代写Basic of Econometrics I代写Web开发

Basic of Econometrics I

Overview

This lecture covers:

Basics of Ordinary Least Squares (OLS)

Understanding and identifying Omitted Variable Bias (OVB)

The importance of including Control Variables

Interpreting Regression Output Tables

Ordinary Least Squares (OLS)

What is OLS?

OLS estimates the relationship between a dependent variable y and one or more independent variables x.

Simple linear regression model: yi = β0 + β1xi + ui

βo: intercept, β1: slope, ui: error term

The goal is to find the line that best fits the observed data.

OLS Estimation

OLS chooses  and  to minimize the sum of squared residuals:

Closed-form. solutions:

Omitted Variable Bias (OVB)

What is Omitted Variable Bias?

OVB occurs when a relevant variable is left out of the regression model.

This omitted variable must:

Affect the dependent variable (y)

Be correlated with an included independent variable (x)

Example of OVB

Suppose we regress income on years of education.

If ability is omitted and is positively correlated with both education and income, then the OLS estimate of education is upward biased.

Control Variables

Why Use Control Variables?

Control variables help account for omitted variable bias.

By including them, we hold other factors constant, isolating the effect of the variable of interest.

Example: yi = β0 + β1xi + β2zi + ui

Example with Control Variables

Example: Regressing income on education without experience may bias results.

Including experience as a control improves estimate accuracy.