NEW EVIDENCE ON NATIONAL BOARD CERTIFICATION AS A SIGNAL OF TEACHER QUALITY

Using longitudinal data from North Carolina that contains detailed identifiers, we estimate the effect of having a National Board for Professional Teaching Standards (NBPTS) teacher on academic achievement. We identify the effects of an NBPTS teacher exploiting multiple sources of variation including traditional‐lagged achievement models, twin‐ and sibling‐fixed effects, and aggregate grade‐level variation. Our preferred estimates show that students taught by National Board certified teachers have higher math and reading scores by 0.04 and 0.01 of a standard deviation. We find that an NBPTS math teacher increases the present value of students' lifetime income by $48,000. (JEL I20, I21, J2444)     

Testing for Additivity at Select Mixture Groups of Interest Based on Statistical Equivalence Testing Methods

Several assumptions, defined and undefined, are used in the toxicity assessment of chemical mixtures. In scientific practice mixture components in the low-dose region, particularly subthreshold doses, are often assumed to behave additively (i.e., zero interaction) based on heuristic arguments. This assumption has important implications in the practice of risk assessment, but has not been experimentally tested. We have developed methodology to test for additivity in the sense of Berenbaum (Advances in Cancer Research, 1981), based on the statistical equivalence testing literature where the null hypothesis of interaction is rejected for the alternative hypothesis of additivity when data support the claim. The implication of this approach is that conclusions of additivity are made with a false positive rate controlled by the experimenter. The claim of additivity is based on prespecified additivity margins, which are chosen using expert biological judgment such that small deviations from additivity, which are not considered to be biologically important, are not statistically significant. This approach is in contrast to the usual hypothesis-testing framework that assumes additivity in the null hypothesis and rejects when there is significant evidence of interaction. In this scenario, failure to reject may be due to lack of statistical power making the claim of additivity problematic. The proposed method is illustrated in a mixture of five organophosphorus pesticides that were experimentally evaluated alone and at relevant mixing ratios. Motor activity was assessed in adult male rats following acute exposure. Four low-dose mixture groups were evaluated. Evidence of additivity is found in three of the four low-dose mixture groups. The proposed method tests for additivity of the whole mixture and does not take into account subset interactions (e.g., synergistic, antagonistic) that may have occurred and cancelled each other out.