# 0 6 7 introduction omitting relevant variable

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Unformatted text preview: l A Below are the 6 assumptions of Model A: A.1 The model is linear in parameters and correctly speciﬁed. A.2 There is some variation in each regressor and no exact linear relationship between regressors in the sample. A.3 The disturbance term has zero expectation. A.4 The disturbance term is homoscedastic. A.5 The values of the disturbance term have independent distributions. A.6 The disturbance term has a normal distribution. Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Today’s Lecture Gauss-Markov Theorem Theorem Provided that Model A assumptions are satisﬁed, the OLS estimators are BLUE: Best; most efﬁcient Linear; in terms of how Yi ’s enter the estimator expressions Unbiased; expectation of the estimator equals the true value of the parameter Estimator. Introduction Omitting Relevant Variable Including Irrelevant Variables Today’s Lecture Today’s Pathology Of Least Squares OLS and some estimation issues in the context of Model A: Omitting Relevant Variable and OVB (Chapter 6) Including Irrelevant Variables (Chapter 6) Heteroscedasticity (Chapter 7) Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Today’s Lecture Today’s Pathology Of Least Squares OLS and some estimation issues in the context of Model A: Omitting Relevant Variable and OVB (Chapter 6) Including Irrelevant Variables (Chapter 6) What assumption of Model A is violated? A.1 as the model is not correctly speciﬁed. Past Exam Practice Question Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Deﬁnition Disease 1: Omitted Variable Bias True Model: Y = β1 + β2 X2 + β3 X3 + u But estimate β2 with OLS estimator using (incorrect) model: Y = β1 + β2 X2 + u (1) Our OLS estimator of slope coefﬁcient β2 is: b2 = n ¯ i =1 (X2,i − X2 )(Yi − n ¯2 i =1 (X2,i − X2 ) ¯ Y) → We omit a variable that ought to be included in regression model, X3 . This is exactly why assumption A.1 is violated here! (2) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences Deriving the Estimator To analyze (incorrect) estimator’s properties, insert true model for dependent variable: b2 = n ¯ i =1 (X2,i − X2 )(Yi − n ¯2 i =1 (X2,i − X2 ) ¯ Y) (3) (4) (5) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences Deriving the Estimator To analyze (incorrect) estimator’s properties, insert true model for dependent variable: b2 = = n ¯ ¯ i =1 (X2,i − X2 )(Yi − Y ) n ¯2 )2 i =1 (X2,i − X n ¯ ¯ i =1 (X2,i − X2 )(β2 (X2,i − X2 ) n i =1 (X2,i (3) ¯ ¯ + β3 (X3,i − X3 ) + (ui − u )) ¯2 )2 −X (4) (5) Introduction Omitting Relevant Variable Including Irrelevant Variables Past Exam Practice Question Consequences Deriving the Estimator To analyze (incorrect) estimator’s properties, insert true model f...
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