Equation 1: Rebound Effect

While there is scientific consensus regarding the existence of rebound effects, there is little agreement on their size. Values provided in scientific literature for increases in energy efficiency vary considerably (Kolstadt et al., 2014). However, while it is difficult to estimate the size of rebound effects, the implicit assumption of zero rebound in many studies is not supported by scientific evidence (Maxwell et al, 2011). De Haan et al. (2015) point to the complications of assessing the size of rebounds and argue that studies based on top-down evaluations of time series tend to overestimate effects due to problems of separating increased resource consumption caused by economic growth and increasing consumers’ wealth from increased resource consumption caused by increased efficiencies. On the other hand, they consider process-based, bottom-up studies to generally underestimate rebound sizes because they cannot account for economy wide effects. 

For the agricultural sector, there are a number of studies investigating rebound effects of introducing more efficient irrigation technologies (Berbel & Mateos, 2014; Dumont et al, 2013; Loch & Adamson, 2015, Mehmeti et al., 2016), some even reporting rebound effects greater than 100% (Pfeiffer & Lin, 2014; Sun et al.,2016). For other resources used in agricultural management, very few studies exist at the time of writing and studies focussed on efficiency gains mostly ignore rebound effects. Lambin & Meyfroidt (2011) discuss potential implications of rebound effects from raising agricultural productivity on the global demand for agricultural land. Also related to the effect of yield improvements on demand for cropland, Ewers et al. (2009) show in a global study on yields and land use between 1979 and 1999 that land sparing occurred in some cases, but that for developed countries there was no evidence that increases in agricultural productivity resulted in lower per capita cropland demand. For the link between agricultural productivity and greenhouse gas emissions, Valin et al. (2013) found strong demand-based rebound effects in a global modelling study until the year 2050. These rebounds severely reduced modelled greenhouse gas savings. 

Rebound effect sizes vary and can be greater than 100% in extreme cases. This phenomenon is called backfire or Jevons´s paradox, after British economist W.S. Jevons who observed in his book “The coal question” (1865) that more efficient use of coal through technical innovation led to higher instead of lower total consumption. Based on this, he postulated that higher fuel efficiencies always led to higher resource exploitation (Jevons, 1865; Alcott, 2005). The same theory was reiterated in the 1980s by economists Khazzoom and Brookes and termed by Saunders (1992) the Khazzoom–Brookes postulate. 

While Jevons’s paradox was formulated for the energy sector, cases where both resource use efficiency and total resource use increased are also found in other sectors. Pfeiffer & Lin (2014) report an example from western Kansas/ USA, where a shift to more efficient irrigation technologies correlated with increased total water use. They explain this effect by farmers changing from non-irrigated to irrigated crops, reducing fallow periods and increasing per hectare irrigation. Similarly, Sun et al. (2016) found that increased water use efficiencies in Bayannur /Inner Mongolia in the period between 2000 and 2010 coincided with increased total water consumption. They state that savings were utilised to increase production rather than to alleviate pressures on the environment.

Estimating size of the rebound effects
Rebound effects result from changes in the behaviour of relevant actors. They are based on multiple variables and are therefore very difficult to quantify. For rebounds resulting from economic feedbacks, general equilibrium models can help to estimate reactions of market participants. For rebounds due to social-psychological factors, only very little research exits (Maxwell, 2011).

In general, rebound sizes are considered to correlate with the following factors (de Haan et al., 2015): 

-  Relative size of the efficiency improvement (%)
-  Relative share of savings of total production costs (%)
-  Degree to which production is limited by availability of the more efficiently 
   used resource (e.g. limited allocation of irrigation water, limited amount of 
   allowable fertiliser application)
-  Degree to which the more efficient process can be used to substitute other   
   production factors
-  Relative price reductions for the final product (%)
-  Degree by which the consumption of the product is perceived as more positive  
   (e.g. social or environmentally friendly) than before
-  Demand elasticity, degree to which is demand currently unsaturated
-  Low degree of other costs associated with product consumption 
   (e.g. in the field of mobility, travel-time is often more relevant than travel-cost)
-  Degree to which the more efficiently used resource is also used in the 
   production of alternative good and services (the demand for which might  
   increase with increasing wealth)
-  Degree to which the more efficient resource use triggers technical innovation 
   in other sectors