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ECON 4550Econometrics Memorial University of Newfoundland
Adapted from Vera Tabakova’s notes
2.1 An Economic Model 2.2 An Econometric Model 2.3 Estimating the Regression Parameters 2.4 Assessing the Least Squares Estimators 2.5 The Gauss-Markov Theorem 2.6 The Probability Distributions of the Least
Squares Estimators 2.7 Estimating the Variance of the Error Term
FIRST
First:2.1 An Economic Model2.2 An Econometric Model
FIRST
Figure 2.1a Probability distribution of food expenditure y given income x = $1000
Slide 2-Slide 2-44
Figure 2.1b Probability distributions of food expenditures y given incomes x = $1000 and x = $2000
Slide 2- 2-55
The simple regression function
E y x xy x( | ) | 1 2
Figure 2.2 The economic model: a linear relationship between average per person food expenditure and income
Slide 2-7
Slope of regression line
“Δ” denotes “change in”
2
E y x
x
dE y x
dx
( | ) ( | )
Figure 2.3 The probability density function for y at two levels of income
Slide 2-9Principles of Econometrics, 3rd Edition
Slide 2-10Principles of Econometrics, 3rd Edition
1 2|E y x x
Slide 2-11Principles of Econometrics, 3rd Edition
2var |y x
Slide 2-12Principles of Econometrics, 3rd Edition
cov , 0i jy y
Slide 2-13Principles of Econometrics, 3rd Edition
Slide 2-14Principles of Econometrics, 3rd Edition
y~N 1 2X, 2
Slide 2-15Principles of Econometrics, 3rd Edition
1 2( | )E y x x
2var( | )y x
cov , 0i jy y
21 2~ ,y N x
2.2.1 Introducing the Error Term The random error term is defined as
Rearranging gives
y is dependent variable; x is independent variable
Slide 2-16Principles of Econometrics, 3rd Edition
1 2( | )e y E y x y x
y x e 1 2
The expected value of the error term, given x, is
The mean value of the error term, given x, is zero.
Slide 2-17Principles of Econometrics, 3rd Edition
1 2| | 0E e x E y x x
Figure 2.4 Probability density functions for e and y
Slide 2-18Principles of Econometrics, 3rd Edition
Slide 2-19Principles of Econometrics, 3rd Edition
1 2y x e
Slide 2-20Principles of Econometrics, 3rd Edition
( ) 0E e
1 2( )E y x
Slide 2-21Principles of Econometrics, 3rd Edition
2var( ) var( )e y
Slide 2-22Principles of Econometrics, 3rd Edition
cov( , ) cov( , ) 0i j i je e y y
Slide 2-23Principles of Econometrics, 3rd Edition
Slide 2-24Principles of Econometrics, 3rd Edition
e~N0, 2
Slide 2-25Principles of Econometrics, 3rd Edition
y x e 1 2
( ) 0E e 1 2( )E y x 2var( ) var( )e y
cov( , ) cov( , )e e y yi j i j 0
e N~ ( , )0 2
Figure 2.5 The relationship among y, e and the true regression line
Slide 2-26Principles of Econometrics, 3rd Edition
Slide 2-27Principles of Econometrics, 3rd Edition