Estimating input-mix efficiency in a parametric framework: application to state-level agricultural data for the United States

This paper contributes to the productivity literature by demonstrating novel econometric methods to estimate input-mix efficiency (IME) in a parametric framework. Input-mix efficiency is defined as the potential improvement in productivity with change in input mix. Any change in input-mix (e.g., land to labou r ratio) will result in change in productivity. The advantage of this approach is that it does not require data on input prices to estimate the mix efficiency levels. A nonlinear input-aggregator function (e.g., Constant Elasticity of Substitution) is used to derive an expression for input-mix efficiency. Bayesian stochastic frontier is estimated for obtaining mix efficiency using US state-level agricultural data for the period 1960–2004. Significant variation in input-mix efficiency is noted across the states and regions, attributable to diverse topographic and geographic conditions. Furthermore, comparisons of allocative and mix efficiencies provide insightful policy implications. The production incentives such as taxes and subsidies could help farmers in adjusting their input mix in response to changes in input prices, which can affect the US agricultural productivity significantly. The proposed methodology can be extended by i) using flexible functional forms; ii) introducing various time- and region-varying input aggregators; and iii) defining more sophisticated weights for input aggregators.