Getting deeply into the weeds on whether much observed social mobility is actually error in measuring "true status". The answer ape to be "no": Martin Nybom and Kelly Vosters: Intergenerational Transmission of Socioeconomic Status: "There is no simple law of mobility: In 2014, Gregory Clark proposed a ‘simple law of mobility’ suggesting that intergenerational mobility is much lower than previously believed, and relatively uniform across countries.... This column tests this... using US and Swedish data... no evidence of a rise in intergenerational persistence and no evidence of uniformity across countries...
...We argue that a methodological approach from Lubotsky and Wittenberg (2006) for combining information from multiple proxies for a single latent variable is ideally suited for this particular scenario (Vosters 2018). The basic idea is that if we believe each measure is essentially the unobserved latent status plus some noise or error–and that these errors are correlated across measures–we can include all of these in an OLS regression, and then add the resulting OLS coefficients optimally using weights. This aggregates the information from these measures in the sense that we obtain the greatest lower bound for (or least-attenuated estimate of) the persistence parameter.
To test for evidence of the simple law in the US, Vosters (2018) applies this method to data from the US Panel Study of Income Dynamics, specifically using a sample of fathers and sons very similar to those used in earlier studies about which the controversial claims are being made. Estimating regressions using income alone and then progressively adding other measures of status does not indicate that this aggregation leads to substantially higher estimates of persistence. As shown in Figure 1, the estimates relating sons’ status to fathers’ status rise only from 0.44 based on income alone, to a slightly higher 0.47 after also incorporating fathers’ education and occupation – still in line with prior research and far from the 0.75 proposed in the simple law...
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