  This paper revisits the simple, but empirically salient, problem of inference
on a real-valued parameter that is partially identified through upper and lower
bounds with asymptotically normal estimators. A simple confidence interval is
proposed and is shown to have the following properties:
  - It is never empty or awkwardly short, including when the sample analog of
the identified set is empty.
  - It is valid for a well-defined pseudotrue parameter whether or not the
model is well-specified.
  - It involves no tuning parameters and minimal computation.
  Computing the interval requires concentrating out one scalar nuisance
parameter. In most cases, the practical result will be simple: To achieve 95%
coverage, report the union of a simple 90% (!) confidence interval for the
identified set and a standard 95% confidence interval for the pseudotrue
parameter.
  For uncorrelated estimators -- notably if bounds are estimated from distinct
subsamples -- and conventional coverage levels, validity of this simple
procedure can be shown analytically. The case obtains in the motivating
empirical application (de Quidt, Haushofer, and Roth, 2018), in which
improvement over existing inference methods is demonstrated. More generally,
simulations suggest that the novel confidence interval has excellent length and
size control. This is partly because, in anticipation of never being empty, the
interval can be made shorter than conventional ones in relevant regions of
sample space.
