Building on recent advances in the literature and using a rich data set for two cohorts of children aged between one and twelve for Andhra Pradesh, India, we investigate the determinants of children's cognitive as well as non-cognitive skills. We find evidence of self-productivity for cognitive skills and cross-productivity effects from cognitive on non-cognitive skills. Moreover, we demonstrate that parental investment has contemporaneously positive effects on skill levels for all age groups. Investigating other determinants of these skills, we find child health at age one to influence cognitive abilities at age five, whilst child health at age one is influenced by parental care already during pregnancy and earliest childhood. Understanding the determinants which account explicitly for the effect of a large number of child, caregiver and household characteristics provides insights with regard to possible policy interventions to improve the chances of children in poor environments of developing cognitive and non-cognitive skills crucial for success in many spheres of life.