This paper characterizes the optimal monetary policy reaction function in the presence of a zero lower bound on the nominal interest rate. We analytically prove and numerically show that the function is highly non-linear, more expansionary, and more aggressive than the Taylor rule. We then test its empirical validity taking the case of Japan in the 1990s. Qualitatively, we find some evidence of non-linear monetary policy. Quantitatively, we find the actual monetary policy to be too contractionary during the first half of the decade, while the low interest policy during the latter half turns out to be fairly consistent with the simulated path.
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