Omitted variables correlated with race bias the discrimination estimate

Evidence

The error term εdjc captures all other factors that impact the outcome Y. Any determinant of Y that is left out and not included in Equation (1) is embedded in the error term ε. The key assumption in the analysis of judicial decisions with a regression model, as in Equation (1), is that any left-out, unobserved factor, captured by the error term, is not correlated with the variable Minority Defendant. For example, if defendant income is not included in regression Equation (1) (if income is not part of the vector X), this implies that income is embedded in the error term (ε). To the extent that minority status and income are correlated, the error term ε (which now captures income) and the variable Minority Defendant will be correlated. Thus, any variation in incomes between defendants will translate into variation in the error terms and therefore in the case outcomes between the defendants, and such income variation will also impact the key explanatory variable Minority Defendant. In this situation it is impossible to obtain an unbiased estimate of the parameter β1 to determine the true impact of the defendant’s minority status on the outcome of interest. That is, it would not be possible to disentangle the true “causal” impact of minority status from the impact of income on the outcome. — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law, 736

Categorization

• DEFINE: Explains the omitted-variable bias premise that limits causal inference about race from observational judicial outcomes.
• XREF: Frames the reader’s measured-vs-professed bias question: observed conviction gaps cannot be cleanly attributed to bias when confounds correlate with race.
• corroborated: 2 independent passages support this claim — Joseph Avery, Jim Sidanius, Joel Cooper, Gregory Davis, Amanda N., Bias in the Law: A Definitive Look at…, 736