## Philipp Ketz* and Adam McCloskey

Confidence intervals, taking into account the uncertainty inherent in the use of sample data, provide a range of plausible values for unknown (population) quantities such as partial effects. We may, for example, be interested in the effect of experience on wages, holding other factors such as education constant. Standard confidence intervals do not make any assumptions about the directions of the (partial) effects of the “other” factors. In some cases, however, a researcher may have a priori knowledge about the directions of some of the “other” factors’ effects. For example, a researcher may know, or be willing to assume, that the partial effect of education is nonnegative. This additional information can also be useful for the partial effect of interest in the sense that it may lower the associated sampling uncertainty. However, the construction of confidence intervals that correctly reflect this reduced sampling uncertainty is not trivial. While it is always possible to construct a confidence interval by test inversion, this can be very computationally expensive: First, a grid search needs to be performed, i.e., all possible values (of the unknown quantity of interest) need to “checked” for their plausibility. Second, the statistical tests available in the literature-to-date that correctly reflect this reduced sampling uncertainty and that could be used to perform these “checks” are computationally expensive themselves. Therefore, test inversion is often impractical.

In a recent paper, Philipp Ketz and Adam McCloskey propose new confidence intervals that correctly reflect this reduced sampling uncertainty and, thus, can be shorter than the standard confidence intervals. Furthermore, the proposed confidence intervals are computationally trivial and, thus, close an important gap in the literature. A shorter confidence interval is attractive because it reduces the range of plausible values. One challenge in the construction is to avoid that the confidence interval can be too small, incorrectly excluding plausible values for the quantity of interest and, thus, understating the sampling uncertainty. To illustrate the usefulness of their suggested confidence intervals, the authors apply them in the context of a field experiment that uses a 2×2 factorial design. In particular, they revisit Blattman et al. (2017) who study the effects of “therapy” and “cash” on violent and criminal behavior in Liberia (1). Assuming that the (partial) effects of “therapy” and “cash” are nonnegative, they find their proposed confidence intervals, for some of the treatment effects under study, to be up to 36% shorter than the corresponding standard confidence intervals.

References
Original title of the article : Short and Simple Confidence Intervals when the Directions of Some Effects are Known
Published in : arXiv Working Paper
Available at : arXiv:2109.08222

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* PSE Researcher

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