From Mean to Machine Learning: Evolution and Econometric Synthesis Review of Granger Causality Methods

Abstract

Granger causality remains a central framework for studying predictive causal relations in economics and finance, but its methodological scope now extends far beyond classical linear vector autoregression. Existing surveys often examine linear tests, nonlinear tests, quantile causality, distributional causality, and machine-learning-based causal discovery as separate methodological strands. This review provides an econometric synthesis that connects these strands under a common predictive-causality logic. It argues that the evolution of Granger causality can be understood through three connected dimensions: the statistical object being predicted, the dependence structure being represented, and the algorithm used for estimation and inference. Based on this logic, the review develops a distributional hierarchy from conditional means to variances, quantiles, conditional densities, full distributions, and high-dimensional machine-learning settings. It further proposes a distribution, structure, and algorithm framework for comparing traditional econometric tests, nonlinear and distributional methods, sparse high-dimensional models, graph-learning approaches, and neural-network-based Granger causality. A bibliometric analysis of 2,170 Web of Science records from 2010 to 2025 complements the methodological review by identifying source-journal patterns, country-level contributions, co-citation clusters, keyword evolution, and recent shifts toward nonlinear, network-based, and data-driven causal analysis. The review also provides a method-software mapping that links empirical objectives to implementation tools in Stata, EViews, MATLAB, R, and Python. A central conclusion is that machine-learning approaches expand the scope of Granger-causality analysis, but their value depends on formal validation, robustness to structural breaks, post-selection assessment, and interpretable causal attribution. The paper contributes a critical and practical framework for selecting, implementing, and interpreting Granger-causality methods in modern macroeconomic and financial research.