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ECS4863 Assignment 3 2026 (Answer Guide) – Due 18 August 2026
VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN REQUIRED FORMAT AND WITHIN
GIVEN GUIDELINES. IT IS GOOD TO USE AS A GUIDE AND FOR REFERENCE, NEVER
PLAGARIZE. Thank you and success in your academics.
UNISA, 2026
QUESTION 1: THEORY-BASED QUESTIONS (14 Marks)
1.1 Reasons for Using Panel Data and South African
Examples
Answer:
Reasons for using panel data:
1. Controls for unobserved heterogeneity - accounts for time-invariant individual
characteristics that may affect the dependent variable, reducing omitted variable bias.
2. More efficient estimation - provides more variability, less collinearity, and greater
degrees of freedom than pure cross-section or time-series data.
3. Enables dynamic analysis - allows researchers to study how individuals, firms, or
countries change over time.
South African Examples:
National Income Dynamics Study (NIDS) - tracks the same households over time
Quarterly Labour Force Survey (QLFS) - has a rotating panel component that tracks
households over multiple quarters
1.2 Reasons for Preferring Random Effects over Pooled
OLS
Answer:
Random Effects (RE) is preferred over Pooled OLS for three main reasons:
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1. Corrects for serial correlation in the error term: The composite error in panel data
is vit=ai+uitvit=ai+uit, where aiai is the unobserved individual effect. Pooled OLS
ignores the resulting serial correlation, leading to incorrect standard errors. RE uses
Generalized Least Squares (GLS) to correct this problem.
2. Greater efficiency: The RE estimator optimally weights within- and between-individual
variation through quasi-demeaning, producing more efficient (smaller variance)
estimates than Pooled OLS.
3. Reduces bias: RE partially addresses omitted variable bias by modeling the error
structure, providing more reliable estimates when unobserved individual effects exist.
The Breusch-Pagan Lagrange Multiplier test can formally determine whether RE is
preferred over Pooled OLS.
1.3 Determining the Better Model: Pooled OLS vs. LSDV
Answer:
To determine whether Pooled OLS or LSDV is preferred, follow these steps:
Step 1: Estimate both models and conduct an F-test for the joint significance of the
individual dummy variables in the LSDV model.
Step 2: Interpret the F-test:
Null Hypothesis (H0H0) All dummy coefficients = 0 (no individual effects exist)
Alternative (H1H1) At least one dummy coefficient ≠ 0 (individual effects exist)
Step 3: Decision Rule:
Reject H0H0 (p-value < 0.05) → Prefer LSDV because individual-specific effects are
significant. Pooled OLS would suffer from omitted variable bias.
Fail to reject H0H0 (p-value ≥ 0.05) → Prefer Pooled OLS because there is no
evidence of individual effects. LSDV would unnecessarily reduce efficiency.
Additional Considerations:
If NN is large and TT is small, LSDV may lose too many degrees of freedom
Time-invariant variables cannot be included in LSDV as they are perfectly collinear with
the dummies
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1.4 Assumptions for First-Differencing Estimator to be
BLUE
Answer:
For the First-Differencing (FD) estimator to be the Best Linear Unbiased Estimator
(BLUE) conditional on the explanatory variables, the following five assumptions must
hold:
Assumption Description
1. No Perfect The differenced explanatory variables (ΔxitkΔxitk) must not be perfectly collinear
Collinearity and must have variation over time
2. Zero Conditional E(Δuit∣Δxi)=0E(Δuit∣Δxi)=0 - the differenced error has zero mean conditional
Mean on the regressors (strict exogeneity)
3. Homoskedasticity Var(Δuit∣Xi)=σ2Var(Δuit∣Xi)=σ2 - constant variance of the differenced errors
4. No Serial Corr(Δuit,Δuis∣Xi)=0Corr(Δuit,Δuis∣Xi)=0 for t≠st =s - the differenced
Correlation errors are not serially correlated
5. No Measurement The explanatory variables in the differenced equation must be measured without
Error error
QUESTION 2: WAGE-UNEMPLOYMENT ANALYSIS (21
Marks)
Step-by-Step EViews Guide for Question 2
PART A: Data Preparation (Before Opening EViews)
Step 1: Prepare Your Excel Data in "Long" Format
ECS4863 Assignment 3 2026 (Answer Guide) – Due 18 August 2026
VERIFIED AND CERTIFIED ANSWERS. WRITTEN IN REQUIRED FORMAT AND WITHIN
GIVEN GUIDELINES. IT IS GOOD TO USE AS A GUIDE AND FOR REFERENCE, NEVER
PLAGARIZE. Thank you and success in your academics.
UNISA, 2026
QUESTION 1: THEORY-BASED QUESTIONS (14 Marks)
1.1 Reasons for Using Panel Data and South African
Examples
Answer:
Reasons for using panel data:
1. Controls for unobserved heterogeneity - accounts for time-invariant individual
characteristics that may affect the dependent variable, reducing omitted variable bias.
2. More efficient estimation - provides more variability, less collinearity, and greater
degrees of freedom than pure cross-section or time-series data.
3. Enables dynamic analysis - allows researchers to study how individuals, firms, or
countries change over time.
South African Examples:
National Income Dynamics Study (NIDS) - tracks the same households over time
Quarterly Labour Force Survey (QLFS) - has a rotating panel component that tracks
households over multiple quarters
1.2 Reasons for Preferring Random Effects over Pooled
OLS
Answer:
Random Effects (RE) is preferred over Pooled OLS for three main reasons:
, 2|Page
1. Corrects for serial correlation in the error term: The composite error in panel data
is vit=ai+uitvit=ai+uit, where aiai is the unobserved individual effect. Pooled OLS
ignores the resulting serial correlation, leading to incorrect standard errors. RE uses
Generalized Least Squares (GLS) to correct this problem.
2. Greater efficiency: The RE estimator optimally weights within- and between-individual
variation through quasi-demeaning, producing more efficient (smaller variance)
estimates than Pooled OLS.
3. Reduces bias: RE partially addresses omitted variable bias by modeling the error
structure, providing more reliable estimates when unobserved individual effects exist.
The Breusch-Pagan Lagrange Multiplier test can formally determine whether RE is
preferred over Pooled OLS.
1.3 Determining the Better Model: Pooled OLS vs. LSDV
Answer:
To determine whether Pooled OLS or LSDV is preferred, follow these steps:
Step 1: Estimate both models and conduct an F-test for the joint significance of the
individual dummy variables in the LSDV model.
Step 2: Interpret the F-test:
Null Hypothesis (H0H0) All dummy coefficients = 0 (no individual effects exist)
Alternative (H1H1) At least one dummy coefficient ≠ 0 (individual effects exist)
Step 3: Decision Rule:
Reject H0H0 (p-value < 0.05) → Prefer LSDV because individual-specific effects are
significant. Pooled OLS would suffer from omitted variable bias.
Fail to reject H0H0 (p-value ≥ 0.05) → Prefer Pooled OLS because there is no
evidence of individual effects. LSDV would unnecessarily reduce efficiency.
Additional Considerations:
If NN is large and TT is small, LSDV may lose too many degrees of freedom
Time-invariant variables cannot be included in LSDV as they are perfectly collinear with
the dummies
, 3|Page
1.4 Assumptions for First-Differencing Estimator to be
BLUE
Answer:
For the First-Differencing (FD) estimator to be the Best Linear Unbiased Estimator
(BLUE) conditional on the explanatory variables, the following five assumptions must
hold:
Assumption Description
1. No Perfect The differenced explanatory variables (ΔxitkΔxitk) must not be perfectly collinear
Collinearity and must have variation over time
2. Zero Conditional E(Δuit∣Δxi)=0E(Δuit∣Δxi)=0 - the differenced error has zero mean conditional
Mean on the regressors (strict exogeneity)
3. Homoskedasticity Var(Δuit∣Xi)=σ2Var(Δuit∣Xi)=σ2 - constant variance of the differenced errors
4. No Serial Corr(Δuit,Δuis∣Xi)=0Corr(Δuit,Δuis∣Xi)=0 for t≠st =s - the differenced
Correlation errors are not serially correlated
5. No Measurement The explanatory variables in the differenced equation must be measured without
Error error
QUESTION 2: WAGE-UNEMPLOYMENT ANALYSIS (21
Marks)
Step-by-Step EViews Guide for Question 2
PART A: Data Preparation (Before Opening EViews)
Step 1: Prepare Your Excel Data in "Long" Format
