Tuesday, February 24, 2015

Thinking clearly about the gender wage gap

Patricia Arquette recently promoted gender equality particularly as it relates to the wage gap at the Oscars. Some Facebook discussion followed, and Bob Murphy encouraged me to put my position in a blog post, so here it is.

My frustration with the empirics of the wage gap come in whenever - following something like the Arquette statement, or a mention of "77 cents on the dollar" in the State of the Union - people get up and assert that the wage gap is a "myth" or a "fallacy" simply because there are explanations for different contributions to the gap (some of these explanations are better than others). I think that's very misleading and that it's a mistake to use conditional mean differences in a regression to argue that the gap is mythical. I have always liked Claudia Goldin's approach (I linked to her first thing when I saw the Arquette news). Goldin says of the 77 cents on the dollar figure that "it's an accurate statement of what it is". The gap isn't a myth - it's real. The question is, what is the gap?

Some people are tempted to perform the following exercise:
1. Add a bunch of controls in a wage regression.
2. Note that the difference in conditional means between men and women shrinks when you do that.
3. Call the gap a "myth" or a "fallacy".

This is wrong for a number of reasons, and how it's wrong largely depends on how it's executed, interpreted, and qualified by the author. In other words doing steps 1 and 2 is totally fine. The problem comes in with step 3.

All adding occupational and educational controls does is parse out the within-occupation/education and between-occupation/education variation in the gap. Specifically, you are removing the between-occupation/education variation and leaving behind the within-occupation/education variation. Economists think wages and employment - prices and quantities - are jointly determined by supply and demand. Labor market disparities facing women are going to express themselves partly in the wage determination in a given occupation, and partly through the distribution of women across occupations. The analogy I made yesterday is that it would be nonsensical to say that blacks didn't face labor market discrimination in the postbellum South because black sharecroppers were approximately as a dirt poor as white sharecroppers (hypothetically - I'm not sure what the disparity was in sharecropping). That ignores the fact that differential treatment of blacks by employers lowered within-occupation wages and drove them to lower wage occupations. You can't separate the two points and you certainly can't dismiss the disparity because it shows up between occupations rather than within occupations.

The picture of between- and within-variation gets even more complicated when you consider the point that women are not passive actors in the labor market. They sort across occupations in response to anticipated earnings and other benefits. Women will sort into occupations where they have the greatest comparative advantage and likewise for men. If within-occupation variation (which drives this sorting behavior) is random this sorting won't matter much, but if within-occupation variation is correlated with between-occupation variation then it can matter a lot. This sort of effect was pointed out a long time ago by Roy (1951), and it's going to lead to bias in the coefficients on occupation (or perhaps it's better to say it's going to impact how you interpret the coefficients on occupation). Claudia Goldin has done a lot of work on where the within-occupation wage gaps are, but I'm not sure that she has looked into how this has impacted sorting behavior.

The take-away from all this is that it's misleading to say the wage gap is a myth by pointing at occupational controls. It is much sounder to follow Goldin's lead in her AEA presidential address and treat them as clues for understanding the various factors driving a very non-mythical wage gap.

Now if you want to go a step further and assert that you, individually, don't care about certain parts of the wage gap that's one thing. This gets very heated when we think about employment practices around pregnancy, for example. You're welcome to do that. But don't mislead about what the data say.

The good news is things are getting better. The wage gap has shrunk, female labor force participation and human capital investment is up. The last big thing to tackle is how the labor market handles pregnancy and children.


  1. "77 cents on the dollar" does not work as a mantra or a creed although it is clearly used as such. Likewise "how the labor market handles pregnancy and children" seems to counter one of the basic tenets of economics: People face choices.

    1. I don't see how an open question can counter a basic tenet of economics.

  2. Good points, but does Bob or anyone else actually disagree with the arguments you lay out? I don't know exactly what Bob said on Facebook, but I can say that I've never read anyone argue "the wage gap is a myth", full stop.

    Instead, I've seen many pundits argue that it is a "myth" that women are paid 23-cents less on the dollar than man **for the same work**. And they are right! If your question is whether a woman will earn less than a man with the same credentials in the same job, then comparing raw means or medians is the wrong thing to do for exactly the reasons you mention (e.g. self-selection across occupations). And that is the context you find a lot of people calling the gap a "myth".

    For example, you mention that people got up in arms when President Obama cited the 23-cent wage gap during the State of the Union. But you have to remember that he was citing that figure in support of the Paycheck Fairness Act, which makes it illegal to pay different wages to men and women ***for the same work***. Wouldn't you agree with the skeptics that in this context there are more informative statistics than the 23-cent wage gap figure?

    1. This might be of interest: http://factsandotherstubbornthings.blogspot.com/2014/04/strong-and-weak-forms-of-gender-pay-gap.html

      There are varying degrees of wrongness. I think some people make some of the caveats that you're pointing out although I don't think throwing in some occupation dummies really gets to "for the same work".

      Anyway, I think the President's SOTU and Arquette are a hell of a lot more accurate than people who call it a myth, even though there's plenty more to be said. It's incredibly misleading to call it a myth. Obama and Arquette commit a sin of omission. Guys like Perry and Biggs commit a sin of commission. Since Obama and Arquette are not economists I don't hesitate to judge them less harshly.

    2. Thanks for the link! I will check this out. :)

      I also agree that Arquette should be given some slack. But Obama? If he honestly wrote the SOTU without any input from an economist, he deserves any and all criticism he gets. More likely, I figure he knows it is problematic to use the 23-cent wage gap figure to advocate for the Paycheck Fairness Act, but he's not trying to educate the public on an economic issue. Instead, he's trying to sell a bill he supports. And part of me can't blame him for that. That's what politicians do. But at the same time, I also can't then blame folks that point out that using that wage gap statistic in that context is misleading BS.

    3. "The gender pay gap is a myth!" is a pretty unsophisticated way of tackling this. The more sophisticated criticism of "Give us legislation! We must force everyone to pay men and women the same!!!!" is that the major drivers of the pay gap have to do with life choices men and women make (and yes, women are more than capable of and certainly "allowed" to make pretty much whatever life choice they want in 2015), not systemic and extreme discrimination. This isn't to say that discrimination doesn't exist, but that the data (and sound theory about the market disadvantages of discrimination) suggest that life choices largely explain the pay gap. The "Factual Feminist" on YouTube had a video about this several months ago.

    4. Levi,

      I'd have to agree. It seems there is little evidence that women are being paid less for the same work. So, right away, we should be skeptical about the impact things like the Paycheck Fairness Acts will have on the wage gap.

      Given that, I'm not sure what the policy response should, if any. Goldin stresses that increased work flexibility would dramatically narrow the wage gap and Daniel seems to agree. But what reason do we have to think that current labor agreements are not optimal? As you point out, what we observe is an equilibrium that is the result of men's and women's choices. They have self-selected into jobs knowing there is a trade-off between earnings and time off. Why should we second guess those choices or assume an alternative arrangement would be better?

    5. All good points, Dallas.

      In the extreme, this sort of choice limitation by legislative fiat is at least partially responsible for young girls in 3rd world countries leaving the sweatshops for sex work. Neither are very good, but the latter is far worse than the former.

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  4. Perhaps I misunderstood your final statement. I read a normative statement - how do we make the markets compensate for raising a family - while your response suggests there is a positive question - what is the effect of childbirth on the pay discrepancy. Given that that portion of the equation has been been quantified, I'm not quite sure what there is left to tackle.

    1. Well I wouldn't exactly say it's just a positive issue (although certainly I think the positive issue is interesting in its own right). I guess I don't understand why a particular normative perspective or question counters the tenet you identify. There are all sorts of scenarios where we recognize people face choices and we declare that we don't want them to have to face those choices. I can bring economic science to bear on the choice between feeding your kids and paying your rent but I am not denying a tenet of economics by saying I want policies or social organizations or employment practices that are directed at ensuring that people don't have to make that choice.

      To keep your normative/positive point I guess I'd just say that tenets of economics revolve around the positive claims about choices. If you take a normative stance on those choices you're not necessarily countering the positive point at all.

    2. I think that my problem lies with the juxtaposition of the penultimate sentence with the final sentence: does economic science have less to bear on female labor force participation and human capital investment now that the wage gap has shrunk? It is not at all clear that those are "solutions" rather than "problems" if people are making choices that they (rather than an economist) are unhappy with.

    3. re: "It is not at all clear that those are "solutions" rather than "problems" if people are making choices that they (rather than an economist) are unhappy with."

      Well I agree with that. But that's going to be wildly variant depending on the people making the choice and it's going to be a problem no matter what view anyone takes - they could always be wrong.

      I'm staking my claim that much of the rise of female labor force participation is a choice that most women are pretty happy with and it's come about because barriers on women's choices have been removed. I'm not staking the claim that's universally true, but I am that it's largely true. I feel pretty good about that but if anyone wants to make the opposite claim they're going to run up against your last sentence just as surely as I am, right?

    4. "...a choice that most women are pretty happy with" (probably true) but at the cost of? The education system failing males? Baby-boomers retiring, thus kicking the can down the road?

      Anyway...your post is good and timely and if I push too much harder I will be exposing my own weakness on the subject.

  5. I smell a mote-and-bailey fallacy. Activists stretch and go wild with their interpretations, and when called on it, they fall back to the uncontroversial facts ("that's what we meant all along, you denier!").

    The aggregate gender pay gap is real, and I doubt Bob questions it. But it is usually stated as women getting payed less "for the same job" or "for the same skills", explicitly or implicitly as the result of employer discrimination.
    That is simply incorrect and deserves to be called false, fallacious, a myth. Plus it offers no legs to the associated policy recommendation (forcing employers to pay "fairly").

    "The good news is things are getting better. The wage gap has shrunk"

    Hum, you stray from factual analysis. You are stating that the gender gap is a bad thing and implying that zero aggregate difference is the just target.
    The gender pay gap is really the sum an occupation gap, a long-hours gap, a priorities gap, a risk gap, an education gap, a stay-at-home gap, maybe some discrimination (only maybe, because discrimination is whatever we cannot explain yet), and probably some other factors we don't yet understand.
    I don't see where you explained that those gaps are bad, any more than you explained why the size gap between basketball players and non-basketball players is bad.

    1. I disagree with Gene below.

      I'm not an activist, for one thing. So if you want to refine the activist's point that's fine - my contention is that they would be much better served reading Goldin than reading Perry and Biggs if we're going to do that. My contention is that Perry and Biggs are very misleading where Goldin is not.

      I also disagree with your characterization of how it's usually stated - if you look at the president, AAUW statements, etc. the 77 cents point is usually (not always, of course) accurately described and then they follow up with concerns about equal pay for equal work. I don't see the problem with that. I don't often see the 23 cent gap referred to as entirely due to unequal pay for unequal work although certainly if that came up I'd disagree with it too. What makes you think I wouldn't?

      I don't understand the second half of your comment - I've never said and I don't think I've implied all these gaps need to be zero.

      I do think some ought to be.

    2. Some elaboration Julien: http://factsandotherstubbornthings.blogspot.com/2015/02/is-my-gender-wage-gap-view-motte-and.html

      I appreciate the introduction to the term but I think you're wildly off base. Maybe Obama is guilty of this, I don't know. I, of course, am not Obama.

    3. Bryan Caplan used it last December: http://econlog.econlib.org/archives/2014/12/outsourced_to_s.html

    4. Daniel, thanks for your reponse. I replied on the first part in your elaboration post.

      For the second part, I was addressing this specific statement: "The good news is things are getting better. The wage gap has shrunk".
      I replied "You are stating that the gender gap [notice the singular] is a bad thing and implying that zero aggregate difference is the just target."
      Why do you think shrinking the wage gap (singular) is good?
      If zero is not your target, then what value would satisfy you and why?

  6. If men could get pregnant, abortion would be a sacrament


    If men were paid less then woman, L Summers would be chair of a blue ribbon presidential panel examining how to solve the crisis

  7. But what is the gap, though? From the rhetoric of those touting it, such as Arquette or Obama, and the government intervention that is suggested to correct it, we ought to suspect that the gender gap is something undersirable, since it would be odd to think they were advocating getting rid of something desirable. Therefore, if it can be shown that this wage gap can be explained by things that aren't "bads," which it seems is the primary purpose of criticizing the wage gap, isn't it reasonable to call this a myth? Obviously this is directed at the political side of the debate, as your post makes some good points, but that is how the "77 cents" has been used, as a political football. They can describe the 77 cents as a difference between to statistical categories, but when its followed up with concerns about equal pay for equal work, doesn't that immediately show their ignorance of it? Obviously they are trying to use this as an empirical demonstration that equal pay for equal work is not what is happening, by presenting this statistic as if it was an apples-to-apples comparison. That is much more misleading than trying to show that it is not an apples to apples comparison but ignoring some of the other ways, such as between occupations like you mention, in which differences in treatment could manifest themself.

  8. Ok, so what would you do about it? Is there a better system than to simply allow actors to voluntarily trade goods and services? How will you prevent politicians from bundling (and abusing) any implementation of policy? Of course, politicians act in regards to the average voting citizen who knows next to nothing of what you've written.

    Equal work for equal pay? Who decides? It's difficult enough for a manager working closely with employees to decide what pay levels should be. Yes, some jobs have rigid pay scales, but are those the type of pay systems you think create productive work environments? Would you force those systems on everyone?

    I think you'd agree it is difficult to determine how much of the 23cent gap should be closed. How will we know when it is "fixed"? Do we do it by measuring in aggregates and lower the 23cent gap to 15? How do you account for variances in business, environment and individuals? What bureaucracy will continue to monitor and measure the thousands of every changing factors that decide policy? And, really, is there ANY hope at all that government employees can pull this off? I'd really like to see your detailed plan that can deal with all this.

    You've written an extremely intelligent and well thought out piece here, but it means nothing because nothing works better than leaving individuals alone to trade as they wish.


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