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I am currently working on a project investigating the impact of investment on wage inequality, where wage inequality corresponds to the average wage in a sector compared to the average wage in the same sector across countries. The question I want to answer is if the sectors that invest increase their wage inequality. Both measures, investment and wage inequality, are thus on the sector-country-year level.

In my specification I include sector-country and year fixed effects besides various controls. My take is that sector-country fixed effects should absorb the unobserved heterogeneity of a specific sector in a specific country like labor regulations in German automotive (assuming they are constant), while time fixed effects control for shocks that hit all industries the same but change over time (lets say the Global Financial crisis 2007/08).

But the longer I think about this specification, the more I have doubts about the fixed effects structure. I think the confusion comes because my dependent variable, wage inequality, is calculated within sector but across countries. So when I control for sector-country fixed effects I am essentially holding constant German automotive. So what is the variation I am actually capturing, and what groups am I comparing? Is it the variation within a sector-country over time?

A similar question was raised here What exactly is controled for in a model with country, industry, and year fixed effects?, but not in relation to interacted fixed effects, or here What is the difference between region, year and region-year fixed effects? but more in relation to the software approach.

AllDoe_1
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  • Some thoughts about this: If investment differs between (/is related with) sector-country then adding sector-country as a fixed effect does not only absorb some unobserved heterogeneity but it also explains some of the variance that you want the investment variable to explain. I think this is usually avoided by using sector-country (or variables of the sort) as random effects in a mixed model, which are subject to shrinkage and thereby don't "steal" the variance from the fixed effects. Same goes for using year as a fixed effect. – MrMax Dec 20 '22 at 12:35
  • I do not really understand the dependent variable. Your explanations "average wage in a sector compared to the average wage in the same sector across countries" and later "wage inequality, is calculated within sector but across countries" do not really make it transparent for me. Maybe others feel the same? Maybe your question would get more traction if you find a way to make this clearer (although I do not know how)? – MrMax Dec 20 '22 at 12:43

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