We update developments on modeling technology including unintended outputs and show how these can, at least to a large extent, be incorporated in a network model framework. Recently there have been efforts to specify more detailed models which include multiple functions to separately capture intended and unintended products. Yet another recent strand of the recent literature has also explicitly tried to include a material balance condition in the model. We see this general evolution as beginning with what might be called a black box technology, with inputs entering the box, and good and bad outputs exiting the box. The more sophisticated models can be thought of as filling in the black box with the more detailed processes involved with production, prevention and abatement, with production accompanied by undesirable byproducts subject to legal regulations and laws of nature. This can be modeled as a network within the black box.

Network models provide a general representation of inter-connected system dynamics. This ability to connect systems has led to a proliferation of network models for economic productivity analysis, primarily estimated non-parametrically using Data Envelopment Analysis (DEA). While network DEA models can be used to measure system performance, they lack a statistical framework for inference, due in part to the complex structure of network processes. We fill this gap by developing a general framework to infer the network structure in a Bayesian sense, in order to better understand the underlying relationships driving system performance. Our approach draws on recent advances in information science, machine learning and statistical inference from the physics of complex systems to estimate unobserved network linkages. To illustrate, we apply our framework to analyze the production of knowledge, via own and cross-disciplinary research, for a world-country panel of bibliometric data. We find significant interactions between related disciplinary research output, both in terms of quantity and quality. In the context of research productivity, our results on cross-disciplinary linkages could be used to better target research funding across disciplines and institutions. More generally, our framework for inferring the underlying network production technology could be applied to both public and private settings which entail spillovers, including intra- and inter-firm managerial decisions and public agency coordination. This framework also provides a systematic approach to model selection when the underlying network structure is unknown.

This paper provides a brief overview of methods to incorporate ecosystem service values into measures of agricultural total factor productivity (TFP), both in theory and in practice. This includes a review of the academic literature, a summary of related economic index theory, and a comparison of agency guidelines. We consider areas of consensus between the agencies and the research literature, as well as open debates surrounding the implementation of a standardized ecosystem accounting framework to integrate with existing TFP measures. This helps to bridge the gap between theoretical approaches to measurement and valuation in the research literature and their implementation in practice by national accounting agencies. Better connecting theory to practice also serves to highlight common challenges in the field, including questions of definition, scope, and scale for ecosystem services, as well as data collection and dissemination. We end with a summary of recommendations for moving forward.