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# Week1Notes - 1 ECON3300/7360 APPLIED ECONOMETRICS Week 1...

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1 ECON3300/7360 A PPLIED E CONOMETRICS Week 1 Lecture Outline 1. Assumptions underlying OLS Estimation – Any Econometrics Textbook Chapter 1 or 2 2. Outliers and Data Transformation – Chapter 3 of Mukerjee Text 3. Example 1 Multiple Regression Model – Page 165 of Mukerjee Text 4. Dummy Variable Trap – Pages 206-207 of Hill (ECON2300 Text) 5. Example 2 Dummy Variable Model – Pages 203-205 of Hill Text 6. Example 3 Model with Interaction Between Variables – Pages 220-222 of Hill Text 7. Functional Form and Elasticities

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2 The Classical Linear Regression Model Y = f (x) Consumption = f (Income) Y = β 1 + β 2 X + C = β 1 + β 2 Y + ε ε What is the interpretation of β 1 and β 2 ? i i i i 2 1 i X 2 . 1 3 . 0 Y ˆ X ˆ ˆ Y + = ε + β + β = Note: Y i i X 2 . 1 3 . 0 Y ˆ + = . . . ( ) Y X , . . X Why will the mid-point of X and Y always lie on the estimated linear equation? Y i = 0.3 + 1.2 X i Sum both sides of the equation () ∑∑ + = + = + = == i i n i n i i n i n i i i X n Y X X Y 2 . 1 3 . 0 2 . 1 3 . 0 2 . 1 3 . 0 11 Divide throughout by n X 2 . 1 3 . 0 Y n X 2 . 1 3 . 0 n Y i i + = + =
3 Ceteris Paribus Condition β β + + ε + β = 2 2 1 1 0 X X Y Consider = Y where t = time ε + β + β + β 2 3 2 1 t t Is β 2 the marginal impact of time on Y holding t 2 constant? Assumptions underlying error term (1) E( ε i ) = 0 ε N(0, σ 2 ) (2) Var( ε i ) = σ 2 (3) No autocorrelation ( ) () () j i i j i y , y cov 0 j , cov j i all for 0 E = = ε ε = ε ε (4) E(X i ε i ) = 0 non-random random/stochastic non-stochastic For a simple linear regression y = β 1 + β 2 X + ε , what is (a) E(y) and (b) Var(y)? (a) y = β 1 + β 2 X + ε E(y) = E( β 1 ) + E( β 2 X) + E( ε ) E(y) = β 1 + β 2 X Then () { ε + = y E y ε = y - E(y) = y - β 1 - β 2 X (b) y = β 1 + β 2 X + ε Var(y) = Var ( β 1 + β 2 X ) + Var( ε ) observed = 0 + Var( ε ) = σ 2 random component systematic component

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4 Let Y = f (X 1 , X 2 ) Y = β 0 + β 1 X 1 + β 2 X 2 Residuals versus fitted values 0 Residuals of Y on X 1 , X 2 0 Fitted values of Y Residuals against time
5 Data Transformation – Using Logs Log 10 = common log Log e = natural log denoted as Ln (1) To estimate non-linear models Y = α L β K α (non-linear in variables) Ln Y = δ + β Ln L + α Ln K (linear in terms of unknown parameters) (2) To eliminate skewness

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Week1Notes - 1 ECON3300/7360 APPLIED ECONOMETRICS Week 1...

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