suggestion by Zabel (1992) and include group means as additional determinants. Specifically, we estimate the augmented model: β α β α where shand share the means of sht and sht over time. Note that the mean effects are a decomposition of fixed household effects. A simulated maximum likelihood method is used to estimate both versions of the model.<sup>15</sup> Our estimation strategy follows the parametric approach suggested by Greene (2007), based on Verbeek (1990); Zabel (1992); and Verbeek and Nijman (1992), which we prefer to nonparametric approaches.<sup>16</sup> While there is an advantage to the nonparametric estimators, as they are robust to distributional misspecifications of the correlation between the unobserved effects and observed variables, from a practical perspective, the approach is less useful for policy-motivated research. As Greene (2007: E30-2) emphasizes, the parameters of the selection model are not the slopes of the index function, the implicit behavioral component of the model. Consequently, nonparametric models lack the more detailed assumptions about underlying functional form and parametric families are needed to interpret the conditional means and partial effects from the model, which are often key to policy discussions.

# <u>Model determinants</u>

Variables used in the selection and input demand equations of the empirical model are listed and described in Table 1; the associated summary statistics are given in Table 2. The determinants of the selection equation are chosen to account for differences in the sets of economic fertilizer-using technologies available to households in the sample. Included in the list are variables directly indicating the provision of market services by agents, specifically whether or not agents are available locally to sell fertilizer, and whether households have access to credit and extension services. The next determinants are measures of production and price risk: average rainfall (climate) and price variability.<sup>17</sup> These variables are included to represent obstacles to agents that might offer services locally and also to account for the hurdles that households face when agents are unwilling to provide risk-mitigating services.<sup>18</sup> The next set of variables is meant to capture the households’ capacity to compensate for services that agents do not provide. Three variables are included

> 15 LIMDEP 9 is used to estimate the model. See Greene (2007) for greater detail.

> 16 See, for example, Kyriazidou (1997), and Honore and Kyriazidou (2000).

> 17 The variables may also have non-contemporaneous reinforcing characteristics that work to build household resources. Alem et al. (2010) argue that ample rainfall seasons boost incomes, helping farmers resolve liquidity problems in subsequent seasons. Rosenzweig and Binswanger (1993) also draw the connection between positive climatic environments and wealth.

> 18 Spielman et al. (2010) point to some along the fertilizer supply chain that stand in the way of robust markets in Ethiopia, including the high cost of delivering small amounts of fertilizer to a large number of geographically dispersed smallholders with limited cash resources; they note that the 2-3 market window planting for rainfed crops in Ethiopia combined with variable year-to-year rainfall patterns generate high inter-year variability in the demand for fertilizer, increasing the risk to fertilizer dealers that purchased inventories will go unsold or sell at lower than expected prices.

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