could be a source of endogeneity given potential reverse causality (for instance, if places that have stable cropland attract roads). Although this omission could be a source of omitted variable bias, the risk of such bias is greatly reduced by controlling for distance to the nearest city, which also proxies for the presence of infrastructure.

Following this first step, we recover the country-fixed effects and then run a country-level regression of those fixed effects on variables that capture the national context. The specification is: where FEc is the set of country fixed effects estimated in the first stage, Zcl are the national-level variables for country c , and μl is the error term. We use four national variables, including GDP per capita in constant dollar terms, the Gini Index for 2018, cropland per capita for 2018, and the Doing Business Quality of Land Administration for 2020.<sup>7</sup> We also experimented with two other institutional variables in lieu of the Doing Business variable, including a measure of Rural land tenure insecurity that we constructed using the 2012 Institutional Profile Database and the overall indicator in the 2017 Enabling Business of Agriculture dataset (see the data section above).

For movements into cropland, the approach is similar to assessing the determinants of movements out of cropland. The sample is different though as we need to consider the hundreds of millions of pixels that were not cropland in 2003, raising computational issues. To address the large dimensionality of the problem, we restrict ourselves to the sample of pixels within 3 kilometers of other pixels that were initially classified as cropland in 2003. There are 30.3 million such pixels, of which 4.29 million (covering 107.2 million hectares) transitioned to cropland between 2003 and 2018. This 3-kilometer buffer thus captures 90.1 percent of cropland gains over the period (119 million hectares). We then proceed to a similar 2- stage approach for our assessment of the drivers of cropland loss. In the first stage, we run a regression similar to specification (1) where  Yi is now a dummy variable equal to 1 if pixel _i_ (in country _c_ ) transitioned into cropland between 2003 and 2018 and is equal to 0 if the pixel remained non-cropped. We consider the same set of explanatory variables Xik as before. The country-fixed effects are then recovered and regressed on the same national-level characteristics specified in (2).

# **Samples and descriptive statistics**

For the first stage regression of cropland losses, we consider the universe of 48.3 million pixels that were initially under cropland in 2003. Appendix Table A3.1 shows global summary statistics for the five explanatory variables associated with these pixels, including distance to a city, a coast, and a river, the number of drought months over the studied period, and land suitability for agriculture. The figures in the table show the existence of large global variations for these variables. For the first stage regression of cropland gains, we consider the 30.3 million pixels located within 3 kilometers of a cropland pixel in 2003 but that were not cropland at the time. Appendix Table A3.1 also shows descriptive statistics for this sample for the same five explanatory variables. As expected, the latter sample is more “peripheral” and

> 7 - The Gini index is from the World Development Indicators (https://databank.worldbank.org/source/world <u>development-indicators). Cropland per capita is constructed using MCD12Q1 and population from the Word</u> Development Indicators. The Quality of land administration index ranges between 0 and 30 and measures the reliability, transparency, and coverage of land administration, as well as protection against land disputes and equal access to property rights.

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