is spatially progressive in six countries and spatially regressive in seven, based on second-order stochastic dominance.

The findings from comparing MPS and PSCT distributions suggest that MPS subsidies are more spatially regressive. Agriculture subsidies in Argentina, Kazakhstan, and India have flipped from being progressive with PSCT to being regressive with MPS. Our analysis of MPS distribution was limited to 13 countries, compared to the 16 with PSCT, because several countries do not have MPS, and restricted to eight crops, compared to 23 for PSCT, because countries have MPS for fewer crops than PSCT.<sup>6</sup> Nevertheless, the results of these analyses suggest that fiscal subsidies tend to be more spatially progressive than MPS.

# **6 Input subsidy results**

Next, we analyze the spatial distribution of input subsidies within countries. Using our estimate of spatially explicit input subsidy data described in section 3, we repeat the methodology employed for output subsidies. The results in table 3 show that the spatial incidence of input subsidies is regressive in nine countries, progressive in 11, and neutral in three. As with output subsidies, results are mixed and vary significantly between countries. But some patterns emerge: upper-middle and high-income countries tend to have progressive input subsidy schemes, while the spatial distribution tends to be more regressive in African countries. The clear exceptions to these patterns are Kenya, which has the most progressive spatial incidence of all countries, and the EU-28, which has among the most regressive. The EU result is unsurprising, given that the input-subsidy spatial distribution correlates with output and value. The EU CAP has also received significant criticism for how regressive it is, particularly in its early stages (Kaditi and Nitsi 2011; OECD 2003).

To examine the environmental consequences of input subsidies—more specifically, the relationship between input subsidies and fertilizer use—we use a cross-sectional model and spatially disaggregated data on average annual nitrogen fertilizer used per hectare of cropland from Lu and Tian (2017). To match our data on subsidies, we use fertilizer use data for 2010 and aggregate data over our 0.5-degree grid cells. We then use regression analysis to estimate the relationship between subsidies and fertilizer use. Given the cross-sectional nature of the analysis, unobserved correlation between subsidies and other factors may influence fertilizer use. To alleviate some of these concerns of omitted variable bias, we include additional controls. These include country-fixed effects that account for time-invariant characteristics that are specific to a country, such as geographic or institutional features, and grid-level characteristics, such as terrain roughness by using the standard deviation of elevation in a grid cell, and “wetness index”, the compound topographic index (CTI) derived from HYDRO1k, which correlates with soil moisture.

Figure 5 shows a positive relationship between input subsidies and nitrogen fertilizer use. The histograms for input subsidies and nitrogen levels in fertilizer on the axes depict their distribution across different values. Because we have demeaned the values for fertilizer and input subsidies within countries, these may take negative values. Positive values are above the country average, and negative values are below the country average. The trend indicates a positive correlation between input subsidies and nitrogen

> 6 Sugar, wheat, rice, maize, barley, rapeseed, coffee, and tea are among the crops studied in the MPS analysis.

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