  We briefly review the formulation of effective field theories (EFTs) in
time-dependent situations, with particular attention paid to their domain of
validity. Our main interest is the extent to which solutions of the EFT capture
the dynamics of the full theory. For a simple model we show by explicit
calculation that the low-energy action obtained from a sensible UV completion
need not take the restrictive form required to obtain only second-order field
equations, and we clarify why runaway solutions are nevertheless typically not
a problem for the EFT. Although our results will not be surprising to many, to
our knowledge they are only mentioned tangentially in the EFT literature, which
(with a few exceptions) largely addresses time-independent situations.
