We study a simple, microfounded macroeconomic system in which the monetary authority employs a Taylor-type policy rule. We analyze situations in which the self-confirming equilibrium is unique and learnable according to Bullard and Mitra (2002). We explore the prospects for the use of "large deviation" theory in this context, as employed by Sargent (1999), Williams (2004), and Cho, Williams, and Sargent (2002). We show that our system can sometimes depart from the self-confirming equilibrium towards a non-equilibrium outcome characterized by persistently low nominal interest rates and persistently low inflation. Thus we generate events that have some of the properties of "liquidity traps" observed in the data, even though the policymaker remains committed to a Taylor-type policy rule which otherwise has desirable stabilization properties.