A Framework for Using Value-Added in Regressions

TL;DR

This paper develops a GMM-based framework to correctly estimate standard errors in regressions involving value-added measures, addressing common inaccuracies and proposing more efficient estimation methods.

Contribution

It introduces a GMM approach for VA regressions, corrects standard error calculations, and offers an improved estimator for more accurate inference.

Findings

Correct SEs significantly differ from traditional OLS SEs.

GMM framework provides more accurate inference in VA regressions.

Empirical application shows substantial SE adjustments in real data.

Abstract

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.