lecture 4 the micro-foundations of the demand for money
TRANSCRIPT
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Lecture 4
The Micro-foundations of the Demand for Money
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• Keynes’ Demand for Money
• Sound micro-foundations on the demand for money based on risk and return
• Extension of risk-return analysis to a multi-asset framework
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The Keynesian Demand for Money
• Demand for money = demand for active balances + demand for idle balances
• The Motives approach - 3 motives
• 1) Transactions
• 2) Precautionary
• 3) Speculative
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Regressive Expectations
• Agent’s expectations of interest rate adjustment depended on their subjective evaluation of the ‘normal’ rate of interest.
• The normal rate varies between individuals
• If the normal rate is above the current rate, the interest rate is expected to rise
• If the normal rate is below the current rate, the interest rate is expected to fall
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All or Nothing Theory
Ve = expected value of a bondV = current value of a bondre = normal rate of interestB = coupon on a perpetuity (consol)
Capital gain is g where
e
e
ee
rr
rrB
r
B
r
BVVg
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Expectations of capital gain or loss
• So
• g > 0 if r > re
• g < 0 if r < re
•
• But this evaluation is for one agent only and will differ for different agents
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When interest income from the bond is just offset by the expected capital loss, the investoris indifferent between money and bonds. So:
*1
01
01
0
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R
M TotalMT
R*
Idle balances
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Md
R
M
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The breakdown in liquidity preference
• The special case is when all expectations merge between agents
• If all agents have the same expectation then the speculative demand for money breaks down
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The Liquidity Trap
Md
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Criticism
• No portfolio diversification - all or nothing model
• Psychological basis for the expectation of the rate of interest is not explained - inelastic expectations
• Only a short-run argument. If the rate of interest is constant for any length of time, then agents would revise their normal rate.
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Tobin Model
• Assumptions
• .Agents choose between two assets, Money (M) with zero yield and bonds (consols) (V) with known coupon B per period.
• .No borrowing• .No transactions costs• .Each agent has a quadratic utility function in return R• .Wealth W = M + V
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Tobin continued
• Let = share of money in wealth, let = share of bonds in wealth and g = capital gain
• Return on the portfolio is R
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Tobin preliminaries
• W=M+V; = M/W and = V/W + = 1
• Capital gain = g
• R = (r + g) 0< <1g = E(g) = 0 g ~ N(0, 2
g)
R = E(R) = E[(r+g)] = r
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- +0
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Mathematical preliminariesThe variance of R is
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gEgE
gErEgrE
dRRfgrEgr
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The Opportunity Set
Since R = rThen
Rg
R
g
RR
r
r
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R
R0
PP’
= 1
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Risk averter - plunger
R
R
U0
U1
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Risk averter - diversifier
U0
U1
R
R
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Risk lover
U1
U0
R
R
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Risk lover - always at maximum risk position
U0
U1
R
R
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Plunger - all or nothing
U0
U1
R
R
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Diversifier
U1
U0
R
R
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Quadratic utility function
• U = aR + bR2 a > 0, b < 0
• It can be shown that all that is relevant to the agents choice is the first and second moments of the distribution of returns
• dU/dR = a + 2bR > 0 (positive marginal utility)
• d2U/dR2 = 2b < 0 (risk aversion)
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Implications
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First 2 moments
Totally differentiating and setting to zero
It can be seen that this is a risk averter, diversifier
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Conclusion
• While Keynes is based on ad-hoc theories of psychology, Tobin’s theory is based on explicit optimising behaviour
• Wealth effect may outweigh substitution effect
• Analysis based on first 2 moments only
• Assumes cash is riskless
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More ?
• Money is dominated by income certain riskless assets
• Better at explaining the diversified portfolio between income certain bonds and risky bonds
• Capital risk may not be the motivation for holding safe assets
• Not robust to state of nature
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Multi - asset application
• The model can be extended to dealing with money and a composite bundle of risky assets
• 2 stage process
• Stage 1 - identify the combination of assets that is superior in risk and return - efficient set
• Stage 2 - allocate wealth between money and composite
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B
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