  We study the implications of recursivity and state monotonicity in
intertemporal consumption problems under ambiguity. We show that monotone
recursive preferences admit a recursive and ex-ante representation, both with
translation invariant certainty equivalents. Translation invariance restricts
the decision maker's absolute ambiguity attitudes to be constant. As a
byproduct, this restriction implies that monotone recursive and convex
preferences collapse to the variational model. Using dynamic consistency, we
show that our two representations are connected by a condition that extends the
standard rectangularity notion for recursive multiple priors. This "generalized
rectangularity" condition allows us to uniquely retrieve the ex-ante
representation starting fromthe recursive one and to obtain dynamic consistency
conditions for preferences exhibiting constant absolute ambiguity aversion.
Interpreting generalized rectangularity as a law of iterated nonlinear
expectations, we discuss its relevance with respect to large sample theory.
