Abstract
This paper models the firm’s production process as a system of simultaneous technologies for desirable and undesirable outputs. Desirable outputs are produced by transforming inputs via the conventional transformation function, whereas (consistent with the material balance condition) undesirable outputs are by-produced via the so-called “residual generation technology”. By separating the production of undesirable outputs from that of desirable outputs, not only do we ensure that undesirable outputs are not modeled as inputs and thus satisfy costly disposability, but we are also able to differentiate between the traditional (desirable-output-oriented) technical productivity and the undesirable-output-oriented environmental, or so-called “green”, productivity. To measure the latter, we derive a Solow-type Divisia environmental productivity index which, unlike conventional productivity indices, allows crediting the ceteris paribus reduction in undesirable outputs. Our index also provides a meaningful way to decompose environmental productivity into environmental technological and efficiency changes.
Highlights
The by-production of undesirable, or so-called “bad”, outputs is an inherent attribute of many production processes
We follow a different path to modeling the production process with undesirable outputs in the spirit of Fernández et al [11,12], Forsund [13] and Murty et al [7]
Desirable outputs are produced by transforming inputs via the conventional transformation function satisfying all standard assumptions
Summary
The by-production of undesirable, or so-called “bad”, outputs is an inherent attribute of many production processes. When modeling the production technology via a (single) directional distance function (e.g., [6]), the inefficiency is defined over the entire vector of outputs, both desirable and undesirable. Modeling undesirable outputs via the standard directional functions precludes researchers from disentangling the technical inefficiency/productivity, conventionally oriented along desirable outputs, from the environmental, or so-called “green”, inefficiency/productivity, oriented along undesirable outputs.. We model the firm’s production process as a system of separate simultaneous production technologies for desirable and undesirable outputs In this setup, desirable outputs are produced by transforming inputs via the conventional transformation function satisfying all standard assumptions. Färe and Grosskopf [10] have recently proposed the slacks-based directional distance function which allows inefficiency to be input- and output-specific The estimation of such slacks-based inefficiencies is feasible under the deterministic treatment of the production technology only.
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