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Lecture 3 on money and finance.

Expectations theory of term structure, the demand for money, and equilibrium in the money market

Note on theory of the term structureMany businesses and households borrow risky long-term

(mortgages, bonds, etc.).

These differ from the federal funds rate in two respects:

- term structure (discuss now)

- risk premium (postpone)

The elementary theory of the term structure is the “expectations theory.”

It says that long rates are determined by expected future short rates.

Two period example (where rt,T is rate from period t to T):

(*) (1+i0,2)2 = (1+i0,1) (1+E(i1,2))

More generally:

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0, 0,1 0 1,2 0 1,(1 ) (1 )(1 ( )) (1 ( ))tt t ti i E i E i

Note on theory of the term structureMany businesses and households borrow risky long-term

(mortgages, bonds, etc.).

These differ from the federal funds rate in two respects:

- term structure (discuss now)

- risk premium (postpone)

The elementary theory of the term structure is the “expectations theory.”

It says that long rates are determined by expected future short rates.

Two period example (where rt,T is rate from period t to T):

(*) (1+i0,2)2 = (1+i0,1) (1+E(i1,2))

More generally:

This is “first order theory.” Other theories involve “market segmentation” and “liquidity.”

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0, 0,1 0 1,2 0 1,(1 ) (1 )(1 ( )) (1 ( ))tt t ti i E i E i

Example

Short rates:1 year T-bond = 0.41 % per year2 year T-bond = 1.03 % per year

Implicit expected future rate from 1 to 2 is: (1+r0,2)2 = (1+r0,1) [1+E(r1,2)]

(1+.0103)2 = (1+ .0041) [1+E(r1,2)]

This implies:E(r1,2) = 1.65 % per year

*For simple analytics, see “TermStructureRomer” in Readings on classes.v2, primarily pp. 519-520.

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Recent term structure interest rates (Treasury)

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Expectations theory says that short rates are expected to rise in coming years.

Note that this can explain why Fed makes statement about future rates (look back at Fed statement.)

Older term structure interest rates (Treasury)

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Yiel

d to

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Term or maturity of bond

9/18/2009 9/17/2008

9/19/2006 May-81

In period of very tight money (1981-82) short rates were very high, and people expected them to fall.

So what was the purpose of Operation Forward Guidance?

To lower long run interest rates by lowering expected future short term rates!

This is a problem on Pset 2 for Wednesday.

MAKE SURE YOU FOLLOW RULES ON PROBLEM SETS.

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Fed funds to short rates

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Federal funds rate3 month Treasury bill rate

Short rates to long rates

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10 year T bond3 month T bill

Real interest rate for businesses

Real interest rate for businesses

rb = risky rate – inflation rate= iff + term premium + risk premium -

inflation

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The real interest rate for business:the cost of capital today is back to normal!

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Financial crisis

Real interest rate for businesses

The demand for money

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What is money?

1. Means of exchange (pay bills)2. Unit of account (what are units in balance sheets)3. Operational:

- M1 = Cu (public) + checking balances (of the public)- “M1 is defined as the sum of currency held by the public

and transaction deposits at depository institutions (which are financial institutions that obtain their funds mainly through deposits from the public, such as commercial banks…).”

- $2552 billion in August 2013, $1140 billion of currency (why so much currency?)

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Equations of normal short-run interest determination• Supply of R:

• Fed supplies non-borrowed reserves (NBR) by open-market operations (OMO). We omit bank borrowings as normally tiny.

• (1) Rs = NBR• Demand for R:• Banks are required to hold reserves on checking deposits

(D).• (2) R = hD Equality in normal times (not now!)• The demand for checking deposits (Dd) is determined by

output and interest rate:• (3) Dd = M(i, Y)• This leads to the demand for reserves by banks in normal

times:(4) Rd = h M(i, Y)

• Which yields equilibrium of the market for reserves

• (5) h M(i, Y) = NBR + BR(d)

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Equations of normal short-run interest determination• Supply of R:

• Fed supplies non-borrowed reserves (NBR) by open-market operations (OMO). We omit bank borrowings as normally tiny.

• (1) Rs = NBR• Demand for R:• Banks are required to hold reserves on checking deposits

(D).• (2) R = hD Equality in normal times (not now!)• The demand for checking deposits (Dd) is determined by

output and interest rate:• (3) Dd = M(i, Y)• This leads to the demand for reserves by banks in normal

times:(4) Rd = h M(i, Y)

• Which yields equilibrium of the market for reserves

• (5) h M(i, Y) = NBR + BR(d) Today’s topic

Balance Sheet of Households

Assets Liabilities

Money (M1) Mortgage

Other

Net Worth

Total Assets Liabilities and NW

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1717Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $.

Real Wealth of US Households after the Crisis

Balance sheet of households 2007 2009 ChangeTotal assets 29,366 24,847 -4,519

Tangible assets 24,674 20,026 -4,648

Real estate 22,146 18,272 -3,874

Financial assets 52,071 42,361 -9,710

Deposits and currency 7,232 7,760 528

Checkable deposits and currency 210 300 90

Credit market instruments (ex. equities) 3,806 4,327 520

Corporate equities 10,457 6,266 -4,191

Mutual fund share holdings 4,981 3,741 -1,240

Pension fund reserves 13,765 10,656 -3,109

Proprietors' equity 1,361 1,379 18

Misc …

Total financial liabilities 14,276 14,068 -208

Home mortgages 10,509 10,402 -108

Consumer credit 2,499 2,476 -23

Misc. …

Net worth (market value) 67,161 53,140 -14,021

Source: Federal Reserve, flow of funds, Table B.100

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Simplification for now

• Assume no inflation, so inflation = п =0 and r = i.• Assume that nominal interest rate on money = 0. Interest rate on

bonds is i.• In short run, wealth is fixed, so this reduces to the demand for

money equation:

• This is the canonical equation used in macroeconomics.

Impact of interest rates on demand for M:• In earlier periods, monetarists assumed money was (virtually

completely) interest inelastic – quantity theory.• Today, most economists agree that money demand responds to

interest rates.

( )/ ( ) [ ( ), ( )] [ ( ), ( )]M t P t D r t Y t D i t Y t

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Md

Mdi

Interest rateon bonds (i)

Demand for transactions deposits

Demand for money

function

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Real M1

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Tbill

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The demand for money and interest rates, 1990 - 2013

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Md

Mdi

Interest rateon bonds (i)

Demand for transactions deposits

SMSM’

Equilibrium in the money market

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Central Bankers’ Nightmare: The Liquidity Trap

• In depressions or deep recessions, when i close to zero, have highly elastic demand for money and reserves– US 1930s, Japan 1990s and 2000s, US 2008 to at

least 2015!• Conventional monetary policy is therefore ineffective

(note what happens when M supply shifts from S’’ to S’’’ in figure on next page).

• The Fed must turn to “unconventional instruments”• These have been undertaken since 2008:

– Forward guidance– Buying long-term assets (quantitative easing, or

Large-Scale Asset Purchase Program*)– Setting goals that state that policy will be

accommodative until reach full employment.• US led the way on these, and followed by ECB, BOJ, and

other central banks.

* See http://www.federalreserve.gov/faqs/what-are-the-federal-reserves-large-scale-asset-purchases.htm

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Bank reserves

Fed fu

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The supply and demand for bank reserves, 1990-2013

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S’

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S’’ S’’’

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Short Summary of Monetary Policy

• Starts with short-run interest rate (federal funds rate)

• Supply of reserves determined by central bank (Fed, ECB, …),

• Demand for transactions money (M1) depends upon interest rate,

• Demand for reserves is derived demand from demand for money,

• THEN: Equilibrium of supply and demand for reserves → short-term nominal risk-free interest rate.

• Then to other assets and rates:• Short rates + expectations → long risk-free rate by term

structure theory• Risky rates = risk-free rate + risk premiums• Real rate = nominal rate – inflation (Fisher effect)