Evolving the Latent Variable Model for the Reduction of Undesirable Outputs as an Optimal Environmental Data Envelopment Technology

Abstract

This dissertation tests several nonparametric DEA models for their ability to accurately decompose CO2 Emissions change using a Malmquist decomposition framework. The Latent Variable Model exhibited the best results against previous studies from the literature. The new Latent Variable radial input-oriented technology, introduced here as an environmental DEA, simultaneously reduces inputs and undesirable outputs by employing Input Disposability rather than using the Weak Output Disposability assumptions of previous studies. Empirical testing shows that the new Latent Variable Model is closely associated with the Slacks Based Model. Hence, a suitable proof was constructed to show that the Latent Variable radial model is, in fact, equivalent to its additive Slacks Based counterpart in terms of Pareto-Koopmans„ Efficiency. This eliminates the need for a two phase DEA method which is widely used to determine optimal efficiency. That is, the single step Latent Variable radial model independently eliminates slacks and congestion within a production oriented DEA problem and returns an optimal solution. Further to this discovery, the Latent Variable technology can be extended to simultaneously reduce both inputs or outputs depending on their „desirability‟ within a system space as a whole. Burning fossil fuels, for example, is „undesirable‟ within the context of the environment, but is conventionally considered as a „desirable‟ input. Under the General LV model, hydrocarbon use can be reduced as an undesirable input while other green inputs can be simultaneously increased as substitutes. Similarly, the Generalized Latent Variable Model (GLVM) can greatly enhance the use of DEA: It can be applied to any causal system of inputs and outputs using appropriate Weak Disposability as its key attribute, thus optimizing efficiency comparisons. The General LVM employs a partitioning scheme of seven mutually exclusive sets based on their interaction within a system space. The purpose of such partitions is to classify inputs and outputs in terms of their impact on a system: either positive, negative, neutral or ambient. Previous analysis has been limited to only a single target efficiency partition such as a set of minimized inputs or maximized outputs, and generally these exclude externalities. In the GLVM, a Latent Variable is placed on each partition to track the efficiency impact of each set upon the system as a whole. Thus the Total Factor Productivity and its interdependencies within the system space are determined by a series of seven Latent Variable efficiency ratings, not just one as in traditional DEA. Thus the GLVM implies multi-criteria benchmarking while completely characterizing the internal efficiencies of each DMU relative to its peers. Thus, the General Latent Variable Model not only offers a new level of inclusiveness for management and production studies, but it can potentially serve as a basis for quantitative efficiency analysis within any interdependent system of causally related variables in the social or environmental sciences.