Energetic and Economic Aspects of Rebound, Part I: Foundations of a Rigorous Analytical Framework

With colleagues and friends Gregor Semieniuk (economist) and Paul Brockway (energy analyst), I developed a mathematical framework to describe the rebound effect. More than six years in the making, Part I of our two-part paper was published today at https://doi.org/10.1177/01956574251331969. The paper speaks for itself (with more than 200 equations!). In this blog post, I want to recount the process that led to its publication, a story that is rarely told for journal articles.

The idea for the article was born during June 2019 meetings with co-author Paul Brockway prior to the 13th International Conference of the European Society for Ecological Economics (ESEE) in Turku, Finland. I had the idea that re-spent financial savings from energy efficiency could “spin” around the economy, generating economic growth like loans made by banks. (The difference, of course, is that banks create money while energy efficiency saves money.) Given that every dollar spent in an economy has energy implications (on average at the energy intensity of the economy, I), the economic growth will pull up energy consumption, thereby “taking back” the original energy savings. Classic rebound.

I saved my notes from those early conversations, but for an unknown reason the first page is missing. The second page survives.

Paul suggested that I discuss the idea with co-author Gregor Semieniuk whom we met for lunch. During a proverbial “back of the envelope” conversation, Gregor thought the idea might have some promise.

What followed was several years of joy and pain leading to a pair of papers, the first of which is now available online, the second of which is being typeset and soon will be. The pains included
(a) a desk rejection the day before Christmas from the first journal to which we submitted after the paper sat for a year on the editor’s desk and
(b) waiting for nearly 15 months for the first reviews from the The Energy Journal.

The joys include
(a) working with my co-author teams,
(b) writing an R package (ReboundTools) to do the analysis,
(c) developing new ways to visualize rebound (rebound planes), and
(d) solving problems with the analyses and associated graphs.

An example illustrates our working relationship. I proposed a way to illustrate rebound dynamics in what we came to call energy and expenditure planes. (The planes appear in Part II.) Gregor noted that we could also create a consumption plane that describes both the consumer’s budget constraint and their indifference curve. Paul found data on prices, energy efficiencies, and elasticities needed to create the graphs. I wrote code in the ReboundTools package to create the graphs, but Gregor noticed something not quite right: the budget constraint line was not perfectly tangent to the indifference curve at equilibrium points in the consumption plane. Maybe my R code was wrong? I looked through the code and didn’t find any problems. Paul applied the framework in an Excel spreadsheet to confirm the results from the ReboundTools package. Gregor went back to find that our utility model was only an approximation (often used in the literature) that is usually good but not precise enough for the paper. (Specifically, the approximation is good for marginal efficiency increases and energy service price decreases, but our framework applies to non-marginal efficiency and service prices changes.) Together, we decided to try a Constant Elasticity of Substitution (CES) utility function. Gregor searched and found examples. I suggested normalizing to original utility and consumption, and Gregor agreed. (That’s the only way units are reasonable and coefficients are comparable across studies.) I modified the code and re-built the consumption plane to find that … it works! Paul re-did the Excel calculations using the updated utility model as described in the paper to verify that a reader could do the calculations. The improved consumption planes are presented in Part II.

All this is to say that papers are written by teams of real people surrounded by communities of researchers who need to communicate well as they share ideas, critique each other, and respond to reviews.

Looking back, we are grateful for the thoughtful and challenging reviews, even if they took more than a year. As usual, the reviews made the paper so much better. And I’m hopeful that the framework can be used by others, especially by those who build energy-economy models. Incorporating rebound in those models would go some way toward understanding the complicated effects of energy efficiency in the economy.