Estimating Regression Models in Which the Dependent Variable Is Based on Estimates

e-mail: jblewis{at}ucla.edu (corresponding author) e-mail: dlinzer{at}ucla.edu Researchers often use as dependent variables quantities estimatedfrom auxiliary data sets. Estimated dependent variable (EDV)models arise, for example, in studies where counties or statesare the units of analysis and the dependent variable is an estimatedmean, proportion, or regression coefficient. Scholars fittingEDV models have generally recognized that variation in the samplingvariance of the observations on the dependent variable willinduce heteroscedasticity. We show that the most common approachto this problem, weighted least squares, will usually lead toinefficient estimates and underestimated standard errors. Inmany cases, OLS with White's or Efron heteroscedastic consistentstandard errors yields better results. We also suggest two simplealternative FGLS approaches that are more efficient and yieldconsistent standard error estimates. Finally, we apply the variousalternative estimators to a replication of Cohen's (2004) cross-nationalstudy of presidential approval.