farms. Thus, small and large farm behavior tends to diverge, since farms in the lower deciles of the land productivity distribution experience IR for a smaller range of farm sizes than farmers of the higher deciles. The results are consistent across countries, and in the pooled analysis.

The main conclusions of this analysis, which are corroborated by the results in the present paper, can be summarized as follows: (1) ALP will display respectively a negative (the IR) or a positive correlation with farm operating size, depending on whether the threshold effect (the higher incentive for larger farms to hold undeveloped land as an option) prevails or is overwhelmed by the management effect (the tendency of ALP to increase with farm size since larger farms attract better managers).

(2) Depending on the functional form of their relationship, the two tendencies may equal each other, once a threshold of farm size is reached, after which the net effect on ALP will be reversed.

(3) Both tendencies and the level of the threshold will depend on the management quality and thus can be expected to vary across farmers, depending on the distribution of management quality and the extent to which the market for managers succeeds in allocating them to larger farms.

These conclusions support the idea that the IR relationship may indeed be present in many farming systems, but we should expect it to be neither ubiquitous nor monotonic. In particular, if farmers face dynamic uncertainty by holding a waiting option for land development and unobservable management quality is positively correlated with farm size, both a reverse and a direct effect of operating size on average productivity may be present at any one time. This in turn implies that the net impact of increasing operating size on land productivity will depend on whether a threshold is crossed where the two effects exactly balance each other.

On the technical estimation side, we further argue that OLS will generally provide an estimate of the relationship based on mean response if factor productivity is distributed normally, with a constant variance. In other words, OLS will allow us to estimate a response coefficient that will quantify the average response of the dependent variable (e.g. land productivity) to farm size increases. If the distribution of the response around the mean, estimated according with OLS, is not satisfactorily described by a single variance, however, quantile regression (Koenker and Basset, 1978) promises a more robust and appropriate estimate, especially if variance is systematically related to the increase in the response variable (heteroscedasticity). We also conjecture that the relationship between productivity and alternative measures of size (land available, land under cultivation etc.) may be considerably different for farmers who, for various reasons that cannot be captured by the econometric model, have to operate at lower productivity levels, with respect to farmers that operate at higher productivity levels.

# **2. Conceptual Framework**

Consider the relationship between land productivity and farm size in the stylized form. For simplicity, we omit the time period: <u>��</u> = β� + β��� + γ�� + ε� (1) �� where y� is some measure of production for the ith farm, �� is a correspondent measure of farm size (e.g. operated area), �� a set of exogenous variables, and ε� a random disturbance. It is important to underline the fact that equation (1) is not a production function, but the result of farmers’ choices, on the basis, inter 5