On the Rank-Rank Model of Intergenerational Mobility: Pitfalls for Policy Evaluation

We analyze the challenges in adopting the rank-rank model of intergenerational mobility for policy evaluation. For rank-based analysis of intergenerational mobility, it is standard to calculate cohort-specific ranks from the national distribution, but separately for children's and parents' generations. This ensures that children's inherited socioeconomic status and their life outcomes are measured on common scales irrespective of location and social groups. However, national ranks put the treatment and comparison groups together, and thus, a policy intervention leads to mechanical changes in ranks in the comparison group when the ranks of the treated individuals change because of the policy. We discuss how to deal with this contaminated comparison problem in the context of widely-used research designs: RCTs, Instrumental Variables (IV), and Difference-inDifference (DiD). In a RCT design with a binary treatment assignment, a simple solution is to calculate the ranks separately for the treatment and control groups. In an IV design, the ranks should be calculated separately for different values of the instrument. For a DiD design, an additional concern is how to avoid mechanical changes in the ranks of the pre cohorts following the policy intervention: calculate the ranks separately for pre and post periods. If the policy affects only the children, then, for all research designs, it is desirable to keep the parental ranks at the national level so that children's inherited socioeconomic status is measured on a common scale. As an empirical application, we provide evidence on the effects of Inpres schools on intergenerational educational mobility in Indonesia using the DiD design developed by Duflo (2001). The evidence suggests that the conclusions regarding the impact of Inpres schools depend critically on the way ranks are calculated. If we follow the current practices when calculating the ranks, the DiD estimates suggest that the 61,000 primary schools failed to affect relative mobility even though it improved absolute mobility for the children from low-educated families. In contrast, when the ranks are calculated to tackle the mechanical contamination problem, the evidence, especially from the correct functional form (quadratic), suggests that Inpres schools improved both relative and absolute mobility of the disadvantaged children. The Inpres schools led to higher intercept and quadratic coefficient of the mobility equation while reducing the linear coefficient. The analysis presented here has important implications for economists and sociologists working on intergenerational mobility.