ECS4863
Assignment 1
Memo | Due 16
May 2025
NO PLAGIARISM
[DATE]
[COMPANY NAME]
[Company address]
,Exam (elaborations)
ECS4863 Assignment 1 Memo | Due 16 May
2025
Course
Advanced Econometrics (ECS4863)
Institution
University Of South Africa (Unisa)
Book
Introductory Econometrics
ECS4863 Assignment 1 Memo | Due 16 May 2025. All questions fully
answered.
Question 1: (15 marks) 1.1 Explain the concept of omitted variable bias and
distinguish between positive and negative bias ( 4)
Question 1.1 (15 marks)
Explain the concept of omitted variable bias and distinguish between positive and negative
bias.
Omitted Variable Bias (OVB):
Omitted variable bias occurs in statistical analysis, particularly in regression models, when a
relevant explanatory variable is left out of the model. This omitted variable must both influence
the dependent variable and be correlated with one or more of the included independent variables.
When this happens, the estimated coefficients of the included variables become biased and
inconsistent, meaning they do not reflect the true relationship between the independent and
dependent variables.
The bias occurs because the effect of the omitted variable is wrongly attributed to the included
variables, leading to inaccurate conclusions and policy implications.
Example:
Suppose we want to study the effect of education (X) on income (Y), but we omit the variable
"ability" (Z), which affects both education and income. If individuals with higher ability tend to
get more education and also earn more, omitting ability will bias the estimate of the return to
education.
Positive vs. Negative Bias:
, Positive Bias:
This occurs when the omitted variable is positively correlated with both the dependent
variable and the included independent variable, or negatively correlated with both. This
leads to an overestimation of the effect of the included variable.
Example: If ability is positively correlated with education and income, the regression will
attribute some of ability’s effect to education, making it look like education increases
income more than it really does.
Negative Bias:
This occurs when the omitted variable is positively correlated with one variable and
negatively correlated with the other. This leads to an underestimation (or possibly a
reversal) of the true effect of the included variable.
Example: If stress level is negatively correlated with income (higher income = less stress)
and positively correlated with working hours, omitting stress could understate the effect
of working hours on income.
In summary:
Omitted variable bias leads to incorrect estimates in regression analysis. It is positive if the bias
inflates the estimated effect and negative if it deflates it. The direction of the bias depends on the
relationships between the omitted variable, the included variables, and the dependent variable.
1.2 Explain in your own words how you test serial correlation with strictly
exogenous variables (3)
Question 1.2 (15 marks)
Explain in your own words how you test serial correlation with strictly exogenous
variables.
To test for serial correlation (also known as autocorrelation) in a regression model with strictly
exogenous variables, we are checking whether the error terms (residuals) in the regression are
correlated with each other over time. Serial correlation violates one of the key assumptions of the
classical linear regression model and can lead to inefficient estimates and incorrect standard
errors.
Strict exogeneity means that the independent variables (X) are not correlated with the error term
(u) in any time period—past, present, or future. This assumption allows us to use simple tests for
serial correlation, like the Durbin-Watson (DW) test, because the X variables are treated as
fixed and uncorrelated with the error term.
Assignment 1
Memo | Due 16
May 2025
NO PLAGIARISM
[DATE]
[COMPANY NAME]
[Company address]
,Exam (elaborations)
ECS4863 Assignment 1 Memo | Due 16 May
2025
Course
Advanced Econometrics (ECS4863)
Institution
University Of South Africa (Unisa)
Book
Introductory Econometrics
ECS4863 Assignment 1 Memo | Due 16 May 2025. All questions fully
answered.
Question 1: (15 marks) 1.1 Explain the concept of omitted variable bias and
distinguish between positive and negative bias ( 4)
Question 1.1 (15 marks)
Explain the concept of omitted variable bias and distinguish between positive and negative
bias.
Omitted Variable Bias (OVB):
Omitted variable bias occurs in statistical analysis, particularly in regression models, when a
relevant explanatory variable is left out of the model. This omitted variable must both influence
the dependent variable and be correlated with one or more of the included independent variables.
When this happens, the estimated coefficients of the included variables become biased and
inconsistent, meaning they do not reflect the true relationship between the independent and
dependent variables.
The bias occurs because the effect of the omitted variable is wrongly attributed to the included
variables, leading to inaccurate conclusions and policy implications.
Example:
Suppose we want to study the effect of education (X) on income (Y), but we omit the variable
"ability" (Z), which affects both education and income. If individuals with higher ability tend to
get more education and also earn more, omitting ability will bias the estimate of the return to
education.
Positive vs. Negative Bias:
, Positive Bias:
This occurs when the omitted variable is positively correlated with both the dependent
variable and the included independent variable, or negatively correlated with both. This
leads to an overestimation of the effect of the included variable.
Example: If ability is positively correlated with education and income, the regression will
attribute some of ability’s effect to education, making it look like education increases
income more than it really does.
Negative Bias:
This occurs when the omitted variable is positively correlated with one variable and
negatively correlated with the other. This leads to an underestimation (or possibly a
reversal) of the true effect of the included variable.
Example: If stress level is negatively correlated with income (higher income = less stress)
and positively correlated with working hours, omitting stress could understate the effect
of working hours on income.
In summary:
Omitted variable bias leads to incorrect estimates in regression analysis. It is positive if the bias
inflates the estimated effect and negative if it deflates it. The direction of the bias depends on the
relationships between the omitted variable, the included variables, and the dependent variable.
1.2 Explain in your own words how you test serial correlation with strictly
exogenous variables (3)
Question 1.2 (15 marks)
Explain in your own words how you test serial correlation with strictly exogenous
variables.
To test for serial correlation (also known as autocorrelation) in a regression model with strictly
exogenous variables, we are checking whether the error terms (residuals) in the regression are
correlated with each other over time. Serial correlation violates one of the key assumptions of the
classical linear regression model and can lead to inefficient estimates and incorrect standard
errors.
Strict exogeneity means that the independent variables (X) are not correlated with the error term
(u) in any time period—past, present, or future. This assumption allows us to use simple tests for
serial correlation, like the Durbin-Watson (DW) test, because the X variables are treated as
fixed and uncorrelated with the error term.
