Blogwork 3 SIMEX, ISLM and SIM

Question 1

a) In SIMEX model Money obtains an extremely important function which is, to act as a buffer whenever expectations turn out to be incorrect. Model SIM had the strong assumption that consumers have perfect foresight with regard to their income. Also for SIM model, Money is the form in which wealth is held (equilibrium).

b) The stability of the model is not threatened by the mistaken expectations. As we reach the same answer in a different way. In the case of mistaken expectations the convergence is much slower than in the perfect foresight case, as it takes many more periods to approach to the steady state.

c)




Question 2
SIM Model and ISLM model share the basic principle in consumption function which is essential to an equilibrium model, so it is possible to replicate the ISLM model from the SIM model.

The consumption function in the SIM model is developed as follows. Household consumption is supposed to determined by two sources of wealth: ⑴ current disposable income(YD); ⑵ accumulated wealth from past time (Hh−1). For each part of wealth, households have different propensity to consume them (α1 & α2). So the consumption for household in SIM model is:

Cd =α1 × Y D +α2×Hh−1


Then the cash held by households(ΔHh) = Hh-Hh−1= Y D- Cd.
When the consumption function is applied to the wealth function, we can conclude that:-
ΔHh =(1-α1) × Y D-α2×Hh−1
ΔHh =α2×(α3 × Y D-Hh−1)
In the equation above, α3= (1-α1)/ α2, is the stock-flow norm of household, then we define α3× Y D as a target level of wealth.

When it comes to a steady state, α3=1, then the target wealth is YD. 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. But we can’t accept the version of consumption function as C=α1 × Y D. This is because if 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 for ever (by an amount equal in each period to YD-C)

Then the equation C=α0+α1× Y D (α0 is constant) represents autonomous consumption. The consumption is independent of current income. Thus the consumption function in ISLM model is replicated, the same is the ISLM model.



Resource: Godley and Lavoie, 2006