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Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609Introductory Econometrics 4th Edition by Jeffrey Wooldridge
Edition 4ISBN: 978-0324660609 Exercise 5
Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let ![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_c97c_8edd_7fc98ccb005c_SM2712_11.jpg)
be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by ![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f08d_8edd_d74b9281652d_SM2712_11.jpg)
= (Z X)1Z y.
(i) Show that E(![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f08e_8edd_6349aec452df_SM2712_11.jpg)
X) , so that ![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f08f_8edd_47705548b89e_SM2712_11.jpg)
is also unbiased conditional on X.
(ii) Find Var(![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f090_8edd_83b43ddefee9_SM2712_11.jpg)
X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2.
(iii) Which estimator do you prefer,![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f091_8edd_07810816db35_SM2712_11.jpg)
or ![Assume that the model y = X + u satisfies the Gauss-Markov assumptions and let be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y. (i) Show that E( X) , so that is also unbiased conditional on X. (ii) Find Var( X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2. (iii) Which estimator do you prefer, or Explain](https://d2lvgg3v3hfg70.cloudfront.net/SM2712/11eb9ee2_f058_f092_8edd_d7b546bbf23b_SM2712_11.jpg)
Explain
be the OLS estimator of . Let Z = G(X) be an n × (k + 1) matrix function of × and assume that Z X [a (k + 1) × (k + 1) matrix] is nonsingular. Define a new estimator of by = (Z X)1Z y.(i) Show that E(
X) , so that is also unbiased conditional on X.(ii) Find Var(
X). Make sure this is a symmetric, (k + 1) × (k + 1) matrix that depends on Z, X, and 2.(iii) Which estimator do you prefer,
or ExplainExplanation
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Verified
Given:
1) 
satisfies the Gauss-Markov as...
Introductory Econometrics 4th Edition by Jeffrey Wooldridge
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