1 

# The benefits of energy efficiency standards and how policies may accelerate declines in appliance costs

R D Van Buskirk 1 

### , C L S Kantner 1 

### , B F Gerke 1 

### , L-B Desroches 1 

### and S Chu 2

1 

### Environmental Energy Technologies Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkel ey, California, U.S.A. 94720-8136
2 

### Department of Physics and Department of Molecular and Cellular Physiology, Varian Bldg., Room 252, Stanford Univ ersity, Stanford, CA, U.S.A. 94305-4060

E-mail: RDVanBuskirk@lbl.gov

Abstract. We perform a retrospective analysis of multi-decade trends in price and life-cycle cost for home appliances in periods with and without energy-efficiency standards. In contrast to the classical picture of the impact of efficien cy standards, the introduction and updating of appliance standards is not associated with a long- term increase in purchase price; rather, qualityadjusted prices undergo a continued or accelerated long-term decline. We also show that the incremental price of efficiency improvements has declined much faster than the baseline product price. Both observations are consistent with an a lternative picture of energy efficiency standards in which such policies increase long term rates of learning-by-doing for both price and life-cycle

cost.



### Subject Classification Number, MSC2010: 91B84 Keywords: appliance standards, energy efficienc y, technological lear ning, life-cycle cost2 1. Introduction Energy efficiency (EE) standards are widely viewed as a key policy tool for reducing energy consumption, saving money, and mitigating climate change [1]. There has been substantial debate, however, in both the academic litera ture and the political discourse rega rding the impact of standards on both the life-cycle cost of ownership (LCC) and on the purchase price of home appliances. Many studies argue that appliance standards achieve a net neutra l or beneficial economic impact by decreasing the operating energy costs more than the increase in pur chase price expected to result from compliance with the standard [2, 3, 4, 5, 6]. Other papers assert that such mandates as EE standards are inefficient and costly means of decreasing CO 2 emissions based on assumed parameters [7] or are likely to lead to expensive products that may force budget-constraine d consumers to choose products of lower quality or reduced features [8]

. There also exists a fairly extensive litera ture on innovation that may be induced by regulation. This literature discusses a diverse range of cases where regulation may have caused private
firms to create innovations that would not have occurred in the absence of regulation [9].

Over the past quarter century, the academic debate on the costs and benefits of EE standards has been based on short-term snapshots of appliance market conditions and has not addressed the impacts of EE
standards on innovation. From this short-term perspective—which assu mes that innovation effects are not significant—the primary problems addressed by the regulation are market failures associated with environmental externalities, imperfect information, principal-agent issues, liquidity constraints, or behavioral anomalies [10]. Energy policies, such as minimum EE standards and labeling policies (e.g., ENERGY STAR Program), are devised to address these market failures and informational problems that lead to socially suboptimal outcomes. In the classi cal regulatory impact analysis picture, labels and mandates bring the market to a new equilibrium wh ere appliances have higher prices and lower operating costs. The lower operating costs and internalized mark et externalities of the more efficient appliances are thought to justify the higher purchase prices paid by consumers.

Recent empirical work with appliance market data sugg ests that price-efficiency relationships observed in appliance markets may be far from static [11]. Some studies argue that the prices decline faster than forecast in regulatory analyses due to technological innovation [12]. Additionally, a recent study of the
2004 and 2007 US EE standards for clothes washers fi nds that the rate of decline in appliance prices appears to have accelerated after the EE standards came into effect [13]. This observation is largely inconsistent with the static picture of EE standards impact that is traditionally used in policy analysis which would have predicted a price increase. As a growing number of observers examine the retrospective data on appliance price changes associat ed with EE standards, there appears to be an expanding body of evidence suggesting that the traditi onal static picture of EE standards impacts on costs may be inconsistent with observed market behavior [14].

In this paper, we investigate long-term trends in a ppliance prices and energy use in an effort to better understand interactions between polic y and rates of change in appliance markets. Specifically, we examine the long-term dynamics of markets for effici ent products and estimate l ong-term rates of change of appliance first costs and operating costs for periods both with no EE policy and with active EE standards and labeling programs. Our analysis consider s mandatory EE standards, but the results may also be applicable to EE labeling programs that allow cons umers to make cost-effective trade-offs between the price of efficiency and energy-cost savings [15].3 The discussion of market failures in the literature wi th regard to EE technology has largely focused on
factors that hinder consumers’ choice of efficient t echnologies that are cost-effective on a life-cycle-coast basis—the so-called energy-efficiency gap. From the long-term-dynamics perspective, an economically inefficient market equilibrium at a particular point in time may not be the only market failure addressed by regulation. Another market failure that regul ation may potentially address is the well-known market failure regarding underinvestment in research, develo pment and innovation [16, 17, 18]. In particular, the structure of the supply markets for appliances may lead to underinvestment in innovation, thus hindering EE in the menu of products offered to consumers. There is evidence that the supply markets for appliances are not perfectly competitive and there are va rying levels of industry concentration, which can lead to price discrimination and under-investment in EE by manufacturers [19]. In a theoretical model [20], Fischer demonstrated that when suppliers di scriminate on price, they will offer less efficient products to the low-income consumers and extract their entire economic surplus, while charging highincome consumers more for the higher efficiency a ppliances than in a perfectly competitive market. In this situation, minimum EE standards will increase c onsumer welfare. This study examines new economic evidence regarding rates of change in quality-adjust ed product prices and EE, which may indicate that changes in consumer costs and welfare over the long term are driven by changes in EE policy.

2. Life-cycle cost EE standards effectively mandate the manufacturing of appliances and equipment that may have a higher first cost but which have lower operating costs. The total consumer impacts of EE standards are estimated by calculating the energy-related * LCC of an appliance, which is a sum of the purchase price P A and the energy-related operating costs over time, OC(t) . LCC includes a discounted sum of operating costs, because money spent on operating costs y years in the future is worth less than the same amount of money in the present which could be invested at some interest rate. † Assuming a yearly compound interest rate i, the present value of an expense y years in the future is discounted to 

### ( ) / (1 ) y 

### OC y i  , so that the total present value of operating costs over the appliance lifetime of L -years is given by

1 

### ( )

(1 ) L

L y y 

### OC

i V y P OC

 

###  



#  (1)

The sum of price and present value of operating co sts then provides an estimate of the LCC of that appliance:

A L 

### LCC P PVOC   (2)

* This analysis assumes that non energy-related operating costs (e.g., maintenance and repair costs) are independent of EE and therefore irrelevant to the effect of EE policy on LCC. † If operating cost is measured in inflation-adjusted dollars , the inflation-adjusted interest rate is used. We assume operating costs and interest are charged at th e end of the year in which they occur.4 3. Experience curve calculations Experience curves (also called learning curves) can be used to describe price trends for many technologies ‡ by modeling price P as a power-law function of the total cumulative quantity Q of units deployed: P = P o Q -b where P o and b are empirically determined parameters [21, 22, 23]. Q is the observable variable used as proxy for cumulativ e manufacturing experience [24]. The parameter b is a parameter that describes the relation between fractiona l increases in experience and fractional declines in price. The experience curve concep t is based on the empirical observation that people and organizations complete tasks more efficiently as they accumulate experience, thus reducing the marginal cost of production. However, there are other mechanisms that could also yield a correlation between price and cumulative experience (e.g., changes in pricing stra tegies or globalization of manufacturing operations and supply chains). In this study, we will use the phrase experience curve as shorthand to refer to any empirical correlation between price and cumulative experience, without necessarily linking observed trends to learning-by-doing processes.

To calculate the experience curves, we estimate inflation- and quality-adjusted prices over time by projecting current prices into the past using product-specific price indices. Price indices provide a method of accounting for changes in the mix of products offe red in the market, as well as the quality and features of those products. For example, th e refrigerators that were available for sale in the 1960s are no longer available today, and the technologies, features and conf igurations of refrigerators today did not exist in the 1960s. Any measurement of long term price tren ds needs to account for these gradual but significant changes.

For US data, we use price indices published by the Bureau of Labor Statistics (BLS) and the Bureau of Economic Analysis. [See the Supplemental Informati on (SI) for additional detail regarding price indices and the calculation of experience curves.] The B LS provides both consumer price indices for retail purchase prices and producer price indices for the prices received by producers for their products. We use the all-items consumer price index (CPI) to adjust for inflation in our analysis. In some cases our CPI data is sourced indirectly from the BLS using tables published by Gordon [25].

In the LCC calculations, to estimate an average pric e in a recent year, we use the shipment-weighted average price obtained from the LCC spreadsheets asso ciated with the Department of Energy’s (DOE) most recent rulemaking or notice of proposed rule making for a particular appliance. These spreadsheets are available on the DOE’s Appliance Standards webs ite as part of technical support documents created for each rulemaking. We obtain the historical infla tion- and quality-adjusted prices by multiplying this recent shipment-weighted price by the appropriate inflation- and quality-adjusted price index.

We obtained data to estimate historical average ener gy use from a variety of different sources, including the Association of Home Appliance Manufacturers (AHAM), recent DOE rulemakings, DOE’s Energy Information Administration’s (EIA) Residential En ergy Consumption Surveys [26], and the published literature [27]. For periods with missing or incomplete data, we interpolate from the historical trends. In the case of clothes washers, we also consider water usage and water efficiency when calculating operating costs. Water usage data were obtained from recent DOE rulemakings.

‡ The experience curve literature focuses on product cost ra ther than price. Although price often deviates from the cost of production, we assume that on average the pr ice trend is a good approximation of the cost trend.5 We use historical average retail prices of electric ity for residential consumers from the Annual Energy Review published by EIA [28]. For years prior to 1960, we extrapolate the retail price of electricity using the CPI for electricity [29]. In the case of water, the average retail price in 2008 was obtained from a recent DOE rulemaking analysis, and extrapolated to prior years using the CPI for water and sewage
maintenance.

Cumulative unit shipments to the US market for each product are estimated using annual shipment data from recent DOE rulemaking analyses. Other inputs to the LCC calculation, such as the appliance lifetime and discount rate, are similarly estimated using data from these DOE analyses. We follow DOE’s practice of using a weighted-average consumer cost of capita l from a variety of debt and asset classes to represent the discount rate, because that average represents the fi nancial cost of money to a consumer. For a review and discussion of the issues surrounding discount rates and the energy efficiency gap, we recommend Jaffe and Stavins [30]. Depending on the rulemaking, the average discount rate for each appliance type was found to be 5.0 ±0.5%. For simplicity, we use an average real discount rate of 5.0% in the LCC calculations for all appliances.

For refrigerators in the Netherlands, we obtained pr ice and energy use data from Weiss et.al. [31] and
from the German market research firm The GfK Gr oup. These refrigerator price data are not qualityadjusted. We calculate the inflation adjustment us ing the Harmonized Index of Consumer Prices (HICP) from Eurostat [32]. We obtained nominal pre-tax electricity prices from Eurostat [33], and estimate posttax electricity prices using tax rates from the U.K. De partment of Energy and Climate Change [34]. We use the average tax rate for 2008 and 2009 as the assu med tax rate for the analysis period. Historic shipments were obtained from an Ecocold report [35] . Shipments to the EU-15 nations were used as the basis for experience, since manufacturers tend to sell products across the European market. The lifetime
and discount rates are assumed to be constant in time and the same as those of US refrigerators.

The ultimate product of this data collection, processing, and integration is a set of yearly time series for cumulative shipments, prices, and LCCs, for four US appliances and for refrigerators in the Netherlands. Shipments data refer only to the US market (or th e EU market for Netherlands refrigerators). Global shipments would be a closer indicator of cumulative experience, but provided that manufacturers’ global shipments grow consistently with their US/EU ship ments, power-law experience curves can be accurately fitted using the more limited data set. We combine th e price and LCC data with the shipments data to obtain experience curves, P(Q) and LCC(Q)

.

4. Efficiency policy and changes in long term trends Figure 1 shows the results of fitting experience curves to price and LCC for four major US appliances (refrigerators, clothes washers, room air conditioners and central air conditioners) and for refrigerators in the Netherlands. These products were chosen b ecause multi-decadal information was available both before and after the establishment of standards (“pre- standards” and “post-standards,” respectively). In all cases, the price and LCC generally decline with time, and a significant transition can be seen in the LCC decline rate parameter near the initia tion of standards. A distinct acceler ation of the price decline can also be seen for clothes washers, room air conditioners, central air conditioners, and refrigerators in the
Netherlands.6 We consider the post-standards period to begin after th e issuance of the first standard likely to affect the market under consideration. In most cases, the first standard corresponds to a federal standard, or to a European Union standard in the case of refrigerators in the Netherlands. We also consider California standards given that California is the most populous US State and therefore constitutes a significant fraction of the US appliance market. In some case s, California efficiency standards may have been effectively treated as a national standard by manufacturers.

We fit the data with a simple mathematical mode l that includes two power-law experience curves with different decline-rate parameters b , corresponding to the periods before and after a transition year. The decline rates, transition year, and overall normalizati on are treated as free parameters, allowing us to calculate the transition year within a 95% conf idence interval using standard maximum-likelihood techniques. [See the SI for further details. The SI also evaluates the sensitivity of results to variations in model formulation.] Table 1 provides the resulting transition years and confidence intervals of these experience-curve fits for US refrigerators, clothes w ashers, room air conditioners, central air conditioners, and Netherlands refrigerators, and compares them to the first year of efficiency standards for these products.

Table 1. Results for least-squares, two-slope experience curve model fit of price and LCC for the appliances considered in this study; 95% confiden ce intervals were calculated from the appropriate   distribution. For reference, the year of the first effi ciency standard implementation is also shown for each appliance.

Transition Year Pre-Transition Decline Rate b Post-Transition Decline Rate b

Appliance First Efficiency Standard Year LCC Price LCC Pr ice LCC Price
Refrigerators (US) 1977 1977.2 ିଷ.ଶ ାଶ.ଷ 1995.0 ି଼.଴ ାଷ.଻ 0.36 ି଴.଴଼ ା଴.଴ଵ 0.84 ି଴.଴଴ ା଴.଴ହ 1.25 ି଴.଴ହ ା଴.଴଴ 1.51 ି଴.ଵସ ା଴.଴ସ

Clothes Washers (US) 1988 1989.8 ିଵ.ଶ ାଵ.ଽ 1986.9 ିଵ.ହ ାଵ.ଷ 0.12 ି଴.଴଴ ା଴.଴ସ 0.45 ି଴.଴ଷ ା଴.଴ଷ 1.20 ି଴.ଵ଴ ା଴.଴ଵ 0.98 ି଴.଴ଷ ା଴.଴଴

Room Air Conditioners (US) 1979 1976.3 ିଶ.଼ ାଵ.଼ 1972.8 ିଵ.଺ ାଵ.ଷ 0.16 ି଴.଴ଵ ା଴.଴ସ 0.27 ି଴.଴ସ ା଴.଴ଵ 0.76 ି଴.଴ସ ା଴.଴଴ 0.75 ି଴.଴ସ ା଴.଴ଵ

Central Air Conditioners (US) 1979 1975.5 ି଴.ଽ ାସ.଴ 1973.9 ିଶ.ଷ ାଷ.ଵ 0.01 ି଴.଴଴ ା଴.଴ଷ 0.07 ି଴.଴ଷ ା଴.଴ଷ 0.39 ି଴.଴ଷ ା଴.଴ଶ 0.28 ି଴.଴ଷ ା଴.଴଴

Refrigerators (Netherlands) 1999 2000 ିଶ଺ ାସ 2001 ିଵସ ାଶ 0.45 ି଴.ଵହ ା଴.ଵସ 0.25 ି଴.ଵସ ା଴.ଷଶ 1.08 ି଴.ଵଵ ା଴.ଵଵ 0.80 ି଴.ଵଶ ା଴.ଵଶ

The correspondence between calculated transition year a nd first efficiency standard year can be seen in figure 2 with 95% confidence intervals shown as error ba rs. In almost all cases, the data yield a transition year that is close to the onset of standards, w ith the exception of US refrigerator purchase price. The confidence intervals for the Netherlands refrigerato r case are relatively large because of the larger variance in the available price and efficiency data.7 Figure 1. Price and LCC trends for appliances pre-st andards and post-standards. Unfilled symbols indicate pre-standards data, while solid symbols indi cate the post-standards era. Lines indicate best-fit experience curves from the two-trend model. Circles indi cate transition points in the decline rates. Data
are shown for United States ( A ) refrigerators, ( B ) clothes washers, ( C ) room air conditioners, and ( D ) central air conditioners, as well as for ( E ) Netherlands refrigerators. Ne therlands refrigerator price and LCC are shown per 100 liters of volume, and cumulative shipments are for the EU. In figures 1( A) – (D)

, Room AC 

### C

5 25 50 250 Central AC 

### D

Cumulative Shipments (millions) 250 500 750 1000 2500 5000 7500 10000

Refrigerators 

### APrice and LCC(2008$)

25 50 75 100 250 500

750 1000 2500 5000 7500 10000

Clothes Washers 

### BPrice and LCC(2008$)

Cumulative Shipments (millions)

50 75 100 250 500 100 250 500 750 1000 

### E

EU 15 Cumulative Shipments (millions)Netherlands RefrigeratorsPrice and LCC (2008$)

Pre-standards Price Post-Standards Price Pre-standards LCC Post-Standards LCC Two power law fit197819801987199019932001197919811983198519922005197919812000199019882004199419992002Price and LCC per 100 L volume (2008$)8 the dashed and solid arrows represent California a nd Federal standards, respectively. In figure 1( E) , the dashed arrows indicate a voluntary agreement with manufacturers, and solid arrows indicate mandatory
standards.

Figure 2. The calculated year of transition to an accelerat ed price or LCC decline, as a function of the year standards are first enacted. Open symbols corres pond to price transition year, closed symbols to LCC transition year. If the change in slope of the expe rience curves in figure 1 o ccurred at the time the standard was introduced, the data poi nts would lie on the dashed line.

5. Trends in the incremental price of efficiency: the case of US refrigerators The price and LCC trends observed in figure 1 clearly diverge from historical, pre-2011 US regulatory forecasts, which assumed no future price declines in the absence of new standards, and which projected an increase in appliance price following the introduc tion and subsequent upda tes of standards. We compiled historical, engineering-based estimates of the relationship between appliance price and efficiency that were developed in DOE regulator y analyses accompanying the consideration of new or updated efficiency standards for refrigerators. For re frigerators, new mandatory Federal EE standards had initial compliance dates of 1990, 1993, 2001 and 20 14, with supporting analyses performed in 1982, 1987, 1989, 1995, and 2010. At the time each analysis w as done, the incremental cost of higher efficiency was based on the current market costs of introducing technologies to achieve a given efficiency. The full historical sequence of price-efficiency estimates fo r 17- to 18-cubic-foot refrigerators with top-mount freezers and automatic defrost is shown in figure 3 (A) . Note that the most energy-efficient refrigerator considered in 1989 had higher energy use than the l east efficient refrigerator considered in 2010, and the estimated price of achieving that efficiency was roug hly twice the price estimate of the least efficient9 2010 refrigerator. Over the period considered, the e fficiency of the least efficient refrigerator on the market improved at an average rate of 4% per year while its price dropped 2.5% per year.

Figure 3. Modeling of energy use vs. price. ( A ) Engineering-based estimated purchase price of US 17- to 18-cubic-foot top-mounted refrigerator-freezers as a func tion of annual energy. Solid lines show the fit to the data using equation (2). ( B ) Evolution in the modeled price of the baseline, least efficient refrigerator 200 400 600 800 1000 1200 1400 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700



## A 1982 1987 1989 1995 2010 FitInflation-adjusted Purchase Price,PA(2008$)



### Annual Energy Use, UEC (kWh/yr)10 on the US market in each year (green points); a refrige rator with a fixed efficiency of a 1982-era baseline unit (blue points); and the incremental price associat ed with a fixed efficiency increase relative to the 1982 baseline (red points). Solid lines show the exponen tial fit of (4) to the red and blue points. The incremental price for 1982 (hollow symbol) is excl uded from the fit because 490 kilowatt-hours per year (kWh/yr) is well outside the estimated price-efficiency ra nge for that year, so this point is derived from an extreme extrapolation.

We mathematically characterize the pric e-efficiency relation as a baseline price ܲ ௠௜௡ plus a power-law relation between unit energy consumption (UEC) and th e additional price of achieving that efficiency
level:

0 

### ( ) min UEC A 

### UEC

U P UEC C P P E 





###         (3)

Here, min 

### P is the minimum price of an appliance, UEC 

### P is the additional price required to purchase an
appliance whose energy consumption takes a reference value 0 

### UEC (which we are free to choose), and



###  is the power law exponent, which, in economic term s, represents the elasticity of the energy-related price component with respect to efficiency. Figure 3 (A) illustrates a reasonably good fit to the engineering-based price-efficiency estimates using this simple functional form, where we have fit the model in (3) to each of the five price-efficiency estim ates separately, yielding five sets of fit parameters (see Table 2).

Table 2 . Results of fitting engineering-based price-effici ency estimates for refrigerators with a power-law model (3).

Year P min P UE C UEC 0  R 2
1982 1260 38.1 1350 2.32 0.995 1987 1270 20.7 925 6.47 0.991 1989 961 37.6 955 4.07 0.995 1995 796 67.9 700 2.65 0.993 2010 717 36.8 482 5.90 0.991

From these fits we can estimate the evolution of the pr ice of a refrigerator with fixed efficiency and of the incremental price of a fixed increase in efficiency . For each of the five fits shown in figure 3 (A) , figure
3 (B) shows the actual baseline price, the modeled price of a 1982-era baseline unit, and the modeled price increase required to improve the 1982 baseline unit to a reference energy consumption of 490 kWh/yr, a value chosen since it lies in or near the range of UE C values covered by most of the engineering estimates
after 1982.

The evolution of our fit parameters over time demonstrat es that the price of efficiency declines at a much faster rate than the price of the baseline appliance. We can quantify this by fitting our price measurements to a Moore’s-law type model in which price declines exponentially with time:

0 ( ) 0 X t t X X 

### P Pe 

  

###  (4)11 where X represents either the 1982-baseline-efficiency unit or a unit with a UEC of 490 kWh/yr ( see the SI for more detailed discussion of Moore’s-law type pr ice trends). If the price of refrigerator efficiency mirrored the overall trend in refrigerator price, we mi ght expect the incremental price of a fixed increase in efficiency to decrease at the sa me rate as the quality-adjusted price: 2.5% per year. This assumption has been used in recent appliance standards rulemakings that have incorporated experience curves [36]. Instead, the data presented here show that while the pr ice of a fixed, low-efficiency refrigerator declines
at that rate, 

### 0.025 min 

###   , the incremental price of improving that efficiency by a fixed amount drops
much more quickly: 

### 0.19 UEC 

###   , or a rate of price decline of roughly 19% per year between 1987 and
2010 (see figure 3 (B) )

This rapid drop in the price of efficiency may be what allowed the price of refrigerators to continue to decline even as efficiency has improved at 4% per year. The incremental price increase of a given efficiency improvement rapidly became negligible co mpared to the more slowly declining baseline price.

6. Price-efficiency trends for European Union refrigerators While the results for US refrigerators give some indi cation that the price of efficiency may have rapidly decreased over time, engineering curves are estimat es, not observed prices. Aggregated European refrigerator sales data from ten European countri es (Austria, Belgium, Great Britain, Italy, the Netherlands, Germany, Spain, and France, Sweden and Portugal) enable us to model the observed efficiency-categorized price over time directly. § Equivalent data are not available for the US because the US does not have labeling requirements with multiple EE categories.

§ Europe uses a substantially different refrigerator test procedure than does the US; energy use figures are not directly comparable.12 Figure 4 . Market-based price-efficiency estimates for European refrigerators illustrating the evolution over time. Points correspond to categorical averages ove r several years. Solid curves show the fit to these categorical averages using (5).

As with the Netherlands data, we use sales-weight ed averages of retail prices (not quality-adjusted) obtained from The GfK Group. We adjusted prices for both inflation and consumer purchasing power differences between countries [37] and converted all prices into 2008 Austrian purchasing power parity (PPP) Euros. We obtained comparative price indices for purchasing power parity adjustments between countries from table 1357 of the 2012 US Statistical Abstract [38].

We obtained refrigerator price data binned according to EE grade, which range from A++ to G for each country in the sample. The grades correspond to an en ergy efficiency index (EEI), which is defined as a unit’s energy consumption divided by the consumptio n of an average model (based on all models on the market from 1990–1992) for units of the same adju sted volume. The European Commission adopted the grades in 1992 (92/75/EC). The grades were implem ented into national ordi nances between 1994 and 1998. The A+ and A++ grades were introduced in 20 03 (2003/66/EC) and began being implemented in 2004. To scale the EEI to the energy use of a refrigera tor, we set an EEI of 100% at 463 kWh/yr, the value the European Commission cited in its COLD II report [39]. Refrigerator volume was approximated as constant during 1995–2009.

Similar to the Netherlands refrigerator analysis, Euro pean electricity prices are estimated using data from Eurostat [40] and UK Department of Energy and C limate Change [41]. We use the same lifetime and discount rate assumptions as those for US refrigerato rs: 17.1 years and 5.0% per year, respectively.

We perform a simplified fit to the European data using (5) and assuming an e xponential dependence of price on time (i.e. a form of Moore’s law: see SI for details): 120 150 180 210 240 270 300 330 360 390 420 300 400 500 600 700 800



## CInflation-adjusted Price, PA(2008 Euro)



### Energy Consumption, UEC (kWh/yr) 1995-1998 1999-2002 2003-2005 2006-201013 0 ( ) 0 0 

### ( ,) ( / ) t t UEC UEC 

### P UEC t P e UEC UEC  

   

###  (5)

where is a reference price at a particular reference annual energy use UEC 0 and reference time t 0 .

Figure 4 shows the fit to the European market data , which describes the data reasonably well (see SI for additional details). Within a category corresponding to an EE grade, the average inflation-adjusted price declined by 4.5% per year between 1995 and 2009, while the average shipment-weighted inflationadjusted price computed across all efficiency cate gories declined by approximately 1.3% per year. The market average estimated UEC simultaneously decreased by 4.2% per year. As in the US, European refrigerator prices have declined even as efficiency po licies have increased the av erage efficiency on the
market.

7. Life-cycle cost optimization By analyzing price trends for baseline prices and fo r the incremental price of efficiency, it may be possible to generate more accurate price-efficiency forecasts and thereby devise more optimally beneficial policies. We can combine (2) and (3) above to ob tain an equation for LCC as a function of UEC. Minimizing this equation with respect to UEC then yi elds the following optimization condition (see the SI for a detailed derivation):

min A UEC 

### LCC P P   

. (6)

Inserting the Moore’s-Law model for the time evoluti on of price from (4) gives an equation for the time
evolution of the minimum LCC:

0 0 1 ( )/(1 ) 0 0
0 ( ) 

### ( ) ( ) min UEC tt tt A UEC
U C L

E 

### PVOC UEC LCC t P e P e P  

   

###     

   

###  

      , (7)

where 0 

### ( ) L 

### PVOC UEC is the present value of the operating costs for an appliance with lifetime L whose
UEC is equal to 0 

### UEC . Equations similar to this one could be used to derive more accurate forecasts of
the LCC-minimizing UEC value, thus enabling EE po licies that more precisely maximize the economic
benefit to consumers.

Figure 5 illustrates using these equations to forecast the UEC that minimizes refrigerator LCC in 2020, based on the 2010 price-efficiency relation shown in figure 3 (A) . If the price of all refrigerators is predicted to decline by 2.5% per year regardless of efficiency level, the LCC-minimizing UEC is expected to decline from 410 kWh/yr in 2010 to 400 kWh/yr in 2020. This is the approach to price trends that is currently used in DOE EE standards analys is, and which was first utilized in support of the refrigerator standard issued in 2011 [36, 42]

. If, instead, the incremental pri ce of efficiency is forecast to decline at 19% per year (while P min continues to decline at 2.5% per year), the LCC minimum point is expected to decrease an additional 17.5% to 330 kWh/ yr, yielding an additional LCC reduction of $97 for each of the estimated 13 million refrigerators sold in the US in 2020 [42]. If all the refrigerators purchased in 2020 saved the additional 70 kWh/yr enable d by the faster incremental price decline, they 0 UEC 

### P14 would save a cumulative 15 TWh of electricity over their 17-year lifetime, which corresponds to approximately 9 million metric tons/yr of avoided CO 2 emissions with present-day electricity generation. Determining price trends at the required level of gran ularity for such a forecast is challenging, and it may not always be possible to produce forecasts with suffici ent certainty for use in a regulatory analysis. In this case, given the potentially rapid price evolution of efficient technologies, regular regulatory updates are especially important to maintaining EE polic ies that are close to the social optimum.

Figure 5. Dependence of LCC on baseline and incremental price declines. The blue curve shows the dependence of refrigerator LCC on UEC in 2010 according to the model in figure 3 (A) (the LCC rises at high UEC because increased energy costs outweigh decre ased first cost). The solid portion of the line indicates the range of efficiencies considered in the refrigerator rule published in 2011. The green curve shows how the LCC may change in 2020 if both the baseline and incremental price of efficiency decrease at 2.5% per year. The magenta curve illustrates how the LCC in 2020 may change more rapidly if the incremental price decreases at 19% per year instead . The arrows with corresponding color indicate the
LCC minima. The black arrow indicates the minimu m efficiency performance standard that was determined in 2011 and will go into effect in 2014.

8. Conclusion By examining the 35-year history of appliance standard s, we observe an accelerat ed decline in appliance LCC post-standards in all cases studied and an accelerat ed decline in appliance price in most cases. We 

### 200 300 400 500 600 1000 1100 1200 1300 1400 1500 1600 1700 1800
2010 2020, Uniform Price Decline 2020, Faster Incremental Price DeclineLife-cycle Cost, LCC (2008$)



## Unit Energy Consum ption, UEC (kWh/yr)15 also find that the incremental price of efficiency ge nerally decreases faster than the baseline price of appliances, which may help explain the sustaine d long-term price decline under standards.

Since 1978, the US Department of Energy has anal yzed energy-efficiency standards for a growing number of residential appliances and devices using a standard-setting process that is governed by a number of procedural and technical requirements. Th e regulatory analysis of each standard includes a “bottom-up” engineering estimate for the incremental cost of achieving higher efficiency. Prior to 2011, declines in cost described by learning curve trends were not included in this analysis. Since 2011, learning-curve trends have been used in the determ ination of US appliance efficiency standards. The regulatory analysis currently uses only the learning trends of the base price and assumes no additional innovation induced by EE standards. The present analysis suggests that this approach is likely to be
conservative.

Our analysis indicates that the rate of price decline fo r the incremental price of efficiency may be as much as an order of magnitude faster than for the baseline price. If this observation is correct, better modeling of the potentially much faster price decline fo r efficient technologies may produce more accurate forecasts of cost-effective energy savings. Future r esearch could help determine how to model dynamic market reactions to regulation and the potentially co mplex time dependence of market distributions for regulated products.

Some of the possibilities for future research may be indicated by some of the new models of price dynamics in regulated appliance markets have been e xplored by very recent work undertaken by Spurlock [13] and Van Buskirk [11].

Spurlock evaluated a model of second-degree pr ice discrimination in a quality-differentiated market for household durables based on the classic work by Mussa a nd Rosen [43] for US clothes washer standards in 2004 and 2007. Spurlock found th at “along with a level drop in prices at the time the new standard went into effect, price trends broke downward, pa rticularly following the 2007 standard change. The within-model downward trend in prices was particularly pronounced in the higher efficiency categories.”

In a similar exploration of a differentiated market, Va n Buskirk explored a different style of model for the dynamics of the European refrigerator market wher e learning-by-doing occurred at different rates for different efficiency categories of refrigerators. Becau se cumulative experience scaled up more rapidly on a per-category basis as higher efficiency refrigerators were adopted by the market, this model reproduced the observation of a rapidly changing incremental cost of efficiency that is noted by the present study.

Alternatively, some of the observations of the accelerated decline of appliance purchase price under standards may also be explained as a spillover effect [44] of improved efficiency technology. That is, learning -curve-driven productivity improvements in the manufacture of high-efficiency products could spillover and potentially yield productivit y improvements for baseline products.

Substantial research into multiple potential modeling approaches will likely be required to settle on new modeling techniques that can reliably produce forecasts c onsistent with the empirical observations of this study. But if such new models can be develope d, they may improve the dynamic forecasting of the interplay between innovation and regulatory impacts. Such improved forecast methods are likely to aid in16 the development of more optimal energy-efficiency policies that could provide additional economic benefits for consumers and climate mitigation efforts.

Acknowledgements This research is supported, in part, by the US Depa rtment of Energy, Office of Energy Efficiency and Renewable Energy, under contract No. DE-AC02-05C H11231. Gabrielle Dreyfus assisted with review and preparation of manuscript for submission. Th e corresponding author acknowledges funding support from the Collaborative Labeling a nd Appliance Standards Program ( www.clasponline.org ).i REFERENCES

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