A recent literature studies the role of grandparents in status transmission. Results have been mixed, and theoretical contributions highlight biases that complicate the interpretation of these studies. We use newly harmonized income tax records on more than 700,000 Swedish lineages to establish four empirical facts. First, a model that includes both mothers and fathers and takes a multidimensional view of stratification reduces the residual three-generation association in our population to a trivial size. Second, data on fathers' cognitive ability show that even extensive controls for standard socioeconomic variables fail to remove omitted variable bias. Third, the common finding that grandparents compensate poor parental resources can be attributed to greater difficulty of observing parent status accurately at the lower end of the distribution. Fourth, the lower the data quality, and the less detailed the model, the greater is the size of the estimated grandparent coefficient. Future work on multigenerational mobility should pay less attention to the size and significance of this association, which depends heavily on arbitrary sample and specification characteristics, and go on to establish a set of more robust descriptive facts.