# Trouble understanding the intuition of unconfoundedness

In order to understand how to use and apply Propensity Score Matching(PSM), I read the articles "Some Practical Guidance for the Implementation of PSM" (Caliendo and Bonn 2008) and "Causal Effects in Nonexperimental Studies: Reevaluating the Evaluation of Training Programs" (Dehejia and Wahba 1999).

One of the main hypothesis is unconfoundedness; it states that $$\{(Y_{i1},Y_{i0}) \perp T_i \} | X_i$$ where $X_i$ are the (observable) covariates of unit $i$, $T_i=\{1,0\}$ if the subject is treated or not treated; and $Y_{i1}, Y_{i0}$ are the outcome if the subject is treated or not treated.

I understand the motivation of the hypothesis, and why it is used. However, I have a hard time understanding its intuition though I guess I can state its meaning: Given I know the covariates of an individual, the possible outcomes of the individual are independent of (not)being treated. But, this hyphoteses really means? I also have done my research on the internet and came to explanations such as Unconfoundedness in Rubin's Causal Model- Layman's explanation, but I still feel I don't get the idea.

In order to show my (mis)conception, I have both created and example and try to explain my interpretation. Let's suppose that 90% of people who participate in a certain program are males and poor, and that, in average, the program decreases the unemployment rate of the treated by 4%. Let's also assume that $X=(sex,poor)$ are all the covariates I need to observe.

If I observe a person that is both male and poor i.e. I know "everything" about him, then the fact that that this person participates in the program doesn't give me any information of whether this person is in the labor force?

What am I missing here?

An intuition is that potential outcomes are characteristics of an individual before that individual is assigned to a treatment condition. Those potential outcomes depend on some covariates (e.g., your potential earnings depend on being male whether or not you receive treatment). Confounding occurs when potential outcomes are not independent of treatment because they share a common cause (e.g., maleness, in this example). Unconfoundedness mean that there are no such qualities on which your potential outcomes depend that also relate to selection into treatment (i.e., they are independent of treatment). Conditional exchangeability (the expression you wrote above) means that conditional on a sufficient set of covariates $X$, the potential outcomes are independent of treatment (which is to say, again, that there are no common causes of the potential outcomes and treatment).
It's also important to note that this is not a hypothesis but rather an assumption which cannot be proven. If this assumption holds (along with a few others), then it is possible to identify the causal effect of the treatment on the outcome by using methods that condition on $X$. Laden in this assumption is the assumption that $X$ contains a sufficient set of variables to eliminate confounding. If you condition on the $X$, then the potential outcomes are unrelated to treatment.