Attached is an Excel Spreadsheet with a "simple" linear forecasting model. Your task is to attempt to stabilize the economy with appropriate monetary and fiscal policy.
Model Description:
This model extends out for 25 years, and each year has its own column.
First, the exogenous variables in this model include AT (autonomous taxes), AI (autonomous investment), G (government purchases), MB (monetary base), DR (discount rate), Y* (rest of the world GDP), P* (rest of the world price level), and R* (rest of the world interest rate). Initial values are AT=0, AI=500, G=1900, MB=1000, DR=4%, Y*=30,000, P*=100, and R*=3%. I assume that AT, AI, G, and MB all grow at a rate of 2.5% per year.
The three primary endogenous variables include Y (nominal GDP), R (the real interest rate), and E (the direct nominal exchange rate). We then assume a basic Keynesian model:
C (consumption) = 200 + 0.85 (Y - T) -- the MPC is 0.85In the money market, MS (money supply) = money demand. Real money demand is L, which is a function of real GDP and the nominal interest rate (the real interest rate plus IE, the expected inflation rate). The money supply is equal to the monetary base times DEM (the deposit expansion multiplier), which is a function of the discount rate:
T (net taxes) = AT + 0.2 Y
I (investment) = AI + 0.1 Y - 4000 R -- note that an accelerator is present.
EX (exports) = 0.01 Y* + 300 E P* / P, where E is the direct exchange rate (the average price of foreign currency), P* (the foreign price level) = 100, and P (our price level) is also initially 100.
IM (imports) = 0.1 (Y - T)
Y = C + I + G + EX - IM
MS/P = L = 0.6 Y/P - 200 (R+IE)We assume equilibrium in the foreign exchange market, so that the current account balance (CAB) plus net foreign savings inflows (Sf) adds up to zero. Sf is assumed to be a function of the difference between our real interest rates and foreign interest rates, thus:
MS = MB (6 - 25 DR)
CAB + Sf = 0From these equations we can solve for Y, R, and E, and then use these variables to solve for C, T, I, EX, IM, CAB, DEM, MS, and L. We can also solve for Sp (private savings, both business and household), Sg (the government budget surplus), and Sf, since we know:
CAB = EX - IM
Sf = 10,000 (R - R*)
Sp = Y - T - CThe economy has a potential full-employment GDP (YFE) that is a function of technology (Tech), the capital stock (Kstock), and labor supply (LS). I assume that Tech is initially 1 and grows by 1% per year, LS = 100 and is constant, and Kstock = previous year's Kstock less 10% depreciation plus previous year's investment.
Sg = T - G
Sf = IM - EX
Consistent with a Keynesian model, we assume that prices do not adjust in the very short-term. Instead, we assume there is a lag with adaptive expectations, and price inflation is a function of the previous year's inflation rate plus a proportion of the GDP gap (the percentage difference between Y/P and YFE). The nice thing about this lagged price approach is that it tends to make the math much easier, and it does not require us to assume that the economy is always producing at full employment. The bad thing, as you will see, is that this lag in adjustment has a tendency to destabilize the economy excessively, especially when you combine it with a multiplier-accelerator model.
Finally, there is a chart in the file that compares real GDP to full-employment GDP, and also shows the price level.
Project #3 Assignment
Part 1. Go into the exogenous variables in period five
and make the following changes to the economy. Make the changes one-at-a-time,
and in each case return to the original equilibrium before changing the
next variable. In each case the change, the change is expected to
be permanent. In each case, describe the significant effects on the endogenous
variables in both the current and the immediately-following period.
Explain whether this is consistent with the theory you have learned so
far in this class.
a) Autonomous taxes (AT) rise from 0 to 100.
b) Autonomous investment (AI) drops from 566 to 400.
c) Government purchases (G) falls from 2150 to 2000.
d) The Monetary Base (MB) falls from 1131 to 900.
e) The Discount Rate (DR) rises from 4% to 5%.
f) Foreign GDP (Y*) rises from 30,000 to 35,000.
g) Foreign Prices (P*) rise from 100 to 110.
h) Foreign interest rates (R*) fall from 3% to 2%.
Part 2. Go back to the original equilibrium, and then assume that autonomous investment (AI) drops permanently from 566 to 400, and then proceeds to grow as before. Describe what happens to real GDP over the next 20 years. (There is a chart to look at.) Then, using only fiscal and monetary variables -- AT (which can be negative), G, MB, and DR - in period 6 and later, try to return the economy to full-employment, stabilize the price level and also stabilize real GDP in the long-run. Describe what you chose to do, and how it may have significantly affected the other endogenous variables in the economy.
Project #4 (Optional)
Solve for equilibrium in a simpler version of this model. Assume that:
C (consumption) = 200 + 0.85 (Y - T)Ignore the foreign exchange market and price adjustment.
T (net taxes) = 0.2 Y
I (investment) = AI + 0.1 Y - 4000 R, where AI = 500
G (government purchases) = 1900
EX (exports) = 600
IM (imports) = 0.1 (Y - T)
Y = C + I + G + EX - IM
L = 0.6*Y/P - 200 R
MS/P = 50
MS/P = L
First solve for the product market (Y = C + I + G + EX - IM) and the money market (MS/P = L) as functions of Y and R. Then solve for the equilibrium Y and R. Then solve for T, C, I, and IM, and check your solution by showing that Y = C + I + G + EX - IM and MS/P = L.
Next, assume that AI falls from 500 to 400 and EX falls from 600 to
500. Solve for equilibrium Y and R, then solve for T, C, I, and IM.
How do your answers compare to those in your exam and those in Assignment
#1 above. Explain why these answers differ, using what you have learned
in class.