Summary of Godley Chapter 4

Government Money with Portfolio Choice

Overview
Government Money with Portfolio Choice introduces a model which enhances and expands on Model SIM developed and explained in the previous chapter. The new model, Model PC as it is called is that which introduces a new sector, the central bank, which hitherto had implicitly been part of government in Model SIM.

With respect to the updated transactions-flow matrix which now reflect the addition of this new participant, the central bank has two accounts: current and capital. It’s current account refers to inflows/outflows which happen as part of it’s day-to-day business. The capital account refers to changes which may results from alterations to the central banks balance sheet.

Another enhancement is the introduction of government bills (commonly called Treasury Bills ) which households and the central bank can purchase. The government pays holders of these bills interest and as a consequence household income increases to reflect this. Taxable income also increases to reflect this additional income and so “The state takes back with one hand part of what it has paid out with the other” as Godley et. al put it. The central bank also receives interest for holding government bills, but any profits made are returned to government coffers.

Equations and portfolio decisions
Households make a two-stage decision in how much they will save out of their income (consumption decision) and secondly how to allocate their wealth (allocation decision). A households total wealth is the sum of it’s wealth in the last period plus the difference in disposable income and consumption:

V = V-1 + (YD-C)
Where C = α1.YD + α2.V-1

In Model PC a decision must be made by households on how to allocate their wealth between money and bonds. The equations (Brainard-Tobin formula) which describe a households allocation of wealth to bills and money can be described as follows:

Hh/V = (1 - λ0) – λ1 . r + λ2 . (YD/V)

Bh/V = λ0 + λ1 . r - λ2 . (YD/V)

Households will hold a certain proportion (λ0) of wealth as bills and a certain proportion (1 - λ0 ) as money. The two mitigating factors which determine these proportions are: Interest rates and level of disposable income YD. This has a strong intuitive appeal. Higher interest rates results in higher bill coupon payments and as a result households may wish to allocate more of their wealth to bills than to money. Also, the lower the households level of disposable income, the lower the proportion of wealth that will be held in bills.

With respect to the government and central bank sectors, government deficits are financed by newly issued bills. Also, the central bank sector purchases any bills which households do not wish to hold for that particular rate of interest. In this sense, the central bank sector is said to provide cash money on demand. Cash money is therefore endogenous (internal) to the system. Interest rates on the other hand are said to be exogenous (external) or to put it another way it is a facet of monetary policy.

Expectations
In terms of the expectations of Model PC, as was the case with Model SIM, the notion that consumption depends on expected income applies but also that expectations of income can turn out to be incorrect. Since households cannot know in advance what their income will be at the end of any given period, those equations which describe portfolio allocations must be updated to reflect those expectations. The updated equations are as follows (subscript ‘d’ is utilised for assets demanded at the beginning of the period, superscript ‘e’ refers to expectations)


Hd/Ve = (1 - λ0) – λ1 . r + λ2 . (YDe/Ve)

Bd/Ve = λ0 + λ1 . r - λ2 . (YDe/Ve)

What Godley et. al describe as a ‘crucial assumption’ made when expectations of income are incorrect, and hence expectations of wealth are incorrect at the end of a period is that “money balances are the element of flexibility in a monetary system of production” in which money balances are the “buffer that absorbs unexpected flows of funds”. This can explained by way of example. If say disposable income is higher than expected, this model assumes that the unexpected income is saved in the form of cash money balances. Thus any unexpected change in disposable income is absorbed by a similar unexpected change in money balances. Ultimately, this means that households invest in bills with respect to their expectations of disposable income at the beginning of period.

If even there is a random element thrown into the mix such that expected disposable income YDe = YD . (1 + Ra) where Ra is a random process, then the difference between the amount of money held by households and the amount demanded by them is equal to the difference between realised and expected income or to put it another way: Hh – Hd = YD - YDe. Finally, the cash held by a household at the end of any given period should provide a telling signal as to how they should modify their consumption in the next period.

Steady State
When Model PC is simulated numerically, some interesting observations are to be made. Firstly, as interest rates tend higher, households tend to own more bills. This has a sound intuitive grounding: higher rates of return per unit risk on an asset would encourage further investment one would imagine. However, it can also be observed that as interest rates tend higher so too do disposable income and consumption. This does tend to fly in the face of conventional wisdom which would suggest that consumption would tend to decrease as a result of higher interest rates. To explain what is observed in the model, the steady-state solution for national income and consumption need to be examined:

Y* = G + r.Bh*.(1 - θ)/θ
C* = YD* = Y* + r.Bh* - T* = Y* + r.Bh* - θ.(Y* + r.Bh*)

Both equations (note that the asterisk refers to steady-state solutions) are increasing functions of interest rates. Increasing interest rates result in higher national income and consumption. Model PC interest rates do not have an effect on aggregate demand (the model assumes that supply meets demand instantaneously), and as a result a fall off in consumption is not observed in this case. Finally, a steady-state solution is derived and takes the form:

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

where α3 = (1 – α1)/α2

Implications
In examining the above steady-state solution to national income and by varying the parameters, some further observations can be made:

1.An increase in government expenditure G leads to an increase in the national income.
2.A decrease in the overall tax rate θ leads to an increase in the national income.
3.An increase in interest rates, leads to an increase in national income. This is somewhat counter intuitive as explained above, but with reasoning with respect to the model is reasonable.
4.A reduction in liquidity preference (an increase in the desire to hold bills) leads to an increase in national income. This is because any increase in the desire to hold bills leads to an increase in interest rates.
5.When the propensities to consume from income and wealth (α1, α2) become increasingly smaller, α3 or the propensity to invest in bills become larger, then national income becomes larger.

Also to note is that when household consumption is plotted along with expected disposable income and lagged wealth, it is observed that national income rises in the short run for a given amount of accumulated wealth; the increase in consumption expenditure out of current income leads to an increase in aggregate demand; this affect is only short-lived however. As the propensity to save decreases, so too does overall wealth. As wealth decreases, consumption also decreases, and eventually impacts on national income. Household wealth and government debt decrease together by the same amount in this model. This effect may continue until a new steady-state is reached.

Re-examining the curious relationship between higher interest rates and higher national income, the assumption that the propensity to save is constant is quashed. α1
is redefined such that it assumes a value which is negatively dependant on rate of interest.

α1 = α10 –i. r-1

Substituting into the previous equation for α3 :

α3 = (1 - α10 –i. r-1 )/ α2

Simulating the model PC with this new definition causes an initial decrease in economic activity. Consumption falls as does national income. This is consistent with existing short-run economic models. However, with the reduction in propensity to consume and the increase in target wealth to income ratio, there is a gradual increase in the level of wealth. While interest rates do have a negative impact in the short run, it is shown in the long run that the income flow is still a function of interest rates. The negative impact of higher taxes which results in a decrease in consumption leads to a decrease in government tax take – this creates a government deficit until a new steady-state is reached. This adjustment to the model shows the curious short-run effect of a higher interest rates on government fiscal position.

Debt/Income Ratio
Godley et. al finish this chapter by discussing the debt-to-income ratio. Firstly, this ratio is usually measured by dividing public debt by the GDP. In the Model PC however, this can be defined as V/ Y where V is the wealth of households which corresponds to government debt. This ratio is determined by the behaviour of households and as such there is nothing the government can to alter this ratio. However, in reality governments can reduce interests or increase tax rates either of which will lead to a decrease in income. This is incompatible with maintaining full employment in the long run however and consequently it is advised debt-to-income ratio be ignored.

Summary
To summarise, Model PC has been introduced as an enhancement to Model SIM explained in chapter 3. A new participant has been added: the central bank, which is comprised of two accounts under the transaction flow matrix. Also, Treasury bills are introduced into the Model. Households and the central banks can purchase these bills; the government must pay interest to holders of the bills. Households now have further decisions to make in order to determine how much money to allocate to cash and how much to bills. Influencing this decision are interest rates and disposable income. The model was simulated and the implications changing it’s parameters were examined. Interestingly, it was shown that higher interest rates lead to higher national income which though counter intuitive, could be explained by examining the steady-state solution to national income. Finally, the debt-to-income ratio was discussed and it was advised that seeking to alter this ratio was incompatible with maintaining full employment.