Authors often add covariates to a base model sequentially either to test a particular coefficient’s “robustness” or to account for the “effects” on this coefficient of adding covariates. This is problematic, due to sequence sensitivity when added covariates are intercorrelated. Using the omitted variables bias formula, I construct a conditional decomposition that accounts for various covariates’ role in moving base regressors’ coefficients. I also provide a consistent covariance formula. I illustrate this conditional decomposition with NLSY data in an application that exhibits sequence sensitivity. Related extensions include instrumental variables, the fact that my decomposition nests the Oaxaca-Blinder decomposition, and a Hausman test result.

We measure impacts of entry conditions on labor market outcomes for the US college graduating classes of 1974–2011. A large recession reduces initial earnings by 10%, through full-time work and wages, with small persistent impacts on wages. Those in high-paying majors experience smaller impacts on most labor market outcomes, widening earnings inequality across majors. In the Great Recession, early earnings losses are much larger than predicted given past patterns and the size of the recession. This is partially because the cyclical sensitivity of demand for college graduates has more than doubled. Recession effects also became more evenly distributed across majors.