When Raj Chetty publishes a paper, it generally comes with a splash. The last one is no exception. His paper (co-authored), picked up by David Leonhardt at the New York Times and Justin Wolfers on Twitter, basically measures the American dream : what are your chances to do better than your parents. The stunning conclusion is that someone born in 1940 had a 90%+ chance of “out-earning” his parents compared with a few points above 50% for those born in the 1980s. I am not convinced. Well, when I am not convinced, I am saying I am not convincing about how big the drop is! I think the drop is smoother (the slope of decline is gentler) and the starting point for the 1940 cohort is too high. As a big fan of Chetty, I must press this point.

More precisely, I am saying that the bar (income threshold) over which someone had to jump in 1940 is underestimated and overestimated in 1980. Setting the bar too low (high) means very high (low) chances of “out-earning” your parents. To set the bar too low, you must underestimate (overestimate) the income of the parents. This could occur if household economies of scale are not accounted for.

An income of 30,000$ for 3 persons is not the same as an income of 60,000$ for 6 peoples. On a per capita basis, the income is the same. But, if you adjust for economies of scale in housing and furnitures, there are differences (the simplest is square root). This gives you income per adult equivalent. Chetty et al. are aware of that and they provided a sensitivity analysis which is not mentioned by those who are relaying the article. Since household size has tended to fall over time, the growth in per capita income is faster than the growth in income per adult equivalent (a better measure). Any correction for this long-term demographic trend would attenuate the slope of the decline of the chance to out-earn your parents. And indeed, once Chetty et al. make the correction, the decline is much more modest (but still present – see below).

Simultaneously, Chetty et al. also present other important sensitivity checks. All of them relevant. But, in a strange decision, Chetty et al. decided to isolate each of the sensitivity checks rather than compile them. Taken individual, they all seem minor – except adjusting for family size. But compound this with the other sensitivity check proposed by Chetty et al.: price deflators. Using the well-known bias in the the CPI that overestimates inflation by 0.8%, Chetty et al. find that, by the end of their perod, there is roughly a ten percentage point difference between the baseline uncorrected CPI and the corrected CPI (see below). Compound this with the corrections for family and you still get a decline – but again the slope of the decline is much more modest. If you add panel B from figure 3 in Chetty et al – which includes taxes and transfers – you probably get a few extra points up. There will still probably be a decline, but a moderate one.

Finally, at footnote 19, Chetty et al. also point out that they do not account for in-kind transfers prior to 1967 (there were some). And, on page 13, they point out that “one may be concerned that levels of absolute mobility for recent cohorts may still be understated because of increases in fringe benefits, nonmarket goods, or under-reporting of income in the CPS”. Add in all these little extra problems to the family size, the transfers and the inflation correction and I am not sure how big the drop from 1940 to the end of the studied period is. Finally, I would also add that an understudied point in economic history is what the distribution of in-kind payments according to income was. From studying the British industrial revolution, I have generally to see that it is the poorest workers who receive in-kind payments (which are not measured) and the richest receive much fewer of those in proportion of their incomes. One of the few to note that distributional was the hardcore left-leaning scholar Gabriel Kolko who mentioned this issue in Dissent back in the 1950s. If Kolko is correct, then the income of “poor parents” in 1940 is underestimated. As a result, the bar over which the children of said parents must jump is set mildly too low. If that is the case, the odds for the 1940 birth cohort are overestimated.

Combine all of these things together and I am not sure that the drop is as dramatic as many are making it out to be. I would be very satisfied if Chetty et al. would publish all the corrections they did and do a sensitivity check with hypothetical regarding a sliding-scale of in-kind payments in 1940 according to income (10% of income for poorest to 0% for the richest). I would just like to see how much it matters.