Although lack of input prices and labor input in our data makes it difficult to compute profits or estimate a production function, low incidence of purchased input use by small farmers suggests that indicator variables for whether or not certain inputs or practices were applied may be a reasonable approximation. To assess the impact of purchased input use and improved cultivation practices on output for specific crops and at the same time provide a simple test of the farm size-productivity relationship, we use data for 2008, 2012 and 2014 to run simple yield regressions.<sup>17</sup> Our estimating equation takes the form ����� ���������� ��������� �������� ������� ������ ��� ��� ����� (2) where _Ykijt_ is the natural log of yield from a main crop _k_ (maize, cassava, sorghum, peanut, rice or sugarcane)<sup>18</sup> for small farm _i_ in district _j_ in year _t_ ; _Akijt_ is the natural log of farm size; _Zkijt_ is a vector of indicator variables for crop-specific input use including improved seed, fertilizer, pesticide and irrigation; _Xijt_ is a vector of basic household characteristics and indicator variables for hiring workers, animal traction, and agronomic practices; _Rjt_ is a vector including the absolute value of the _z_ score of the rainfall deviation from the long-term trend and an indicator variable indicating whether this deviation is positive or negative shock; _δt_ is a time trend; and _δj_ is a district fixed effect.<sup>19</sup> Results, in table 5, point to three conclusions. First, improved cultivation practices seem associated with higher yields although the relationship, which is strongest for maize where use of intercropping, line sowing, animal traction, and crop rotation -estimated to be associated with yield increases by 15.5, 12.1, 11.1 and 8.3 points, respectively- is not always significant. Animal traction, line sowing and irrigation (15.1%, 13.7% and 56.2%) are significant for cassava, while intercropping, line sowing, and crop rotation are so for peanuts (11.6%, 9.1% & 8.8%). Intercropping and line sowing are weakly significant for sorghum, but none seem to affect yields for rice or sugarcane. Second, once other factors are controlled for, 2012 and 2014 yields are indeed significant above 2008 ones for all crops. Third, with the exception of peanuts and sugarcane, the relationship between farm size and yield is U-shaped with the minimum attained for maize, cassava, sorghum, and rice estimated at 184, 2930, 593, and 15 ha, respectively, well beyond the range for which we have data, implying a negative relationship over the entire support.

Lack information on household characteristics and agronomic practices for large farms makes even simple yield regressions difficult to interpret. Figure 4 thus plots the kernel-weighted local polynomial relationship between farm size and yields for different crops. While there is a strong negative relationship between farm size and productivity for farms below 1 ha in all commodities except rice, yields tend to increase with farm

> 17 We do not include earlier years because we do not have crop-specific use of inputs.

> 18 Yield is value (MT) per hectare for sugarcane and kilogram per hectare for other crops.

> 19 We include a EA fixed effect in equation (1) but a district fixed effect in equation (2), because the 2008 data set is not a panel with 2012 and 2014 data sets at EA level.

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