After aggregating plot-level survey data on manure application and cash crop cultivation to the parcel level,<sup>13</sup> we estimate: i i i i (1) where i is defined above; controls for unobserved household fixed effects such as risk-bearing capacity that do not vary across parcels;ii i is a vector of parcel-specific indicators of land rights for those who YY αα report or are reported as land owners; i is a vector of parcel controls including size, soil type, slope, and RR location in a swamp/wetland;<sup>14</sup> and i is an error term. As public programs including input subsidies XX (Asfaw _et al._ 2017) are administered by any one of Malawi’s 28 districts, we cluster errors at the districtεε level and use the wild cluster bootstrap (Roodman _et al._ 2018) to account for the small number of clusters. The coefficient of interest is _β_ , the vector of coefficients capturing the effect of different types of land rights on land-attached agricultural investment. To allow for heterogeneity of effects by gender, we denote women’s and men’s land rights by i and i , ff mm respectively. i is an indicator variable for women’s land rights, equaling one if at least one woman in RR RR ff household _j_ reports (or, in the case of IHS4 data are reported as) having land rights of a certain type to RR parcel _i_ . Similarly, i is the equivalent indicator variable for men’s land rights that equals one if at least mm one man in household _j_ has rights of a certain nature to parcel _i_ . We modify (1) as follows RR i 1 i 2 i i i (2) ff mm ii where and YY = αα + ββ RR + ββ RR + γγXX + εε + i 1 i 2 i i i (2) where 1 and 2 are estimated effects of land rights being held by women or men, respectively, and 1 + 2 denotes the estimated effect of rights being held jointly by male and female household members. ββ ββ ββ As the nature of rights and ability to enforce them can vary by inheritance regime, we let ββ be an indicator variable for household _j_ living in a community with a patrilineal/mixed inheritance regime and estimate ii II i 1 i 2 i 3 i 4 i i i (3) ff mm ff mm ii ii ii ii where 1 and YY2 indicate estimated effects of women’s and men’s rights in matrilineal communities while = αα + ββ RR + ββ RR + ββ RR ∗II + ββ RR ∗II + γγXX + εε 3 and 4 indicate if women’s or men’s rights affect outcomes differently in non-matrilineal communities. ββ ββ ββ ββ

> 13 Formally, we index plots by _s_ , parcels by _i_ and households by _j_ and compute organic fertilizer application or plating of cash crops on parcel _i_ of household _j_ as i = ∑SSss=1∑ yys <u>s×aas</u> s <u>s</u> = �<sup>1  i</sup> where is an indicator variable for organic fertilizer application or planting of cash crops by household YY SSss=1 aa ss , yyssi<sup>ooooiioo iiffooiiffiifoo wwooww ooaffiiffaa oowwh oooaaww aaffoppffaa o</sup> _j_ on plot<sup>aaffoopp ww</sup> _s_ of parcel _i_ , and is the plot size in hectares. 0  oopphffoowwiiwwff 14 ssi ssi Parcel size is in logs, soil types considered are sand, sandy/clay or clay; inclination can be flat, slightly sloped, moderately sloped, or hilly. These yy oo

> 14 parcel characteristics are also aggregated from plot information. They are also weighted by plot size.

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