The war against taxes (and the unmarried)
The American Enterprise Institute, conservative think-tank, is releasing a report today. It’s called For richer, for poorer: How family structures economic success in America, and there is also an event in DC today from 9:30am til 12:15pm that will be livestreamed. The report takes a look at statistics for various races and income levels at how marriage is associated with increased hours works and income, for men especially.
It uses a technique called the “fixed-effects model,” and since I’d never studied that I took a look at it on the wikipedia page, and in this worked-out example on Josh Blumenstock’s webpage of massage prices in various cities, and in this example, on Richard William’s webpage, where it’s also a logit model, for girls in and out of poverty.
The critical thing to know about fixed effects models is that we need more than one snapshot of an object of interest – in this case a person who is or isn’t married – in order to use that person as a control against themselves. So in 1990 Person A is 18 and unmarried, but in 2000 he is 28 and married, and makes way more money. Similarly, in 1990 Person B is 18 and unmarried, but in 2000 he is 28 and still unmarried, and makes more money but not quite as much more money as Person A.
The AEI report cannot claim causality – and even notes as much on page 8 of their report – so instead they talk about a bunch of “suggested causal relationships” between marriage and income. But really what they are seeing is that, as men get more hours at work, they also tend to get married. Not sure why the married thing would cause the hours, though. As women get married, they tend to work fewer hours. I’m guessing this is because pregnancy causes both.
The AEI report concludes, rightly, that people who get married, and come from homes where there were married parents, make more money. But that doesn’t mean we can “prescribe” marriage to a population and expect to see that effect. Causality is a bitch.
On the other hand, that’s not what the AEI says we should do. Instead, the AEI is recommending (what else?) tax breaks to encourage people to get married. Most bizarre of their suggestions, at least to me, is to expand tax benefits for single, childless adults to “increase their marriageability.” What? Isn’t that also an incentive to stay single and childless?
What I’m worried about is that this report will be cleverly marketed, using the phrase “fixed effects,” to make it seem like they have indeed proven “mathematically” that individuals, yet again, are to be blamed for the structural failure of our nation’s work problems, and if they would only get married already we’d all be ok and have great jobs. All problems will be solved by tax breaks.
mathbabe 
Thanks for using logic, reason and some math skills to expose this hypocrisy.
Do they really propose tax cuts to single people to encourage marriage? Wow!
If they are worried about marriageability, they should give basic income to poor people. Those who would benefit from tax cuts are rich enough not to need them.
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“The AEI report concludes, rightly, that people who get married, and come from homes where there were married parents, make more money.”
There *couldn’t* be any selection bias into the married population. Nope. None at all…
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I got a laugh imagining the report suggesting lower taxes for married people as an incentive for marriage and lower taxes for singles as an incentive for marriage. Of course, it makes sense when you start from the assumption that lower taxes are good for everything in all cases.
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“I’m guessing this is because pregnancy causes both.”
Hahahaha!
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I haven’t read the paper [ducks], but this sounds more like repeated measures than fixed effects?
(and the pregnancy line cracked me up as well…)
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I haven’t studied that either! Where is it used?
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Or does “repeated measures” refer to the way data is collected and “fixed effects” to the way it is analyzed?
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It’s hard to tell from their paper whether they used fixed effects properly. It’s meant to control for unobservable, constant differences at individual or group levels in longitudinal data.
It’s been a few years since I did any of this, but you might think of individual-level fixed effects as creating a dummy for each person in the data that follows them across years.
I normally see fixed effects used geographically (i.e. states). A dummy variable for each state to capture unobserved differences over time for individuals living in each state – due to any number of factors specific to each state.
It’s hard to tell how they’re applying fixed effects as opposed to just dummy variables. Of course, none of this would get at all kinds of selection biases underlying the likelihood of getting married. There is all kinds of sorting going on between men/women along family background, socioeconomic status, ability, employment, education, etc.
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Fixed effects are one of the most confusing terms in stats (e.g., http://andrewgelman.com/2005/01/25/why_i_dont_use/). When I’ve used them, it’s sensu Gelman #3 (or when I’ve adequately sampled each of the states for a given effect), though I agree with Gelman’s paper (linked in the post)–just abandon them & go with random effects.
Repeated measures design is what one typically uses when you follow particular individuals through time (what Heritage study did, though I didn’t read the paper…). In contrast, one could simply contrast 28 year-olds who are married and unmarried. Obviously, repeated measures, when you can do it (following subjects through time isn’t always possible), can be quite powerful, as it allows you to factor out individual differences (the Wikipeda page on repeated measures design is pretty good).
Re-reading your explanation, what they did really doesn’t sound like a fixed vs. random effects issue at all, but a repeated measures design.
I think someone at Heritage is just playing with big, important sounding words….
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To be fair I didn’t see their code! And to be even more fair they didn’t explain it precisely.
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“Most bizarre of their suggestions, at least to me, is to expand tax benefits for single, childless adults to “increase their marriageability.” What? Isn’t that also an incentive to stay single and childless?”
Sure, it’s an economic incentive. But the AEI does not necessarily subscribe to the limited psychology of economists. (I dunno, I hardly pay any attention to them.) It is possible that the causal effects of hours and marriage runs, at least in part, from hours to marriage via increased income. Having grown up in a conservative environment, I know that people talked about making enough money to get married. The AEI claim is consistent with that norm.
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Oh, yeah. Tax breaks for married people plus tax breaks for singles without children amounts to a tax hit for singles with children.
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This paper gets most of my concerns. He suggests that a good chunk of the differences in criminality between married & unmarried men is due to selection.
He also calls into question the use of fixed-effects of this type for causal analysis and suggests that fixed effects may drastically overstate the causal effect of marriage on subsequent outcomes. He is looking at marriage & criminality:
“In general, fixed-effects type estimators can only provide an unbiased estimate of the
causal effect of some treatment [marriage] on individual criminality if one can truly believe that the reason individuals obtain the [marriage] at a given point in time is because an opportunity for obtaining [marriage] randomly arose at a given point in time that was not available previously.”
And
“For men, the timing of marriage may not just reflect when they met the right woman, but is a byproduct of a broader decision by these individuals that it is ‘‘time to grow up.’’ This decision to grow-up may cause these individuals not only to move toward building stable family lives through marriage, but also move away from committing crimes. If this scenario describes even a modest fraction of marriages, a fixed-effects estimator will overstate the impact of the actual state of being married on criminality because it conflates any true direct effect of marriage on crime with the broader effects of whatever it was that prompted the individual’s decision to grow up.”
Click to access fixedeffects_JQCreprint.pdf
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100% approve of this rant. Very similar to the paper a month or so ago that found unmarried women to be more likely victims of abuse by their partners, and I think then recommended that those women get married (presumably to their abusive partners).
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With a tiny bit of rewriting, this would make an important NYT opinion piece. It’s critical for someone with your skillset to officially call BS on this.
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lol am all in favor of tax breaks paid for by the rich but of course thats one of the great classic switcheroos along with “tax cuts” being focused on the rich via bush…. another one of the great marketing/ propaganda events of all time….
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Not sure why the hostility towards fixed effects models. From my perspective (quantitative sociologists) they are much better at showing causality than OLS models or cross-sectional data. There is some debate as to whether to use fixed effects models or random-effects models adjusted to behave like fixed effects models, but I think everyone agrees that they are better than your run-of-the-mill regression. Given the data they have, I’d argue that fixed effects are actually the right model to use.
Now having glanced at their report, I do think they can argue for causality in Table 2, since
Now having glanced over their report, I think they can argue for a causal effect in table 2, although it would be much more convincing if they lagged marriage and explained later earnings changes. BUT it is worth pointing out that there is plenty of research in gender studies indicating that men tend to get a marriage premium while women get a marriage penalty. This is arguably one of the dominant factors in maintaining the gender gap. And that is what this AEI report is showing, but they are claiming that since the premium is higher than the penalty, marriage is a net benefit for families and we should ignore any effects on the gender wage gap.
Just to explain fixed effects further—for those interested. Fixed effects are basically estimating the effects of changes on changes. So if you are measuring the relationship between income and health, an FE model would test how a $10k increase in income affected a 5% increase in some measure of health. How is this different from a “random effects” model? Well a random effects model would be explaining the absolute level, so you would be explaining not just the change but also the baseline level. And as one might imagine there are all sorts of characteristics that might affect both—background, education, etc. So a fixed effects model reduces the set of confounding variables, and provides a more direct test of the effects of changes. In fact, you get the same coefficients if you run a fixed effects model and a regular OLS with dummy terms for every individual.
There’s more complexity, but that’s the basic idea. Also worth pointing out is that the name “fixed effects” is unnecessarily confusing and refers to assumptions about the error term.
Also, there’s a good post on this report on Phil Cohen’s excellent “Family Inequality” blog.
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