EC6012 Blogwork 3

Question 1

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

In a steady state the key variables remain in a constant relationship to each other. This must include both flows and stocks. In general, the steady state will be a growing economy where ratios of variables remain constant.

The model SIM omits growth, holding all other levels in the state constant, i.e. a stationary steady state. In such a state:
· There is no change in the stock of money
· Government expenditure must equal tax receipts
· Consumption must be equal to disposable income
· Household savings converges to zero

Model SIM is based on the assumption that consumers have perfect foresight as to their income. When uncertainty is introduced, actual income is substituted for expected income. This assumes households estimate the income they will receive and base consumption over a 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 any extra income received will be saved.
The existence of uncertainty provides a more recursive picture of the system and allows us to define the model SIMEX. Here as periods succeed period’s people amend their consumption as they find their wealth stocks unexpectedly excessive or depleted and as expectations about future income get revised.

In the SIM model wealth is the equilibrium mechanism similar to the “buffer” in the SIMEX model. In comparison the role of money has a much greater importance in the SIMEX model. The same national level of income is reached in both models given fixed expectations in the SIMEX and perfect foresight in the SIM. The convergence rate is different for both models been much slower for fixed or false expectations. Stationary equilibrium is the same in the two models.

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

The introduction of expectations into the Sim Model introduces the possibility of mistakes. If people act on wrong expectations i.e. overstating disposable income saving is lower than expected and the stock of wealth which was built up decreases. This wealth fall off is due to consumption being above expectations of disposable income. Future income expectations will get revised in this scenario. The stability of the model will remain unchanged but differences in income expectations and current income will cause a convergence towards the same figure.

People continue to consume even when expectations are not met. Consumption (spending today) is seen to be more important than saving (saving for tomorrow).


3) Solve SIMEX for the following values for 3 periods: G = 30, α1 = 0.6, α2 = 0.4, θ = 0.2. Follow the format of table 3.6 on page 81 of GL in presenting your results?

Question 2

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

Yes, it is possible to specify a version of SIM that replicates the ISLM model. The ISLM model is in equilibrium at the intersection of the IS and the LM curve which could be compared to the steady state of the SIM model. To replicate a version of SIM to the ISLM curve we believe that the intersection of the IS and LM curve is equal to YD=C in the SIM model. Both models have similar consumption functions.

In the IS/LM curve consumption depends on three factors. First, there is some autonomous level of consumption defined c° even at zero levels of disposable income. Second, consumption depends on disposable income (Y-T) which is subject to parameter “b” that represents the marginal propensity to consume; i.e. when income goes up by a dollar, consumption goes up by 80cents when b=0.8. Third, consumption is a negative function of the interest rate r; as interest rates goes up, consumers will save a larger fraction of their income and consume a small fraction of their income.
C=c° + b(Y-T) – a r

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

As we look at the wealth function, ∆Hh=α2*[(1- α1) *YD / α2 -Hh-1], households now have a target level of wealth, given by VT= (1- α1) *YD / α2. The α3 = (1- α1) / α2 coefficient is the stock-flow norm of households. When the target wealth is equal to disposable income since α3 =1, it means that the target wealth is higher than realized wealth, so that households save in their attempt to adjust their historically given level of wealth to their target wealth. As a result, consumption is systematically below disposable income, until the new stationary state is reached, at which point Hh=VT=YD=C, as we mentioned above.

Moreover, there is another consumption function C= α0+ α1*YD with α0 a positive constant, which is similar to the equation C= α1*YD, 0< α1<1. c="YD">

Reference: Godley, W., and M. Lavoie (2007) Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth, Palgrave Macmillan. http://pages.stern.nyu.edu/~nroubini/NOTES/CHAP9.HTM#topic1