{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,26]],"date-time":"2026-01-26T00:32:40Z","timestamp":1769387560778,"version":"3.49.0"},"reference-count":76,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,11]],"date-time":"2020-12-11T00:00:00Z","timestamp":1607644800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010682","name":"H2020 Society","doi-asserted-by":"publisher","award":["N\u00b0 824091"],"award-info":[{"award-number":["N\u00b0 824091"]}],"id":[{"id":"10.13039\/100010682","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e22121401","type":"journal-article","created":{"date-parts":[[2020,12,13]],"date-time":"2020-12-13T20:56:57Z","timestamp":1607893017000},"page":"1401","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Reconstructing Nonparametric Productivity Networks"],"prefix":"10.3390","volume":"22","author":[{"given":"Moriah B.","family":"Bostian","sequence":"first","affiliation":[{"name":"Department of Economics, Lewis and Clark College, Portland, OR 97219, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4825-0071","authenticated-orcid":false,"given":"Cinzia","family":"Daraio","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering A. Ruberti (DIAG), Sapienza University of Rome, 00185 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rolf","family":"F\u00e4re","sequence":"additional","affiliation":[{"name":"Department of Applied Economics, Oregon State University, Corvallis, OR 97331, USA"},{"name":"Department of Economics, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6939-2709","authenticated-orcid":false,"given":"Shawna","family":"Grosskopf","sequence":"additional","affiliation":[{"name":"Department of Economics, Oregon State University, Corvallis, OR 97331, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria Grazia","family":"Izzo","sequence":"additional","affiliation":[{"name":"Department of Computer, Control and Management Engineering A. Ruberti (DIAG), Sapienza University of Rome, 00185 Rome, Italy"},{"name":"Center for Life Nano Science, Fondazione Istituto Italiano di Tecnologia (IIT), 16163 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luca","family":"Leuzzi","sequence":"additional","affiliation":[{"name":"Soft and Living Matter Lab, Institute of Nanotechnology, 00161 Rome, Italy"},{"name":"Department of Physics, Sapienza University of Rome, 00185 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2762-9533","authenticated-orcid":false,"given":"Giancarlo","family":"Ruocco","sequence":"additional","affiliation":[{"name":"Center for Life Nano Science, Fondazione Istituto Italiano di Tecnologia (IIT), 16163 Rome, Italy"},{"name":"Department of Physics, Sapienza University of Rome, 00185 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William L.","family":"Weber","sequence":"additional","affiliation":[{"name":"Department of Accounting, Economics and Finance, Southeast Missouri State University, Cape Girardeau, MO 63701, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"F\u00e4re, R., and Grosskopf, S. 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