Data envelopment analysis with missing data: a multiple imputation approach

Traditional data envelopment analysis (DEA) is used under the premise that inputs and outputs are exact values. If it is not true, the DEA approach is unavailable. However, it is common that some of the entries in the data are missing in practice. As a result, the current paper performs efficiency evaluation with missing data considering the missing-data properties (missing-data patterns and missing-data mechanisms). A multiple imputation (MI) approach is used to estimate the missing values. The MI approach is applied to a forest reorganisation problem for reliability. An example of public secondary schools is given to illustrate the proposed technique. When input or output values for decision making units (DMUs) continuously vary under an interval, the current paper characterises a DMU's pessimistic and optimistic efficiency functions of an input or output of most interest. A Monte Carlo simulation technique is used to obtain a DMU's efficiency distribution.