ECS4863
ASSIGNMENT 1
MEMO | DUE 16
MAY 2025
NO PLAGIARISM
Abstract
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[Email 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 Omitted Variable Bias
Omitted variable bias (OVB) occurs in a regression model when a relevant variable that
influences the dependent variable is not included in the analysis, and this omitted variable is
correlated with one or more of the independent variables that are included in the model. As a
result, the estimated coefficients of the included variables may be biased, as they may be
capturing some of the effect of the omitted variable.
To understand positive and negative bias, consider the following:
Let the true model be: y=β1x1+β2x2+ϵ where y is the dependent variable, x1 is the included
independent variable, x2 is the omitted variable, and ϵ is the error term.
If we estimate a simplified model by omitting x2: y=β~1x1+v where v is the new error term.
The bias in the estimated coefficient β~1 is related to β2 (the effect of the omitted variable on y)
and the correlation between x1 and x2.
, Positive Bias: This occurs when the estimated coefficient β~1 is greater than the true
coefficient β1. This typically happens when:
o The omitted variable (x2) has a positive effect on the dependent variable (y), i.e.,
β2>0.
o The omitted variable (x2) is positively correlated with the included independent
variable (x1).
In this case, the effect of the omitted variable gets attributed to the included variable, inflating its
estimated coefficient.
Negative Bias: This occurs when the estimated coefficient β~1 is smaller than the true
coefficient β1. This typically happens when:
o The omitted variable (x2) has a positive effect on the dependent variable (y), i.e.,
β2>0, and it is negatively correlated with the included independent variable (x1).
o OR, the omitted variable (x2) has a negative effect on the dependent variable (y),
i.e., β2<0, and it is positively correlated with the included independent variable
(x1).
In these scenarios, the effect of the omitted variable works to reduce the estimated
coefficient of the included variable.
In summary:
Positive bias means we overestimate the effect of the included variable.
Negative bias means we underestimate the effect of the included variable.
The direction of the bias depends on both the relationship between the omitted variable and the
dependent variable, and the relationship between the omitted variable and the included
independent 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.
ASSIGNMENT 1
MEMO | DUE 16
MAY 2025
NO PLAGIARISM
Abstract
[Draw your reader in with an engaging abstract. It is typically a short summary of the document.
When you’re ready to add your content, just click here and start typing.]
user
[Email 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 Omitted Variable Bias
Omitted variable bias (OVB) occurs in a regression model when a relevant variable that
influences the dependent variable is not included in the analysis, and this omitted variable is
correlated with one or more of the independent variables that are included in the model. As a
result, the estimated coefficients of the included variables may be biased, as they may be
capturing some of the effect of the omitted variable.
To understand positive and negative bias, consider the following:
Let the true model be: y=β1x1+β2x2+ϵ where y is the dependent variable, x1 is the included
independent variable, x2 is the omitted variable, and ϵ is the error term.
If we estimate a simplified model by omitting x2: y=β~1x1+v where v is the new error term.
The bias in the estimated coefficient β~1 is related to β2 (the effect of the omitted variable on y)
and the correlation between x1 and x2.
, Positive Bias: This occurs when the estimated coefficient β~1 is greater than the true
coefficient β1. This typically happens when:
o The omitted variable (x2) has a positive effect on the dependent variable (y), i.e.,
β2>0.
o The omitted variable (x2) is positively correlated with the included independent
variable (x1).
In this case, the effect of the omitted variable gets attributed to the included variable, inflating its
estimated coefficient.
Negative Bias: This occurs when the estimated coefficient β~1 is smaller than the true
coefficient β1. This typically happens when:
o The omitted variable (x2) has a positive effect on the dependent variable (y), i.e.,
β2>0, and it is negatively correlated with the included independent variable (x1).
o OR, the omitted variable (x2) has a negative effect on the dependent variable (y),
i.e., β2<0, and it is positively correlated with the included independent variable
(x1).
In these scenarios, the effect of the omitted variable works to reduce the estimated
coefficient of the included variable.
In summary:
Positive bias means we overestimate the effect of the included variable.
Negative bias means we underestimate the effect of the included variable.
The direction of the bias depends on both the relationship between the omitted variable and the
dependent variable, and the relationship between the omitted variable and the included
independent 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.
