The case for the use of multiple imputation missing data methods in stochastic frontier analysis with illustration using English local highway data

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Multiple imputation (MI) methods have been widely applied in economic applications as a robust statistical way to incorporate data where some observations have missing values for some variables. However in stochastic frontier analysis (SFA), application of these techniques has been sparse and the case for such models has not received attention in the appropriate academic literature. This paper fills this gap and explores the robust properties of MI within the stochastic frontier context. From a methodological perspective, we depart from the standard MI literature by demonstrating, conceptually and through simulation, that it is not appropriate to use imputations of the dependent variable within the SFA modelling, although they can be useful to predict the values of missing explanatory variables. Fundamentally, this is because efficiency analysis involves decomposing a residual into noise and inefficiency and as a result any imputation of a dependent variable would be imputing efficiency based on some concept of average inefficiency in the sample. A further contribution that we discuss and illustrate for the first time in the SFA literature, is that using auxiliary variables (outside of those contained in the SFA model) can enhance the imputations of missing values. Our empirical example neatly articulates that often the source of missing data is only a sub-set of components comprising a part of a composite (or complex) measure and that the other parts that are observed are very useful in predicting the value.