The complexity now is that x s are also random

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Unformatted text preview: Does this mean 1st is better? Trick question! R 2 ’s are not comparable as dependent variables differ in two specifications. Fundamental answer: Prefer second. Why? As 2nd specification is free from heteroscedasticity, OLS is BLUE by G-M Theorem. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)b)i) Obtain an expression for variance of ut Don’t let the time-series keyword fool you. It is still a heteroscedasticity question. Let ut = ut −1 + t Here you may assume ut = u0 be a given value (hence variance=0). Iterative substitution yields: ut = ut −1 + t = ut −2 + . . . t −1 + t t = u0 + τ τ =1 Hence taking variances: t t var (ut ) = var (u0 + τ) τ =1 var ( τ ) = t σ 2 =0+ τ =1 Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B 2007 Question 4 4)b)ii) State whether ut is heteroscedastic Since variance changes across observations it is heteroscedastic. It is not the same type of heteroscedasticity as we saw in previous part a) Conventionally when we say heteroscedasticity, we imply variance changing in relation to values of regressors. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Introducing Stochastic Regressors Difference Between Model A and Model B Up until Chapter 8, we assumed that regressors were nonstochastic. Introduction Heteroscedasticity Past Exam Practice Question Moving Forward: Model B Introducing Stochastic Regressors Difference Between Model A and Model B Up until Chapter 8, we assumed that regressors were nonstochastic. Hence their values were treated like constants. Introduction Heteroscedasticity Past Exam...
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