  In econometrics, many parameters of interest can be written as ratios of
expectations. The main approach to construct confidence intervals for such
parameters is the delta method. However, this asymptotic procedure yields
intervals that may not be relevant for small sample sizes or, more generally,
in a sequence-of-model framework that allows the expectation in the denominator
to decrease to $0$ with the sample size. In this setting, we prove a
generalization of the delta method for ratios of expectations and the
consistency of the nonparametric percentile bootstrap. We also investigate
finite-sample inference and show a partial impossibility result: nonasymptotic
uniform confidence intervals can be built for ratios of expectations but not at
every level. Based on this, we propose an easy-to-compute index to appraise the
reliability of the intervals based on the delta method. Simulations and an
application illustrate our results and the practical usefulness of our rule of
thumb.
