Despite their widespread use, there is little academic evidence on whether applicant selection instruments can improve teacher hiring. We examine the relationship between two screening instruments used by Spokane Public Schools to select classroom teachers and three teacher outcomes: value added, absences, and attrition. We observe all applicants to the district (not only those who are hired), allowing us to estimate sample selection-corrected models using random tally errors and variation in the level of competition across job postings as instruments. Ratings on the screening instruments significantly predict value added in math and teacher attrition, but not absences--an increase of one standard deviation in screening scores is associated with an increase of about 0.06 standard deviations of student math achievement, and a decrease in teacher attrition of 3 percentage points. Hence the use of selection instruments appears to be a key means of improving the quality of the teacher workforce.