Causal Sufficiency Assumption

The conclusion that nightlights cause nearsightedness is false because it overlooks a hidden common cause. Nearsighted parents are more likely to use nightlights for their children and pass on genes for nearsightedness. The Causal Sufficiency Assumption is the belief that you have successfully identified and measured all such important common causes. If you miss one, like parental genetics, you might draw the wrong conclusion from a correlation.

Ask this: When I see a correlation, what unmeasured factor might be causing both things?

The Causal Sufficiency Assumption is a cornerstone of establishing cause and effect. It means that for any two variables you're studying (e.g., an action and an outcome), there are no unmeasured 'confounders'—hidden outside factors that influence both.

Think of it as trying to have a 'closed system' for your analysis. If there's a leak—an unmeasured common cause—its influence can spill over and create a misleading relationship between the variables you are looking at. Violating this assumption is one of the most common ways to mistake correlation for causation.

For example, a business might see that employees who participate in a voluntary wellness program have fewer sick days. Does the program make them healthier? Possibly, but it's more likely that employees who are already health-conscious and proactive are the ones who both sign up for the program and naturally have fewer sick days. Pre-existing health consciousness is the unmeasured confounder.

Similarly, an analysis might show that cities with more symphony orchestras have lower unemployment. Instead of concluding that orchestras create jobs, it's more plausible that a strong local economy (a common cause) supports both the arts and high employment levels. Acknowledging this assumption forces us to think critically about what we aren't seeing in the data.

In modern causal inference, this concept is formalized using Directed Acyclic Graphs (DAGs). A distinction is made between two related ideas. A system is considered globally 'causally sufficient' if there are no unmeasured common causes of any pair of variables in the model. However, for estimating a specific causal effect (e.g., of a treatment on an outcome), a more targeted assumption is needed: 'no unmeasured confounding' between that specific pair. This means that all common causes of the treatment and outcome have been measured, allowing their influence to be controlled for in the analysis.

• Pearl frames the assumption of no unmeasured confounding as a prerequisite for moving from observation to intervention; without it, one cannot reliably predict the effect of a new policy or action [1]. (2018)
• Hernán and Robins stress that this is an untestable assumption that must be justified with subject-matter expertise, as no statistical test can prove the absence of an unmeasured variable [2]. (2020)
• The re-analysis of the nightlight study is a classic example where the initial assumption was violated, with parental myopia acting as the unmeasured confounder that explained the original correlation [3]. (2000)

The assumption of no unmeasured confounding is almost never perfectly true in complex real-world systems. Since it is untestable with the observed data, researchers must argue for its plausibility using domain knowledge. To address this challenge, 'sensitivity analyses' have been developed to formally assess how robust a conclusion is to potential unmeasured confounders. For example, Rosenbaum's methods test how strong an unmeasured confounder would need to be to alter a study's conclusion [5]. More recently, the E-value was introduced as an intuitive metric; it represents the minimum strength of association an unmeasured variable would need to have with both the treatment and the outcome to explain away the observed effect [6].