captured by the OLS technique, and depending on conditional expectations. Using quantile regression, S-S found a U-shape and an inverted U-shape relation with sign switches at different points of the distribution of farms’ productivity in all the countries.

In this paper, we corroborate the above S-S results, using two rounds of the Ethiopian Rural Household Survey (ERHS),<sup>1</sup> a unique multi-purpose longitudinal household data set representative of the rural population of the country. The contribution of our paper is twofold. First, we test the productivity– farm size relationship, taking into account farmers’ heterogeneity; second, we consider the possible interaction between productivity and management quality and efficiency.

By considering the entire distribution of agriculture productivity, we found sign switches across the distribution pointing to the existence of a “Direct-Inverse-Direct” (DID) relationship. Less productive farmers exhibit an inverted U-shape relationship between land productivity and farm size, while the more productive farmers show a U-shape relationship that reverses the relationship. In both cases the relationship points towards the existence of a threshold value of farm size, which is, however a minimum for the less productive farmers and a maximum for the more productive ones. The results show that the inverse relationship holds for middle size farms. To the left of the threshold, for very small farmers, the relationship between productivity and farm size is positive, and farmers can invest in the extensive margins through land expansion as a safety-first strategy to achieve a minimum level of production to guarantee subsistence. For the range of middle farm size, the relationship is negative. Middle farmers tend to invest in new agriculture technologies and income diversification to increase their productivity. They may improve their position by increasing their intensive margins, namely getting more productivity from land already under cultivation. To the right of the threshold the relationship is direct (positive) again.

Our findings indicate that, while IR may be important for certain ranges of farm efficiency and size, it is by no means a ubiquitous characteristic of agriculture. Whether the relationship between productivity and size is positive or negative in fact appears to depend crucially on other factors, including agroecological conditions and non-farm opportunities.

The plan of the rest of the paper is as follows. First, we provide some background and motivation through a brief survey and discussion of the literature. Second, we describe the conceptual framework and the estimation strategy. We turn next to a discussion of the model used, the data employed, the estimation techniques and the discussion of the results. The paper concludes with policy recommendations.

# **1. Background and Motivation**

The fact that land productivity is negatively related to the size of the land operated (both owned and rented) appears historically established by a variety of studies starting in the late 1970s (e.g. Berry and Cline, 1979, Kutcher and Scandizzo, 1981, Binswanger et al., 1995).

The literature has emphasized different explanations for this “empirical regularity”. The early studies focused on factor market imperfections in land and other markets such as credit and modern inputs (Scandizzo and Kutcher, 1981; Eswaran and Kotwal, 1985; 1986; Barrett, 1996; Benjamin and Brandt 2002; Berry and Cline 1979; Feder 1985; Binswanger et al. 1995, Ali and Deininger, 2014). More recently the literature has focused on statistical issues and measurement errors in land and agriculture output, omission of soil quality measurements that are inversely correlated with farm or plot size but positively associated with yields (Lamb, 2003; Barrett et al., 2010; Goldstein and Udry, 1999, De Groote and Traorè, 2005). The availability of sophisticated remote sensing and georeferenced data has increased the statistical debate of the IR. Carletto et al. (2013 and 2015) show that the IR persists even after controlling for more objective GPS-based land area measures. Deininger et al. (2012) and Kilic et al. (2017) showed that the inverse relationship could be driven by errors in self-reported survey data on crop production. Desiere and Jolliffe

> 1 The project was conducted by 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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