INTRODUCTION TO THE MACROSIM1 and MACROSIM2 SIMULATION MODELS

Macrosim1 and Macrosim2 are macroeconomic simulation models both contained in a general program called Macrosim (macrosim.exe), which is provided separately from this assignment. (Macrosim.exe also includes a program called budsim which is not used in this class). If Macrosim is available, it might be useful, although not necessary to load it and have it available.

Macrosim1 replicates the standard simple “Keynesian Cross” model that appears in most introductory macroeconomics textbooks. As such, it does not include a financial sector. Although it allows for the existence of a budget deficit, it does not concern itself with how that deficit is financed. Likewise, it treats investment as purely autonomous (not determined within the model), unaffected by interest rates (there are no interest rates in the model). The user of the model arbitrarily chooses the level of investment.

Macrosim2 is similar to Macrosim1 and the “Keynesian Cross” model, except it includes a financial sector, including a money supply. Generally, Macrosim2 has the Loanable Funds model built into its structure. Savings and investment are both influenced by interest rates, and the budget deficit affects the interest rate and, hence, indirectly influences the level of investment.

Macrosim1 is best understood by looking at its mathematical structure.

TABLE 1: MATHEMATICAL DESCRIPTION OF MACROSIM1

(1)	Y = C + I^o + G^o	Gross Domestic Product (Y) equals Consumption (C), Investment (I), plus Government Spending (G), where I and G are autonomous, determined by the user.
(2)	C = a + b(YD)	Consumption is determined by Disposable Income (YD) where “a” is autonomous consumption and “b” is the consumption rate from disposable income.
(3)	YD = (1 – t)Y	Disposable Income is after-tax income and “t” is the income tax rate.
(4)	D = G^o - tY	The Budget Deficit (D) is equal to Government S pending less tax collections.
(5a)	S = YD - C	National Savings (S) equals Disposable Income minus Consumption.
(5b)	S = I^o + D	This is an accounting identity: Investment and the Budget Deficit are financed with borrowed money, which in turn is financed by savings and at equilibrium this identity holds.

This simple equilibrium model is clearly a demand-driven model. Gross Domestic Product is equal to the three primary components of aggregate (national) demand, Consumption, Investment, and Government Spending (equation 1). In this model both Investment and Government are “autonomous,” determined by the model user outside of the model and loaded in as an assumption. Investment can be thought of as externally determined by conditions in the financial markets, including interest rates, which are not represented by the model, and Government Spending can be thought of as a “policy variable” that the user can set.

Consumption is determined the proportion of Disposable Income that we spend (“b”), which will be a value like 0.90 (equation 2).

In turn, the level of Disposable Income is equal to whatever is left over after we pay taxes (equation 3). Taxes are determined by the income tax rate (“t”), which, like Government Spending, can be thought of a “policy variable” that the user can set.

Equation 5a tells us that the level of national Savings will equal after-tax Disposable Income minus what is spent for Consumption. Savings is a residual value, left over after consumers have made their purchases.

Equation 5b, an equilibrium accounting identity, is a little harder to explain. It assumes that the Government Budget Deficit and all business Investment is financed from borrowed money. At equilibrium that borrowed money must equal the level of Savings in the economy generated by the activity represented by equation 5a. This simple assumption will be overturned in Macrosim2, which will provide an additional source of funding, new money creation.

Macrosim1 is a comparative statics equilibrium model. As such, it is interesting only when we “shock” the model by changing the value of one of the autonomous variables, such as Government Spending (G), Investment (I), the tax rate (“t”), or the proportion of Disposable Income consumed (“b”). In the simulation version of the model, default values for all of these are loaded into the model and the equilibrium solution values for all of the dependent variables, including Gross Domestic Product (Y) are determined by the simulation.

Once the model is “shocked,” the user can see what effect the change had upon the final equilibrium value of Gross Domestic Product and the other variables.

[Note: If the reader has access to the Macrosim simulation models, it is worthwhile at this point to launch the model, choose the MS1 option, see the default assumptions, and see how the model determines the level of Gross Domestic Product. Don’t experiment with the model at this stage. More instruction is needed].

THE MULTIPLIER

Both of the Macrosim models employ a very useful concept called the multiplier. The multiplier suggests that an increase in autonomous spending, such an increase in Government Spending (G) can have a multiple effect upon equilibrium Gross Domestic Product (Y). For example, given the default values in Macrosim1, if government spending is increased by one (1), from 40 to 41, and nothing else is done, Gross Domestic Product increases not by 1 but by 2.5!

This is because an increase in autonomous spending not only registers its initial impact, but because it raises Disposable Income (YD) and, hence, Consumption (C), there is a secondary impact upon Gross Domestic Product.

The value of the multiplier indicates by what multiple an increase in autonomous spending will increase Gross Domestic Product.

The mathematical value of the multiplier can be derived by converting some of the original Macrosim equations from Table 1 above into elementary difference equations.

TABLE 2: MATHEMATICAL DERIVATION OF THE MULTIPLIER

(1)	DY = DC + DX^o	From (1) in Table 1, where X^o is either I^o or G^o, either of the two categories of autonomous spending.
(2)	DC = b(DYD)	From (2) in Table 1.
(3)	DYD = (1 – t) DY	From (3) in Table 1.
(4)	DY = b(1 – t) DY + DX^o	Combining (1), (2), and (3)
(5)	[1 – b(1 – t)] DY = DX^o	Rearranging (4)
(6)	DY = (1 / (1 – b(1 – t)) DX^o	Solving for DY.
(7)	m = (1 / (1 – b(1 – t))	Because DY = mDX^o.

For example, if the consumption coefficient is .80 and the income tax rate is .25, then the multiplier is equal to, then according to equation (7) in Table 2 above, the multiplier should equal 2.5:

1 / (1 - .8(1 - .25)) = 2.50 = m

Further, it does not matter whether the stimulus is due to a rise in Government Spending or Investment (which might be provoked outside of the model by lower interest rates, for example). In Macrosim1, the effect upon GDP is the same.

MACROSIM1 HOMEWORK

Now that the structure of the model is understood, it is time to discover the insights and deficiencies of the Macrosim1 model. At this point, launch the Macrosim model and do the Macrosim1 Homework. When this is completed, we will study the Macrosim2 model, which includes a financial sector.