  As increasingly popular metrics of worker and institutional quality,
estimated value-added (VA) measures are now widely used as dependent or
explanatory variables in regressions. For example, VA is used as an explanatory
variable when examining the relationship between teacher VA and students'
long-run outcomes. Due to the multi-step nature of VA estimation, the standard
errors (SEs) researchers routinely use when including VA measures in OLS
regressions are incorrect. In this paper, I show that the assumptions
underpinning VA models naturally lead to a generalized method of moments (GMM)
framework. Using this insight, I construct correct SEs' for regressions that
use VA as an explanatory variable and for regressions where VA is the outcome.
In addition, I identify the causes of incorrect SEs when using OLS, discuss the
need to adjust SEs under different sets of assumptions, and propose a more
efficient estimator for using VA as an explanatory variable. Finally, I
illustrate my results using data from North Carolina, and show that correcting
SEs results in an increase that is larger than the impact of clustering SEs.
