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. However, except for large positive correlation of bound estimators, the practical result will be simple: To achieve 95 %DIFDELCMD < \\%%% %DIF < coverage, compute both a simple 90\\% (!) confidence interval for the identified set and a standard 95\\% confidence interval for the pseudotrue parameter and report the union of these intervals. 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, in which improvement over existing inference methods is demonstrated. More generally, simulations suggest that the novel confidence interval has excellent length and size control.abstract 
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 %DIFDELCMD < \\%%% %DIF < coverage, compute both a simple 90\\% (!) confidence interval for the identified set and a standard 95\\% confidence interval for the pseudotrue parameter and report the union of these intervals. 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, in which improvement over existing inference methods is demonstrated. More generally, simulations suggest that the novel confidence interval has excellent length and size control.abstract \% 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.
R
However, except for large positive correlation of bound estimators,
In most cases,
A
\% 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.