This paper studies the contribution of parental influence in accounting for cross-country gaps in human capital achievements. We argue that the cross-country variation in unobserved parental characteristics is at least as important as the one in commonly used observable proxies of parental socio-economic background. We infer this through an indirect empirical approach, based on the comparison of the school performance of second-generation immigrants. We document that, within the same host country or even the same school, students whose parents come from high-scoring countries in the PISA test do better than their peers with similar socioeconomic backgrounds. Differential selection into emigration does not explain this finding. The result is larger when parents have little education and have recently emigrated, suggesting the importance of country-specific cultural traits that parents progressively lose as they integrate in the new host country, rather than of an intergenerational transmission of education quality. Unobserved parental characteristics account for about 15% of the cross-country variance in test scores, roughly doubling the overall contribution of parental influence.