RDP 2022-08: The Consequences of Low Interest Rates for the Australian Banking Sector 5. Investigating the ‘Reversal Rate’ in Australia

The ‘reversal rate’ is the point at which any further reduction in the central bank's policy rate will cause banks to increase their lending rates, such that policy rate reductions become counterproductive. In simple theoretical models (Brunnermeier and Koby 2018), the reversal rate results from banks being subject to an occasionally binding equity constraint (essentially a minimum capital ratio).^[15] If this constraint binds (i.e. they cannot avoid it by raising external equity), reductions in the policy rate tighten the constraint by reducing banks' net interest income. The only margin of adjustment available to the banks in this scenario is their credit supply, so they respond to this constraint tightening by reducing credit supply (i.e. increasing lending rates and reducing lending volumes). At some point, this credit supply reduction more than offsets the effect on funding costs, such that lending rates increase in response to the policy rate reduction.

Subsequent research has shown that the existence of a reversal rate is not assured, and even in theory is highly model dependent. Repullo (2020) shows that even in Brunnermeier and Koby (2018)'s model, the reversal rate only exists for banks that are net investors in debt securities; this is particularly relevant for Australian banks, who have historically been net borrowers in debt markets. Repullo then proposes an alternative model in which banks retain access to external equity markets, and shows that the reversal rate never exists in this model.

As far as I am aware, there is little empirical evidence of a reversal rate having been reached in any jurisdiction:

• There is no evidence of a reversal rate being reached in Denmark, despite policy rates being negative between 2012 and mid-2022, and reaching -0.75 per cent (Kuchler et al 2020).
• Arce et al (2018) look specifically at the effect of an extended period of low rates in Spain and find that while some banks reduce their credit supply, there is no evidence of an aggregate reduction in credit supply (let alone a reversal rate).
• While Eggertsson et al (2019) find some evidence of the reversal rate having been reached in Sweden, their evidence is not statistically significant.
• Bech and Malkhozov (2016) suggest that Swiss mortgage rates increased in response to policy rate reductions into negative territory. However, their analysis does not control for any potentially confounding factors. Conversely, the more thorough analysis of Baeriswyl et al (2021) provides mixed results, and suggests that, if anything, it is only temporarily negative policy rates that lead to a reversal rate, whereas a low-for-long scenario retains positive (albeit muted) pass-through (this is the opposite of the theoretical reversal rate predictions).
• Central banks that have implemented negative rates state that negative rates have ‘contributed to the achievement of their policy goals’ (CGFS 2019), suggesting that they do not perceive the reversal rate as having been reached.
• Darracq Pariès et al (2020) construct a New Keynesian DSGE model that can produce a reversal rate under some calibrations. A reversal rate exists in their model when calibrated to the euro area, but it is at a lower level than any policy rate set by the ECB. So its existence remains theoretical.

Moving beyond the theoretical models and international evidence, BA-MARTIN provides an environment well suited to investigating whether a reversal rate exists in Australia, and if so, its determinants. During banking crises, the banks in BA-MARTIN lose access to external equity markets. As a result, any capital shortfall can only be replenished by either retained earnings or reducing assets. Without a change in credit supply, cash rate reductions both reduce banks' NIMs and increase loan demand, thereby making it harder for banks to replenish capital. So BA-MARTIN has the same fundamental mechanism as in Brunnermeier and Koby (2018)'s model.

But having the same mechanism does not mean a reversal rate necessarily exists, as BA-MARTIN is a more detailed modelling framework than either the Brunnermeier and Koby (2018) or Repullo (2020) models. In the remainder of this section, I will investigate whether a reversal rate exists in Australia.

5.1 A reversal rate does not exist in the baseline BA-MARTIN model

From Brassil et al (2022), period t lending rates in the Australian economy (r_M,t) can be expressed as the sum of banks' cost of debt (including deposit) funding (r_D,t), a spread that is unrelated to domestic economic conditions (s_M,t), and an endogenous response to a deterioration in their capital $\left(z_t^{*}\right)$:^[16]

Given that I am exploring the existence of the reversal rate, I want to explore scenarios in which pass-through is as low as possible. So in the remainder of Section 5, and in Appendix A, I assume that banks' provisioning for losses has already returned to normal (so the amplifying channel of pass-through described in Section 4 is not operational) but that they still have a capital shortfall when the cash rate is reduced further. This leaves four channels that permit pass-through to be lower than normal, thereby potentially culminating in a reversal rate:

1. Deposit ELB – while this lower bound mutes the pass-through of monetary policy at low rates, it cannot, by itself, make the pass-through of monetary policy negative.
2. NIM compression – from Equation (1), reductions in banks' costs of funding reduce their NIMs, which slows the speed at which banks replenish their capital via retained earnings (holding lending spreads and all else equal).
3. Credit growth – increased credit growth increases the denominator of banks' capital ratios. Therefore, the accelerated credit growth that comes with interest rate reductions would slow the speed at which banks return to their capital ratio targets (holding lending spreads and all else equal).
4. Credit risk – if channels 2 and 3 slow the speed of capital ratio increases, the risk for banks' creditors would remain elevated for longer. This would increase banks' costs of debt funding.

In reality, all else is obviously not equal, and banks may respond by increasing $z_t^{*}$. The question is, can the banks' endogenous $z_t^{*}$ responses more than offset the reductions in r_D,t that come from cash rate reductions at low interest rates?

In the BA-MARTIN model, which is designed to reflect the Australian banking system, the answer is no. This is because in BA-MARTIN, as in reality, most of Australian banks' assets are loans (over which they have pricing discretion), while they have a significant share of liabilities that follow hedged wholesale market pricing. This means that, rather than keeping lending spreads constant (as they do in normal times, Section 3.2), if banks instead kept their lending rates constant then their NIMs would increase as their funding costs fell.^[17] So zero pass-through is enough to more than offset the NIM compression channel discussed above.

Moreover, with zero pass-through there would be no direct change in credit demand.^[18] So zero pass-through is also enough to offset the credit growth channel discussed above.

With the structure of Australian banks' balance sheets meaning zero pass-through is sufficient to offset both the NIM compression and credit growth channels, there can be no Brunnermeier and Koby (2018) reversal rate – this result is consistent with Repullo (2020)'s critique that the reversal rate requires banks to be net investors in debt securities. I confirm this intuition in Appendix A, by showing mathematically that even a very conservative pass-through lower bound in the baseline version of BA-MARTIN is above zero, and that even if the parameters in the model changed from the baseline calibration, zero pass-through would always be sufficient.^[19]

5.1.2 A ‘credit risk’ reversal rate is theoretically possible but highly unlikely, and does not occur in the baseline calibration

The ‘credit risk’ channel is a potential reversal rate channel not covered by the Brunnermeier and Koby (2018) framework, and it works in quite a different way. While the Brunnermeier and Koby channel is all about banks endogenously responding to a binding constraint, the credit risk channel arises if banks are not sufficiently responsive to any deterioration in their capital ratio. With the credit risk channel, it would be a sufficiently strong response from banks' creditors that could lead to a reversal rate.

In Appendix A, I show that Australian banks are estimated to be sufficiently responsive, and the response of creditors to be sufficiently small, that this credit risk channel does not lead to a reversal rate. I also show how banks becoming less responsive to capital ratio shortfalls would increase the likelihood of the credit risk channel leading to a reversal rate. But that a credit risk reversal rate would still require an extreme and highly unlikely scenario in which banks remain below their target capital ratio for an extended period of time, they remain excluded from external equity markets for this entire period, and there is no regulatory/government policy response that alleviates the problem despite the effect such a scenario would be having on the Australian economy.

All that said, my analysis is based on the current structure/behaviour of the Australian banking system. Were this to change, a reversal rate could emerge. An example highlighted by Brunnermeier and Koby (2018) is that quantitative easing (QE) may increase both the share of non-discretionary assets held by banks and the share of low-interest deposits, both of which increase the likelihood of a reversal rate. QE enacted by the RBA has caused some shift in this direction (RBA 2020). However, large Australian banks' holdings of securities and central bank reserves generally remain smaller than their funding that follows wholesale market pricing.

Footnotes

Darracq Pariès, Kok and Rottner (2020), Heider and Leonello (2021) and Koenig and Schliephake (2022) also construct theoretical models that produce a reversal rate under some calibrations. [15]

In BA-MARTIN, debt funding costs and banks' endogenous responses have the same effect on all lending rates. [16]

From Equation (1), if lending rates were held constant then $\frac{d\text{NIM}}{d{i}_L}=\frac{-L}{A}<0.$ [17]

The effect of the cash rate reduction on the parts of the economy that are not intermediated by the banking sector (e.g. the exchange rate channel) would still lead to a small indirect increase in credit demand. [18]

BA-MARTIN is an aggregate model that does not account for heterogeneity among the banks. That said, even if some small banks are net investors in debt securities, competition from the majority of banks that aren't net investors would mean these smaller banks could achieve their desired reduction in credit growth with smaller lending rate increases than if all banks were net investors in debt securities. This means the amount of ‘reversal’ experienced by these smaller banks would be muted, and therefore any spillover to the majority would also be muted. Still, further research incorporating bank heterogeneity should be conducted. [19]