6. Discussion
Although the breadth and number of cases is good evidence of the difficulty of achieving dematerialization for a broad range of technical performance improvement rates, there are limitations that suggest care in making too broad a generalization based upon our results. First, our economic model is simple essentially using demand elasticity as the mechanism for quantifying rebound. More in depth -but necessarily less broad analysis- is given in Liddle (2015) who gives robust estimates of elasticity of Carbon emissions with respect to population and income. Interesting future work would be to extend Liddle's analysis to include dematerialization cases. Second, the method we developed for extracting elasticity from the time series data rely upon the assumption that demand elasticity due to income increases and the demand elasticity due to more attractive products are equal and constant over time. Third, we do not attempt to estimate the lifespan or the recycling path of retired systems, devices and materials. Balancing the simplicity of the economic model is the fact that we use (to our knowledge for the first time) a richer quantification of technical progress that is firmly based upon other empirical work (the generalized Moore's Law). Considering lifespan and recycling paths would have to address the fact that higher rates of technological progress increase incentives to earlier retirement of systems and that technological change that underlies the performance improvements often involve materials changes (Magee, 2012). Balancing the simplicity of the model for lifespan and recycling is that all the data considered in this research includes all real-world recycling so the lack of a case that achieves absolute dematerialization remains an important finding. Overall, it is our contention that this simple model is useful for three reasons: 1) because it leads to simple visualization (the graphical representation); 2) because the assumptions underlying the model are clear and 3) because it enabled broader empirical tests. Further modeling and empirical work should be able to probe the importance of the assumptions and the adequacy of the time series data we have used.