Testing the robustness of the NHB migration result

Never say "beyond reasonable doubt". No sooner had I made this boast than Panu Pelkonen called my bluff on twitter:












This could indeed be a concern. For example, we show that polygenic scores for educational attainment  are higher for those leaving coalmining areas than those staying in them. But what if that is only true in those clustered areas (which represent UKBiobank Assessment centres, by the way - not all of them are necessarily big cities)?

One way to address this critique is to check whether the result varies much within the sample. This isn't perfect, because there still could be variation beyond the sample. (To understand this, consider another variable – age. Almost all UK Biobank respondents are over 40. Our results hold across all the age groups within the sample: for example, among 40-50 year olds, 50-60 year olds, and so on. But that doesn't prove the result would hold for 20-30 year olds. Maybe mining areas have started to attract talent back among the younger generation – I doubt it, but it is not a question our data can answer.)

Nevertheless, if we see the result is pretty robust wherever we look within our sample, that should give us some comfort that it is unlikely to be different outside the sample.

So, this afternoon I took a look. I reran the basic analysis for each separate UKBiobank assessment centre. I discarded any assessment centres which had no people living in coalmining areas (or everybody living in a coalmining area). Then, I looked among people born in a coalmining area, and living near that centre. Within this group, I looked at the average polygenic score for educational attainment (PSEA) among people currently living in a coalmining area, and currently living outside a coalmining area. And I took the difference of the two. Our overall result was that PSEA was higher among those not living in a coalmining area ("movers away"). Would this hold across all the different assessment centres?

Here's the answer:

Difference in PSEA between "stayers" (still living in a coalmining area) and "leavers" (born in a coalmining area but not living in one now). Lines show 95% confidence intervals (standard errors clustered by census geography)

Basically, yes. Stayers have lower PSEA than leavers for almost all the 17 centres I looked at, and significantly so for most of them. There is a single assessment centre where stayers have higher PSEA than leavers. This comprises just 361 people; I would guess that near this centre, the ex-coalmining area is richer than non-coalmining areas. Overall, then, the result seems quite geographically robust.