The National Bureau of Economic Research (NBER) recently released a circulated but not-yet internally or externally reviewed study titled “The Gap within the Gap: Using Longitudinal Data to Understand Income Differences in Student Achievement.” Note that we have covered NBER studies such as this in the past in this blog, so in all fairness and like I have noted in the past, this paper should also be critically consumed, as well as my interpretations of the authors’ findings.

Nevertheless, this study is authored by Katherine Michelmore — Assistant Professor of Public Administration and International Affairs at Syracuse University, and Susan Dynarski — Professor of Public Policy, Education, and Economics at the University of Michigan, and this study is entirely relevant to value-added models (VAMs). Hence, below I cover their key highlights and takeaways, as I see them. I should note up front, however, that the authors did not directly examine how the new measure of economic disadvantage that they introduce (see below) actually affects calculations of teacher-level value-added. Rather, they motivate their analyses by saying that calculating teacher value-added is one application of their analyses.

The background to their study is as follows: “Gaps in educational achievement between high- and low-income children are growing” (p. 1), but the data that are used to capture “high- and low-income” in the state of Michigan (i.e., the state in which their study took place) and many if not most other states throughout the US, capture “income” demographics in very rudimentary, blunt, and often binary ways (i.e., “yes” for students who are eligible to receive federally funded free-or-reduced lunches and “no” for the ineligible).

Consequently, in this study the authors “leverage[d] the longitudinal structure of these data sets to develop a new measure of persistent economic disadvantage” (p. 1), all the while defining “persistent economic disadvantage” by the extent to which students were “eligible for subsidized meals in every grade since kindergarten” (p. 8). Students “who [were] never eligible for subsidized meals during those grades [were] defined as never [being economically] disadvantaged” (p. 8), and students who were eligible for subsidized meals for variable years were defined as “transitorily disadvantaged” (p. 8). This all runs counter, however, to the binary codes typically used, again, across the nation.

Appropriately, then, their goal (among other things) was to see how a new measure they constructed to better measure and capture “persistent economic disadvantage” might help when calculating teacher-level value-added. They accordingly argue (among other things) that, perhaps, not accounting for persistent disadvantage might subsequently cause more biased value-added estimates “against teachers of [and perhaps schools educating] persistently disadvantaged children” (p. 3). This, of course, also depends on how persistently disadvantaged students are (non)randomly assigned to teachers.

With statistics like the following as also reported in their report: “Students [in Michigan] [persistently] disadvantaged by 8th grade were six times more likely to be black and four times more likely to be Hispanic, compared to those who were never disadvantaged,” their assertions speak volumes not only to the importance of their findings for educational policy, but also for the teachers and schools still being evaluated using value-added scores and the researchers investigating, criticizing, promoting, or even trying to make these models better (if that is possible). In short, though, teachers who are disproportionately teaching in urban areas with more students akin to their equally disadvantaged peers, might realize relatively more biased value-added estimates as a result.

For value-added purposes, then, it is clear that the assumptions that controlling for student disadvantage by using such basal indicators of current economic disadvantage is overly simplistic, and just using test scores to also count for this economic disadvantage (i.e., as promoted in most versions of the Education Value-Added Assessment System (EVAAS)) is likely worse. More specifically, the assumption that economic disadvantage also does not impact some students more than others over time, or over the period of data being used to capture value-added (typically 3-5 years of students’ test score data), is also highly susceptible. “[T]hat children who are persistently disadvantaged perform worse than those who are disadvantaged in only some grades” (p. 14) also violates another fundamental assumption that teachers’ effects are consistent over time for similar students who learn at more or less consistent rates over time, regardless of these and other demographics.

The bottom line here, then, is that the indicator that should be used instead of our currently used proxies for current economic disadvantage is the number of grades students spend in economic disadvantage. If the value-added indicator does not effectively account for the “negative, nearly linear relationship between [students’ test] scores and the number of grades spent in economic disadvantage” (p. 18), while controlling for other student demographics and school fixed effects, value-added estimates will likely be (even) more biased against teachers who teach these students as a result.

Otherwise, teachers who teach students with persistent economic disadvantages will likely have it worse (i.e., in terms of bias) than teachers who teach students with current economic disadvantages, teachers who teach students with economically disadvantaged in their current or past histories will have it worse than teachers who teach students without (m)any prior economic disadvantages, and so on.

Citation: Michelmore, K., & Dynarski, S. (2016). The gap within the gap: Using longitudinal data to understand income differences in student achievement. Cambridge, MA: National Bureau of Economic Research (NBER). Retrieved from http://www.nber.org/papers/w22474