Consider a linear regression model yi =β0 +β1x1i +β2x2i +εi, where we assume that 1. E(εi) = 0, 2. x1i is iid and x2i is

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Consider a linear regression model
yi =β0 +β1x1i +β2x2i +εi,
where we assume that
1. E(εi) = 0,
2. x1i is iid and x2i is iid
3. x1i and x2i are independent of εi.
i=1,2,...,N. (1)
Section A
Judge if each statement given below
is correct or incorrect and explain why in 3-4
lines.
(a) [5] Assume that the εi’s are iid and the variance
of εi is σ2. The conditional expectation
of yi given x1i and x2i is β0 + β1x1i + β2x2i + σ2.
(b) [5] Assume that the distribution of εi is
the normal distribution with mean 0 and
variance σ2 and cov(εi, εi−1) > 0. It
is correct to use White standard errors.
(c) [5] Assume that εi is iid and var(εi)
= σ2 < ∞. To perform inference for β,
i.e., constructing confidence intervals for each parameter
in β, it is wrong to use robust standard errors.
(d) [5] Let βˆ = (βˆ0,βˆ1,βˆ2)′ be the
ordinary least squares estimator for the regression
coefficients β = (β0,β1,β2)′. If we test multiple
hypotheses β1 + β2 = 0 and β0 = 3
using the Wald statistic at significance level 1%, an
asymptotically valid critical value for the test is obtained by the
0.5% quantile in the χ2-distribution with 2 degrees of
freedom.
(e) [5] Assume that the εi’s are iid and the
distribution of εi is the normal distribution with mean 0
and variance σ2. Consider estimating β by max- imum
likelihood. This maximum likelihood estimator for β is
consistent even when εi is not normally distributed.