Bivariate Regression Model - Econometrics - Lecture Slides, Slides of Econometrics and Mathematical Economics

Download Bivariate Regression Model - Econometrics - Lecture Slides and more Slides Econometrics and Mathematical Economics in PDF only on Docsity!

Econometrics

Chapter 4: Bivariate Regression Model

Population Regression Function

= relationship between dependent and independent variable in the population.

Sample regression function

• Relationship between the dependent and independent variables in the sample
• Requires estimation of intercept and slope parameters from sample data

Population regression function and

sample observations

Assumptions of the classical regression

model

• Ideal conditions that guarantee that estimated parameters are unbiased, consistent, and attain the lowest variance among linear unbiased estimators.

Assumption 1: linearity

• Linear relationship between dependent and independent variable:

Assumption 3: Homoskedasticity

• The error terms have a constant variance:

Heteroskedastic vs. homoskedastic

error processes

Assumption 5: Nonstochastic X

• The X (^) i are nonstochastic (not random)
• Common violations:
  • measurement error
  • endogenous variables
• This assumption guarantees that the covariance between the independent variable and the error term will be zero.

• Assumption 2: E(u)=
• • E(ui )=
• Violation of Assumption

OLS estimation

• Ordinary least squares estimation:

OLS Estimators

Variance of the intercept estimator

Variance of the slope estimator