(3) where _i_ indexes household; ii ii ii represents various measures of poverty; ii ii _A_ denotes agricultural WW = ααAA + XX ββ+ HH γγ + εε productivity; _X_ is a vector of variables measuring other sources of household income including income from wages, income from forestry products, income from off-farm businesses, and income WW from other sources; is a vector of household characteristics, consisting of household size, landholding in hectares, age of household head, gender of household head, education of household head, area of residence of household (rural/urban; west/east/center), whether the household owns HH livestock, and whether the household cultivates forestry products; and is the stochastic error term. , and are parameters; is the parameter of interest—the effect of agricultural productivity on household welfare. εε αα ββ γγ αα Depending on the poverty indicator, the effect of agricultural expenditure on welfare is estimated using a logit estimator, ordinary least squares (OLS) estimator, a two-part estimator, or orderedprobit estimator. The household logit estimator is used when poverty is measured with a binary indicator (1 = poor; 0 otherwise); OLS is used when poverty is measured by per capita annual consumption expenditure and relative deprivation in terms of consumption expenditure; and the two-part estimator is used when it is measured using either poverty gap or poverty severity.<sup>8</sup> The first part of the two-part estimator estimates the probability of being poor using a logit estimator, while the second part estimates the extent of poverty conditional on being poor using the fractional logit estimator (Belotti and Manning, 2015).

Exploratory analyses are used to identify the constraints to increasing agricultural productivity and a simple household-level OLS specification to assess the determinants of agricultural productivity. The OLS model is specified as follows: (4) where ii _C_ is a vector of binary variables indicating whether a household used chemicals (organic ii ii ii ii ii ii ii ii YY = αα+ CC ββ+ HH γγ+ MM ρρ+ LL δδ+ SS θθ+ AA ττ+ II σσ+ εε fertilizers, manure, pesticides, or herbicides) in crop production; is a vector of household characteristics that affect crop production: household size, access to durable goods, gender of household head, age of household head, education of household head, household participation in HH farmers’ group, access to remittance, and household residence (urban/rural, west/east/center); _M_ is a vector of binary variables representing the utilization of mechanized inputs like tractors and irrigation in crop production; _L_ is a vector of labor variables (male, female, child hired and family labor), _S_ is a vector of variables indicating a household’s access to services including extension and credit; _A_ is vector of variables on plot allocation including the share of land allocated to tree crops and plantations; _I_ is a vector of variables representing a household’s engagement in other economic activities including livestock, fishing, and wage-earning jobs. are parameters to be estimated. is the stochastic error term, representing variables that the model could not control for. αα, ββ, γγ, ρρ, δδ, θθ, ττ a dd σσ εε

> 8 The two-part estimator is implemented using the _twopm_ command in stata (Belotti and Manning, 2015). _twopm_ has a variety of estimators that can be used for the first and second parts depending on the research interest. More importantly, marginal effects for the combined model can be easily recovered using the margins command.

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