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A fully-coherent simple model of the central bank with portfolio choice by households

A fully-coherent simple model of the central bank with portfolio choice by households. Model PC. The PC model: national accounting equations. Portfolio decisions, based on expected wealth and values: The Brainard-Tobin formula amended.

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A fully-coherent simple model of the central bank with portfolio choice by households

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  1. A fully-coherent simple model of the central bank with portfolio choice by households Model PC

  2. The PC model: national accounting equations

  3. Portfolio decisions, based on expected wealth and values:The Brainard-Tobin formula amended

  4. The consumption function with propensities to consume out of income and out of wealth (the so-called Modigliani consumption function)is equivalent to a wealth adjustement mechanism with a target wealth to disposable income ratio. The assumption of stable stock-flow norms (Godley and Cripps 1982) is derived from the assumption of relatively stable propensities to consume The wealth to income ratio is: V/YD = 3

  5. Realized and expected values

  6. The government, the central bank, and the hidden equation

  7. Chart 4.1a: The stock of Hd & Hh over time with random fluctuations in disposable income

  8. Chart 4.1b: Changes of Hd & Hh over time (1st differences) With random fluctuations in disposable income

  9. Chart 4.2: Bills (Bh) & Cash (Hh) held by households after an increase in the interest rate on bills (in 1960)

  10. Chart 4.3: Y, YD and V after an increase in the interest rate (in 1960) When propensities to consume are constants

  11. Chart 4.4: Y, YD and V after an increase in the propensity to consume (a1) in 1960

  12. Chart 4.5: Bills (Bh) & Cash (Hh) held by households after an increase of the propensity to consume (a1) in 1960:

  13. Chart 4.6: Y, YD V and C after a rise in the interest rate (in 1960) which affects the propensity to consume a1 and hence the implicit target wealth to income ratio.

  14. Replace the equation: Bcb = Bs – Bh Delete the interest rate equation (where r was a constant) Set Bcb as a constant (through open market operations) Add the equation Bh = Bs – Bcb We now have two equations that set Bh. The rate of interest must become a price-clearing variable (in the portfolio equation) Alternative closuresIt is possible to have an alternative closure, a neoclassical one, by assuming the following changes

  15. Variations on the PC model:Adding long-term bonds • It is easy to add long-term bonds to the PC model, with their possible capital gains or losses • Both the short and the long rates can be made exogenous, if the Treasury accepts to see wide fluctuations in the composition of its liabilities. • Or the long rate of interest can be made endogenous, either because the Treasury changes long rates when the share of bonds in national debt diverges from a band; or because the monetary authorities let the prices on long-term bonds fluctuate freely, keeping still the amount or the share of bonds in total debt.

  16. Share of bonds being detained by the public: Bonds/(bonds+bills) 55 % Acceptable range 45 %

  17. Adding-up constraints in portfolio choice • Brainard-Tobin have emphasized the vertical adding-up constraints • Godley has emphasized the horizontal adding-up constraints • B. Friedman has advocated the symmetry constraints • With symmetry and vertical constraints, horizontal constraints are necessarily fulfilled.

  18. Symmetry constraints • (ADUP.7) λ12 = λ21 • (ADUP.8) λ13 = λ31 • (ADUP.9) λ23 = λ32 • (ADUP.10) λ14 = λ41 • (ADUP.11) λ24 = λ42 • (ADUP.12) λ34 = λ43

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