A Note on "How Robust Standard Errors Expose Methodological Problems   They Do Not Fix, and What to Do About It"
  King and Roberts (2015, KR) claim that a disagreement between robust and classical standard errors exposes model misspecification. We emphasize that KR's claim only generally applies to parametric models: models that assume a restrictive form of the distribution of the outcome. Many common models in use in political science, including the linear model, are not necessarily parametric -- rather they may be semiparametric. Common estimators of model parameters such as ordinary least squares have both robust (corresponding to a semiparametric model) and classical (corresponding to a more restrictive model) standard error estimates. Given a properly specified semiparametric model and mild regularity conditions, the classical standard errors are not generally consistent, but the robust standard errors are. To illustrate this point, we consider the case of the regression estimate of a semiparametric linear model with no model misspecification, and show that robust standard errors may nevertheless systematically differ from classical standard errors. We show that a disagreement between robust and classical standard errors is not generally suitable as a diagnostic for regression estimators, and that KR's reanalyses of Neumayer (2003) and B\"uthe and Milner (2008) are predicated on strong assumptions that the original authors did not invoke nor require. 
Peter M. Aronow
stat.ME