Lecture Applied econometrics course - Chapter 1: Simple regression model

Lecture Applied econometrics course - Chapter 1: Simple regression model has content: What is simple regression model, how to estimate simple regression model, R – Square, assumption, variance and standard error of parameters,... and other contents.

CHAPTER I SIMPLE REGRESSION MODEL APPLIED ECONOMETRICS COURSE

TODAY’S TALK

 What is simple regression model

 How to estimate simple regression model

I WHAT IS SIMPLE REGRESSION MODEL?

 Linear simple regression:

Y: Dependent variable, Explained variable

X: Independent variable, Explanatory variable U: Error term, disturbance

β: Parameters need to be estimated

 SIMPLE regression model = AN independent variable (X)

 An important assumption:

 Take the expectation of (1.1) and use equation (1.2), we have:

 Equation (1.3) is so called population regression function (PRF)

 Attention: distinction between PRF and SRF

II ESTIMATION: ORDINARY LEAST SQUARE (OLS)

2 2

1

ˆ

n

i i i

n

i i

 Equation (1.5) can be expressed as:

II ESTIMATION: ORDINARY LEAST SQUARE (OLS)

 we have:

 The fitted Y is computed as:

 The disturbance is followed by :

II ESTIMATION: ORDINARY LEAST SQUARE (OLS)

EXAMPLE 1: EXPENDITURE.wf

Suppose that we have the data expenditure (Y: $/week) and income (X:

$/week) of 10 families as the table below:

Xi 80 100 120 140 160 180 200 220 240 260

Let’s estimate a linear regression model describing the relationship between expenditure and income?

SOLVE THE EXAMPLE 1 BY HAND

Explain the meaning of your estimated parameters?

SOLVE THE EXAMPLE 1 BY HAND

ESTIMATION BY COMPUTER

R – SQUARE BY COMPUTER

 The free lunch policy in US:

 what is the signal of that you expect?

 Using MEAP93.wf, we estimate the above model, and we have:

0 110

V VARIANCE AND STANDARD ERROR OF PARAMETERS

 Assumption 5: Homoskedasticity

2

Var( ) ui  

 Under the assumptions 1- 5, the variance of the estimators is

unbiased, this is:

Theorem 2: The Unbiasedness of estimator’s variance

ˆ

 where 2 is substituted by

2

2 1

0

2 1

ˆ var( )

n

i i

n i i

V COMPUTE VARIANCE AND STANDARD ERROR BY HAND

2

n

i i

u n

STANDARD ERROR BY COMPUTER

VI MEASUREMENT UNIT

 Consider the two models below:

VII FUNCTION FORM

LOG - LIN

 Consider the model:

 Meaning:

(1.23)

END OF CHAPTER I

APPLIED ECONOMETRICS COURSE