The Theoretical Framework and Methodology to Estimate the Farm Labour and Other Factor-Derived Demand and Output Supply Systems

This paper provides a conceptual framework for the estimation of the farm labour and other factorderived demand and output supply systems. In order to analyse the drivers of labour demand in agriculture and account for the impact of policies on those decisions, it is necessary to acknowledge the interaction between the different factor markets. For this purpose, we present a review of the theoretical background to primal and dual representations of production and some empirical literature that has made use of derived demand systems. The main focus of the empirical work is to study the effect of market distortions in one market, through inefficient pricing, on the demand for other inputs. Therefore, own-price and cross-price elasticities of demand become key variables in the analysis. The dual cost function is selected as the most appropriate approach, where input prices are assumed to be exogenous. A commonly employed specification – and one that is particularly convenient due to its flexible form – is the translog cost function. The analysis consists of estimating the system of costshare equations, in order to obtain the derived demand functions for inputs. Thus, the elasticities of factor substitution can be used to examine the complementarity/substitutability between inputs.