slope, and soil type. Standard errors are clustered at the administrative level to account for spatial and temporal correlation in the disturbance terms.

To the extent that unobservable factors like farmers' agronomic know-how might be correlated with both yields and inputs, the estimation could lead to an underestimation of the impact of increasing fertilizer use on yields, and therefore these results should be interpreted as lower bound estimates.

To account for the varying distribution of nitrogen usage in each region, equation (1) is modified to estimate region level regressions based on regional-specific quintiles. In the regional analysis, five quintiles are used and the middle or third quintile is omitted and becomes the reference quintile. The responsiveness of yield to the first, second, fourth and fifth quintiles are therefore measured relative to quintile three. Note that depending on the spread of the distribution of fertilizer in each region, the third quintile may or may not represent the optimum level of nitrogen.

To estimate the impact of nitrogen fertilizer on water pollution, equation 1 is modified to examine the total impact of nitrogen fertilizer use on water pollution spillovers. The sample period for this analysis extends from 1995 to 2013. A considerable body of literature has attempted to explain how human and environmental changes impact freshwater quality. Many of these pollution elasticities are available for individual countries or case specific studies but have not previously been quantified at the global level for water pollution. This paper employs a global gridded dataset of nitrogen fertilizer and nitrogen pollution in water to calculate the change in water quality for every percentage change in nitrogen fertilizer use.

The following equation is estimated at the global scale where i denotes grid cell and t denotes year: ′ i 1 1 i i i (2) Water quality data is sourced from GEMStat which is a globally harmonized database on freshwater ln(WWQQ ) = αα + ββ ln (NN ) + XX λλ+ ffcc(tt) + θθii + γγii + εε quality developed by UNEP-GEMS, maintained by the International Centre for Water Resources and Global Change (ICWRGC) and hosted by the Federal Institute of Hydrology in Koblenz, Germany (www.gemstat.org). Data from river monitoring stations in the GEMStat database are used to measure concentrations of nitrogen in rivers. Total nitrogen in water, i , is measured using a combination of nitrates and nitrites, and aggregated to the 0.5-degree grid to match the resolution of nitrogen fertilizer WWQQ data, i . Various other factors can also affect the relationship between nitrogen fertilizer and water quality. Control variables, including various fixed effects and time trends, are included to isolate the NN impact of nitrogen fertilizer as much as possible from other factors: are year fixed effects, are grid cell fixed effects, are country-specific time trends. Finally, ′i is a vector of other control variables, ii ii θθ γγ including annual rainfall, temperature, runoff, and log of population. In some specifications, the cc ff (tt) XX extensive or intensive margin of land use such as cropped area and yields are also included. Together, these controls account for baseline differences in water quality patterns and other factors that vary by year. These are meant to control for changes in agricultural policies, development levels, input availability, technological levels, and time-invariant factors such as terrain slope, soil type, and distance to coast or water bodies.

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