Omitted variables correlated with race make regression estimates of judicial bias unreliable

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

Category: Causal Relationships

• DEFINE: Explains the omitted-variable/endogeneity problem in plain terms: when a correlated omitted factor like income hides in the error term, causality claims about race break down.
• XREF: The omitted-variable bias logic connects to the reader’s broader institutional economics reading, where all causal inference problems trace back to identifying variation that isn’t confounded.

Related

• Omitted variables correlated with race bias the discrimination estimate (similarity 0.95)