Modeling the Textbook Fractional Reserve Banking System.

1. Modeling the Textbook Fractional Reserve Banking System. Jacky Mallett jmallett@ieee.org

2. Fractional Reserve Banking • Quantity of Loans banks make is a function of their deposits. • Physical money is deposited at banks • Loans create additional bank deposits (money) • Depositors retain the rights to all money in their accounts. • Evolved from Goldsmiths making short term loans against their gold holdings in 1600’s • Mutated from a system that was based on physical currency to one that is (or soon will be) entirely based on electronic bank accounts • Fractional reserve banking because historically Banks were required to only to lend a fraction of their total deposits, and had to retain a reserve.

3. Although generally referred to as monetary expansion – in reality the critical issue is Bank Deposit expansion Bank B Inter-bank transfers / Customer cheques. Bank A Physical deposits and withdrawals of physical money Bank C System originated as a way of regulating physical money in proportion to gold deposits, but has experienced substantial structural changes over time. e.g. Various forms of Gold Standard Regulation (19th century) Bretton Woods (1944 – 1971) Basel Capital Accords (1988 – to date)

4. Textbook model of Fractional Reserve Banking Bank A Bank B Bank C Bank D Where x is the initial deposit and R is the reserve percentage

5. Source: Macmillan Report to the British Parliament 1931Author: John Maynard Keynes

6. Under Textbook Economics assumptions the limit on the capital amount of all outstanding bank loans in the Banking System is 90% of total Money Supply Model Predicts expansion to a stable state with a money multiplier of 1/Reserve requirement

7. Missing from the Textbook Model • Loan Defaults • Loan Repayments • Interbank Lending. • Capital Holdings of the banks (owner’s reserve against defaults) • Required reserves at the Central Bank. • Direct Intervention by the Central Bank (Quantitative easing, lender of last resort) • Critically there appears to be no empirical evidence supporting the limits that are predicted by the model (ever).

8. Euro 1998 - 2007

9. USA M2

10. China – 2006 - 2010 Reserve requirements increased to over 20% since 2006 in failed attempt to constrain growth

12. UK 1999 - 2008 Note that M2 measures and higher (M3, M4) include debt instruments in several forms (money market, retail money market funds)

13. Japanese M2 1980 – 2010 M2 Percentage Change December 29th 1989 Nikkei reaches peak of 38,597 Japanese Credit Bubble

14. Simulation Model – Establishing a flow relationship Loans& Salary payments Bank A Bank A: Employee/Depositors Bank B Bank B: Employee/Depositors Loan repayments • Each Round • Bank lends money to employees • Bank pays employees each round from interest received on loans • Defaults are handled as delays in repayment

15. Model

16. Results • Textbook example cannot work as shown • Banks cannot stay in regulation without Interbank Lending • Lending flows between banks can cause instability • Money Multiplier is a function of loan duration and the reserve requirement • Central Banks appear to be a “Feature” • Larger banks in the system have a lending advantage over smaller banks that increases their size over time • Interbank lending introduces a money creating race condition • Lack of demand for loans can cause contraction in money supply • System exhibits multiple instabilities.

17. Model is not representative of any actual Banking System • Loan Default not explicitly included • Uses Simple Interest calculations rather than Compound Interest • Doesn’t model reserves at the central bank or capital reserves. • Doesn’t model central bank role as lender of last resort. • Complete model would need: • Compound interest • Implementation of Gold Standard regulatory framework • Implementation of Basel Accord frameworks • Modeling of local variations • index linked loans ( Iceland) • Fixed vs variable interest rates • Banks lending more than their deposits(Basel) • Software validation

18. Monetary Cycles. Expansion due to Interbank lending leaks, new bank creation, equity capital expansion, etc. Money / Loan Supply Contraction due to loan defaults, drops in loan demand, monetary flows Time

19. Effects of Changes on Price Level Two types of Price Inflation/Deflation: Monetary – resulting from changes in the total quantity of money Productive - resulting from changes in the total quantity of all goods purchased with money For any given change in prices it is not possible to determine the exact causes without additional information.

20. Quantity Theory of Money (Irving Fisher circa 1911): • Assuming a constant supply of money and a market based economy • MV = PT where M is total quantity of money • V is velocity of circulation of money • P is the price level • T is the total number of transactions purchased with money • But: • we know that every Transaction is purchased with units of money and there must • be at least V transactions. • i.e. M x V = P x T’ x V • Cancelling: • Mt ≈ PtxTt • where t is the period of measurement.

21. Quantity Theory of Money Chapter 2, Section 1: “Let us begin with the money side. If the number of dollars in a country is 5,000,000, and their velocity of circulation is twenty times per year, then the total amount of money changing hands (for goods) per year is 5,000,000 times twenty, or $100,000,000. This is the money side of the equation of exchange. Since the money side of the equation is $100,000,000, the goods side must be the same. For if $100,000,000 has been spent for goods in the course of the year, then $100,000,000 worth of goods must have been sold in that year.”

22. UK 1999 - 2008 Note that M2 measures and higher (M3, M4) often include debt instruments in several forms (money market, retail money market funds)

23. Source: The Purchasing Power of Money: Its Determination and Relation to Credit, Interest, and Crises Irving Fisher 1911 http://www.econlib.org/library/YPDBooks/Fisher/fshPPM.html Chapter 2: “But while a bank deposit transferable by check is included as circulating media, it is not money. A bank note, on the other hand, is both circulating medium and money.” Chapter 3: “The study of banking operations, then, discloses two species of currency: one, bank notes, belonging to the category of money; and the other, deposits, belonging outside of that category, but constituting an excellent substitute. Referring these to the larger category of goods, we have a threefold classification of goods: first, money; second, deposit currency, or simply deposits; and third, all other goods.”

24. Research Questions • Evolution over time of different regulatory regimes. • Full model of Basel System • Full model of Gold Standard system • Effects of different forms of intervention. • Influence of new forms of financial instrument (especially debt based). • What is the “correct” amount of debt and bounds on interest for optimal economic activity? • How do long term regional flows of money affect the price level within single currencies? • How would an economy with a constant money supply behave? • How do we prevent accidental and deliberate exploits?

25. Background Material

26. 1668 1800 1890 1914 1925 1929 1931 1945 -1972 1972 1988 SverigesRiksbank – First Central Bank European Gold and Bimetallism Period – fixed rates of exchange between gold and banknotes. American Free Banking and other experiments Economists begin to question status of Bank Deposits in relation to money World War 1 - British Empire suspends convertibility of banknotes (Gold standard) Britain returns to to Gold Standard American Stock Exchange crash, caused by speculative leveraged borrowing, triggers bank failure and massive monetary contraction. British Parliament Report of the MacMillan Committee – contains deposit expansion explanation Bretton Woods agreement fixes currency relationships with US dollar and gold Nixon abandons the gold standard – floating currency regime returns 1st Basel Treaty – Shifts focus of banking regulation to risk, and capital based reserves

27. Total Lending sourced from Banking System - USA Estimated 2010: $10 trillion commercial bank assets (loans) + $7 trillion asset backed securities Versus $10 trillion liabilities (deposits) Situation is replicated in many major economies. This is new

28. Basel Accord Framework Money, Things that can be bought with money (i.e. Preferential shares), and some flows of money – subordinate debt, hybrid capital (Basel 2 – removed in Basel 3) Banks can increase their lending, by increasing their deposits and equity capital holdings - should be simple movements around the system, purchased with money - one bank gains, another loses. But, if any form of Bank issued debt is allowed into equity capital, then this form of regulation fails. - debt used to regulate debt - new debt creates money Flows of money Money

29. Asset Backed Securities Sale of Bank Loans to entities outside of the regulated banking system. Fannie Mae, created in 1938 , purchases and securitises bank loans in order to create liquidity for loans. (Loans were primarily sold to pension funds, and individual retirement funds) 1973 Bob Dall as part of then Salomon Brothers, created Mortgage Backed Securities (MBS) 1980’s extended to other types of loans, credit card, car loans, etc. Use spreads internationally, in particular UK, Australia, Ireland, New Zealand, Belgium, Holland, etc. Late 1990’s, begins to be used within financial system to finance lending to speculators – including Hedge funds and private equity. Criticized for causing banks to lend irresponsibly as there was no impact on the bank from loan defaults

30. What happened in Iceland? • Equity Capital Manipulation – loans to Bank employees to buy shares, Glitnir “kiddy loans” • Asset Backed Security lending – foreign currency loans, and inflation linked Icelandic bonds • Inflation linked loans, especially mortgages with no recourse conditions. • Very bad idea in the context of an unsuccessfully regulated banking system • Increases in the loan supply cause increase in money supply, triggering inflationary feedback loop • How exactly is it being accounted?

31. Icelandic Inflation Linking Accounting is critical – if inflation linking causes an increase in loan capital Basel requirement is: Loans (Assets) = Equity Capital + Deposits (liabilities) If inflation linking causes an increase in Assets – how is the deposit/equity capital imbalance handled?

32. Iceland – LandsbankiM.Kr.Consolidated Accounts: Annual Report 2000-2007 Assets > Liabilities + Equity Capital

33. Bank B Bank A Bank C Bank D

34. Money is a token of Exchange – Debt is a flow of Money. Bank Loans represent asymmetric flows of money over time. e.g. 25 year loan for $100,000 Total repaid @ 5% $175,000 @ 7.5% $222,000 @ 10% $272,000 Bank A

35. What is Money? • Before the 20th century – money was gold and bank notes of deposit representing it • Bank deposit accounts were not recognized as money • Gold standard regulation established a relationship between gold and bank notes • Bank deposits were not explicitly regulated • Bank deposit expansion was also a feature of gold standard regulation, but was not recognized until late 19th century • Economics: “Money is a matter of functions four, a medium, a measure, a standard, a store” • But – this is not what money is, this is what money is used for.

36. Rothbard Fallacy “I set up a Rothbard Bank, and invest $1,000 of cash (whether gold or government paper does not matter here). Then I “lend out” $10,000 to someone, either for consumer spending or to invest in his business.” Murray Rothbard, Fractional Reserve Banking, 1995 Hearing this, Computer Scientists Alice, Bob and Eve set up two banks Bank Alice lends Eve $10,000 Eve deposits this at Bank Bob Bank Bob lends Eve $100,000 Eve repays $10,000 debt and deposits $90,000 at Bank Alice Bank Alice lends Eve $1,000,000 Eve deposits this at Bank Bob… Several rounds later they all retire to a sub-tropical paradise.

37. Modern Systems use Equity Capital • Under Basel Accords, loan regulation has shifted to equity capital or capital adequacy ratio • (Tier 1+Tier 2 Equity Capital)/Assets ≥ ~10% • From USA Call Reports: • Total Assets ≤ Total Liabilities + Equity Capital • Equity capital provides a separate buffer of money from deposits to compensate for loan loss • Introduces stability issues due to leverage effects if equity capital is tapped to cover defaults. • Regulatory emphasis is on reducing the risk of equity capital losses. • No longer a fractional reserve system, total lending exceeds total deposits • Regulation of total equity capital across the system appears to be implicit

38. Economic activity is conducted as a series of flows of money within the economy: • Direct transfers in exchange for goods and services • Bank originated debt and repayments • Government and Corporate originated debt and repayments (Bonds). • Money essentially functions as a unit of information transfer • Fixed number of units. • In a market based economy Price is established continuously as money flows through the economy. • Price Level is established as a function of the total Quantity of Money (M), and the total quantity of transactions involving money. (T) • Note: • All transactions count – Inflation measures like CPI don’t include share and asset prices, but they should.

39. Debt is an asymmetric flow of money Debt Loan capital A loan is a commitment to provide a flow of monetary tokens over time. e.g. Initial Loan $100,000 @ 6.5% over 25 years $100,000 received - $202,000 repaid Money Loan “capital” is a varying quantity over time that represents the amount outstanding of the initial loan.