John Taylor has one of the weirdest applications of Friedman's plucking model that I've ever seen

This is the weirdest application of Friedman's plucking model I've ever seen. Friedman did not show deep recessions can't have slow recoveries, he showed that the magnitude of the recovery is correlated with the magnitude of the crash and not vice versa (which is an argument against "cycle theories" where the reverse is true).


And as far as I know no one claims that deep recessions have to have slow recoveries (what Taylor claims Friedman demonstrated was false). What they claim is that recessions caused by financial crises are both deep and have slow recoveries. In the past when Taylor has made this point he's qualified that it's worse than other cases with financial crises - that may be true but it's quite different from what he's saying here.


Notice also the metric that he use (change in the employment to population ratio). It's not a bad thing to think about but it's worth looking at the long-run evolution of that metric. We were facing E/P headwinds before the Great Recession because the increase in female labor force participation was petering off and because of the aging population (the situation was very different on both fronts in the 80s). So it's a little misleading to compare the two periods on this metric.

Wage gaps and occupational coefficients: with a specific example from a commenter

I've said here before that in work I've done I've often used the word "disparity" rather than "discrimination" because "discrimination" confuses people - they think they know what it is, but it's a wishy-washy term. "Disparity" is broad but at least it's clear.


At Bob's blog I asked commenter Scott D to be more specific about what he meant by "discrimination" (how you interpret a wage regression can vary dramatically depending on how you conceptualize "discrimination"). His response is fine I think - a perfectly reasonable definition - and it's also a great opportunity to illustrate why I think people often misinterpret occupational coefficients in wage regressions. Scott D writes: "Discrimination in this context would constitute an error in decision-making. It would be a case of a worker’s real productivity being discounted irrationally, resulting in them losing out to another candidate with weaker credentials."


I think other people would have other definitions of discrimination but this is a great one. I'm willing to run with it.


So let's say a woman faces discrimination by this definition - she loses out to a man with weaker credentials. "Loses out" itself is pretty vague and could reasonably be consistent with several different observed labor market outcomes, two of which are:


Outcome A: She gets hired to the same job as the man but at lower pay, and
Outcome B: She doesn't get the job and instead takes her next best offer in a different occupation at lower pay. Let's further say that she is paid her real productivity in this job.


Let's say the woman's wage in Outcome A and the wage in Outcome B is exactly the same.


Under Outcome A, a wage regression with occupational dummies and a gender dummy is going reliably report the magnitude of the discrimination in the gender dummy. Under Outcome B, a wage regression with occupational dummies and a gender dummy is going to report all of the discrimination under the occupational dummies. If you interpret the results thinking that "discrimination" as Scott D defines it is only in the gender coefficient, you would say there is discrimination in the case of Outcome A, but that there's no discrimination in the case of Outcome B.


It would be one thing if these were very, very different sorts of discrimination but these are two reasonable outcomes from the exact same act of discrimination.


This is why people like Claudia Goldin see occupational dummies as describing the components of the wage gap and not as some way of eliminating part of the gap that isn't really about gender.


"Equal pay for equal work" is a principle that I should hope everyone can agree on. It's great stuff. And I for one think the courts might have some role to play in ensuring the principle is abided by in our society. But it's a pretty vacuous phrase when it comes to economic science. It's not entirely clear what it means or how it can be operationalized. Outcome A is clearly not equal pay for equal work, but what about Outcome B? After all the woman is being paid "fairly" for the work she ended up doing. Is that equal pay for equal work? You could make the argument but it doesn't feel right and in any case it's clearly incommensurate with the data analysis we're doing. When two things are incommensurate it's typically a good idea to keep them separate. Let "equal pay for equal work" ring out as a rallying call for a basic point of fairness and don't act like you can either affirm it or refute it with economic science. As far as I can tell you can't.

Postmodernism, pragmatism, and motte and bailey - a quick note

Whenever I identify my philosophical leanings I always like to qualify that I'm by no means a professional philosopher - it's simply what resonates with me of what I've read which is of course limited. That having been said for a while now I've identified with American pragmatism and in particular (although not on all points) Richard Rorty, who I've spent the most time with of all the pragmatists. Pragmatism of course has a lot of similarities to postmodernism.


In reading up a little on the motte and bailey fallacy after Julien's comment on the wage gap post, it seems that it's used by Shackel to point out the problems with postmodernism. Now I don't know what Shackel thinks of pragmatism (that's probably worth checking out) but it strikes me that a lot of what I like about pragmatism is precisely that pragmatism is sort of postmodernism without the motte and bailey fallacy. Postmodernism has a defensible core having to do with some sort of anti-foundationalism and social construction, etc. (their motte), and that's fine and Shackel seems to indicate that's fine. But then they build that out into much bigger claims that are less defensible. At pragmatism's core of course is the same anti-foundationalism but they are much less willing to go the extra step. Rorty constantly insists that he's not a relativist, that he's fine with concepts like progress as meaningful concepts, etc. His practical claims about human life are typically not that out of the ordinary. He only insists that we don't pretend they have what he'll often refer to as the Platonic foundation that we like to pretend they have.


Keep the postmodernist motte, skip the bailey.


I do like this concept a lot. So much of our discourse is a constellation of related arguments rather than a single argument and this helps to treat and evaluate that constellation of arguments as a whole.


I'm happy to have reactions to this - it was my spur of the moment reaction but I could be wrong.

Is my gender wage gap view a Motte and Bailey Doctrine?

Commenter Julien Couvreur taught me a fantastic new term today: the motte and bailey fallacy. I don't think his comment is persuasive at all, but it's interesting enough to spend some time talking about. A motte and bailey fallacy (for those of you who, like me, weren't aware of it) is according to Nicholas Shackel less a fallacy and more of a doctrine - or if you'd like a style of presenting an argument. You can read the Shackel link for background but the gist is that you promote and live in and enjoy in a less defensible but more desirable argumentative terrain when you can (the bailey), but when things get tough you retreat to the more defensible but less desirable terrain (the motte) and you treat them like the same thing. Julien alleges this is what I'm doing. Absolutely unequivocally I am not, but let's start with his comment:


"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 problem here is I am not an activist. I am not Obama. I am not Arquette. My bailey is what I posted, and as far as I know I don't have a motte. Now Obama or Arquette might be guilty of the motte and bailey fallacy if they were pressed but I am absolutely not. I've never made anything like the switch that Julien describes.


A possible candidate for this (although I don't want to be too accusatory because I can't read his mind or his intentions) is Steve Horwitz's video on the wage gap. He leads with calling the wage gap a fallacy and only in the last minute or so of the video does he get into some of the qualifications that should lead to the conclusion that it's not a fallacy at all. So if one wanted to accuse him of a motte and bailey fallacy the first four minutes or so are his bailey and the last minute is his motte. Because of the time ordering that is possibly appropriate. Certainly enough people have mistakenly thought the first four minutes were his position that he had to do damage control and write a post correcting them. I don't want to push that too hard because keeping the qualifications towards the end doesn't in and of itself guarantee a motte and bailey fallacy (although it might not be the most strategic approach if you think that last minute is important to your point).


I also want to reemphasize an analytic point that I think Julien might have missed. He writes "The aggregate gender pay gap is real, and I doubt Bob questions it." I want to be clear that I am not concerned that anyone thinks the aggregate pay gap isn't real. I'm assuming everyone thinks it's real. I'm concerned that people are badly misinterpreting the meaning of the coefficients on the occupational dummies.

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.

Peter Lewin on Thomas Piketty

I've pointed out several times now that there are a few basic points that seem to commonly trip people up on Piketty. A confusing new critique of Piketty by Peter Lewin illustrates the trouble people often get into with at least a few of these points (HT Bob Murphy). I'd summarize the basic points I have in mind as:

1. r > g did not surprise any economist. It's not a radical result at all, and it's very familiar and well understood. 

2. r > g does not imply that the capital stock as a share of income will go off to infinity. In fact as long as r and g (and s) remain fairly stable it implies an equilibrium capital stock level (Piketty guesses it will level off at around 700% of income). 

3. The capital share of income is not the same thing as "inequality". The capital share informs us about the source of income. Inequality is about it's distribution across the population. On inequality Piketty prefers to use the 10% share and the 1% share of income. 

4. Inequality for Piketty is not directly governed by r > g, it's primarily determined by institutional factors. Piketty does think r > g makes inheritance a more important factor, but the ultimate impact of inheritance on inequality is mediated by institutions.

Lewin's simple framework


I'll focus mainly on Lewin's "simple framework" in the first half of the post, although I have a few thoughts on the rest of the post as well. The framework is a straightforward national income equation, Y = rK + wL. Lewin then decomposes the growth rates of each component of national income to talk about Piketty's thinking on r > g and capital's share of income. This is all fine, until he brings Piketty into the picture. Lewin writes that "Piketty’s project is to show that the laws of capitalism imply that s_K/s_L rises without limit, thus destabilizing the society." In Lewin's post, s_K/s_L is capital's share of national income divided by labor's share of national income. This is where the problems start, of course. With a little bit of algebra we can see that Lewin is getting confused about my point #2 above. It is not Piketty's project to show that capital's share of income increases without limit. Piketty has two "fundamental laws" (a bit of an aggrandizement but the equations themselves are fine):


α = r*β, and
β = s/g


For Piketty, α is the same as Lewin's s_K - it is capital's share of income. s is the savings rate and β is the capital stock divided by income. Therefore, 1- α is going to be equivalent to Lewin's s_L. So Lewin is interested in α/(1-α). Substituting Piketty's second law into his first it's clear that α = rs/g, so α/(1-α) = rs/(g-rs). Piketty never puts it in these terms, of course. He's just concerned with α. But this is still the equilibrium value of the quantity Lewin thinks Piketty is concerned with. Does this "rise without limit"? No, of course not. And Piketty never says it does. In fact there's quite a bit of discussion in the book about the stability of α (and therefore the stability of α/(1-α)). Indeed the stability of α is at the very top of the list of Kaldor's facts, and the subject of quite a bit of recent discussion as labor's share has slipped a little.


Piketty spends a lot of time discussing all these issues and the steady growth of the capital share in the late 20th century (see Chapters 5 and 6), but he never claims that capital is growing without limit because r > g, which doesn't imply anything in particular about the capital share. He says there's been some increase because r has a tendency to grow somewhat with β (see pgs. 220-221), so as β climbs to its equilibrium level you're going to see some increase in r and some increase in the capital share, but only to rs/g, not an "increase without limit" as Lewin has it.


So Lewin seems to run up against my points #1 and #2 in some fashion at least. He goes on to confuse #3 as well. He writes "Piketty reasons that if the earnings of K grow more rapidly than earnings in general, this must imply that K’s share is growing, thus increasing inequality." This is where Lewin decomposes the growth rates. The problem is, the capital share is not the same thing as inequality. The capital share has to do with payments to factors of production, while inequality is a statement about the distribution of those payments across the population.


One of the strangest things about Lewin equating the two is that two of the biggest narratives that come out of Piketty's discussion of inequality directly contradict the conflation of the capital share with inequality. These are: (1.) the rise in the capital holdings of the middle class due to homeownership, and (2.) the critical role that labor income plays in the share of income held by the top 10% and the top 1%. Capital income doesn't dominate labor income until the very top of the income distribution. Piketty calls these earners of labor income the "super-managers". The capital share discussion is in Part II of the book, which deals with capital. The inequality discussion is in Part III of the book, which deals with inequality. They are not the same thing and the fundamental laws of capitalism certainly don't imply anything about inequality, at least not without a great deal of ambiguity.


The rest of the post


The rest of Lewin's post is a mixed bag. I agree with him on some of the points, and I think he agrees with Piketty more than he realizes on some of the others. After his "simple framework" Lewin explains that factor income is not the same as income inequality. Indeed, and Piketty thinks so as well which I point out above. He then criticizes Piketty for excluding human capital. I've had this concern in the past as well (as has David Weil at the AEA meeting). Lewin calls the exclusion "cavalier" which I think is extremely unfair. It makes perfect sense why Piketty would exclude human capital from this discussion. It can't be sold on capital markets, and it can't be inherited so it's not directly relevant to his discussion of physical and financial capital. I get that, but I do think it's an important part of the income distribution story which is why I'd love to hear more about it (plus I'm a labor economist so of course I'm interested).


I find the next few sections of Lewin odd. My impression is that Piketty agrees with Lewin on the rest of the post. From the very beginning of the discussion of the fundamental laws, Piketty talks about how capital is heterogeneous and how different types of capital have different rates of return (pg. 52). Lewin is also wrong when he says "It [K] is meant to be an index of the physical magnitude of the capital of the economy". No, it's not! It's the value of the capital, not a physical quantity!


Finally Lewin criticizes Piketty for allegedly equating the rate of return with the interest rate. He doesn't do this either, of course. On page 52 he writes "the rate of return on capital measures the yield on capital over the course of a year regardless of its legal form (profits, rent, dividends, interest, royalties, capital gains, etc.), expressed as a percentage of the value of capital invested. It is therefore a broader notion than the "rate of profit," and much broader than the "rate of interest," while incorporating both."


So tread carefully when reading Lewin, I think. But it is a nice illustration of some common confusions about Piketty.