Thursday, April 23, 2015

David Henderson on Barbara Bergmann and the wage gap

I wanted to highlight this post by David Henderson on the late Barbara Bergmann, much of which is a discussion of her writing on the wage gap. He promises more to come.

One of the things I like about this post is that it shows how both sides have to be careful with wage regression interpretations when talking about the wage gap. David's criticisms of Barbara are very much along the same lines as my criticisms of guys like Mark Perry. (I am not deeply knowledgeable about what she's written on it, so to a certain extent I'm taking David's word on it but it's a very common way of talking about things).

While I'm posting more on her, I'll also point out that Taylor and Francis is providing free access to a special issue of Feminist Economics on Barbara Bergmann this month. So download those pdfs before it's too late!

Tuesday, April 7, 2015

Does anybody have experience with a distributed lag model for panel data?

Does anybody have experience with a distributed lag model for a panel dataset? I'm getting this odd result where I'm trying a bunch of different lag lengths and no matter what I run the two longest lags have much bigger coefficients than the rest. So when I run with six lags, five and six have big coefficients but when I run with sixteen lags fifteen and sixteen do. I feel like this has to indicate something about the data structure and the model - it can't be real to always show that no matter what the lag length. I'm just not sure what it indicates. If it matters - I'm looking at size of apprenticeship programs in an unbalanced panel with lags of the unemployment rate. No lags of the dependent variable.

Data adjustments - not a conspiracy, just a part of empirical work in economics

I got an email today announcing an Urban seminar, and the abstract reminded me of some of the Piketty debates around Bob Murphy and Phil Magness's paper and subsequent discussions. Here it is:
"ABSTRACT: The 2014 Current Population Survey, Annual Social and Economic Supplement (CPS-ASEC) introduced major changes to the income questions. The questions were introduced in a split-sample design—with 3/8 of the sample asked the new questions and 5/8 asked the traditional questions. Census Bureau analysis of the 3/8 and 5/8 samples finds large increases in retirement, disability, and asset income and modest increases in Social Security and public assistance benefits under the new questions. However, despite the additional income, poverty rates are higher for children and the elderly in the sample asked the new questions. In this brownbag, we discuss the changes to the survey, the effects of the changes on retirement and other income, and describe how compositional differences among families with children in the 3/8 and 5/8 samples may explain the unexpectedly higher poverty rates in the 3/8 sample. The discussion has practical as well as theoretical importance, as researchers will have a choice of datasets to choose from when analyzing the 2014 CPS-ASEC data—the 3/8 sample weighted to national totals, the 5/8 sample weighted to national totals, a combined sample, and possibly also an additional file prepared by the Census Bureau that imputes certain income data to the 5/8 sample based on responses in the 3/8 sample."

The CPS is typically not used to address inequality for all sorts of reasons, including the nature of the questions, coverage, and top-coding. But it still has income questions, and note that a recent redesign changes asset income reports. Of course if we were to use the CPS to think about some of Piketty's research questions, this change would be important. Moreover, if  you wanted to use a consistent series from the CPS you would have to adjust the data to either move down the newer half of the series, or (probably preferably if this redesign represents an improvement) moving up the older half of the series. They do split samples discussed in the abstract so that you can understand the sort of adjustment that might be appropriate.

This is what Piketty is doing too when he harmonizes several of the wealth inequality series, and he uses years when the data series overlap to develop the adjustment factors. The figure Murphy and Magness like to call the "Frankenstein graph" suggests that certain blocks of the series come from different datasets, but in reality Piketty is typically taking data from several datasets to provide a harmonized estimate (for example, combining the Kopczuk and Saez data and the SCF data). This is how you'd want to merge several datasets, and it's generally not "pivoting" between datasets or "overstating" them as Murphy and Magness put it.

Anyone can criticize these sorts of data decisions, but it's a normal part of empirical work. If your criticism is just that the data decisions result in the conclusion that Piketty draws, that's not a very reasonable criticism. It's entirely circular: Piketty's conclusions are bad because his data decisions are bad. How do  you know his data decisions are bad? Because they correspond to his conclusions!

Saturday, March 14, 2015

Fairness and policy

In the last sentence of the last post I alluded to the fact that things get more complicated when we move from caring about inequality to doing something about inequality. You can obviously never just use "fairness" to justify a policy solution not just because ends don't justify means (you have to know something about the ethics of the solution) but also because you have to demonstrate that there aren't other attendant ends that you don't want. A simple example is communism. We can dispute communism because the ends don't justify the means - the goal of equality does not justify violating property rights. But we can also dispute it on the grounds that in addition to making everyone equal it makes them miserable and poorer than they otherwise would be.

This is very much a "no duh" point. A sense of fairness doesn't in and of itself tell you how to respond - certainly not in the case of policy and likely not in your own capacity either. But it reminds me of what I think is a more interesting point from Rawls on the limits of "fairness" as a moral framework and the real utility of fairness as a way of approaching political questions and really questions of social organization generally. It is an old point about tolerance and liberalism, but it draws the connection between tolerance and Rawlsian fairness. This is from "Justice as Fairness: Political not Metaphysical":

Friday, March 13, 2015

Why inequality matters

The last twelve months have really been The Year of Inequality. It started with the English translation of Piketty's book and it has taken over the political agenda. Over the last year I've regularly heard too odd critiques of the preoccupation with inequality:

1. Inequality doesn't matter, poverty does
2. Inequality only matters if it comes through corruption, and in that case it's just a symptom

Obviously both have a kernel of truth. Poverty matters a lot. We have been studying the "wealth of nations" for 250 years because poverty is critically important. We also rarely believe that it would be unfair for everyone to earn the same income. That point goes back to Aristotle at least. What matters is illegitimate inequality, and this is the sentiment that the second objection tries to piggy-back on.

However, caring about poverty and corruption does not eliminate the case for concern about inequality that does not arise from corruption in a relatively wealthy society (e.g., most of the inequality Piketty writes about). We care about inequality because (1.) of our sense of fairness, and (2.) the fact that opportunities or capacities are unevenly distributed independent of any additional corruption that may exacerbate inequality further. As I write this it seems like a basic point. It feels a little silly to even make it. But I've seen both of the above objections with such frequency that I feel like I have to.

So does dealing with this sort of inequality violate Aristotle's principle that the worst form of inequality is making unequal things equal (not that we are obligated to care of course)? It may, but it may not. There are two big problems with Aristotle's principle as I see it (I'm almost certainly reinventing the wheel here - I didn't take much philosophy so you can fill in the details if I am). First, I don't see why any ethical significance attaches to natural and/or random endowments of capacity or opportunity (if random shocks are a random draw by Nature, these can be considered together). I should hope this was obvious from about the time the words left Aristotle's mouth. In fact I should hope a couple sentences down he notes this and it just doesn't get quoted as much.

The second reason why applications of Aristotle's principle are tricky is particularly relevant to Piketty and a capitalist economy: these systems are recursive and intergenerational, so one period's outcomes are the next period's opportunities. That's really the whole point of capital of course - it endures through periods of time and is productive in future periods. How do we think about Aristotle's principle in a recursive system? Is redistributing capital "making unequal things equal" or is failing to redistribute capital "making equal things unequal"? This is tricky enough in one generation because you have to distinguish between effort and luck of birth (assuming you agree with my first point that no ethical significance attaches to natural or random endowments of capacity or opportunity and therefore that redistribution in favor of those born into very unlucky circumstances is permissible). It gets very hard indeed when we move beyond one generation, because the choices of parents become the endowments of children.

Poverty obviously matters but a basic sense of fairness justifies caring about this even in a rich, uncorrupt society.

What we do about it of course compounds the difficulties for a number of well understood reasons having to do with behavioral responses.

Friday, February 27, 2015

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.

Thursday, February 26, 2015

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.

Wednesday, February 25, 2015

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.

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.