1. Consider the following simple Keynesian macroeconomic model of the U.S.
economy.

Y_{t} = C_{t} + I_{t} + G_{t} + NX_{t}

C_{t} = β_{0}
+ β_{1}YD_{t} + β_{2}C_{t-1}
+ ε_{1t}

YD_{t} = Y_{t} – T_{t}

I_{t} = β_{3}
+ β_{4}Y_{t} + β_{5}r_{t-1}
+ ε_{2t}

r_{t} = β_{6}
+ β_{7}Y_{t} + β_{8}M_{t}
+ ε_{3t}

where:

Y_{t} = gross domestic product (GDP) in year t

C_{t} = total personal consumption in year t

I_{t} = total gross private domestic investment in year t

G_{t} = government purchases of goods and services in year t

NX_{t} = net exports of goods and services (exports - imports) in year
t

T_{t} = taxes in year t

r_{t} = the interest rate in year t

M_{t} = the money supply in year t

YD_{t} = disposable income in year t

The endogenous variables are Y_{t}, C_{t}, I_{t}, YD_{t},
and r_{t}. The exogenous and predetermined variables are G_{t},
NX_{t}, C_{t-1}, T_{t},
r_{t-1}, and M_{t}.
Find the reduced form equations for this model.

2. Problem 9.3 on page 276 of the text.

3. (a) For your project, what econometric model do you plan to estimate and
what hypothesis or hypotheses do you plan to test? (b) Depending upon whether
your data are time-series or cross-sectional, test the model for autocorrelation
or heteroskedasticity. (c) If you find a problem with either, explain explicitly how you plan
to correct for it. If the tests do not indicate a problem, explain how you would
have corrected for the problem had the test come out the other way (that is, no
matter how the test comes out, explain how to correct for the problem of heteroskedasticity or autocorrelation as appropriate
for your model).