INDICATORS OF ILL-CONDITIONED DATA SETS AND MODEL MISSPECIFICATION INDATA ENVELOPMENT ANALYSIS - AN EXTENDED FACET APPROACH

Data Envelopment Analysis (DEA) employs mathematical programming to me asure the relative efficiency of Decision Making Units (DMUs). This pa per is concerned with development of indicators to determine whether o r not the specification of the input and output space is supported by data in the sense that the variation in data is sufficient for estimat ion of a frontier of the same dimension as the input output space. Ins ufficient variation in data implies that some inputs/outputs can be su bstituted along the efficient frontier but only in fixed proportions. Data thus locally supports variation in a subspace of a lower dimensio n rather than in the input output space of full dimension. Each segmen t of the efficient frontier is in this sense subject to local collinea rity. Insufficient variation in data provides a bound on admissible di saggregations in cases where substitution in fixed proportions is inco mpatible with a priori information concerning the production process. A data set incapable of estimating a frontier of full dimension will i n this case be denoted ill-conditioned. It is shown that the existence of well-defined marginal rates of substitution along the estimated st rongly efficient frontier segments requires the existence of Full Dime nsional Efficient Facets (FDEFs). A test for the existence of FDEFs is developed, and an operational two-stage procedure for efficiency eval uation relative to an overall non-fixed technology is developed; the t wo-stage procedure provides a lower and an upper bound on the efficien cy index for each DMU.