This note shows that the Nerlovian profit indicator may be aggregated over firms into an industry measure of profit efficiency. The note also provides conditions under which the technical component of the indicator may also be aggregated.

The purpose of this article is to improve the statistical analysis of multiproduct-firm behavior. Specifically, we are interested in modeling and estimating multiproduct technology focusing on size and product-line variation. Thus we offer a new empirical technique that can be used to directly analyze issues such as subadditivity, expansion-path subadditivity, economies of scope, and economies of diversification. Although applied papers employ a wide variety of theoretical multiproduct cost concepts, previous work uses nonfrontier estimation techniques. We show how to introduce frontier approaches to multiproduct cost analysis that can be applied to any of these concepts and improve the statistical analysis. Specifically, we introduce an empirical test using frontier techniques that allows for direct measures of economies of diversification at the firm-specific level.

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.