Stationarity of Heterogeneity in Production Technology using Latent Class Modelling

Latent class modelling (LC) has been advanced as a promising alternative for addressing heterogeneity in frontier analysis models, in particular those where the individual scores are used in regulatory settings. If the production possibility set contains multiple distinct technologies, pooled approaches would result in biased results. We revisit the fundamentals of production theory and formulate a set of criteria for identification of heterogeneity: completeness (the inclusion of all data in the analysis), stationarity (the temporal stability of the identified production technologies), and endogeneity (no ad hoc determination of the cardinality of the classes). We also distinguish between the identification of a sporadic idiosyncratic shock, an outlier observation, and the identification of a time-persistent technology. Using a representative data set for regulation (a panel for Swedish electricity distributors 2000-2006), we test LC modelling for a Cobb-Douglas production function using the defined criteria. The LC results are compared to the pooled stochastic frontier analysis (SFA) model as a benchmark. Outliers are detected using an adjusted DEA super-efficiency procedure. Our results show that about 78% of the distributors are assigned to a single class, the remaining 22% split into two smaller classes that are non-stationary and largely composed of outliers. It is hardly conceivable that a production technology could change over this short horizon, implying that LC should be seen more as an enhanced outlier analysis than as a solid identification method for heterogeneity in the production set. More generally, we argue that the claim for heterogeneity in reference set deserves a more rigorous investigation to control for the multiple effects of sample size bias, specification error and the impact on functional form assumptions.