Question 1. (11 marks)
a) The reasons for preferring random effects over the pooled Ordinary least squares method.
i. It accounts for individual heterogeneity. The random effects model considers the
unobserved heterogeneity across entities (such as individuals, countries and firms) by
allowing for entity-specific random intercepts. This is crucial when the data consists
of multiple observations per entity, as it acknowledges that each entity may have
unique characteristics that affect the dependent variable.
ii. It's more efficient. Random effects estimators are generally more efficient than pooled
OLS estimators because they use both within-entity and between-entity variations.
This combined approach leads to more precise coefficient estimates.
iii. It allows for time-invariant variables. Unlike fixed effects, random effects can
estimate the effects of time-invariant variables, which pooled OLS might not handle
effectively in panel data.
b) How to choose between the Random effects and pooled Ordinary least squares approaches.
State the weakness of the test you will use.
To choose between Random effects and pooled OLS, we use the Breusch-Pagan Lagrange
Multiplier (LM) test. We follow the following process in choosing.
i. Perform the Breusch-Pagan LM test.
ii. Set up the null hypothesis that there are no random effects (that is., pooled OLS is
appropriate).
iii. If the test statistic is significant (p-value < significance level), reject the null
hypothesis and prefer random effects.
iv. If the test statistic is not significant, fail to reject the null hypothesis and use pooled
OLS.
Weakness of the test
A key weakness of the Breusch-Pagan LM test is its reliance on the assumption that the
individual-specific effects are uncorrelated with the explanatory variables. If this assumption
is violated, the test may provide misleading results, and the random effects model might not
be appropriate.
c) What are the implications of not considering the correlation structure in panel data and
how is the situation remedied? (2 marks)
Implications
Ignoring the correlation structure in panel data can lead to biased and inefficient estimates.
Specifically, the pooled OLS model assumes that observations are independently and
identically distributed, which is often violated in panel data due to repeated measurements on
, the same entities. This can result in underestimated standard errors and misleading statistical
inferences.
Remedies
i. Use panel data methods like fixed effects or random effects that account for the
correlation structure.
ii. Apply robust standard errors or clustered standard errors to correct for potential
correlation within panels.
iii. Consider using more advanced techniques like Generalized Least Squares (GLS) or
Feasible Generalised Least Squares (FGLS) that explicitly model the correlation
structure.
Question 2
𝑙𝑛𝑌𝑖𝑡 = 𝑙𝑛𝐴 + 𝛽1 𝑙𝑛𝐾𝑖𝑡 + 𝛽2 𝑙𝑛𝐿𝑖𝑡
2.1. Expected signs of the coefficients
𝛽1 Gross Fixed Capital Formation – positive
Gross fixed capital formation represents investments in physical assets such as machinery,
buildings, and infrastructure. Higher investments in capital typically lead to an increase in
productive capacity and economic output, thus positively impacting GDP.
𝛽2 Total Employment – positive
Total employment reflects the labour input in the production process. Higher employment
levels generally indicate more workers contributing to production, which increases the total
output and, consequently, the GDP.
2.2. GDP Equation in logarithmic form and estimation using Pooled OLS
𝑙𝑛𝑌𝑖𝑡 = 𝑙𝑛𝐴 + 𝛽1 𝑙𝑛𝐾𝑖𝑡 + 𝛽2 𝑙𝑛𝐿𝑖𝑡 + 𝑙𝑛𝑢𝑖𝑡
a) The reasons for preferring random effects over the pooled Ordinary least squares method.
i. It accounts for individual heterogeneity. The random effects model considers the
unobserved heterogeneity across entities (such as individuals, countries and firms) by
allowing for entity-specific random intercepts. This is crucial when the data consists
of multiple observations per entity, as it acknowledges that each entity may have
unique characteristics that affect the dependent variable.
ii. It's more efficient. Random effects estimators are generally more efficient than pooled
OLS estimators because they use both within-entity and between-entity variations.
This combined approach leads to more precise coefficient estimates.
iii. It allows for time-invariant variables. Unlike fixed effects, random effects can
estimate the effects of time-invariant variables, which pooled OLS might not handle
effectively in panel data.
b) How to choose between the Random effects and pooled Ordinary least squares approaches.
State the weakness of the test you will use.
To choose between Random effects and pooled OLS, we use the Breusch-Pagan Lagrange
Multiplier (LM) test. We follow the following process in choosing.
i. Perform the Breusch-Pagan LM test.
ii. Set up the null hypothesis that there are no random effects (that is., pooled OLS is
appropriate).
iii. If the test statistic is significant (p-value < significance level), reject the null
hypothesis and prefer random effects.
iv. If the test statistic is not significant, fail to reject the null hypothesis and use pooled
OLS.
Weakness of the test
A key weakness of the Breusch-Pagan LM test is its reliance on the assumption that the
individual-specific effects are uncorrelated with the explanatory variables. If this assumption
is violated, the test may provide misleading results, and the random effects model might not
be appropriate.
c) What are the implications of not considering the correlation structure in panel data and
how is the situation remedied? (2 marks)
Implications
Ignoring the correlation structure in panel data can lead to biased and inefficient estimates.
Specifically, the pooled OLS model assumes that observations are independently and
identically distributed, which is often violated in panel data due to repeated measurements on
, the same entities. This can result in underestimated standard errors and misleading statistical
inferences.
Remedies
i. Use panel data methods like fixed effects or random effects that account for the
correlation structure.
ii. Apply robust standard errors or clustered standard errors to correct for potential
correlation within panels.
iii. Consider using more advanced techniques like Generalized Least Squares (GLS) or
Feasible Generalised Least Squares (FGLS) that explicitly model the correlation
structure.
Question 2
𝑙𝑛𝑌𝑖𝑡 = 𝑙𝑛𝐴 + 𝛽1 𝑙𝑛𝐾𝑖𝑡 + 𝛽2 𝑙𝑛𝐿𝑖𝑡
2.1. Expected signs of the coefficients
𝛽1 Gross Fixed Capital Formation – positive
Gross fixed capital formation represents investments in physical assets such as machinery,
buildings, and infrastructure. Higher investments in capital typically lead to an increase in
productive capacity and economic output, thus positively impacting GDP.
𝛽2 Total Employment – positive
Total employment reflects the labour input in the production process. Higher employment
levels generally indicate more workers contributing to production, which increases the total
output and, consequently, the GDP.
2.2. GDP Equation in logarithmic form and estimation using Pooled OLS
𝑙𝑛𝑌𝑖𝑡 = 𝑙𝑛𝐴 + 𝛽1 𝑙𝑛𝐾𝑖𝑡 + 𝛽2 𝑙𝑛𝐿𝑖𝑡 + 𝑙𝑛𝑢𝑖𝑡
