# Use Interpolated Median Values to Measure Brain Waste

For a while now, I have been coordinating an IMISCOE research group on brain waste with Marco Pecoraro. Brain waste — not my choice of term — is the underutilization of education and skills in their country of destination, a specific form of educational mismatch also referred to as over-education, over-qualification, over-schooling. The stereotypical case is an immigrant scientist working as a taxi driver.

One way to enumerate brain waste is to look at the average educational or skills level in a specific occupation or occupational group, and then check whether an individual has higher or lower levels of education or skills. That’s quite neat, until it comes to choosing the average. Typically we measure skills and education using ordered scales, and depending on the researcher the mean, median, or mode is used (or sometimes a mix of them). None of them is really appropriate, but with interpolated median values, there is a more appropriate measure out there.

Interpolated median values are generally the most adequate measure of central tendency when there is a limited number of response categories, such as Likert scales or the level of education. To calculate interpolated median values, each response category is understood as a range with width w, and within the median response, linear interpolation is used. In principle, we could estimate any quantile, but we’re interested in the median (q=0.5).

In addition, when comparing groups rather than individuals (which is what we typically do), superimposed kernel distributions would be quite helpful: once for the majority population, and once for the immigrant group studied. The interpolated median could readily be added to give a good sense of how much of a difference there is between the groups in substantive terms.

Now, if you were thinking that the measure of central tendency does not matter, here’s a bunch of distributions (as histograms because of the small number of observations in these examples, say of levels of education), along with their mean (blue line), median (red line), and interpolated median (dashed black line). We can see that in some configurations the choice of central tendency makes no difference at all, in others there is a small difference, and in others still the differences are substantive. It’s these substantive differences we should be worried about.

While I’m at it, here are some other challenges to enumerating brain waste. Typically we do not (attempt to) adjust for quality differences of education, but take diplomas at their face value. Differences in quality may occur across countries, but also within countries across universities etc. Typically we do not distinguish between over-skilled and over-educated, even though conceptually the two are different. Here the lack of adequate questions in the data is a major limitation. Finally, we often should also consider the counterfactual: Would this over-qualified immigrant have been able to realize their potential in the country of origin (or elsewhere)? While being over-qualified is generally a problem, for the individual in question it may still be the ‘optimal’ outcome.

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