Abstract
The Malmquist index is widely used in empirical studies of productivity change over time. The index is based on estimates of the frontier obtained from the convex envelopment of the data as in DEA. The statistical properties of the Malmquist index and its components, i.e. the frontier shift and the efficiency change, have until recently only been subject to a limited number of studies. The asymptotic properties of the geometric mean of the individual Malmquist indexes have been studied in the literature. Permutation tests for performing statistical inference in finite samples have recently been proposed and are easily performed. In the present paper we illustrate the permutation methods by an analysis of data comprising organic and conventional dairy farms in Denmark from 2011–2015. Further, differences between the frontiers of the production possibility sets for two separate samples are studied, specifically those of the organic and the conventional producers. We suggest to use jackknife methods when estimating the differences to ensure that these are not affected by the well-known bias originating from estimation of the frontier. In summary, the paper offers an illustration of how to analyse productivity data, in particular a comparison of two independent groups, and furthermore an analysis of how the separate groups evolve over time is provided.
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Notes
- 1.
It is here worth noting that these angles are not scale invariant. Therefore, one should ensure that all input (output) variables are measured in similar metrics, like, e.g. in the present case where all inputs are costs and the outputs are revenues.
- 2.
Note that since there are only two outputs, the angles are complementary and therefore the test statistics and p values for the two output angles are identical.
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Asmild, M., Kronborg, D., Rsønn-Nielsen, A. (2021). Applying Statistical Methods to Compare Frontiers: Are Organic Dairy Farms Better Than the Conventional?. In: Parmeter, C.F., Sickles, R.C. (eds) Advances in Efficiency and Productivity Analysis. NAPW 2018. Springer Proceedings in Business and Economics. Springer, Cham. https://doi.org/10.1007/978-3-030-47106-4_14
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