Blogwork 3

Question 1

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

For SIM model, wealth is the equilibrium mechanism similar to the buffer in the SIMEX model.

For the SIMEX model the important buffer is the role of money.

Some notional income level is reached given fixed expectations and perfect foresight.

Stationary equilibrium is the same in both models.

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

People act on wrong expectations underestimating disposable income. Savings are higher that expected and hence the stock of wealth grows faster than in the perfect foresight case. Consumption eventually reaches the same steady state value that it would in a perfect foresight model. Expectations about income never changes, however wealth does rise faster than it would otherwise have done and it is this which causes consumption to rise.

A couple of conclusions that can be made from this model are that if expected income is always lower than actual income (people act in wrong expectations) stock of wealth grows. Likewise, if expected income is always higher than actual income, stock of wealth falls.

3. Solve SIMEX for the following values for 3 periods: G = 30, α_{1 = 0.6,} α₂ = 0.4,θ = 0.2. Follow the format of table 3.6 on page 81 of GL in presenting your results.

Those figures in the table above are calculated as follows:

Period 1, it is assumed that there is no economic activity and none has ever existed. Therefore, the cells of first column are all equal to zeros.

Period 2, we start from expected disposable income YD^e, which is equal to G*(1-Ө) =30*(1-0.2) =24. Secondly, since there is a marginal propensity to consume of 0.6, this indicates that actual consumption C is 14.4 (=α₁*YD^e+α₂*H_-1=0.6*24+0.4*0) and hence income Y is 44.4 (=G+C=30+14.4). Thirdly, tax T is 8.88 (=ө*Y=0.2*44.4). Finally, the rest of columns 2 are calculated on the basis of the previous calculation.

Period 3, expected disposable income YD^e is YD from period 2. We calculated C using H_-1 (H from period 2).

Period ∞, Y*=G/Ө is steady state, which is 150.

Question 2:

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

Yes, although it does not have all the properties of the consumption function;

C_d = α₁YD + α₂H_-1

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

Consumption Function: C = α₀ + α₁YD

α₀ represents a positive constant, which represents autonomous consumption, independent of current income.

α₁ represents the Marginal Propensity to Consume.

This version of SIM replicates the ILSM model and will allow us to obtain a coherent stationary state. This is because the average propensity to consume can be unity, i.e. we can have C = YD in the stationary state even though the marginal propensity to consume out of disposable income is below 1. This is due to the constant term α₀ which plays a role similar to that of the consumption out of wealth.