ECS4863 Assignment 1 2025 - DUE 16 May 2025

ECS4863
Assignment 1 2025

DUE DATE: 16 MAY 2025

, ECS4863 Assignment 1 (2025)

Question 1: (15 marks)

1.1 Omitted Variable Bias (4 marks)

Omitted variable bias (OVB) arises in regression analysis when a relevant variable
that affects the dependent variable is left out of the model. This causes the estimated
coefficients of the included variables to be biased and inconsistent because the omitted
variable is likely correlated with both the included independent variable(s) and the
dependent variable.

To illustrate, suppose the true model is:

Y=β0+β1X1+β2X2+uY = \beta_0 + \beta_1X_1 + \beta_2X_2 + u

But we estimate:

Y=α0+α1X1+eY = \alpha_0 + \alpha_1X_1 + e

If X2X_2 is omitted and it is correlated with X1X_1, then X1X_1 will capture some of the
effect of X2X_2, biasing the estimate of α1\alpha_1.

 Positive bias occurs when the omitted variable is positively correlated with both
the dependent variable and the included independent variable. This causes the
estimated coefficient to be overstated.
 Negative bias occurs when the omitted variable is negatively correlated with the
dependent variable or the included independent variable. This leads to an
understated estimate of the coefficient.

Thus, OVB misleads our interpretation of causal effects.




1.2 Testing for Serial Correlation with Strictly Exogenous Variables (3 marks)