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What would be the pattern if keeping the earnings of each education group fixed and allowing only the distribution of education groups to evolve as the actual? It is a bit surprising in the first figure that the earnings of graduate degrees are generally the second lowest while the groups of post-secondary diploma and, in recent years, some secondary and high school are doing that well.... Then why do we see the trends of education in the second figure? Non-monetary motives? Over-supply of high education? Interesting food for thought...

Is the key on the first graph right? Even though all the groups are scaled to be one at the beginning, I still would have expected the "all" group to be the smoothest line, fitting somewhere in the middle i.e. the black line. Or maybe I am misunderstanding what it is measuring?

Frank: Earnings do increase with income; see the previous post I linked to.

mpledger: The level for the total does lie somewhere in the middle; the point is a composition effect in the growth rate. Much of the gains in the total is due to more people being in the group with higher earnings. (The level is

Good post. Slightly off-topic: I saw some graphs a few days back saying that the stagnation in US wages is at least partly a composition effect on white/non-white wages (both groups had increasing wages, but the composition of the average was changing). But as usual, I can't remember where I saw it.

Nick: as the inimitable Larry Wasserman put it, "without causal language— counterfactuals or causal graphs— it is impossible to describe Simpson’s paradox correctly." Is the "right" average the unconditional, the conditional, or neither? The answer depends on causal beliefs that are impossible in principle to read off the data. In Stephen's example, the causal role of education is intuitively persuasive - although not necessarily correct - so his conditional analysis is probably right. Or anyway, I was convinced. But the right causal model in your example is not as clear. Perhaps there is a "white wage" and a "non-white wage" for any given job, and the observed unconditional wage stagnation has been caused by changes in the workforce composition, maybe due to demographic changes. In that case, stagnation is a composition effect of workforce changes. But maybe whites have a higher reservation price of labour than non-whites and wage stagnation has caused changes in workforce commposition; then the latter would be a "decomposition effect" of stagnation. Or perhaps workforce composition is indeed a confounder, but there are other, unobserved confounders, in which case neither the composition nor the decomposition view is accurate.

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