Explaining the Declining Energy Intensity of the U.S. Economy. Ian Sue Wing *

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1 Explanng the Declnng Energy Intensty of the U.S. Economy Ian Sue Wng * Center for Energy & Envronmental Studes and Geography Department, Boston Unversty and Jont Program on the Scence & Polcy of Global Change, MIT Abstract Ths paper reconcles conflctng explanatons for the declne n U.S. energy ntensty over the last 40 years of the 20 th century. Decomposng changes n the energy-gdp rato nto shfts n the structure of sectoral composton and adjustments n the effcency of energy use wthn ndvdual ndustres reveals that whle nter-ndustry structural change was the prncpal drver of the observed declne n aggregate energy ntensty, ntra-ndustry effcency mprovements played a more mportant role n the post-1980 perod. Econometrc results attrbute ths phenomenon to adjustments n quas-fxed nputs partcularly vehcle stocks, and dsemboded autonomous technologcal progress, and show that prce-nduced substtuton of varable nputs generated transtory energy savngs, whle nnovaton nduced by energy prces had only a mnor mpact. JEL classfcaton: Q3, Q4 * Rm. 461, 675 Commonwealth Ave., Boston MA Phone: (617) Emal: Ths paper has benefted from valuable contrbutons by Rchard Eckaus, as well as dscussons wth Glbert Metcalf, M. Scott Taylor, Tm Consdne, Karen Fsher Vanden Davd Popp, Fred Joutz, Peter Wlcoxen and partcpants at the IAEE sessons n the annual meetngs of the Alled Socal Scence Assocaton and the Western Economc Assocaton. Thanks are also due to the edtor and two anonymous referees for very helpful comments and suggestons. The author s solely responsble for errors and omssons. Ths research was supported by U.S. Department of Energy Offce of Scence (BER) Grants Nos. DE-FG02-02ER63484 and DE-FG02-06ER64204.

2 1. Introducton Ths paper nvestgates the sources of the declne n the energy ntensty of the U.S. economy durng the perod , n partcular the mpact of technologcal change and ts mportance relatve to that of other nfluences. Ths ssue, wth whch economsts have wrestled for three decades, s agan a focus of nterest, stmulated by recent energy prce ncreases and proposals to reduce the greenhouse gas (GHG) emssons assocated wth fossl fuel use. The OPEC ol prce shocks of the 1970s and ther adverse economc consequences generated a groundswell of emprcal research on the reacton of technology to such prce changes. However, questons reman about both the sgn and magntude of the effects of energy prces on nnovaton, and the follow-on mpact of technologcal change on the ntensty of energy use. Concern has also arsen over the economc mpacts of measures to deal wth the problem of clmate change, partcularly energy prce ncreases nduced by lmts on carbon doxde emssons from fossl-fuel combuston. Of partcular nterest s the potental for nduced techncal change (ITC), whereby regulatons to reduce emssons stmulate nnovaton whch saves energy and reduces emssons. 1 Fnally, apprehenson over the economc consequences of the current hgh global energy prces has re-kndled nterest n the robustness of U.S. productvty growth to prce shocks. 2 In the present paper I focus on the relatonshp between energy prces and energy productvty, or, more specfcally, ts nverse energy ntensty. Fgure 1 llustrates the hstorcal trends of these varables n the U.S. economy. The most strkng feature s the 1 Energy-savng technologcal change s frequently adduced as the savng grace that wll moderate the costs of abatng CO 2 emssons over the long tme-horzon on whch emsson lmts are antcpated to bnd. Sue Wng (2006) elucdates the mechansms by whch changes n relatve prces nfluence the rate and drecton of frms nnovaton. 2 e.g., Energy and the Economy, remarks by Federal Reserve Charman Ben S. Bernanke before the Economc Club of Chcago, Chcago, IL, 15 June, 2006 (http://www.federalreserve.gov/boarddocs/speeches/2006/ /default.htm). 1

3 sustaned reducton n the energy-gdp rato, whose steepest declne occurs n the perod , durng whch energy prces frst jumped due to the OPEC ol shocks, and then collapsed. I consder three channels through whch prces nfluence energy ntensty: (1) nput substtuton the drect effect of ncreases n energy s relatve prce on the mx of nputs to producton, holdng the state of technology constant, (2) nnovaton resultng from both the secular progress of scentfc advance and the nducement effects of hgh energy prces, and (3) changes n the mx of ndustres n the economy. Despte much pror work scrutnzng each of these mechansms, the emprcal estmates developed by dfferent studes are for the most part ncommensurate. The objectve here s to develop comprehensve and comparable estmates for the magntudes of these nfluences. The frst comprehensve econometrc estmates of the substtuton effects of the energy prce shocks of the 1970s were developed by Jorgenson and Fraumen (1981) and Jorgenson (1984). The prncpal advantage of ths work, whch was conducted at the ndustry level, s ts coverage of the entre supply sde of the U.S. economy. Most controversal have been ts estmates of the effects of dsemboded techncal progress on energy demand, whch ndcate that the majorty of U.S. ndustres exhbt an energy-usng bas of nnovaton. Not only s ths result seemngly at odds wth the observed declne n energy ntensty, t s nconsstent wth the assumpton of aggregate energy-savng techncal change (the autonomous energy effcency mprovement, or AEEI) whch underpns most of the smulatons of future energy use and CO 2 emssons. 3 Indeed, on the bass of ths result Hogan and Jorgenson (1991) argue that the AEEI mght actually be negatve! 3 As dscussed by Hogan (1990), Manne and Rchels (1992) and Wllams (1990), the AEEI s a secular trend reflectng the technologcally-motvated rate of reducton n the demand for energy that, wthout any drected effort, decreases the amounts of CO 2 -emttng fossl fuel necessary for any gven level of economc output. Its frst documented use s Edmonds and Relly (1985), who cte the hstorcal declne n the energy ntensty of GDP wth 2

4 A potental resoluton to ths paradox les n the fact that Jorgenson s fndngs were generated usng a dataset whch ends 1979, when energy prces were at ther peak, just pror to the sharp declne n the energy-gdp rato. Thus, a key theme of ths paper s the queston of whether there s stll evdence for wdespread dsemboded energy-usng nnovaton over a longer sample whch encompasses the perod n Fgure 1 ( ). The bas of techncal change wth respect to energy s also rpe for re-examnaton gven results from more recent nvestgatons of ITC at the mcro level, whch suggest that nnovaton has been energy-savng n character, and has, moreover, been nduced by energy prces. Usng patent data, Popp (2002) demonstrates that the energy prce shocks of the 1970s nduced a substantal amount of energy-savng nnovaton. Complementary work by Newell et al (1999) fnds that energy prces nduced energy-savng changes n the characterstcs of resdental captal. 4 However, there s contnung debate over the magntude of the aggregate mpact of these phenomena, wth two nvestgatons of ts effect on energy use manufacturng sectors reachng very dfferent conclusons. Popp (2001) estmates that one thrd of the reducton n manufacturng ndustres energy-output ratos to the effects of energy-related knowledge emboded n patents. By contrast, Lnn (2006) estmates that adopton of energy-savng technology by new manufacturng plants n response to a ten-percent rse n energy prces resulted n only a one-percent reducton n energy demand. These fndngs rase addtonal questons about the sources of ntensty change: frst, how much has energy prce-nduced ncreasng economc development as justfcaton for a declnng coeffcent on energy nput. They construct a smulaton model that ncorporates an ncreasng ndex of energy-savng technology, whose nverse s appled as an attenuaton factor to the model s fuels demand functons. Ths trck s stll employed n the majorty of clmate polcy models. 4 Newell et al (1999) fnd that energy prces and regulatory stmul postvely affect the energy-effcency characterstcs of consumer durables for heatng and coolng. Popp (2002) fnds that the propensty to patent n energy technology felds was sgnfcantly ncreased by rsng energy prces n the 1970s. 3

5 nnovaton altered the characterstcs of non-resdental captal, and second, what has been the follow-on mpact on aggregate energy ntensty. To address the latter queston t s necessary to understand how the effects of technology on energy demand aggregate up to the level of the macroeconomy. Ths ssue s the focus of decomposton studes (see, e.g., the survey by Ang and Zhang, 2000) whch combne ndustry and macroeconomc data to solate how changes n the mx of economc sectors have affected the evoluton of the energy-gdp rato. These have tended to attrbute much of the declne n ntensty to changes n the composton of output (e.g., Rose and Chen 1991), partcularly among manufacturng ndustres (Hrst et al 1983; Schpper et al 1990). Motvated by these fndngs, the paper nvestgates whether structural change was a more or less mportant contrbutor to aggregate energy ntensty than substtuton or nnovaton. To sort out the contrbutons of these varous nfluences at the aggregate level n a comprehensve and consstent manner, I employ a synthess of the methodologcal approaches outlned above. Followng Jorgenson s lead, I maxmze sectoral coverage by accountng for the sources of change n energy ntensty wthn 35 economc sectors at the approxmate 2-dgt level of aggregaton. To nvestgate the mportance of changes n the composton of ndustres captal relatve to substtuton and nnovaton, I develop an econometrc model of dynamc factor demands whch ncorporates a broad array of quas-fxed nputs, and perform estmatons usng a unque dataset for the perod whch updates Jorgenson s results across the full range of producng sectors n the economy. Fnally, the resultng sectoral estmates are aggregated usng a decomposton technque, thereby reconclng the apparent dfferences between energy ntensty trends at the mcro and macro levels of the economy. 4

6 Emboded n ths approach are two key nnovatons. The frst s the extenson of Popp s (2001) econometrc model of ITC to ncorporate a proxy for the stock of energy-savng knowledge whch s based solely on energy prce data. Ths permts the mpacts of exogenous and nduced techncal progress on ndustres demands for energy to be separately dentfed. The second s the development of a smple decomposton scheme whch attrbutes changes n aggregate energy ntensty to the nfluence of changes n the mx of ndustres and factors whch occur wthn ndustres. Ths scheme provdes a mechansm for aggregatng the econometrc estmates across sectors to yeld comparable measures of the macroeconomc mpacts of substtuton, techncal progress and captal accumulaton. I fnd that change n the sectoral composton of the economy s the man drver of the declne n aggregate energy ntensty over the sample perod. Of the changes that occur wthn ndustres, dsemboded exogenous techncal progress s the predomnant energy-savng nfluence, wth shfts n the composton of captal comng a close second. The nfluence of substtuton s mxed. It had a substantal energy-savng effect durng the perod of hgh energy prces n the 1970s and 80s, but was slghtly energy usng over the remander of the sample perod. Fnally, dsemboded nduced techncal change was energy savng as well, but of the factors consdered t has the smallest mpact, whch only arses n the aftermath of the energy prce shocks. The plan of the paper s as follows. Secton 2 develops an econometrc model of producer behavor whch provdes a natural way to account for the sources of change n the energy ntensty of economc sectors. There I also outlne the decomposton procedure whch facltates consstent aggregaton of the sectoral econometrc estmates. Secton 3 descrbes the data and the estmaton technque. In Secton 4 presents and dscusses the econometrc estmates of the 5

7 sources of change n energy demand wthn the dfferent ndustres. Secton 5 presents the results of the decomposton analyss, whch aggregates over ndustres to elucdate the contrbutons of ther consttuent sources of change to the evoluton of the energy-gdp rato. Secton 6 concludes wth a dscusson of caveats and future research needs n ths area. 2. Modelng The Sources of Change n Energy Demand 2.1. An econometrc model of producer behavor The economy s modeled as a collecton of ndustres, ndexed by = 1,..., N. In each ndustry there s a representatve producer wth a short-run restrcted varable cost functon (RVCF), G [ P, X, Xɺ, Y, t], n whch P s a vector of varable nput prces, X s the level and X ɺ s the change n the vector of quas-fxed nputs to producton, Y s the level of output and t s tme. Each producer faces the problem of choosng the trajectory of quas-fxed nputs to mnmze the present dscounted value of costs: 0 rt (1) mn e { G [ P, X, Xɺ, Y, t] + u x } x, xɺ dt, where r s the nterest rate, u ra + d a = s the user cost of the vector of quas-fxed nputs, a s the vector of ther normalzed acquston (asset) prces, and d s the vector of asset-specfc rates of deprecaton. Berndt, Morrson and Watkns (1981) show that n the statonary equlbrum where X ɺ = 0 and the quas-fxed nputs have fully adjusted to ther long-run optmal levels, * X ɺ, the soluton to the problem n eq. (1) s gven by the equlbrum condton: (2) G[ P, X X * ] = u * G[ P, X ] + r X ɺ. 6

8 Followng Berndt, Morrson and Watkns (1981), Watkns and Berndt (1992), and especally Popp (2001), ndustry s normalzed RVCF s specfed usng a quadratc approxmaton for G: (3) G = L P + P E L E P + P M L M = L + p E E + p 1 2 = Y α 0 + α 0Tt + α v pv + α vv pv + pvt + α vj pv p j v 2 v v v j v X v 2 1 k, 1 + α k X k, 1 + α kk + α kt X k, 1t + α kv X k, 1 pv k 2 k Y k k v 2 1 Xɺ k X k Xɺ, 1, 1 + βk Xɺ k, 1 + β kk + β kt Xɺ k, 1t + β kv Xɺ k, 1 pv + γ kk k 2 k Y k k v k Y In ths expresson, varable nputs are denoted by the ndex = {labor (L), energy (E), materals (M)}, the prces of whch are gven by P v. The prces seres used n the regressons below are normalzed by the wage: p v (v = {E, M}). The varables X k, 1 and X ɺ k, 1 are the levels and changes n k classes of quas-fxed asset stocks, lagged one perod. Henceforth I use the lower M M k, 1 case forms of these varables to denote ther nput ntenstes: x / x ɺ = X ɺ / Y. k = X k, 1 Y and k k, 1 The varable t s a tme trend, whch s desgned to capture the effects of exogenous techncal progress on the demands for varable nputs. The objectve s to estmate the coeffcents α, β and γ. Watkns and Berndt (1992) note the dffculty of emprcally dstngushng the effects of scale and nnovaton n eq. (3). The estmated coeffcents often mply long-run ncreasng returns to scale accompaned by technologcal retrogresson, despte the plausblty and emprcal evdence for long-run constant returns to scale (LRCRTS) at the ndustry level. My dentfyng assumpton s to mpose LRCRTS by employng the net nvestment verson of ther model. 7

9 Industry s nternal costs of adjustment, A, are represented by all the terms n the varable cost functon nvolvng changes n quas-fxed nputs, level of output, adjustment costs are: X ɺ k. When normalzed by the a = A Y = 2 βk xɺ k + βkkxɺ k + βktxɺ kt + βkvxɺ k pv + k 1 2 k k k v k γ x xɺ. kk k k When the stocks of quas-fxed nputs have fully adjusted to ther optmal ntenstes, the change n the levels of these stocks, We therefore have: * x k, both * xɺ k, and the margnal unt adjustment costs must be zero. a * (4) = βk + βktt + βkv pv + γ kkxk = 0, xɺ k * x = x, x = 0 k k k v k k k ɺk whch mples the followng restrcton on the parameters: (5) βk = βkt = βkv = γkk = 0. By Shepard s Lemma, the optmal condtonal short-run nput demands are gven by the dervatves of G wth respect to the normalzed prces of the varable nputs. Imposng LRCRTS usng eq. (5) then yelds condtonal nput demand functons for energy and materals: (6) e = E / Y = α E + α EE p E + α EM pm + α ETt + α (7) m = M / Y = α M + α EM p E + α MM pm + α MTt + α Mk xk. The assocated condtonal demand for labor s derved as a resdual from eq. (3): k k Ek x k (8) l = L / Y = G / Y p 1 2 = α 0 + α 0Tt ( α EE pe, t + 2α EM pe, t pm, t + α α k xk + α kk xk + α kt xkt + β 2 2 k k E e p M k m k MM kk xɺ p 2 k 2 M, t. ) 8

10 Fnally, t s useful to derve the long-run equlbrum effect of quas-fxed nputs on varable cost, whch s found by dfferentatng (3) wth respect to X k : G X k = α + α x + α t + * k kk k kt * X k = X k, Xɺ k = 0 v α kv p v. Ths expresson, along wth eq. (4), mples that the equlbrum condton n (2) may be solved for the optmal quantty of quas-fxed nputs per unt of output: * (9) xk ( α k + α ktt + α kv pv + uk ) / α kk v =. Eqs. (6)-(8) form my econometrc model of producer behavor, n whch the coeffcents on the prces reflect the mpact of substtuton among varable nputs, those on the quas-fxed stocks gve the effects of changes n the level and composton of captal, and those on the tme trends proxy for the nfluence of technologcal progress on the demand for each nput. The strength of ths model s ts ablty to dstngush between the effects on energy demand of shortrun movements n varable nput prces and long-run adjustments of a range of dfferent quasfxed nputs. The marked varaton among dfferent assets n ther servce lves and energy-usng characterstcs suggests that the dfferental accumulaton of quas-fxed nputs s lkely to be the key dver of persstence n ndustres energy demand. In addton, Newell et al s (1999) results suggest that the captalzaton of new technology nto successve generatons of assets s lkely to be an mportant factor whch mtgates ths upward trend. Ths econometrc framework gves us the ablty to separately dentfy the mpacts of both processes on ndustres demand for energy. The model s dsadvantage s ts lmted capablty to dentfy the nfluence of prcenduced energy-savng nnovaton. Lnn (2006) dentfes ths effect usng the dfference between the energy ntenstes of ncumbent and entrant manufacturng plants, whle Popp (2001) uses the cumulated stocks of energy patents n each ndustry as drect proxy for the ntangble output of 9

11 nnovaton. The latter approach s attractve because t s the equvalent of specfyng a stock of dsemboded energy-savng knowledge as a quas-fxed nput n the model, but the absence of data on the use of patents by ndustry prevented me from mplementng ths scheme drectly. 5 The frst novel aspect of ths study s ts use of the trck of cumulatng energy prce ncreases as the proxy for the stock of knowledge. The fundamental assumpton n ths regard s that energy prce shocks stmulate the creaton of energy-savng deas and process and product desgns. The latter make up a stock of ntangble captal whose effect on energy demand s medated by three forces: persstence n the energy-savng effect of prce shocks due to the durablty of nventons and deas, declnng energy-savng effects wth the passage of tme due to the obsolescence of these factors, and lags n the onset of nduced energy savngs due to the tme necessary to conduct research and nnovaton, and to dffuse the resultng nnovatons among the frms n each ndustry. I model these forces n the same way as Popp (2001), representng nducement va energy prce ncreases nstead of patent counts. 6 Followng hs eq. (3), my proxy for the stock of dsemboded energy-savng knowledge n year t (X Knowledge,, t ), s the sum of past energy prce ncreases, πe = 100 max(0, p E ), 7 weghted by the tme-dependent nfluences of knowledge decay and dffuson: (10) X Knowledge,, t = π E, s exp( δ 1 s)[1 exp( δ 2 ( s + 1))] ds. 0 Here, s denotes the number of years before t, whle δ1 and δ2 are endogenous parameters whch ndcate the rates of decay and dffuson. Thus, n eq. (6) the coeffcent on the tme-trend (αet) 5 The key obstacle s the dearth of data on patents by sector of use for the ndustres covered by our dataset, especally mnng ndustres, utltes and communcatons, and servces. 6 The basc dea was ntroduced by Dowlatabad and Oravetz (2006). 7 The factor of 100 s ntroduced to mprove the numercal stablty of the estmaton procedure. 10

12 measures the nfluence of exogenous technologcal advance, whle that on energy-savng knowledge (αe, Knowledge) captures the cumulatve mpact of dsemboded prce-nduced nnovaton. A few caveats should be noted. Frst, ths specfcaton could hardly be more optmstc, as the defnton of πe assumes that any ncrease n energy prces wll nduce energy-savng techncal change. Thus, ITC wll occur even f the postve prce shock comes along after a sgnfcant declne n energy prces below ther long-run average level a stuaton n whch there mght well be lttle or no stmulus to nnovate, as the technques of producton whch are approprate for hgher energy-prce regmes clearly already exst, and may be re-actvated va substtuton. 8 However, the adverse mpact of ths potental msspecfcaton s mtgated by the fact that strength of the nducement effect and the nfluence of the resultng energy-savng knowledge on energy demand depends on δ1 and δ2, whose values are condtoned on the data, controllng for the nfluence of energy-materals substtuton. A second ssue s that the model gves the nducement effect of energy prces perhaps more promnence than s deserved, as t s lkely that the prces of all nputs wll smultaneously nfluence the creaton of dfferent knds of productvty-enhancng knowledge. The stock of knowledge nduced by shocks to the relatve prce of materals s not resolved. 9 Had t been ncluded, the total effect of all types of dsemboded knowledge mght well dffer from that captured solely by eq. (10), suggestng the possblty of omtted varable bas. But to the extent that omtted knowledge stocks ncrease steadly n magntude, ther nfluence wll be captured by the secular tme trend, wth the result that αet wll reflect the addtonal mpact of (latent) nduced nnovaton whch conserves non-energy nputs. 8 See, e.g., the dscusson n Sue Wng (2006: 5-7). 9 Its ncluson was not possble due to lmtatons of computatonal cost, and especally degrees of freedom. 11

13 Fgure 2 llustrates the senstvty of the stock of knowledge to the parameters by showng how eq. (10) depends on the values of πe, δ1 and δ2. Panel A llustrates the mpulse responses to a unt prce shock as a functon of the decay and dffuson parameters. Panel B shows the results of applyng these response functons to the aggregate energy prce seres n Fgure 1, whose postve shocks are ndcated by the shaded areas. Larger (smaller) values of δ1 are assocated wth faster (slower) rates of decay due to obsolescence, and greater (lesser) persstence of the new knowledge whose creaton was nduced by the shock, whle larger (smaller) values of δ2 are assocated wth faster (slower) rates of dffuson, and shorter (longer) lags between the onset of the shock and ts maxmum mpact on knowledge creaton. Consequently, larger values of the decay parameter are assocated wth smaller overall quanttes of knowledge, whle larger values of the dffuson parameter make the tme-paths of the knowledge stocks more volatle. An addtonal feature of panel B s that pror to the md-1970s the aggregate stock of energy-savng knowledge was neglgble, reflectng the fact that energy prces vared only slghtly over ths perod. We shall see that ths ends up havng an mportant bearng on the estmates of the tmng of ITC s mpact The sources of change n energy ntensty n the short and the long run The econometrc model provdes a unfyng framework wth whch to elaborate the sources of change n energy ntensty at the ndustry level. 10 Ths s apparent from the dscrete log-dervatve of eq. (6): e pv π E xk (11) ε Ev + ε ET + µ ET + η Ek. e p π x v v E k k 10 For a smlar approach employng a translog cost functon see Welsch and Ochsen (2005). 12

14 The left-hand sde s the rate of change n sectoral energy ntensty, whle the rght hand sde partton ths rate nto components assocated wth changes n varable nput prces, technology, and stocks of quas-fxed nputs. The parameter εev s the short-run elastcty of energy ntensty wth respect to the prce of the v th varable nput, (12) ε = e / p )( p / e ) = α p / e, Ev ( v v Ev v whch measures the average substtuton response to changes n varable nput prces. The parameters εet and ET are the short-run elastctes of energy ntensty wth respect to tme and contemporaneous energy prce shocks, respectvely: (13) ε ET = ( e / t)(1/ e ) = α ET / e, (14) µ ET = ( e / xe, Knowledge, )( xe, Knowledge, / π E )( π E / e ) = α E, Knowledge, (1 exp( δ 2 )) π E / e. These expressons have a natural nterpretaton as the average rates of exogenous and nduced dsemboded techncal progress. The last set of parameters, ηek, are the long-run net elastctes of energy ntensty wth respect to the k quas-fxed nputs. Followng Berndt, Morrson and Watkns (1981), I use a chan-rule argument to compute these estmates at the pont where the captal stocks adjust to ther long-run optmal levels: 11 * e e x k e (15) η ke = + = α ke xk / e * xk k xk x, k xk The results capture the net effects of adjustments n heterogeneous captal. Subsumed wthn the fnal term on the rght-hand sde of eq. (11) are the long-run nfluences of the evoluton of quas-fxed nput stocks on the prce responsveness and effcency 11 The correspondng short-run elastctes, εek, are zero by defnton. 13

15 of producton. As prevously mentoned, the drect effect of captal accumulaton on energy ntensty wll be postve n so far as assets requre energy to generate economc servces. Emboded nnovatons can drectly counterbalance ths effect by mprovng the energy effcency of successve generatons of assets. But they may also have the more subtle effect of makng the producton process more flexble, ncreasng the elastcty of substtuton and the responsveness of nputs demands to changes n relatve prces. The frst effect s dentfed from the nteracton of captal and tme, whle the second s dentfed from the nteracton of captal and varable nput prces. The proxes for these nfluences are the long-run analogues of (12) and (13) when quasfxed nputs have adjusted to ther equlbrum levels, and they are computed n a manner smlar to eq. (15). The addtonal effect of captal on nput substtutablty s captured by the long-run varable nput prce elastctes, ηev: * e e xk e (16) η = + Ev = ε Ev + ξ pv k xk pv pv k * kv, whle ts mpact on effcency s captured by the long-run average rate of techncal progress, ηet: 12 * 1 (17) e e x E, Knowledge, e xk η = + + ET π = + + E ε ET µ ET ξ * e t xe, Knowledge, π E k xk t k The dfference between the short- and long-run elastctes s the addtonal effect of embodment. Eq. (9) gves us the ablty to dentfy how much of each type of nfluence s assocated wth a gven type of captal: kt. 12 We do not dentfy the long-run rate of nduced techncal progress. To do so, we would have had to estmate k addtonal nteracton terms between D + E and each type of captal, ncurrng an unacceptable loss of degrees of freedom. 14

16 (18) ξ kv α ke kv v = and α α kk e p ξ kt α ke kt =. α α kk e 2.3. The aggregate mplcatons of ndustry-level ntensty change I now turn to the second novel feature of the analyss, whch s a method for assessng the mplcatons of the aforementoned sectoral results at the aggregate level. My approach s to decompose aggregate ntensty change nto ndustry-level ntensty change and structural change. I do ths by modelng the rato of aggregate energy use, E Agg, to GDP, Y Agg, as the weghted sum of the contemporaneous energy ntenstes of the ndustres n the economy: Agg N Agg Et (19) et = = Agg φ, te, t, Y t = 1 where each weght (φ ) s the rato of ndustry 's share of GDP to ts share of total energy use. 13 It s easly shown that the logarthmc dervatve of ths expresson s: 14 (20) e e Agg Agg N N 1 φ 1 e = +. N = 1 φ N = 1 e Φ Ψ The left-hand sde of ths expresson has the natural nterpretaton as the average rate of change n aggregate energy ntensty. Eq. (20) decomposes ths quantty nto two nfluences: the sum of changes n ndustres contrbutons Ψ to aggregate energy ntensty the structural change effect, Φ, and the average of changes n energy ntensty wthn ndustres the effcency change effect, Ψ. The fundamental nsght s that s just the average across ndustres of eq. (11). Thus, n each tme perod, the mpacts on aggregate energy ntensty of substtuton assocated wth 13 Our decomposton s nspred by Hogan and Jorgenson (1991) eq. (8). Although more sophstcated formulae are possble (see, e.g., Ang and Zhang 2000), we employ eq. (19) because of ts tractablty and ease of nterpretaton. 14 The dervaton s dscussed n the supplementary materal to the paper. 15

17 changes n the prces of varable nputs, technologcal progress, or changes n the level and composton of captal, may be found by computng the ndustry average of the relevant term on the left-hand sde of eq. (11). 3. Data and Estmaton To maxmze the ndustry coverage of the econometrc analyss, the KLEM dataset developed by Jorgenson and assocates was used as the prmary data source. Ths dataset records the real prces and quanttes of output and nputs of captal, labor, energy and ntermedate materals n 35 ndustres over the 43-year perod These data defne the prces and quanttes of output and varable nputs. Jorgenson s sectoral energy prce seres were adjusted to brng the correspondng energy quantty seres nto lne wth the trends n energy use by ndustry n offcal statstcs. The frst step was to construct new quantty ndces of sectoral energy nput from a varety of sources and re-base them to 1996 (the Jorgenson dataset s benchmark year). I retan Jorgenson s value of sectoral energy nput, and dvde ths seres by the new quantty ndces to generate new seres of energy prces by ndustry. The precse adjustments are descrbed n detal n the supplementary materals. Informaton on the dfferent classes of quas-fxed nputs s drawn from a secondary dataset, whch s the real cost net captal stocks seres by detaled asset and detaled ndustry from the BEA. 16 The ndustry-by-asset seres are truncated to match the tme perod of the Jorgenson dataset and apportoned among ndustry categores to match Jorgenson s sectoral dsaggregaton (approxmately 2-dgt SIC). The dfferent assets were also aggregated nto fve 15 I thank Jon Samuels for these data. 16 BEA (2003) descrbes ther constructon. 16

18 broad classes that defne the set of quas-fxed nput categores k: nformaton and communcaton technology (IT), electrcal equpment, machnery, vehcles, and buldngs and structures. Descrptve statstcs for the fnal dataset are shown n Table 1. I append random error terms to eqs. (6)-(8) and estmate these expressons as a separate smultaneous equatons tme seres regresson wth 45 free parameters for each ndustry. The resultng system was estmated usng GMM, wth the normalzed varable nput prces, the quas-fxed nput ntenstes, a tme trend and the knowledge stocks as nstruments. Andrews (1991) technque was used to compute the standard errors, whch are robust to autocorrelaton of up to thrd order. To construct the stocks of energy-savng knowledge t s necessary λ to compute the technologcal decay and dffuson coeffcents, δ1 and δ2, n each sector. The values of these ν λ endogenous parameters were estmated along wth the rest of the model usng the method outlned n Popp (2001). Specfcally, I defned auxlary parameters ν, (0, 1) such that ν λ δ1 = and δ 2 =, whch enabled me to perform a grd search over and to fnd the 1 ν 1 λ combnaton of ther values whch mnmzed the GMM crteron. 4. Econometrc Results The estmaton results are too numerous to dscuss n detal. The values, standard errors and levels of sgnfcance of the estmated coeffcents of the energy ntensty equaton (6) for all 35 sectors are tabulated n the supplementary materals. The ft between the estmated equatons and the data s generally good, however, the Durbn-Watson statstcs suggest that frst-order seral correlaton remans an ssue n just under half of the ndustres. 17

19 Below I report summary measures of the elastctes of energy demand wth respect to the covarates. The elastctes computed n secton 2.2 are pont parameters whose values vary wth the temporal evoluton of the dependent and ndependent varables. I therefore report ther average values over the perod of the sample, whch s ndcated by a bar over the relevant parameter. These quanttes are computed by evaluatng the varables n (13)-(18) at the means of the 43 years of data for each ndustry Short- and long-run varable nput prce elastctes The estmates of the average varable nput prce elastctes are shown n Table 2. The average short-run own-prce elastctes, ε EE of ndustres, and mostly of the expected sgn. 17, are unformly nelastc, sgnfcant n the majorty The average short-run cross-prce elastctes for energy and materals, ε EM sgnfcant n just over half of the ndustres, and the majorty of these suggest energy-usng mpacts. The energy-savng nfluence of materals prces s concentrated n mnng, transportaton and utltes, whle the energy-usng mpacts are concentrated n manufacturng. The two elastc responses are both negatve, occurrng n the non-metal mnng and communcatons sectors., are Wth regard to long-run mpacts, 14 of the average own-prce elastctes, η EE, are sgnfcant, wth three beng postve and two beng elastc. 18 We do not report the long-run energy-materal cross-prce elastctes, η EM, only three of whch are sgnfcant, and are mostly 17 The own-prce energy elastctes are postve and sgnfcant only n the ol and gas mnng, metal mnng, gas utltes and wholesale and retal trade sectors. 18 Elastc responses are exhbted by petroleum refnng, whch s large and postve, and electrcal machnery, whch s negatve. 18

20 energy usng. 19 Ths suggests that the nfluence of emboded nnovatons on the fungblty of varable nputs has had a neglgble overall mpact on energy ntensty Quas-fxed nput elastctes Table 2 also presents long-run average net elastctes of sectoral energy ntensty wth respect to the dfferent types of captal, η ke. IT captal, electrcal equpment and machnery all have decdedly mxed mpacts, wth equal numbers of ndustres exhbtng sgnfcant elastctes of ether sgn. IT captal exhbts unformly nelastc responses, whch are sgnfcant n 13 sectors. Elastctes wth respect to electrcal equpment and machnery are sgnfcant n 23 and 21 sectors (respectvely), and are evenly dvded n sgn. Elastc responses to the frst type of captal occur n four ndustres and are all postve, whle responses to the second are postve and elastc n fve ndustres and negatve and elastc n four. Vehcles and structures are both predomnantly energy-usng. The response of energy demand to changes n vehcle stocks s elastc n only three ndustres. 20 By contrast, elastc responses to structures occur n a large number of sectors, wth postve estmates n seven ndustres and negatve estmates n fve. Gven the mx of postve and negatve nfluences assocated wth the dfferent types of captal, the prevous fndng that embodment has lttle net mpact on substtuton s unsurprsng Stocks of Energy-Savng Knowledge I frst present estmates of the stocks of energy-savng knowledge before gong on to descrbe ther effects on energy demand. The estmates of δ1 and δ2 n Table 3 ndcate that the rates of decay and partcularly dffuson of energy-savng knowledge tend to be slow, wth a few 19 Non-metal mnng and furnture manufacturng exhbt elastc responses, wth the former beng negatve and the latter postve. 20 Of these constructon and lumber and wood are postve, whle fnancal servces s negatve. 19

21 sgnal exceptons. 21 The average lag before whch energy prces shocks nduce the maxmum amount of knowledge, T Peak, = log(1 δ2 / δ1) / δ2, 22 ranges from vrtually nstantaneous to several decades, wth a medan value of 2.6 years. Fgure 3 shows the mpulse response of knowledge to technologcal nducement at the medan values of δ1 and δ2. Its tme profle s smlar to Popp s (2001) Fgure 4, but although there s a smlar medan lag between the onset of the prce shock and the maxmum mpact on nnovaton (and energy savngs), the present stocks of knowledge decay twce as fast, and the maxmum mpact on knowledge accumulaton s only 50 percent larger than the nstantaneous effect roughly a quarter of that found by Popp. The mplcaton of these dynamcs s that the effects of ITC dsspate after 20 years, whch has an mportant bearng on the estmates of the effect of techncal progress on energy ntensty Elastctes of techncal change Table 4 summarzes the nfluences of techncal change on ndustres condtonal energy demand. By way of comparson, panels A and B report pror estmates by Jorgenson and Fraumen (1981) and Jorgenson (1984) for the perod pror to Panels C and D present estmates for the parameters αet and αe, Knowledge for the perod , and panels E-G tabulate the correspondng average short-run elastctes of energy ntensty wth respect to exogenous and nduced techncal change, ε ET and µ ET. Jorgenson and Fraumen s (1979) estmates are sgnfcant n all but sx ndustres and suggest that the effect of techncal change s overwhelmngly energy usng. Jorgenson s (1984) results exhbt more varablty, but stll show a domnant pattern of energy-usng techncal progress across ndustres. Hs estmates for both electrc and non-electrc energy nputs are 21 e.g., coal mnng, textles, rubber and plastcs, gas utltes, fnancal servces and government enterprses. 22 Note that T Peak, = arg max t {exp( δ1 t) (1 exp( δ2 t))}. 20

22 postve and sgnfcant n 14 sectors, and negatve and sgnfcant n only three. For the remanng sectors, the secular trends n the condtonal demands for electrcty and non-electrc energy are ether not sgnfcant, or have opposng sgns, suggestng an ambguous overall effect. 23 The magntude of these estmates s generally small, and ther cross-ndustry dstrbuton s negatvely skewed. For both electrc and non-electrc energy, the average of the sgnfcant estmates s negatve whle the medan s postve, reflectng Jorgenson s fndng that pror to 1980 the nfluence of technologcal change on energy demand was small and postve n many ndustres, but large and negatve n a small number of ndustres. 24 The estmates of the effects of the exogenous and nduced components of these trends over the longer sample n panels C and D are n contrast to the earler results. The mpact of exogenous techncal change s sgnfcant n 20 sectors, half of whch exhbt energy savng responses. The proxy for nduced techncal change s sgnfcant n nne sectors, four of whch show a negatve nfluence. The coeffcents on autonomous techncal change are smlar n magntude to those n the Jorgenson studes, whle those on ITC are very large, exceedng the former by one to two orders of magntude. These results ndcate that techncal progress had a negatve overall nfluence on ndustres energy ntensty. Moreover, they suggest that ndustres energy-savng response to nduced nnovaton was very strong, exceedng even that found Popp (cf. hs Table 5), whch s n apparent contrast to Lnn s (2006) fndngs. However, consderable care s necessary n nterpretng these results. The mpacts of ITC depends on the sectoral nput ntenstes of energysavng knowledge (x Knowledge ), whose magntudes tend to be qute small, especally when 23 The latter stuaton prevals n nne ndustres. 24 In the case of electrc energy nput, the ndustres wth the fve largest estmated coeffcents all exhbt an energysavng bas, whle n the case of non-electrc energy nputs, the largest estmated coeffcent s negatve and an order of magntude bgger than the second-largest. 21

23 compared to the stocks of physcal captal. Consequently, ts ultmate mpact s far more modest that the coeffcents n panel D seem to mply. An addtonal ssue s that the ITC coeffcent s not precsely estmated n many ndustres, whch s symptomatc of collnearty between p E and X Knowledge, 25 and reflects the dffcultes that arse from usng an nput based proxy for nnovaton nstead of an observable measure of nnovatory output such as patent counts. Replacng πe wth the latter mght well mprove the estmates n ths regard. However, the extent to whch ths mght change the results, and n what drecton, are questons that I leave to future research. The average elastctes n panels E and F are mostly nelastc, and ther sgns correspond to those of the relevant parameter estmates. Across ndustres, the overall effects on energy ntensty of both exogenous and nduced techncal change are negatve and substantal. Consequently, the average net elastctes of energy demand wth respect to techncal progress, shown n panel G, closely parallel the estmates n panel F. 26 To conserve space I do not report the average long-run elastctes of techncal change, η ET, whch are very smlar to the estmates n panel G. The latter are domnated by the elastc mpacts wth respect to nduced nnovaton n four ndustres: electrcal machnery, whch s energy usng, and constructon, chemcals and servces, whch are all strongly energy savng Emboded techncal change The data on quas-fxed nputs are nosy, consequently the mpact of the evoluton of physcal quas-fxed nputs on nput substtutablty and effcency are estmated wth precson n only n a few ndustres. To conserve space I tabulate the detaled estmates n the supplementary 25 Across ndustres, the correlaton between these varables ranged from 0.67 to 0.83 wth a mean of There are 13 ndustres n whch exogenous techncal change s sgnfcant but the combned effect of exogenous and nduced techncal change s nsgnfcant. By contrast, the latter measure s sgnfcant s every ndustry where nduced techncal change s sgnfcant 22

24 materals, and only gve a bref summary of the key results. The average effects of asset accumulaton on sectors own-prce elastcty of demand for energy, ξ ke, are small and mostly postve. The mpact on ndustres energy-materal cross-prce elastctes s smlarly mnor, wth sgnfcant values of ξ km n fve sectors, all of whch are negatve (wth the excepton of structures n the food products sector). The estmated mpact of embodment on energy effcency, ξ kt, are slghtly energy savng for nformaton technology and electrcal equpment, mxed for machnery, and predomnantly energy usng for vehcles and structures. The dearth of precse estmates makes t dffcult to draw robust conclusons, but the pattern of sgnfcant effects suggests that emboded techncal change may have a more pronounced mpact on effcency mprovement than on the flexblty of producton. There are also ndcatons that whle capacty expanson may lmt the potental to conserve energy n response to energy prce ncreases, t may enhance the substtutablty of materals for energy. Fnally, the sgn of the partcular nfluence changes dependng on the specfc quas-fxed nput under consderaton, wth energy ntensty beng amplfed by the effcency mpacts of vehcles and structures, but attenuated by the effects of IT captal on both effcency and materals-energy substtuton. Φ Ψ 5. Explanng the Trend n Aggregate Energy Intensty 5.1. Results of the decomposton analyss Chaned ndces for the effects and were calculated usng the output quantty and energy nput quantty seres for the 35 ndustres n the dataset. I also calculated the fractonal change n the energy-gdp rato usng aggregate energy consumpton from DOE/EIA (2005) and real GDP from the NIPAs. Fgure 4 presents chaned ndces of the structural change effect, the 23

25 Φ ntensty change effect, and aggregate energy ntensty. The jont mpact of these effects (.e., the sum of the chaned ndces of and Ψ) closely tracks E Φ Ψ Agg / E Agg, ndcatng that the dsparate data sources at the aggregate and sectoral levels tell a consstent story about the character of changes n U.S. energy ntensty. The trajectores of and explan the declne n ntensty n the U.S. from They ndcate that untl 1973, most of the reducton was due to changes n the sectoral composton of the economy. The latter changes are responsble for a 20 percent reducton n aggregate energy ntensty from ts 1958 level. Ths early declne was mostly offset by ncreases n energy ntensty wthn ndustres. After the frst OPEC ol shock the effects of structural change slowed down whle that of effcency change reversed drecton. As a result, throughout the 1980s and 1990s the mpact of changes n the sectoral composton of output was relatvely less mportant, contrbutng to an addtonal 15 percent reducton n aggregate ntensty, whle ndustres unt energy demands declned rapdly untl the end of the sample perod, fallng by 36 percent to end up 15 percentage ponts below ts 1958 level. The ndvdual ndustry dynamcs underlyng these aggregate trends are nosy, but the contrbutons of a few sectors stand out. Metal mnng, crude ol and gas, leather and government enterprses experence large ncreases n energy ntensty relatve to the 1958 base year, but these ndustres are n the mnorty. After the md-1970s, the ntensty of energy use falls n two-thrds of the ndustres n the sample. Most of these declnes were modest, wth cumulatve ntensty Ψ reductons of less than 50 percent relatve to sectors 1958 levels, but those n the chemcals, electrcal and non-electrcal machnery, and communcatons ndustres were very large. Thus, rather than beng drven by large effcency ncreases n a few key sectors, the declne n appears to be the result of slow and systematc mprovements over a broad cross-secton of 24

26 ndustres n the economy. We now employ the econometrc results of the prevous secton to elucdate the orgns of ths phenomenon The sources of effcency change By combnng eqs. (11) and (20), we are able to estmate the mpacts of the dfferent sources of ntra-ndustry effcency change at the aggregate level. We construct chaned ndces of the left-hand sde of eq. (11), whose evoluton s shown n Fgure 5. Over the long run, the substtuton effects assocated wth varable nput prces tended to ncrease aggregate energy ntensty, whle technologcal progress, as well as the net effects of the accumulaton and changes n the composton of quas-fxed nputs, tended to have the opposte effect. The energyusng nfluence of substtuton s slght pror to 1973 and pronounced durng the perod of low energy prces after 1993, ncreasng the ntensty of ndustres energy use by four percent over the 1959 level. In the nterregnum, varable nput prce movements were assocated wth large energy-savng effects, partcularly over the years , where they reduced ntra-sectoral energy ntensty by more than 12 percent relatve to The nfluence of techncal change s very slghtly energy usng pror to 1980 and energy savng thereafter, ultmately gvng rse to a nne-percent reducton n energy ntensty below the 1959 level. Quas-fxed nputs have an energy-usng nfluence over two-thrds of the sample. Pror to 1980 they are assocated wth ncreases n energy ntensty of 17 percent above 1959 levels, but subsequently exhbt a dramatc declne whch reduced energy ntensty by 36 percent below ts startng value. The chaned ndex of the sum of these varous factors tracks the ntra-ndustry effcency ndex reasonably well, but t tends to overstate the reducton n energy ntensty over much of the 25

27 sample. Ths behavor can be traced to the resdual errors n eq. (6), as well as a lack of precson n the estmated coeffcents, whose values were set to zero f they dd not acheve at least the ten percent level of sgnfcance. Fgures 6-8 shed lght on the underpnnngs of these trends. Fgure 6 elucdates the dfferent substtuton responses assocated wth the relatve prces of energy and materals. Whle the dynamcs of the substtuton effect n Fgure 5 are largely drven by energy prces, the aggregate mpact of materal prces s unformly energy-savng, whch reduces ntensty n the long run by more than seven percent below ts 1958 level. Ths effect both moderates the substtuton toward energy when the latter s prce s low, and amplfes the energy-savng nfluence of substtuton throughout the perod of the OPEC prce shocks. Fgure 7 llustrates the effects of the components of techncal change on the effcency of ndustres energy use. Exogenous techncal progress s the prmary drver of the long-run energy-savng mpact of nnovaton seen n Fgure 5, whch reduces ntensty by more than fve percent from ts 1959 level. Induced nnovaton s energy-savng as well, but ts ultmate effect s two-thrds as large. Interestngly, the early 1980s are a watershed perod for techncal change n two respects: The mpact of nduced nnovaton, whch before that tme was neglgble, begns to have a sgnfcant mpact, and the nfluence of autonomous techncal progress swtches drecton from slghtly energy usng to strongly energy savng Ψ It bears emphaszng that the apparent breaks n the aggregate trends n the nfluence of techncal progress on ntensty occurs n the absence of breakponts n the underlyng estmated ndustry-level trends. The clear mplcaton of eq. (6) s that the sgns of αe,t and αe, Knowledge are constant for each ndustry over the entre sample perod, and Table 4 ndcates that the correspondng elastctes εe,t and E,T are postve n some ndustres and negatve n others. The shft n the sgn of ther nfluence at the macro level s a consequence of changes n the contrbutons of the varous sectors to the effcency component of aggregate energy ntensty n partcular the larger weght enjoyed by those sectors whch exhbt an energy-savng bas of techncal change. Ths fact s most transparent n the case of autonomous techncal change, where, by (11), (13) and (20) the component of 1 N α ET attrbutable to ths factor s computed as. Over tme, ndustres n whch αe,t < 0 experence relatvely N e = 1, t 26

28 These estmates suggest that Popp s results on the energy-savng nfluence of nduced nnovaton are n fact consstent wth Jorgenson s early fndng of energy-usng bas of techncal change. The keys to the resoluton of ths puzzle are () the lags n the response of energy-savng knowledge to the energy prce shocks of the 1970s, and () the dfferental responses of ndvdual ndustres energy demands to ther own knowledge stocks, n conjuncton wth () the evolvng relatve contrbutons of dfferent sectors to both GDP and aggregate energy use. It s worth notng the relatvely small nfluence that ITC has on the energy-gdp rato, an mpact whch wll lkely be further attenuated by a less optmstc treatment of the nducement effect of energy prces. Even so, the polcy mplcatons are not mmedately clear especally wth respect to the problem of clmate change. On one hand, the fndng of a lmted role for nduced nnovaton would appear to support the conclusons drawn by Nordhaus (2002) from smulatons. But mtgaton measures are also expected to precptate a steady ncrease n the prces of fossl fuels as constrants on GHG emssons bnd more tghtly on the economy, whch under the current structural assumptons would provde a contnual stmulus to the accumulaton of energy-savng knowledge. As a result, t s also plausble that energy savngs due to ITC wll become ncreasngly mportant over the long tme horzon over whch emsson lmts are projected to bnd. Fgure 8 captures the mplcatons of Newell et al s (1999) results, demonstratng that shfts n the composton of quas-fxed nputs were as mportant as of changes n asset characterstcs for the long-run evoluton of energy ntensty. Pror to 1980, vrtually all types of larger declnes n e, causng the contrbuton of ther nfluence to ncrease, whch eventually reverses the drecton of technology s overall effect on aggregate ntensty. The emergence of a smlar pattern n the case of ITC suggests that both autonomous and nduced nnovatons were actng n the same drecton at the same tme, but ths result rases suspcon as to whether ITC s nfluence s properly dentfed. 27

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