Homework 3

Question 1

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

The model SIM omits growth, with the steady state assuming that both the stocks and flows in the model change at the same rate and remain constant over time. The SIM model assumes:

· ΔH_h = YD – C = 0

· ΔH_g = G - T = 0

The SIM model assumes there is no change in the stock of money.

The government do not have a surplus or deficit as their expenditure is equal to the income they receive through taxation.

Household savings converge to zero as consumption must equal disposable income.

The SIM model is based on the assumption that consumers have perfect foresight and are completely certain of their future income. Wealth is the equilibrium mechanism in the SIM model.

This differs from the SIMEX model due to uncertainty. Consumers have to develop fixed expectations for their future disposable income.

• YD^e = YD_-1

The role of money is the equilibrium mechanism in the SIMEX model. The SIMEX model takes longer to converge to the steady state than the SIM model, but both equilibriums remain the same.

The SIMEX has four more equations to consider in its steady state in comparison to the SIM model. This is due to role of money in the SIMEX model and the fixed expectations of future disposable income rather than perfect foresight.

2. What does it mean for the stability of the model when the presence of mistakes allow household’s incomes suffer? Can you draw any conclusions about the real world from this model?

The stability of the model will remain intact when the presence of mistakes allow household’s incomes to suffer.

For example, if the household underestimates its disposable income in a given period, their savings will increase at a greater rate than expected if their expectations were met. The household will continually have fixed expectations towards disposable income and you use their stock of money as a buffer when expectations are not met. This process continues until expected disposable income equals actual disposable income:

• YD^e = YD

In a real world sense, if people continually underestimate their expected future disposable income, their wealth would grow faster than if they were correct in their expectations at every time period. If people continually overestimate their expected disposable income, their stock of wealth would fall considerably as they would have to use their savings to fund consumption.

3. Solve SIMEX for the following values for 3 periods: G = 30, α₁ = 0.6, α₂ = 0.4, Θ = 0.2.

Question 2

1. Is it possible to specify a version of SIM that replicates the ISLM model?

The version of SIM that replicates the ISLM model is that where

C = α₀ + (α₁ * YD) (1)

where; α₀ represents autonomous consumption, α₁ represents the marginal propensity to consume and YD is the disposable income.

This is so because ISLM is representative of that state which does not take account of stocks of money from previous periods.

2. Write one down and comment on the stability of this model.

First, we will look at the consumption function which is not stable in order to provide a more comprehensive explanation as to why equation (1) is stable.

C = α₁ * YD (2)

This model is not stable over time because it does not take account of cash money from previous periods. According to Godley and Lavoie (2007), this representation of the consumption function does not allow for growth in the model. In order for the model to be stable, there would have to be a “stock disequilibrium”, i.e. if income and consumption remain constant, then the money stock and government debt must be rising for ever (by an amount equal in each period to YD – C)

C = α₀ + (α₁ * YD)

α₀ represents autonomous consumption in this model, i.e. consumption that is independent of income. This consumption function is admissible as the constant term α₀ corrects for the problem in equation (2).