Nonlinear specification and dummy variables, Econometrics

Nonlinear specification and dummy variables, Econometrics

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Suppose you have a model of capital investment by a U.S. rm. Imagine that yt, x1t
and x2t are annual measures of investment, lagged pro t, and lagged capital stock,
all in real dollars. The sample data contains the years 1935-1954. The model can be
written as
yt = 0 + 1x1t + 2x2t +
Dt + "t ; (1)
where Dt is the dummy variable allowing to distinguish between war and non-war
years:
Dt =
{
1 if year=1939,...,1945
0 otherwise
:
Let us de ne a second dummy variable
Ct = 1 ?? Dt
and suppose that in fact we did not run the model (1), but another model (refer to
it as model (2)), where we included both dummies Dt and Ct.
(a) Is there something we should exclude from the model (2) if we want it to be
estimable?
(b) Suppose that we have the following table of results:
Model (2) (3)
Intercept ? ?
D ? (18:099
11:26)
C ? ??(10:190
11:72)
x1 ? ( 0:028
0:0053)
x2 ? (0:163
0:012)
Can you replace the \?" signs in the table? You can use the information that
the covariance matrix of parameters estimate in model (3) is
D C x1 x2
D 126.8591 114.424 -0.0529091 -0.0290572
C 137.3539 -0.052448 -0.0578449
x1 0.00002845202 -0.0000036976
x2 0.0001380281
2

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