When Measures Conflict

A large empirical literature on intergenerational educational mobility measures relative mobility by the slope of a conditional expectation function (CEF) relating children's education to parental education. Three measures are widely used: intergenerational regression coefficient (IGRC) with years of schooling as the indicator of educational attainment, intergenerational correlation (IGC) when years of schooling is normalized by its standard deviation, and intergenerational rank-rank slope (IRRS) when schooling ranks in a generation is adopted. The existing evidence suggests that conclusions from IGRC vs. IGC vary substantially, but there is no systematic evidence on whether the IRRS estimates also lead to conflicting conclusions. Using data free of coresidency bias from three developing countries with 42 percent of world population in 2000 (China, India, Indonesia), the authors provide evidence that the IRRS estimates may lead to dramatically different conclusions about spatial heterogeneity (rural/urban) and evolution across cohorts, especially when the mobility CEF is concave or convex. The rank-rank CEF is consistently more convex (or less concave) compared to the other two CEFs. When different measures lead to conflicting conclusions it is not clear how to interpret the evidence and advise the policymakers. The authors develop a simple approach to interpret the IGC estimate in terms of the Becker-Tomes model that provides a foundation for a comparative study of IGC vs. IGRC. The authors find that the idiosyncratic component of children's schooling variance unrelated to the family background plays an important role in IGC. The elasticity of IGC w.r.t IGRC is less than 1 implying that the IGC estimates are less responsive to changes in economic forces (such as credit constraint and returns to education) raising questions about the suitability of IGC for understanding the role of changing economic conditions in intergenerational mobility. This also provides an explanation for the puzzle in the literature that IGRC estimates across cohorts show substantial improvements, but the IGC estimates suggest no significant changes. When the mobility CEF is quadratic, by construction, the quadratic coefficient of the CEF for IGC is much larger than that of the CEF for IGRC. This implies that IGC estimates mechanically generate much stronger persistence at the top (for convex) or bottom (for concave) of the distribution. The authors report evidence that, unlike income, calculating schooling ranks by mid-rank method may fail to neutralize the effects of changing inequality across generations, making IGC a preferable measure for tackling changes in cross-sectional inequality. It is difficult to interpret IRRS in terms of the Becker-Tomes model. The inequality of opportunity approach (Roemer (1998)) suggests that policy advice should focus on the causal effects of policies on the influence of inherited circumstances on children's education which is captured by IGRC. From this perspective, a policy such as school construction or trade liberalization should be considered effective in improving relative educational mobility if the causal effect on IGRC is negative even when a policy fails to affect IRRS significantly.