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

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Figure 2.1b Probability distributions of food expenditures y given incomes x = $1000 and x = $2000

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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

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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

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1 2|E y x x

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2var |y x

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cov , 0i jy y

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y~N 1 2X, 2

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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

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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.

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1 2| | 0E e x E y x x

Figure 2.4 Probability density functions for e and y

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1 2y x e

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( ) 0E e

1 2( )E y x

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2var( ) var( )e y

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cov( , ) cov( , ) 0i j i je e y y

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e~N0, 2

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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

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