(our soil nutrient content) and locational (distance to markets and towns<sup>9</sup> ), administrative factors that might affect farmers fertilizer application rate and yields, we also explored the Correlated Random Effects (CRE) model which enables us to address time invariant unobserved household characteristics and still recover the coefficients on time invariant variables (Sheahan et al., 2013)<sup>10</sup> To address challenges associated with extreme outliers, both the input and output variables were winsorized at 99% (or 95% where values at 99% still seemed very large). This involves replacing extreme outlier values beyond the 99th percentile with the value at the 99% percentile rather than dropping the variable. However, where fertilizer use per hectare was still larger than 1 ton after winsorizing, such observations were replaced with a cap value of 700 kilograms per hectare<sup>11</sup> . Due to challenges associated with using the labor data for the first wave of data, household adult equivalency units were used as a proxy for available labor<sup>12</sup> . We also use a dummy to account for whether a farmer uses a chemical (herbicide or pesticide) because of problems encountered with the units of measures of the quantity of herbicides and pesticides used by farmers,. To control for the fact that improved seed varieties are often a complementary input to inorganic fertilizer, we include whether seed used was commercially purchased. This assumes that most improved seed is hybrid which needs to be purchased each year and not open pollinated varieties. We also include measures of the plot’s slope (measured in degrees), plot elevation measured in meters above sea, the tropical wetness index /plot wetness potential index and length of growing period (Wilson et al., 2007). A dummy variable is used to distinguish farmers who planted maize as a sole crop on the plot versus those engaged in intercropping. While monocropping could be a sign of specialization in maize production for commercial purposes, intercropping of crops such as maize with legumes is also commonly used to diversify risk and increase maize yields because of the nitrogen fixing effect of legumes. As a source of additional nutrients likely to affect maize yields as well as response of nitrogen application, we control for

> 9 These do not vary over the short duration covered and are indicators of access to extension agents and also indicate likely differences in transportation and other transactions costs

> 10   The full results from the CRE models are not included due to space considerations but are available from the authors. We find that our key output of interest (the MPPs) in the main maize farming systems (where effects are significant) are similar for both the FE and CRE even though the CRE model does indicate that some time invariant characteristics are important. As expected both soil quality and administrative factors appear to be important determinants of maize yields.

> 11 This follows Sheahan and Barrett (2014) as 700kg/hectare  represents an upper-bound limit associated with inorganic fertilizer use in the United States under irrigated corn conditions .

> 12 For this same reason we are not able to explore other dimensions of nitrogen application as the likely role labor availability plays in the effectiveness and profitability of nitrogen application

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