Omitted variable bias (OVB) of OLS estimators is a serious and ubiquitous problem in social science research. Often researchers use the direction of the bias in substantive arguments or to motivate estimation methods to deal with the bias. This paper offers a geometric interpretation of OVB that...

In this paper I discuss three issues related to bias of OLS estimators in a general multivariate setting. First, I discuss the bias that arises from omitting relevant variables. I offer a geometric interpretation of such bias and derive sufficient conditions in terms of sign restrictions that...

Covariate benchmarking is an important part of sensitivity analysis about omitted variable bias and can be used to bound the strength of the unobserved confounder using information and judgments about observed covariates. It is common to carry out formal covariate benchmarking after...

In this paper, I discuss three aspects of the Frisch-Waugh-Lovell theorem. First, I show that the theorem holds for linear instrumental variables estimation of a multiple regression model that is either exactly or overidentified. I show that with linear instrumental variables estimation: (a)...

Covariate benchmarking is an important part of sensitivity analysis about omitted variable bias and can be used to bound the strength of the unobserved confounder using information and judgments about observed covariates. It is common to carry out formal covariate benchmarking under the...

In this paper, I derive an expression for the asymptotic bias in the OLS estimator of the partial effect of a regressor on the dependent variable when there is reverse causality and all variables in the model are covariance stationary. I show that the sign of the asymptotic bias depends only on...

This paper uses a novel empirical strategy to present empirical estimates of the effect of an exogenous shock to distribution on demand and accumulation for the US economy from 1973 to 2018. We use recursive vector autoregressions to identify the impact of shocks to the wage share. We impose...