As discussed, farmers in the study area also apply organic fertilizers. Applications of organic fertilizers provide nutrients directly and build up the organic content of soils, which increases the efficacy of chemical fertilizers.<sup>30</sup> As a result, organic fertilizer use could factor as either a complement or substitute in an input demand equation for fertilizer. To avoid estimation problems, we use livestock density to proxy the quantities of manure available for application rather than application rates, since organic and inorganic fertilizers are likely jointly determined. As discussed earlier, most organic fertilizer originates locally and reaches the farm through non-market channels, so manure availability and manure use are closely associated. Moreover, in addition to addressing a statistical problem, the approach likely accounts for past practices and missing measurements concerning the organic content of soils. Returning to the question of whether chemical fertilizers are substitutes or complements, our findings suggest that organic fertilizers and chemical fertilizers are complements.<sup>31</sup> The results also suggest a statistically significant and negative association between the intensity of fertilizer and farm size. This is contrary to the positive correlation between land size and fertilizer use in Feder, Just and Zilberman (1985), but consistent with the results reported in Croppenstedt and Demeke (2003) in Ethiopia and Nkonya et al. (1997) in Tanzania. In the Tanzanian study, the authors suggest that farmers with larger land holdings sometimes hedge risks by using a mix of fertilizer application strategies that work to lower average rates. Potentially, the relationship could also be related to incomplete labor markets, which limit a household’s ability to take on the complementary tasks of land preparation and application. In either case, these arguments are tied to included-variables (wealth and household labor), yet the scale result remains robust when group means are added to the model, leaving the root cause of this often-found relationship unclear.

Parameter estimates associated with age and the literacy of the household head, which were significant in the adoption of fertilizer-use, were not statistically significant determinants of the intensity of fertilizer use. The finding associated with age is consistent with other studies and indicates the impediments associated with age, once overcome, do not affect the intensity of fertilizer use.<sup>32</sup> Similarly, household size appears to factor into the choice of technology, but not its implementation.<sup>33</sup> In contrast, literacy does have a positive impact on fertilizer use.

As discussed, wealth can mitigate weaknesses in credit and insurance markets. The results suggest this effect is a continuous one, allowing households to risk increasing levels of sunk costs associated with larger applications of fertilizers. While climate plays a role in adoption, our results on the effects of

> 30 Results from Kenya, reported in Marenya and Barrett (2009), suggest that adding organic matter to the soils would raise the expected profits from applying chemical fertilizers.

> 31 Matsumoto and Yamano (2013) report a similar finding using data from Uganda. See Marenya and Barrett (2009) for an intuitive discussion of the physical and economic aspects of fertilizer efficiency and the organic content of soils.

> 32 Nkonya et al (1997), Croppenstedt and Demeke (2003), and Alem et al. (2010) report similar findings.

> 33 Household size is significant in several studies that treat adoption and demand jointly in a censured regression. Dercon and Christiaensen (2011) report results similar to ours.

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