We define path-dependency as the generic phenomenon according to which agents take an action regardless of their private information. Path-dependency can be of two types contingent on whether agents act with the crowd (herding) or against the crowd (contrarianism). We consider a quote-driven market where traders can in some cases observe whether their predecessors were informed, although they cannot observe their private information, while in other cases they are left with the uncertainty that their predecessors acted purely for liquidity motives. In this setting we recover herding and contrarianism and we find that better-informed markets (i.e. where informed traders receive high precision signals) can generate path-dependent behavior more easily than poorly informed ones. Moreover, we illustrate how a market dominated by herding features a price that is more informative of the asset value than the price of a market where traders always follow their signal. We also discuss how contrarianism has the exact opposite effect by decreasing price informativeness.