What is Directional Distance Function

Nitrogen, phosphate, and herbicide use are three main environmental problems caused by agriculture. Modelling these undesirable outputs and other detrimental side effects of production activities has attracted considerable attention and debate among production economists. A common approach is to treat detrimental variables as inputs mainly using Data Envelopment Analysis (DEA), which has enjoyed a lot of success over the years. On the other hand, Free Disposable Hull (FDH) has not enjoyed as much success as its counterpart, DEA. This chapter demonstrates how environmental efficiency can be modelled using both DEA and FDH under strong and weak disposability assumptions. Results show that weak disposability assumption is more superior in achieving relatively high emission reductions and that FDH tends to allocate efficiency to more DMUs compared to DEA.