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ECS4863 ASSIGNMENT 3 ANSWERS OF SEMESTER 2 OF 2024, 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
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