The solution to Equation (3) is found by rewriting the expression as a linear programming problem over the entire sample (see Chamberlain, 1994) and solving for the values of the parameters. Both the squared-error and absolute-error loss functions are symmetric, as the sign of the prediction error is not relevant. While OLS can be inefficient if the errors are highly non-normal, quantile regression is more robust to non-normal errors and outliers. QR also provides a richer characterization of the data, gives information on heterogeneity in the effect of land on the productivity, and allows to consider the impact of a covariate on the entire distribution of y , not merely its conditional mean. In particular, for each quantile, it can be shown whether the effect of farm size on productivity is positive or negative, and how large this effect is compared to other quantiles.

# **3. Data Source and Descriptive Statistics**

We use the last two rounds of the Ethiopian Rural Household Survey (ERHS),<sup>2</sup> a unique multipurpose longitudinal survey conducted since 1989, which covers four of the nine administrative regions in Ethiopia, where the largest proportion of the country’s farmers are located, and includes 15 woredas (districts) stratified over the three major agricultural systems found in five agro-ecological zones. Although not nationally representative, the sample is broadly representative for the main farming systems in the country.

Table 1 shows the main characteristics of farmers in both rounds. With 1.4 ha of land per household and 6 family members, small, resource-poor, subsistence farmers dominate the rural sector in Ethiopia. Given the large number of plots cultivated by a farmer (4.7 and 5.1 plots in 2004 and 2009 respectively), fragmentation and the lack of improved technologies are a major challenge for spurring agriculture productivity and to allowing farmers to meet their subsistence needs. While farm size is on average low and has changed very little between the two rounds (1.4 to 1.5 ha), since its distribution is highly skewed, we complement our descriptive analysis with the concept of midpoint farm size introduced by Hoppe et al. (2013). The statistic is defined as the size at which half of all cropland is on farms with more cropland than the midpoint, and half is on farms with less. It is a more informative measure of land consolidation than either a simple median (in which half of all farms are either larger or smaller) or the simple mean (which is average land per farm). We found that the midpoint farm size in Ethiopia is 1.6 ha in 2004, and 2.15 ha in 2009, 1/2 ha more than the value of average farm size, thereby indicating little variation given the presence of a very large number of very small farms and the high degree of fragmentation.

Only one-third of the farmers employ hired labor, and with an average of 6 members per household, they use family members to farm land. Though young (50 years on average), household heads have received little education, 1.6 years of school on average, and so did family members who obtained a maximum of 4.7 years of education.

Farmers rely heavily on agriculture, which accounts for 78% of total income. It is worth noting, however, that the share of income from agriculture has decreased of 9% from 2004 to 2009, while the opposite has occurred for wage and other income sources thereby suggesting a shift from owner-operated farming to wage labor, perhaps also as a consequence of the high food prices of 2008.

Agriculture productivity has increase over time from 446 to 549 US$/ha with an average of both periods of 497 US$/ha. We recognize the importance of mean effect, but one of the assumption of the OLS regression is that the error term – and the dependent variable – is normally distributed. To investigate whether this assumption is satisfied, we display in Figure 1 the kernel density estimates for gross agriculture income per hectare, separately by agriculture productivity below and above the median and along the whole distribution.

> 2 The ERHS represents a collaborative effort of the Department of Economics at Addis Ababa University, the Centre for the Study of African Economies (CSAE), the University of Oxford and the International Food Policy Research Institute (IFPRI).

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