This article examines the relationship between the concepts of efficiency and corporate social responsibility (CSR). The main aim is to discuss if CSR policy has an effective influence which leads to a high degree of technical efficiency. Accordingly, the image projected to society should be strengthened. Under this scenario, an equivalent level of confidence in the public sector should be expected. Otherwise public decision‐makers should reformulate their SR strategy, since the impact would not only be economic but would also lead to a negative externality in relation to the image that the sector projects to society. Accordingly, a case study for the Defence sector in Spain is part of this article. Given a set of discretionary variables, the Spanish Defence Delegations efficiency for the 2015–2017 period is assessed by means of data envelopment analysis technique. A bootstrap procedure is used to eliminate the bias of the estimates and obtain a robust ranking. The results show that efficient management does not have the expected positive effect on the Army's corporate reputation as measured by the image perceived by the stakeholders. Implications for practice and limitations of this study conclude the article.