A contentious debate in academic as well as policy circles relates to the growth in private schooling in Sub-Saharan Africa and other low-income regions. While proponents highlight the superior learning outcomes of pupils in private schools, others have argued that this is merely a reflection of the more advantaged family background of private school pupils, rather than an effect of private schooling itself. We contribute to this debate by providing estimates derived from household fixed effect models, which control for any observed or unobserved differences between government and private school pupils at the household level. We argue that these can be interpreted as an upper bound estimate of the effect of private schooling on learning. We rely on large-scale, comparable household survey data from Kenya, Uganda, India and Pakistan, focusing on children enrolled in grade 2 to 6 of primary school. Private school attendance ranges from 12% in Kenya to 33% in rural India, with substantial within-household variation. Preliminary findings show that controlling for family background almost eliminates the positive effect of private schooling in rural Pakistan and reduces it by around half in rural India, Kenya and Uganda, to about a quarter of a standard deviation. Subgroup analyses show that the effect of private schooling does not differ substantially between high- and low-SES families. We discuss implications for educational policy.