Cells are indexed by _i_ and years by _t_ . Thus, the unit of observation is the grid cell-year. Here N i is net primary productivity in gridcell i in year t. NPP, which can be measured from satellite imagery, is used to NN measure agricultural performance following the past literature since it provides a common unit of productivity across different crop types (Zaveri, Russ, and Damania, 2020). NPP is linearly related to the amount of solar energy that plants absorb over a growing season and is measured in grams of carbon per square meter. NPP is combined with a land cover data set developed by the European Space Agency’s Climate Change Initiative, which provides information on 37 land cover classes globally at a 300-meter grid. This ensures that plant productivity as measured by NPP is only captured in grid cells that contain significant amounts of agriculture and avoids attributing impacts to forests or other natural habitats.

Data on average annual nitrogen fertilizer used per hectare of cropland is sourced from Lu and Tian (2017). Previous work by McArthur and McCord (2017)<sup>13</sup> finds that a 1 kg/ha increase in fertilizer causes an 8-9 kg/ha increase in yields. This translates to a 10 percent increase in nitrogen fertilizer use, boosting global yields by about 29-32 percent. However, a continuous measure of nitrogen usage can mask heterogeneity in impacts on yields due to the presence of subsidies. This is because although fertilizer subsidies may have enabled fertilizer usage and hence agricultural productivity, subsidies can incentivize farmers to apply more than they need such that the beneficial impacts of nitrogenous fertilizers on productivity can begin to wane beyond a point. To demonstrate the non-linear effects of nitrogen use on agricultural productivity at the global scale, a continuous measure of nitrogen fertilizer use is replaced with indicators for whether the log values of nitrogen usage lie within nine different quantile bins i to assess impacts across the global fertilizer distribution. The quantile coefficients, , are our coefficients of interest. The first quantile is omitted and becomes the reference quantile. bb QQ ββ A plethora of other factors can also affect the relationship between nitrogen fertilizer and yields. Weather data taken from the _Terrestrial Air Temperature and Precipitation Version 4.01_ compiled by the University of Delaware (Willmott and Matsuura 2001) has been widely used in the economics literature (Dell Jones and Olken 2012, Burke Hsiang and Miguel 2015, among others). This data set provides monthly total precipitation and temperature at a 0.5-degree spatial resolution. Data are available for each month between 1901 and 2014.

Control variables include rainfall and temperature from the _Terrestrial Air Temperature and Precipitation Version 4.01_ compiled by the University of Delaware (Willmott and Matsuura 2001). Various fixed effects and time trends are included to isolate the 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, ′i is a vector of other control variables, including precipitation shocks, a quadratic term for ii ii cc θθ γγ ff (tt) mean annual temperature (°C), and log of population. These controls account for baseline differences in XX yield 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

> 13 The authors utilize the economic geography of fertilizer production and transport costs to countries' agricultural heartlands to construct a time-varying instrument for fertilizer use globally for deriving causal estimates of the impacts of fertilizer on economic growth.

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