Biases in technical efficiency scores caused by intra-input aggregation: mathematical analysis and a DEA application using simulated data

In Data Envelopment Analysis (DEA) applications involving multiple inputs and outputs, inputs are aggregated into the total amounts of each type of input. For example, if input types 'labour' and 'capital' are used to produce multiple outputs, the total amount of labour used to produce all outputs is treated as one aggregated input and the total amount of capital as another. Resources are not disaggregated into input variables measuring the amount of labour used to produce the first output, the amount of labour used to produce the second output, the amount of labour used to produce the third output and so on, for both labour and capital. It is shown that such intra-input aggregation causes downward bias in reported technical efficiency scores, with variations in bias unrelated to true technical efficiency. Therefore, with few exceptions, any technical efficiency comparisons among DMUs are invalid. The presence of intra-input aggregation bias is demonstrated mathematically, simulation is used to exhibit its severity, and the exceptions that permit intra-input aggregation without causing bias are identified. It is concluded that, for multiple-input, multiple-output DEA applications, inputs must be disaggregated into the amounts used to produce each output in order to validly report technical efficiency, unless one of the exceptions is present.