returns that farmers could experience. It draws heavily on the analysis by Bold et al. (2017), which conducts a unique, robust analysis of the quality of inputs available to farmers in Uganda and their resulting yield gains. In Section 3.3 we project returns where input quality varies, and show that input use becomes considerably less profitable with lower input quality.

Maize yields increase substantially in response to the use of nitrogen fertilizer and when locally available hybrid seeds are used. Bold et al. (2017) present detailed estimates of maize yields under agronomic research conditions in Uganda for the following four scenarios: traditional seeds and no fertilizer, hybrid seeds and no fertilizer, traditional seeds and optimal fertilizer application—taken to be 108 kg of nitrogen per hectare—and hybrid seeds and optimal fertilizer application.<sup>8</sup> They show significant increases in yields from input use; yields more than double when fertilizer is used, regardless of the type of seeds used (hybrid or traditional). Yield gains are highest when both fertilizer and hybrid seeds are used, underscoring the complementarity of input use (Figure 3.1).

More broadly, yields of all crops increase in response to the application of nitrogen with the yields of rice, beans and maize being particularly responsive. Kaizzi et al. (2012a, 2012b, 2012c) document the returns to the use of nitrogen (N), Phosphate (P) and Potash (K) for a number of crops in Uganda. In general, across all crops, nitrogen application provides a significant yield gain, reflecting the fact that this is a main nutritional deficiency limiting crop growth. Rice, beans and maize are the crops that show the largest return to the use of nitrogen in their study. The yield gain from using nitrogen is shown in Figure 3.2. At the maximum, the additional yield from using nitrogen for maize is approximately 1.9 tonnes per hectare in Figure 3.2, which is of the same order of magnitude as the slightly larger gain recorded in Bold et al. (2017) and shown in Figure 3.1.

Rainfall anomalies reduce these yield gains. Thus far, good weather conditions are assumed. However, too little or too much rain reduces the yield gain from using fertilizer. This is documented in Christiaensen and Dercon (2009) for Ethiopia and is shown in Figure 3.3. The yield gain is largest, about a 33 percent increase, at median rainfall levels but is halved to about 15 percent when rainfall is too low (at the 25th percentile of the rainfall distribution) or too high (the top 25th percentile). Rosenzweig and Udry (2017) also report large variation in returns to investment in crop production in northern Ghana resulting from changing weather conditions. Ideal weather conditions (or at least non‐extreme conditions) are assumed for the field trials used to determine the yield gains to nitrogen application. In the following section, we explore how the estimated results would be affected when weather conditions are not optimal using Christiaensen and Dercon (2009) as a reference.

> 8 Seeding in Bold et al. (2017) is done at a rate of 50kg per hectare and 108kg of fertilizer is applied per hectare in two applications.

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