Cross-Country Regressions and Population Weighting
By Bryan Caplan
Whenever someone presents growth regressions, a robustness check pops into my head: “What happens if you weight for population?” Treating China and Grenada as equally probative data points just seems crazy to me. If you want to understand how human societies function, one gigantic society has far more to teach us than two tiny islands.
Is my intuition econometrically sound? Bill Dickens, my Econ 1 teacher, has a paper subtitled “Is It Ever Worth Weighting” (Review of Economics and Statistics, 1990) – and originally subtitled “Why It’s Never Worth Weighting.” This apparent absolutism prompted me to send Bill the following hypothetical:
Someone is doing a cross-country regression, counting
each member of the European Union as a single data point. A critic says,
“Bill Dickens showed that it is never worth weighting. We should just
treat the whole EU as one data point despite its huge population.”
In your framework, how is the critic wrong? Why then
wouldn’t he be arguably wrong for any large, diverse country?
In conversation, Bill’s response was modest: His paper only addressed a very different rationale for population weighting. For cross-country regressions, population weighting might be entirely suitable.
Last year, Solon et al. published a more comprehensive piece on the topic, entitled “What Are We Weighting For?” (Journal of Human Resources, 2015). While they raise multiple technical issues, their advice is straightforward: When population-weighting matters, researchers should alert their readers and reflect on the source of the contrast.
[W]e recommend reporting both the weighted and unweighted estimates because the contrast serves as a useful joint test against model misspecification and/or misunderstanding of the sampling process.
Who cares? Early this year, I spent weeks reviewing research on ancestry and economic performance. In this research, the three most populous countries on Earth – China, India, and the United States – are major outliers.
This led me to wonder, “What would happen if we weight the results by population?,” but I felt the need to review the econometrics first. Since it now looks like population-weighting is technically acceptable as well as intuitively plausible, I’m now ready to share the results. What’s the bottom line? Stay tuned.