Production Structure, Factor Substitution, and Total Factor Productivity in the South African Agricultural Sector

The production structure of the South African agricultural sector is analyzed using duality theory in production and cost. An unrestricted translog cost function is estimated, and a number of model restrictions (homothetic, homogenous, unitary elasticity of substitution, Hick’s neutral technical change, and no technical change) are tested for, but none of them was found to be statistically significant. The Allen Elasticity of Substitution (AES) and the Morishima Elasticity of Substitution (MES) are calculated to analyze factor substitution, and found that the AES may give erroneous results in the case of number of factors exceeding two. The substitution of land is found to be easiest while that of fuel to be hardest. Furthermore, technical change is found to have a negative impact on agriculture, but there are increasing returns to scale in South African agriculture. However, technical change dominates over scale effect, and results in negative total factor productivity growth. When these results are combined with the finding that, it is easier to substitute machinery by labor than vice-versa, it appears that labor-intensive technologies may be useful for agriculture growth.