This is an interesting paper that discusses the Zero Lower Bound (ZLB) and explains through in a clear fashion the models used to.
U.S. Monetary Policy: A View from Macro Theory by William T. Gavin and Benjamin D. Keen
Here is some excerpts.
From a practical perspective, the zero interest rate bound may be a trap because policymakers tend to look at the Phillips curve when deciding how to set the fed funds rate. Under the …rst alternative assumption with a …xed nominal rate, a rise in real interest rates as the economy recovers will tend to make inflation fall. If inflation is falling and the economy remains short of full employment, the Taylor rule recommends a lower interest rate. Since the Federal Reserve cannot lower the rate below the zero lower bound, it can only simulate the lower nominal rate with LSAP and more forward guidance.
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Under the Fed’s current policy rules, it is dificult to predict a likely situation in which the policy rate is raised. Can policy afect the real interest rate over longer horizons? If not, then maintaining the nominal rate at zero for an extended period will tend to cause deflation if the real economy and real interest rates recover. If the central bank policy can afect the equilibrium real interest rate and there are multiple equilibria as discussed in Bullard (2010), then it may be that choosing to keep the nominal rate at zero causes the economy to coordinate on a low real interest rate, low output growth equilibrium. But such a mechanism has not been worked out in theory.
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