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Question: Give a brief answer, explanation, and/or mathematical derivation to the 3 questions below. All th...

Show transcribed image text Give a brief answer, explanation, and/or mathematical derivation to the 3 questions below. All the parts within this question have equal weight. Consider the following model: Y_i = beta_0 + beta_1X_i + upsilon_i where X_i = Z_i + elementof_1, i and upsilon_i = Z_i + elementof_2, i. Where elementof_1 and elementof_2 are iid random variables and independent from each other and independent of Z. (a) Will the least square regression of Y on X yield a consistent estimator of beta_1? If not, will the estimator be upward or downward biased (with respect to the true value)? Consider Y_t = Y_t – 1 + upsilon_t with upsilon_t iid and Y_0 = 0. (a) Show that Var (Y_t) t sigma^2_upsilon where sigma^2_upsilon is the variance of upsilon_t. (b) Is (Y_t)_t stationary? Why or why not? HAC standard errors should be used because: (please choose the correct choice(s)) They are convenient simplifications of the heteroskedasticity-robust standard errors. Conventional standard errors may result in misleading inference. They are easier to calculate than the heteroskedasticity-robust standard errors and yet still allow you to perform inference correctly. When there is a trend. then conventional standard errors result in misleading inference.

Give a brief answer, explanation, and/or mathematical derivation to the 3 questions below. All the parts within this question have equal weight. Consider the following model: Y_i = beta_0 + beta_1X_i + upsilon_i where X_i = Z_i + elementof_1, i and upsilon_i = Z_i + elementof_2, i. Where elementof_1 and elementof_2 are iid random variables and independent from each other and independent of Z. (a) Will the least square regression of Y on X yield a consistent estimator of beta_1? If not, will the estimator be upward or downward biased (with respect to the true value)? Consider Y_t = Y_t – 1 + upsilon_t with upsilon_t iid and Y_0 = 0. (a) Show that Var (Y_t) t sigma^2_upsilon where sigma^2_upsilon is the variance of upsilon_t. (b) Is (Y_t)_t stationary? Why or why not? HAC standard errors should be used because: (please choose the correct choice(s)) They are convenient simplifications of the heteroskedasticity-robust standard errors. Conventional standard errors may result in misleading inference. They are easier to calculate than the heteroskedasticity-robust standard errors and yet still allow you to perform inference correctly. When there is a trend. then conventional standard errors result in misleading inference.