Background: In a previous study, the total, direct and indirect effects of parental education on reading, mathematics and science achievement have been estimated for Grade 4 pupils of 37 countries that participated in PIRLS and TIMSS 2011 studies (Gustafsson et al. in "TIMSS and PIRLS 2011: Relationships among reading, mathematics, and science achievement at the fourth grade--implications for early learning." pp 183-289, 2013). Several theories proposed to account for the variation were reviewed. With this previous study as the point of departure, the current study was to identify determinants and mechanisms that can explain the substantial variation found in the relationship between parental education and school achievement across the 37 countries in the previous study. Methods: The effects estimated in Gustafsson et al. ("TIMSS and PIRLS 2011: Relationships among reading, mathematics, and science achievement at the fourth grade--implications for early learning." pp 183-289, 2013) formed the empirical data of the current study. In a first step of analysis the total, direct and indirect effects were described for the 37 countries, focusing on countries with a high and low level in these three respects. In the second step of analysis, two indicators of characteristics of the educational system, the Gini index as a measure of degree of economic inequality and the HDI as a measure of general societal development, were related to the estimated coefficients. Results: We found different patterns of relations with the direct and the indirect effects of parental education, and the direct and indirect effects therefore tended to cancel, so that small or no total effects were found. We also found opposite results when we investigated bivariate correlations and when we investigated partial correlation with HDI and Gini. Conclusion: The pattern of empirical findings thus is more complex than expect. There is, potentially, a large number of factors outside of the home which may be of importance mediating the relation between parental education and student achievement. However, the data available for the current study does not allow investigation of such factors, so this will be tasks for further research.