(2017) compared self-reported production and crop-cuts estimates, and found that the IR is stronger when based on self-reported production, but disappears when based on crop-cut estimates. Finally, Bevis and Barrett (2017) identified the “edge of the plot” effect, namely that productivity may be greater along the edge of small plots where labor is concentrated. The standard explanation of the IR is the presence of omitted variables and unobserved heterogeneity: omission of soil quality measurements that are inversely correlated with farm or plot size but positively associated with yields (Carter 1984; Bhalla and Roy 1988; Walker and Ryan, 1990; Benjamin 1995; Lamb 2003; Assunção and Braido, 2007; Assunção and Ghatak, 2007; Benjamin, 1995).

The IR finding, however robust across many studies, seems at the same time puzzling, for several reasons. First, it is not limited to small versus large farms, but in most studies, there is a smooth tendency for land productivity to decline with farm size. This result seems to be in contrast to the equalization of factor prices predicted by market equilibrium theory and not simply explained by lower reservation wages for family farms, because land productivity appears to decline within all ranges of family as well as nonfamily farms. In this respect, Feder’s (1985) alternative explanation appeals to a more general transaction effect, reminiscent of Coase’s theory of the firm. According to this explanation, smaller farms are based on more intense use of family labor, because of its higher efficiency and motivation than hired labor, and the fact that supply of working capital is directly related to farm size. Srinivasan (1972) explains the inverse relationship by yield risk, by defining utility over income, and imposing restrictions on the coefficients of risk aversion and on how risk enters production, under constant returns. Hazell and Scandizzo (1974) provide a rationale for producers to reduce planned production in response to the negative correlation between supply and prices, and Barrett (1996) shows that IR can emerge from price risk if farmers are net buyers of the crop produced, since in this case, risk aversion implies labor overemployment to protect consumption.

As Savastano and Scandizzo (2009) have shown, a relationship between productivity and operated area may arise, because of the risk associated to the investment decision such as, for example, to increase one’s farmland. Under dynamic uncertainty, in fact, the amount of land operated by a farmer will depend on the timing of the exercise of the option to invest in land development. With decreasing returns to scale, this will imply a non-monotonic relationship between revenue per ha and operated land. If land is available on the market in fixed quantities (i.e. supply of plots for rents or sale, or entire farms of discrete size), and/or investment is lumpy, small farms will exhibit lower revenue thresholds for investment, and thus lower revenues per unit of land than larger farms. This implies, in particular, that the relationship between productivity and size may exhibit turning points, as farmers switch from one type of investment to another (e.g. from land improvements to irrigation) as their operating land increases as a result of previous investment decisions.

Most recently, using data from five Sub-Saharan African countries, Scandizzo and Savastano (2017) found a nonlinear relationship between farm size and land productivity, and signs switches across farm size groups. The analysis overcomes the statistical and measurement biases by testing the IR with the LSMS-ISA, nationally representative geo-referenced surveys of Malawi, Niger, Nigeria, Tanzania and Uganda. The estimation approach used also controls for many exogenous common and comparative geo-spatial measures of land quality, infrastructure and access to markets, climate conditions, soil conditions and topography.

Using quantile regression on a cross sectional framework, the results showed that average land productivity (ALP) exhibits an inverted U-shaped relation for less productive farmers, with ALP first rising and then falling after a threshold farm size. ALP shows the opposite pattern of a U-shaped relationship in the upper tail of the productivity distribution, first decreasing and then increasing after reaching a lower threshold. Farms in the lower tail of the ALP distribution thus experienced IR only once they have reached a critical size after which only by moving to a higher ALP class can they avoid the IR relationship from diseconomies of scale. Vice versa, more productive farmers experience IR only if they are below a critical size, which, in general, tends to be larger (and sometime much larger) than the critical size of the lower end 4