model, it is difficult to understand and interpret the economic content of the estimated intergenerational persistence. The theoretical analysis identifies a set of economic mechanisms determining the intercept and the slope of the intergenerational educational persistence equation. In particular, the household-level returns to education in the parental generation determine relative mobility as measured by the slope of the regression function (called intergenerational regression coefficient ( IGRC, for short) in the literature). The intercept which shows the expected schooling attainment of the children from the most disadvantaged family background (fathers with no schooling) is determined by intergenerational persistence in occupation, among other factors.<sup>11</sup> A substantial literature shows that Hukou restrictions affected intergenerational persistence in nonfarm occupations in rural China (Wu and Treiman (2007)).

A credible empirical analysis of the role of occupational dualism in intergenerational educational persistence needs to address two major challenges highlighted in the recent literature: (i) truncation bias due to coresidency restrictions in surveys, and (ii) the role of genetic correlations in the observed intergenerational persistence. Most of the available household surveys, especially in developing countries, suffer from serious sample truncation as household membership is defined in terms of coresidency.<sup>12</sup> Recent evidence indicates that the standard measures of relative mobility, such as IGRC, suffer from substantial _downward_ bias in coresident samples (Emran, Greene, and Shilpi (2018)). Our empirical analysis focuses on the father-son linkage in education, and takes advantage of two exceptionally rich data sets: the rural sample from the China Family Panel Studies (2010) for China and the Rural Economic and Demographic Survey (1999) for India. Both of these surveys are unique in that they include all the children of the household head irrespective of their residency status at the time of the survey.<sup>13</sup> This is especially important in a comparative study such as ours, because cross-country comparisons based on coresident samples can lead to wrong conclusions (see Emran, Greene, and Shilpi (2018) on Bangladesh and contrast, all of the papers on intergenerational educational mobility we are aware of use a linear-in-levels estimating equation. This is partly motivated by the fact that, in many developing countries, 20-40 percent of fathers have zero schooling. However, we are not aware of any published work on developing countries that derives the estimating equation from a theoretical model.

> 11This deserves especial attention because the focus in much of the existing literature has been on the slope-based measures of mobility such as the intergenerational regression coefficient (IGRC) and intergenerational correlation (IGC).

> 12For example, widely used surveys such as LSMS and DHS collect information only on the coresident children.

> 13 Although some surveys collect limited information on the non-resident parents of the household head and spouse, we are aware of only a few surveys that include all children of the household head.

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