Interpreting Tests of School VAM Validity

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).