Mendelian randomization, a method to infer causal relationships, is confounded by genetic correlations reflecting shared etiology. We developed a model in which a latent causal variable mediates the genetic correlation; trait 1 is partially genetically causal for trait 2 if it is strongly genetically correlated with the latent causal variable, quantified using the genetic causality proportion. We fit this model using mixed fourth moments Formula: see text and Formula: see text of marginal effect sizes for each trait; if trait 1 is causal for trait 2, then SNPs affecting trait 1 (large Formula: see text) will have correlated effects on trait 2 (large α α ), but not vice versa. In simulations, our method avoided false positives due to genetic correlations, unlike Mendelian randomization. Across 52 traits (average n = 331,000), we identified 30 causal relationships with high genetic causality proportion estimates. Novel findings included a causal effect of low-density lipoprotein on bone mineral density, consistent with clinical trials of statins in osteoporosis.