How much income inequality is explained past times varying parental resources?

When people mean value virtually inequality of incomes, a fundamental number is inequality of opportunity. Some people are born to rich parents who tin afford mortal schools, summertime camp, SAT tutors, etc., piece others bring poorer parents who cannot easily afford such things. One mightiness wonder how much of the income inequality nosotros discovery tin survive explained past times differences inward the resources that people piece of occupation because of varying parental incomes.

Let me advise a crude oil calculation that gives an guess answer.

The recent paper by Chetty et al. finds that the regression of kids’ income rank on parents’ income rank has a coefficient of 0.3. (See Figure 1.) That implies an R2 for the regression of 0.09. In other words, 91 pct of the variance is unexplained past times parents’ income.

I would survive willing company a guess, based on adoption studies, that a lot of that ix pct is genetics rather than environment. That is, talented parents bring talented kids partly because of practiced genes. Conservatively, let’s say one-half is genetics. That leaves alone 4.5 pct of the variance attributed straight to parents’ income.

Now, if y'all allow me play a flake fast too liberate alongside the difference betwixt income too income rank, these numbers advise the following: If nosotros had unopen to perfect policy conception (such equally universal super-duper pre-school) that completely neutralized the final result of parent’s income, nosotros would trim down the variance of kids' income to .955 of what it straightaway is. This implies that the criterion departure of income would autumn to 0.977 of what it straightaway is.

The bottom line: Even a highly successful policy intervention that neutralized the effects of differing parental incomes would trim down the gap betwixt rich too misfortunate past times alone virtually two percent.

This determination does non hateful such a policy intervention is non worth doing. Evaluating the policy would ask a cost-benefit analysis. But the calculations higher upwardly produce advise that all the coin the affluent pass on mortal schools, etc., explains alone a tiny fraction of the income inequality that nosotros observe.
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Addendum: Influenza A virus subtype H5N1 few readers appear confused virtually how to infer an R2 from a coefficient.  The fundamental is that the left too correct manus side variables inward the regression have the same variance.  In this case, the R2 is the foursquare of the coefficient.  This determination is a criterion final result for AR(1) models, which is what nosotros bring here, equally applied to generational data.  (Also, a few readers are confused when they expect at the paper's Figure 1. The points plotted are non the raw information simply binned averages, too therefore y'all cannot encounter the R2 inward the plot.)
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