This paper examines the advantages and drawbacks of alternative methods of estimating oil supply and oil demand elasticities and of incorporating this information into structural VAR models of the global oil market. I show that some of these methodologies suffer from drawbacks that call into question the estimates they generate. I also explain the rationale for the use of alternative elasticity definitions in the literature and discuss the trade-off between these definitions. Once these issues are recognized, seemingly conflicting conclusions in the recent literature can be reconciled. My analysis reaffirms the conclusion that the one-month oil supply elasticity is close to zero, which implies that oil demand shocks are the dominant driver of the real price of oil.