Identification at the Zero Lower Bound

Sophocles Mavroeidis

doi:10.3982/ecta17388

Abstract

I show that the zero lower bound (ZLB) on interest rates can be used to identify the causal effects of monetary policy. Identification depends on the extent to which the ZLB limits the efficacy of monetary policy. I propose a simple way to test the efficacy of unconventional policies, modeled via a “shadow rate.” I apply this method to U.S. monetary policy using a three‐equation structural vector autoregressive model of inflation, unemployment, and the Federal Funds rate. I reject the null hypothesis that unconventional monetary policy has no effect at the ZLB, but find some evidence that it is not as effective as conventional monetary policy.

Highlights

The first step is to write the model in state-space form
The second algorithm is a fully adapted particle filter (FAPF), which is a sequential importance resampling algorithm designed to address the sample degeneracy problem. It was proposed by Malik and Pitt (2011) and is a special case of the auxiliary particle filter developed by Pitt and Shephard (1999)
Both algorithms require sampling from the predictive density of Y 2t conditional on Y1t Dt = 1, and st−1

Summary

Likelihood

We need to obtain the prediction error densities. The first step is to write the model in state-space form. It was proposed by Malik and Pitt (2011) and is a special case of the auxiliary particle filter developed by Pitt and Shephard (1999) Both algorithms require sampling from the predictive density of Y 2t conditional on Y1t Dt = 1, and st−1. From (26) and (S.20), we see that this is a truncated Normal with original mean μ∗2t = C2Xt + C∗2X∗t + μ2t and standard deviation τ2, where μ2t τ2 are given in (S.21), that is, f2 Y2∗t|Y1t Dt = 1 st−1 ψ = T N μ∗2t τ2 Y ∗2t < b (S.24) Draws from this truncated distribution can be obtained using, for instance, the procedure in Lee (1999).

Then, a

IRFs and Local Projections

Alternative DGP