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When jobs offered by different employers are not perfect substitutes in the minds of workers, employers gain wage-setting power; the extent of this power can be captured by the elasticity of labor supply that each employer faces. Estimates of this parameter reported by the literature vary broadly. We collect 801 estimates from published studies, record 20 aspects of each study's design and perform Bayesian Model Averaging to show that this observed variation is systematic and can be attributed to four groups of factors. First, estimates depend on methodologies used by the researchers: different specifications produce systematically different results that are also affected by whether the study employs an identification strategy; the choice between linear and non-linear estimation techniques also matters. Second, estimates vary with the underlying data: labor markets seem to be more competitive in Europe, and less competitive in developing countries - compared to the US, Canada and Australia. The market for medical workers appears to be more monopsonistic compared to others. Third, there is evidence of publication bias in parts of the literature, which results in negative estimates of supply elasticities receiving lower probability of being reported, and a (slightly) exaggerated mean. Fourth, estimates seem to vary with study quality, with top journals publishing higher estimates and studies using larger data sets producing more evidence of competitive behavior.