# Presentation: 947109

## The Rebound Effect:An Analysis of the Empirical Data for Lighting

**The Rebound Effect:****An Analysis of the Empirical Data for Lighting**

**Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Security Administration under Contract DE-AC04-94AL85000.**

***Jeff Tsao (Sandia National Laboratories)***
***Paul Waide (International Energy Agency)***
***Harry Saunders (Decision Processes Incorporated)***

***1 Consumption of***
***2 Affordability of***
***3 Relationship between***

**White Light**

**RYGB**
**Light Emitting**
**Diodes**

**Color Mixing Optics**

_***Solid-State Lighting***_

_***Decades-to-Centuries Rebound Effect***_

**Notes:**
Good afternoon.  Today, I’d like to describe to you an analysis that we did recently of the empirical data associated with the consumption of artificial light.  Our motivation for doing this analysis was twofold.
Our first motivation was from the narrow and perhaps more practical perspective of lighting itself.
As some of you may know, lighting is at the cusp of a major change from one technology to another.  A new technology, solid-state lighting, is on the horizon.  It uses semiconductor devices (light-emitting diodes of various colors – red, yellow, green, blue) to produce, after appropriate color mixing, visible white light.  Although it is not yet competitive with traditional lamps for general illlumination applications, it soon will be.  Indeed, solid-state lighting has the potential to be 10x more efficient than incandescent lighting, and 2x more efficient than fluorescent and high-intensity-discharge lighting.  Because of this, we in the solid-state lighting community often brag about how we might someday reduce energy consumption for lighting by 2x and perhaps more.  Because lighting represents about 6.5% of the world’s primary energy consumption and 16% of the world’s electricity consumption, this would be a significant reduction.
However, solid-state lighting isn’t just a plug-in replacement for traditional lighting.  It offers a number of features, like compactness, long-lifetime, color tunability, and integrability with digital electronics.  That made us wonder whether, if lighting became both cheaper and had more features, people might actually buy more of it, and we might not save as much energy as we had been bragging about.  In other words, we wondered whether there might be a significant rebound effect in the consumption of light as traditional lighting gave way to solid-state lighting.
Our second motivation was from the broader and perhaps more academic perspective of the nature of the rebound effect itself.
As we looked into this effect, it occurred to us that most studies have taken a relatively short-term, months-to-years view of rebound.  That is, they have asked the question: if you change the efficiency or cost of an energy service, by how much does consumption of that service change over a months-to-years time frame.  Such short-term adjustments in consumption are important, of course, but we suspect they do not tell the entire story.
As noted in the first serious discussion of the rebound effect, by Stanley Jevons in connection with the consumption of coal, much larger adjustments can and do occur over longer periods of time. As the cost of an energy service changes, it may alter whether other products and services are economical or not, and as these alterations occur, there is a feedback effect on consumption of the original energy service.  Moreover, as the cost of an energy service changes, it may spawn new and complementary technological innovations, again with a feedback effect on consumption of the original energy service.  Both of these feedback effects will occur on a much longer, decades to centuries, time scale.
So we began to wonder whether we could use lighting as a quantitative case study to help inform our general understanding of the rebound effect over such long, historical time periods.
So this talk is basically a compendium of empirical data associated with the consumption of light, of interest both to the narrow question of what might the rebound effect be like for lighting as well as to the broader question of the magnitude of the rebound effect on historical time scales.  That data has two parts to it that I will discuss in turn.  The first part is data associated with the consumption of light itself.  The second part is data associated with the factors that enter into the affordability of that consumption: the cost of light and the income of the consumers purchasing the light.  Finally, I’ll end my talk by discussing the relationship that we have found between these two.
But before I begin, let me acknowledge my co-authors:  Paul Waide, from the International Energy Agency, whose datasets and insights were crucial to this work, and Harry Saunders, from Decision Processes Incorporated, who has been instrumental in helping analyze the economics underlying the rebound effect.

## per capita Consumption of Light:φ (Mlmh/[per-yr])

**per capita Consumption of Light:*****φ****** *****(Mlmh/[per-yr])**

**Earth at Night (courtesy of NASA)**

**Mills**
**WRLD-NONGRID 1999: 0.043**

**IEA**
**WRLD-GRID 2005: 32.9**

**Fouquet & Pearson**
**UK**
**2000 Inc+Flu+HID: 46.4**
**1950 Inc:                   5.0**
**1900 Gas+Ker:          0.27**
**1850 Gas+Can:         0.013**
**1800 Can+Oil:           0.0027**
**1750 Can:                  0.0006**
**1700 Can:                  0.00058**

**IEA**
**AU+NZ 2005: 63.4**

**IEA**
**FSU 2000: 38.7**

**IEA**
**OECD-EU 2005: 45.9**

**IEA**
**JP+KR 2005: 71.9**

**CN**
**Li      2006: 16.4**
**IEA   2005: 13.4**
**Mills 1993:   2.7**

**Navigant**
**US 2001: 136**

**Notes:**
Let’s start with the first part: empirical data associated with the consumption of light itself.  Here I show that data, compiled from a number of sources, overlaid on the geographical region it corresponds to on this “earth at night” photo from NASA.  To make it easier to compare the data across countries and groups of countries, we use per capita consumption of light rather than total consumption of light.  The symbol we use for that per capita consumption is lower-case φ, and its units are Mlmh/per-yr, where a lumen is the standard unit of light visible to the human eye.
The most accurate data point is probably the study by Michael Scholand and co-workers at Navigant Consulting of the consumption of light in the U.S. in 2001.  That study took a bottoms-up approach, tabulating all of the various lamp types, their efficiencies and usage patterns, and rolling them all up into an aggregate consumption of light for the U.S. as a whole.  As it turns out, perhaps not unexpectedly, the U.S. is the lumens hog of the world: per capita consumption in 2001 was 136 Mlmh/per-yr.  To put this in perspective, this is the equivalent of the average person in the U.S. being surrounded during his or her waking hours by 17 100W light bulbs!  That high per capita light consumption is illustrated graphically by the high density of wasted light you can see escaping from the U.S. on this photo.
The lumens miser of the world is, also perhaps not surprisingly, the undeveloped world not on grid electricity.  Evan Mills at Lawrence Berkeley National Laboratory estimated the per capita consumption of light in this world in 1999 to be only about 0.043 Mlmh/per-yr.  That’s equivalent to being surrounded during one’s waking hours by a single half Watt light bulb – about ten times less than a typical night light.  That low per capita light consumption is illustrated graphically by the absence of wasted light escaping from the earth from these large regions, e.g., of Africa.
In addition to these two data points, which represent extremes of behavior in the contemporary world, I want to call attention to two data sets, both monumental, but very different in scope.
The first set is represented by the data in grey.  This was the work by Paul Waide and co-workers at the International Energy Agency, and is the most comprehensive in terms of international coverage.  They estimated the consumption of light in a number of countries and groups of countries, including:  OECD Europe, the Former Soviet Union, Japan+Korea, Australia+NewZealand, China, and the developed world on grid electricity.
The second set is represented by the data in brownish red.  This was the monumental work by Roger Fouquet and Peter Pearson in Imperial College in London, and is the most sweeping in terms of long-term history.  Inspired by some original work by William Nordhaus at Yale University, they estimated the consumption of light in the United Kingdom over several centuries and, importantly, over many different lighting technologies: candles, oil, gas, kerosene, and, finally, modern electric lighting using incandescent, fluorescent and high-intensity-discharge lamps.  You can see that the per capita consumption of light spans an extremely large range, from 46.4 Mlmh/per-yr in 2000 down to 0.00058 Mlmh/per-yr in 1700.  Interestingly, the UK in 1850 is roughly comparable to the undeveloped nongrid world in 1999.

## Cost of Light:CoL ($/Mlmh) ≃ CoE/η

**Cost of Light:*****CoL***** ($/Mlmh) ****≃**** *****CoE/******η***

**1       10****1****      10****2****      10****3****     10****4****    10****5**

***CoE***** ($/MWh)**

**Luminous efficacy**
***η***** (lm/W)**

**10****-2**

**100%**
**Efficiency**

**10****-1**

**1**

**10****1**

**10****2**

**10****3**

**1**

**10****1**

**10****2**

**10****3**

**10****4**

**10****5**

**CN 1993**

**WRLD-NONGRID**
**1999**

**WRLD-GRID 2005**

**UK 1800**

**UK 1850**

**UK 1750**

**UK 1700**

**UK 1900**

**UK 1950**

**UK 2000**

**AU+NZ 2005**

**FSU 2000**

**OECD-EU 2005**

**JP+KR 2005**

**CN 2005**
**CN 2006**

**US 2001**

**10****-3****   10****-2****     10****-1****       1       10****1****    10****2**

***N *****(Bper)**

***GDP *****(B$/yr)**

**10****1**

**10****2**

**10****3**

**CN 1993**

**WRLD-NONGRID**
**1999**

**WRLD-GRID 2005**

**UK 1800**

**UK 1850**

**UK 1750**

**UK 1700**

**UK 1900**

**UK 1950**

**UK 2000**

**AU+NZ 2005**

**FSU**
**2000**

**OECD-EU 2005**

**JP+KR 2005**

**CN 2006**

**US 2001**

**CN 2005**

**10****4**

**10****5**

**10****6**

**10****3**

**10****4**

**10****5**

**After Maddison and Univ of Groningen purchase-power-parity tabulations,**
**in 2005 US$**

**10****1.5**

**per capita****gross domestic product:*****gdp***** ($/[per-yr]) = *****GDP/N***

**Notes:**
OK, so that was the first part, the empirical data associated with the consumption of light.  Now let’s turn to the second part, the empirical data associated with the affordability of that consumption: the cost of light, illustrated on the left, and the income of the consumers purchasing the light, illustrated on the right, and which we take here to be per capita gross domestic product.
Let’s start with cost of light.  This cost is actually two costs: the operating cost of the lamp while it is on, and the capital cost of the lamp itself.  It turns out the operating cost is the much larger one, so that is the one that we’ll focus on here.  We can break that operating cost out in the following way.
First, there is the raw cost of the energy that you are putting into the lamp.  That’s labeled CoE, in units of $/MWh, on this bottom axis.  Second, there is the efficiency with which the lamp converts that energy into light, or lumens, visible to the human eye.  That efficiency is called luminous efficacy, and is labled η, with the units lm/W, on this left axis.  To calibrate you, 408 lm/W, up here, represents 100% efficiency – that is, the luminous efficacy associated with converting without any loss every Watt of input power into a visible lumen of light.
Now, the operating cost of light is just the cost of energy divided by the efficiency with which you convert that energy into light, and has the units $/Mlmh.  So if you know the cost of energy and luminous efficacy anywhere on this plot, you also know the cost of light.  To illustrate that, I’ve drawn contours of constant cost of light on this figure, decreasing from 100,000 $/Mlmh down in the lower right all the way to 1 $/Mlmh up in the upper left.  Overlaid on these contours I’ve plotted the empirical data for cost of light corresponding to the countries or combinations of countries for which we have data on the consumption of light.  You can see that, from 1700 until now, the cost of light has decreased by an amazing 4.3 orders of magnitude.  Of that, 1.5 orders of magnitude has been due to a decrease in the cost of energy.  But a much larger 2.8 orders of magnitude has been due to the increase in luminous efficacy, from less than a tenth of a lumen per Watt to nearly 100 lumens per Watt!
Luminous efficacy, of course, is a measure of progress, so this plot just quantifies what we all intuitively know: that lighting technology has made enormous historical progress.
Now let’s turn to the income of the consumers purchasing the light, which, again, we take here to be per capita gross domestic product.
This is of course just the ratio between the two axes of this plot: total gross domestic product in billions of $ per year and population in billions of persons.  And just as we did for the cost of light plot, here we can plot contours of constant per capita gdp, ranging from 1,000 $/per-yr to 100,000 $/per-yr.
Again, we can plot the empirical data for per capita gdp corresponding to the countries or combinations of countries for which we have data on the consumption of light.  For this data we have used tabulations by Angus Maddison and the University of Groningen, converted to 2005 U.S. dollars.  That means all GDPs are purchase-power-parity estimates.
You can see that per capita gdp has increased over time, from the UK in 1700 to the U.S. in 2005.  But the increase hasn’t been nearly as great as the decrease in cost of light: 1.4 orders of magnitude (a factor 20x) compared to 4.3 orders of magnitude (a factor 20,000x).
So one can see that the influence of the cost of light is likely to have been larger than that of income on the consumption of light.

## φ = β·(gdp/CoL)

**10****-5****            10****-2****               10****1****             10****4**

***β******·gdp/CoL***** [Mlmh/(per-yr)]**

***φ***** [Mlmh/(per-yr)]**

**10****4**

**10****1**

**10****-2**

**10****-5**

**CN 1993**

**WRLD-UNDEV 1999**

**WRLD-DEV 2005**

**UK 1800**

**UK 1850**

**UK 1750**

**UK 1700**

**UK 1900**

**UK 1950**

**UK 2000**

**AU+NZ 2005**

**FSU 2000**

**OECD-EU 2005**

**JP+KR 2005**

**CN 2005**

**CN 2006**

**US 2001**

**10****5.4**

**0.0072**

***R******2***** = 0.986**

**Candles**

**Gas**
**Kerosene**

**HID**
**Fluorescent**
**Incandescent**

**SSL**

***Consistent with ******φ****** having unit elasticity with respect to gdp and CoL***
***Over empirical data spanning many orders of magnitude***
***5.4 in ******φ***
***4.3 in CoL***
***1.4 in gdp***
***3 centuries***
***6 continents***
***5 technologies***

**Notes:**
So I’ve shown you the empirical data associated with per capita consumption of light, and then the empirical data associated with affordability of that light.  Let’s turn now to the relationship between consumption and affordability.
Here I show you the key result of our work: a merged scatter plot of the two sets of empirical data along two axes.  The vertical axis is per capita consumption of light, φ, in units of Mlmh per person year.  The bottom axis is a fixed constant, β, times the ratio between per capita gdp and cost of light.  Since per capita gdp has the units $/per-yr, and cost of light has the units $/Mlmh, this ratio also has the units Mlmh/per-year, the same as the vertical axis.  When the fixed constant, β, is 0.0072, you can see that the empirical data fall very closely along a line of slope 1, and the adjusted coefficient of regression for the one-parameter fit of the data to that line is very high: 0.986.  This has two implications.
The first implication is that, over the past few centuries, and even now, the world spends about 0.72% of its gdp on light.  This was the case in the UK in 1700, it is the case in the undeveloped world in modern times, and is the case for the developed world in modern times using the most advanced lighting technologies.  There is still some spread in the modern developed world, because there are differences in the cost of energy and hence cost of light, as well as differences in per capita income.  Japan+Korea and OECD Europe, e.g., have higher costs of energy than the U.S., hence higher costs of light.  Plus, they have slightly lower per capita gdp’s, so their per capita consumptions of light are lower than that of the U.S., by a factor 2 or 3.
The second implication is that, as per capita gdp increases and cost of light decreases, per capita consumption of light increases, linearly.  In other words, the price and income elasticities of the consumption of light are roughly unity.
Now, I want to emphasize that the close fit between per capita consumption of light and this simple expression does not mean there are not other possible ways of explaining per capita consumption of light.  All we’ve shown is that per capita consumption of light is consistent with this expression.  However, I would point out that this consistency spans a very wide, 5.4 orders of magnitude (a factor of 250,000x) in per capita consumption of light, 4.3 orders of magnitude in cost of light, 1.4 orders of magnitude in per capita gdp, 3 centuries, 6 continents, and 5 overall families of lighting technologies.
With that, let me close and thank-you for your attention.