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This study shows value-added models (VAM) and student growth percentile (SGP) models fundamentally disagree regarding estimated teacher effectiveness when the classroom distribution of test scores conditional on prior achievement is skewed (i.e., when a teacher serves a disproportionate number of high-or low-growth students). While conceptually similar, the two models differ in estimation method which can lead to sizable differences in estimated teacher effects. Moreover, the magnitude of conditional skewness needed to drive VAM and SGP models apart often by three and up to 6 deciles is within the ranges observed in actual data. The same teacher may appear weak using one model and strong with the other. Using a simulation, I evaluate the relationship under controllable conditions. I then verify that the results persist in observed student-teacher data from North Carolina.

The Bennati-Drăgulescu-Yakovenko (BDY) game is an agent-based simple exchange game that models a basic economic system. The BDY game results in the agents’ wealth following a Boltzmann-Gibbs distribution. In other words, the result of the game is many “poor” agents and few “wealthy” agents. In this paper, we apply several tax and redistribution models to study their effect on the population’s wealth distribution by computing the resulting Gini coefficient of the system. We find that income taxes, both flat and progressive, that evenly redistributed taxed monies do little to change the Gini coefficient from the Boltzmann-Gibbs distribution. However, income taxes that are redistributed to the poorest agents can significantly lower the Gini coefficient, resulting in a more evenly distributed wealth distribution. Furthermore, we find that a very small wealth tax can lead to significant decreases in the Gini coefficient.

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