This paper improves on the issues of extreme data points and heterogeneity found in the linear programming data envelopment analysis (DEA) by presenting a cluster-adjusted DEA model (DEA with cluster approach). This analysis, based on efficiency, determines the number of clusters via Gap statistic and Elbow methods. We use the December quarterly panel data consisting of 122 U.S agricultural banks across 37 states from 2000 to 2017 to estimate the cluster-adjusted DEA model. Empirical results show differences in the estimated DEA efficiency measures with and without a clustering approach. Furthermore, using non-parametric tests, the results of Ansari-Bradley, Kruskal Wallis, and Wilcoxon Rank Sum tests suggest that the cluster-adjusted DEA model provides statistically better efficiency measures in comparison to the DEA model without a clustering approach.

This paper demonstrates the sensitivity of the linear programming approach in the estimation of productivity measures in the primal framework. Specifically, the sensitivity to the number of constraints (level of dis-aggregation) and imposition of returns to scale constraints is evaluated. Further, the shadow or dual values are recovered from the linear program and compared to the market prices used in the ideal Fisher index approach. Empirical application to U.S. state-level time series data from 1960–2004 reveal productivity change decreases with increases in the number of constraints. Divergence in productivity measures is observed due to the choice of method imposed, various levels of commodity/input aggregation, and technology assumptions. Due to the piecewise linear approximation of the nonparametric programming approach, the shadow share-weights are skewed leading to the difference in the productivity measures due to aggregation.