Measuring Innovation Efficiency Using Stochastic Frontier Analysis

Abstract

Innovation is widely regarded as a key driver of firm competitiveness, technological progress, and long-term economic growth. However, measuring innovation efficiency remains a challenging issue in both academic research and practical policy analysis. Many existing studies rely mainly on innovation input or output indicators, such as R&D expenditure, patent applications, or patent grants. Although these indicators provide useful information, they do not fully reflect how efficiently firms transform innovation resources into actual innovation outcomes. In addition, several commonly used measurement approaches, including simple ratio indicators and Data Envelopment Analysis (DEA), often assume that all deviations from the efficiency frontier are caused entirely by inefficiency. In reality, however, part of these deviations may result from external shocks, statistical noise, or measurement errors, which can lead to biased estimates of innovation efficiency. To address this issue, this paper proposes a more structured framework for measuring firm-level innovation efficiency using Stochastic Frontier Analysis (SFA). Compared with traditional non-parametric approaches, SFA provides the advantage of separating inefficiency effects from random disturbances, thereby offering a more realistic and reliable evaluation of innovation performance. The paper presents the basic theoretical logic of the SFA framework, including model specification, parameter estimation through maximum likelihood methods, and the calculation and interpretation of innovation efficiency scores. In addition, the study discusses the practical applicability of the framework in empirical research and highlights its advantages in handling firm-level panel data. To illustrate the proposed approach, an empirical example is conducted using panel data from Chinese A-share listed firms covering the period from 2012 to 2023, including more than 40,000 firm-year observations. The findings indicate that substantial differences in innovation efficiency exist across firms and industries. The results further suggest that the SFA-based approach is better able to identify these differences and provide more stable efficiency estimates than several conventional measurement methods. Overall, although the framework still has certain limitations, it offers a practical, transparent, and relatively flexible tool for evaluating innovation efficiency, and may provide useful implications for future academic research, enterprise management, and innovation policy design.