Negative interest rate policies have until now been off the table for many central banks. With the COVID-19 shock and its economic repercussions, however, central banks such as the Bank of England and the Federal Reserve are again putting these and other policies back on the table for discussion.

While the European Central Bank has pursued a negative interest rate policy since 2014, influential papers such as Eggertsson et al. (2017) and Brunnermeier and Koby (2018) have argued that negative interest rates can be counterproductive because of the bank lending channel of monetary policy. The story goes like this: The central bank pays negative interest rates on reserves, while the banks are unwilling (or unable) to pass these onto depositors. As a result, banks’ net interest margins are squeezed, and because of agency frictions in financial markets, there is a contraction in credit creation in the economy.

However, negative interest rates, like conventional monetary policy, work through many channels, including an expectations (or signalling) channel. For a central bank that has a preference for smoothing policy, a cut in policy rates today also signals lower policy rates tomorrow. In our recent paper (de Groot and Haas 2020), we study the signalling channel of negative interest rates and illustrate the conditions under which the expansionary signalling channel dominates the contractionary net interest margin channel.^{1}

## Optimal NIRP in a canonical New-Keynesian model

The qualitative trade-off between the signalling channel and the net interest margin channel faced by an optimizing central bank can be captured in simple variant of the canonical New-Keynesian (NK) model. To do so, we make just two assumptions. First, policy rates can turn negative but household deposit rates cannot. This is a reasonable assumption given empirical evidence from the euro area.^{2} The second assumption is that, all else equal, this wedge between a negative policy rate and a zero deposit rate shifts down aggregate demand via a net interest margin-type channel.

The question, in this environment, is whether it is optimal for a central bank to ever set negative interest rates. We establish three results:

1. If the central bank can fully commit to future policy actions, then it has no need of negative rates as a policy tool. It can induce the necessary private sector expectations of the future path of (deposit) interest rates via ‘open mouth’ forward guidance, without resorting to a policy that imposes a cost on banks.

2. Even if the central bank has no ability to commit to future actions (often referred to as discretion or time-consistent policy), it won’t make use of negative rates. In this case, a negative policy rate provides no signal about its future actions and only imposes a cost on the banking system.

So far, the case for negative interest rate policies seems rather bleak. However, these results capture two extreme scenarios. While both are useful benchmarks, neither is likely to be a good description of monetary policy in practice. Our third result builds on work by Woodford (2003) and Nakata and Schmidt (2019) on monetary policy delegation:

3. For a central bank that cannot commit, it is welfare improving to delegate monetary policy to a central banker with a preference for smoothing policy. This policymaker may find it optimal to set a negative interest rate since its preference for smoothing results in an expansionary signalling effect on the future path of interest rates.

Figure 1 illustrates this result. The parameter φ captures the strength of the net interest margin channel. Consider the black line when the signalling channel is weak (i.e. the preference for smoothing in the policymaker’s objective is low) relative to the effect of a squeeze on net interest margins. In this case, the optimal policy (given by the reserve rate), does not turn negative. Consider next the red-dash line when the signalling channel is relatively stronger. In this case, optimal policy prescribes a negative policy rate. While the negative rate does not lower deposit rates on impact since they are constrained by the Zero Lower Bound (ZLB), the signalling channel lowers the future expected path of the deposit rate, boosting aggregate demand today and mitigating some of the fall in output and inflation.

**Figure 1** Optimal policy scenarios to a contraction in aggregate demand

## Effectiveness of NIRP in a quantitative NK model

Since Figure 1 is based on a variant of the canonical NK model, it only provides a qualitative insight into the monetary policy trade-off. In the other half of de Groot and Haas (2020), we employ a carefully calibrated medium-scale DSGE model that quantifies the magnitude of the two channels. A key feature of this model is the banking system, which we discuss in more detail below. We also replace the optimal policymaker with an inertial Taylor-type rule.

Figure 2 highlights our baseline result from this quantitative exercise. In this exercise, we introduce a 25 basis point cut to the policy rate which moves it into negative territory, leaving the deposit rate constrained at zero. The policy in our baseline (black line) is expansionary with both output and inflation rising in response to the monetary policy cut. Output rises by eight basis points whereas inflation rises by a little over three basis points. These responses are around 40% of the effect of an interest rate cut in ‘normal times’. The figure decomposes the baseline response into the signalling and net interest margin channels. While the net interest margin channel (red-dash) causes a contraction in both output and inflation (consistent with Eggertsson et al. 2017, Brunnermeier and Koby 2018), the signalling channel (blue-dot) is expansionary and dominates.

**Figure 2** Contribution of signalling and interest margin channels

*Note*: Impulse responses to a -25 basis point monetary policy shock at the ZLB. Inflation is annualized.

Figure 3 provides sensitivity analysis. It plots the effect on output of a -25 basis point monetary policy shock for different durations of the ZLB (x-axis); different Taylor rule inertia parameter values (left panel); and different levels of excess central bank reserves in the banking system (right panel). The baseline results correspond to a ZLB event of 4 quarters, a Taylor rule inertia parameter of 0.8 and a reserve-to-deposit ratio in the banking system of 0.2. The effect on output is scaled relative to an unconstrained monetary policy shock rather than in absolute terms, thus removing any “forward guidance puzzle” type effects from the analysis.

There are two takeaways from this figure. First, while under the baseline negative interest rates are expansionary, this is not always the case. If the Taylor rule exhibits less inertia or the economy is expected to remain at the ZLB for longer, the signalling channel is weakened, and negative interest rates may become contractionary. Second, when the quantity of reserves in the banking system is large, the net interest margin channel is stronger and negative interest rates are less effective. This is because negative interest rates act as a tax on banks’ reserve holdings, and when the banking system is awash with reserves (after QE), the tax base is commensurately large.

**Figure 3** Sensitivity analysis

*Note*: The x-axis scales with the size of the negative aggregate demand shock that brings the economy to the zero lower bound (ZLB). The y-axis reports the absolute peak response of output to a -25 basis point monetary policy shock in period 1 relative the outcome of the unconstrained (UNC) scenario. The scaling relative to the unconstrained scenario ensures that the results are not a consequence of the ‘forward guidance puzzle’.

## Bank balance sheet dynamics under NIRP

A key feature of the larger, quantitative model is the modelling of the banking sector, which closely follows Gertler and Karadi (2011). As such, it is net worth of the banking sector, rather than the net interest margin per se that is key to understanding the effect of negative interest rates.

Figure 4 decomposes the response of bank profits (the change in net worth) to negative interests into several components. Two things stand out: First, while a shrinking of net interest margin pushes down on net worth (yellow bars), irrespective of whether policy features inertia, the signalling channel can have a significant effect on banks’ balance sheets, especially in terms of asset valuations. When there is no inertia and no signalling (right panel), banks’ assets experience a capital loss (blue bars). In this case, bank net worth falls, lending rates and credit spreads rise, choking off investment demand. In contrast, with policy inertia and signalling, despite the contraction in net interest margins, banks’ net worth rises on impact, coming mainly from a capital gain in assets values. In this case, agency frictions in the banking sector ease, allowing lending rates to fall and supporting investment demand and further credit creation via a financial accelerator type mechanism.^{3}

**Figure 4** Decomposition of bank profits

*Note*: The red-dot line plot the impulse response of bank pro

fits to a -25 basis point monetary policy shock at the ZLB. Stacked bars decompose the impulse response for every period.

## Conclusion

The current COVID-19 crisis will test central banks’ toolkits to the limit. Negative interest rate policies may help central banks signal their commitment to a prolonged period of monetary accommodation and thus be a beneficial additional policy tool that can be employed.

## References

Bhattarai, S, G B Eggertsson and B Gafarov (2015), “Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing”, NBER Working Paper 21336.

Brunnermeier, M K and Y Koby (2018), “The Reversal Interest Rate”, NBER Working Paper 25406.

de Groot, O and A Haas (2020), “The Signalling Channel of Negative Interest Rates”, CEPR Discussion Paper 14268.

Eggertsson, G B, R E Juelsrud and E G Wold (2017), “Are Negative Nominal Interest Rates Expansionary?”, NBER Working Paper 24039.

Eisenschmidt, J and F Smets (2019), “Negative Interest Rates: Lessons from the Euro Area”, *Series on Central Banking Analysis and Economic Policies* no. 26.

Gertler, M and P Karadi (2011), “A Model of Unconventional Monetary Policy”, *Journal of Monetary Economics* 58: 17-34.

Nakata, T and S Schmidt (2019), “Gradualism and Liquidity Traps”, *Review of Economic Dynamics* 31: 182-199.

Woodford, M (2003), “Optimal Interest-Rate Smoothing”, *Review of Economic Studies* 70: 861-886.

## Endnotes

^{1} Our usage of the term "signalling" captures a central bank's ability to give tangible signals about future policy, akin to Bhattarai et al.’s (2019) signalling theory of quantitative easing.

^{2} See for example Eisenschmidt and Smets (2019) as well as de Groot and Haas (2020). More recent evidence suggests that deposit rates are beginning, very gradually, to turn negative in the euro area. Nevertheless, it seems likely that if the Bank of England, for example, were to introduce negative policy rates, that banks in the UK will be equally reluctant or unable to pass on these rates to depositors in the near-term.

^{3} To see the effect on credit spreads and lending rates, see Figures 5 and 6 in de Groot and Haas (2020).