Partial identification (PI) entails estimating bounds on causal effects by encoding different assumptions on data generation as a constrained optimization problem. Such bounds can suffice to inform policy decisions even if the causal effect itself is not identifiable. Often vacuous in practice, practitioners seek to exhaustively encode domain knowledge as additional constraints to make the PI bounds more informative. We introduce known data symmetries -- invariance of the causal effect under certain data transformations -- as a new source of constraints to inform PI. We operationalize this as a shape constraint on the causal function, and via a change of measure against which PI is posed using simple data pre-processing. Both approaches are shown to sharpen bounds under two canonical PI models. This is shown both theoretically for the population case, and via experiments in the finite-sample case. More broadly, our framework establishes data symmetries as a natural, underutilized source of background knowledge for robust causal inference.

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