Formula

Formula for the Real Interest Rate at the Zero Lower Bound

The real interest rate (rr) at the zero lower bound (ZLB) is derived from the Fisher equation (r=iπEr = i - \pi^E) by setting the nominal interest rate (ii) to its floor of 0%. This results in the real interest rate at the ZLB (rZLBr_{\text{ZLB}}) being equal to the negative of the expected inflation rate (πE\pi^E). The formal derivation is:

r=iπEiZLB=0%rZLB=iZLBπE=πE\begin{align*} r &= i - \pi^E \\ i_{\text{ZLB}} &= 0\% \\ r_{\text{ZLB}} &= i_{\text{ZLB}} - \pi^E = -\pi^E \end{align*}

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Updated 2026-01-15

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