Variants affecting gene expression (eQTLs) help explain the genetic basis of human complex traits both in terms of interpreting genome-wide association studies and understanding genome regulatory architecture more generally.1 While many human complex traits are highly polygenic, expression of each individual gene is thought to be regulated by a smaller set of variants.(e.g. 2) Therefore, studying the genetic architecture of gene regulation is a promising point of entry for developing mechanistic understandings of complex traits. However, due to (i) differences in statistical power between SNPs of varying minor allele frequencies and (ii) linkage between causal SNPs, it is difficult to draw conclusions about the space of potential expression-altering mutations from statistically significant eQTL signals alone. Here, we develop a likelihood-based method that utilizes findings from existing eQTL studies to estimate the proportion and effect size distribution of eQTLs. We evaluate the performance of our method using simulations and show that our inference is unbiased when causal variants are sparse, as is believed to be the case. The performance of our method decreases as the density of and linkage between causal variants increases. However, this effect stems not from our inference method, but from biases in effect size estimates introduced by the statistical methods used in eQTL mapping. We therefore employ alternative mapping strategies to reduce biases in effect size estimation and consequently improve inference. Applying this pipeline to existing human eQTL data3,4, we estimate the distribution of effect sizes of causal variants. From this, we infer the expected neutral rate of evolution of gene expression traits. Finally, we compare these estimates across cell types and gene sets to learn about variation in human genome regulatory architecture and gene expression constraints.