UCL ECON7003 Money and Banking Topic 6a The Money Multiplier - PowerPoint PPT Presentation

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UCL ECON7003 Money and Banking Topic 6a The Money Multiplier

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  1. UCL ECON7003 Money and BankingTopic 6aThe Money Multiplier • Stylized history of banking. • Deposit creation. • Actors in the Money Supply process. • Multiple deposit creation. • Simple deposit multiplier and assumptions underlying it. • Deposit creation and money supply.

  2. Stylized history of banking. • Owner of safe house storing gold takes in £100 in gold coins: • Safe house • AssetsLiabilities . • Gold coins + £100 Deposit notes + £100 • Deposit notes become accepted in transactions: • Substitute for payment in gold. • i.e. Gold (‘commodity money’) →‘customary money’ – a financial instrument (‘bank note’)

  3. Safe house owner now makes loans to the value of £900. • Safe house • AssetsLiabilities . • Gold coins £ 100 Deposit notes £1000 • Loans issued £ 900 • £1000 • Note: Trade-off in deciding gold:deposit-note ratio: • Profitability of loans and liquidity. • Liquidity insufficient to meet demands for withdrawal of gold coins may → ‘run’, or panic.

  4. Deposit creation. • Bank of England makes open market purchase of £100 from Bank I. • Bank I uses proceeds to make loan of £100, paid into borrower’s current account. • Bank I • AssetsLiabilities . • Securities - £100 Deposits + £100 • Reserves + £100 • Loans + £100 . • + £100 + £100 • Bank I has expanded balance sheet through issuing credit / creating deposit.

  5. Bank now has ER of £100. • BUT: new deposit created for purpose of loan. • → assumed the sum will soon be withdrawn. • → bank cannot safely make further loans / the £100 ER short term only. • → Likely net outcome : • ΔD=0, ΔR=0, ΔL=100.

  6. Bank I’s customer uses loan to make purchase by cheque. • Firm receiving cheque pays it into its account at Bank A. • Bank A takes full advantage of corresponding ER↑ to make loan to another customer. • Bank A • AssetsLiabilities . • Reserves + £ 10 Deposits + £100 • Loans + £ 90 . • + £100 + £100

  7. Actors in money supply process: • (a) The expansion of Bank I’s deposit creation capacity • Bank I’s deposit creation capacity was outcome of decision by CB to expand MB. • Controls MB with certainty through OMOs. • Commercial banks, their borrowers, their depositors: • No part in this decision.

  8. Actors in money supply process: • (b) Bank I’s loan to its customer • Bank I’s own independent decision. • Its borrowers may have affected decision through their level of demand for loans → rL. • CB: • no direct part in decision, • though influence or control over interest rates may have affected it indirectly.

  9. Actors in money supply process: • (c) Use the customer makes of loan. • Customer’s action involved two decisions relevant to MS process: • (α) use entire loan for purchase > hold as deposit • (β) make purchase by cheque > cash

  10. Multiple deposit creation. Increase in deposits in banking system as a whole so far: Deposits created Bk A receives £100 from customer of Bk I £100 Bk B receives £90 from customer of Bk A £ 90 Total deposits created £190

  11. Bank A’s customer uses loan to make purchase by cheque from a further firm. • Firm pays this into its account at Bank B. • Bank B takes full advantage of ER↑ to make loan to another customer. • Bank B • AssetsLiabilities . • Reserves + £ 9 Deposits + £ 90 • Loans + £ 81 . • + £ 90 + £ 90

  12. Increase in deposits in banking system as a whole so far: • Deposits created • Bk A receives £100 from customer of Bk I £100 • Bk B receives £90 from customer of Bk A £ 90 • Bk C receives £81 from customer of Bk B £ 81 • Total deposits created £271

  13. Series of further transactions involving loans by Banks C, D, E, F. • Assumption: Banks make loans to full amount of ER. • Bank ΔD ΔR ΔLoans • I £ 0.00 £ 0.00 £100.00 • A £100.00 £10.00 £ 90.00 • B £ 90.00 £ 9.00 £ 81.00 • C £ 81.00 £ 8.10 £ 72.90 • D £ 72.90 £ 7.29 £ 65.61 • E £ 65.61 £ 6.56 £ 59.05 • F £ 59.05 £ 5.91 £ 53.14 • … … … … • → ∞ → £0 → £0 → £0 • £1000.00 £100.00 £1000.00 • Or: • ΔD = 100 { 1 + 0.9 + (0.9)2 + (0.9)3 + (0.9)4 + . . . (0.9)n }

  14. ‘Simple deposit multiplier’. • R = RR + ER, and RR = r.D, where r ≡ RRR • ER = 0 → R = RR = r.D • R = r.D → D = (1/r).R • → • ΔD = (1/r).ΔRSimple deposit multiplier

  15. Equilibrium: Point at which process ends, • i.e. deposit creation ceases: • In terms of number of transactions in ‘chain’: • Reached at limit as n → ∞ • i.e. as (0.9)n → 0. • In terms of level of ER in banking system: • Reached at limit as all ER exhausted • i.e. as ER → 0. • In terms of total R in banking system: • R = RR + ER • ER → 0 • → R → RR = r.D • i.e. ER exhausted, R reaches min. level consistent with RRR.

  16. OMP of £100 → £900 expansion of deposits in banking system: • Banking System • AssetsLiabilities . • Securities - £100 Deposits + £900 • Reserves + £100 • Loans + £900 . • + £900 + £900 • ER not yet exhausted: ER = £10 > 0. • Equivalently R not yet → equilibrium level: R = 100 > r.D = 90. • i.e. Simple deposit multiplication process has not yet reached equilibrium.

  17. Once process has reached equilibrium, we have. • Banking System • AssetsLiabilities . • Securities - £ 100 Deposits + £1000 • Reserves + £ 100 • Loans + £1000 . • + £1000 + £1000 • ΔD = (1/r).ΔR • r = 0.10 and ΔR = 100 • → ΔD = (1/0.10).100 = 10.(100) = 1000

  18. Now banks use 50% of ER to purchase secs. > make loans. • No difference to deposit creation process / equilibrium! • Banking System • AssetsLiabilities . • Securities - £ 100 Deposits + £1000 • Reserves + £ 100 • Securities + £ 500 • Loans + £ 500 . • + £1000 + £1000 • Or, simplifying: Banking System • AssetsLiabilities . • Reserves + £ 100 Deposits + £1000 • Securities + £ 400 • Loans + £ 500 . • + £1000 + £1000

  19. The assumptions underlying the simple deposit multiplier. • Note: Money here defined as M1 ≡ C + bank deposits • (1) All banks exhaust ER in making loans. • i.e. till ER = 0, or equivalently to maximum extent consistent with RRR (i.e. R = r.D). • (2) All transactions are carried out by cheque. • → Amount of currency in circulation unaffected (ΔC = 0). • Lifting these assumptions: • Deposit creation process is interrupted: • (1) Banks retain ER > lend to full amount possible consistent with RRR • (2) Customers shift into cash; money ‘leaks’ out of the banking system.

  20. Deposit creation and money supply: • M ≡ M1 = C + D • → deposit creation is supply of money. • Extent to which the two processes proceed: • MS process is interrupted before deposit creation → equilibrium of SDM. • Assumptions on which SDM equilibrium rests are unrealistic.

  21. If the two assumptions underlying the SDM held, CB would have full control over MS process: • Assumption (1) • BB continue deposit creation until ER exhausted. • i.e. the process continues till equilibrium implied by SDM. • i.e. with certainty, given the level of R in the economy. • Assumption (2) • CB can control R with certainty, since MB = R + C, and ΔC = 0. • The CB is thus sole ‘actor’ with determining role in MS process.

  22. Lifting the assumptions, we have: • CB no longer has full control of MS process: • Assumption (1) • If BB decide not to issue loans to full extent of ER resulting from OMP, and instead to hold ER > 0: • Some of the ΔR from the OMP ‘leak’ out of the deposit creation process. • Process is interrupted / does not reach equilibrium level implied by SDM.

  23. Assumption (2) • If banks’ borrowers decide to shift from cheque to cash transactions: • ΔC > 0 and some of the ΔR from the OMP ‘leaks’ out of the banking system, → out of deposit creation process. • i.e. Lifting the assumptions: • → CB no longer sole actor in MS process: • Decisions of banks, depositors, borrowers now also affect extent to which process proceeds.

  24. To allow for lifting of these assumptions, 2 additional ratios: • Lifting of assumption (1), we need: • e ≡ ER / D excess reserve ratio • Lifting of assumption (2), we need: • c ≡ C / D currency ratio • Model that will incorporate these ratios. • The money multiplier ≡ m: • m = (1 + c) / (r + e + c)

  25. ΔD = (1/r).ΔRSimple deposit multiplier • Underlyingassumptions: • (1) Banks exhaust all ER in making loans. • (2) All transactions are carried out by cheque. • Lifting these assumptions: Deposit creation process is interrupted. • To allow for lifting of these assumptions, 2 additional ratios: • e ≡ ER / D excess reserve ratio • c ≡ C / D currency ratio • Model that will incorporate these ratios. • The money multiplier ≡ m: • m = (1 + c) / (r + e + c)

  26. Deriving the money multiplier • MB = R + C • R = RR + ER and RR = r.D , so we can write • R = r.D + ER • → MB = r.D + ER + C • Note: Parameter of 1 on ER and C: • → increase in MB that public decides to hold in cash • → one-for-one increase in MB / not multiplied through creation of additional deposits. • Similarly, increase that goes into ER.

  27. MB = r.D + ER + C • e = ER / D → ER = e.D • c = C /D → C = c.D • → MB = r.D + e.D + c.D • MB = (r + e + c).D • D = {1 / (r + e + c)} . MB

  28. M ≡ M1 ≡ D + C • Substituting C = c.D: • M = D + c.D = (1 + c ).D • We have D = {1 / (r + e + c)} . MB • → M = { (1 + c) / (r + e + c) }.MB • We thus have: • m = (1 + c) / (r + e + c) the money multiplier

  29. m = (1 + c) / (r + e + c) the money multiplier • i.e. The change in M (≡ M1) resulting from given change in MB. • In terms of calculus: m = dM / dMB. • Note: • Outside money: Created by CB (i.e. through expansion of MB). • Inside money: created by the commercial banking system. • i.e. through multiple deposit creation.

  30. Money multiplier: numerical example. • We have: • r = 0.10 • C = £400 bn • D = £800 bn • ER = £0.8 bn • c = C / D = 400 / 800 = 0.5 • e = ER / D = 0.8 / 800 = 0.001 • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.10 + 0.001 + 0.5) = 1.5 / 0.601 • = 2.496

  31. We have: • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.10 + 0.001 + 0.5) = 1.5 / 0.601 • = 2.496 • Note: • If ER = 0 and no leakage into cash transactions (i.e. e = c = 0), • m would reduce to: • (1 + 0) / (r + 0 + 0) = 1/r • i.e. the SDM model would hold / m would be: • 1 / r = 1 / 0.1 = 10 • i.e. about 4 times greater.

  32. Determinants of money supply (a) required reserve ratio. • Inverse relationship (ceteris paribus) between RRR and MS: • r↑ → supportable D↓ • → Bank must contract loans and consequently deposits. • i.e. A contraction in MS. • Relationship (ceteris paribus) between RRR and m: • Also inverse -- r is in denominator of m!

  33. Recall above example: • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.10 + 0.001 + 0.5) = 1.5 / 0.601 • = 2.496 • Now suppose r ↑from 0.10 to 0.15: • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.15 + 0.001 + 0.5) = 1.5 / 0.651 • = 2.304 • i.e. m has fallen from 2.496 to 2.304.

  34. Determinants of money supply (b) cash ratio. • Relationship (ceteris paribus) between NBP’s cash to deposits ratio and • money supply • money multiplier • Deposits undergo multiple expansion; currency does not. • → shift from deposits into cash, i.e. rise in c, is switch from component of M that undergoes multiplication into one that does not. • i.e. both m and M are negatively related to c.

  35. Recall above example: • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.10 + 0.001 + 0.5) = 1.5 / 0.601 • = 2.496 • Now suppose c rises from 0.5 to 0.75 (cet. par.): • m = m = (1 + c) / (r + e + c) • = (1 + 0.75) / (0.10 + 0.001 + 0.75) = 1.75 / 0.851 • = 2.056 • m falls from 2.496 to 2.009.

  36. Determinants of money supply (c) excess reserve ratio. • Recall above example: • m = (1 + c) / (r + e + c) • = (1 + 0.5) / (0.10 + 0.001 + 0.5) = 1.5 / 0.601 • = 2.496 • Now suppose fivefold increase in e: • m = (1 + 0.5) / (0.10 + 0.005 + 0.5) = 1.5 / 0.605 = 2.479 • i.e. The increase in r has reduced m VERY LITTLE -- from 2.496 to 2.479.

  37. Note: RRR ↑ is equivalent to ER↑. • Both: bank reduces amount of deposits supported by given level of R. • Bank determines e by costs and benefits of holding ER. • Two main factors: • Market interest rates • Expected deposit outflows.