y = xB + y is a (nx 1) vector of observations on the dependent variable...

 

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y = xB + y is a (nx 1) vector of observations on the dependent variable is a vector of K parameters to be estimated X is a (n x K) matrix of observations on the regressors & is a (nx 1) vector of unobserved disturbances (a) Set up the minimisation problem for Ordinary Least Squares (OLS) estimation. (b) Derive the corresponding first order conditions under OLS estimation using matrix algebra. (c) What are the implications of your answer for (b) for the OLS residuals? Provide brief comments. (d) Mathematically, provide the conditions required to verify minimisation of the sum of squared residuals under OLS estimation and briefly comment on the conditions. (e) Using matrix notation, derive the variance of the OLS estimator under the Gauss- Markov theorem. State any required assumptions for this derivation. (f) What are the implications of omitted variables bias (OVB) for your estimator of 3? Provide an advanced econometric exposition using matrix notation. y = xB + y is a (nx 1) vector of observations on the dependent variable is a vector of K parameters to be estimated X is a (n x K) matrix of observations on the regressors & is a (nx 1) vector of unobserved disturbances (a) Set up the minimisation problem for Ordinary Least Squares (OLS) estimation. (b) Derive the corresponding first order conditions under OLS estimation using matrix algebra. (c) What are the implications of your answer for (b) for the OLS residuals? Provide brief comments. (d) Mathematically, provide the conditions required to verify minimisation of the sum of squared residuals under OLS estimation and briefly comment on the conditions. (e) Using matrix notation, derive the variance of the OLS estimator under the Gauss- Markov theorem. State any required assumptions for this derivation. (f) What are the implications of omitted variables bias (OVB) for your estimator of 3? Provide an advanced econometric exposition using matrix notation.

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a The minimization problem for Ordinary Least Squares OLS estimation involves minimizing the sum of squared residuals Mathematically it is formulated ... View the full answer