Banks individually optimize their liquidity risk management, often neglecting the externalities generated by their choices on the overall risk of the financial system. This is the main argument to support the regulation of liquidity risk. However, there may be incentives, related for instance to the role of the lender of last resort, for banks to optimize their choices not strictly at the individual level, but engaging instead in collective risk taking strategies, which may intensify systemic risk. In this paper we look for evidence of such herding behaviors, with an emphasis on the period preceding the global financial crisis. Herding is significant only among the largest banks, after adequately controlling for relevant endogeneity problems associated with the estimation of peer effects. This result suggests that the regulation of systemically important financial institutions may play an important role in mitigating this specific component of liquidity risk.