2 Consider the linear regression model Y₁ = x + εi (i= 1,..., n) wherea, is a k x 1 vector of regressors, B is the kx 1 vector of unknown parameters and ₁ is the unobservable error term. Assume that the random vector w; = [yi, is i.i.d. and that E (x₁) = 0. Let B = (1) ydenote the least squares estimator for B. (a) Quoting any additional assumptions that you find appropriate, show that is consistent for B.

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2 Consider the linear regression model
Yi = xß + εi (i = 1,..., n)
where x, is a k x 1 vector of regressors, ß is the kx 1 vector of unknown parameters and Ei
is the unobservable error term. Assume that the random vector w; = [yi, x is i.i.d. and
that E (x₁) = 0. Let B = (₁₁) iyi denote the least squares estimator
for B.
(a) Quoting any additional assumptions that you find appropriate, show that B is consistent
for B.
Transcribed Image Text:2 Consider the linear regression model Yi = xß + εi (i = 1,..., n) where x, is a k x 1 vector of regressors, ß is the kx 1 vector of unknown parameters and Ei is the unobservable error term. Assume that the random vector w; = [yi, x is i.i.d. and that E (x₁) = 0. Let B = (₁₁) iyi denote the least squares estimator for B. (a) Quoting any additional assumptions that you find appropriate, show that B is consistent for B.
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