1. An economist friend tells you that the assumption that the observations (yi
, xi) are i.i.d.
implies that the regression yi = x
iβ + ei
is homoskedastic. Do you agree with your friend?
How would you explain your position?
2. Consider estimation of the parameter θ from iid data {xi}
n
i=1, where
θ =
(
0 if xi ∼ Uniform [0, 2]
1 if xi ∼ Uniform [1, 3]
.
Discuss issues of estimation and inference in this model, considering at least two different
consistent estimators of θ.
3. The true model is
yi = xi1β1 + xi2β2 + ei
, E [xiei
] = 0.
However, you are missing data on x and only have access to {yi
, xm
i1
, xm
i2
}
n
i=1 where the x
m
are noisy measures of the x :
x
m
i1 ≡ xi1 +
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