The Micro-foundations of the Demand for Money

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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

• Agents 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
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Expectations of capital gain or loss

• So
• g gt 0 if r gt re
• g lt 0 if r lt re
• But this evaluation is for one agent only and
  will differ for different agents

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R
R
Idle balances
M Total
MT
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R
Md
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

• WMV ? M/W and ? V/W
• ? ? 1
• Capital gain g
• R ?(r g) 0lt ?lt1
• ?g E(g) 0 g N(0, ?2g)
• ?R E(R) E?(rg) ?r

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-

0
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Mathematical preliminaries
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The Opportunity Set
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?R
P
P
?R
0
? 1
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Risk averter - plunger
?R
U1
U0
?R
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Risk averter - diversifier
?R
U1
U0
?R
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Risk lover
?R
U1
U0
?R
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Risk lover - always at maximum risk position
?R
U1
U0
?R
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Plunger - all or nothing
?R
U1
U0
?R
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Diversifier
?R
U1
U0
?R
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Quadratic utility function

• U aR bR2 a gt 0, b lt 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 gt 0 (positive marginal utility)
• d2U/dR2 2b lt 0 (risk aversion)

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Implications
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First 2 moments
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Conclusion

• While Keynes is based on ad-hoc theories of
  psychology, Tobins 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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?
U0
C
A
B
?
0