Fleeting extinction? Unraveling the persistence of noise traders in financial markets with learning and replacement

We describe an agent-based model of a financial market where agents can learn whether to buy costly information on returns, to use noise as if it were information, or to disregard any signals. We show that while learning alone drives all noise traders to extinction in stationary populations, allowing for small rates of replacement of existing agents with new ones suffices to generate substantial levels of persistent noise trading, with the equilibrium share of agents using irrelevant news reaching double digits. Remarkably, the presence of noise traders, when replacement is realistically considered, inflates the share of agents who use costly information relative to the benchmark scenario without replacement.