I was wondering if anybody knows how input distance functions (IDF) and output distance functions (ODF) relate to each other. One of the advantages of distance functions over cost and revenue functions is that they don't require the assumption of cost-minimizing or revenue-maximizing behavior. Thus, I thought the estimated coefficients - and thus measures like economies of scale - of IDFs and ODFs should be similar. However in my empirical example, I obtain unreasonably high economies of scale for the IDF (about 3.2) and quite reasonable scale economies for the ODF (about 1.25). Can anybody think of an explanation for this?
Thank you very much in advance, every hint or thought will be highly appreciated.