In our simulations, we cannot estimate ∑j using LD score regressions because we directly simulate effect sizes rather than data. Nonetheless, we would like to use a matrix for ∑^j that contains the same amount of sampling variance that would have been present if we had simulated data and then ran LD score regressions. To accomplish this, in each replication we directly generated ∑^j by adding noise to the true value of ∑j. The variance of the noise was calibrated against the LD-score-regression intercept standard errors for the GWAS results of DEP, NEUR, and SWB that we estimate in our empirical application but scaled to be larger or smaller when the simulated GWAS had more power (Supplementary Note).
