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)

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Money and finance: The superstars of all time

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Irving Fisher, Yale(1867-1947)

James Tobin, Yale(1918-2002)

Milton Friedman, Chicago(1912-2006)

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Equations of short-run interest determination• Demand for R:• Bank regulation: reserve requirement on checking deposits

(D).• (1’) R = hD In normal times (not now!)• The demand for checking deposits (Dd) is determined by

output and interest rate:

(2) Dd = M(i, Y)

• This leads to the demand for reserves by banks in normal times:

(3) Rd = h M(i, Y)

• Supply of R:• Fed supplies non-borrowed reserves (NBR) by open-market

operations (OMO). We omit bank borrowings as usually tiny.• (4) Rs = NBR• Which yields equilibrium of the market for reserves• (5) h M(i, Y) = NBR + BR(d)

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Balance Sheet of Household

Assets

Cu D Bh (net)

E

Liabilities

NW = household net worth

Cu = currency Bh = household bonds (net of

debts and mortgages) D = checkable deposits

E = equity NW =HH net worth

7Source: Federal Reserve, Flow of Funds, Table B.100; in 2009 $.

Real Wealth of US Households (corrected from class)

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 macro

• In macro, we assume 2 assets (money and bonds).• Further assume no inflation, so inflation = п =0 and r = i.• Assume that nominal interest rate on money = 0.• In short run, wealth is fixed, so this reduces to the demand for

money equation:

• This is the canonical equation used in macroeconomics.

( )/ ( ) [ ( ), ( )] [ ( ), ( )]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

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Cash in advance (transactions) demand for money

• The transactions demand is a specific case of an inventory demand theory (think shoe store)

• Used in advanced macro in “cash-in-advance models”

• Simple example: earn Y at beginning (example is per year; more

generally would be per payment period of say month)

spend evenly at rate of Y per period constant price level money has yield of 0 no opportunity to move from money to other

assets. In this case, we see that the average money

holdings:M* = Y/2

This leads to “monetarist” theory of Milton Friedman;

money demand insensitive to interest rates and “only money matters.”

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Y

0 1

Average money balance

M = Y/2

What’s wrong with this theory?

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More general demand for money

• What happens if we have other assets? • If have bonds as well as money, then can move some of money

to bonds to earn interest.• See next slide for example.• This leads to more general theories in which the demand for

money is interest-elastic• Baumol-Tobin model.

• This is an explicit model of how income, interest rates, and other factors determine how often we move money to bonds.

• Typical methodology of macroeconomics.• Not in textbook. I have a little note, and this will be covered in

section.

Example of how companies keep M = 0.

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Baumol-Tobin model

• Say that can move back and forth into and out of bonds (M and B)

• Bonds yield iB > iM = 0.• Go to bank at beginning of period and deposit half

in bonds; then go in mid-period to move to money so that you can buy your pizzas.

• For one trip, have only half the money and the other half is earning interest.

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Y

0 1

Average money balances are triangles labeled “Money”

For 2 trips to the bank, have M* = Y/4

Bonds

Money

Money

For N trips to the bank, have M* = Y/2N

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• Optimizing money balances (special case of optimal inventory):

• Total cost = C(N) = Forgone Interest + Cost of trips

= iY/(2N) + FN• Maximizing to determine optimal number of trips (N*):

• dC/dN = 0 = - iY/(2N*2) + FN* = (iY/2F)½

• Optimal average money holding are

• M* = Y/(2N*) = (YF/2i)½

• This is the “square root inventory rule” for money holdings• What are elasticities of M w.r.t. Y and i (EM,Y and EM,i )? [E

=½ ]• This is the crux of the debate between monetarists and

Keynesians:• Is the interest elasticity EM,i = 0 or < 0? • If = 0, monetarist; if < 0 then Keynesian• Huge debate in 1960s and 1970s; pretty much settled now.

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Is money demand interest elastic (1975-2012)?

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Real money demand

3 m

on

th T

rea

sury

bill

ra

te

Dependent Variable: ln(Real M1)Method: Least SquaresSample (adjusted): 1959Q2 2011Q2

Coefficient t-Statistic Prob.  

ln(3 mo Tbill) -0.040 -5.0 0.0000ln(real GDP) 0.31 10 0.0016Constant

Standard error regression = 0.085******************************************************************************

************

Elasticities have correct sign and are statistically significant but interest rate coefficient is small.• Why is EM,i so small? Wrong model? Behavioral

economics? Corner solution?19

Econometric estimate of money demand equation

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DM

DMi

Equilibrium in the money market

SM

i*

M*

Money balances

SM

i*

M*

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Monetary policy helpless: 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”• This is the nightmare scenario for the economy and

explains (in part) why the recovery has been so slow.

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0 400 800 1,200

Bank reserves

Fed

eral

fund

s ra

te

The supply and demand for bank reserves, 1950-2012

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S’

S

S’’ S’’’

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Overview of Supply and Demand for Money

• 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;

• 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)

Daily life in macroeconomics

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What will my tax rates be?

Election uncertainties

Eurozone on brink of collapse

What will happen to debt?