Environmental Efficiency under Materials Balance: A Minimum-Distance Directional Slack Approach

TY - JOUR

T1 - Environmental Efficiency under Materials Balance: A Minimum-Distance Directional Slack Approach

AU - Fukuyama, Hirofumi

AU - Kourtzidis, Stavros

AU - Matousek, Roman

AU - Tzeremes, Nickolaos G.

N1 - © 2026 The Author(s)

PY - 2026/7/1

Y1 - 2026/7/1

N2 - This study develops a two-stage environmental–economic framework for U.S. states over 1998–2017 within a materials-balance setting. In the first stage, we construct a convexified materials-balance technology in which undesirable outputs are directly linked to an emission-generating input through materials-balance conditions, and we derive an environment-oriented sub-vector efficiency measure in the spirit of Hampf and Rødseth (HR). The resulting radial environmental efficiency scores are then used to transform the pollution-related variables and define a second benchmark technology from which we obtain a materials-balance-based minimum-distance directional slack inefficiency (minDistDSI) measure. This dual structure permits a comparison between a conventional frontier perspective and a minimum-distance perspective, thereby distinguishing deeper structural inefficiency from proximity to feasible improvement targets. In the second stage, we embed both indices in a Bayesian difference-in-differences design with staggered policy adoption and event-study diagnostics to assess the causal effects of state environmental interventions. The results indicate meaningful reductions in major air pollutants, whereas average policy effects on the efficiency indices are modest and imprecisely estimated. Overall, the evidence supports a tiered policy approach in which minimum-distance benchmarks guide attainable short-run improvements, while the HR-based measure identifies longer-run environmental performance gains requiring broader structural adjustment.

AB - This study develops a two-stage environmental–economic framework for U.S. states over 1998–2017 within a materials-balance setting. In the first stage, we construct a convexified materials-balance technology in which undesirable outputs are directly linked to an emission-generating input through materials-balance conditions, and we derive an environment-oriented sub-vector efficiency measure in the spirit of Hampf and Rødseth (HR). The resulting radial environmental efficiency scores are then used to transform the pollution-related variables and define a second benchmark technology from which we obtain a materials-balance-based minimum-distance directional slack inefficiency (minDistDSI) measure. This dual structure permits a comparison between a conventional frontier perspective and a minimum-distance perspective, thereby distinguishing deeper structural inefficiency from proximity to feasible improvement targets. In the second stage, we embed both indices in a Bayesian difference-in-differences design with staggered policy adoption and event-study diagnostics to assess the causal effects of state environmental interventions. The results indicate meaningful reductions in major air pollutants, whereas average policy effects on the efficiency indices are modest and imprecisely estimated. Overall, the evidence supports a tiered policy approach in which minimum-distance benchmarks guide attainable short-run improvements, while the HR-based measure identifies longer-run environmental performance gains requiring broader structural adjustment.

KW - Data envelopment analysis

KW - Environmental efficiency

KW - Environmental performance strategies

KW - US states

U2 - 10.1016/j.ejor.2026.06.042

DO - 10.1016/j.ejor.2026.06.042

M3 - Article

SN - 0377-2217

JO - European Journal of Operational Research

JF - European Journal of Operational Research

ER -