Chapter 4 – Government Money with Portfolio Choice

This posting is outside the 700 word boundary. It was decided that to reduce any further would mean losing clarity of summary, and the omittance of important facets of the theory.

Model portfolio choice (PC) adds T-Bills (US Treasury Bills) and interest payments into model SIM while also making the assumption that there is no production sector thus the household makes up the whole private sector. T-Bills are issued on a discount basis. At maturity you are offered the face value of the bill. The amount paid for the right to the face value at time T is lower i.e. at a discount, the difference being the interest rate.

The new balance sheet matrix shows that households can either hold cash or bills the sum of the two being the net worth. The total public debt is then equal to the bills held by the households and the bills held by the central bank. The central bank also takes deposits from the households.

The flow matrix in this chapter has two main changes to the previous chapter. Firstly the change in bills figures are added to the flow of funds accounts. Also there are now interest payments arising from government debt which must be accounted for. The central bank sector is now divided into current account and capital account. The current account deals with the inflows and outflows from the current operations of the central bank while the capital account describes any changes in the balance sheet of the central bank e.g. the purchase of new bills.

The Equations
The equations are built on the presumption that producers sell whatever is demanded and that householders have correct expectations regarding their incomes.

Y = C + G
Production is equal to consumption + government expenditure.

YD = Y – T + r-1 . Bh-1
Disposable income is enlarged by adding interest payments on government debt.

T = Ø . (Y + r-1 . Bh-1)
Taxable income is enlarged by adding interest payments on bills held by households.

The Portfolio Decision
Two decisions households face – How much they will save and how they will allocate wealth. The second decision is dependant on the first.

V = V-1 + (YD – C)
Difference between disposable income and consumption is equal to total change in wealth.

C = α1 . YD + α2. V-1, 0< α2 < α1 < 1
Money is replaced by wealth.

4.6A)
Households want to hold a certain amount (λ0) of wealth in bills and the rest (λ0-1) in money. The proportions are dependant on the level of interest on bills and the level of disposable income relative to wealth.

4.7)
Follows from equation 4.6A to show what has to be the share that people hold in the form of bills.

The endogeneity of the money supply

∆BS = Bs – Bs-1 = (G + r-1 . Bs-1) – (T + r-1 . Bcb-1)
The government deficit is financed by bills issued by the treasury department.

∆Hs = Hs - Hs-1 = ∆Bcb
Additions to the stock of high powered money are equal to the additional demand for bills by the central bank.

Bcb = Bs - Bh
r = r¯
The central bank is the residual purchaser of bills. It purchases all the bills offered by the government that the householders are not will to purchase at a given interest rate.

Hh = Hs
The amount of cash that households hold is equal to the amount of cash supplied by the central bank.


4.5 The Steady State Solutions Of The Model

4.5.1 The Puzzling Impact Of Interest Rates

By adding 100 Basis points to the interest rate the Banks set out in Model PC we can identify the difference between it and Model SIM. This results in an expected increase in Households holding more interest paying bills and an unexpected rise in disposable income and consumption. On this occasion when getting steady state solutions of the model government balances means that state revenues plus the profits of the central banks must be equal to pure government expenditures on goods and services plus the cost of servicing the government debt. We arrive at: (4.18)

Y* = G + r.B*h . (1 – θ) / θ = GnT/ θ

This is the steady-state value for national income. Likewise the steady-state solution for disposable income can be obtained by assuming consumption here equals disposable income and substituting Y* for its value in 4.18 we arrive at: (4.19)
C* = YD* = (G + r.N*h).[(1 – θ)/θ]

Both equations are, in full stationary state, an increasing function of the interest rate. This explains the earlier higher interest rates are associated with a higher steady-state national income. Ultimately higher interest rates mean larger absolute amount of bills and households are encouraged to hold a larger proportion of their wealth in the form of bills both leading to larger interest payments on debt.

4.5.2 Fully Developed Steady State Solutions
To formally demonstrate that an increase in the rate of interest will lead to an increase in the amount of bills held by households and an increase in the overall interest payments received by households we must find the value of B*h and substitute it into equations 4.18 amd 4.19. We first turn the consumption function (4.5) into a wealth accumulation function and combine equations 4.4 and 4.5 to get:
∆V = α2 . (α3 . YD – V – 1)
After identifying the value of ∆V = 0 and getting the ratio for wealth and disposable income we combine equations 4.21 and 4.7 we get a value for B*h. After much manipulation we arrive at:


Y* = (G/ θ) { 1 + α3. (1 – θ) . ѓ/[θ/(1- θ)] - α3 . ѓ }

4.6 Implications of changes in parameter values for temporary and steady-state income

4.6.1 Some Puzzling results

If there were an increase in the permanent level of government expenditures G or any permanent decrease in the overall tax rate θ would lead to an increase in the stationary level of income and disposable income: dY/dθ < 0 . Higher rates of interest leads to an increase in the flow of payments that arise from the government sector which leads to an increase of the steady-state level of disposable income and households holding more interest paying government debt. Also increases in the α3 parameter also eventually leads to an increase in stationary income or disposable income.


4.6.2 A Graphical Analysis
As discussed earlier, an increase in any of the propensities to consume means a decrease in the target wealth to disposable income ratio will result. Godley goes on to state that the effect of a higher propensity to consume out of expected disposable income is positive in the short-term, with GDP rising, but, on the other hand, GDP congregates to a new steady-state value in the long run, which is lower than the original steady-state.

Furthermore, National Income rises in the short-term, but then again this effect is only momentary. A lower propensity to save by individuals results in the stock of wealth decreasing, because consumption exceeds disposable income. However, the reduced consumption ultimately compensates for the higher consumption out of current income, so as the wealth continues to decrease, consumption and the interest income on government debt also continue to drop; until it reaches a “new stationary state”, which is lower than the previous steady-state.

Since this is a simplified model, both the household wealth and government debt decrease together, because households are consuming more and therefore, dissaving; while the government benefits from this boost in economic activity, through the generation of increased tax revenues.

In Model PC the relationship between disposable income (YD) and national income (Y) is more complicated than Model SIM, as it goes beyond taxes and takes into account interest payments on debt:

Y = r-1 * Bh-1 + YD /(1- θ)

This equation shows that any increase in the interest rate, or in the propensity to consume leads to a temporary increase in disposable income and national income.

Godley then goes on to state that when one is comparing steady-states, the aggregate income flow is still an increasing function of the interest rate, albeit the short-term impact of interest rates is to reduce consumption and hence income.

Finally, Godley explains that if government officials want to decrease the public debt-to-GDP ratio, they would need to increase tax rates or reduce interest rates, which would lead to a lower level of stationary income. Therefore, they should disregard the debt-to-income ratio if they want to maintain full-employment income.