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Central banks commonly use some rent on the interbank market to conduct monetary policy. Central banks could for example decrease the rent aiming to stimulate consumption and investments.

However, an important link in the transmission is the commercial banks who potentially could be reluctant to pass on negative rents to bank customers. If this is the case it could be expected that monetary policy would have a dampened effect when rents are negative.

Is there any empirical evidence to support such an expectation?

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Yes there is some evidence for this but to be honest literature is too fresh, dust still needs to settle.

For example, Eggertsson, Juelsrud, Summers, & Wold,(2019) investigate this. From their abstract:

We investigate the bank lending channel of negative nominal policy rates from an empirical and theoretical perspective. We find that retail household deposit rates are subject to a lower bound (DLB). Empirically, once the DLB is met, the pass-through to lending rates and credit volumes is substantially lower and bank equity values decline in response to further policy rate cuts. We construct a banking sector model and use our estimate of the pass-through of negative policy rates to lending rates as an identified moment to parameterize the model and assess the impact of negative policy rates in general equilibrium. Using the theoretical framework, we derive a sufficient statistic for when negative policy rates are expansionary and when they are not.

The authors show that negative interest rates can be contractionary, but it is not enough for them to be just negative, they have to be sufficiently negative to hit DLB. The paper also presents some empirical evidence for this.

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