JoshuaAngrist1, PeterHull2, ParagPathak3 and ChristopherWalters4
1Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, and NBER (e-mail: [email protected])
2Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (e-mail: [email protected])
3Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, and NBER (e-mail: [email protected])
4University of California, Berkeley, 530 Evans Hall, Berkeley, CA 94720, and NBER (e-mail: [email protected])
Abstract
We develop over-identification tests that use admissions lotteries to assess the predictive value of regression-based value-added models (VAMs). These tests have degrees of freedom equal to the number of quasi-experiments available to estimate school effects. By contrast, previously implemented VAM validation strategies look at a single restriction only, sometimes said to measure forecast bias. Tests of forecast bias may be misleading when the test statistic is constructed from many lotteries or quasi-experiments, some of which have weak first stage effects on school attendance. The theory developed here is applied to data from the Charlotte-Mecklenberg School district analyzed by Deming (2014).