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

A Simple, Short, but Never-Empty Confidence Interval for Partially Identified Parameters