Permutation tests on returns to scale and common production frontiers in nonparametric models

Permutation techniques, where one recompute the test statistic over permutations of data, have a long history in statistics and have become increasingly useful as the availability of computational power has increased. Until now, no permutation tests for examining returns to scale assumptions, nor for test of common production possibility sets, when analysing productivity have been available. We develop three novel tests based on permutations of the observations. The first is a test for constant returns to scale. The other two are, respectively, tests for frontier differences and for whether the production possibility sets are nested. All tests are based on data envelopment analysis (DEA) estimates of efficiencies and are easily implementable. We show that our suggested permutations of the observations satisfy the necessary randomisation assumptions, and hereby that the sizes of the proposed tests are controlled. The advantages of permutation tests are that they are reliable even for relatively small samples and their size can generally be controlled upwards. We further add a lower bound showing that the proposed tests are very close to being exact. Finally, we show that our tests are consistent and illustrate the rate of convergence in simulation studies

Exact tests on returns to scale and comparisons of production frontiers in nonparametric models

When benchmarking production units by non-parametric methods like data envelopment analysis (DEA), an assumption has to be made about the returns to scale of the underlying technology. Moreover, it is often also relevant to compare the frontiers across samples of producers. Until now, no exact tests for examining returns to scale assumptions in DEA, or for test of equality of frontiers, have been available. The few existing tests are based on asymptotic theory relying on large sample sizes, whereas situations with relatively small samples are often encountered in practical applications. In this paper we propose three novel tests based on permutations. The tests are easily implementable from the algorithms provided, and give exact significance probabilities as they are not based on asymptotic properties. The first of the proposed tests is a test for the hypothesis of constant returns to scale in DEA. The others are tests for general frontier differences and whether the production possibility sets are, in fact, nested. The theoretical advantages of permutation tests are that they are appropriate for small samples and have the correct size. Simulation studies show that the proposed tests do, indeed, have the correct size and furthermore higher power than the existing alternative tests based on asymptotic theory

Testing productivity change, frontier shift, and efficiency change

Inference about productivity change over time based on data envelopment (DEA) has focused primarily on the Malmquist index and is based on asymptotic properties of the index. In this paper we propose a novel set of significance tests for DEA based productivity change measures based on permutations and accounting for the inherent correlations when panel data are observed. The tests are easily implementable and give exact significance probabilities as they are not based on asymptotic properties. Tests are formulated both for the geometric means of the Malmquist index, and also of its components, i.e. the frontier shift index and the efficiency change index, which together enable analysis of not only the presence of differences, but also gives an indication of whether the productivity change is due to shifts in the frontiers and/or changes in the efficiency distributions. Simulation results show the power of, and suggest how to interpret the results of, the proposed tests. Finally, the tests are illustrated using a data set from the literature

Dietary inclusion of methanotrophic microbial cell-derived protein in the early postweaning period sustains growth performance and intestinal health of weaner piglets

The global demand for sustainably produced protein feeds for animal production is increasing. Methanotrophic bacteria grow on methane and convert it into microbial cell protein (MCP) that has been shown to have high nutritive value for growing pigs. The present aimed to investigate how increasing amounts of MCP in diets fed during the first 15 days after weaning affect the growth performance of piglets from weaning until day 43 postweaning. Furthermore, the effect of MCP on intestinal morphology and histopathology was assessed on day 15 after weaning. During seven consecutive weeks, approximately 480 piglets were recruited for the experiment per batch. The piglets were divided into four groups and housed in eight double pens with 60 piglets per pen. The piglets were fed one of four experimental diets with 0, 3, 6, or 10% of MCP included at the expense of fishmeal and subsequently potato protein for the first 15 days postweaning. Thereafter, all pigs were fed commercial weaner diets in two phases (days 16–30 and days 31–43) until day 43 postweaning. All diets were without medicinal zinc. Feed intake and growth were registered on double pen level during all three phases. On day 15 after weaning, 10 piglets per treatment were randomly selected, autopsied, and sampled for intestinal morphology and histopathology. Daily gain during the first 15 days postweaning tended (P = 0.09) to be affected by the inclusion of MCP in the weaning diet being lowest in the group fed 10% MCP. Treatment did not affect daily feed intake; however, Feed Conversion Ratio (FCR) was significantly affected (P = 0.003) showing the highest FCR in piglets fed 10% MCP. Growth performance was not affected by the experimental treatment during the following phases. In the small intestine, villous height tended (P = 0.09) to show a quadratic response to level of MCP in the diet with the longest villi observed after feeding 6% MCP. Dietary treatment did not affect crypt depth. The villous height to crypt depth (VC) ratio showed a quadratic response to increased dietary inclusion of MCP (P = 0.02) with piglets fed 6% MCP having the highest VC ratio. In conclusion, this study demonstrated that MCP could constitute 6% of diets as-fed (22% of total CP), at the expense of fishmeal and potato protein, for newly weaned piglets without negative effects on growth rates and FCR. The inclusion of MCP in diets for newly weaned piglets could be part of improving the sustainability of pig production

Evaluation of the methane mitigating potential of hemp using solid phase extraction, untargeted metabolomics and in vitro rumen fermentation

Methane is a highly potent greenhouse gas, which contributes to climate change. Therefore there is an increasing need to develop additives to cow diets with methane mitigating potential