Why Have Fractional Reserve Banking?

Rajnish MehraArizona State University

Edward C. PrescottArizona State University

14 August 2014

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Definition of a Commercial Bank

A bank is an institution which BOTH

Accepts demand deposits from the public

Originates loans

*Definition is the one in the 1971 U.S. Banking Act of 1971* From Raghuram G. Rajan, “Do We Still Need Commercial Banks?”

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The definition rules out:

Money market funds as they do not originate loans

Finance companies as they do not offer demand deposits

* From Raghuram G. Rajan, “Do we Still Need Commercial Banks?”

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Two Economic Reasons For Commercial Banks In the Past Are:

1. They economized on resources allocated to digging gold out of the ground when there was a gold standard

2. There typically was not enough US government debt to serve as reserves for all demand deposits – now there is

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A Bogus Argument for Fractional Reserves

Save on costly equity financing Admati, DeMarzo, Hellwig and Pfleiderer

demolishes that argument in, “Fallacies, Irrelevant Facts, and Myths in the Discussion of Capital Requirements: Why Bank Equity is not Expensive” (2011)

It comes down to the Modigliani-Miller Theorem

Value cannot be created by shuffling balance sheets

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“There is a pervasive sense in discussions of bank capital regulation that ‘equity is expensive’ and that higher equity requirements, while beneficial, also entail a significant cost. The arguments we examine, which represent those most often made in this context, are fallacious, irrelevant, or very weak.”

Admati, DeMarzo, Hellwig, and Pfleiderer (2011)

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Transactions are not Part of Theory of Value

With valuation theory, the primitives include the commodity space

Households and firms can exchange each commodity for value and value for each commodity

Households face a value (budget) constraint

An agent selecting the commodity vector in a technology set picks the one that maximizes value

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What is Value?Relative prices are determined in the theory of

value

Irving Fisher hypothesize that MV = PT, the quantity theory, where one unit of M is one unit of value for determining P

Meltzer estimated the M1 demand function,

M = v(i) Y, where i is the nominal interest rate

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Lucas developed micro foundations for this money demand function

Lucas and Nicolini (2013) make a case that the demand for money theory for transactions is still alive

Cooley and Hansen (1991,JME) established that with this transaction based theory of money, the consequences of monetary policy for output and employment are small

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Do Banks Perform a Socially ValuableMaturity Transformation Function?

Data source: Flow of Funds for end of 2012

Demand deposits small relative to total business sector borrowing

Checkable deposits 0.08 GNPs (L104, line 10)

Time and savings deposits 0.57 GNPs (L105, line 12)

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Business borrowing, 2.30 GNPs !

This includes household businesses (home mortgages)

Bigger number if car loans treated like home mortgages

Non-collateralized loans (credit cards) are small

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PROPOSAL:Abolish Fractional Reserve Banking

Replace commercial banks with transaction banks

A sister trust corporation to a transaction bank would remain

It would set up and monitor trust that are used to make business and other loans

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The people evaluating loan applications at a bank and trust company would continue to do what they have been doing though they would all be employees of the trust companies

There is no loss of information relative to a system with commercial banks

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Transaction BanksTransaction Banks would have 100% reserve, on which

they receive tax-free interest. Any interest they pay demand depositors is tax free Reserves are a type of Federal Government debt that

only the Fed can hold (R)

The other government debt is privately held (D)

Fed can increase R by issuing reserves to buy some D

D automatically becomes R when held by the Fed The composition of government debt changes

accordingly

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With this SystemNo too-big-to-fail problem

No possibility of a bank run

No need for costly commercial bank regulation and deposit insurance

Resource costs of deposit insurance is at least 50 basis point a year per dollar of deposits

Currently small banks are going out of business because of big regulation costs

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What About Financing Businesses?

The value of US businesses is about 3.5 GNPs

Currently half financed by debt and half by equity

In 1960 three-quarters funded by equity

Fact: Currently very little of businesses are financed by commercial banks accepting demand deposits and making loans to businesses

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Types of Businesses in NIPACorporations, with value about 1.5 GNPs (L213 Line 23)

Unincorporated businesses, with value about 0.5 GNPs (B103 Line 33)

Household businesses value about 1.5 GNPs (B.100 Line 2)

Add 1 GNP of government debt yields household net worth, 4.5 GNPs

Net asset position of Rest of the World is near zero for most countries including the U.S.

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Theory of Value and the D-D Environment

The D-D model is probably the most important paper in banking. It has fostered so much important research

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Does the Diamond-Dybvig Model Establish a Reason for

Fractional Reserve Banking?

We make a distinction between the D-D environment and their banking mechanism. The latter is a particular mechanism

One of the equilibria to their mechanism supports the anonymous social optimum for their particular environment

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Essence of D-D EnvironmentA long term investment that has a high return and

is costly to liquidate

A preference shock that results in some people wanting consumption in period 1. It is called a liquidity shock

Preference shocks are private information All people identical ex-ante Social welfare is their ex-ante expected utility

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Mechanism Design Problem

There are environments for which the good D-D equilibrium allocation is optimal

BUT, there are D-D type environments for which this equilibrium is not the optimal allocation

How can this be?

ANSWER…

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In the private information economies with one ex ante type, if there are shocks to preferences the optimum can have non-degenerate lotteries

Happens when they are useful in differentiating the ex post types

See Prescott and Townsend (1984, IER) and Cole (1989, IER) for an example.

Bottom line: Fact that it is a good mechanism in some environment does not mean it should be set up

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Diamond-Dybvig EnvironmentsWe distinguish between the environment and the

banking mechanism they employ

The D-D environments can be represented as economies using the Prescott-Townsend extension of the theory of value to environments with private information

Equilibrium exists, is optimal and generically unique

Is the use of this theory appropriate for D-D environments?

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Banking is not a Mechanism Design Problem as Argued by Wallace (1996)

Can’t justify setting up the D-D banking arrangement because it’s good equilibrium supports the anonymous Pareto optimum for the D-D environment

Modifying the preference ordering, but not the technologies, in a way that preserves liquidity demand in period 1, the good D-D equilibrium is not optimal

This is accomplished by selecting preferences such that the valuation equilibrium has consumption lotteries which are non degenerate

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Runs are a Characteristic of the Optimal Arrangement for Some Environments

Tri Vi Dang, Gary Gorton, and Bengt Holmstrom (2010) have an example where banking crises are a propriety of the optimal mechanism in “Financial Crises and the Optimality of Debt for Liquidity Provision”

This implies banking crises are not prima facie evidence of market failure

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This is a good use of mechanism design theory

Establishes some observation does not establish a market failure

CONCLUSION….

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Mechanism Design Theory is of Little Use in Designing a

Financial System

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Properties of a Good SystemShould be nearly optimal

Borrowing lending system is optimal if people can privately save at the market rate (Cole and Kocherlakota, 2001)

Hansen and Imrohoroglu (1992) show the simple borrowing and lending arrangement is nearly as good as the costless AD allocation of unemployment risk

The proposed transaction bank system is a borrowing and lending arrangement Given the high cost of insurance, only big idiosyncratic

loses should be insured

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A Good System Permits InnovationOur financial system has been improving

Bid-ask spreads down – assets very liquid Fees for managing assets down Cost of diversifying down – index funds Brokerage fees down – ETF’s zero at Vanguard

There will be new products and arrangement

Some will fail Others will make the system better

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The proposed transaction banking system has these properties

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A Possible ProblemPrivate agents may create substitute for this

interest bearing currency to make transactions.

This is commonly called shadow banking

Money market funds and similar institutions will carry out transactions if interest on government debt higher than interest on reserves.

Is there a solution?

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A Possible SolutionPut a 100% tax on net interest income of limited

liability businesses

This would make borrowing from one group and lending at a higher interest rate to another unprofitable

Maybe I am overlooking something and smart people will figure out a way to get around it

If a way occurs to you, please let me know

We want to be confident that a system will work before implementing it

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With this System How will Businesses be Financed?

Answer: By mutual organizations Equity financing is a mutual arrangement

Households pooling money and lending to business and to state and local governments is a mutual arrangement

There are mutual funds and trusts that hold mortgages

Insurance and pensions funds have a mutual element

Maybe banning limited liability insurance businesses would be a good thing

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Mutual Arrangements is the Way to Finance Businesses

Most currently is financed mutually

Let’s look at US capital accounts and private sector net worth accounts

My unit is GNP, which equals Gross National Income

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How are U.S. Businesses Financed?

Following statistics come from McGrattan and Prescott (2010) published paper. All data and computer programs are available on Minneapolis Federal Reserve Bank website.

TANGIBLE CAPITAL, END OF PERIODA 4.053 Private assets, private, FA 1.1 2.175 Fixed assets, public, FA 1.1 .580 Consumer durables, FA 1.1 .306 Inventories, NIPA 5.7.5 .137 Land, FOF B.100-B.103 .856

INTANGIBLE CAPITAL, END OF PERIODB 1.718 Plant specific 1.198 Technology capital .519

TOTAL Capital 5.771

U.S. Fixed Asset TablesAverages Relative to GNP, 1999-2008

U.S. Capital StocksRelative to GNP, 1999-2008

TANGIBLE CAPITAL, END OF PERIOD 4.053

Private assets, private, FA 1.1 2.175

Fixed assets, public, FA 1.1 .580

Consumer durables, FA 1.1 .306

Inventories, NIPA 5.7.5 .137

Land, FOF B.100-B.103 .856

INTANGIBLE CAPITAL, END OF PERIOD 1.718

Plant specific 1.198

Technology capital .519

TOTAL Capital 5.771

Private Sector Balance SheetAverages for 1999-2008 Relative to GNP

Total Assets 6.79

Tangible assets 3.78

Government debt 0.50

Private debt 2.51

Total Liabilities 2.51

Net Worth 4.28

Source: Flow of Funds Tables D3 and B100.e

Question: Why Net Worth Less than K?

K is 5.77 GNPS

Private sector net worth less government debt is 3.78 GNPs

What about the 2 GNPs difference?

K is 5.77 GNPS

Private sector net worth less government debt is3.78 GNPs

What about the 2 GNPs difference?

Answer: The nature of the tax code.

Question: Why Net Worth Less than K?

The cost of intangible capital to a business is half it costs because intangible capital investment are expensed and not capitalized

Effectively the government pays half the cost and gets half the return. Thus it is half owner.

Answer: The Nature of the Tax Code

Concluding RemarkWe need financial reform

The new system should be simple and transparent to mitigate the time-inconsistency problem This helps insulate the transaction system

political manipulation

We should rely even more on mutual arrangements for the financing of businesses