RDP 2024-08: Modelling Reserve Demand with Deposits and the Cost of Collateral 6. Model

6.1 Reserve demand

As in Lopez-Salido and Vissing-Jørgensen (2024), I model reserve demand as the benefit of holdings reserves:

In this framework, the demand curve is downward sloping as additional reserves increase convenience and relative value benefits, while reducing monetisation risks. As mentioned in Section 4, additional reserves have diminishing marginal benefit for managing a given stock of short-term liabilities or for holding against a liquidity stress event – making the demand curve nonlinear. An increase in deposits will shift the demand curve to the right as a result of increased transactional and precautionary demand.

Then, the profit-maximising condition for a bank borrowing via repo and investing in reserves sets the marginal cost of borrowing (repo rate plus the cost of giving up collateral) equal to the marginal benefit of investing in reserves (the ES rate plus the marginal benefit from holding reserves net of any balance sheet costs A):

Following Lopez-Salido and Vissing-Jørgensen (2024), I assume ${f^{\prime }}_{Reserves}$ (Reserves, Deposits) net of balance sheet costs is log-linear in reserves and deposits as a base case:

Re-arranging Equation (4), including the assumption around the marginal benefit of holding reserves, I can express banks' reserve demand with respect to repo funding as:

An important determinant of repo rates is the balance of supply and demand for bonds financed under repo (the cost of the underlying collateral). If there are more cash lenders who want collateral than there are those who want to finance bonds under repo, GC repo rates tend to fall. For example, demand to accept German bunds as collateral leads GC repo rates collateralised by German bunds to be lower than GC repo rates collateralised by Italian or Spanish government bonds (Arrata et al 2020). On the other hand, repo rates can increase in response to bond issuance due to a corresponding increase in the demand to finance bonds under repo.

An appropriate measure of the cost of collateral should respond to changes in the supply of and demand for government bonds, but not be influenced by changes in the GC repo rate (relative to the ES rate) driven by other factors. On the face of it, asset swap spreads seem like an appropriate measure. Asset swap spreads are defined by the difference in the yield on government bonds and the expectation for BBSW over the life of the swap. Thus, shortages in the supply of government bonds that push down government bond yields are reflected by asset swap spreads moving lower. Asset swap spreads can also respond to increases in the GC repo rate driven by the demand to finance bonds under repo. This relationship is highlighted through the trade where market participants can pay the GC repo rate to fund a bond purchase and execute an asset swap – receiving a floating unsecured rate (BBSW) plus the asset spread. This means that asset swap spreads can respond to the expectation, over the life of the swap, for the difference between secured and unsecured rates, which could be rising due to increased demand for collateral.

However, through this mechanism, there is a possible endogeneity issue with using asset swap spreads if they respond to changes in repo rates caused by other factors. One measure which is highly correlated with asset swap spreads is the proportion of specials in the repo market (Figure 11). The advantage of using this measure is that rates on specials transactions are negotiated relative to the GC repo rate such that changes in the GC repo rate should not affect the proportion of bonds trading special. I proceed with this measure to proxy for the value of collateral posted under repo.

6.2 Reserve supply

Regressing the GC repo rate on the quantity of reserves only reveals the demand curve if all changes in the quantity of reserves represent shocks to supply. This is true if the quantity of reserves changes only for reasons other than responding to demand shocks or if the demand shocks that do change the quantity of reserves are controlled for in estimation. In the Australian context, a shock to demand for reserves could result in banks borrowing more from full-allotment OMO repo, which increases the quantity of reserves. The RBA balance sheet identity shows that reserves can be driven by changes in full-allotment OMO repo as well as ‘exogenous factors’, including changes to other central bank assets and liabilities.^[9]

other assets and other liabilities are plausibly exogenous to the demand for reserves – making it a valid instrument to use in estimation. The main assets on the RBA's balance sheet during the sample period are bonds bought through unconventional monetary policy, TFF loans and the foreign exchange portfolio. Changes in these assets during the sample period have mostly been for monetary policy purposes and not heavily influenced by the demand for repo financing.

The main liabilities on the RBA's balance sheet during the sample period are government deposits, banknotes and other deposit accounts held predominately by foreign clients (e.g. other central banks). Movements in government deposits due to government spending, tax receipts, and bond issuance/maturities are likely independent of banks' reserve demand, once I control for the commercial bank deposits that these transactions create. In other words, the exclusion restriction would not hold if I excluded commercial bank deposits from the regression as the instrument would affect repo rates through a variable not controlled for. Deposit accounts held by foreign clients might respond to shifts in reserve demand. For example, a positive reserve demand shock leading to higher repo rates could incentivise foreign clients at the RBA to withdraw deposits and invest in repo – increasing the quantity of reserves. Foreign deposits declined substantially from around $26 billion in November 2021 to around $5 billion in June 2022. Since June 2022, these balances have been relatively small and stable. I include foreign deposits in my instrument to account for any potential endogeneity.

Taken together, other assets and other liabilities (besides foreign deposits) on the RBA balance sheet are broadly unaffected by shocks to reserve demand but highly correlated with reserves. Through the balance sheet identity, reserves minus full-allotment OMO and foreign deposits makes a valid instrument to use in estimation.

Footnote

Other liabilities include the RBA's capital position which is excluded here for simplicity. [9]