In comparing econometrics, statistics, and machine learning methodologies, one must distinguish between standard and advanced machine learning. The former, exemplified by deep learning and neural networks, fits a function to a stream of data and plays the same role as statistical analysis, taking us from samples to properties of distribution functions. Advanced machine learning, on the other hand, goes beyond distributions onto the process that generates the data, and so, allows us to manage policy interventions and counterfactual reasoning (e.g., “what if we have done things differently”)
Advanced machine learning was developed in artificial intelligence in the past 25 years, under the rubric “causal inference” or “structural causal models” (SCM). It is now impacting several application areas, including policy interventions https://ucla.in/2Iz3OnD, data fusion https://ucla.in/2Jc1kdD, fairness analysis https://causalai.net/r30.pdf, http://arixiv.org/pdf/1902.08283.pdf, mediation analysis https://ucla.in/2N5Gdk2, and missing data https://ucla.in/2LdEjZW
A detailed summary of these tasks, as well the overall philosophy of SCM and its relation to standard machine learning methods can be found in “The Seven Tools of Causal Inference with Reflections on Machine Learning,” https://ucla.in/2umzd65 . A gentle introduction is provided in The Book of Why https://ucla.in/2KYvzau
Starting with Haavelmo (1943) and the Cowles Commission (1940-1970), econometrics too has aimed at estimating causal effects, primarily to guide decision making and social policies https://ucla.in/2mhxKdO. However, the tools developed in the econometric literature cover only a fraction of the tasks that are currently managed by SCM. In particular, the latter provides a transparent and compact encoding of causal assumptions, which enables researchers to discern the plausibility of the assumptions and test their compatibility with the available data. In contrast, the encoding language provided by econometric methods usually invokes “conditional ignorability” assumptions, which are both opaque and intractable: http://causality.cs.ucla.edu/blog/index.php/2014/10/27/are-economists-smarter-than-epidemiologists-comments-on-imbenss-recent-paper/ …
Sections 3&4 of https://ucla.in/2mhxKdO, provide a detailed comparison of the two frameworks, including illustrated examples of advantages and weaknesses.