When Eva Zschirnt and I were working on the meta-analysis on ethnic discrimination in hiring, I also run one of these tests for publication bias (included in the supplementary material S12). According to the test, there are a couple of studies “missing”, and we left this as a puzzle. Here’s what I wrote at the time: “Given that studies report discrimination against minority groups rather consistently, we suspect that a study finding no difference between the minority and majority population, or even one that indicates positive discrimination in favour of the minority groups would actually be easier to publish.” (emphasis in original).
We were actually quite confident not to have missed many studies. One way is to dismiss the assumptions between the tests for publication bias. Perhaps a soft target, but who are we to say that there are no missing studies?
Here’s another explanation that didn’t occur to me at the time, and nobody we asked about it explicitly came up with it. It’s just a guess, and will remain one. David Neumark has suggested a correction for what he calls the “Heckman critique” in 2012. We were aware of this, but I did not connect the dots until reading David Neumark and Judith Rich‘s 2016 NBER working paper where they apply this correction to 9 existing correspondent tests. They find that the level of discrimination is often over-estimated without the correction: “For the labor market studies, in contrast, the evidence is less robust; in about half of cases covered in these studies, the estimated effect of discrimination either falls to near zero or becomes statistically insignificant.”
This means that the “Heckman critique” seems justified, and at least in the labour market some of the field experiments seem to overstate the degree of discrimination. Assuming that this is not unique to the papers they could re-examine, the distribution of effect sizes in the meta-analysis would be a bit different and include more studies towards the no discrimination end. I can imagine that in this case, the test for publication bias would no longer suggest “missing” studies. Put different, these “missing” studies were not missing, but reported biased estimates.
The unfortunate bit is that we cannot find out, because the correction provided by David Neumark has data requirements not all existing studies can meet. But at least I have a potential explanation to that puzzle: bias of a different kind than publication bias and the so-called file-drawer problem.
Neumark, D. (2012). ‘Detecting discrimination in audit and correspondence studies’, Journal of Human Resources, 47(4), pp. 1128-157
Neumark, David, and Judith Rich. 2016. “Do Field Experiments on Labor and Housing Markets Overstate Discrimination? Re-Examination of the Evidence.” NBER Working Papers w22278 (May). http://www.nber.org/papers/w22278.pdf.
Zschirnt, Eva, and Didier Ruedin. 2016. “Ethnic Discrimination in Hiring Decisions: A Meta-Analysis of Correspondence Tests 1990–2015.” Journal of Ethnic and Migration Studies 42 (7): 1115–34. doi:10.1080/1369183X.2015.1133279.