ELSEVIER 

## RESOURCE and ENERGY ECONOMICS Resource and Energy Economics 16 ~,~994)91-122



## The energy paradox and the diffusion conservation technology

Adam B. Jaffe:~*and Robert N. Stavinsb 

## of

D~Tartment ,!fEconomics, ttarrard University, andNational BureauofEconomicResearch, Cambridge, MA, USA hJohn F.Kennedy School~?¢ Government, ttarrard Unirersit)',andResourcesforthe Future, 79John F. Kenned.rStreet, Cambridge, MA 02138, USA
Final versionreceivedNovember 1993

Abstract

We develop a frameworkfor thinking about the 'paradox' ofverygradual diffusionof apparently cost-effective energy-conservation technologies. Our analysis provides

some keys to understanding why this technology-diffusion process i.s gradual, and focuses attention on the factors that cause this to be the case, including those associated with potential market failures - information problems, principal/agent slippage, and unobserved costs - and those explanations that do not represent market failures - private information costs, high discount rates, and heterogeneity among potential adopters. Additionally, our analysis indicates how alternative policy instruments - both economicincentives and direct regulations can hasten the diffusion of energy-conservingtechnologies.

Key words: Energyefficiency.;Cons:lvation; Technologydiffusion
JEL classification: Q48; 033

*Correspondingauthor.Tel:617-495-1820;Fax: 617-495-1635. Jaffe is an Associate Professor of Economics at Harvard University and Faculty Research Fellow of the National Bureau of Economic Research.Stavins is ar~ Associate Professor of Public Policy and a Senior Research Associate of the Center for Scienceand International Affairsat the John F. Kennedy School ofGovernment, Harvard University, and a University Fellow ofResources for the Future. This paper is part ofan ongoing research project on the diffusion of energy-conserving technology. We thank Harvey Brgoks, Trudy Cameron, James Hines. Maryellen Kelley, Sharon Oster, Ariel Pakes,Alex Pfaff,Peter Wilcoxen,Richard Zeckhauser, and participants at the NBER SummerInstitute, the NBER-Umversities Research Conferenceon the Economicsofthe Environmenl, and the KennedySchoolFaculty Seminar for

0928-7655/94/$07.00 ~('i1994ElsevierScienceB.V.Allrightsreserved SSD! 0928-7655(94)E00003-392 A.B. Ja!ie and R.N. Stavm.~ Resource aml Em'rgv Ecommm'~ 16 ¢19941 91 122

I. Introduction
In the long run, the development and ",videsrread adoplion of ne~ technologies can greatly ameliorate what, in the short run. sometimes appear to be overwhelmingconflicts between economic well-being and environmental quality. With existing technology, problems such as emissions of greenhouse gases and disposal of l~azardous wastes pose difficult choices between potentially irreversible damage to the environment and high economic costs ofcontrol. But ifhistory isany guide, we know that over a period ofdecades changes in technology can alter dramatically the nature of these tradeoffs. Therefore, the effect ofpublic policies on the development and spread ofnew' technologies may, in the long run, be among the most important determinants of success or failure in environmental protection tKneese and Schultz, 1978). In order to achicve widespread benefits from new technology, three steps
arc required: im'ention - the development of a new technical idea; innoration

- the incorporation of a new idea into a marketable product or a usable commercial process for the first time; and dijli~sion - the typically gradual process of adoption of the new product or process by potential users. The third element - the diffusion phase - has historically been neglected both by research and public pc,': 'v.t Recently, however, technology diffusion has moved into the policy spotlight as a r,.zsultof concern over the role played by carbon dioxide (CO:) emissions in fo,_~teringglobal climate change. The largest anthropogenic sour~'c of CO, emissions is combustion of fossil fuels for energy generation,

so reduction in energy use is potentially or,e ofthe most potent options that cx~st~ fo: reducing the risk of ~lobal climate change. It is widely accepted that energy use could be reduced significantly through more widespread adoption of existing technologies (Norberg-Bohm, 1990). It is almost as widely accepted that much un-adopted technology is cost-effective at current prices.-" This has led to a decade-long discussion of the 'paradox' (Shama,

helpful comments on earlier work of the project, and we thank ,'in anonymous reviewer for hc!pful conmlcnls on this paper. Research assistance bv Jesse Gordon and funding from the U.S. l!.qxironmcntal Protcclion Agency arc gratefully acknowledged. t-or a recent example ofan invcsligaliort ofthe innt~vation component, see Georg el al. (19921. A set of ca~,e~tt,dies of the three elements in the ct~ntext of "environmental lechnologies" is pro,,idcd b,, Kemp cl al. 119921.

:The constrain! on energy improvements m the short term is not primaril~ technological. The t~rimar.~barrier i~,in,~ufficient implementation ofexisting cost-effectivetechnologies' (Carlsmilh et al.. 1990. p. 251."Our stock ofhousing and appliances is still far less energy efficient than would be ccom~mic:dl~ optimal" ~I_'.S.Department of |'~nergy 1991. p. 42L Prominent support for this notion came from the N;llional Academy of Science.,. 119911in its finding that U.S. carbon dioxide 1('O21 cruise,

ions could be significanll.~ reduced ;is parl of :In effort to address the threat of grce'o.housc-iilduccd c]imale change lh:ough The adoption ofcurrently cost-effectiveenergy efficient,, lechmdogies.A.B. Jalle and R,N. sIovm.~ Rc.~o**rccand Enert,y t'~',m,m~i~',~I~ ~19~4p91 122 93



### 1983) of inadequate diffusion of apparently cost-effective energy-conserving technologies. If all of the costs and benefits of energy use were internalized, then the potential existence of such a paradox might be of academic interest, but it would not have obvious policy relevance. Ifthere are significant externalities associated with burning fossil fuels, however, then the paradox becomes much more important. Indeed, the existence ofsuch externalities couldjustify public policies tt, reduce energy use. The relative effectiveness and efficiencyofalternative policy mechanisms to achieve this goal will depend on the nature of the energy-conserving technology diffusion process. In particular, ifthe diffusion process is unaffected by economic forces, then the economist's standard argument that some sort of market mechanism is the best way to internalize the social costs of CO2 emissions would presumably carry much less weight than otherwise. If people are not using technologies that are cost-effective at today's prices, should we rely on carbon taxes or other policies that would raise the cost of energy use? We are much more likely to achieve success, the argument goes, with regulatory mandates requiring the use ofparticular technologies.3 The climate-change/energy-conservation arena presents a particularly timely example ofthe broader debate about the relative merits of'commandand-control' regulation - legal standards requiring particular levels of perforn .nce or particular technologies - and "economic incentives' - such as emission charges, tradeable permits, deposit-refund systems, and elimination ofgovernment subsidies.4 This paper provides a conceptual framework within which wecan examine

3Thetechnology-standardapproach hasbeenthefavoredapproach in thepast and continuesto be favored by most politicians today. Widely discussed possibilities include uniform national building codes and mandatory energy efficiencystandards for heating and cooling equipment and othermajorappliances. 4For descriptions and examples of these various categories of command-and-control and market-based environmental-protection mechanisms, see Hahn and Stavins {1991).There are two distinct dimensions along which incentive-based and conventional environmental policies differ. First, incentive-based policies can lead. in theory, to a cost-effective(cost-minimizing) allocation among firms of the overall burden of achieving any given level of environmental protection, in contrast with technology standards and {uniform) performance standards, which typicallydo not lead to cost-effectiveallocations. Second,incentive-based approaches can result in 'dynamicefficiency'byprovidingon-goingir.centivesforfirmsto adopt new,improved 1lower cost} pollution-control technologies; Ihis is in contrast with command-and-control approaches, which tend to lock in existing technologies(Bohm and Russell, 1985).It is this latler, dynamic, superiority that i'~examined in this paper. In general and on a theore!ical level,the superiority {in terms of inducing technological innovation and diffusion) of incentive-based approaches, compared with conventt,ot~al command-and-control approaches is clear {Milliman and Prince, 1989; Downing and White, 1986). It should also be recognized, however, that under certain circumstancesincentive-based approaches could actually reduce firms' incentives to adopt new technology{Malueg, 1989).94 A.B. Ja/]i'and R.N. Stavin.~ Re.wmrce and Energy Ectmomic.~16 (1994) 91- 122



### two inextricably !raked questions: what factors determine the rate of adoption of energy-conserving technologies; and what effects can economic incentives and c,mventional regulations have,in encouraging such adoption. By framing these questions within economic models, we hope to help clarify the 'paradox' of existing adoption patterns,s We proceed by developing a pair of theoretical models that: (1) are rooted in existing thought on the economics of technology diffusion: 12) are based on firm and individual optimizing behavior; (31 incorporate aspects c( the process that some observers claim explain the 'paradox:' and (4) allow for the impact of regulaticn on the adoption decision. Our two models reflec, the two important contexts in chich adoption decisir,ns take place. First, there are situations in which a particular activity is being undertaken which prompts 

### a decision about whether or not 

### to incorporate an energy-conserving technology at a specified point in time. Second, there are situations in which a decision must be made not only about whether or not to adopt an energy-efficiency technology, but also about when 

### to do so, if at all. In order to analyze both situations, we consider the incorporation ofenergy-conserving technologies in new residential structures and in existing ones. The use of such technologies in buildings is important in overall energy use,~' and the existence of building codes provides a context in ,shich to contrast the potential effects of economic incentives and regulations in encouraging adoption behavior. The next section of the paper provides some background on technology diffusion and cnergy-conscrva:ion investment decisions. Section 3 develops a thcorctical model of the decision to incorporate a given technology in a newly constructed home, while Section 4 focuses on decisions to retrofit a technology in an existing structure. We explore the policy implications ofthe analv:is in Section 5, and we provide a brief summary and conclusion in Section 6.



### 2. Background:technology diffusionandenergyconservation
2.I. Economic mo&'L~"oftechnological d(/.lUsion"



### From the mcch.mical reaper of the nineteenth century {David, 1966), through hybrid corn seed (Griliches. 1957), chemical process innovations

Needles.,, ~o ,,ay, approaches other lhan e¢Ollqinlic models can be used to examine these queqions. See, forexample, Cebon (1992). "About 25",, ofprin,:,.ryenergy consumplion is used for heating, cooling, hot water and lighting in residential and commercial buildings IU.S. Departmenl ofEnergy, 199I~. -Thb, section pravide,~ a brief o,,erview, of tke te~.hnologv diffusi,m lilcrature. For more ~horo.;gh re~ic~s, see Stoneman {1983k Stt~n~lll:.tnil9~6): David ~1986): and Thirtle and Ruttan {ItJ,R.6 ~.A.B. Jal]~' and R,N. Sire'ins Rcsm~rcc and Fm,rgy,'con+m+ic.~16 ~/994~91 122 q5



### (Davies, 1979),steel furnaces {Oster, 1982)and optical scanners tLevin et al., 1987) in tile twentieth century, research has consistently shown that diffusion of new, economically superior ~echnologies is never instantaneous. It typically follows an s-shaped or "sigmoid" curve, such that the adoption rate is initially slow, then faster, and then slower again as saturation is approached. Most models of technological diffusion are intended to pl'Oduce dynamic paths with these general properties Perhaps the simplest way to generate an s-shaped diffusion curve is with

an 'epidemic model" (Stoneman, 1983).This approach focuses on the spread of information regarding the existence and profitability of the innovation. People cannot use a technology of which they are unaware, and they are unlikely to use a technology that they do not understand. If knowledge of existence and profitability are increasing functions of prevalence of use of a technology, then use of that technology can be expected to spread like a disease: the probability that a non-user will adopt in any time period ,~illbe

an increasing function of the fraction of the population that has already adopted, Ifwe denote the stock ofusers that have adopted the technolog2 ry time t as S,, and the universe of potential adopters as 

### U,, then a simple epidemic model suggests that the technology will diffuse according to: 

# ds, (s,). s,) di=..\u,]

The first factor in brackets is the probability ofencountering an "infected' agent and contracting the disease (adopting): the second fa,'tor is the proportion of the population that is "healthy' atd thereby candidates for 'infection' (adoption). The multiplier, a, is the 'infectiousness' of the disease, and parameterizes the speed of the diffusion process. Integration of this equation with respect to time yields the logistic function with the characteristic

## shape. in its simplest form, the epidemic model has little economic or other analytical content, but the constant, a, can depend on economic forces. In this way, the "infectiousness' of the disease can be linked to the profitability of the diffusing innovation. The pioneering work of Griliches (1957) established the notion that the process of a gradually diffusing, superior technology could thus be understood in an economic framework, with the rate of diffusion being partly determined by the (expected) economic return to adoption. Subsequently, Mansfield (1968) demonstrated that ttw rate of diffusion can also depend on the size of adopting firms, the perceived riskiness of new technology, and the absolute magnitude of the required investment. In such models, it is possible that the new technoit~gy is profitable for all firms: it takes time for all to adopt only because some have not been "exposed." Indeed, these models generate gradual diffusion even ifall96 .-I.B.,tal/i' aml R.N. ,gtari*r.~ Re.~ot~rct' tltltlEtl~'r~,.t" E¢'ttlomit'.~ 16 r1994) 91- 122

potential adopters are identical. Economic factors explain which innovations diffuse fastest, or in which regions a particular innovation diffuses fastest, but not ~hich potential adopters actually use lhe technology first. As an alternative, David ~1969~proposed heteroge~eity among potential adopters as an explanation (or the gradual nature of the diffusion process. His model -- based on inherent difference~ among adopters - is sometimes known as the 'probit" approach (Stonem.~n. 19831. ~ David posited that the population of potential adopter.', of an ~,:~,~vation differ from one another in v~ays that affect the desirability of tech:~ological adoption. For example. consider the innovation to be triple-pane c,indow glazing and the important dinaension that affects its desirability '.,, be local climatic conditions. An individual deciding whether to adopt ~iq:.~innovation faces an investment decision. Hc can incur a certain cost ~,"Jav, which will reduce his home heating costs now and in tt~efuture, or hc can wait. thus saving the cost of purchasing and installintz tim technolog.,,. The co!der the climate in winter
.,,,a ,h,, '"~""'*'" the ,4

.....',- m ~,um

...... ,,,. more att,,.c,,ve will this li,~l I 1 ~t! ,L&L%, investment be. In this framework, one can think of there being a 'threshold' climatic inde:,;,'~ above which it is profitable to adopt the innovation and below which it is not. Over time, the cost of the triple-pane windows may fall and/

or their performance may improve, encouraging homes in more temperate climates to adopt the technology as tl:e climatic threshold shifts to the left. This movement of the tl,reshold sxveeps out the distribution of climatic indexes: if this distribution is smom,, "nd unimodal, the familiar sigmoid path ofdiffusionwill result. Snell a conceptu:d model of diffusion is applicable to any situation in ~;hich potential adopters trade off some up-front cost - cost of equipment, cost of learning about a new technology, cost of adapting existing processes, etc. - against expected future benefits of i.he technology. The improvement in the attractiveness of the innovation o~er time can also be very general, including the spread of better informatior~ on its -se, which makes it less costly to adopt. Finally. of course, it is not essential that the value of the

Tile term refers to the commonly employed si:ltb,ticat model for limited dependent variables, which .,,hares a conceptual foundation ,a,ith David's diffusion model. See also Davies (1979); Sommers (19g0): and Casx~ell et al. (19901: and Cas,aell and Zilberman (1990). Another set of models haxe also focused on the impacts of firm size and market structure on adoption decis:ons: hazard~rate models are employed hv Hann,m and McDm~ell (!994) to examine the faclors affecting the adoption of automated teller machines (ATM's) and by Levin ct al. (1987) to in:estigate adoption of optical scanners at retail grocery stores. Rose and Joskow (1990) extend the hazard model of adoption to take advantage of a~ailable information on adopters midnon-adopters. "This index would pre~umabRy be some flmction of heating-degree days ~nd cooling-degreeA.B. Ja//b ami R.N. Stavm.~ Re.~our~ c amt Emrgy E,~momics 16 :19~4'i 91 122 97



### innovation depend on local climate. What iscrucial isthat potential adopters be 

### heterogeneous along some dime,lsion tha! affects the value of the innovation,to The "heterogeneous adopters' and "epidemic"models each capture important aspects ofthe diffusion process: the modds wedevelop below incorporate both strands of thought, by allowing adoption decisions to be driven b3, adoption costs that have an unobscrved heterogeneous component and another component that depends on the prevalence ofthe technology among the stock ofpotential adopters.



### 2.2. The workhzgs ofincentive-based umtconventiomd reeulations

From the previous discussion, we can begin to perceive how economicincentive approaches to environmental problems would affectthe diffusion of environmentally beneficial technology. Whether through the diffusion speed in the epidemic model or the adoption threshold in the 'heterogeneous adopters" model, any policy that increased the profitability of a technology would speed its diffusion. It is lessobvious how, in an economic context, to model the effects of regulation intended to foster technology adoption. Indeed, most of the economic literature on the effectsof regulation on technologyfocuses on its inhibiting effects.~ Non-economists have discussed the "technoiogy-forcing' benefits of command-and-control regulation.~2 It iscertainly plausible that enacting and enforcing a law that mandates the use of triple-glazed windows (or some overall energy efficiency s~andard), for example, in new home construction would affectthe prevalence of that practice. It is lessclear what is the best way to incorporate that possibility in an internally-consistent conceptual model. Below, we suggest that the effects of such regulations can be embedded in an economic model by postulating that builders perceive that the (expected) cost of adopting a new technology is affectedby building codes"treatment ofthat technology. Beforedeveloping that model, we return to the specificsof energy-conserving technologies, and the arguments that have been put forward to explain their observed adoption rates.



### 2.3. Explanations l'orthe 

### 'parudov'

Various explanations I.avebeen put forward to explain the observed rates

~oIn the present context, the heterogeneity could likem'ise be associated with the type of home heating plant Ifurnace),the size ofhome, or indi'~idual preferencesforindoor temperature.

~See,forexample, Oster and Quigle.~ (19771. ~2See,forexample, Ashford el a[. 11985).98 ,4.B. Ja//eand R.N. Stavin.s Resource andEnergy Economics 16f1994) 91-122



### of adoption of new energy-conserving technologies. Although some facts are in dispute, for our purposes wc will take as given that there exist proven technologies that engineering calculations show to be cost-effective at current technology and energy prices, but that are not widely used.13 

### Some energypolicy authorities (particularly non-economists) have interpreted this as evidence of a failure of the invisible hand that should be corrected by government intervention: frequently advocated interventions have included minimum energy-efficiency standards for particular products and construction design standards (U.S. Department ofEnergy, 1991). When most economists observe the same set offacts, their responses tend to fall broadly into two categories. One type ofresponse is to seek to identify the specific market failure that might explain the apparent non-optimizing behavior. The other category of responses consists of reasons why observed behavior is indeed {privately) optimal, despite engineers" calculations.



### 2.3.1. Marketfailureexphmations

One obvious source ofpotential market failure affecting adoption decisions is lack of information about available technologies. It is costly for people to learn ofan innovation's existence and to learn enou~,h about it to know ifit is profitable and how to use it. Since information has public-good attributes, it is certainly possible that it is underprovided by the market. Further, if others' use ofthe technology is an important source ofinformation (as in the 'epidemic" model), then adoption creates a positive externality because it generates information that is valuable to others. Another po3sible source of market failure consists of principal/agent problems that can arise when energy-efficiency decisions are made by parties other those who pay the bills. In this case, difficulties in observability can make it impossible for the investing party to recover the investment from the party that pays the energy bills. This pk,,,blem could take several forms. Ifthe builder of a new house cannot credibly represent its energy efficiency to potential buyers, then the sale price may not fully reflect efficiency attributes. Similarly, a landlord may not be able to recover all of the value ofenergy efficiency investments where renters pay fuel bills. Conversely, there may be sit,rations where renters would have to make the investment but the landlord pays for fuei.~4 Finally, consumers may face artificially low energy prices that explain their disinterest in conservation (Sutherland, 1991). First, electricity and natural gas are typically priced on an average-cost basis that conceals from

~3Examples that are often cited include compact fluorescenl light-bulbs, improved insulation malerials, and energy-efficientappliances ~ Norberg-Bohm, lq90~. 1.~See Fisher and RothkopfIlgggJ.,4.B, JalaP'and R.N. Stavmx R~'s~mr~'~'~nd Em'rgl E~ommU~,~ 16 ¢19~4~91 ;22 q9



### customers the incremental cost of new energy supplies. Second, electricity is highly subsidized in some parts of the country. Third, uninternalized environmental externalities may be associated with the use of energy from particular sources ~including fossil fuels, nuclear, and hydroelectric sources).

2.3.2. Non-marketzfaihu'e explanations

Another set of possible "economic responses' to observed conservation technology adoption behavior is to conclude that there exist costs of adoption that engineers are ignoring or at least underestimating. Beyond the obvious tautological validity of such a claim, there are some reasons to give credence to this assertion. One aspect of cost is that of learning about the

new technology. As noted above, the pure information-creation part of this cost has public-good aspects and therefore fits into the market failure category. But there is also a purely private part of this cost that relates to information acquisition and absorption. It is by no means costless to learn how a generic ~echnological improvement fits into one's own home or firm,

nor is it costless to learn about reliable suppliers.~5 Thus, even after basic information about a technology has been generated and disseminated, the "purchase price" of the new product is no more than a lower bound on its adoption cost; transaction costs of adoption (of various kinds) can be significant relative to the magnitude ofthe net benefits ofadoption.~6 Another way of explaining low adoption rates is to posit that users halve relatively high implicit discount rates.17 Hence, another way to make this behavior consistent with underlying optimizing behavior is to explain why discount rates relating to these investments should be unusually high. Sutherland (1991) notes that high discount rates may be appropriate. These

are irreversible investments with much uncertainty about their payback, both because future energy prices are highly uncertain, and because actual energy life-cyclesavings in any particular application can only be estimated. Finally, even if a given technology is profitable on average, there will be

J5Some have argued that not only costly information acquisition but also biased estimates by individuals oflikelyenergy savings play a role. Consumers may not believeexperts" assessments ofthe benefitsofnew technologies.On the other hand,the bias maygo in theopposite direction of the energy paradox, since some studies inOicate that consumers systematically overestimate energy savings associated with some typesofnew technologies(Stern. 1986). 1,SeeJoskow and Marron (1992). t, Hausman (1979) estimated that consumers used avzrage implicit discount rates of 20,° for purchasing room air conditioners (with substantial ,ariation by income class): and Dubin and McFadden (1984) found average implicit disc~ :nt rates of 20°/;for space-heating and waterheating investments (again, with significant variation by incomet. In a comment on Hausman (1979), Gately (1980) estimated discount rates of 45"0 to 3000, for refrigerators. Likewise. Ruderman el al. [1987) found personal (implicitt discount rates as low at 20",, and as high as 800", forheatingand coolingeqmpment, and residential appliances.l(i(~ .4.B Jail(' arm R N. ,%taLtpls R('~our, c ~md E'r('rgl Economtc.s 16 ~1994~91 122

some individuals or firms for whom it is not profitable, if the relewmt population is heterogenous with respect to the amount of energy they use, for example, even a technology that looks very good for the average user will not be attractive for a portion of the population. Referring again to the "heterogeneous adopters model,' we can interpret the engineer's costeffectiveness calculations to mean that the technology is profitable for the

mean household or t2cm. Depending on the rate of movement of the threshold, and the shape ivariance and skewness) of the underlyingdistribution, it could be quite some time after the threshold cvo,"~esthe mean before all or even most households or firms adopt (although heterogeneity does not explainextremely low adoption rates for "cost-effective" technologies). The models developed below incorporate a number ofthese market-failure and non-market-failure explanations of the 'energy paradox', including information problems, principal/agent slippage, incompletc pricing, unobserved costs, heterogeneity, and potentially highdiscount rates.Is



### 3. I_Jseofenergy-conserving technologies in pewconstruction

We begin with the decision to incorporate a potential energy-saving technology in the construction ofa new home. We imagine a builder at 

### time 7" in politicaljurisdiction i considering the incorporation of a new technology into the design ofhousej. We take the decision to build the house, and its design features other than the technology under consideration as given. We assume that the builder designs the house to maximizeexpected profits. To do this, she will need to trade off the incremental cost of the new technology against the expected increase in selling price associated with a
more energy-efficienthouse. In order to allow for the considerations discussed in section 2 ofthe paper,
we assume that houses are heterogeneous in their energy use and that the housing market may discount energy savings because builders cannot represent them credibly. On the cost side, we allow for the possibleeffect on incrcmcntalcosts ofthe prevalence ofthe practice among buildersin the area and of the builder's own experience with lhe technology. We allow for regulation to affect the decision by modifying the cost of the new technology.]'~ We also allow for the possibility of a tax credit or other subsidy to the use ofenergy-conservingtechnologies.

I,~As discussed later in !he text. ~vedo nol deal explicitly with uncerlaint3. See Howarth and Anderson (19921. ~'*One interpretation is that regulation requires the use ofthe technology,creating an explicit or implicit penally for not using i:. Alternatively, regulation may merely encourage use of the technology by, for cx~mpIe, selling an overall energy budget for the house. Under either inlerpretatBon, we Ireal the ~nagni~,ude ofthis perceived effeclas an unknown parameter.

### The builder's decision may thus bc modelied as an attempt to maximize

the sum of the base selling price of the house ~tinthe :~bsence of the energysaving technolog3~ and ~hc present discounted value of the expected energ3 savings if lhe |ethnology is adopted (tl~ecapitaEized ,+alucof the ins~aEled technology} minus the costs ofadoption {where these include costs associated with up-front pvrchase and instat~ation, the impmicitor explicit costs effect of regulation, and k rning effects due to pre~ious use by t|~isbuilder or current
use by other builders in the areal. We assume that the builder recognizes that uncertainty is embodied in a number of the relevam variables, that the builder forms point estimates {expected values} of these variables, and that when making decisions the builder treat these expected vatues as ifthey were known with 

### certainty,a° Thus, we treat the overall decision problem in a fullydeterministic framework,et Formally, the builder's problem is: 

# I 1 maxnor= B+ I-6"[1 - w}.j"

### gtko,,,u,j,}.e "dt {!~ 1"



### - I"[Heir.Sot,hr)-TDir- Xir] 12~

where upper case letters represent stocks or present values: lower case letters represent flows: and greek letters represent parameters {except for n and p. as indicated below}. The variables are: 7~jT

i=

B= 6= 

### profit associatcd with adopting the technology in constructing housej in geographic area land politicaljurisdiction) iat time T: indicator ofchoice to adopt the technology t!= 1ifthe technology isused, and 0 otherwise):" the base sel!ing price ofthe house withoet the technology; discount {0~<6< 1)or premium (6> 1)

### applied hy market to rah. o/
energy sm'ings:23

~oIn other words, only the means of the respective probability distribution:q are taken into
account in the optimization problem. 21As we indicated earlier in our discussion of possible ,~:,.f, la;,a:ions of thc energ2, paradox. uncertainty may play a significant role in technology diffusion. It would be pas'dble to focus on .~hatdimension ofthe energy-conservation diffusion proce.~', as do Hassett and Mel,.atf 11992~. For broader treatments ofthis perspective,see.forexample. Pind3,ck <1991I.and Di+~ilt1992~.

zzWe focus on a simple discrete technology for purposes of explication. The model can be generalized to represent multi-valued discrete or continuous technological choices, such ;is installation ofinsulation of ~,ario.~s"R-values"in exterior walls. 2.~This parameter is included in our formulation to allow for principal-agent problems that may arise when a builder cannot credibly represent a new home's energy efficiency to potential buyersland hencenot capture the full value ofefficiencyattributes in the housing price). In such

as case, 0~<b< 1. Alternatively, ifbuyers of homes place excessively high valuations on energy efficiencyattributes ofnew hc,n,es, we would find lhal +~ > i.1112 4.B Jalti' and R.N. Stm.m~ R,,.~,mr,.,,and Energy Economics 16 ¢19941 91 122



### w= index ofaverage quantity ofenerp_yused by the technology relative to energy consumption ifthe technology were not used 10<w~<I); 

### k,jr= vector of current and expected future valucs of observable characteristics ofthe home (for example, size. type of heating plant), and region (for example, price of fuel, climate, average income and educationl; lt,j,= an unobserved factor affectingenergy use: g(.)= tunction that relates elements ofk#, to annual fuel expenditures;

e= base ofnatural logarithms;

r= real market rate ofinterest; C~r= engineering estimate of purchase and installation cost of adoption ofthe technology: S,~r= the cumulative stock of houses built previously by builderj that incorporate the technology; qr= fraction ofnewly constructc,J 'aomes injurisdiction i that incorporate the technology: L(.)= a function that generates the "effective cost' ofinstallation from the engineering cost and the prevalence ofuse ofthe technology; 

### D~r= dummy variable set to unity ifjurisdiction i has regulation in year T requiring that the technology be installed;-'~ 7= parameter that captures the average perceived monetary equivalent cost ofignoring regulation, presumably a function of the nature of the regulations, the magnitude of penalties, perceived probabilities ofenforcement, and likely stigma:z~and X~r= subsidy or tax credit injurisdiction ifor adopting technology.
This formulation incorporates many of the features of the problem suggested above. The heterogeneity of potential adopters is reflected in the unobserved l:~j,.The 'epidemic effect' related to the prevalence ofthe practice is represented by the L(.) function. Thus, in our formulation ofthe problem, the essence ofthe epidemic model is that potential adopters must learn about the new technology before they can use it, and the probability that such learning will occur depends on the fraction of the population ihat has adopted. Implicit in our formulation is that such learning can be viewed as
one component of the overall cost of adopting a new technology. The idea that information spreads by contact with previous adopters is captured by allowing the cost of adoption to depend on the 'regional" prevalence of use. Once we have allowed cost to depend on the extent to which 

### other builders

are using the technology 

### (rcr), it seems natural to allow the builder's own experience with the technology (Sqr) to reduce effective cost as well.

_,aAgain, in this simple model, ~'e deal with a "0- I"regulation. :5 See Russell et al. ~[9861.A.B. Jaf/'eamlR N, Starms Resm~r,'e amlEnergy Ec~m.mh's 16 ¢1994) 91 122 103



### The potential effect ofregulation is captured by converting it to equivalent cost terms in the form of 7. Finally, we also allow for the possibility that

some sort oftax credit or subsidy might be used to encourage adoption. The first-order, necessary condition for this problem compares the overall cost ofadopting the new technology with the expected increase in the selling price of the house.26 Denoting the expected discounted present value of the function g(.) as G{.), the condition for adoption is that the technology should beemployed if:


### fi"(! - 

### w)"G(kol,,lzor) + "i'DiT> L{CiT,Sijr,z',iT)- X iT 

### (3)

Thus, the builder will use the technology if the valuation placed by the market on the savings in expected energy costs plus the implicit or explicit value of complying with regulation lif any) exceeds the cost of installation. The "cost ofinstallation" includes the purchase and installation cost and the cost oflearning about the technology, and may be reduced by a government subsidy. The next steps are to specify functional forms for the G(') and L(.) functions and to make assumptions about the distribution of the unobservable /~, all from Eq. (2L above. Some relationships in the equations ,.re inherently multiplicative (such as price of fuel and quantity of fuel used), while others are inherently additive {such as gross installation costs and tax credits). Thus the choice offimctional form isinherently somewhat arbitrary. For simplicity, let the function G{') be Cobb-Douglas. Recall that the vector k;j, includes the price of fuel and attributes ofthe region, house, and household that affect energy use. Let 

### k j,* denote the m'uelement ofthe 1xM vector 

### kit,, and, in particular, let k~s, t=P;j,, the price of fuel to house j in region i in year t. To keep things simple, other elements of k~, {other than price) may be assumed either to be such that the agent holds static expectations about them 

### or to be constant (that is,

### ks,"=k jr" forall t> 

### T, for m=2

... M). Finally, the unobservable ~ is posited to enter multiplicatively. The function G(-) from Eq. {3)can now be written as:


# r 1 G(')= ~(Pij,)e-"dt " (kijT'n) #m 

### "FtljT LT m=2 

### (4)

where the specific elements comprising the vector 

### kijr might vary depending

on the particular technology in question, but would include variables such as

2.This ignores the possibility implied by Eq. 12~that the builder might take into account the future reduction in costs (parameterized by ~a) that v,ould be brought about by using the technologytoday.104 .q.B,Ja//i' aml R.N. Stavins Rest,ur,r and Em,r,¢y E~om,mir.~ 16 (1994) 91 122



### number of rooms in the house, number of heating degree-da>,s in the area, and income and education ofthe homeowncr. The cost/learning funttion L(.) can reasonably be ba~¢edon proportionate reductions in the cost ofinstallation as cithcr the builder's own cxpericx~ceor the prevalence ofthe technology being instalh;'J ~ncrease:



### L(

.)=(C~rl',.(r~r)~'-.(Sory ~

\~3/ 

### (5)

Thus, overall cost is the product ofthree factors tnat depend respectively on: the engineering cost estimate, C~r; 

### the prevalence of installation of the techno!ogy within the area, fir; and the builder's own cumulative expe6ence with the technology, S~ir. 

### Eq. (5) implies that the cngineering cost estimate, C~r, 

### will be the actual cost ifcveryonc iscurrently installing the technology (Z:/r= i), and the builder has "typical" experience, parameterized by :x 3. When installation is less prevalent (z:~r<1), the cost is higher, with the sensitivity parameterized by :t2 (assumed to be less than zero). For builders with more or less experience than the typical level x3, costs are higher or lower, with the own-experience sensitivity parameterized by ~.~.2-7 Next, we rearrange the condilion for adoption - Eq. (3) - ir~the form ofa benefit/cost ratio:

6"(1 - w)"G(k:j.r,/l~jr) ] L(Cii.Sij.l.,t,i.1.)

_ Xil --TDiTJ >~I 

### (6)

Substituting Eqs. (4) and (5) into Eq. (6), and taking natural logarithms of both sides yieldsthe following expression:



# (i /" log(f)+log(l-w)+fftlog (P;j,)e "dt + ~ 

## [/~r.log(k~jr)]

T z m:2



### (7)

Eq. (7) conveniently illustrates how a variety of factors can affect the diffusion of energy efficiency technologies. First of all, principal/agent problems associated with the builder/homeowner relationship will have an

'- The exponent :~t. on lhe engineering cost cstimale should bc unity.A.B.Ja[h' and R.N. Slarms Res¢mrce and Energy Ecomunh's 16 ~1994) 91 122 105



### unambiguously negative effect on the rate of adoption. If principal/agent slackexists, the parameter6 will be greaterthan zero but less than unity (see Eq. (2)},and so log(61 in Eq.(7)will be negative. Likewise,individuals do not have perfect information about the path offuture energy prices. To whatever degree they tend to underestimate (the present discounted value of) future energy prices, the qkelihood ofadoption ofan energy-conserving technology will be reduced Similarly, if energy prices, Pij,, are "a~tificiallylow,'28 adoption will be slower than it would otherwise be.z'~ Furthermore, it is clearfrom Eq. (7) that ifdecision makershold relatively high discount rates, r, the anticipated energy savings and hence the tendency to adopt the new technology willbe lessthan otherwise. Focusing next on the term behind the summation sign in Eq. (7), we can
see that climatic departures from temperate conditions (increases in heating and/or cooling degree daysj will encourage adoption, ceteris paribus. Other factors affecting energy use, such as income or education, could also matter.3° Turning to the second line of Eq. (7), we can see that decreases in adoption costs will accelerate technology diffusion. This could be due to changes in the direct costs of equipment purchase and installation (Cir), or changes in "effectivecosts of adoption' associated with 

### learning, inversely correlated in our model with the prevalence ofinstallation ofthe technology within the region, t'~r;and the builder's own cumulative experience with the technology, S.~r.Thus, depending on the magnitude of the parameter, :~2,

asThe "artificiallylow" energy prices could be due to any one of a number of factors, as we suggesteti earlier: departures from marginal-cost pricing of electricity by utilities: subsidies for

somefuels;and/or uninternalizedenvironmental externalities. 29The question of how individual expectatio:~', of future energy prices are formed is also relevant. Ifpeople have staticexpectations, onlycurrent prices matter: for adaptive expectations,

some combination ofcurrent and past prices will be determinate; for rational expectations, all relevant informationavailable at timet willmatter. 30In order tojudge the significanceofparticular effects, Eq. (7) could be estimated, at least in principle. Whether specific effects could actually be verified would depend, of course, on the identification of respective parameters. This is largely an empirical issue, but by examining the extent to ,,~hichvarious effectsare even potentiallyidentifiablewecan shed someadditional light

on the disputes regarding the 'paradox"ofslow adoption. For example, it isclear that the effects of household and regional factors on expected energy use Ifl2 to flu in both modelst are identified. Thus, it is theoretically possible to separate out the effects of these factors on adoption decisions. On the other hand, there is a rather convoluted relationship among: the discount applied by the housing ~narket to energy savings 16L the interest rate {rl. and the sensitivity of the decision to the price of fuel (fllJ in the new construction case. If there is a 'paradox,' it suggests that the adoption decision is not as sensitive to fuel prices as would be suggested by the simple.st benefit/cost analysis. That is. principal/agent slack could be present {fi<lL the implicit discount rate could be relatively high. or measured fuel prices could be having a relatively mild impact on expected prices (fl~< I~. Our model suggests that it may be difficultto separate out these factorsfrom one another.106 A.B. Ja/h' and R.N. Stavin.~ Resource ,rodL)wrgy Economics 16 {1994) 91 122



### there may be a dynamic externality in which increast,d adoption today fosters future adoption by increasing v,. Next, direct regulations - such as ~'.:ii'di,,,¢codes -.-can have a direct, positive effect on adoptio~ by, in effect. decreasing the expected costs ofadopting {7), 3~ and government programs in the form of subsidies or tax credits {X~r)can directly reduce adoption cost and thereby spur diffusion ofthe technology.



### 4. Retrofitting energy-conserving technologies inexisting structures

We next examine the adoption decision faced by an individual considering the installation ofan energy-saving technology in an existing home. Thus, for example, we may consider a homeowner who is thinking about the possibility ofinjecting blown insulation into exterior walls.32We posit that such an individual will attempt to minimize expected costs, subject to various constraints, taking as given all relevant prices and government policies.33 By formulating the problem this way, we are assuming that ifthe homeowner is not risk-neutral, her attitude toward risk is such that the riskiness of the investment can be captured by appropriate adjustment ofthe interest rate.34 Because ofthe possibility that the technology may be significantly cheaper in the future (either because oftcchnological change or 'epidemic' learning), this is not a 'yes/no' decision like that ofthe builder; the homeowner must decide
at what time 

### (ifany) to perform the retrofit installation.3s The costs that the homeowner wishes to minimize consist ofthree elements

- the present discounted value (PV) 

### ofannual energy costs from the present to the time of adoption of the energy-saving technology, the PV 

### of annual energy costs after the adoption, and the PV 

### ofthe one-time cost ofadoption ofthe energy-saving technology:

3~The magnitude of this impact is clearly an empirical matter. See, for example, Jaffe and Stavins (1993b). 32Whereas in the previous model we highlighted the principal/agent problem (and employed the parameter, 6, to allowfor itseffect),in the retrofit model we focuson homeowners and therefore do not need to consider the agency problems that may exist in the landlord-tenant relationship. The parameter, 6, refers instead exclusively to homeowners' possible lack of knowledge about theeffectivenessofa given technology. 33It isals~ possible that enew.yconservation enters directlyin somepeople's utilityfunctions.

• x'~Hassett and Metcalf (1991) examine the effect of uncertainty on the retrofit decision. By focussing on utility-maximization instead of cost-minimization, we could also investigate the possibility that the optimal consumption ofenergy services (for example, the thermostat setting) will change ifthe house becomes more energy-efficient. 3sBecause retrofitting an existing building is typicallymuch more expensive than incorporating

a new technology at the time of construction, our analysis of new conswruction reasonably ignores the possibility that the retrofit option affects the initial installation optimization problem.A.B. Jaffe and R.N. Slavins Resourt'e ~:ndEnergy Et'onomi(,~"16 (1994) 91 122 I07

T dt 

### min

### PV(T)= Sg(kij,,l%)'e-r'dt

### +w

.~g(k~j,,l%) " e-r'dt IT) o T

T



### +[L(C~r,V~r)- 

### X~r]"e-'r +~,.~D~,"e-'*dt (8) 0


### ~")';'" >10 .,,.,,,j,.,.,to T (9)

where: T= the time ofadoption (installation); V~r= the fraction ofretrofit candidates injurisdiction i that have adopted the technology by time T; and all other variables are as defined previously. This formulation is consistent with that used above for new construction, including the treatment of heterogeneity and the effect of regulation. We allow for the impact of regulations although such interventions are typically not utilized in this retrofitting context, because in other possible applications - such as industrial pollution control - regulations can be designed either to affect all

sources (thus requiring retrofitting at existing sources) or can be designed to affect only new sources. The effect of regulations enters into the objective function as the final term in the second line ofEq. (8).Thus, we are viewing regulations as an additional cost to be minimized, where this cost is equal to the "effectivepenalty' ofnon-compliance from the present time to the date of adoption (and thus compliance). Alternatively, the limits ofthe integral in the regulation term could be the time ofadoptien, T, and infinity, in which case the term would be subtracted instead of added. Then we would be viewing the effect of regulation as providing a benefit (an 'avoided cost') to the adopter from the time of adoption onward. Note that these two specifications of the impact of regulations are equivalent: in either case, the same first-order condition follows, as we will seebelow in Eq. (12). Returning to the optimization problem, note that the installation cost is formulated slightly differently from the new-construction case. Since the homeowner will not typically have previous experience with the technology,

we take the effective cost to depend only on the engineering cost and the local prevalence of the technology; because of the nature of the retrofit situation, we take this prevalence to be represented by the fraction of the stock that has been retrofitted, rather than the current retrofit rate First-order conditions for maximizing 

### PV(T) in Eq. (8) subject to the constraint ofEq. (9) are:


### (~PV(T)>_ f?,PV(T)~. ~T ,/0 and \ ~T ,] T=O 

### (Io)log ,.I.B. Jatli' and R.N. Stavins R,'~ource and Energy Econonlic.~ 16 ¢1994) 91 122

The first condition indicates that retrofitting should occur at a time T such that waiting longer will not decrease the present value oi costs. The second condition indicates that retrofitting should occur either at T=0 (when installation is first considered) or when the derivative of the present value of costs with respect to time iszero. It is useful to reformulate the conditions in into a condensed form in which adoption should occur in year T if:3~'

?PV(T) >>.0and adoption has not yet occurred. ?T (11)

Evaluatingthe inequalitycondition in Eq. (11) yields:

-rT [(1-6"w)g(k~ir,lqjr)-r'[L(C~r,V~r)- X ,r] + 7Dir] "e 

### ~L



# ., -/', ,.*J-t (12)

Dividingby e ,r and rearranging terms, adoption is predicted to occur at time T such that: 

### (I --~ "w)g(kijr,l:i

jr)4-TDiT> r "[L(Cir,V,rI- X ir]



### \?C,r) \ dTJ \?V,r} \ dTJ+ (13)

The left-hand side ofEq. (I3) indicates that higher annual energy costs can encourage adoption of the energy-saving technology, as can the effectiveness of the technology3v and the existence of relevant regulations. The first term
on the right-hand side of the equation indicates that higher adoption costs (whether direct or indirect) and higher interest rates discourage installation, and that government subsidiescan encourage adoption. Finally,the presence ofthe last set ofterms - the time derivative ofadoption cost - indicates that adoption is discouraged by expectations of decreased (effective) costs of adoption in the future. Thus, even ifthe current savings in energy costs are greater than (the annual annuity of} adoption costs, it can pay to wait (f those adoption costs are expected to fallover time at a sufficientlyrapid rate. Notice that Eq. (13) is a statemcnt about the current rate of energy savings: it does not involvepresent values offuture streams {in contrast with Eq. (3) in the new construction model). This may seem counter-intuitive, but note that it is the standard condition for the purchase of a capital asset: the instantaneous r,.,.teof earnings from tile asset (tile left-haled sicie) shouid be

3, Sufficiencydepends upon the satisfaction ofsecond-order conditions, which w,ediscuss later. ~' Recall that 1-&v is the expected proportion ofenergy saved.A.B. Ja[]'e and R.N. Stavins Resm,r,'e and Encr,ey Ec~momi,'s I~ ;19V4i 91-122 109



### greater than or equal to the carrying cost (the first line of the right-hand side) minus the instantaneous rate of capital appreciation (the last line). "Earnings' from the asset are the energy savings: the "cost' of the asset includes the installation cost and the cost of acquiring the necessary information, adjusted for the effecls ofregulation and subsidies. The ~capital appreciation rate' has terms corresponding to each of the elements of the cost ofadoption. To the extent that the overall cost ofadoption is expected to fall (that is, the sum ofthe last set ofterms is negative), it isas i~"the asset
were suffering a capital loss; instantaneous earning ~,illhave to be greater to justify the investment. To put it concretely, to the extent that one expects that compact fluorescent light bulbs are getting cheaper or easier to find or easier to install, one might wait until next year to purchase and install them

even ifthey are currently economical.38 Ifit still seems counter-intuitive that the adoption condition depends only

on current values (and not on present values of ft.ture expectations), note that ifthe second-order condition is satisfied, the function 

## PV(T) will have (at most) a single optimum, which will be 

### just at the point when the instantaneous investment condition holds. It does not matter how large the savings will be in the future; overall costs are minimized by adopting at the instant when marginal costs equal marginal benefits, as represented by condition.39 Many of the issues addressed previously regarding functional forms for g(') and L(-) arise, ofcourse, in the retrofit context, as well. The addition of the terms invelving the time derivatives of the cost components makes the retrofit model, on balance, 'more linear' than the new construction model, so
we proceed with such a formulation. Consider the following form of the energy-cost function:

M 

### g(')=Por" ~ 

## fl,,,k,'~T+POT (14)

rn=2


### First of all, note that current annual prices are en,pioyed, unlike the new-construction case, where the present value of a future stream was appropriate. Relevant features of the house and region contribute additively

38Thus the model produces a polenlial 'non-market-failure" explanation of the 'paradox." beyond those suggested above. This is parallel to results derived in models with explicit uncertainty (Dixit, 1992). 39The intuition that expectatic,as of future prices should matter would be correct, however, if the second-order condition is violated. In this case, th-, first-order ,:,mdition of Eq. ~13) is a necessary but not a suJficient condition for optimal adoption. The condition could hold at a local maximum ofdiscounted costs that is not a global maximum, as it could at a local minimum that is not globally optimal. Hence, present discounted values would matter and thus future costs {prices)would matter.II0 A.B. Ja[li' and RN. Stavins
' Res,mrce and En('ret Economics 16 11994) 91-122



### to energy use: the fuel bill is the product of this additive function and the price of fuel. Since g(') is multiplied by (1-a.w) in Eq. ~13),the new technology reduces the overall fuel bill proportionately. The learning/adoption-cost function can also be specified in linear form:

L{ ") = ~t

3-{-~tiCir+~t2Vil

. 

### (!5)

Note that in contrast to Eel.(5), there is no term for 'own experience.' Now, substituting Eqs. (14) and {15)and into Eq. (13t, and evaluating the various derivatives yields:



# r . ] 

# l(l--6"w)"P,jr" Y', IJ,,k~r +TDir

ill ~ 2 

### -r' [:~3

### +~tCir+~zVir-Xir]



## +r ) +r (16)

As explained above, this indicates that adoption decisions are made on the basis ofcurrent energy prices without concern for future energy price paths; nevertheless Eq. (16) indicates that interest rates still matter since it is the annuity of adoption costs that is critical. In particular, higher implicit discount rates, r, will tend to retard adoption. As in the new-construction case, adoption will be slowed by 'artificially low' energy prices (Pur); climatic departures from lemperate conditions will encourage adoption; and so will other factors that increase energy use. The existence of relevant regulations

can likewise encourage adoption. The second bracketed term on the first line of Eq. (16) implies that high adoption costs will unambiguously discourage adoption, whether these adoption costs are associated with: direct cost~ of equipment purchase and installation (C~r); changes in effective costs of adoption associated with 

### learning (inversely correlated with cumulative adoption in the area, V~r);or government programs in the form ofsubsidies or tax credits (Xir). Finally, note that although the future paths ofenergy prices turn out not to be relevant for adoption behavior in the retrofit case, Eq. (16) reminds us that the current time rate ofchange of adoption costs, 

### broadly defined, does matter, in pamcular, ifpurchase and/or installation costs are falling, it can pay to wait, despite the fact that 

### current net bcnefits ofadoption are positive. Likewise, if adoption is taking place very fast and information about the technology is thus increasing rapidly, it can pay to wait (since ~2<0). Finally, if government subsidies or tax credits are increasing sufficiently rapidly over time, one may choose to wait Ifor the higher subsidy at a later datet despite the fact that the current benefit-cost picture is otherwise positive.A.B. Jal.h' and R.N. St¢svms Resource amyEnergy Ecfmomh's 16 ¢1994 ' 91-t22 I!1



### 5. Policy implications

Our analysis indicates that market imperfections and other factors can slow diffusion and thus help explain the observed 'energy paradox.' Some of the factors we identify suggest a role for government intervention, but others should not 

### be taken as meriting policy responses. In particular, the "nonmarket-failure causes" may help to explain the gradual diffusion of energy conservation technologies, but they do not 

### argue for government intervention. Falling into this category are high di:~countrates,'*°the private costs of information acquisition, heterogeneity of potential adopters, and the "dynamic wait-and-see' conditions that emerge in theretrofit case. The other major set of factors we have examined - the market-failures - not only help explain the 'energy paradox" but also provide a set ofpotential justifications for government intervention. We summarize these policy implications in Table 1. Some ofthese implicatior~s arise from simple inspection of

our final behavioral equations; others require investigation of respective partial derivatives; and some - because ofthe dynamic nature ofthe model - are best examined through dynamic simulations. The simulation approach also enables us to view the results in graphical terms. For illustrative purposes, we employ a simulation model of aggregate technological diffusion in the new home conslruction case, based upon the related behavioral inequality, Eq. (7). By assuming that the unobserved energy intensity, lt, has a legistic distribution and is independent ofthe other house-specific variables, the fraction ofhomes in year T that will incorporate the technology is simply the probability that condition (7) holds, which is equal to the logistic cumulative probability function evaluated at the lefthand side ofEq. (7), or:



### I Vr= l +e -AT 

### (17)

where vr is the fraction of newly constructed homes in year T that use the technology; and Ar is the left-hand side ofEq. (7). 4~ A base-case (no new policy) diffusion path is found in Fig. 1. We use the time oeriod 1978--1988 for the simulations because this encompasses a

40As noted below, to whatever degree high persenal discount rates reflect the public good aspect of incomplete information (uncertainty), high discount rates do pro,~ide a potential justification forgovernment intervention. 4~Given the assumption ofindependence ofIt and the other variables, lhose variables in Eq. (7) that vary across i and/orj are ewtluated at their means. To keep things simple for the policy analysis, wedrop the term with Sorfrom the learning function; i.e.,weset ~4in Eq. (7)equal to
zero. Otherwise it would be nece:~sary to simulate multiple builder decisions simultaneously. Also, for the simulation model, w,: replace re; by the previous period's :alue, v,..; 1: and we adopt simple staticexpectations on prices, so that P#,isreplaced by P~j~.112 A.B. JaHe and R,S. Stavms Resource and Encrgv Economics 16 ~19941 91 122

Table I Markct ¢:nlurc and poliQ prescriptions
Problen3

Incomplete information Public Good Aspect)

Principal Agent Issues iBuilder Buyerl

Departures from Marginal Cost Pricing by Electrical Utilities
Federal and Stale Energy Subsidies
I)nintern;dizcd Environmental Externalities
Insufficient Research & Development
Positive Adoption Externalities the diffusmn ofenergy conser,,ation technologies Policy Consequences ofpolicy'm models prescription New Retrofit construction
Establish standards fi~r ,Sl' energy audits and disclosure for new' buildings Public information ~'i T,~tt, L,r,[ campaigns Product lat3elling :~t 6"[ rcquirements guidelines
l-edcral home energ} 6]' rating s~stem Standards I\~raudits and fit disclosure :t3L6"f

Change from average to Po, T marginal cost electricity pricing
Elirninate red.ce fuel P,j,T subsidies 

### Pul

t',s.l" f

In'erna!ize externalities P,j,T PisrT
Regulation Dirt D,rT (]overnment support for ('il~.. ~]. C,1~..w~ technological R&I) Adoption subsidies X,IT X,tl" Tax credils XaT X,rT



### significant turning point in real energy prices. The resulting non-monotonic diffusion curve found in Fig. 1is not atypical of the experience wilh energyefficiency technologies in new homes over this time period, in fact, our basecase parameter and variable values reflect actual data for triple-pane windows {Tables 2 and 3),'*-'and the simulated diffusion curve is similar to the observed diffusion path ofthat technology in the United States.".3

"~-"These base-case parameter values reflect all of the assumptions previously specified regarding the underlying behavioral relationships. For example, we use values for ~t t and ~t 2that yield the appropriately shaped cost learning functkm Referring to Eq. (5},we find that gL[.)/Cv~_t<0, ?21~'}"?vT ~:>0, dlJ-l/z¢2<0, and d21j •)d~t,2>O.Thus, as I-, ~approaches I.O {ils maximum value) and as zt

2approaches 0 {from belo~L the effective cost of adoption fal!s and approaches the simple engineering cost.

• ,3 Not surprisingly, the nort-monoh~nicity of Ihe diffusion path is partly a consequence of the related path of(expecledD real ener%' prices. SeeJaffetrod Stavins [1993aj.A.B. Ja//c and R. '~: Stavm,~ Re.,m~rcc and Em'rg.v Ecom*mic,x /6
,I994 ~9t I22 I[3

XT ~.6~?.r~. C,L.~v,~ 

# /

m2';

II ';

I I I I I I I I I Iq7~ i~80 19~2 Iq84 1986 1988 Year

Fig. I. Base-case simulation and the effectofalternative constant policychanges.



### With the help of the simulation model, simple differential calculus, or simpler inspection of the behavioral relationships, we can now proceed to investigate the implications ofpotential public policies. First ofall, the public good aspect of incomplete information can suggest a number of policy responses, depending upon the nature of the incomplete information. For situations in which there is uncertainty surrounding the potential benefits of energy conservation technologies in new construction, our analysis suggests that government could conceivably establish standards for energy audits and disclosure requirements for new buildings, thereby increasing 6. Graphically, the effect of this is to shift the diffusion path in Fig. 1 upward. Likewise, public information campaigns about the potential benefits and costs of adopting new technologies could be effective both in the new construction

case (fiT,~lJ,, r~) and the retrofit case (:z3,[,r,l).4'~Focusing on the attributes of the technologies themselves, product labelling requirements or guidelines could be effectivefor new construction (7~,L,f`r) and retrofitting (:z3,L,6Tt.

~4.As with increases in 6, so too with decreases in the Iconstant~ interest rate. r, the effect is to shift the diffusion path upward, while retaining its basic (non-monotonic) shape. What is striking, however, is lh~ dramatic effect ofdecreases in interest rates. Whereas increasing 6 from 0.50 to 0.75 shifts the peak ofthe diffusion path (in the year 1983) from a 5.8'!,,adoption rate to 8.50,,,decreasing real interest rates from 5'~,,tthe base case} to 1",,shifts the peak ofthe adoption

curve from 11.2",, to over 40",,. On the other hand. note that 'the relath~nship between intercsl rates ~nd adoption is not linear; an increase in the interest rate from 5". to 10",~has a much smaller effecton adoption, shiftingthe peak downward from 11.2,,, to 5.8",,.114 A.B. JaHe and R.N %tavm~ Re~ourcc and Energy E~ononm's 16 (1994) 91 ;2:

Table 2 B:Jse-case parameter and variable value,:
Parameter or Description Base-case ~,duc variable

t Engineeringcost coefficient 1.00 ~2 Learning-effectcoefficient 0.05 fl~ Expected-price coefficient 1.00 f12

... JIM Observable characteristic 0.(~

coefficients ,5 Market's discount ofvalue of I.(hq

energy savings ;, Cost ofregulatorynon- 0.00

compliance

r Real market rate ofinterest 0.05

ro Initial rate of~echnological ~.10

adoption C, Engineeringpurchase and $240.00

installationcost D, Regulatoryrequirement dummy 0.00

variable k

.... k~ Observable characteristics of 1.00

home and region
w, Relativeenergyuse of 0.87

technology .\, Subsidy or tax c~edit for 0.00

adopting technology P, Expected energyprice in ,,'ear t
"Time series ofbase-case energy prices are found in Table 3.

Table 3 Base-caseenerg~ prices
Year Effectiveenergyprice"
1978 9.73 1979 10.18 1980 Ii.25 -) -) 1q81 1_.0.. 1982 12.51 1983 13.03 1984 12.56 1985 12.32 1986 11,q3 1987 1!.43 1988 10.95 "Average effectwe energy price fl~r48 slates, in 1988 dollars per million BTU's; a weighted aveage of prices of alternative fuels of newly built homes.

### Principalagent problems can be particularly ~-<',,~crein the new construction case Ifa builder cannot credibly represent :~~omc's energ~ efficiency to potential buyers, th,.:sales price will not fully retqcc:efficiency attributes This

concern has led in ~,, past to legislation in the Congress to require the U,S. Department of Energy to develop a 

### volumary home energy lating system to provide consumers with better information on ~i3eefficiency of prospective homes (6'f}.Standards for audits and disclosure '<ould have the same basic result. We noted earlier that there are a set of reasc<s why the price of energy may be artificially low. Not surprisingly, the app~-opriate policy response will depend upon the reason for the problematic pricing. Changes from averagecost to marginal-cost pricing ofelectricity at utilities are one approach. The result in our models would be to increase energy prices (P,j,T). Similarly, consideration should be given ~o eliminating or at !east reducing the subsidies that exist for particular fuels [P~/tTL ~n this same context, the existence of uninternalized environmental externaiities associated with particular sources ofenergy clearly calls for those ex~e.cnalities to be internalized, such as through pollution taxes, tradeable permi~systems, or other economic instruments (P,j,T},or through conventional c~>~rmand-and-control regulations

## (D~rl'). It is frequently asserted that free-rider problm~,s will lead to less than the socially optimal amount of research and development by private firms. To the extent that this is true in the energy-efficiency technology area, government support for technological research and development may be called for. In our analysis, this could translate into decreases in the purchase and installation costs ofnew technologies 

### {C~rJ,)and increases in the effectiveness (engineering efficiency) of those technologies (wJ,). Finally, we noted at the outset that adoption behavior can itself result in positive externalities if others' use of a technology is an important source of valuable information. In this case, there is an argument in favor of government employing 'adoption subsidies' or tax credits 

### (X~rT).45 As indicated, some energy-efficiency technologies used in new home construction - such as triple-pane windows - have exhibited non-monotonic diffusion paths, apparently as a result of the turning point in real energy prices experienced in the early 1980's. From the perspective ofpublic policy, it is natural to ask what policics could have been used to foster a monotonicly increasing diffusion path, in the fac,,offallingreal energy prices. First of all, ifadoption costs had been falling sufficiently fast over time, the

• ,5 In the new home construction case, simulations ofdecreases in the purchase arid installation costs of new technologies, C;r, increases in those technologies" engineering efficiency 1-w. and increases in adoption subsidies or tax credits. X,;. exhibit lhe same effect upwar'J shifts of the non-monotonic diffusion path tsee Fig. !).116 ,-IB ,h*lli' wld R.N. .S'Iarm,~ Rc.~<,urcc and l:'m'r.,.,.l l'~c<momics 16 ~1~94 191 122

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Fig 2. The cffecl ofdecreasingadoplioll o.~sls on tcchmN~gicaldiffusioll.
depressing incentive effects offailing energy prices would have been reversed. Indeed, various counterfactual time paths of falling adoption costs {C,r) produce diffusion paths in which the "negative effect"of failing energy prices after 1983 is overcome. Depending upon the rate at which adoption costs fall. the diffusion path of the technology can take on a constantly rising pa',tcrn or a classical sigmoid shape {Fig. 2}.a'' As noted above, government support of technological research and development efforts could have the effect of driving down ('~r- tiow else might government policy be employed to counteract the post-19g3 price effects and maintain a&~ption rates or even push them to continually higher levels'? First, government support of research and development an approach thal is favorably viewed by Ihe present Administration for a host of erwironmental and resource problems can not only have the effect of decreasing adoptk,n costs but can also increase the efficiency of available technologies t~vJ,

t. As depicted in l:ig. 3, as w fat's over time from an initial value oft}.99lindicating virtually no efficiency advantage) to 0.50 (indicating that the technology cuts energy demand by 511 percent), annual adoption

4+,AI',~:, lhcrc i~ ;I ]c~ t'~,trcn~¢ c'OUll!Cl.f;tctli;l] palh oJ ;ltl ~plltHl C~I'~ lh:II ~lll case 3dol~lloll.4.B. 3a!i('a~.l R.~V Sgarm.~

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increases monotonicly in an essentially sigmoid path from zero to 30 percent of newly constructed homes. Other dynamic government policies could - in theory - be employed to compensate for falling energy prices. The simulated diffusion path in Fig. 4 illustrates that a 

### co,tim.,~slv i,creasin'4 subsidy [X,r) of sufficient magnitude could bc used to maintain adoption ra[e.~at their peak level (again. in the118 .4.B. &tileand RN. Starins Rcsm~rce attdEnergy Economics 16 ~1994) 91 122

",F ~, II, ~MI • Mu ~PTI~,t;

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Fig. 5. The effectofa one-timeincrease in regulatol/slringency on technological diffusion.

face of falling energy pricest. Subsidies of various magnitudes can be employed to have essentially whatever effect is desired. At one extreme, a constant subsidy set equal to the basic engineering cost of the technology results in a 100 percent rate of adoption after only eight years (the delay being due to the effect oflearning on effective costs ofadoption). The obvious alternative to a subsidy on the technology (or a tax on energy prices) is a conventional regulatory approach, such as use of building codes in the new-construction context. As indicated above and in Table 1, regulations can in theory - have the desired effect. Our dynamic simulations illustrate, however, that a one-time change in regulatory stringency should not be expected to lead aut,;matically to an increasing or
even a constant level of annual adoption. Fig. 5 represents a situation in which a command-and-control regulation is initiated in the year 1981. As expected, adoption increases dramatically in that year and then continues to increase at a much slower rate to the peak year of 1983. Subsequent to that time, hov,ever, the effects of falling energy prices dominate, and we find the rate of diffusion falling gradually despite the constant level of regulation. Con,<ntional resulations, like market-based instruments, can be effective, but neither are likely to be a panacea in the face of strong, contrary forces in the eCOllO?]~y. Either conventional command-and-control regulatory policies or incentivebased ecom-~micinstrqments can be used to achieve various levels and rates of change c,f technological diffusion desired by policy makers, whetherA.B. Ju([~'and R.N. Sta~'ins Resourc,"and Fm'rgy Economics 16 (1994j 91-122 | tt)

because of (economically legitimate} market-failure reasons or otherwise. Which policy instruments will be best will depend in well-definedways upon the relative importance ofthe various causes ofthe gradual diffusiono7those technologies, in the first place.



### 6. Summaryandconclusions

In this paper, we have developed a framework for thinking about the "paradox' of very gradual diffusion of apparently cost-effective energyconservation technologies. Our analysisprovides some keysto understanding why this technology-diffusionprocess is gradual, and focuses attention on the factors that cause this to be the case, including those associated with potential market failures - information problems, principal/agent slippage, and unobserved costs - and those explanations that do not represent market failures - private information costs, high discount rates, and heterogeneity among potential adopters. Furthermore, our analysis indicates how alternative policy instruments - both economic incentives and direct regulations - can hasten the diffusionofenergy-conservingtechnologies. Because there are two important contexts in which energy conservation adoption decisions can take place, our analysis builds upc,n two conceptual models: a model in which an activity is being undertaken which prompts a decision about whether or not to adopt an energy-conservingtechnology at a specified point in time (our new construction case); and a model in which a decision must be made not oniy about whether or not to adopt an energyefficiencytechnology, but also about when to do so (our retrofit case). Our analysis focused on the incorporation of energy-conserving technologies in

new residential structures and retrofitting inexistinghomes. First of all, in the case of new residential construction, our analysis demonstrates how principal/agent problems thought to arise in that context
can directly inhibit the diffusion of energy efficiency technologies. We also found that "artificially low' energy prices -ctue to electrical utility pricing practices, government fuel subsidies, or environmental externalities - can provide another market-failure explanation ofthe paradox. Ashas frequently been discussed in the empirical literature, relatively high individual discount rates can significantlyretard adoption and diffusion. Similarly,our analysis illustrated how decreases in the costs of adoption will accelerate technology diffusion, whether due to changes in the direct costs of equipment purchase and installation,or changes in the 'effectivecosts ofadoption' associated with learning about the technology and its application. We also saw how regulations - such as building codes - can have a direct, positive effect on adoption, as can other government programs, including subsidies and tax credits. Of somewhat less concern in terms ofpublic policy perhaps, we also121) A.B. A!['Ii'and R.,V. Stavins Resource aml Fncrgy Economics 16 ~1994) 91 122



### noted how departures from temperate climatic conditions, and increases in income and education can accelerate diffusion. Second, we examined the case ofretrofitting energy-efficiency technologies in existing residential structures. We found, somewhat counter-intuitively, that under certain circumstances adoption decisions are influenced bycurrent energy prices, without concern for future energy price paths. Nevertheless, high discount rates can impede adoption by driving up the adoption-cost annuity. As in the new-construction case, we found that adoption will be slowed by 'artificially low' energy prices: and that climatic departures from temperate conditions will encourage adoption. Not surprisingly, low adoption costs will unambiguously encourage adoption, as may government programs in the form ofsubsidies or tax credits. Although the future paths ofenergy prices turn out not to be relevant for adoption behavior in the retrofit case, the current time rate of change of adoption costs, 

### br,.adly &:l~m'd, does matter. In particular, ifpurchase and/or installation costs are failing, it can pay to wait, despite the fact that 

### current net benefits of adoplion are positive. Likewise, if adoption is taking place very fast and information about the technology is thus increasing rapidly, it

can pay to wait. Finally, ifgovernment subsidies or tax credits are increasing sufficiently rapidly over time, one may choose to wait (for the higher subsidy at a later date} despite the fact that the current benefit-cost picture is otherwise positive. In conclusion, if the 'energy paradox' of gradual diffusion of apparently cost-effective energy-efficiency technologies does exist - as many observers have claimed - it is necessary to understand the sources of the gradual diffusion beforc identifying appropriate policy responses. One set ofcauses of the paradox, which we have labelled the 'non-market-failure' causes, do not provide legitimate justifications for government intervention. On the other hand, a fairly large number of potential market-failure explanations of the paradox can provide solid arguments for government action. Which specific policy instruments will be appropriate, however, will depend in well-defined ways upon the relative importance of the various underlying explanations of the energy paradox.

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