The discussion of random assignment experiments in Section 16.1 includes models both with (Equation 16.2) and without (Equation 16.1) two additional observable factors (X₁ and X₂). In contrast, the discussion of natural experiments in Section 16.1 jumped immediately to Equation 16.3 below (which includes these factors) without discussing an equation similar to Equation 16.1.

ΔOUTCOME_i = β₀ + β₁TREATMENT_i + β₂X_1i + β₃X_2i + ε_i

Was this a mistake? What reasons are there for thinking that a natural experiment is more likely to benefit from the inclusion of additional observable factors than is a random assignment experiment? Explain.