Testing the consistency and feasibility of the standard Malmquist-Luenberger index: Environmental productivity in world air emissions.

Over the last twenty years an increasing number of studies have relied on the standard definition of the Malmquist-Luenberger index proposed by Chung et al. (1997) [J. Environ. Manage., 51, 229-240], to assess environmental sensitive productivity change. While recent contributions have shown that it suffers from relevant drawbacks related to inconsistencies and infeasibilities, no one has studied systematically the performance of the original model, and to what extent the existing results are unreliable. We introduce the optimization techniques that implement the model by Aparicio et al. (2013) [Eur. J. Oper. Res., 229(3), 738-742] solving these problems, and using a country level database on air pollutants systematically compare the results obtained with both approaches. Over the 1995-2007 period environmental productivity stagnation prevails across developed and developing countries, and while increasing technical progress takes place in the later years, it is offset by declining efficiency. Results show also that inconsistencies and infeasibilities in the original model are increasing in the number of undesirable outputs included, reaching remarkable values that seriously question the reliability of results, and compromise any environmental policy recommendation based on them.