IME Group 6: Blogwork 3

Homework 3

Question 1

1) Below are the differences between SIM and SIMEX when both models are in their steady states.

Firstly, a steady state is a state where the key variables remain in a constant relationship to each other. This must include both flows and stocks. When in addition, the levels of the variables are constant; the steady state is a stationary state. In general the steady state will be a growing economy, where ratios of variables remain constant.

In Model SIM we are thus making two behavioural assumptions: first, that firms sell whatever is demanded and secondly, that there are no inventories, which implies that sales are equal to output. In Model SIM there is no investment. This implies that social saving, the saving of the overall economy must sum to zero (Godley and Lavoie, 2007).

The Model SIM deals with the stationary state. As we omit growth we assume a stationary steady state in which neither stocks nor flows change, government expenditure must be equal to tax receipts, that is, there is neither a government deficit nor a government surplus. This is the condition for a zero change in the stock of money (i.e. government debt). Therefore we have:

G = T* = θ.W.N* = θ.Y*

Hence the stationary state flow of aggregate income must be:

Y* = G / θ

The G / θ ratio we call fiscal stance. This is the ratio of government expenditure to its income share (Godley and Cripps, 1983:111). It plays a fundamental role in all of our models with a government sector, since it determines GDP in the steady state.

Another property of the stationary state is that consumption must be equal to disposable income. In other words, in a model without growth, the average propensity to consume must be equal to unity. Finally we must compute the stationary value of stock of household wealth, that is the stationary value of cash money balances which is also the stationary value of the stock of government debt (Godley and Lavoie, 2007).

Furthermore the difference between SIM and SIMEX Model in their steady state is the addition of four more equations with the SIMEX Model as described below. Model SIM was based on the assumption consumers have perfect foresight as to their income but we now introduce uncertainty thus substituting actual income for expected income (SIMEX Model). This assumes households estimate the income they will receive and base consumption over the current period on this. Money stocks that will be held at the end of the period are also estimated. As the level of consumption has already been decided upon, any additional income received will be saved to cash balances. The inclusion of uncertainty yields a more recursive picture of system and allows us to define model SIMEX. As period succeeds period, people amend their consumption decisions as they find their wealth stocks unexpectedly excessive and as their expectations about future income get revised. In sequences, the realized stock of money links each period to the period which comes after. The wealth acts as an equilibrium mechanism similar to the buffer in SIMEX model. Also the convergence rate is different; it’s much slower for a fix or falsified expectations. But stationary equilibrium is the same in both models.

In the SIMEX model consumers do not know precisely what their income is going to be , thus the only change which has to be made to the model is to substitute expected for actual disposable income in the consumption. The new consumption function is therefore:

C_d = α₁ . YD^e + α₂ . H_h-1 : where the superscript e denotes an expected value.

The model SIM uses the assumption that consumers have perfect foresight regarding their income. It assumes that households make some estimate on their income. Demand is added to the equation as households decide at the beginning of a period how much money they desire to have at the end of the period.

∆H_d = Hd – H_h-1 = YD^e – C_d

This equation below shows that if realized income (YD) is above expected income (YD^e), households will hold the difference in the form of larger than expected cash money balances.

H_h – H_d = YD – YD^e

As households can no longer perfectly predict their disposable income at the start of a period the best they can achieve is an estimate (YD^e). Therefore let us for the time being assume that expected income YD^e is equal to the realized income of the previous period YD-1.

YD^e = Y_d-1

i) Mistaken expectations concerning income are relatively unimportant in a stock flow model, that is in a model where changes in stocks are taken into consideration and where some flows depend on the values taken by the stocks, as is the case here with the consumption function. Uncertainty is introduced into the model here by making consumption depend on expected income – not actual income, which households can only guess. A new and extremely important function for money is that it acts as a ‘buffer’ whenever expectations turn out to be incorrect, i.e. “when the presence of mistakes allow household’s incomes to suffer”

ii) Model SIM was built under the assumption of a stationary steady state. We saw that in such a steady state, the government budget had to balance. However, in the real world e.g. a growing system, the private sector will be accumulating wealth, here cash money. The rate of accumulation of wealth will be equal to the rate of growth of GDP. This implies that, in a steady state, the government budget position must be such that cash money is continuously being issued by government. In a growing steady state, in a model such as ours, the government has to be deficit. Thus to sum up, ‘if nominal income is growing, the appropriate equilibrium condition calls not for a balanced budget but for a deficit big enough to keep the debt growing in proportion to income, the income being determined by portfolio considerations’(Solow in Worswick & Trevithick, 1983 : 165).

3) The Impact of $30 of government expenditures, with mistaken expectations

Question 2

Yes, it is possible to specify a version of SIM that replicates the ISLM model.

Let’s start from the consumption function in model SIM.

Households consume on basis of two influences: their current disposable income YD and the wealth they have accumulated in the past H-1. So consumption is determined

as some proportion α1 of the flow of disposable income and some smaller proportion α2 of the opening stock of money.

C_d =α1 × Y D +α2 ×Hh-1 0<α2<α1<>

The cash being held by household equals

∆Hh= Hh-Hh-1= Y D- C_d

So,

C= Y D - ∆Hh = α1 × Y D + α2 × Hh-1

We turn the consumption function into a wealth function, hence:

∆Hh= (1-α1) × Y D-α2 ×Hh-1

∆h = α2 × (α3 × Y D-Hh-1)

α3= (1-α1)/ α2

Households now have a target level of wealth, given by α3× Y D. The α3 coefficient is the stock-flow norm of households.

When reaching the steady state, the target wealth equals to YD since α3=1, the realized wealth remained lower than the target wealth. As a result, consumption is systematically below disposable income, until the new stationary state is reached, at which point Hh =α3× Y D= YD= C.

When the target is reached, no more saving will occur. However we cannot accept the version of consumption function as C=α1 × Y D 0<α1<>α1 is less than unity, the equation implies that if ever a flow stationary state were reached, there would have to be a stock disequilibrium, with C and YD constant, the money stock and government debt must be rising forever (by an amount equal in each period to YD-C).

However, the equation C=α0+α1 × Y D with α0 a positive constant, represents autonomous consumption, independent of current income.

This can replicate IS-LM model.

With this function, it is possible to achieve a coherent stationery state. The average propensity to consume can be unity, we can have C=YD in the stationary state even though α1 is below one. The constant term α0 plays a role similar to that of the consumption out of wealth.