On estimating optimal α-returns to scale

From a theoretical point of view, α $ \alpha $ -returns to scale is a relevant alternative to traditional DEA models for estimating production technologies under global returns to scale assumptions such as strictly increasing or strictly decreasing returns to scale. However, from a methodological and empirical point of view, a remaining question is the estimation of α $ \alpha $ . This contribution proposes an effective methodology to estimate an optimal value of α $ \alpha $ based upon a goodness-of-fit strategy. A global method using a grid search is presented first. Second, for generalised FDH technologies, a minimum extrapolation principle is developed to estimate directly the optimal α $ \alpha $ -returns from a linear program. An illustration on 63 US industries over the period 1987–2012 shows the relevancy of our approach.