the supply of credit, hence **_ci*_** > 0) and takes the value of one if the household is constrained. The dependent variable, **_yi_** , is observed for households in each group where **_y0i_** is for unconstrained households and **_y1i_** is for constrained households. By definition **_y0i_** and **_y1i_** are never observed simultaneously for a given household _i_ . **_Xi_** is a vector of household characteristics that would influence both **_yi_** and **_ci*_** . **_Zi_** is a vector of characteristics that explain **_yi_** only and they are not expected to influence regime selection (being constrained or unconstrained). **_Wi_** is a vector of identifying instruments on the selection equation (1). The instruments do not have a direct impact on the dependent variable other than through selection in one or the other group. **_δ_** , **_θ_** , **_β_** , and **_γ_** are vectors of parameters to be estimated while **_ui_ ,** **_ε0i_** and **_ε1i_** are the error terms assumed to be jointly normally distributed.

As some unobserved characteristics that affect the probability of being credit constrained could also affect the outcome variable, the error terms of the selection and the outcome equation may be correlated. Neglect of this could bias the estimated parameters. To address this issue of endogenous switching, we estimate the parameters simultaneously using the Full Information Maximum Likelihood (FIML) method.<sup>3</sup> While previous studies estimate each equation separately (Carter, 1989; Feder et al., 1990; Carter and Olinto, 2003; Petrick, 2004; Guirkinger and Boucher, 2008), the FIML method estimates both selection and outcome equations simultaneously, generating consistent standard errors (Lokshin and Sajaia, 2004). Both Wooldridge (2010) and Greene (2008) characterize the FIML as generally the most efficient estimation strategy to estimate models with endogenous switching providing there are no specification errors.

# **3. Data and descriptive statistics**

# **3.1 Data**

Ways to increase agricultural productivity and diversify income sources are particularly relevant for Rwanda, the most densely populated African country, in light of the fact that subsistence agriculture still contributes 36 percent of GDP, employs 80 percent of the population, and accounts for 45 percent of exports (World Bank, 2011). Our empirical analysis is based on a large nationally representative survey conducted by the World Bank in early 2011.<sup>4</sup> Sampled enumeration areas (EAs) were drawn from a complete list of EAs provided by the National Institute of Statistics of Rwanda (NISR) and a three-stage stratified sampling strategy was followed: First, 100 sectors (4 in each of the country’s 25 districts) were randomly selected. Three EAs were then drawn from each sampled sector. Finally, a cluster of 12

> 3 We use the movestay STATA command that implements the maximum likelihood method to estimate the endogenous switching regression model (Lokshin and Sajaia, 2004). It allows to simultaneously fit binary and continuous parts to yield consistent standard errors.

> 4 The data is from the first round survey for the impact evaluation of the Government of Rwanda’s Land Tenure Regularization Program.The study population excludes areas where, at the time of data collection, the project had already started. As a result, Kigali Province, Kirehe district in Eastern Province and Rubavu district in Western Province as well as sectors (about 20% of the total) where program implementation had already been started by September 2010 were dropped to avoid potential contamination.

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