As in the case of AEP, we assume that today’s urban gravity is correlated with UG over the past, during which migration, fertility, infrastructure investment decision were made, and therefore the coefficients of today’s urban gravity capture both current and past impacts of UG. Since urban populations and incomes have changed very rapidly over the past decades, the errors in variable problem associated with past UG being imperfectly correlated with current UG is more severe than in the case of AEP. Again, for the intensification problem that change more quickly over time the problem will be less.

# **Public infrastructure**

We used two variables as proxy of public infrastructure: distance to the main road, and distance to key market center. Both variables are included in the set of GEO variables collected under the LSMS-ISA project by means of households’ GEO coordinates. The former is the distance in Kms to the nearest trunk road while the latter is the Household’s distance to nearest major market.

# **Owned and operated land**

In the data we have the farmer’s self-reported area of each plot<sup>9</sup> . Areas measured by GPS are available for a significant share of the plots, however, in each country regression analysis was used to relate self-reported area to area measured by GPS. The estimated regression coefficients were then used to estimate a predicted GPS area for those plots where that area is not reported.

We distinguish between owned and operated area. Operated area is defined as owned area plus rented in area minus rented out area.

# **Land use intensity**

The primary variable we use for land use the cropping intensity (CI) of cropped land, rather than Boserup’s and Ruthenberg’s R-value. This is because, as we shall see, in most countries fallow rates are now very low, and we are no longer looking at the transition from long or short fallow systems to permanent agriculture, for which the R-value is best suited.<sup>10</sup> Cropping intensity takes account of multiple cropping, the use of the land for more than one crop a year, which is observed in several countries. We define C = (5) GG∗100 Where NN is gross cropped, the sum of the areas cropped in the main season plus the areas cropped in the second season, and is net cropped area, the area cropped in the main cropping season. If there is only single cropping, GG C is 100%. It rises to 200 % when all cropland is used in both seasons, and can go higher when some land is used more than 2 times in a year. The cropping NN intensity is calculated as the mean over households in an EA, while the population density is the man over communities as defined in the Harvest Choice data sets.

# **Irrigation and technology variables**

For irrigation we use the share of cropped land that is irrigated. Data on inputs and outputs is collected at the plot level, which is a subdivision of the parcel. The data does not contain the area of each plot. Because different plots may use different inputs and techniques, this means that we cannot estimate area under a particular technique in this data set. Instead we have to focus on whether a farmer does use, or does not use a particular technique. We estimate the proportion of

> 9 In some countries the GPS is available for parcel, in order for plots

> 10 Ruthenberg's (1980) R-value RV  = N*100 / (N+F), where N is net cropped area (also called cultivated area) and F is fallow area.

10