by RCT — no guide to the future To see what RCTs show, let me define the Cartesian product of X2, X3, . . . , Xn by Z. What RCTs show is that there exists some z ∈ Z, such that if we have the world in state (x, z) ∈ X instead of (y, z) ∈ X, the world in the next period will be in state a ∈ X instead of state b ∈ X. This is like saying, other things being the same (that is, z), if you vaccinate people, in the next period, there will be no influenza. But if you do not vaccinate them, there will be influenza. If we accept the determinist axiom, as many do, then this demonstration means that whenever we switch from (y, z) to (x, z), the world will switch in the next period from b to a. It is the “whenever” that makes this a causal claim. This is what I am referring to as “circumstantial causality”. Given a certain set of circumstances, changing y to x has a predictable consequence. The discovery of circumstantial causal connections, as has happened with the rise of RCT studies, is valuable and, at the same time, of limited consequence, more so than the proponents believe. On the one hand, RCTs have given us numerous valuable descriptions of what happened in the past and numerous instances of causes in the past (provided of course that one is willing to accept the determinist axiom). On the other, what they show is very limited.
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Lars Pålsson Syll considers the following as important: Statistics & Econometrics
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RCT — no guide to the future
To see what RCTs show, let me define the Cartesian product of X2, X3, . . . , Xn by Z. What RCTs show is that there exists some z ∈ Z, such that if we have the world in state (x, z) ∈ X instead of (y, z) ∈ X, the world in the next period will be in state a ∈ X instead of state b ∈ X. This is like saying, other things being the same (that is, z), if you vaccinate people, in the next period, there will be no influenza. But if you do not vaccinate them, there will be influenza. If we accept the determinist axiom, as many do, then this demonstration means that whenever we switch from (y, z) to (x, z), the world will switch in the next period from b to a. It is the “whenever” that makes this a causal claim. This is what I am referring to as “circumstantial causality”. Given a certain set of circumstances, changing y to x has a predictable consequence.
The discovery of circumstantial causal connections, as has happened with the rise of RCT studies, is valuable and, at the same time, of limited consequence, more so than the proponents believe. On the one hand, RCTs have given us numerous valuable descriptions of what happened in the past and numerous instances of causes in the past (provided of course that one is willing to accept the determinist axiom). On the other, what they show is very limited. This is because when they show that it was the switch from y to x that caused the switch from b to a, what they are saying is that this was true under certain historical conditions (z), but they cannot tell you what those historical conditions are. RCT discoveries never graduate from something “was a cause” of something else to something “is a cause”. RCTs give us no insight into universal causality because they cannot tell us what it was that was being held constant (z in the above example), when we switched some intervention b to a. For Bengal, in a certain period, electing a woman leader of the local government caused water provisioning to be better. This is no guide to the future because we do not fully know what Bengal in a certain period is like. Henceforth, a reference to causality without a qualifying epithet should be taken to be a reference to universal causality because for policy purposes, that is what is of essence.