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

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

Realized and expected values

The government, the central bank, and the hidden equation

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

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

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

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

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

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

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.

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

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.

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

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.

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