Table 2.

Conditional expectations of productivity, treatment, and heterogeneity effects

Household types	MHHs	FHHs	Treatment effects
MHHs	a) $E\left(y_m\right)\left|G=\left(1\right)\right)$	c) $E\left(y_f\left|G=\left(1\right)\right)\right)$	$\mathit{MHHsP}$ = (a − c)
FHHs	d) $E\left(y_m\left|G=\left(0\right)\right)\right)$	b) $E\left(y_f\left|G=\left(0\right)\right)\right)$	$\mathit{FHHsP}$  = (d − b)
Heterogeneity effect (difference caused by unobserved characteristics)	$B{H}_m$  = (a − d)	$B{H}_f$  = (c – b)

Cells a) and b) denote the average productivity that is observed in a sample for MHHs and FHHs, respectively; cells c) and d) denote the counterfactual expected productivity

$G=1$ if the household head is male; $G=0$ if the household head is female

$y_m$ = maize productivity indicator for MHH

$y_f$ = maize productivity indicator for FHHs

$B{H}_m\text{and}B{H}_f$ are the differences in productivity between the MHHs and FHHs, respectively, caused by unobserved factors

MHHsP and FHHsP denote the expected productivity effects of gender for those households randomly chosen from the MHHs and FHHs, respectively