Incarceration -> Class

The reason that mass incarceration is so terrible to begin with, of course, is that it grinds up so many lives. Ex-convicts have trouble finding work, and if they can find work, they take home lower wages, and see lower wage growth. This is in addition to the financial strain that is put on families when a family member is locked away, and in addition to the strain on the health and emotional and psychological well-being of both the convict and the convict’s family. There is no doubt about this; it is both well-studied, and painfully obvious.

Recently, People’s Policy Project released my report on mass incarceration, which made the strong claim that it is class, and not race, that is by far the dominant factor in determining your chances of being locked up. However, because I used current markers of class, such as current income level, and a measure of incarceration which asks whether somebody has been locked up in the past, it is perfectly reasonable to wonder if my results are confounded by the fact that incarceration itself has an impact on income, etc.:

The short answer is that, because I used household income at adolescence as a strong control in my analysis, with the measure of incarceration starting at age 18, this is not a problem. I will now demonstrate this.

Let’s start with the assumption that prison reduces income by 20%. Note that the research here demonstrates a broad range (some of it even shows no change in income), but I think that this is a reasonable assumption to make, given the body of evidence. However, for several reasons, my guess is that prison reduces income more for lower class people than for higher class people, but we will leave that aside for now. The only other factor that we will consider is education level, and we will reduce this to a dummy variable which says whether or not somebody has a high school diploma, since this is mostly determined before the age of 18 (i.e. when we start measuring incarceration.)

The analysis presented in the paper breaks income level into quintiles. Here we will treat income as a continuous variable, in order to more accurately reflect the effects of modifying it. Because I expect that incarceration rates won’t follow a linear relationship to dollar amount of income (i.e. the proportional difference in probabilities between $20k income and $100K income will be less than that between $100k and $200k), we will log transform the income variable, after it has been adjusted by household size.

Our first model will look only at race, sex, and income as it is reported in the latest wave of the Add Health survey, with no adjustment. We will see how these variables affect the probability of somebody having served more than a year in prison. In other words, this is what it would look like if we assume that income is the only aspect of class, and that incarceration has no impact on income. It is just for comparison purposes.

Our second model will be the same, except we will add 0.25 to log income if somebody has been to prison for more than a year. This is the same as saying that somebody’s income would have been 20% higher, had they not gone to prison.

Our third and fourth models will be the same as the first two, except we will now add education level, at the high school threshold, since that is unlikely to be confounded by adult incarceration.

Our fifth and sixth models will be the same as models 3 and 4, but now we will add a parental income variable, broken into quintiles, in order to demonstrate how that variable regulates our model.

Below is a comparison of the models. Because interpreting log odd coefficients can be a headache, particularly when one of the variables itself is log transformed, I have listed probabilities for selected combinations of race and class for males below the regression table. All of the variables are statistically significant, except for “Parental income 2.”

There is a lot going on here. First, I’ll note again that it is better to get more specific with your definition of class. The incarceration rates for both blacks and whites making $15K/year presented in both models 1 and 2 seem unrealistically low to me. The log scale could be throwing us off (a square root scale may be more accurate at the lower end), but we see that, once we add education into the mix in models 3 and 4, we start to see more realistic numbers. (Of course we don’t want to add too many variables, especially with a logistic regression, as things can start to get confused, which is yet another reason to prefer a single composite variable.)

Still, we can learn something from our first two models. Going from the first model to the second model we see the lower class incarceration rates go down, the higher class incarceration rates go up, and the racial gap within both class levels widen. All of this would indicate that our first model is being confounded, and that we’re actually measuring some of the effect of incarceration on class, rather than the other way around.

Models 3 and 4 are an improvement, because they include education. Specifying whether or not someone has a high school degree tells us whether or not they are closer to their peak earning years; it may tell us something about what a judge would factor in during sentencing, or how a police officer would judge a situation; it may correct for situations where, for example, somebody is still in college, or temporarily between jobs, etc. Although the pattern is slightly different from when we moved from model 1 to 2, the effects are largely the same in moving from 3 to 4: the effect of class shrinks, the effect of race grows stronger once we adjust for income lost due to imprisonment.

This is all a preamble to what is happening in models 5 and 6, which is where we factor in parental income. What I would want people to focus on are the differences in probabilities that the regression assigns to blacks making $60k/year, but with varying levels of parental income. The really interesting thing here is that as the total class level goes up, as driven entirely by changes in parental income, the probability of incarceration also goes up. This makes complete sense, in the context of why we are including the parental income variable in the first place.

$60k/year translates to somewhere in the middle of the 4th quintile of current income (2008 dollars, household-size adjusted.) All else equal, we would expect parental income to also be in the 4th quintile. If it’s not, then something happened to cause income mobility in one direction or another, and that “something” could be any number of things, but one thing that it could be is incarceration. Thus, somebody in the 4th income quintile whose parents were in the 5th quintile is more likely to have been incarcerated than somebody who is in the 4th income quintile whose parents were also in that quintile. At the same time, this difference isn’t too dramatic (less than 1 percentage point), because there are a lot of reasons why somebody can fall down the social ladder, and incarceration is only one of many.

Following from this, it also makes perfect sense why somebody higher on the social ladder than their parents is less like to have been incarcerated, as seen in the example of the black person from the 4th current quintile having a lower chance of incarceration if his parents were in the 3rd income quintile; he has climbed the social ladder, and so more probably has not been held back by incarceration.

This adjustment mechanism does not always seem to work so well. For example, we can tell by looking at the coefficients from model 5 that somebody in the 1st current income quintile will perversely show a lower chance of incarceration if their parents were in the 3rd quintile instead of the 2nd or 1st. In practice, this is not a problem, since 1) the vast majority of people in the first income quintile had parents below the third income quintile and 2) those in the first quintile whose parents were in the third quintile have a much lower chance of ending up in prison, at least according to this weighted sample. Here are the percentages:

All of this says that including the parental income variable in our measure works exactly how it is intended to: first and foremost, as a control for the fact that the rest of our variables are measured post-incarceration.

For a lot of reasons, which I won’t get into at this point, because this is already running long, I think that this is a far better control than crudely assuming that incarceration leads to a 20% loss of income across the board. Tellingly, we see that in model 6, where we do the crude income adjustment, the effect is the opposite of what we should expect; we should expect the income adjustment to reduce the class effect, but here it increases it, by raising the probability at the lower end, and lowering it at the higher end. This is because we have already made this adjustment by including parental income in the first place, and all we are doing is bringing incarcerated income higher, and so closer to what we would expect it to be given parental income. Thus the model is going to see less of a discrepancy between parental income and offspring income, in the case where offspring income has fallen exactly due to being incarcerated.

I think that the parental income control is even better than taking a pre-incarceration measure of class, for, again, a lot of reasons. Say that somebody is first incarcerated at 19 years old. Unless they live with their parents, they are almost certainly going to have low household income, because income is deeply correlated with age. So you are not going to have much of a range to pick from, and you are not going to be able to predict what it would have looked like 20 years down the line. With parental income, you can predict this, though imperfectly, since offspring can climb up or down the social ladder for many different reasons, though tend to stay close to where they started from. Thus, in addition to correcting for the incarceration -> class confounder, parental income sharpens the measurement of class itself.

With all of that said, I would not try to argue that I have definitely eliminated all traces of incarceration -> class from my main analysis, though I have done my best to do so. I think that I have offered a more careful and accurate measurement of class -> incarceration than I have been able to find elsewhere. If the true relationship is meaningfully different from I what have presented, I would be very surprised, for analytic reasons which I hope I have mostly made clear here.