To estimate environmental efficiency in some crop production (for example wheat) you
first need to estimate technical efficiency which you can do by using stochastic
production frontier approach. Further to derive environmental efficiency from the production function, you can follow the approach used Abedullah et al. 2015. I am giving the link for the publication in which they mentioned the whole method for EE determination. If you don't have access to this link then let me know.
From an ecological perspective, some have used the eco-exergy, which is a measure of the work (in Joules) that can be done by an ecosystem - a concept developed mainly by Prof. Sven E. Jørgensen. There is a small but useful body of literature on its application to agriculture.
Efficiency is defined by a ratio of an environmental indicator and production indicators.
The most difficult part is certainly to calculate environmental indicators, but you have several methods available in the literature (eco-exergy as suggested by Serge-Etienne, emergy, life cycle assessment, etc.).
Once these environmental indicators calculated, you will easily calculate some basic environmental efficiency indicators by linking them to production indicators (Gases emission by surface, nitrogen leak by Kg of production, etc...).
Beyond this bi-dimensional analysis, and as suggested Muhammad, you can explore multi-dimensional efficiency indicators through efficiency frontiers. Parametric and non parametric approach can be implemented, but i would suggest non-parametric approach (e.g. Data Envelopment Analysis) for a first exploration by non-expert users.
With those methods, you will define environmental efficiency indicators on a multidimensional plan, taking into account levels of each inputs and outputs of your production process.
I hope you will achieved your objective to implement those methods in crop production in Nigera, as we don't see a lof of literature on environmental efficiency in crop production in this area : good luck !
there are indeed more than one eligible approach to measure eco-efficiency, each having own pro and cons. see also the answer of David Berre, but besides there are also many overview articles on the multi dimensional approaches, among which the SFA and DEA methods are very popular. However, there is not yet full concensus on how the incorporate environmental outcomes in such types of efficiency models. I'm glad to refer to one of my own articles (which also contains references to other reveiws) in which I reveiw and classify various types of models.
regards
Ludwig
Lauwers, L 2009, 'Justifying the incorporation of the materials balance principle into frontier-based eco-efficiency models' Ecological Economics, vol 68, nr. 6, 1605-1614
As pointed out by Ludwig there is are several approaches to the measurement of environmental efficiency.
These approaches differ in (a) the measurement method (SFA, FEA), and (b) in the underlying assumptions for the pollution & production process.
The latter assumptions in particular have led to a lot of discussion. The recent insight is that the analysis should distinguish the intended-output and the residual-generation technology separately, with the residuals seen as distinct by-products (Murty, Russell and Levkoff, 2012).
In fact this idea has been in use in environmental measurement practice for some time. It means that environmental efficiency is to be calculated separately from the technical and economic efficiency as discussed in De Koeijer et al. (2002).
The latter article is on crop farming and itshows how the assessment provides useful management information.
Article Measuring agricultural sustainability in terms of efficiency...