Analyzing Environmental Policies with IGEM, an Intertemporal General Equilibrium Model of U.S. Growth and the Environment Part 2

Transcription

1 Analyzng Envronmenal Polces wh IGEM, an Ineremporal General Equlbrum Model of U.S. Growh and he Envronmen Par 2 Rchard Goele Mun S. Ho Dale W. Jorgenson Danel T. Slesnc Peer J. Wlcoxen Ocober 2009 Prepared by Dale Jorgenson Assocaes for U.S. Envronmenal Proecon Agency, Offce of Amospherc Programs, Clmae Change Dvson. 1-

2 PART 2 1. Dealed descrpon of Model 1.1 Producon 1.2 Household model 1.3 Invesmen and he cos of capal 1.4 Governmen revenues, expendures, and defcs 1.5 Res of he world (expors, mpors and oal supply) 1.6 Mare balance and neremporal equlbrum 1.7 Emssons and damage funcons 1.8 Exogenous elemens n proecons 2. Esmang he demand sde of he US economy 2.1 Esmang household demands and labor supply 2.2 Personal Consumpon Expendures and wor hours, Esmang consumpon funcon subers 2.4 Esmang he neremporal consumpon funcon 2.5 Esmang nvesmen funcon subers 2.6 Esmang expor demand funcons 3. Esmang he supply sde of he US economy 3.1 U.S. economc performance a he ndusry level Esmang producon funcons for IGEM; op er 3.3 Esmang producon funcons for IGEM; sub-ers 3.4 Esmang mpor demand funcons Appendx A. Summary equaons of model Appendx B. Inpu-oupu accouns Appendx C. Measurng ndusry labor npu Appendx D. Measurng ndusry capal npu Appendx E. Esmaed parameers producon funcons. Appendx F. Supplemenary deals for consumpon model esmaon Appendx G. Governmen accouns and ax raes, daa and esmaes Appendx H. Supplemenary deals for he envronmenal analyses Appendx I. Model Soluon Algorhm 1-

3 Par 2. Analyzng Envronmenal Polces wh IGEM Chaper 1. Dealed Descrpon of he Ineremporal General Equlbrum Model (IGEM) of he U.S. Economy. Ocober 1, Dealed Descrpon of he Ineremporal General Equlbrum Model of he U.S. Economy. 1.1 Producon model Noaon Top er producon model Lower ers producon funcon for nermedae npus Relaon beween commodes and ndusres, and oupu axes. 1.2 Household model Noaon Household model 1 s sage (neremporal opmzaon) Household model 2 nd sage (goods and lesure wh demographc deals) Lnng CEX uns o NIPA uns Household model 3 rd sage (allocaon of consumpon bases) Lnng NIPA uns o Inpu-Oupu uns Oher household accouns 1.3 Invesmen and he cos of capal Aggregae nvesmen and cos of capal Invesmen by dealed commodes 1.4 Governmen revenues, expendures, and defcs 1.5 Res of he world (expors, mpors and oal supply) 1.6 Mare balance and neremporal equlbrum 1-1

4 In Chaper 1 of Par 1 we have presened a bref overvew of he Ineremporal General Equlbrum Model (IGEM) of he U.S. Economy. In hs chaper we descrbe he model n much greaer deal. The defnng characersc of a general equlbrum model s ha prces are deermned ogeher wh quanes hrough he neracons beween supply and demand. The producon secor s cenral o he supply sde of he model, whle he household secor forms he core of he demand sde. The model s compleed by mare-clearng condons ha deermne supples and demands for all commodes along wh he correspondng prces. Ineremporal equlbrum requres ha mare-clearng condons are sasfed for each commody a each pon of me. In addon, he mares are lned by nvesmens n capal goods and asse prces. Asse prcng mpars forward-loong dynamcs o IGEM, snce he prce of an asse s equal he dscouned value of he prces of capal servces over he asse s fuure lfeme. Capal servces are generaed by socs of asses accumulaed hrough pas nvesmens, so ha capal accumulaon provdes bacward-loong dynamcs for he model. A dsngushng feaure of IGEM s ha parameers of he behavoral equaons are esmaed economercally, raher han calbraed from esmaes aen from he leraure. We oulne esmaon of he demand sde of he model n Chaper 2 and he supply sde n Chaper 3. The demand sde ncludes he household secor, nvesmen demand, and demand for expors. The supply sde ncludes producon sub-models for 35 ndvdual ndusres and he demand for mpors. In descrbng he model we use smplfed noaon o avod a needless prolferaon of symbols. A complee ls of he 2000 equaons of he model s gven n Appendx A. Secon A.8 of hs Appendx provdes a glossary of all he symbols used. We recall ha Fgure 1 n he overvew chaper n Par 1 llusraes he flow of goods and facor servces among he four man secors of he economy producon, household, governmen, and res of he world. The flows of paymens among hese secors deermne he expendure paerns for he economy as a whole, ncludng consumpon, nvesmen, governmen, expors, and mpors. 1-2

5 1.1. Producon We focus aenon on mare-based polces, such as energy and envronmenal axes and radable perms. Envronmenal and energy axes nser ax wedges beween supply and demand prces and generae governmen revenue. The supply and demand for radable perms can be modeled along wh demands and supples for commodes. The coss assocaed wh mare-based polces are deermned hrough he prce responses o changes n polcy. The ey o analyzng he economc mpacs of energy and envronmenal polcy s he subsuably among producve npus, especally energy npus, n response o prce changes nduced by polcy. Whle producon paerns reflec subsuably among npus n response o prce changes, paerns of producon also depend on changes n echnology. In he long run he maeral well beng of he populaon depends on he growh of producvy. In addon, he relave demands for npus may be alered by based echncal change. For example, energy use may declne n nensy due o energy-savng changes n echnology, as well as subsuon away from hgher-prced energy. A complee characerzaon of producon requres boh subsuon and echncal change. Snce he rends ha underle changes n he paerns of producon are que complex, he specfcaon of models of producon suable for he analyss of energy and envronmenal polcy requres economerc mehods. Esmaes are no avalable n he leraure for he parameers ha descrbe subsuably and echncal change for all he ndusral secors ha comprse he U.S. economy. An alernave approach would be o adop assumed parameer values, such as elasces of subsuon equal o zero, as n npu-oupu analyss. However, he vas scale of energy conservaon snce he energy crses of he 1970 s has made he fxed coeffcens assumpon of npu-oupu models oally mplausble. We subdvde he busness secor no he 35 ndusres lsed n Table The governmen and household secors also used energy bu are excluded from he busness secor. Fve of he ndusres are energy producers Coal Mnng (ndusry 3), Ol and Gas Mnng (4), Peroleum Refnng (16), Elecrc Ules (30), and Gas Ules (31). We have chosen he classfcaon of he non-energy ndusres o dsngush among 1-3

6 secors ha dffer n he nensy of ulzaon of dfferen npus, especally energy, and exhb dfferen paerns of echncal change. The oupu of he producon secor s dvded among 35 commodes, each he prmary produc of one of he 35 ndusres. For example, seel s a prmary produc of he Prmary Meals ndusry, whle broerage servces are ncluded n he Fnance, Insurance, and Real Esae ndusry. Many ndusres produce secondary producs as well, for example, Peroleum Refnng produces commodes ha are he prmary oupus of he Chemcals ndusry. The model perms on producon of hs nd for all secors and all commodes. We model on producon along wh subsuon and echncal change for each ndusry. The parameers of our producon model are esmaed economercally from a hsorcal daa base coverng he perod The daa base s descrbed n Appendces B, C, and D, and ncludes a me seres of npu-oupu ables n curren and consan prces, as well as daa on he prces and quanes of capal and labor servces. 2 These daa comprse he ndusry-level producon accoun of he new archecure for he U.S. naonal accouns developed by Jorgenson (2009) and Jorgenson and Landefeld (2006, 2009). The npu-oupu ables conss of use and mae marces for each year. The use marx gves he npus used by each ndusry nermedae npus suppled by oher ndusres, noncompeng mpors, capal servces and labor servces. Ths marx also gves commody use by each caegory of fnal demand consumpon, nvesmen, governmen, expors, and mpors. The use marx s llusraed n Fgure 1.1. The rows of hs able correspond o commodes, whle he columns correspond o ndusres. Each enry n he able s he amoun of a gven commody used by a parcular ndusry. The sum of all enres n a row s equal o he oal demand for he commody, whle he sum of all enres n a column s he value of all he npus used n a gven ndusry. The mae marx descrbes an essenal par of he echnology of he U.S. economy. The rows of he mae marx correspond o ndusres, whle he columns 1 See also Table 1.1 n Par 1. 2 The mehodology and daa sources are presened n much greaer deal by Jorgenson, Ho, and Sroh (2005). 1-4

7 correspond o commodes. Each enry n he able s he amoun of a commody suppled or made by a gven ndusry. The domesc supply of he commody s he sum of all he enres n he correspondng column, whle he sum of all he enres n a row represens he value of he commodes produced by a gven ndusry. In shor, he ner-ndusry accouns of he sysem of U.S. naonal accouns are crcal componens of he hsorcal daa base for IGEM. The ner-ndusry accouns n curren and consan prces are dscussed n deal n Appendx B and Chaper 4 of Jorgenson, Ho, and Sroh (2005). The use marx ncludes values of capal and labor npus. Le he ner-ndusry flows, hese values are dvded no prces and quanes. The value of capal servces consss of all propery-ype ncome profs and oher operang surplus, deprecaon, and axes on propery and propery-ype ncome. The prce of capal servces consss of he prce of he correspondng asse, mulpled by an annualzaon facor ha we denoe he cos of capal. The cos of capal consss of he rae of reurn, he rae of deprecaon, less capal gans or plus capal losses, all adused for axes. The prce of capal servces and he cos of capal are dscussed n much greaer deal n Appendx D, n Jorgenson and Yun (2001), and n Chaper 5 of Jorgenson, Ho, and Sroh (2005). The quany of capal servces s he annual flow from a gven ype of asse. The asses ncluded n our hsorcal daa base are plan, equpmen, nvenores, and land. Plan and equpmen are sub-dvded no dealed caegores. For example, equpmen ncludes dfferen ypes of equpmen, rangng from moor vehcles and consrucon equpmen o compuers and sofware. We consruc prces and quanes of capal servces for each ndusral secor by aggregang prces and quanes of capal servces o oban a prce and a quany ndex of capal servces for each secor. Each ype of capal soc s weghed by he renal prce of capal servces, raher han he asse prce used n aggregang dfferen ypes of asses o oban capal socs. Smlarly, he value of labor servces ncludes all labor-ype ncome wages and salares, labor ncome from self-employmen, supplemens such as conrbuons o socal nsurance, and axes such as payroll axes. The quany of labor npu for each demographc caegory of labor npu s hours wored. We consruc a prce and a quany ndex of labor servces by aggregang over he prces and quanes of labor servces 1-5

8 from he dfferen demographc groups employed n each secor. These range from young worers wh only secondary educaon o maure worers wh advanced degrees. The prce and quany of labor servces are descrbed n more deal n Appendx C and Chaper 6 of Jorgenson, Ho, and Sroh (2005). Our mehods for aggregang over dealed caegores of capal and labor servces are an essenal feaure of our hsorcal daa se. Arhmec aggregaes conssng of smple sums of hours wored or asse quanes would no capure he subsuon possbles whn each aggregae. For example, a smple sum of compuers and sofware wh ndusral buldngs would fal o reflec he mpac on capal npu of a shf n composon oward nformaon echnology equpmen and sofware. Smlarly, a smple sum of hours wored over college-educaed and non-college worers would no reveal he mpac on labor npu of ncreases n educaonal aanmen of he U.S. wor force Noaon To descrbe our submodel for producer behavor we begn wh some noaon. The general sysem s o use P for prces and Gree leers for parameers. QI quany of oupu of ndusry PO prce of oupu o producers n ndusry PI prce of oupu o purchasers from ndusry QP quany of commody npu no ndusry PS prce of commody o buyers KD quany of capal npu no LD quany of labor npu no E ndex of energy nermedae npu no M ndex of oal nonenergy nermedae npu no P E, prce of energy nermedae npu no P M, prce of oal nonenergy nermedae npu no PKD prce of oal capal npu o ndusry PLD prce of oal labor npu o ndusry v value shares QC quany of domescally produced commody PC M, prce of domescally produced commody MAKE marx; value of commody made by ndusry 1-6

9 1.1.2 Top er producon funcon wh echncal change The producon funcon represens oupu from capal servces, labor servces, and nermedae npus. Oupu also depends on he level of echnology, so ha for ndusry : (1.1) QI = f ( KD, LD, QP1, QP2,... QPm, ), (=1,2,...,35) Ths form of he producon funcon s nracable as sands. We assume ha he producon funcon s separable n energy and maerals npus, so ha oupu a he frs sage of he producon model depends on quanes of energy npu and npu of nonenergy maerals, as well as npus of capal and labor servces: QI = f( KD, LD, E, M, ); (1.2) E = E( QP...); M = M ( QP,...) 3 1 In he second sage of he producon model he energy and non-energy npus depend on he componens of each of he aggregaes. For example, energy npu depends on npus of coal, crude ol, refned peroleum producs, naural gas, and elecrcy. These are prmary oupus of Coal Mnng, Ol and Gas Mnng, Peroleum Refnng, Elecrc Ules, and Gas Ules. Smlarly, non-energy npu depends on all he non-energy commodes lsed n Table 1.1. Ths ncludes maerals such as prmary and fabrcaed meals and servces such as fnancal servces. We assume consan reurns o scale and compeve mares, so ha he producon funcon (1.1) s homogeneous of degree one and he value of oupu s equal o he sum of he values of all npus: (1.3) POQI = PKDKD + PLDLD + PEE + PMM P E = PS QP + PS QP PS QP E P M = PS QP + PS QP PS QP M NCI, NCI, In order o characerze subsuon and echncal change we fnd more convenen o wor wh he prce funcon, raher han he producon funcon (1.1) 3. 3 The prce funcon conans he same nformaon abou echnology as he producon funcon. For furher deal, see Jorgenson (1986). 1-7

10 The prce funcon expresses he prce of oupu as a funcon of he npu prces and echnology, so ha for ndusry : PO = p( PKD, PLD, P, P, ). E M We have chosen he ranslog form of he prce funcon, so ha subsuably can be characerzed n a flexble manner and changes n echnology can be represened by laen varables hrough he Kalman fler, as n Jn and Jorgenson (2009): 1 p (1.4) ln PO = α + α ln p + β ln p ln p + ln p f + f p 0 2, p,, p ={PKD,PLD,P E,P M } α, β and α 0 are parameers ha are separaely esmaed for each ndusry, and we have dropped he ndusry subscrp for smplcy. The vecor of laen varables p p p p p ξ = (1, f, f, f, f, Δ f )' K L E M s generaed by a frs-order vecor auoregressve scheme: (1.5) ξ = Fξ 1 + v. The producon sub-model (1.4) and (1.5) acheves consderable flexbly n he represenaon of subsuon and echncal change. An mporan advanage of hs model s ha generaes equaons for he npu shares ha are lnear n he logarhms of he prces and he laen varables. Dfferenang equaon (1.4) wh respec o he logarhms of he prces, we oban equaons for he shares of npus. For example, f we dfferenae wh respec o he prce of capal servces, we oban he share of capal npu: PKDKD p (1.6) vk = = αk + βk ln P + fk. PO QI The parameers { β } are share elasces, gvng he change n he share of he h npu n he value of oupu wh respec o a proporonal change n he prce of he h npu. These parameers represen he degree of subsuably among he capal (K), labor (L), energy (E), and non-energy (M) npus. If he share elascy s posve, he value share ncreases wh a change n he prce of he npu, whle f he share elascy s negave, he share decreases wh a change n he prce. A share elascy equal o zero 1-8

11 mples ha he value share s consan, as n a lnear-logarhmc or Cobb-Douglas specfcaon of he echnology. The prce funcon s homogeneous of degree one, so ha a doublng of npu prces resuls n a doublng of he oupu prce. Ths mples ha he row and column sums of he marx of share elasces mus be equal o zero: (1.7) β = 0 for each ; β = 0 for each. Symmery of he prce effecs mples ha he marx of share elasces s symmerc. Monooncy and concavy of he prce funcon are dscussed n Chaper 3. The level of echnology evolve accordng o equaon (1.5). The laen varable f, ogeher wh he bases of echncal change { f p }, p echnology. The frs dfference of he level of echnology aes he form: p p p p p p (1.8) Δ f = Fp1 + FpK fk, 1 + FpL fl, 1 + FpE fe, 1 + FpM fm, 1+ FppΔ f 1+ vp f p represens he level of A more dealed descrpon of he producon sub-model, ncludng he prce funcon, s presened n Chaper 3. Here we descrbe a few of he ey feaures of hs model. The laen varables { f p } descrbe he bases of echncal change. A decrease n one of hese laen varables mples ha he npu share decreases as echnology changes. For example, f he energy share declnes, holdng prces of all npus consan, he bas wh respec o energy s negave and we say ha echncal change s energy-savng. Smlarly, a posve bas mples ha echncal change s energy-usng. Noe ha whle he parameers descrbng subsuon are consan, reflecng responses o varyng prce changes, he bases of echncal change are may vary from me o me, snce hsorcal paerns nvolve boh energy-usng and energy-savng echncal change Lower er producon funcons for nermedae npus In modelng producer behavor n Secon we have nroduced mul-sage allocaon n order o avod an nracable specfcaon of he producon funcon (1.1). In he lower ers of he model energy and non-energy maerals npus are allocaed o he ndvdual commodes. Repeang he second sage from (1.2): (1.9) E E QP3 QP4 QP16 QP30 QP31 M M QP1 QPNCI = (,,,, ); = (,... ). 1-9

12 To llusrae he elemens of he er srucure we consder he prce funcon for energy npu: (1.10) ln P = α + α ln P + β ln P ln P + f ln P P, 1 P, P, node = E P, E 0 2 energy, energy P { PS, PS, PS, PS, PS } PE, whle he share equaons are: (1.11) PS QP v P f, 3 3, ln P E node = = = α + β E + 3 PE E energy for coal mnng, he frs componen, and so on, for componens correspondng o crude peroleum, refned peroleum producs, elecrcy, and naural gas. The componens of he non-energy maerals (M) npu nclude he oher hry commodes n Table 1.1, n addon o noncompeng mpors, a commody no produced by any domesc ndusry. Ths s denoed X NCI n Fgure 1.1. We model he demand for ndvdual commodes whn he non-energy maerals aggregae for each ndusry by means of a herarchcal er srucure of ranslog prce funcons. The prce funcons for he sub-ers (1.10) dffer from he prce funcon (1.4), snce here s no laen varable represenng he level of echnology. Ths reflecs he fac ha he prce of energy s an ndex number consruced from he prces of he ndvdual componens, whle he prce of oupu s measured separaely from he prces of capal, labor, energy, and non-energy maerals npus. The prce of oupu could fall, relave o he npu prces, as producvy rses. As before, he parameers { β } are share elasces represenng he degree of subsuably among he fve ypes of energy. The laen varables of he Kalman fler { change. For example, an ncrease n he laen varable f30 f node } represen he bases of echncal node= E mples ha he elecrcy share of oal energy npu s ncreasng, so ha echncal change s elecrcy-usng, whle a decrease n hs laen varable mples ha echncal changes n elecrcysavng. The laen varables are generaed by a vecor auoregresson, as n (1.5). The long ls of commodes ncluded among he non-energy maerals npus requres ha he sub-models of hese npus mus be arranged n a herarchcal fashon. The er srucure for producer behavor n each ndusry s gven n Table 1.2. The non- 1-10

13 energy maerals npu consss of fve sub-aggregaes consrucon, agrculure maerals, meal maerals, non-meal maerals, servces. Each of hese sub-aggregaes n urn s a funcon of sub-groups, and so on, unl all he 31 commodes are ncluded. Each node o he er srucure employs a prce funcon le equaon (1.10) Relaon beween commodes and ndusres, and oupu axes. Producon or sales axes are proporonal o he prce of oupu. These axes are ncluded for all 35 secors of he producon model and nroduce wedges beween he prces faced by sellers and buyers of he correspondng commodes. We have noed above ha each ndusry maes a prmary commody and many ndusres mae secondary producs ha are he prmary oupus of oher ndusres. Denong he buyer s prce of he oupu of ndusry by full (1.12) PI = (1 + ) PO, The value of ndusry s oupu s VT and value of commody by, PC, QC and QI PI, we have: = PI QI. We denoe he prce, quany, QC V respecvely, all from he purchasers pon of vew. For column, le he shares conrbued by he varous ndusres o ha commody n he base year be denoed: (1.13) m M = ; m = 1 V, = T QC, = T For row, le he shares of he oupu of ndusry be allocaed o he varous commodes be denoed: (1.14) m row M row = ; m = 1 VT, = T QI, = T The shares (1.13) and (1.14) are fxed for all perods afer he base year. We assume ha he producon funcon for each commody s a lnear logarhmc or Cobb- Douglas aggregae of he oupus from he varous ndusres. The weghs are he base year shares. Tha s, we wre he prce of commody as: m1 mm (1.15) PC = PI1... PIm for =1,2,...35 The values and quanes are gven by: 1-11

14 (1.16) V = m PI QI for =1,2,...35 QC row (1.17). QC V = PC QC 1.2. Household model Polces ha affec energy prces have dfferen mpacs on dfferen households. On average households n warmer regons have larger elecrcy blls for coolng, elderly persons drve less, and households wh chldren drve more. To capure hese dfferences we subdvde he household secor no demographc groups. We rea each household as a consumng un, ha s, a un wh preferences over commodes and lesure. Our household model has hree sages. A he frs sage lfeme ncome s allocaed beween consumpon and savngs. Consumpon consss of commodes and lesure and we refer o hs as full consumpon. In he second sage full consumpon s allocaed o lesure and hree commody groups nondurables, capal servces, and servces. In he hrd sage he hree commody groups are allocaed o he 36 commodes, ncludng he fve ypes of energy. We now descrbe he hree sages of he model, begnnng wh a defnon of he symbols used Noaon A vecor of demographc characerscs of household X C quany of consumpon of commody C quany of consumpon of commody by household F quany of full consumpon R quany of aggregae lesure m R LS m KS n PF L P quany of lesure quany of aggregae labor supply value of full expendures of household quany of aggregae capal soc a end of perod growh rae of populaon prce of F prce of labor o employer, economy average 1-12

15 K P r Y S renal prce of capal, economy average rae of reurn beween -1 and household dsposable ncome household savngs Household model 1 s sage, neremporal opmzaon. Le V denoe he uly of household derved from consumng goods and lesure durng perod. In he frs sage household maxmzes an addvely separable neremporal uly funcon: T ( 1) V (1.18) maxf U = E{ (1 + δ ) [ ]} (1 σ ) = 1 subec o he lfeme budge consran: (1.19) T = 1 (1 + r) PF F W ( 1) (1 σ ) where F s he full consumpon n perod, F s s prce, r s he nomnal neres rae, and W s he full wealh a me 0. σ s an ner-emporal curvaure parameer, and δ s he subecve rae of me preference. The whn-perod uly funcon s logarhmc f σ s equal o one: ( 1) (1.18b) max F U { (1 ) ln } = E + δ V. T = 1 The erm full wealh refers o he presen value of fuure earnngs from he supply of angble asses and labor, plus ransfers from he governmen and mpuaons for he value of lesure. Tangble asses nclude domesc capal, governmen bonds and ne foregn asses. Equaons (1.18) and (1.19) are sandard n growh models found n macroeconomcs exboos 4 and we noe here ha he opmaly condon s expressed n an Euler equaon: Δ ln = (1 σ ) Δ ln +Δln( ( )) + ln(1 + ) ln(1 + δ ) (1.20) PF, + 1 F, + 1 V, + 1 D p, + 1 r+ 1 where D( p ) s a funcon of he prces of goods and lesure gven n (1.29) below. 4 See, for example, Barro and Sala--Marn (2003). 1-13

16 Chaper 2 descrbes how hs household Euler equaon s esmaed usng synhec cohors by addng over all households n each cohor. From hs we derve an aggregae Euler equaon. Ths Euler equaon s forward-loong, so ha he curren level of full consumpon ncorporaes expecaons abou all fuure prces and dscoun raes. The fuure prces and dscoun raes deermned by he model ener full consumpon for earler perods hrough he assumpon of raonal expecaons. The soluon of he model ncludes forward-loong dynamcs n every perod. From he value of full consumpon n any perod we have he ey elemens o derve he savngs n ha perod. The above srucure descrbes he mos dealed mplemenaon of he neremporal sage n IGEM. In verson 16 of IGEM we use a smpler verson wh an aggregae Euler equaon derved from aggregae goods consumpon and aggregae lesure. As descrbed n Chaper 2, hs aggregae Euler equaon (2.30) s smply: F (1 + n)(1 + r) PF 1 (1.20b) = F 1 + ρ PF 1 where n s he rae of growh of populaon Household model 2 nd sage, goods and lesure. In he second sage of he household model full consumpon s dvded beween he value of lesure me and personal consumpon expendures on commodes. Gven he me endowmen of he household secor, he choce of lesure me also deermnes he supply of labor. The allocaon of full consumpon employs a very dealed household demand model ha ncorporaes demographc characerscs of he populaon. The daa base for hs model ncludes he Consumer Expendure Survey (CEX) and Personal Consumpon Expendures (PCE) from he U.S. Naonal Income and Produc Accouns. Concepually, we deermne he consumpon X C of commody for household by maxmzng a uly funcon UC ( X 1,.. X.., X C CR; A ), where C X R s lesure and A denoes he demographc characerscs of household, such as he number of chldren and age of head of household. Summaon over all households gves he oal demand for commody : 1-14

17 (1.21) PC C = P C =1,2,,R X X CX X The prce P CX s he prce of good faced by household, he superscrp X denoes ha hs s a CEX measure ha mus be dsngushed from measures based on he Naonal Income and Produc Accouns and Iner-ndusry Transacons Accouns dscussed below. Smlarly, oal lesure demand s he sum over all household s lesure demands ( P CX R C X R deermned s sage 1: (1.22) PF F = PC C + PC C ), and he sum of goods and lesure gves he full consumpon X X X R R The ls of commodes ncluded n he household model s presened n Table 1.3 along wh he values n These are defned n erms of caegores of Personal Consumpon Expendures (PCE) and he las column of he able gves he precse defnons. One maor dfference beween our classfcaon sysem and he PCE s he reamen of consumers durables. Purchases of new housng are ncluded n nvesmen n he NIPAs, whle only he annual renal value of housng s ncluded n he PCE. Purchases of consumer durables such as auomobles are reaed as consumpon expendures n he PCE. In he new archecure for he U.S. naonal accouns dscussed by Jorgenson (2009), purchases are ncluded n nvesmen and annual renal values are reaed as consumpon. Ths has he advanage of achevng symmery n he reamen of housng and consumers durables. The annual flow of capal servces from hese asses s gven as em 35 n Table 1.3. X X A uly funcon wren as UC ( 1,..., CR; A ) s nracable. Accordngly, we mpose a er srucure much le he demand from nermedae npus n he producon model of Secon 1.1. A he op er uly funcon depends on nondurables, capal servces, servces, and lesure: (1.23) U = U( CND,, CK,, CSV,, CR, ; A ) C C C C C ND = ( 1, 2,... 16) ; SV = 17 C C( C,... C ) Consumer nondurables (C ND ) and servces (C SV ) are furher allocaed o he 36 commodes n he hrd sage of he household model. For he remander on hs sub- NCI 1-15

18 secon we focus on he op er. We frs descrbe he CEX daa used o esmae he parameers of he household model. We hen ndcae how he model for ndvdual households s aggregaed o oban he model of he household secor n IGEM. In order o characerze subsuably among lesure and he commody groups, we fnd convenen o derve household s demands from a ranslog ndrec uly funcon V( p, m; A ), where: H p p 1 H p p (1.24) lnv 0 ln 2 ln ' ln ln = α + α + B + ' BAA. m m m m H where p s a vecor of prces faced by household, α s a vecor of parameers, B H and B A are marces of parameers ha descrbe prce, oal expendure, and demographc effecs and A s a vecor of varables ha descrbe he demographc characerscs of household. 5 The value of full expendure on lesure and he hree commody groups s: (1.25) m = P C + P C + P C + P C. C C C C ND ND K K SV SV R R In (1.24) demands are allowed o be non-homohec, so ha full expendure elasces are no requred o be equal o uny. The commody groups n (1.23) and (1.24) represen consumpon of hese commodes by household. The lesure consumed by household s a more complcaed measure, snce we have o ae no accoun he dfferen opporuny coss of me of dfferen members of he household. We assume ha he effecve quany of lesure of person m ( R ) s non-wor hours mulpled by he afer ax wage, relave o m he base wage q = p / p. m m 0 R R We assume a me endowmen of H = 14 hours a day for each adul. The annual lesure of person m s he me endowmen less hours wored LS: (1.26) R m = q m ( H m LS m ) = q m (14*365 hours wored m ) The quany of lesure for household s he sum over all adul members: m (1.27) CR = R m and he value s: 5 The aggregaon properes of hs ndrec uly funcon s dscussed n Jorgenson and Slesnc (2008). 1-16

19 (1.28) PC = p R = p( H LS ) C 0 m m m m R R R R m m The demand funcons for commodes and lesure are derved from he ndrec uly funcon (1.24) by applyng Roy s Ideny: (1.29) w 1 H H H = ( α + B ln p ι' B ln m + B A ) D( p ) A where w s he vecor of shares of full consumpon, ι s a vecor of ones, and H D( p ) = 1 + ι ' B ln p. For example, he demand for consumer nondurables s:: 1 H H H (1.30) wnd, = ( αnd + BND ln p ιb ln m + BA, ND A ) D( p ) where B H ND denoes he op row of he B H marx of share elasces. We requre ha he ndrec uly funcon mus obey he resrcons: H H H H (1.31) B = B ' ; ι' B ι = 0, ι ' = 0, ια ' = 1, where B A H H B are he share elasces, ι ' B represens he full expendure effec, and he h column of B deermnes how he demands of demographc group dffers from he A base group. These resrcons are mpled by he heory of ndvdual consumer behavor and he requremen ha ndvdual demand funcons can be aggregaed exacly o oban he aggregae demand funcons used n he model. The resrcons are dscussed n greaer deal n Chaper 2. The esmaon of he parameers descrbng consumer demand from household survey daa s also descrbed n Chaper 2. The demographc characerscs employed n he model nclude he number of chldren, he four Census regons, and race, sex and hree age groups for he head of household. Snce s nfeasble o nclude demand funcons for ndvdual households n IGEM, we creae an aggregae verson of he demand funcons (1.29). To do hs we nerpre w as he vecor of full expendure shares and m as full expendures of a household of ype. Le n be he number of households of ype. Then he vecor of demand shares CX X CX X CX X CX X PND CND PK CK PSV CSV PR CR for he U.S. economy, w = (,,, )', s obaned by X X X X MF MF MF MF aggregang over all ypes of households: 1-17

20 (1.32) w = nmw nm = 1 H H H d L B ln p B B A D( p) α + ι ξ + ξ where he dsrbuon erms are: d (1.33) ξ = nm ln m / M; M = nm L (1.34) ξ = nma / M (1.35) For example, he nondurables componen of he aggregae share vecor s: w ND CX PND C = MF X ND X where MF X denoe he naonal value of full consumpon expendures n CEX uns: (1.36) MF = n m = P C + P C + P C + P C X CX X CX X CX X CX X ND ND K K SV SV R R By consrucng an aggregae model of consumer demand hrough exac aggregaon over ndvdual demands, we are able o ncorporae he resrcons mpled by he heory of ndvdual consumer behavor. In addon, we ncorporae demographc nformaon hrough he dsrbuon erms (1.33) and (1.34). For he sample perod we have he acual values of hese dsrbuon erms. For he perod beyond he sample we proec he dsrbuon erms, usng proecons of he populaon by sex and race. Tha s, we proec he number of households of ype, n, by lnng he age and race of he head of household o he proeced populaon. Ths s explaned furher n secon 1.8 on exogenous proecons Lnng he CEX o he NIPAs. The op er household model s esmaed from daa n he Consumer Expendure Survey (CEX). As explaned n Chaper 2, Personal Consumpon Expendures (PCE) n he Naonal Income and Produc Accouns (NIPAs), ncludes many ems mssed by he Survey. Snce we base IGEM on he NIPAs, we mus reconcle he CEX-based esmaes 1-18

21 o he NIPAs-based esmaes 6. We denoe he quany of consumpon of em n he NIPAs by N, and he prce by PN, =1,2, 35,R, as lsed n Table 1.3. Tha s, PN denoes he prce aen from he ables for PCE. Correspondng o he nondurables C ND and servces C SV commody groups, we we have he quanes from he NIPAs, N ND and N SV, and her prces, PN ND and PN SV. The prce of lesure PN R s derved by aggregaon over he populaon n (1.56), as explaned below. The equaons (1.32) allocae full consumpon among he shares w ND, w K, w SV, and w R. We denoe he shares based on he CEX as SC o he shares based on NIPAs: X = w. We need o reconcle hese ND ND K K CS CS R R N PN N PN N PN N PN N (1.37) SC,,, ' N N N N MF MF MF MF where MF N s full consumpon. We do hs by expressng he dfference beween he wo shares as an auoregressve process: (1.38) Δ SC = SC SC ={ND,K,CS,R} N X (1.39) Δ SC = α + βδ SC 1 + ε ε = ρε 1 + u We esmae (1.39) from sample perod daa and hen proec forward. Ths gves us an exogenous proecon of he dfference beween he wo ses of shares and (1.38) gves us he shares SC N based on he NIPAs. The value of full consumpon n CEX uns (1.22) can be rewren as he sum of he value of lesure and expendure on commodes: MF = P C + P C + P C + P C X CX X CX X CX X CX X ND ND K K SV SV R R = P CC + P C CC, X X CX X R R Afer rescalng o NIPA uns he value of full consumpon s: CC R R PFF = P CC + PN N (1.40) R R = PNN + PN N where P CC denoes he value of aggregae angble consumpon. Ths s he value ha CC s mached o he Euler equaon (1.20) n sage 1. 6 The esmaes dscussed n Chaper 2 are enrely based on he CEX, so ha daa from he NIPAs are no used. 1-19

22 1.2.4 Household model 3 rd sage, allocaon of demands for commodes. In he hrd and fnal sage of he household model we allocae he quanes of nondurables, capal servces, and oher servces N ND, N K and N CS o he 35 commodes, noncompeve mpors and capal servces. We do no employ demographc nformaon for hs allocaon, bu ulze a herarchcal model le he one employed for producon n Secon 1.1. A hs sage we mpose homohecy on each of he sub-models. There s a oal of 34 commody groups, one ype of capal servces, and one ype of lesure, as lsed n Table 1.3. These are arranged n 17 nodes, as shown n Table 1.4. Ths se of nodes s denoed as I CNODE n Appendx A. A each node m we represen m Hm he demand by a ranslog ndrec uly funcon, V ( P, m ; ) : Hm Hm Hm Hm m Hm P 1 P Hm P Hm P (1.41) lnv = α0 + α ln + 2 ln ' B ln + f ln m ICNODE m m m m m m m m Hm ln P (ln PN,...,ln PN,...,ln PN )' I The value of expendures a node m s: (1.42) m = PN 1N PN, N, m m m m m m m m1 m m, m CNODEm The shares of full consumpon derved from (1.41) are smlar o (1.29), bu exclude demographc varables and nclude laen varables represenng changes n Hm preferences f. When we mpose homohecy, ι ' B = 0, he demands smplfy o an Hm expresson ha s ndependen of he level of expendures (m m ): m (1.43) PN N / PN N m m m1 m1 m Hm Hm Hm Hm SN = = α + B ln PN + f m m PNmm, Nmm, / PN N Wh hs smplfcaon he ndrec uly funcon reduces o: 1 (1.44) lnv m = α Hm ln P Hm + ln P Hm ' B Hm ln P Hm + f Hm ln P Hm ln m m 2 The frs hree erms n (1.44) are analogous o he prce funcon (1.4) n he producon model. We can defne he prce of he m h base as: 1-20

23 1 (1.45) ln PN = α ln P + ln P ' B ln P + f ln P m Hm Hm Hm Hm Hm Hm Hm 2 If we also express he value of expendures as he prce (1.45), mulpled by he correspondng quany: (1.46) mm m m = PN N. Subsung (1.44) and (1.45) no (1.43), he uly ndex s he quany of he m h base, V m m = N. As an example, n he m=3 node he energy aggregae s a funcon of N 6 (gasolne), N FC (fuel-coal aggregae), N 18 (elecrcy), and N 19 (gas). The demand shares are: (1.47) PN N / PN N SN = = α + B ln PN + f m= 3 m= 3 PN19N19 / PN N m= 3 m= m= 3 H3 H3 H3 H3 The energy value ha appears n he nex hgher node (m=2) s: PN N = PN N + PN N + PN N + PN N. EN EN FC FC (1.48) Lnng he NIPAs o he Inpu-Oupu ables. The caegores of Personal Consumpon Expendures (PCE) from he Naonal Income and Produc Accouns (NIPAs) are gven n Table 1.3. The expendures are n purchasers prces, whch nclude he rade and ransporaon margns. These prces mus be lned o he supply sde of he model, where expendures are n producers prces. In he offcal npu-oupu ables hs ln s provded by a brdge able 7, for example, he PCE expendures of $32.9 bllon n 1992 for shoes s comprsed of he followng commody groups from he npu-oupu ables: $3.7 bllon from rubber and plasc, $11.2 bllon from leaher, $0.12 bllon from ransporaon and $17.8 bllon from rade. Le us denoe he brdge marx by H, where H s he of commody from he npu-oupu accouns n PCE em. The value of oal demand by households for commody s: 7 For he 1992 Benchmar n he Survey of Curren Busness, November 1997, hs s gven n Table D, Inpu-Oupu Commody Composon of NIPA Personal Consumpon Expendure Caegores. 1-21

24 (1.49) VC = HPN N. The prces from he NIPAs are also lned o npu-oupu prces hrough he brdge marx. Usng PS o denoe he supply prce of commody (explaned n more deal n secon 1.5 below), he prce of PCE em s expressed n erms of he ranspose of he brdge marx: (1.50) PN = H PS T C The quany of commody consumed by he household secor s: : C (1.51) C = VC / PS I COM The value of oal personal consumpon expendures s he sum over all commodes n eher defnon: (1.52) PCCCC = VC = PNN We emphasze agan ha he consumpon expendures n IGEM exclude he purchases of new consumer durables bu nclude he servce flow from he soc of durables. Purchases of new durables are reaed as nvesmen n order o preserve symmery beween housng and consumers durables Oher household accouns The demand for lesure n CEX uns s gven by he fourh elemen of he share vecor n (1.32). The aggregae demand for lesure n NIPA uns (N R ) s obaned by applyng he exogenous dfference from (1.38). Indvdual lesure s relaed o hours suppled o he labor mare n (1.26). We consruc an aggregae verson of hs equaon by defnng he aggregae me endowmen LH as an ndex number of he populaon, where ndvduals are dsngushed by gender, age, and educaonal aanmen. Le POP denoe he number of people n group a me, and he prce of me s he afer- m ax hourly wage of person, (1 l ) P L allocang 14 hours a day o each person, s: h m L (1.53) PLH = VLH = (1 l ) P *14*365* POP. The value of he aggregae me endowmen, We express he value of lesure as he produc of he quany LH and he prce of 1-22

25 hours P h. The Tornqvs ndex for he quany of he me endowmen s: 1 L L (1.54) dln LH = ( v + v ) dln(14 * 365* POP ) v 2 1 m L (1 l ) P *14*365* POP = ={gender,age,educaon} VLH L The prce of aggregae me endowmen s he value dvded by hs quany ndex: (1.55) P h VLH h = ; Pbaseyear 1 LH In a smlar manner we can defne he quany of lesure by aggregang over all populaon groups, where he annual hours of lesure for a person n group s denoed by R H : R 1 R R R (1.56) dln N = ( v + v ) dln( H * POP ) v 2 1 m L R (1 l ) P * H * POP = ={gender,age,educaon} VR R The lesure hours of group are derved from he accouns for hours wored descrbed n Appendx C. These accouns are used for esmang he quany of labor npu n Secon 1.1. Lesure s equal o he annual me endowmen, less he average hours wored for ndvduals n group : R (1.57) H = 14 * 365 HH The value of aggregae lesure s: m L R (1.58) VR = (1 l ) P * H * POP. The prce of aggregae lesure s he value dvded by he quany ndex: (1.59) PN R VR R = ; PNbaseyear 1 N R I should be poned ou ha he prce of aggregae me endowmen s no he same as he prce of aggregae lesure even hough a he level of he person n group hey are he same. Ths s due o he dfferences n aggregaon weghs and we relae he wo wh a lesure prce aggregaon coeffcen: (1.60) PN = ψ P R R h C 1-23

26 Tang he aggregaon coeffcen (1.60) no accoun, we defne labor supply as me endowmen, less adused lesure: (1.61) LS = LH ψ N R C R Ths mples ha he prce of lesure s dencal o he prce of me endowmen and he values are relaed as: (1.62) h h R R PLH= PLS+ PN N As explaned laer n Secon 1.6, he value of labor supply s relaed o he paymens by employers n he followng way: h m (1.63) PLS= (1 l ) PLDLD Gven he labor accouns, we nex descrbe he household fnancal accouns. In F he lfeme budge consran (1.19), W 0 represens he presen value of he sream of household full ncome, ha s, angble ncome plus he mpued value of lesure. Household angble ncome, Y, s he sum of afer-ax capal ncome (YK ne ), labor ncome (YL), and ransfers from he governmen (G TRAN ): ne TRAN (1.64) Y = YK + YL + G TLUMP ww 1 Labor ncome s: 1-24

27 (1.65) a h 1-l a YL = P LS = (1 l ) PLD m LD 1-l We dsngush beween margnal ax raes and average ax raes. The prce of he me endowmen and lesure refers o he margnal prce, he wage rae reduced by he margnal ax rae, whle ncome s defned n erms of he wage rae less average ncome axes. Capal ncome s he sum of ncome from he prvae soc of physcal asses and fnancal asses n he form of clams on he governmen and res-of-he-world: ne gov row (1.66) YK = (1 ) YK ppk 1K 1 YK + (1 ) ( GINT + Y ) The componens of capal ncome wll be explaned n more deal n secon 1.3 on capal, secon 1.4 on governmen, and secon 1.5 on he foregn accouns. Oher ems n (1.64) wll be dscussed n more deal n secon 1.4 on he governmen accouns. Full ncome ncludes he value of he me endowmen and s equal o household angble ncome Y plus he value of lesure: ne N R TRAN (1.67) YF = YK + YL + PN N + G TLUMP ww 1 Prvae household savngs s ncome less consumpon, non-ax paymens o he governmen (TAXN), and ransfers o res-of-he-world (CR) : (1.68) S = YF PF F CR TAXN + cvcc CC exemp = Y P CC CR TAXN + cvcc exemp 1-25

28 1.3 Invesmen and he cos of capal The prmary facors of producon n IGEM are capal and labor servces. Capal ncludes srucures, producer s durable equpmen, land, nvenores, and consumer durables. Ths dffers from nvesmen n he NIPAs whch nclude purchases of consumers durables as par of Personal Consumpon Expendures 8. We focus on capal owned by he prvae secor n hs secon; governmen-owned capal s no par of he capal mare and s dscussed laer. There are wo sdes o he capal accoun. The capal soc s rened o he producers descrbed n secon 1.1 and he annual renal paymen s he capal ncome of he household secor. The flow of nvesmen s purchased annually o replace and augmen he capal soc. We consder boh aspecs of he capal mare Aggregae nvesmen and cos of capal We assume ha he supply of capal s deermned by pas nvesmens; however, capal can may be moved coslessly among ndusres whn any perod. We also assume ha here are no nsallaon or adusmen coss n converng new nvesmen goods no capal socs. Wh hese assumpons, he savngs decson s dencal o he nvesmen decson. We presen an alernave approach o he savngs-nvesmen decson n order o clarfy he role of he cos of capal, a ey equaon of IGEM. The owner of he soc of capal chooses he me pah of nvesmen by maxmzng he presen value of he sream of afer-ax capal ncome, subec o a capal accumulaon consran: (1- )( PKDψ K -1- ppk -1)-(1- ) PII I (1.69) Max = u (1.70) K = (1 δ)k 1 +ψ I I a K ITC a s= u 1+ r s Afer-ax capal ncome (1- )( PKDψ K K -1- ppk -1) s relaed o he YK ne erm n household ncome (1.60), and he dscoun rae r s s he same as ha n he Euler equaon (1.20). The soc of capal avalable a he end of he perod s K.. The renal prce of 8 Land s n he fxed, non-reproducble asse caegory, and s no par of Invesmen n GDP (land s ransferred, no produced). The renal from land s, of course, ncluded n he ncome sde of GDP. 1-26

29 K capal servces s PKD. We requre an aggregaon coeffcen ψ o conver he soc measure o a flow of servces. 9 The remanng erms are p, he propery ax rae,, he capal ncome ax rae, and PK he prce of he capal soc. Fnally, I s he quany of ITC aggregae nvesmen and (1 ) PII s s prce ne of he nvesmen ax cred. In hs verson of he model we have gnored ax deals such as deprecaon allowances and he dsncon beween deb and equy. Aggregae nvesmen s a bundle of commodes, rangng from compuers o srucures. Capal soc s also an aggregae of hese commodes, bu wh dfferen weghs. A he level of he ndvdual commody, he capal accumulaon equaon s he famlar KS = (1 δ ) KS, 1+ I. Aggregaon over all he commodes resuls n (1.70) wh he coeffcen ψ I, an ndex of aggregae nvesmen qualy, and he aggregae deprecaon rae, δ. The soluon of he maxmzaon problem gves he Euler equaon (see A.3.3 n Appendx A): ITC ITC (1 ) PII 1 K (1 ) PII (1.71) (1 + r) = (1 )( PKDψ ppk 1) (1 δ) I + I ψ ψ 1 ITC There s a smple nerpreaon of hs equaon: If we were o pu (1 ) PII 1 dollars ITC n a ban n perod -1 we would earn a gross reurn of (1 + r)(1 ) PII 1 a. On he oher hand, f we used hose dollars o buy one un of nvesmen goods (= ψ I uns of capal) we would collec a renal for one perod, pay axes, and he deprecaed capal ITC would be worh (1 δ )(1 ) PII n perod prces. In a model whou uncerany hese wo reurns are equal. The assumpon of no nsallaon coss mples ha new nvesmen goods are perfecly subsuable for exsng capal as n (1.70). Ths means ha he prce of capal soc s lned o he prce of aggregae nvesmen: PK ITC (1.72) PK = ψ PII (1 ) a 9 These conceps are explaned n Appendx D descrbng he consrucon of hsorcal daa for nvesmen and capal. 1-27

30 The aggregaon coeffcen ψ plays a symmercal role o PK I ψ and s used o reconcle he sample perod dfferences n he nflaon of hese prces. The aggregaon coeffcens are aen as exogenous n he polcy smulaons. In equlbrum he prce of one un of capal soc (PK) s he presen value of he dscouned sream of renal paymens (PKD). Capal renal prces, asse prces, prces of capal soc, raes of reurn, and neres raes for each perod are relaed by (1.71). Ths ncorporaes he forward-loong dynamcs of asse prcng no our model of neremporal equlbrum. The asse accumulaon equaon (1.70) mpars bacwardloong dynamcs. Combnng (1.72) and he Euler equaon (1.71), we oban he well-nown cos of capal equaon (Jorgenson 1963): 1 (1.73) PKD = [( r π) + δ(1 + π) + p] PK 1 (1 ) where π = ( PK PK 1)/ PK 1 s he asse nflaon rae. The renal prce of capal equaes he demands for capal by he 35 ndusres and households wh he supply gven by K -1. As we explan n secon 1.6 below, he capal soc K -1 s he supply ha mees he demand for capal servces from he 35 producers and he household secor. Recall ha ha he renal paymen by ndusry s PKD KD. The sum over all ndusres s he gross ncome n eq. (1.69): K (1.74) PKDψ K = 1 PKD KD We denoe he afer-ax oal paymens by DIV (o nvoe he noon of dvdends). Ths s gross capal ncome less he propery ax and he capal ncome ax: hh PKD36KD36 (1.75) DIV = (1 )[ PKD KD ppkk] hh 1 Dvdend ncome s he maor componen of household capal ncome, YK ne, n (1.64) above. To recapulae: In IGEM capal formaon s he oucome of neremporal opmzaon. Decsons oday are based on expecaons of fuure prces and raes of reurn. Polces announced oday ha affec fuure prces wll affec decsons oday. 1-28

31 1.3.2 Invesmen by commody s a The quany of oal nvesmen demanded by he household/nvesor n perod I when he prce s PII. In he Naonal Income and Produc Accouns hs s an aggregae of nvesmen by dealed asse classes srucures, producer durable equpmen, consumer durables and nvenores. The value of nvesmen by hese asse ypes n 2005 s gven n Table In he benchmar npu-oupu ables, expendures n purchaser s prces are lned o producer prces va brdge ables 11. Usng hese brdge ables, we have consruced a me seres of nvesmen demands by he 35 commody groups employed n IGEM. We allocae nvesmen demand a I o he 35 ndvdual commodes by means of a herarchcal er srucure of producon models smlar o he demand for nermedae npus n he producer model. A he op er we express hs as a funcon of fxed and nvenory nvesmen: (1.76) I a = I( I fxed, I nvenory ) = I( I1, I2,..., I35) We denoe he value of prvae nvesmen by VII: (1.77) a fxed nvenory VII = PIII = VII + VII The demands for nermedae npus are derved from a herarchcal er srucure of ranslog prce funcons n equaons ( ) and Table 1.2. Smlarly, we derve fxed nvesmen commody demands from a nesed srucure of nvesmen prce fxed funcons. Tha s, we use he prce dual o he funcon, I = I( IF1, IF2,... IF35). The er srucure s gven n Table 1.6, here s a oal of 15 nodes domnaed by consrucon, vehcles and machnery. The se of nodes s denoed by I INV. The ranslog prce funcon for node m s a funcon of he componen prces {PII m1,...,pii m,m } and he laen varables Im f. Ths s wren as: 10 Ths able s updaed from Jorgenson, Ho and Sroh (2005) Table 5.1 whch ncludes nformaon on deprecaon raes. 11 In he 1992 Inpu-Oupu Benchmar hs brdge able s Table E n he Survey of Curren Busness, November For example, he $43.6 bllon nvesmen n he asse compuers and perpheral equpmen s made up of he followng commodes a producer prces: 32.7 from machnery, 3.4 from servces, 0.4 from ransporaon, and 7.1 from rade. 1-29

32 (1.78) m Im Im 1 Im Im Im Im Im I ln PII = α ln P + ln P ' B ln P + ln P ' f + log λ m I 2 INV The Kalman fler erm ( ) I INVm lnp Im ln PII m1,,lnpii m,,lnpii m,m f plays a role dencal o ha of f node n (1.10) for he Im producer model, and s modeled as a VAR le (1.5). The share demands correspondng o he prce funcon are: (1.79) PII IF / PII IF m m m1 m1 m Im Im Im Im SI = = α + B ln PII + f m m PIImm, IFmm, / PII IF m I m I INV INVm As an example, n he m=7 node he machnery aggregae s a funcon of IF 22 (ndusral machnery), IF 23 (elecrcal machnery) and IF MO (oher machnery). The demand shares are: (1.80) (1.81) PII IF / PII IF SI PII IF PII IF B PII + f PII IF / PII IF m= 7 m= m=7 m= 7 m= 7 I 7 I 7 I 7 I 7 = / = α + ln MO MO m= 7 m= 7 Toal nvenory nvesmen s specfed as a share of aggregae nvesmen: VII nvenory IY = α VII IY where he share α s aen from sample daa. Toal nvenory demand s specfed as a Cobb-Douglas funcon of he commodes, usng acual shares n he sample perod and he share for he fnal year of he sample for proecons. The value of nvenory nvesmen n commody s: (1.82) nvy IY nvy VII = α VII ICOM The oal nvesmen demand for commody s he sum of he fxed nvesmen and nvenory componens: (1.83) VI = VI + VI PS I PII IF VI fxed nvenory nvenory = + Ths se of equaons s specfed n complee deal n Appendx A, eq. A