To assess the magnitude of the finite-sample bias in MTAG’s standard errors from ignoring sampling variation in Ω^ and ∑^j, we simulate GWAS summary statistics for up to T=20 traits and apply MTAG using Ω^ and ∑^j (as in any real-data application of MTAG). We then calculate the inflation of the mean χ2-statistic, defined relative to what the mean χ2-statistic would be if the true values Ω and ∑j were used. Figures 1a and 1b plots the inflation as a function of T, where each GWAS has mean χ2-statistic of 1.1, 1.4, or 2.0. The effect-size correlation between every pair of traits is rβ=0
