the relationships observed were linear or, at least, a linear approximation to a monotonic relationship. It appears not only that the relationship is pronouncedly non-monotonic, but also that it is drastically different across farms, depending on their position in the distribution of productivity. The policy implications of these findings are also significant. For farms in the lowest TFP ranks, this result in fact implies that some land expansion may be beneficial, but lack of management ability soon creates diseconomies of scale so that better management and technology are needed more than land increases. Moreover, this implication holds also for farms that are less dynamic in terms of their productivity growth. On the contrary, for farms that already have a patrimony of technological know-how and good management, and thus are in the highest deciles of the distribution of productivity or productivity increase, land expansion, and the associated economies of scale, may be the only policy that can make their productivity grow.

# **Conclusions**

The inverse relationship (IR) between average land productivity (ALP) and land size has been the object of a voluminous literature, raising both objections and explanations. In this study, after a brief review of some of the main arguments, we have presented evidence from two rounds of data from Ethiopia that offers a new and more comprehensive explanation for the relationship. The survey data used are from detailed household interviews and contain accurate georeferenced information on farmers’ location, distance from the markets, distance from the main road, and land quality. In order to estimate the ALP–farm size relationship and to test the IR hypothesis, we have used a specification entirely relying on exogenous variables and estimation procedures according to the quantile regression model.

Our results suggest that farm size displays a robust impact on ALP, but this impact is nonlinear and switches shape across farms according with their performance. For low performers the impact is first positive and then negative, while the opposite is true for high performers As already noted, although in a different context by Evenson and Mwabu (2001), this may be due to individual management factors, so that in the two areas of the ALP distribution, different complementary and substitute relations exist between land sizes and unobserved human capital variables, such as farmers’ abilities, skills and experience. In turn, these results are consistent with a revised version of Savastano and Scandizzo’s (2009) option model, where management quality is supposed to be positively correlated with farm size.

Interpreted across the range of farm sizes, our results also point to the possible existence of an S- shaped relationship between ALP and acreage at least for a range of performances, with ALP first increasing then decreasing, then increasing again. This DID relationship implies a turning point for the lower quantiles of the ALP residual distribution at which a positive (DR) relationship becomes negative (IR) and one for the upper quantiles where IR becomes positive again (DR). Both turning points are for small to medium farm sizes, but the ones of the lower quantiles tend to be smaller than those for the upper quantiles. Thus, while there is some significant negative relationship between productivity and operating size for low performers over a relevant range of farm sizes, higher performers tend to display IR only over a range from small to medium farm sizes. The interpretation of these results is thus that low productivity farms may exploit to some extent economies of scale for a limited range of farm size increases, but need to become more productive by exercising the right options to invest and not to incur into diseconomies once a maximum farm size is reached. Farmers in the higher quantiles of the productivity distribution, on the other hand, can exploit the economies of scale related to farm size only after they cross a minimum threshold of farm size. Furthermore, a similar relationship holds for productivity growth, in the sense that more productive and more dynamic farms are those that can exploit more fully farm expansion as a source of scale economies and that the IR relationship holds only if they are below a minimum economic level of farm size.

One could question whether the DID relationship could hold in a new external context characterized by new trends such as emergent or mega farm operators, and large-scale land acquisitions (Collier, 2009; Collier and Dercon, 2014; Sitko and Jayne, 2014). We argue that even though our nationally 13