  The causal inference literature frequently focuses on estimating the mean of
the potential outcome, whereas the quantiles of the potential outcome may carry
important additional information. We propose a universal approach, based on the
inverse estimating equations, to generalize a wide class of causal inference
solutions from estimating the mean of the potential outcome to its quantiles.
We assume that an identifying moment function is available to identify the mean
of the threshold-transformed potential outcome, based on which a convenient
construction of the estimating equation of quantiles of potential outcome is
proposed. In addition, we also give a general construction of the efficient
influence functions of the mean and quantiles of potential outcomes, and
identify their connection. We motivate estimators for the quantile estimands
with the efficient influence function, and develop their asymptotic properties
when either parametric models or data-adaptive machine learners are used to
estimate the nuisance functions. A broad implication of our results is that one
can rework the existing result for mean causal estimands to facilitate causal
inference on quantiles, rather than starting from scratch. Our results are
illustrated by several examples.
