Mobility: Location (Part 1)

Across a number of studies, Raj Chetty Raj Chetty. In Wikipedia, Nathaniel Hendren, and their co-authors linked millions of tax records between parents and their children. They used this to produce compelling evidence that where you grow up has significant causal effects on your earnings, in expectation. This page essentially just summarizes that work, with an emphasis on income and geography. I encourage you to read the actual papers for plenty of additional fascinating information such as how race and sex affects income and how they relate to geography.

Finally, the reason we using correlational evidence here is simply that the causal evidence is so scant. For instance, the largest study I know of examining the causal effect of childhood geography on adulthood income is this one The effects of exposure to better neighborhoods on children: New evidence from the moving to opportunity experiment and its standard errors are very large.

Establishing Correlation

Chetty et al started publishing papers on geographic income mobility using parent-child-linked tax data way back in 2014 Where is the land of opportunity?. The analysis was relatively simple and the results were interesting, but there wasn't any compelling evidence of causality.

Still, in order to best appreciate and understand the later results, it's useful to start with where it began, since much of the analysis is pretty beyond Stats 101 and is used consistently in following papers.

Let's get started.

The traditional approach of measuring income mobility is to consider the correlation between parent and child income, typically after applying a logarithmic transformation on each. Chetty et al prefer looking at the percentile rank ("rank") in the distribution that parents and their children occupy for two reasons:

1. It's robust against outliers: both very rich and very poor (the log(0) is -infinity).
2. It allows for non-parametric analysis, which means the framework can be applied with far fewer assumptions.

In particular, they can first find the rank of all the parents and then compute the mean rank of the children. This allows them to abandon the fairly strong assumptions of linear regression (linearity, Gaussian error, etc).

I'll let them describe their sample

and their income definition:

What do they find when they run their rank (percentile) analysis? This

They perform a number of robustness checks, but I'll only include a couple here - the ones I most appreciate.

First, they consider the child's age when their income is measured. The association between parent income and child income increases through a child's 20s (as they leave school) but stops changing in the early 30s, and might even start to decline a bit after that.

They also consider measuring parent income over less or more than the five years in their primary analysis. They find going from 1 year to 5 years increases the rank-rank slope by about 6% and that going from 5 years to 17 years increases it by another 3%. They find it matters even less for measuring child income, with the slope increasing just 2% when measuring over 6 years rather than 2.

Alright, now let's introduce geography.

The US is partitioned into ~3000 counties, which are grouped into ~740 commuting zones. This paper focuses on CZs, but I promise we'll get to counties (and even neighborhoods!) in a moment. They assign children to CZs via the address on their tax returns.

So, they repeat the above analysis within each CZ, reproducing the same general graphs:

They then consider the children of parents in the 25th percentile and make a map of those children's average adulthood rank:

Again, many robustness checks are done - the one I think is most important is they try dividing the parent and child incomes by the cost of living of where they are living. The results are essentially unchanged (r~0.99), largely because few children live in CZs that are significantly more/less expensive than where they grew up.

Causal Considerations

As we all know, correlation doesn't imply causation. We also know that it is notoriously difficult to establish causation by controlling for confounders Stop Confounding Yourself! Stop Confounding Yourself! More Confounders.

After the first paper paper, Chetty, Hendren, and their co-authors wrote several different papers that attempted to link the correlations they established in 2014 with causation The impacts of neighborhoods on intergenerational mobility I: Childhood exposure effects The impacts of neighborhoods on intergenerational mobility II: County-level estimates The opportunity atlas: Mapping the childhood roots of social mobility.

In my opinion, they succeeded.

Their general strategy is to consider siblings, who, by virtue of their different ages, spend different numbers of years in different places. Then, they assume the effect of living in a place scales linearly with the time spent there and sums over your childhood. Finally, they compare these correlational (maybe causal) estimates with the naive correlational estimates discussed above and find roughly 60% of the naive effects persists.

They give various reasons to support the idea that these new estimates are, in fact, causal, and I discuss later reasons why traditional confounders are much less of an issue than it typically the case in correlational studies.

Establishing Causation: Movers

The authors start in The impacts of neighborhoods on intergenerational mobility I: Childhood exposure effects. They start out with analysis very similar to first study Where is the land of opportunity?: they consider millions of families whose children grew up in different places. However, this time they make two notable changes:

1. They restrict the sample to CZs with at least 250,000 people (80% of families).
2. They divide the sample into two sub-samples: "permanent residents", who remain in the same CZ between 1996 and 2012, and "movers", who do not.

First, the repeat the analysis from the original paper using the permanent residents and, unsurprisingly, find very similar results.

Next, they consider the set of movers who moved only once and who moved at least 100 miles. They partition that dataset by parent income decile, birth cohort (year), and original CZ. They use the analysis of permanent residents to assign a kind of "naive goodness" score to each CZ. Finally, they assume the effect of moving out of the original CZ is equal to some parameter that varies with age times the change in the naive goodness of the CZ.

Ultimately, they find that for 13-year-olds, 62% of the difference in "naive goodness" remains in their average ranks. That is, this quasi-experimental approach suggests at least 38% of the naive approach was due to confounders.

They then compare this value at different ages, finding

Note: the fact the slope goes to 0 after the age of 23 makes sense since children are generally not living with their parents by that point. The fact the estimated coefficient isn't 0 by this point reflects the confounding effects: something (X) causes parents to move to better (worse) CZs after their child leaves the house and also appears to cause the children to have better (worse) outcomes.

Finally, we get to family fixed effects (FEs). The authors reproduce the analysis of movers using family FEs. Then, for good measure, they add controls for changes in marital status and parental income around the time of the move:

In short, controlling for these confounders didn't reduce the (hopefully) causal estimates at all (the slope). Meanwhile, the evidence of confounding (X above) has disappeared.

The authors also consider a number of other tests to help establish causality. We'll come back to some additional evidence of causation in a moment, but the above is the main argument. See the paper The impacts of neighborhoods on intergenerational mobility I: Childhood exposure effects for details.

Confounders

Alright, now that we've discussed the results, I just want to briefly discuss why I think this establishes causation and is not merely correlation despite the fact that it is generally quite challenging to turn the latter into the former.

First it's important to establish that you don't have to "control for everything" to establish causation. Once you've ruled out reverse-causation (which is impossible here because child income cannot affect past parent income), you just have to control for all confounders - that is you have to control for things that can causally affect both the dependent and independent variable.

So the question we have to answer is whether any confounders remain within a pair of siblings that cause both one sibling to earn more and also that sibling to spend more of their childhood in a better (or worse) area.

First, note that children don't choose where they live - their parents do - so differences between the children are, a priori, unlikely to cause them to live different places. This minimizes concern over a wide class of confounders that might otherwise be a problem. For instance, if we are checking the impact of smoking marijuana, sibling FEs are quite imperfect, since something about each sibling (e.g. rebelliousness) likely causes both marijuana smoking and whatever outcome you're concerned about. Such concerns are much less likely here.

Second, obviously, siblings (by definition) share the same "shared environment" and (almost by definition) share half the same genes - so we automatically control for these huge factors.

The obvious concern is the other half of genes, but I contend that this shouldn't matter, but the argument is a little nuanced. First, realize that the half of genetic variance that isn't controlled represents the variance the comes from the completely random selection of chromosomes when creating eggs and sperm. Because this process is random, we can rule out X → genes → [neighborhood, outcome] as a confounder, a priori.

This leaves only the issue of genes -> [neighborhood, outcome]. I don't take this seriously, because it seems very unlikely to me that a child's genes affect where their parents choose to live.

Indeed, this last point makes me skeptical of confounders in general: what mysterious X can affect both where a child's parents choose to live and also how much that child earns in their early 30s?

Moreover, note that when we added family FEs to the mover model, the causal effect sizes barely dropped at all: if controlling for shared environment and half of genes barely drops the effect sizes, what confounder on Earth could possibly cause a significant drop??

That being said, despite all the above, there are some potential confounders we should probably mention.

One possible confounder is birth order effects, a fairly common topic in the online spaces I frequent Age Gaps and Birth Order Effects. Indeed, based on the largest study I could find, there does appear to be an effect of birth order on earnings early in one's career, but it largely disappears 10 years in Bertoni, which is roughly when it's measured in the above studies.

Moreover, birth order effects will only confound our estimates of the causal impact of location to the extent that it causes both higher earnings in the older sibling and the extent to which it causes parents to move somewhere better or worse. As mentioned, the evidence suggests the former effect is small and I'd be shocked if the latter effect wasn't also small. Overall, then, I expect any confounding from birth order to be negligible.

But the biggest confounders are probably Adverse Childhood Experiences Adverse childhood experiences. In Wikipedia. Maybe, after one sibling has left the home, the parents divorce and, no longer having dual incomes, each have to move to a worse neighborhood. Meanwhile the stress from the divorce causes the kid to do poorly in school. Or maybe the ACE is a parent losing a job or getting cancer, etc. There are, likewise, obvious positive analogs.

As mentioned above, the authors do consider changes in marital status and parental income and found the (presumed) causal effects of moving remained just as strong.

Given this and the other general arguments I've presented above, I think that it is pretty unlikely that such "shocks" noticeably confound the geographic causal estimates.

And, at the end of the day, I think the most compelling evidence of causality is that adding family FEs to the "movers" model didn't shrink causal effects at all. To reiterate one last time: if controlling for all of shared environment and half of genes didn't shrink the causal estimates at all, what on Earth would!?

Robustness ("But What About?")

• Cost of Living - TODO
• TODO

Smaller Geographies

Alright, so hopefully you buy the causal nature of the estimates by this point for large moves (100+ miles) between commuting zones. The next step is to extend the results to smaller geographic. Chetty et al do this in two steps: to counties The impacts of neighborhoods on intergenerational mobility II: County-level estimates and then to census tracts The opportunity atlas: Mapping the childhood roots of social mobility.

TODO: counties

TODO: census tracts

Conclusions

TODO The Opportunity Atlas. Opportunity Insights Data Library: Publicly available data we've produced and replication code