Does Scale Efficiency Tell Us Anything About Optimal Scale?

In DEA, scale efficiency is routinely calculated. This measure may, however, tell us very little about whether a production unit is over- or undersized. An empirical case is used to illustrate that, under some circumstances, scale inefficiency may simply reflect that a production unit is producing too little, given its use of factors of production, and not that is over- or undersized. A fictitious sample based on a production function with variable returns to scale is used for demonstrating that in small samples with large deviations from the efficiency frontier and limited variability between units in terms of factor proportions scale efficiency may not reflect very well how far the production units are from being of an optimal size.