cause, which is assuming a structural model of the labor market, but rarely are they explicit about this.

I will not be claiming a particular structural model is more plausible than another or better fits the data. That is beyond my knowledge of the subject, if you have this knowledge, feel free to comment and add on. I just wish to highlight that both of these arguments are reliant on certain structural assumptions that are rarely stated.

First, let us consider a common claim , see here.

Easiest business plan ever for profits. Only hire women, at 77% the price. Free 23% profit, right?

Let’s talk about the simplest (not necessarily the most realistic) model that will make this argument true. This is Becker’s Taste for Discrimination perfectly competitive labor markets.

In Becker’s taste for discrimination some firms don’t like hiring X group and pay them less and pocket the difference as compensation for dealing with this group that they don’t like to hire. This means that discrimination will be affected through a market process.

See relevant Heckman

The impact of market discrimination is not determined by the most discriminatory participants in the market, or even by the average level of discrimination among firms, but rather by the level of discrimination at the firms where ethnic minorities or women actually end up buying, working and borrowing. It is at the margin that economic values are set. This point is largely ignored in the papers in this symposium.

Basically what Heckman means here is it doesn’t matter if the average firm is a discriminator, it matters if the firm that hires the minority is a discriminator. The reasoning is actually very similar to why marginal costs matter much more than average costs. This marginal firm leads us to two important conclusions about the labor market for the group we are looking at.

If

1. There are not enough non-discriminatory firms to hire all the group members

2. The group members cannot easily find these non-discriminatory firms

We will likely see a wage gap. Fortunately in this one, we have assumed option 2 away because we have perfectly competitive labor markets. The group’s members know exactly how many openings non-discriminatory firms offer, because of perfect information.

So let’s focus on 1. If there are enough firms in the industry to employ all this disadvantaged group, we will see no wage gap. It doesn’t matter if discriminatory firms exist, the group will be able to avoid them easily. If a firm offers discriminatory wages and someone takes it, they will be offered scooped up by the non-discriminatory firm. These discriminatory wage gaps will not exist in equilibrium. This seems to basically be the argument presented above (but not really fleshed out).

If there aren’t enough non-discriminatory firms, things get more dicey. The group will be forced to take jobs at discriminatory firms. Furthermore, even nondiscriminatory firms will pay lower wages. This is because they can take this disadvantaged group from these discriminatory firms, so if they paid wages = marginal product, they could fire there current workers and hire from the worker pool at discriminatory firms. This will grant these firms economic profits.

If we have free entry (another assumption) and the firms entering with free entry aren’t discriminators (another assumption), we will see non-discriminators drive out discriminators. Essentially, the fact they don’t have a discriminatory preferences gives them a competitive advantage, much like them being a firm with say, more efficient technology. They can hire labor cheaper.

If we don’t have free entry and not enough non-discriminatory firms, or the firms entering are discriminators, then we will see a wage gap. Competition will not eliminate the wage gap. Strangely enough, this case is actually perfectly efficient. This is because preferences are exogenous, much like the weather. I think it is often underappreciated how odd exogenous preferences is as an assumption at times.

Finally, I will note that relaxing 2 can lead to a mess. Even if there are enough non-discriminatory firms, non-discriminators will know that marginalized groups have less bargaining power and will, for profit seeking reasons, offer them less. For example, marginalized groups could face more stringent search frictions (e.g. they have a harder time finding a firm without a taste for discrimination) and firms could know they have more leverage over them as a result and offer them less money, even though they have no taste for discrimination themselves. There are lots of ways we could go with this and maybe you could add other features that counter act these factors and reduce/eliminate the wage gap. However, my point still stands that you need to specifically outline these features, not claim it’s logically incoherent for there to be a wage gap.

Next I will go after the citations I see of audit studies where it is found that the average firm is a discriminator. I actually think many of these are correct and the average firm is a discriminator. However, this brings us back to the marginal firm vs. average firm problem.

Heckman again

The impact of market discrimination is not determined by the most discriminatory participants in the market, or even by the average level of discrimination among firms, but rather by the level of discrimination at the firms where ethnic minorities or women actually end up buying, working and borrowing. It is at the margin that economic values are set. This point is largely ignored in the papers in this symposium.

This is why I lumped them together. The problem is these audit studies (say, comparing resumes that are the same except for the race of the applicant). They cannot tell us how easily the applicant can dodge discrimination. Sure, marginalized groups may be less likely to get interviews and jobs, but if they can still find those non-discriminatory jobs, they won’t have a discriminatory gap.

To use an extreme example, I may have 100 job offers, 99 will give me a discriminator gap and 1 does not. I will not actually suffer from discrimination.*

*I don’t find this plausible. More accurately, I’d worry audit studies might overstate discrimination, by not factoring in marginalized groups ability to dodge discrimination. (If anyone has evidence that this is or is not happening, please post it)

These groups being able to dodge it easily will be reliant on no search frictions and having enough non-discriminatory employers, for the as reasons I mentioned about.

All in all, I suspect both sides are reliant on more assumptions than I outlined (I mentioned mostly perfectly competitive labor markets and only one type of discrimination). However, I wanted to focus on the # of non-discriminatory firms and how easily marginalized groups can find them, because those are key structural parameters that most of these arguments completely ignore. It’s not that these arguments are wrong per se, it’s that they are incomplete.