Short and Simple Confidence Intervals When the Directions of Some Effects Are Known

We introduce adaptive confidence intervals on a parameter of interest in the presence of nuisance parameters, such as coefficients on control variables, with known signs. Our confidence intervals are trivial to compute and can provide significant length reductions relative to standard ones when the nuisance parameters are small. At the same time, they entail minimal length increases at any parameter values. We apply our confidence intervals to the linear regression model, prove their uniform validity, and illustrate their length properties in an empirical application to a factorial design field experiment and a Monte Carlo study calibrated to the empirical application.