Lecture 4

1. Lecture 4 The Micro-foundations of the Demand for Money

2. 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

3. 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

4. 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

5. All or Nothing Theory

6. 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

8. R R* Idle balances MT M Total

9. R Md M

10. 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

11. The Liquidity Trap Md

12. 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.

13. 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

14. Tobin continued • Let  = share of money in wealth, let  = share of bonds in wealth and g = capital gain • Return on the portfolio is R

15. Tobin preliminaries • W=M+V;  = M/W and  = V/W •  +  = 1 • Capital gain = g • R = (r + g) 0< <1 • g = E(g) = 0 g ~ N(0, 2g) • R = E(R) = E[(r+g)] = r

16. - + 0

17. Mathematical preliminaries

18. The Opportunity Set

19. R P’ P 0 R  = 1

20. Risk averter - plunger R U1 U0 R

21. Risk averter - diversifier R U1 U0 R

22. Risk lover R U1 U0 R

23. Risk lover - always at maximum risk position R U1 U0 R

24. Plunger - all or nothing R U1 U0 R

25. Diversifier R U1 U0 R

26. 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)

27. Implications

28. First 2 moments

29. 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

30. 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

31. 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

32.  U0 C A B  0