we have computed the share of households who decided to invest in soil conservation practices in the second round of the panel. We observe that in 2009, 18 percent of farmers decided to combat land degradation and invest in one or more soil conservation practices such as physical structures (cross-slope barriers, terraces, and biological practices – mainly agro-forestry). In general, farmers invest in a set of soil conservation practices rather than in a single one; therefore, we use a combined option, instead of focusing on individual options such as agro-forestry, which is exercised only by 5% of the farmers in the sample.

# 4. **Empirical Strategy**

# **_4.1.Estimation of the IR with panel data_**

Our estimates at the household level are based on the functional form originally proposed by Binswanger, Deininger and Feder (1995), in line with more recent approaches (Barrett et al. 2010) but in the context of panel data: In (4) ��� represent the unit value of gross revenue from agriculture production of household � at time �= 1, 2 . ��� is farmers’ land endowment in each year, and ���� .is the square term to test for non-linearities in the purported relationship. ��� is a matrix of household and farm characteristics such as head’s age, education of the head, and gender of the head. To account for time-variant differences in land quality, we add some soil quality variables, as well as variables related to topography. We also control for the impact of non-farm activities by introducing the value of non-farm income. We draw on Reardon (1997) who found that in 23 field studies in Africa, the share (on average) of non-farm income in total income was twice as great in upper income tercile househoIds as in lower tercile households.

We use a linear approximation strategy over log-linear and log-log approaches for two main reasons. First, neither of those were found to provide a better fit with the data, and second, because the presence of outliers is not our major concern since the QR approach inherits its robustness property from median regression, and can produce good and reliable estimates even in the presence of extreme outliers.

We investigate the existence of an average land productivity (ALP)- farm size relationship by using different models. First, we run a pooled OLS regression and compare the results with a fixed-effect regression over the two periods of time (Table 2). We complement our analysis with a panel quantile regression model following Powel (2016) to test the robustness of the results, and to extend them to the entire distribution of farm productivity (Table 3).

The fixed-effects (FE) model allows us to control for time-invariant, unobserved idiosyncratic factors which may affect farmers’ ALP, such as know-how, ability and expertise in farming activities, and which are included in the α� term, whereas ��� represents the time-varying error term that is uncorrelated with the ALP outcome variable.

The time-invariant component may encompass any form of latent individual effects, or farmers’ non-ignorable heterogeneity and even unobserved farmers’ personality traits or cognitive and noncognitive abilities (Almlund et al., 2011; Heckman, 2011; Ravallion 2012). Considering that the unobserved characteristics do not change over time, any change in the dependent variable can be attributed to influences other than these fixed characteristics. Farmers’ intrinsic characteristics or risky attitude will determine their willingness to exercise different options, and embark on productivity enhancing activities. The whole of these idiosyncratic characteristics that we define as farmers’ abilities does not vary over time, once we control for a full set of predictors. According to this definition, the farmer is able to maximize the level of his ALP over time, given a set of initial endowments in terms of factors of production or household characteristics.

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