Estimación de una función de producción de una plantación cañera en Colombia

Sugarcane is one of the most important productive crops in the world, with a presence in more than one hundred tropical and subtropical countries. For the year 2018, more than 53% of the world’s production of sugarcane was generated by countries in the Americas. Although Colombia is not among the top producing and exporting countries, it is important to highlight its high productivity per hectare. Given this singularity and the regional importance that this crop has in southwestern Colombia, this work aims to estimate a Cobb-Douglas production function for a plantation, divided into sub-plantations called suertes, located in the Tierradura village, Miranda Municipality, Department of Cauca, Colombia. To do this, we collected and classified historical information for each of the sub-plantations for the period 2003-2019. To conduct the estimation and considering the inaccuracy and bias problems of panel data models estimated by instrumental variables (IV) or by the generalized method of moments (GMM) when the number of observations is small, we proceeded to carry out the estimation using Least Squares with Corrected Dichotomous Variables. This is done using Stata's xtlsdv command. This command allows the use of 3 possible options to correct the inconsistency: Anderson-Hsiao, Arellano-Bond, and Blundell-Bond, being the Arellano-Bond the most efficient option since it is supported by a greater number of internal instruments. The estimated results obtained by the Arellano-Bond method indicate, first, that the process can be described by a constant returns to scale production function and, second, that the number of hectares of cultivated land and total wages have the expected signs (0.778 and 0.067) and are statistically significant at 1% and 10%, respectively. Particularly, this means that if either the area of cultivated land or total wages is increased by 1%, sugarcane production would increase by 0.778% or 0.067%, correspondingly.