Emisiones Potenciales (PTE, Potencial To Emit)

This subsection provides evidence that the mis-measurement of individual income in the historical data is unlikely to be driving the documented shift in the geography of upward mobility. While Chetty et al. (2018) have information on actual earnings from tax records, 1950-based occupation income scores were used to construct the historical measure of upward mobility instead. This introduces errors at two levels. First, occupation scores based on incomes in 1950 may not reflect the relative standings of occupations in earlier decades. Second, even if they did, occupation scores are still imperfect proxies for actual earnings. I consider these limitations in turn.

1.4.2.1 Occupation Standings Before 1950

How well do 1950-based occupation scores reflect the hierarchy of occupations in prior decades? This depends, in part, on the proportion of farmers in the population, given that farmers comprised a relatively large share of the workforce during the early 20th century and their socio-economic status was also higher further back in time. Among the sons in my 1910-1940 linked sample, 40.8 percent have fathers who are farm owners or tenants in 1910, while only 14.0 percent of the sons themselves become farm owners or tenants by 1940. Errors due to the changing status of farmers may thus appear to be more important when ranking fathers than when ranking sons. My use of absolute rather than relative mobility, however, implies that even errors in the former are unlikely to pose a major problem. Notice from definition (1) that with absolute upward mobility, a father’s rank only serves to determine if his son forms

part of the population that is used to compute the level of mobility in a given CZ. Once this population has been selected, the father’s actual position plays no role in the computation. This means that as long as the earnings of farmers were generally below the national median before 1950, errors in the ranking of fathers due to the changing status of farmers are unlikely to severely distort the historical measures of upward mobility.

To show empirically that the baseline results are not driven by changes in occupa- tion standings over time, I use an alternative version of occupation scores that may better reflect the hierarchy of occupations at the start of the 20th century. Specif- ically, I follow Olivetti and Paserman (2015) in using the 1900 occupation income distribution based on the tabulations in Preston and Haines (1991) and by imputing the earnings of farmers with data from the 1900 Census of Agriculture.46,47 The 1900 occupation scores are used to rank both sons and fathers, from which estimates of upward mobility can then be re-computed for each CZ. Implementing specification (3) with this alternative measure of upward mobility yields a rank-rank coefficient of -0.463 (S.E.=0.046), which is similar to the baseline correlation in Figure 1.2.48 _Er-

rors due to changes in occupation standings over time, introduced when 1950-based scores are used to compute upward mobility in earlier decades, are thus unlikely to be driving the shift in the land of opportunity.

1.4.2.2 Occupation Scores as Imperfect Proxies for Income

46_{The tabulations in Preston and Haines (1991) are based on the 1901 Cost of Living Survey. One}

limitation of this survey is its exclusive focus on families residing in industrial areas.

47_{Olivetti and Paserman (2015) impute the income of farmers by assigning farm owners the dif-}

ference between the value of farm products and expenditure, assigning farm tenants the income of specialized workers in Preston and Haines (1991), and then taking an average of the two. As an alternative, Olivetti and Paserman (2015) also use a weighted average of the earnings across farming occupations in Preston and Haines (1991), where the weights are based on the frequency of each farming occupation in the 1910 census. Both imputations are available in the replication package of Olivetti and Paserman (2015). I use the imputation from the first method here, but a similar rank-rank correlation can be obtained with the alternative imputation.

Even if 1950-based occupation scores accurately reflect the relative standings of occu- pations in 1910 and 1940, they are nonetheless imperfect proxies for actual earnings. This necessarily introduces errors into the early 20th-century measures of upward mobility. Of greater importance, however, is whether such errors are large enough to alter the historical ranking of CZs and to bias the estimated rank-rank correlations. I present suggestive evidence below that this is unlikely to be the case.

For a subset of sons in the 1910-1940 linked sample, one can evaluate how the use of occupation scores rather than actual earnings may affect the estimated rank- rank correlations. Specifically, I focus on sons who are wage and salary workers in 1940, since the 1940 census records wages but not non-wage income.49 _{Two sets of}

individual-level ranks can be generated for this subset of sons: one based on occupa- tion scores, and another based on annual wages.50 From these rankings, alternative estimates of upward mobility can then be computed before re-estimating regression (3). Comparing the rank-rank correlations from the two different mobility estimates can shed light on the impact of using occupation scores instead of actual income. Table 1.2 presents the results.

I find evidence of substantial change in the geography of upward mobility re- gardless of whether occupation scores or wages are used to construct the historical measures of mobility. As a benchmark, column (1) of Table 1.2 reproduces the base- line rank-rank correlation from Figure 1.2. Restricting the sample to wage and salary workers will significantly reduce the number of linked individuals and thus result in a smaller subset of CZs for which estimates of upward mobility can be computed. Col- umn (2) thus checks that this reduction in the sample of CZs does not alter the initial

49_{Sons with missing wages are dropped. Among sons who are wage and salary workers in 1940,}

and whose fathers were from the bottom half of the national occupation income distribution in 1910, 1.94 percent have missing wages.

50_{Fathers will continue to be ranked by occupation income scores since wage data are not available}

rank-rank correlation significantly. Column (3) then limits the underlying population to wage and salary workers but continues to rank sons by their occupation scores. While the point estimate becomes less negative, it remains well below 1 and continues to point toward an important change in the landscape of upward mobility. Finally, column (4) takes the population of wage and salary workers and ranks them by their annual wages. The resulting rank-rank coefficient is similar to that in column (3), suggesting that the use of occupation scores over actual earnings to compute upward mobility is unlikely to have severely distorted the baseline findings.51

The robustness of the baseline rank-rank correlation to using occupation scores based on the 1900 occupation income distribution and to ranking wage and salary workers by annual wages suggests that errors in the measurement of individual income, while necessarily present, are not large enough to explain the changes observed in the spatial patterns of upward mobility.