The impact of Basel III on money creation : a synthetic theoretical analysis

Inspired by the extensive criticisms against the textbook fractional reserve theory, this paper revisits the mechanics of money creation process and complements the traditional focus on the reserve requirement by elaborating on the roles of three prudential regulations proposed in the Basel III accord. In particular, the authors consider such conditions where the financial markets are imperfect and suffer from various frictions that the commercial bank cannot readily modulate their liquidity and capital buffers, especially at an aggregate level or within a short period. Meanwhile, as a result of maturity mismatch and fundamental uncertainty, the credit and money creation activities inevitably add to the liquidity and insolvency risks faced by the bank. Under the assumptions that the levels of bank reserves, capital and government bonds are exogenously given, and that the concerned prudential regulations are always binding, the authors examine the determinants of the broad money aggregate and the money multiplier. Specifically, they find that 1) the money multiplier under Basel III is not constant but a decreasing function of the monetary base; 2) the determinants of the bank’s money creation capacity are regulation specific; 3) when multiple regulations are imposed simultaneously, the effective binding regulation and the corresponding money multiplier will vary across different economic states and bank balance sheet conditions. JEL E51 G28 G18 E60

and the bank's balance sheet structure. Consequently, the corresponding money 176 multiplier and its determinants will also vary. We argue that this result calls for 177 special attention from the policy makers because the same policy may have distinct 178 consequences in different scenarios. 179 The following of the paper is structured as follows. Section 2 elaborates the  The most fundamental way for a bank to profit is to earn the interest spread 201 between its assets (e.g. loans) and liabilities (e.g. deposits), which gives the bank a this constraint has ceased to be an influential concern when banks make loans.

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In addition, driven by the desire for profit, banks are often prone to underesti-   In the Basel III accord framework, the liquidity risk is addressed by the LCR 261 regulation while the solvency risk is attended by the CAR and LR regulations.

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Next, we will explain the meanings of these regulations and how they limit bank 263 lending and the money supply. with the highest quality classification, over the risk-weighted assets, i.e.
Compared to Basel II, the minimum requirement of CET 1 over RWA is raised 292 from 2% to 4.5%, while the mandatory "capital conservation buffer" requires 2.5% 293 and the "discretionary counter-cyclical buffer" ranges from 0% to 2.5%. Therefore, 294 the actual minimum requirement of CAR facing by banks is 7% in all periods and 295 even up to 9.5% in certain conditions.

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Leverage Ratio The leverage ratio regulation is a non-risk-based capital re-297 quirement. It is calculated by dividing the amount of Tier 1 capital by the bank's 298 average total consolidated assets(TA), which includes the exposures of all assets 299 and non-balance sheet items. In other words, the leverage ratio is defined as The leverage ratio is introduced as a backstop to the risk-based capital adequacy   Along with the increase of the loan stock, banks are exposed to higher liquidity and solvency risks. As a result, the net cash outflow, risk-weighted assets and total assets rise accordingly. However, the amount of high quality liquid assets (including reserves and zero-risk-weight government bonds) and bank capital, which serve as the credit base for banks to guard against liquidity and solvency risks, do not change. (c) Because of the increasing denominators and the constant nominators, the actual liquidity coverage ratio, risk-based capital adequacy ratio and the leverage ratio drop and approach to their corresponding minimum requirements set by the Basel III regulations. Therefore, given no improvement of the bank's credit base, the implementation of prudential regulations casts a maximum limit for the amount of loans and deposits that can be created by the bank.
In essence, the Basel III accord sets a minimum limit on the banks' holdings of 311 high liquid assets and core capital, which serve as the credit base to guard against Suppose time is discrete and the unit of each time step is one month. Due to 372 the accounting consistency, the following identity between assets and liabilities 373 should always hold: addition to reserves, deposits and loans. Such extension allows us to explore the constraining effects of different prudential regulation including the LCR, CAR and LR regulations. www.economics-ejournal.org The stocks of reserves, government bonds and bank capital are assumed to be 376 always positive and exogenously given. In other words, For the initial period, we assume there is no loans (L(1) = 0) and D(1) = Because the amount of deposits cannot 391 be negative, R + G −C ≥ 0 must hold.

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For simplicity, we also assume all loans are amortized with an average maturity 393 of θ . In other words, a new loan made at month t , LF(t ), will be paid off at 394 month t + θ . Thus the amount of repayment for this loan due at month t, denoted Thus, the total repayment flow due at time t, RP(t), can be computed as the sum of 398 repayments due for all loans made in the past θ periods, which is given by should be no more than its difference with the maximum loan stock L max , i.e.
411 When the dynamical model reaches the stock-flow equilibrium, all stocks and 412 flows should be constant. Thus, supposing the system reaches equilibrium at time Correspondingly, based on Eqs. 6,7 and 8, the money multiplier m, defined as the 434 ratio of the broad money supply and monetary base, is then given by Henceforth, based on this model, we move on to examine the specific impacts  Note that because we do not consider banks' voluntary holdings of excessive reserves and bank equities above the minimum prudential requirement, these expressions reflect the banking system's maximum ability to create money. Since our purpose is to evaluate the policy impact of the Basel III regulation on money creation rather than estimating the real values of the money supply and the money multiplier, we will focus on the relative changes of these values when the regulation of concern is different or when the economic condition varies.

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where µ is the run-off ratio of deposit loss to total deposits. The total cash inflow 466 (IF) is supposed to be constituted by the expected loan repayment due in one 467 month with a discount rate of 50% 10 due to the assumption of stressed condition, regulation is equivalent to the following constraint: 482 10 According to the official document regarding the LCR regulation provided by the Basel committee(Basel Committee on Banking Supervision, 2013), different inflow rate are set by the Basel III accord for different types of bank assets. For instance, the accord requires that a bank should assume that maturing reverse repurchase or securities borrowing agreement secured by Level 1 assets (which corresponds to overnment bonds and bank reserves in our model) will be rolled-over and will not give rise to any cash inflows (0%). On the other hand, the inflow rate for non-HQLA assets varies from 0%-100% for different types of counterparties based on their abilities to fulfill debt obligations in stressed conditions. Here we take 50% as an exemplary inflow discount rate for the repayments received from outstanding bank loans. Discussions for relaxing this assumption are given in Appendix C.
Due to the accounting consistency in Equation 5, we can rewrite the above inequality as a function of L(t):

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As a result, the equilibrium money supply and money multiplier are respectively 522 given by other hand, serve as the non-debt financing source that is not exposed to liquidity 541 risk and as the signal of the bank's health for its creditors. Therefore, other things 542 equal, well capitalized banks are able to have more expected cash inflow and less 543 outflow in a liquidity stressed condition than low-capital banks. In other words, 544 the banking system's ability to create money is higher when it holds more capital.

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Apart from the amount of high quality liquid assets and bank capital, we can In summary, the full expressions for the equilibrium money supply and money 560 multiplier are respectively given by where C(t) = C and the amount of risk-weighted assets RWA is computed as the Furthermore, it can be demonstrated that The leverage ratio With the minimum requirement of leverage ratio being r LR , 594 the bank faces the following constraint: where C(t) = C and TA(t) = R + G + L(t) = D(t) +C. When the equality is taken, the loan stock reaches its maximum limit, which is given by

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Correspondingly, the equilibrium money supply and money multiplier are The responses of money supply and money multiplier to reserve shocks are respec-604 tively given by  Table 2. We find that 1) the tightening of both the prudential 617 requirements and the reserve requirement will have a negative impact on the bank-  On the other hand, the stability of the bank's debt-based financing source and the 628 maturity structure of loans only matter when the LCR regulation is taking effect.
conomics Discussion Paper Equilibrium expression for money multiplier Response of money supply and money multiplier to the shock to monetary base Response of money supply and money multiplier to the shock to the concerned minimum policy ratio Other determinants of money supply Other determinants of money multiplier Monetary control: changing the required reserve ratio may restrict commercial bank balance sheet growth when reserve money cannot easily be increased, and may influence the spread between deposit and lending rates and thus impact the growth of monetary aggregates and thus inflation; Prudential purpose: reserves provide protection against both liquidity risk. See Simon (2011) for more discussion about the purpose of the reserve requirement.
12 r RR is the minimum required reserve ratio. we denote the ratio of government bonds to reserves as g = G R and the ratio of bank 648 capital to reserves as c = C R . In specific, the boundary condition between the LCR 649 and CAR regulations is given by 650 4(1 + g)

Collective impact of multiple regulations under different economic con-
The boundary condition between the LCR and LR regulations is conomics Discussion Paper The boundary condition between the CAR and LR regulations is For the two expressions for LCR regulation to take identity, 656 4(1 + g)  In Scenario 2, there is no change in the bank's debt-based financing source but 710 the level of bank capital is much lower than that in Scenario 1. As a result, the 711 capital constraint becomes the bank's biggest concern. As shown in Fig. 4(b), only The bank holds high level of capital c = 2 but faces high liability run-off ratio µ = 0.55 with (c) demonstrating results for maturity less than 6 months and (d) for maturity larger than 6 months. All results are obtained for g = 3. In both (c) and (d), the LCR regulation alone takes effect. In all three scenarios, the money multiplier is generally higher with high capital holdings, low run-off ratio, low default risk and short maturity length.
less than 2 months, the net cash outflow is solely determined by the expected cash 736 outflow. In this case, the money multiplier is independent of the average loan 737 maturity and the loan default risk and is generally lower than Scenario 1 and 2.
outflow is governed by the difference between the total cash outflow and cash 740 inflow. In this case, the bank faces large loss in its funding source, and at the

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where ω is denoted as the inflow rate of the repayments for outstanding bank loans.   This table provides the historical data of reserves and capital for the U.S. banking system from 1992 to 2009 used for the calibration of the model parameter c, the capital-to-reserve ratio. Data are obtained by author based on the work of Slovik and Cournède (2011). Based on the ratio of bank capital to reserves (C/R) and the ratio of core-Tier 1 capital to reserves (CET 1/R), we determine that c = 0.8 corresponds to relatively low capital positions and c = 2 indicates relatively high capital positions.