where A is the agro-ecological potential of all field crops in US dollars at international prices, and UG is the distance-modulated urban gravity of all cities with recent population greater than 500,000. AA kk

## **The dependent variables are as follows:**

- Population density of the EA

- Distance to the nearest road and the nearest markets

- Average owned or cropped area per household

- Cropping intensity, defined as gross cropped area per net cropped area

- Proportion or area of land area under fallow

- Proportion of net crop area irrigated

- Proportion of households using different technologies: high yielding varieties, organic manure, fertilizer, or pesticides

Equations are estimated for each of the dependent variable, and in double logarithmic form.

# **Definition of the variables**

## **Agroecological potential**

We calculate the agro-ecological potential from the currently available GAEZ data of the International Institute for Systems Analysis and the Food and Agriculture Organization (Tóth et al, 2012).

For each 5 arc-minute grid cell of agricultural land of the World the data set uses crop models to calculate _agroclimatic yields_ , for 280 crops and land-use types. These are progressively aggregated to 49 crops. Agroclimatic yield takes account of all climate related constraints and uses and optimum crop calendar. GAEZ then calculates _Agroecological suitability and productivity_ that takes account of the distribution of grid-specific soil and terrain conditions and fallow requirements. We use the data on “ _Potential yield_ ” that does adjust for fallow requirements. GAEZ constrain potential yield for 28 crops, of which we use those for which international prices are available. We end up with potential yield for the following crops: wheat, rice, maize, barley, millet, sorghum, white potatoes, cassava, soybean, coffee, cotton, groundnut, banana, sweet potatoes, and beans.

These potentials are calculated for the past, current and potential future climates; and for low, medium and high input levels, of which the current values at intermediate level is the most appropriate for us: “In the case of intermediate input/improved management assumption, the farming system is partly market oriented. Production for subsistence plus commercial sale is a management objective. Production is based on improved varieties, on manual labor with hand tools and/or animal traction and some mechanization. It is medium labor intensive, uses some fertilizer application and chemical pest, disease and weed control, adequate fallows and some conservation measures.” (Tótz et al. 2012, p 18) In light of the limited irrigation in Africa we are using the data for the rain-fed category. To summarize, we will use the _agro-ecological level for the current climate conditions at intermediate levels of input use under rain-fed conditions._ The data in the GAEZ system are for each crop. But we want to characterize the aggregate agro-climatic potential in the communities being analyzed. Therefore we need to assign a value to the potential crop productivities across crop. In order for the calculations to be comparable across countries, we did it with respect to average world market prices of for the past three years during which the LSMS studies were carried out. The commodities include the 15 crops mentioned above 7