The two measures have different meanings. The mean of shares more accurately reflects a household-level diversification strategy, regardless of the magnitude of income. The share of means reflects the importance of a given income source in the aggregate income of rural households in general or for any given group of households. The two measures will give similar results if the distribution of the shares of a given source of income is constant over the income distribution, which is clearly not always the case. If, for example, those households with the highest share of crop income are also the households with the highest quantity of crop income, then the share of agricultural income in total income (over a given group of households) using the share of means will be greater than the share using the mean of shares. Since the household is our basic unit of analysis, we use the mean of shares throughout this paper.

In analyzing spatially the patterns of income diversification in our sample of LSMS-ISA data sets, we use a set of geo-referenced variables from external data sets that can be linked to household-level data via their GPS attributes (Murray, 2013). These variables are available for a subset of the SubSaharan African countries in the dataset: Ethiopia, Malawi, Niger, Nigeria, Tanzania, and Uganda. First, we use an aridity index as proxy for agricultural potential. The aridity Index is defined as the ration between mean annual precipitation and mean annual potential evapo-transpiration so that a higher valued of the index identifies wetter areas<sup>6</sup> . This is a purely physical, exogenous indicator that reflects long-term conditions in a locality. We maintain this is superior for this use to alternatives that embed the profitability or value of agricultural production in a given area, as those incorporate contingent factors such as prices and terms of trade. In this application we value the fact that the aridity index be truly exogenous.

Second, we proxy market access, distance and agglomeration effects with variables that measure the Euclidean (‘crow -fly’) distance to cities of 20, 100 , 500 and 1 million inhabitants. We choose this measure due to a concern with the potential endogeneity of travel time measures—roads and travel infrastructure may be built in response to agricultural production or potential (Fafchamps and Shilpi, 2005; Deichmann, et al, 2008)). The Euclidean distance is independent of travel infrastructure, but provides a good measure of the spatial dispersion of households with regards to urban populations.

# **III. Describing income diversification in Sub-Saharan Africa**

_The diversification of income sources in rural Sub-Saharan Africa_ We look first at household participation<sup>7</sup> in and the share of income from rural income-generating activities (participation rates can be found in Table 2, while shares can be found in Table 3). First and foremost, the near totality of rural households in the countries of our sample are engaged in own account agriculture. This is true both in Africa (92 percent on average) and in other regions (85 percent), with some form of on farm activity, even at higher levels of GDP (Figure 1). While for some households the importance of this participation is relatively minor, since it includes consumption of a few animals or patio crop production, agriculture continues to play a fundamental role in the rural household economic portfolio. In this and the figures that follow, we have added a separate trend line for the African countries in the sample<sup>8</sup> .

> 6 CGIAR, 2014.

> 7 Participation is defined in the RIGA database as the household having a non-zero or non-missing value in the income variable of an activity.

> 8 In most of the figures that follow we have included an additional fitted line for Africa excluding Nigeria, which is an outlier for several of the indicators being plotted.

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