Energetic and Economic Aspects of Rebound, Part I: Foundations of a Rigorous Analytical Framework
Introduction
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. Such stories are too rarely told.
The idea
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 thought that freed cash (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), the subsequent 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 Gregor who would become a co-author and whom we met for lunch. During a proverbial “back of the envelope” conversation, he said the idea had some promise.
A pair of papers
What followed were 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,
now the papers’ home.
The joys were
(a) working with my co-authors,
(b) writing an R package
(ReboundTools)
to assist our analyses,
(c) developing new ways to visualize rebound
(rebound planes), and
(d) solving problems with the analyses and associated graphs.
Working together
An example illustrates our working relationship. I proposed a graphical approach to illustrate rebound dynamics that we came to call energy and expenditure planes. Gregor suggested that we could add a consumption plane to describe both the consumer’s budget constraint and their indifference curve. Paul found data on prices, energy efficiencies, and elasticities. I wrote code in the ReboundTools package to generate the planes for the paper, 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 and confirmed the results from the ReboundTools package. So Gregor went back to basics to find that our utility model was only an approximation (often used in the literature) and not accurate enough for our purposes. (Specifically, the approximation is good for marginal efficiency increases and energy service price decreases, but our framework applies to non-marginal efficiency and service price 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 worked! Finally, 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, enhancing replicability.
In the example below (Figure 7 from the Part II paper), the gray o—o line (the consumer’s original budget constraint) is tangent to the black io—io line (the consumer’s indifference curve). After emplacement of the LED lamp, the new budget constraint (the gray ^—^ line) is also tangent to the indifference curve (the black io—io line), as required for the utility-optimizing consumer. After spending the freed cash from energy efficiency, the final budget constraint (the gray - — - line) is tangent to the new indifference curve (the black i—i line).
The improved consumption planes appear as Figures 4 and 7 in Part II. (See my short post about Part II.)
All this is to say that academic papers are written by teams of real people surrounded by communities of researchers who need to communicate well as they share ideas, gather data, perform analyses, critique each other, and respond to reviews. All of that takes time. Sometimes a lot of time!
In the rear view mirror
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 measurably better. And we’re 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 and surprising effects of energy efficiency in the economy.