Much like last time, the heavy lifting will be done using ordered probit. Unlike last time, I ditched assumptions of normality for a few variables and just went with categorical transformations. Here's an example.
This comes from an OLS regression for income on age and sex with immigrant status and highest degree received as controls. Here's the STATA command:
reg loginc i.degree i.female i.immcat i.age , cluster(year)
The margins plot you see up there isn't a core result of this inquiry, but it does give you a snapshot of how nonlinear variable transformations can possibly be troublesome. Sure, I could include different squared, cubed, log, whatever transformations of age to get useful OLS coefficients, but if you ask me, puzzling through interpretations of third degree polynomial estimates is far more trouble than what I've presented here. I mean, look at that. That plot has lifecycle effects, it captures teenagers still living with their parents, (uncontrolled) gender-based wage premiums, and it shows you the importance of noise. If you look really closely, you can even see a white-space bubble during women's child-bearing years. The point is, after some fiddling around with alternate econometric specifications, I found that an expanded role for indicator variables useful for expository purposes.
Here's another example, this time using an ordered probit with degree attained as the dependent variable. For this, I was curious what effect immigration status and parents' education had on respondents' own educational attainment. The specification is:
oprobit degree i.immcat i.female i.race i.madeg i.padeg i.year age age2 if age >= 24, vce(robust)
I chose 24 as my age breakpoint more or less arbitrarily, but one-year increments up to age 30 made no meaningful difference to the results, so I beg you to grant me some latitude. Anyway, here's the margins of father's degree interacted with immigrant category for [less than high school]:
So, as you'd expect, high school dropouts tend to have kids who are high school dropouts. No surprise there, but note how this relationship weakens for immigrants. It's unlikely for college-educated parents to have HS dropout kids, but it's even less likely for immigrants to exhibit this pattern. This basic pattern holds for HS diploma as well, but there's an inflection in the margins for junior college:
Now, we've got a case where low-educated immigrants tend to have better-educated children. Except for the elite: immigrant doctors don't tend to have (marginally) poorly educated children. They, perhaps predictably, tend to have well-educated kids:
So the basic story these graphs tell supports an established empirical result: immigrants take education more seriously than native-born Americans. I don't necessarily want to get into underlying causes here, but you can pretty easily imagine what some of the lurking variables might be: conscientiousness, selection, conformity, or something similar might be good candidates. These naive, unpartitioned estimates are meant more to show you why I've been using categorical variables and that the contents of the GSS sample I've got are consistent with the established literature. Nothing fancy, people.
To the meat of today's post, then. Here's a question about foreign aid:
oprobit nataid i.immcat, cluster(year)
Ordered Probit | n | = | 31506 | |||
Regression | Wald chi2(3) | = | 258.65 | |||
Prob > chi2 | = | 0.0000 | ||||
Pseudo R2 | = | 0.0084 | ||||
Log Pseudolikelihood | = | -23582.334 | ||||
Foreign Aid [NATAID] |
Coef.
|
Robust
Std. Err.
|
z
|
P>z
| [95 % Conf. Interval] | |
---|---|---|---|---|---|---|
Immigrant Category | ||||||
First-Gen | -0.5415 | 0.0524 | -10.34 | 0.000 | -0.6441 | -0.4389 |
Second-Gen | -0.0498 | 0.0486 | -1.03 | 0.305 | -0.1451 | 0.0454 |
Third-Gen | -0.0047 | 0.0411 | -0.11 | 0.909 | -0.0852 | 0.0759 |
/cut 1 | -1.5952 | 0.0340 | -1.6619 | -1.5286 | ||
/cut 2 | -0.5862 | 0.0298 | -0.6446 | -0.5287 |
This is one of what I call a "Goldilocks" questions. It has three response possibilities: too little, just right, and too much. Unfortunately, there's no saliency measure. My dodge around this is that there's no saliency measure in voting either (I agree that this is a poor dodge for some issues given the possibility of Coasean bargaining, but that's a subject for a follow-up post). Anyway, here are the marginsplots for each outcome, in order:
Too Little
About Right
Too Much
The specific result is (if you ask me) less relevant than the pattern. First-generation immigrants' preferences depart from those of native-born Americans, and second- or third-generation immigrants are statistically indistinguishable from native-born citizens who can trace their ancestry to the 50 states back to at least their grandparents.
Now then, I checked every government-spending policy question available in the GSS and cut it up this way. Most of the questions weren't even this dramatic. For example, on environmental spending, no immigrant category was any different than any other.
For others, the immigrant bias was either in favor of the status quo or in favor of less spending (roads, for example). First-generation immigrants tend to favor more income redistribution, but not second or third.
The one unusual example I found was spending on NASA, which was strong for third generation immigrants. Of course, this largely went away once I introduced controls, meaning that immigrant status was masking other variables (in this instance, education).
Environment (about right)
For others, the immigrant bias was either in favor of the status quo or in favor of less spending (roads, for example). First-generation immigrants tend to favor more income redistribution, but not second or third.
Income Redistribution (too little)
The one unusual example I found was spending on NASA, which was strong for third generation immigrants. Of course, this largely went away once I introduced controls, meaning that immigrant status was masking other variables (in this instance, education).
Another thing I did was to take a few of these questions and look at more finely divided margins. Sure, immigrant status predicts policy positions on a few of these issues, but how does it stack up against education, sex, race, or politics? The short answer is that it's piffling. The long answer is that we can look at the actual plots.
And the long answer is sufficiently long that it deserves its own post, which I'll save for another day. Once again, please stay tuned. I'll try to make it so that you don't have to wait six months between updates.
I really try to live my life void of judgment. It is tough at times, but when I arrive up against somebody who appears to wipe me incorrect I ask myself some questions.Nice post
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