Causal inference is a growing interdisciplinary subfield in statistics, computer science, economics, epidemiology, and the social sciences. In contrast with both traditional quantitative methods and cutting-edge approaches like machine learning, causal inference questions are defined in relation to potential outcomes, or variable values that are counterfactual to the observed world and therefore cannot be answered from joint probabilities alone, even with infinite data. The fact that one can possibly observe at most one potential outcome among those of interest is known as the “fundamental problem of causal inference.” For example, in this framework, the economic return to college education can be defined as a comparison between two potential outcomes: the wages of an individual with a college education versus the wages that the same individual would have received had he or she not attended college. In general, researchers are interested in estimating such effects for certain groups and comparing the effects for different subpopulations. Critical to causal inference is recognizing that, to answer causal questions from observed data, one has to rely on untestable assumptions about how the data were generated. In other words, there is no particular statistical method that would render a conclusion “causal”; the validity of such an interpretation depends on a combination of data, assumptions about the data-generating process based on expert judgment, and estimation techniques. In the last several decades, our understanding of causality has improved enormously, owing to a conceptual apparatus and a mathematical language that enables rigorous conceptualization of causal quantities and formal representation of causal assumptions, while still employing familiar statistical methods. Potential outcomes or the Neyman-Rubin causal model and structural equations encoded as directed acyclic graphs (DAGs, also known as structural causal models) are two common approaches for conceptualizing causal relationships. The symbiosis of both languages offers a powerful framework to address causal questions. This review covers developments in both causal identification (i.e., deciding if a quantity of interest would be recoverable from infinite data, based on our assumptions) and causal effect estimation (i.e., the use of statistical methods to approximate that answer with finite, although potentially big, data). The literature is presented following the type of assumptions and questions frequently encountered in empirical research, ending with a discussion of promising new directions in the field.
Bridging Finite and Super Population Causal Inference
