Table 1.

Definitions of the measures and their estimates defined with bias factors.

Measure name	Scale	Estimand	Estimate^b
Linear difference, D_j	Absolute	D_j = Y_j,1 − Y_j,0	${\hat{D}}_{j} = {\hat{Y}}_{j, 1} - {\hat{Y}}_{j, 0} = (Y_{j, 1} + α_{j, 1}) - (Y_{j, 0} + α_{j, 0})$
Ratio, R_j	Relative	$R_{j} = \frac{Y_{j, 1}}{Y_{j, 0}}$	${\hat{R}}_{j} = \frac{{\hat{Y}}_{j, 1}}{{\hat{Y}}_{j, 0}} = \frac{Y_{j, 1} * β_{j, 1}}{Y_{j, 0} * β_{j, 0}}$
Percent difference,^a PD_j	Relative	$P D_{j} = \frac{Y_{j, 1}}{Y_{j, 0}} - 1$	${\hat{P D}}_{j} = \frac{{\hat{Y}}_{j, 1}}{{\hat{Y}}_{j, 0}} - 1 = \frac{Y_{j, 1} * β_{j, 1}}{Y_{j, 0} * β_{j, 0}} - 1$
Difference in differences, DD	Absolute	DiD = (Y_1,1 − Y_1,0) − (Y_0,1 − Y_0,0)	$\hat{D l D} = ({\hat{Y}}_{1, 1} - {\hat{Y}}_{1, 0}) - ({\hat{Y}}_{0, 1} - {\hat{Y}}_{0, 0}) = ((Y_{1, 1} + α_{1, 1}) - (Y_{1, 0} + α_{1, 0})) - ((Y_{0, 1} + α_{0, 1}) - (Y_{0, 0} + α_{0, 0}))$
Ratio of ratios, RR	Relative	$R o R = \frac{\frac{Y_{1.1}}{Y_{1, 0}}}{\frac{Y_{0, 1}}{Y_{0, 0}}}$	$\hat{R O R} = \frac{\frac{{\hat{Y}}_{1, 1}}{{\hat{Y}}_{1, 0}}}{\frac{{\hat{Y}}_{0, 1}}{{\hat{Y}}_{0, 0}}} = \frac{\frac{Y_{1, 1} * β_{1, 1}}{Y_{1, 0} * β_{1, 0}}}{\frac{Y_{0, 1} * β_{0, 1}}{Y_{0, 0} * β_{0, 0}}}$
Ratio of percent differences, RPD	Relative	$R P D = \frac{\frac{Y_{1, 1}}{Y_{1, 0}} - 1}{\frac{Y_{0, 1}}{Y_{0, 0}} - 1}$	$\hat{R P D} = \frac{\frac{{\hat{Y}}_{1, 1}}{{\hat{Y}}_{1, 0}} - 1}{\frac{{\hat{Y}}_{0, 1}}{{\hat{Y}}_{0, 0}} - 1} = \frac{\frac{Y_{1, 1} * β_{1, 1}}{Y_{1, 0} * β_{1, 0}} - 1}{\frac{Y_{0, 1} * β_{0, 1}}{Y_{0, 0} * β_{0, 0}} - 1}$

We omit the 100% multiplier for simplicity of notation; it does not affect conclusions.

For expressions involving the relative bias factor, we stipulate that β_j,t ≠ 0 so that the adjacent Y_j,t does not drop out of the expression, creating unusual results.