Ordinary Least Square, the cornerstone of Econometric Theory; A literature Inquiry
DOI:
https://doi.org/10.54536/ajase.v5i1.6473Keywords:
Econometrics, Model Selection, Ordinary Least Squares (OLS), Regression AnalysisAbstract
The widespread application of Ordinary Least Squares (OLS) is increasingly challenged by assumption violations, numerical instability, and inefficiencies in complex data structures. This review systematically explores the historical evolution, strengths, limitations, and modern adaptations of OLS in contemporary econometric practice. Following a structured scoping review methodology, this study synthesises literature on OLS and its alternatives. The review identifies key themes, including the historical development of OLS, its theoretical foundations, empirical strengths and weaknesses, and emerging econometric techniques that address its limitations. Thematic coding and a comparative analysis of alternative estimation methods are applied to critically assess the role of OLS in modern econometrics. The findings highlight that while OLS remains a robust estimation technique under classical assumptions, it faces significant challenges in practical applications. Studies indicate that OLS is particularly limited in handling multicollinearity, heteroscedasticity, endogeneity, and non-linear relationships. Alternative methods such as Generalized Least Squares (GLS), Instrumental Variables (IV), Maximum Likelihood Estimation (MLE), Ridge Regression, and machine learning-based techniques provide improved estimation in scenarios where OLS fails. The review further identifies an ongoing methodological shift where OLS is increasingly integrated with modern econometric techniques rather than being used in isolation. OLS continues to serve as a fundamental econometric tool, particularly in well-behaved datasets. However, its role is evolving as researchers incorporate robust statistical techniques to mitigate its limitations. Future research should focus on the empirical trade-offs between OLS and modern alternatives, the integration of OLS with machine learning approaches, and the ethical implications of model selection in econometric analysis
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Appendix I: Combined Search Query
(“Ordinary Least Squares” OR “OLS regression” OR “Least Squares Method” OR “linear regression estimat*” OR “OLS model” OR “OLS estimat*”)
AND
((“historical development” OR “histor*” OR “evolution” OR “origin*” OR “Gauss” OR “Legendre” OR “statistical origin*” OR “early application*” OR “develop* of OLS”)
OR
(“limitation*” OR “bias*” OR “weakness*” OR “criticism*” OR “pitfall*” OR “assumption* fail*” OR “multicollinear*” OR “heteroscedastic*” OR “endogen*” OR “overfit*” OR “mis-specification*” OR “OLS inefficien*”)
OR
(“application*” OR “use case*” OR “applied econometric*” OR “real-world implement*” OR “economic model*ing” OR “economic model*ling” OR “policy evaluat*” OR “forecast*” OR “time-series analys*” OR “market analys*” OR “financial econometric*” OR “panel data analys*”)
OR
(“alternative method*” OR “Generalized Least Squares” OR “Generalised Least Squares” OR “GLS regression” OR “Instrumental Variable*” OR “IV regression” OR “Maximum Likelihood Estimat*” OR “MLE” OR “Bayesian regression” OR “Machine learning regression” OR “Ridge regression” OR “Lasso regression” OR “Quantile regression” OR “Regulari?ed regression” OR “Robust regression” OR “Nonparametric method*”))
AND
(“econometric model*ing” OR “econometric model*ling” OR “statistical infer*” OR “regression analys*” OR “prediction model*” OR “econometric estimation technique*” OR “statistical estimat*” OR “linear model*”)
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