20Genetic correlation is a key population parameter that describes the shared genetic architecture 21 of complex traits and diseases. It can be estimated by current state-of-art methods, i.e. linkage 22 disequilibrium score regression (LDSC) and genomic restricted maximum likelihood (GREML). 23The massively reduced computing burden of LDSC compared to GREML makes it an attractive 24 tool for analyses of many traits, achieved through use of GWAS summary statistics rather than 25 individual level genotype data. While both methods generate unbiased estimates of the genetic 26 correlation from genome-wide single nucleotide polymorphism (SNP) data, the accuracy of the 27 LDSC estimates has not been thoroughly studied. In simulation, we show that the accuracy of 28 GREML is generally higher than that of LDSC, which is more obvious when using a smaller 29 number of SNPs (< 500K). When there is a genetic heterogeneity between the actual sample and 30 reference data from which LD scores are estimated, the accuracy of LDSC decreases further. For 31 genomic partitioning analyses, LDSC estimates can be biased. This is also confirmed with real 32 data analyses, showing that GREML estimates based on ~150,000 individuals give a higher 33 accuracy and power than LDSC estimates based on ~400,000 individuals (from combined meta-34 data) in estimating genetic correlation between SCZ and BMI 15 for GREML vs. -0.087 SE=0.019 and p-value=4.91E-06 for LDSC). We show a GREML 36 genomic partitioning analysis reveals that the genetic correlation between SCZ and height is 37 significantly negative for regulatory regions, which cannot be found by non-partitioned GREML 38 or by LDSC (whole genome or partitioned). We conclude that LDSC estimates should be 39 carefully interpreted as there can be uncertainty about homogeneity among combined meta-data 40 sets. We suggest that any interesting findings from massive LDSC analysis for a large number of 41 complex traits should be followed up, where possible, with more detailed analyses with 42.