# **IV. Modelling location and income diversification in LSMS-ISA countries**

# _Estimation approach_

As we have noted earlier, much of the literature on rural income diversification in developing countries has sought to explain how assets endowments and barriers to entry tend to push or pull different households and individuals into different activities. Location may also be an important factor in the determining households’ income diversification strategy decisions, but the literature is much more silent on this point mainly due to the lack of data that would allow spatially explicit analysis. The geo-referenced household data we work with, make efforts to start filling that gap possible.

In what follows our approach is similar to a meta-regression analysis in that (i) for each of the countries analyzed common metrics are used, (ii) explanatory variables for each country have been created in a uniform manner, and (iii) a standard regression model is employed in each case. This approach then minimizes the possibility that differences in results are driven by differences in the variables used or in the empirical approach, and facilitates our ability to compare results across countries.

Our modeling approach is to employ a multinomial logit model (separately for each country) to assess how location is associated with the likelihood that a household diversifies out of farming, controlling for other household characteristics. The choice of the multinomial logit is motivated by the fact that we have several unordered but mutually exclusive categories that we use to characterize household income strategies: A household can either be diversified, or fall within one of six diversification categories<sup>13</sup> . In the multinomial logit, _k-1_ models are estimated for any outcome consisting of _k_ unordered categories. Parameters estimates are then interpreted with reference to the excluded base category (farm specialization in our case).

For a unit change in the regressor, the logit of the model outcome relative to the reference group is expected to change by its parameter estimate, holding other variables constant (UCLA, 2014). As we use farm specialization as the base category the coefficients on the main variables of interest can be immediately interpreted in terms of association with higher or lower likelihood that a household diversifies or specializes in off-farm activities, compared to being a farm specializer.

In a multinomial logit, given an unordered categorical outcome variable _y_ with _k_ outcomes, and a set of regressors _X_ , one estimates a set of _β_ coefficients for each outcome _i_ from 1 to _k-1_ corresponding to: Pr(yy= ii) = ee<sup>XXββ(ii)</sup> ee<sup>XXββ(1)</sup> + ee<sup>XXββ(2)</sup> + ⋯+ ee<sup>XXββ(kk)</sup> The model can be solved by Maximum Likelihood methods by setting _β(k)_ equal to 0, and measuring the other coefficients in terms of changes relative to the _k_ reference category (Long and Freese, 2006).

Previous studies have discussed the role of other key household characteristics, namely different forms of capital (human, natural, physical, social) and those findings are pretty consistent and robust across studies. One concern with that evidence is however the extent to which different levels and

> 13 For the econometric estimation we reduce the specialization categories to five, as we collapse ‘transfers’ and ‘other income’ into one category.

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