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Value-added estimates - estimates based on the evolution rather than level of achievement - are viewed by most researchers as more reliable than cross-sectional comparisons since they ostensibly "difference out" the influence of omitted fixed inputs, such as wealth and ability. We show that the restricted value-added model, which assumes that past achievement carries over with no loss, is clearly rejected by the data, and that the more flexible lagged value-added model is biased by measurement error and omitted heterogeneity that enters each period. Using dynamic panel methods that address these biases and data on public and private schools in Pakistan, we find that the restricted value-added model yields wildly biased estimates for the private school effect, sometimes even flipping the sign. The lagged value-added model performs better due to countervailing measurement error and heterogeneity biases. More generally, rapid and potentially heterogenous achievement decay or "fade-out", which evidence suggests underlies our results, has broad implications for experimental and non-experimental program evaluation, and value-added accountability systems.