Abstract Title Page Title: Test Score Measurement Error, Short-term Knowledge, and Lagged Dependent Variables in Models of the Education Production Function Authors and Affiliations:

Researchers and policymakers are interested in the causal effects of educational inputs on student achievement. Unfortunately, it is not possible to directly observe student learning, so test score data is often used as an approximate measure. To measure their achievement at a given point in time (e.g., in the spring of the school year) students typically complete standardized tests composed of around forty to fifty questions per subject over one or two days of the school year. Given the small number of items, the test is an incomplete measure of students ' achievement. In addition, students can get sick during testing, be distracted, or can cram, either on their own or through their teachers, all of which will affect their scores. Guessing is also an issue due to the small number of items on the tests. Combined, these factors mean that test scores are a noisy measure of a student's true level of knowledge, and so estimation of causal effects may be affected. As discussed by Todd and Wolpin (2003), one class of models that are particularly vulnerable to measurement error are those that include lagged test scores as regressors. Under classical measurement error assumptions, the estimate of the coefficient on the lagged test score will suffer from attenuation bias. Even if this coefficient is not of interest, the bias can b