, ECS4863 Assignment 3 (COMPLETE ANSWERS) 2025 – DUE 18
August 2025; 100% correct solutions and explanations.
Question 1
(a): Explain the reasons for preferring random effects over the pooled Ordinary Least
Squares (OLS) method
Random effects models are often preferred over the pooled Ordinary Least Squares (OLS)
method for several key reasons:
1. Accounts for Unobserved Heterogeneity: Random effects models consider the
individual-specific effects (differences across entities, like people, firms, or countries)
that are assumed to be random and uncorrelated with the explanatory variables. In
contrast, pooled OLS ignores these differences, which can lead to biased estimates if
individual effects exist.
2. Efficiency of Estimates: By incorporating the variation across entities, random effects
models provide more efficient (less variable) estimates than pooled OLS because they use
both within-entity and between-entity information.
3. Suitable for Time-Invariant Variables: Random effects models allow the inclusion of
variables that do not change over time. Pooled OLS can include them too, but it does not
properly separate the individual-specific effects from the random error term, which can
distort the results.
4. Improved Generalizability: Since random effects treat individual-specific differences as
random draws from a larger population, the results can be generalized beyond the sample.
Pooled OLS assumes all observations are identical in terms of unobserved characteristics,
limiting generalizability.
5. Avoids Omitted Variable Bias: By modeling the random individual effects, random
effects reduce potential omitted variable bias that could arise if these effects were
correlated with the dependent variable but ignored in pooled OLS.
In summary, random effects models are preferred over pooled OLS when there are unobserved
differences across entities that are assumed to be random, as they yield more reliable, efficient,
and generalizable estimates.
(b): Explain how to choose between the Random Effects and Pooled Ordinary Least
Squares (OLS) approaches and state the weakness of the test used
To decide whether to use a Random Effects model or a Pooled OLS approach, researchers
commonly use the Breusch-Pagan Lagrange Multiplier (LM) test. This test examines whether
the variance of the unobserved individual effects is significantly different from zero.
Procedure:
1. Estimate the pooled OLS model.
August 2025; 100% correct solutions and explanations.
Question 1
(a): Explain the reasons for preferring random effects over the pooled Ordinary Least
Squares (OLS) method
Random effects models are often preferred over the pooled Ordinary Least Squares (OLS)
method for several key reasons:
1. Accounts for Unobserved Heterogeneity: Random effects models consider the
individual-specific effects (differences across entities, like people, firms, or countries)
that are assumed to be random and uncorrelated with the explanatory variables. In
contrast, pooled OLS ignores these differences, which can lead to biased estimates if
individual effects exist.
2. Efficiency of Estimates: By incorporating the variation across entities, random effects
models provide more efficient (less variable) estimates than pooled OLS because they use
both within-entity and between-entity information.
3. Suitable for Time-Invariant Variables: Random effects models allow the inclusion of
variables that do not change over time. Pooled OLS can include them too, but it does not
properly separate the individual-specific effects from the random error term, which can
distort the results.
4. Improved Generalizability: Since random effects treat individual-specific differences as
random draws from a larger population, the results can be generalized beyond the sample.
Pooled OLS assumes all observations are identical in terms of unobserved characteristics,
limiting generalizability.
5. Avoids Omitted Variable Bias: By modeling the random individual effects, random
effects reduce potential omitted variable bias that could arise if these effects were
correlated with the dependent variable but ignored in pooled OLS.
In summary, random effects models are preferred over pooled OLS when there are unobserved
differences across entities that are assumed to be random, as they yield more reliable, efficient,
and generalizable estimates.
(b): Explain how to choose between the Random Effects and Pooled Ordinary Least
Squares (OLS) approaches and state the weakness of the test used
To decide whether to use a Random Effects model or a Pooled OLS approach, researchers
commonly use the Breusch-Pagan Lagrange Multiplier (LM) test. This test examines whether
the variance of the unobserved individual effects is significantly different from zero.
Procedure:
1. Estimate the pooled OLS model.
