overheads

Central bank balance sheetCentral Bank – gold standard

_____________________________________________________________________________Gold ($ value = Pg·G) | BanknotesLoans | Commercial bank deposits

The Federal Reserve System – fiat money __________________________________________________________________________________Government securities (GS) | Federal Reserve notes (C+V)Loans to financial institutions (DL) | Commercial bank deposits (BD)Foreign exchange reserves (FX, $ value) | Other liabilities (e.g Treas. Deposits)Other assets |

C = Federal Reserve notes held by non-bank public (currency in circulation)V = Federal Reserve notes held by banks in vaults or ATMBD = Commercial bank deposits at the FedR = Bank reserves = V + BDB = Monetary base = C + R (the Fed’s primary liabilities)

US Monetary System

Fed

__________________________________________________________________________________Government securities (TS) | Currency (C) (Base money)Discount loans (DL) | Reserves (R) (Base money)Foreign exchange reserves (FX) | Other liabilities (e.g. Treas. Deposits)Other assets |

Link to current Fed balance sheet: http://www.federalreserve.gov/releases/h41/Current/

Of note:• Securities held outright• TAC and discount loans• Maiden Lane• Other assets• Currency in circulation• Other liabilities include Treasury deposits• Reserves

http://www.federalreserve.gov/releases/h41/Current/

US Monetary SystemFed

__________________________________________________________________________________Government securities (GS) | Currency (C) (Base money)Discount loans (DL) | Reserves (R) (Base money)Foreign exchange reserves (FX) | Other liabilities (Treasury Deposits)Other assets |

Commercial Banks

_________________________________________________________________________________Reserves (R) | Checkable deposits (D)Bank loans (L) | Loans from the central bank (DL)Other assets (e.g. gov’t securities) | Capital (ownership claims)

Private sector (non-bank public)____________________________________________________________________________Checkable deposits (D) (Money) | Bank loans (L) Currency (C) (Money) | Other liabilities Other assets (e.g. physical capital) | Net worth

Monetary base = B = C + RMoney supply = M = C + D

US Monetary System

MONEY SUPPLY

BASE MONEY

US Monetary System

Money supply = Base · MultiplierMultiplier is the multiple by which the money supply

exceeds the base. Under a fractional reserve system with bank loans and credit money, this will be greater than 1.

A simple model of the money supply process:Fed → Base (through its balance sheet)Fed, banks, public → Multiplier (and independent of the

base)

The Fed’s control of the monetary base

The following cause the base to rise (all other factors the same):

• Purchase of government securities

• Increase in discount loans

• Increase in foreign reserves

• Increase in other assets

• Decrease in other liabilities


T-bill purchase by the Fed FED

______________________________________________________T-bills +1000 | +1000 Base

Increase in Treasury deposits (e.g. public pays taxes) FED

______________________________________________________| -1000 Base| +1000 Treas. Dep.

‘Sterilized’ discount loan FED

______________________________________________________T-bills −1000 | 0 BaseDL +1000 |


The Fed and banks accommodate the public’s demand for currency. This reflects the public’s preference for the composition of money it holds. But the base can be independent of this preference.

FED

______________________________________________________

| +1000 Currency

| −1000 Reserves

The monetary base and the government’s budget

The government’s budget constraint:

Government expenditures during the year = tax revenues + treasury securities sold to banks and the public + treasury securities sold to the Fed.

Budget deficits increase the monetary base (monetization) only if the Fed buys new securities

The monetary base and the government’s budget

Government deficit = $100 billion during the year. Fed purchases half of the security issue:

The purchase FED______________________________________________________T-bills +50 billion | +50 billion Treas. Deposits

Treasury spends FED______________________________________________________

| +50 billion Base| −50 billion Treas. Deposits

The money multiplierFed

_______________________________________________GS | C

| R|

Commercial Banks______________________________________________

R | DL |

M = C + DB = C + RL = D – R (assuming other assets/liabilities = DL = 0)

M/B = m = (C+D)/(C+R) = (k+1)/(k+q) > 1L/B = λ = (D–R)/(C+R) = (1–q)/(k+q)

M = m·B → ∆M = m∙∆BL = λ∙B → ∆L = λ∙∆B

The money multiplier

m is the money multiplier. We assume it is determined independently of the base.

λ is the loan multiplier. It is also independent of the base.

k is the currency-deposit ratio, determined by the preferences of the non-bank public.

q is the desired reserve ratio, determined partly by the Fed and partly by banks.

We assume that both k and q are independent of the quantity of base money.

The money multiplier

Example: Fed purchase of t-bill

∆B = $1,000q = 0.10k = 0.50

→ m = 2.50→ λ = 1.50

∆M = 2.50∙1000 = $2,500∆L = 1.50∙1000 = $1,500

∆M = ∆C+∆D = (1+k)∆D∆D = ∆M/(1+k) = $1,667

∆C = ∆M – ∆D = $833∆R = ∆B – ∆C = $167

The multiplier process in a simple case

Assume k=0 (no currency) and q = 10%. Consider balance sheet effects of a t-bill purchase:

Central Bank

______________________________________________________________________T-bills +1000 | + 1000 Reserves (R)

Bank of America______________________________________________________________________Reserves (R) +1000 | + 1000 Deposits (D)

Bank of America______________________________________________________________________Loans (L) +900 | Reserves (R) −900 |

Bank of America (net effect)______________________________________________________________________R +100 | +1000 DL +900 |


Goldman Sachs______________________________________________________________________R +900 | + 900 D

Goldman Sachs______________________________________________________________________L +810 | Reserves (R) −810 |

Goldman Sachs (net effect)______________________________________________________________________R + 90 | +900 DL +810 |


Citi______________________________________________________________________R +810 | + 810 D

Citi______________________________________________________________________L +729 | Reserves (R) −729 |

Citi (net effect)______________________________________________________________________R + 81 | +810 DL +729 |

and so on…


Summary of the entire process involving the banking system:

∆R = 1000∆ L = 900 + 810 + 729 + …= 9,000∆ D = 1000 + 900 + 810 + … = 10,000

m = (1/q) = 10∆ D = 10·∆R = 1000 (which is the change in M given no currency).

The money supply increases by a multiple of the initial injection of reserves because of bank lending.

Removing reserves from the banking system will have the opposite effect (negative signs).

Factors determining the reserve ratio, q

q is determined by Fed and optimizing behavior by banks. Desired reserves consist of required reserves and excess reserves.

• Required reserves (determined by the Fed)• Likelihood of net deposit withdrawals (excess reserves determined by

banks)Higher deposit variability, higher the likelihood of net cash outflows → higher is q.

• Perceived risk of loans/alternative investments (excess reserves determined by banks).

• Interest rate on loans relative to interest rate paid by Fed on reserves (excess reserves determined by banks). This spread reflects the opportunity cost of reserves; higher the spread, lower q.

Change in q

The money multiplier is negatively related to q.

If q = .25 (instead of .10, with k=.50) in the previous example, m = 2.

As banks accumulate reserves, the monetary base can support a smaller amount of deposits and thus money because banks make fewer loans for any given injection of reserves.

Change in q

Suppose market interest rates on loans rise.q = .10, k = 0 Banking system______________________________________________________R 1000 | 10,000 DL 9000 |

q = .20, k=0 Banking system______________________________________________________R 1000 | 5,000 DL 4000 |

m falls from 10 to 5. As loans are paid off, banks will make fewer loans, so that deposits decrease. Remember that total reserves are determined by Fed.

Factors determining the currency ratio, k

k is determined by optimal behavior of the private sector, in this case households (the non-bank sector).

• Interest rates on deposits (negative effect)• Risk of bank deposits (positive effect)• Transactions costs of cash versus checks (the more

convenient is cash relative to checks, higher k)

Change in k

The money multiplier is negatively related to k. (A change in k has a larger proportional effect on the denominator.)

m = (k+1)/(k+q)

k = .50, q = .10 → m = 2.5

k = .60, q = .10 → m = 2.3

Change in k

q = .10, k = .40 → m = 2.8

Fed___________________________________________

GS 10000 | 8000 C| 2000 R

Banking system___________________________________________

R 2000 | 20000 DL 18000 |

B = $10,000M = $28,000

Banking panic:

q = .10, k = .90 → m = 1.9

Fed___________________________________________

GS 10000 | 9000 C| 1000 R

Banking system___________________________________________

R 1000 | 10000 DL 9000 |

B = $10,000M = $19,000Note: The composition of the base has changed as public

converts deposits to cash. The initial withdrawal of $1000 leads to a large change in D and M because of the decline in bank lending.

Change in kHow could the Fed respond to $9,000 decline in M? To stabilize M, open market purchase would

work (reserve compensation).

∆M = m· ∆B∆B = ∆M / m = 9000/1.9 = 4,737

Fed__________________________________________GS 14,737 | 13,263 C

| 1,474 R

Banking system__________________________________________R 1,474 | 14,737 DL 13,263 |

In current environment, q and k are rising, the multiplier is falling. Thus some of the recent increase in base money is compensation for falling multiplier, and not necessarily inflationary

Money during the Great Depression

• Stock market crash in 1929, and other factors, led to banking panic and runs from October 1930 to March 1933: loss of confidence in the system.

• Beginning Oct. 1930, we see C rising quickly, and D falling, as the public rushed to banks.

• Reserves and monetary base fairly steady.• Money stock fell drastically from 1930 to 1933,

despite steady growth in the monetary base.

The Check Tax

In 1932, in the midst of the contraction of money and credit, Congress imposed a 2 cent tax on checks written (independent of the amount of the check). This increased the costs of using checks, and thus reduced the relative cost of using cash. We estimated an additional 10-15% decline in money caused by this tax.

Justification for the tax – to balance the federal budget.

Current trends

Currency-checkable deposit ratio has risen:

• Financial innovations reducing value of demand deposits at banks.

• Foreign demand for US currency.

This has caused instability in M1, but M2 growth has been steady.

2008 data

2008 data

Private banknotes and the multiplier

Since 1914, private banks have not issued banknotes; Fed has monopoly over currency. As we have seen, the quantity of money supply is sensitive to changes in the composition of money, through the currency ratio k.

However, private banknote issue can alleviate this problem in the face of ‘currency’ runs (as opposed to ‘redemption’ runs).

Private banknotes and the multiplier

An example: assume Fed issues only reserves, no currency. Banknotes serve as currency. Banks hold same fraction of reserves on banknotes as on deposits.

k = 1/3 Banking system______________________________________________R 1000 | 2500 BanknotesL 9000 | 7500 D

M = 10,000; B = 1000

k = 1/2 Banking system______________________________________________R 1000 | 5000 BanknotesL 9000 | 5000 D

M = 10,000; B = 1000 → change in composition affects neither the base nor the multiplier.

Balance sheet analysis of TARP US Treasury

__________________________________________

Tr. Dep. + 500 | +500 T-bills

|

Public

__________________________________________

T-bills +500 |

D −500 |

Banking system

__________________________________________

R −500 | −500 D

|

Fed

__________________________________________

| −500 R

| +500 Tr. Dep.


__________________________________________

Tr. Dep. −500 |

Toxic assets +500 |

Public

__________________________________________

0 | 0

|

Banking system

__________________________________________

R +500 |

Toxic assets −500 |

Fed

__________________________________________

| +500 R

| −500 Tr. Dep.


__________________________________________

Tr. Dep. +300 |

Toxic assets −500 |

TPL +200 |

TPL = taxpayer liability

Public

__________________________________________

Assets +300 | +200 TPL

D −300 | −200 NW

Banking system

__________________________________________

R −300 | −300 D

|

Fed

__________________________________________

| −300 R | +300

Tr. Dep.


__________________________________________

Tr. Dep. −300 | −500 T-bills

TPL −200 |

Public

__________________________________________

T-bills −500 | −200 TPL

D +300 |

Banking system

__________________________________________

R +300 | +300 D

|

Fed

__________________________________________

| +300 R | −300

Tr. Dep.


__________________________________________

0 | 0

Public

__________________________________________

Assets +300 | −200 NW

D −500 |

(If Treasury sells assets for, say, $600, then assets go up by 600, D goes down by 500, and NW increases by 100.)

Banking system

__________________________________________

Toxic assets −500 | −500 D

|

Fed

__________________________________________

0 | 0

Summary: Ultimately, Public converts deposits into assets, but loses $200 of wealth (because Treasury sells at a loss). Banks’ assets and liabilities fall, so asset-to-capital ratio rises.

Balance sheet analysis of capital infusion plan

US Treasury

__________________________________________

Tr. Dep. +250 | +250 T-bills

Public

__________________________________________

T-bills +250 |

D −250 |

Banking system

__________________________________________

R − 250 | − 250 D

Fed

__________________________________________

| −250 R

| +250 Tr. Dep.


US Treasury

__________________________________________

Tr. Dep. − 250 |

Bank equity + 250 |

Public

__________________________________________

|

|

Banking system

__________________________________________

R +250 | + 250 Equity

Fed

__________________________________________

| +250 R

| −250 Tr. Dep.


US Treasury

__________________________________________

Bank equity + 250 | +250 T-bills

|

Public

__________________________________________

T-bills +250 |

D −250 |

Banking system

__________________________________________

| −250 D

| + 250 Equity

Fed

__________________________________________

0 | 0

|

Summary: Ultimately, Public (through the Treasury) converts bank liabilities into bank equity. Bank’s asset-to-debt ratio increases. (If the Fed monetizes, it buys $250 t-bills from public, but R would go up by $500. )

The Federal Reserve SystemFederal Reserve Act of 1914 created the Federal Reserve system in three parts:

– Federal Reserve Board (US Treasury Secretary, Comptroller of the Currency, plus five), headquartered in D.C.

– 12 district banks (Atlanta, NY, Boston, etc.). Board of each elects a President. – member commercial banks, which buy stock in the Fed. (Hence, the Fed is privately owned!) National

banks must be members.

Amendments in 1933, 1935– Reconstituted FRB as Board of Governors of the Fed, with 7 members appointed by the President, each

for 14 year terms.– Created FOMC, and authorized open market operations. Consists of 7 Board members plus 5 presidents

who serve on a rotating basis (as voting members). NY Fed President always on as voting member.– Authorized reserve requirements on demand deposits of member banks (now on all banks, since 1980

DIDMCA).

Section 13(3): “In unusual and exigent circumstances, the Board of Governors of the Federal Reserve System, by the affirmative vote of not less than five members, may authorize any Federal reserve bank… to discount for any individual, partnership, or corporation, notes, drafts, and bills of exchange when such notes, drafts, and bills of exchange are indorsed or otherwise secured to the satisfaction of the Federal Reserve bank.” This section has been invoked recently to allow the Fed to buy commercial paper and make loans to JPMorgan and AIG.

The Federal Reserve Act. http://www.federalreserve.gov/aboutthefed/fract.htm

http://www.federalreserve.gov/aboutthefed/fract.htm

Fed Independence

Although Fed is technically privately owned, it is run by the government. But it has been set up to be independent of the branches of government. This is important because of the pressures for manipulating the money stock for political reasons.

An independent central bank is (potentially) a good substitute for a commodity money standard. A credible central bank can provide monetary discipline in the absence of an underlying commodity.

Tools of monetary policy

The Fed has the following tools to control the money supply (and thereby influence interest rates, output and inflation):

• Reserve requirements

• Open market operations

• Discount policy (very old)

• Interest payments on bank reserves (brand new)

Reserve requirements

• 0% on checkable deposits up to 9.3 million, 3% on deposits between 9.3 million and $43.9 million, and 10% beyond.

• An increase in reserve requirements will reduce the money multiplier and the money stock (assuming desired excess reserves do not change to offset).

• The Fed seldom systematically changes reserve requirements for policy purposes.

Reserve Requirements

1 7 14 31 38 45|-------------|-------------|---------|------------|------------|Tu M M Th W Computation period Maintenance period

Computation period: daily average balance on checking accounts and vault cash → required reserves determined.

Maintenance period: must hold average daily balance as deposit at the fed equal to difference between required reserves and vault cash.

Reserve Requirements

Computation period: Tuesday, May 27 to Monday, June 9.

Average daily balance of bank’s checking accounts = $75

Average daily vault cash = $1 million. Required reserves = (0.03)(43.9 – 9.3) + (0.10) (75 –

43.9) = $4.12 million. Required reserve balance to be held as Fed deposit

during the maintenance period (beginning June 26) = $3.12 million.

Reserve requirements

Until recently, reserves paid no interest. In this case, a reserve requirement is just like a tax.

Assume a bank holds no reserves, and thus lends all deposits. If r is the interest rate charged on loans (L) and i the rate charged on deposits (D), then the banks profits are

Profit = r∙L – i∙D = (r – i)D

With a reserve requirement (q) on deposits:

Profit = r(D – R) – i∙D = r(D – qD) – i∙D = [r(1 – q) – i ]D

Example: r = 8%, i = 2%, and q = 10%, instead of 6% return, banks earn 5.2%

Open market operations

Purchases and sales of government securities on the open market (i.e. just like everyone else who buys and sells securities). They give the Fed direct control over bank reserves.

FOMC Trading DeskSecurities markets

Policy directive Purchases/sales

Target level for reserves

Open market operations

• Outright purchases or sales• Repurchase agreements (repo’s): buy gov’t

securities from a dealer, who agrees to repurchase at a given price.

• Dynamic: active change in policy.• Defensive: sterilization of other changes in

base or multiplier.

Fed’s balance sheet (again): http://www.federalreserve.gov/releases/h41/Current/


Discount policyThe Fed’s oldest tool, and means of serving as lender of last resort.

Fed_____________________________________DL +1 million | +1 million R

Banking system_____________________________________R +1 million | +1 million DL

The discount loan shows up as a liability to the bank, but provides the bank additional liquidity (reserves) to make loans or pay of other liabilities. Alternatively, the Fed might require collateral.

Discount policy

Primary credit: for healthy banks in need of temporary liquidity; funds are unrestricted but are charged a penalty rate (say 25 basis points above the federal funds rate). Prior to 2003, discount rate was set below fed funds rate.

Secondary credit: for less healthy banks who don’t qualify for primary credit; rate set at 50 basis points above federal funds rate, and funds are restricted.

For primary and seasonal credit, the Fed sets a discount rate, then banks request a loan amount.



New discount policy tools• Term Auction Facility (Dec. 12, 2007)• Primary Dealers Credit Facility (Dec. 2007)• Term Securities Lending Facility (Dec. 2007)• Asset-backed Commercial Paper MMMF Facility (Sept. 2008)• Commercial Paper Funding Facility (Oct. 7, 2008) • Another facility to buy assets/make loans to MMMF (Oct. 21, 2008)

Prior to these dates, primary and secondary credit were extended to banks, for overnight loans backed by safe and secure collateral. These new tools broadly extend the scope of discount lending to non-banks, non-financial institutions, for longer terms (30 to 85 days), and secured by potentially distressed assets.

The injections of funds through these facilities has been massive: http://research.stlouisfed.org/fred2/series/BORROW?cid=122

http://research.stlouisfed.org/fred2/series/BORROW?cid=122

Term Auction Facility

Fed sets the amount of the funds it is willing to lend, and lets banks anonymously bid for these funds. The bid includes the amount requested and an interest rate. The Fed accepts bids from those banks offering the highest yields until the funds run out. Originally set up as temporary, but it is likely to remain permanent.

For example, suppose the Fed offers $20 billion for auction, and receives bids totaling $30 billion. Then, it orders the bids from highest yield to lowest, and chooses the offers with the highest yields until the $20 is allocated. The actual rate charged is the lowest accepted bid rate.

Term Auction Facility

$20 $30

3%

4%

5%

Rate

$ bid

Sterilization of lending facilities

To a large extent, the Fed has ‘sterilized’ new lending, to prevent reserves from rising too much.

This can be seen from the Fed’s balance sheet – large decreases in t-bills held outright.

Selected balance sheet items: http://research.stlouisfed.org/publications/usfd/page16.pdf

http://research.stlouisfed.org/publications/usfd/page16.pdf

Sterilization of lending facilities

To sterilize, Fed needs enough t-bills to sell. The Treasury has been issuing securities to the Fed for this purpose. In effect, the Fed buys t-bills issued by Treasury, but pays for them by crediting the Treasury’s deposits, not by creating reserves.

See Fed’s balance sheet: Treasury deposits, special financing account.

Fed_____________________________________________________T-bills +459 billion | +459 billion Treas. Dep.

Fed_____________________________________________________T-bills -100 billion | -100 billion Reserves

An additional new tool

• As part of the Emergency Economic Stabilization Act of 2008, the Fed was given authority to pay interest on bank reserves.

• Allows the Fed to set interest rate policy independently of liquidity policy.

• Open market operations will become less important as a tool, because adjustments in reserves will not be necessary to target interest rates.

Documents

overheads