Linear Input Aggregation Bias in Nonparametric Technical Efficiency Measurement Arthur C. Thomas1 and Loren W. Tauer2 ‘Graduate zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA research assistant, Department of Agricultural Economics, Cornell University, Ithaca, New York. 2Professor, Department of Agricultural Economics, Cornell University, Ithaca, New York. Received 2 February 1993, accepted 18 October 1993 zyxwvutsrqponmlkjihgfedcbaZYXW An attraction of the nonparametric approach to measuring technical eflciency is that no zyxwvutsrqponmlkjihgfedcbaZY a priori structure is placed on the production process of the j2-m. However, inputs are typically linearly aggregated, either explicitly or implicitly. It is shown that this introduces bias in the technical eficiency measurement. i%e computed technical eugiciency measure becomes an economic efficiency measure comprised of both technical and allocative eficiency. An empirical application demonstrates the bias. Un des attraits de 1‘approche non parametrique pour la mesure de 1 ‘eficience technique est qu ‘elle n ‘impose aucune structure a priori sur le processus de production d’une entreprise. Cependant, les intrants sont, de manitre typique, lineairement agreges, soit explicitement soit implicitement. Les auteurs demontrent que cela introduit un biais dans la mesure de 1‘eficience technique. La mesure calculee de l’eficience technique devient une mesure d ‘eficience economique composee de 1‘ejfkience tech- nique et de 1‘eficience d ‘affectation des ressources. L ‘existence de ce biais est demontree au moyen d ‘une application empirique. INTRODUCTION Measuring technical and allocative efficiency has become prominent work for production economists. Efforts have occurred along two parallel procedures: the functional or para- metric approach and the data envelopment or nonparametric approach. Econometric methods have advanced to the point where stochastic parametric frontiers can be esti- mated (Bauer 1990). Nonparametric mathe- matical programming procedures need no longer assume that technology sets exhibit constant returns to scale (Banker, Charnes and Cooper 1984). One area that has received inadequate attention is the impact of input aggregation on technical efficiency measures. When aggrega- tion occurs in economic analysis, bias is often expected unless the aggregation meets specific requirements. In nearly all empirical analyses, aggregated inputs or outputs must be used. Some of the inputs used in production analy- ses must consist of expenditures in an input category. Typically, the expenditure data are linear aggregations of inputs weighted by their respective prices. Thus, structure is implicitly imposed on the production process of the firms. Fare and Love11 (1988) address the effects of input aggregation on efficiency measure- ment using the parametric method. They show that technical efficiencies are not biased under aggregation if the aggregating production function is homothetically separable. More- over, it is necessary that the correct aggregating function be employed. These requirements are consistent with standard production function analyses (Blackorby, Primont and Russell 1978). Unfortunately, the zyxwvutsrqpo Canadian Journal of Agricultural Economics 42 (1994) 77-86 77 Table of Contents