Assignment Week 4

Question 1

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

In the steady state both models converge towards the same steady state levels, however the path followed may vary. Furthermore, the SIM model converges more quickly to the steady state as a result of the role of expectations in the SIMEX model.

The wealth stock in the SIMEX steady state is higher than that of the SIM model. This is largely because the role of money in this model is of greater significance. If income is higher than expected, the accumulation of wealth is also higher than expected, and therefore consumption will increase to a point where wealth is so high that additional consumption is equal to the consumption lost for mistaken expectations. This is a sequential system with a built in mechanism for correcting mistakes.

If Yd is underestimated, realized income is above expected and households will add it to their cash balances, so the stock of cash people find themselves holding at the end of each period is not the outcome of a plan. Consequently, savings is higher than expected and the stock of wealth increases faster than in perfect foresight, causing consumption to rise up to C*.

2) What does it mean for stability of the model when the presences of mistakes allow households’ income to suffer? Can you draw any general conclusions about the real world from this model?

The same expected mistake could happen but in the opposite direction, in this case the expected Yd is overestimated, so households will have to take some extra cash from their cash balances, reducing savings and decreasing wealth and decreasing consumption. Eventually, the steady state is reached at the same levels as in the SIM model, but since savings decreased during the process, wealth is lower.

In reality incorrect expectations can occur. Therefore, savings represent a cushion that ensures consumption levels are in a constant growth rate. However, households are rational agents and therefore have either adaptive expectations or rational expectations (taking into account all new information), so expecting Yd at a constant level would be rather unusual.


3) Solve SIMEX for the following values for 3 periods: G=30, alpha1 = 0.6, alpha2 = 0.4, tax rate = 0.2.



Question 2

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

Yes. The ISLM model relates investment, savings, liquidity and money supply with a consumption function given as C = α0 + α1YD. α0: represents autonomous consumption.

The consumption function for the SIM model is given by Cd = (α1 ) (YD) + (α2)(Hh-1) where α1 = the marginal propensity to consume and α2 is the marginal propensity to consume out of opening stock of money (Hh-1). Since the ISLM model does not include money from the previous period Hh-1 becomes zero. Details below.

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

The Consumption Function is depicted by the following: C = α0 + α1YD

α0: represents autonomous consumption, independent of current income, and
α1 represents the Marginal Propensity to Consume.

It was illustrated in tutorials that the above consumption function is not stable as it does not take into account money generated in previous periods. In other words, the consumption function outlined above does not facilitate growth through the model. Therefore, in order for the model to be stable, the level of income and consumption would have to remain constant, and the following relation would hold (C = YD).


Reading:

Leddin, J.A. and Walsh, B. M. (2003) The Macroeconomy of the Eurozone: An Irish Perspective, chapter 17.

Godley and Lavoie (2007) chapter 3.



Websites:
http://pages.stern.nyu.edu/~nroubini/NOTES/CHAP9.HTM#topic1
web.mit.edu/rigobon/www/Cursos/islmclosed.pdf
http://www.egwald.com/macroeconomics/basicislm.php