Depreciation of Business R&D Capital

Transcription

1 Deprecaton of Busness R&D Captal U.S. Bureau of Economc Analyss Abstract R&D deprecaton rates are crtcal to calculatng the rates of return to R&D nvestments and captal servce costs, whch are mportant for captalzng R&D nvestments n the natonal ncome accounts and harmonzng BEA statstcs wth those of the productvty program of BLS. Although mportant, measurng R&D deprecaton rates s extremely dffcult because both the prce and output of R&D captal are generally unobservable. To resolve these dffcultes, economsts have adopted varous approaches to estmate ndustry-specfc R&D deprecaton rates, but the dfferences n ther results cannot easly be reconcled. In addton, many of ther calculatons rely on unverfable or oversmplfed assumptons. As of now, measurng R&D deprecaton rates remans an unresolved problem. To ncorporate the effect of ndustres technologcal and competton envronments, as well as gestaton lags, I develop an R&D nvestment model to derve ndustry-specfc R&D deprecaton rates for four R&D ntensve ndustres, the pharmaceutcal ndustry, the IT hardware ndustry, the semconductor ndustry, and the software ndustry. Based on Compustat company-based dataset, the model has produced results that not only algn wth conclusons from most recent lterature but also ndcate the dynamc technologcal changes across ndustres. The data cover the perod from 1989 to The constant ndustry-specfc R&D deprecaton rates are: ± 0.73 % for the pharmaceutcal ndustry, ± 1.00 % for the IT hardware ndustry, ± 1.78 % for the semconductor ndustry, and ± 1.89 % for the software ndustry. The ndustry rankngs of these R&D deprecaton rates are consstent wth the conclusons n most recent lterature. Tme-varyng ndustry-specfc R&D deprecaton rates are also presented n ths paper, and they further enhance our understandng about the dynamcs of technologcal change and competton across ndustres. 1

2 1. Introducton In an ncreasngly knowledge-based U.S. economy, measurng ntangble assets, ncludng R&D assets, s crtcal to capturng ths development and explanng ts sources of growth. Corrado et al. (2006) pont out that after 1995, ntangble assets reached party wth tangble assets as a source growth. Despte the ncreasng mpact of ntangble assets on economc growth, t s dffcult to captalze ntangble assets n the natonal ncome accounts and capture ther mpacts on economc growth. The dffcultes arse because the captalzaton nvolves several crtcal but dffcult measurement ssues. One of them s the measurement of the deprecaton rate of ntangble or R&D assets. The deprecaton rate of R&D assets s crtcal to captalzng R&D nvestments n natonal ncome accounts for two reasons. Frst, the deprecaton rate s requred to construct knowledge stocks and s also the only asset-specfc element n the commonly adopted user cost formula. Ths user cost formula s used to calculate the flow of captal servces (Jorgenson (1963), Hall and Jorgenson (1967), Corrado et al (2006), Azcorbe et al. (2009)), whch s mportant for examnng how R&D captal affects the productvty growth of the U.S. economy (Okubo et al (2006)). Second, the deprecaton rate s requred n the current commonly adopted approaches of measurng the rate of return to R&D (Hall 2007). As Grlches (1996) concludes, the measurement of R&D deprecaton s the central unresolved problem n the measurement of the rate of return to R&D. The problem arses from the fact that both the prce and output of R&D captal are unobservable. Addtonally, there s no arms-length market for most R&D assets and 2

3 majorty of R&D captal s developed for own use by the frms. It s, hence, hard to ndependently calculate the deprecaton rate of R&D captal (Corrado et al. 2006). Moreover, unlke tangble captal whch deprecates due to physcal decay or wear and tear, R&D, or ntangble, captal deprecates because ts contrbuton to a frm s proft declnes over tme and the man drvng forces are obsolescence and competton (Hall 2007), both of whch reflect ndvdual ndustry technologcal and compettve envronments. Gven that these envronments can vary mmensely across ndustres and over tme, the resultng R&D deprecaton rates should also vary across ndustres and over tme. In response to these measurement dffcultes, economsts have adopted four major approaches to calculate R&D deprecaton rates: producton functon, amortzaton, patent renewal, and market valuaton approaches (Mead 2007). As summarzed by Mead (2007), all approaches encounter the problem of nsuffcent data on varaton and thus cannot separately dentfy R&D deprecaton rates wthout mposng strong dentfyng assumptons. In addton, the patent renewal approach cannot capture all nnovaton actvtes; the producton functon approach reles on the questonable assumpton of ntal R&D stock and deprecaton rate. Currently, no consensus exsts on whch approach can provde the best soluton. Furthermore, because of the complexty nvolved n ncorporatng the gestaton lag nto the model, most research fals to deal wth the ssue of the gestaton lag by treatng t as zero or one to calculate the R&D captal stock (Corrado et al. 2006). Because product lfe cycle vares across ndustres, ths treatment s questonable for R&D assets. The majorty of research also gnores the rsky nature of R&D nvestments. 3

4 Falure to nclude ths rsk factor leads to nconsstent estmates of the returns to R&D and ts mpled R&D deprecaton rates because the dfferences n the realzed proftablty levels fal to reflect the true margnal mpact of R&D nvestment (Warusawtharana 2008). To captalze R&D nvestments nto ts Input-Output accounts around 2012 and other core accounts around 2013, the Bureau of Economc Analyss (BEA) has establshed an R&D Satellte Account (R&DSA) and contnues to develop methodologes to measure R&D deprecaton rates. In the 2006 R&DSA, BEA used an aggregate deprecaton rate for all R&D captal. In the baselne scenaro, BEA used 15% as the annual deprecaton rate for all R&D captal. In the alternatve scenaros, BEA used the deprecaton rate of nonresdental equpment and software for all R&D captal before 1987 and the deprecaton rate of nformaton processng equpment after that date. In the 2007 R&DSA, BEA adopted a two-step process to derve ndustry-specfc R&D deprecaton rates. In the frst step, BEA chose the mdponts of the range of estmates gven by exstng studes calculated for each ndustry (Mead 2007). In the second step, those mdponts were scaled down so that the recommended rates were more closely centered on a value of 15% and that the overall rankng of ndustry-level rates suggested by the lterature was preserved. The resultng R&D deprecaton rates are: 18.0% for transportaton equpment, 16.5% for computer and electroncs, 11.0% for chemcals, and 15.0% for all other ndustres. However, ths approach assumes that each set of estmates from the exstng research s equally vald and future deprecaton patterns wll be dentcal to those n the study perod. Moreover, the most recent studes conclude that deprecaton rates for busness R&D are lkely to be more varable due to dfferent 4

5 competton envronments across ndustres and hgher than the tradtonal 15% assumpton (Hall 2007). The purpose of ths paper s to develop an R&D nvestment model to derve ndustry-specfc R&D deprecaton rates by ncorporatng ndvdual ndustry s gestaton lags, as well as technologcal and competton envronments. The model s bult on the core concept that unlke tangble assets whch deprecate due to physcal decay or wear and tear, R&D captal deprecates because ts contrbuton to a frm s proft declnes over tme. Wthout employng any unverfable assumptons adopted by other methods, ths model contans very few parameters and allows us to utlze data on sales and R&D nvestments. In ths research, I use my model to derve ndustry-specfc R&D deprecaton rates for pharmaceutcal, IT hardware, semconductor, and software ndustres. The Compustat data cover the perod 1989 to The constant ndustry-specfc R&D deprecaton rates are: ± 0.73 % for the pharmaceutcal ndustry, ± 1.00 % for the IT hardware ndustry, ± 1.78 % for the semconductor ndustry, and ± 1.89 % for the software ndustry. The results demonstrate the promsng potental of the model n that: these derved R&D deprecaton rates fall wthn the range of estmates from the exstng lterature. The tme-varyng ndustry-specfc R&D deprecaton rates are also presented. The ndustry rankngs of constant and tme-varyng R&D deprecaton rates are consstent wth the conclusons n most recent lterature. In addton, the tmevaryng ndustry-specfc R&D deprecaton rates further enhance our understandng about the dynamcs of technologcal change and competton across ndustres. 5

6 Ths paper s organzed as follows. Secton 2 sets out the R&D nvestment model, followed by the descrpton of data analyss n Secton 3. Secton 4 concludes and dscuss topcs for future nvestgaton. 2. R&D Investment Model The premse of my model s that busness R&D captal deprecates because ts contrbuton to a frm s proft declnes over tme (Hall 2007). R&D captal generates prvately approprable returns; thus, t deprecates when ts approprable return declnes over tme. R&D deprecaton rate s a necessary and mportant component of a frm s R&D nvestment model. A frm pursung proft maxmzaton wll nvest n R&D optmally such that the margnal beneft equals the margnal cost. That s, n each perod, a frm wll choose an R&D nvestment amount to maxmze the net present value of the returns to R&D nvestment: j q I( RD )(1 ) max RD, (1) RD J 1 jd jd j0 (1 r) where RD s the R&D nvestment amount n perod, s the sales n perod, I(RD ) s the ncrease n proft percentage due to R&D nvestment RD, δ s the R&D deprecaton rate, and d s the gestaton lag and s assumed to be an nteger whch s equal to or greater than 1. Perod s R&D nvestment RD wll contrbute to the profts n later perods,.e., +d, +d+1,, +d+(j-1), but at a geometrcally declnng rate. s the length that should be large enough to cover at least the length of the servce lves of R&D assets. r s the cost of captal. 6

7 In the analyss presented later, we have found that, wth the same values of and, δ s dfferent across ndustres. It should be ponted out that J s not the length of the servce lves of R&D assets. can be n theory, but n practce any suffcently large value can be used n calculatons. We have confrmed that, wth greater than the servce lves of R&D assets, the derved deprecaton rates are very stable when we vary the number of n small ncrements. It s necessary to note here that, when a frm decdes the amount of R&D nvestment for perod, the sales q for perods later than are not avalable but can be forecasted. In ths study the past sales records are used to forecast the future sales to be ncluded n the estmaton of the deprecaton rate. The tme seres of sales data s frst taken logs and dfferenced n order to satsfy the statonary condton, and the converted tme seres s modeled by the autoregressve (AR) process. For the varous types of ndustral data ncluded n ths study, the optmal order of the AR model as dentfed by the Akake Informaton Crteron [Mlls, 1990] s found to range from 0 to 2. To mantan the consstency throughout the study, AR(1) s used to forecast future sales. The forecast error of the AR model wll also affect the estmaton of the deprecaton rate. To examne ths effect, we performed a Monte Carlo calculaton wth 1000 replcatons. In each replcaton, the forecast error of AR(1) at k steps ahead,, was calculated wth where was obtaned by AR estmaton. Ths error s then added to the forecast values based on the AR(1) model. For every ndustry ncluded n ths study, the 1000 estmates of the deprecaton rate exhbt a Gaussan dstrbuton. 7

8 In the followng the predcted sales n perod s denoted as qˆ. In addton, the choce of J can be a large number as long as t well covers the duraton of R&D assets contrbuton to a frm s proft. In ths study, we use 20 for J except for the pharmaceutcal ndustry J = 25 s used due to the longer product lfe cycle. To derve the optmal soluton, we defne as a concave functon: RD I[ RD] I 1 exp (2) The functonal form of has very few parameters but stll gves us the requred concave property to derve the optmalty condton. s the upper bound of ncrease n proft rate due to R&D nvestments. And, defnes the curvature of and s a reference number. That s, can ndcate how fast the R&D nvestment helps a frm acheve a hgher proft rate. Note that based on equaton (2), we have From the graph below, we can see that for example, when RD, the current-perod R&D nvestment amount, equals to, the ncrease n proft rate due to ths nvestment wll reach 0.64I Ω. When RD equals to 2, the ncrease n proft rate due to ths nvestment wll reach 0.87I Ω. We should be able to see dfferent ndustres have dfferent R&D nvestment scales reachng I Ω. 8

9 I(RD) I Ω 0.87I Ω 0.64I Ω 0 2 RD The value of can vary from ndustry to ndustry, and, as the data demonstrate an ncrease n R&D nvestment by multple folds n two decades, s expected to gradually grow wth tme as well. We model the tme-dependent feature of by, n whch 2000 s the value for year The coeffcent s estmated by a lnear regresson of log(rd) for the assocated ndustry. The R&D nvestment model becomes: RD RD J 1 I j0 qˆ jd I( RD ) 1 jd (1 r) RD 1 exp ( 2000, ) j J 1 j0 qˆ jd 1 (1 r) jd j (4) The optmal condton s met when RD 0, that s, I J 1 ( 2000, ) qˆ RD 0 exp j ( 2000, ) jd 1 (1 r) jd j (5), and through ths equaton we can estmate the deprecaton rate. 9

10 3. Industry-Level Analyss As a frst step n our emprcal analyss, we estmate the constant R&D deprecaton rate δ for four ndustres (pharmaceutcals, semconductor, IT hardware, and software) by usng the data from 1989 to 2008 to check whether our model gves us R&D deprecaton rates n lne wth rates n past studes. These ndustres are mportant for the ntal test of our model because the combned R&D nvestments of these four ndustres account for 54.56% of U.S. total busness R&D nvestments n We take the average values of annual sales and R&D nvestment n each ndustry from Compustat for estmaton. 1 The Compustat dataset contans frm-level sales and R&D nvestments for SICbased ndustres: pharmaceutcal, IT hardware, semconductor, and software. Ther correspondng SIC codes lsted n Table 1. The data covers the perod from 1989 to Fgure 1 dsplays the tme-seres plots of three ndustres for each dataset. Table 1. Industry and ts correspondent SIC codes Industry SIC codes Pharmaceutcals 2830, 2831, IT Hardware , , 3695 Semconductor 3622, , , 3810, 3812 Software We conduct ths calculaton from the data of 463 frms n semconductor ndustres (SIC codes 3622, , , 3810, 3812), 153 frms n IT hardware (SIC codes , , 3695), 651 frms n software (SIC code 7372), and 551 frms n pharmaceutcals (SIC codes 2830, 2831, ). 10

11 Q (n mllons) Q (n mllons) RD (n mllons) RD (n mllons) Q (n mllons) Q (n mllons) RD (n mllons) RD (n mllons) Prelmnary verson. Please do not crculate. 300 Pharmaceutcals 400 Hardware Year Year 300 Semconductor 200 Software Year Year Fgure 1. Mean values of ndustral R&D nvestments and sales for years calculated from the Compustat frm-level database The value of I Ω can be nferred from the Bureau of Economc Analyss (BEA) annual return rates of all assets for non-fnancal corporatons. As Jorgenson and Grlches (1967) argue, n equlbrum the rates of return for all assets should be equal to ensure no arbtrage, and so we can use a common rate of return for both tangbles and ntangbles (such as R&D assets). For smplcty, we use the average return rates of all assets for non-fnancal corporatons durng , 8.9%, for I Ω. In addton, n equlbrum the rate of returns should be equal to the cost of captal. Therefore, we use 8.9% for r. 11

12 We use Equaton (5) as the model to estmate the R&D deprecaton rate from data. As I Ω = r = 0.089, and as RD and q can be known from data, the only unknown parameters n the equaton are and. Because Equaton (5) holds when the true values of and are gven, the dfference between the left hand sde and the rght hand sde of Equaton (5) s expected to be zero or close to zero when we conduct a least square fttng to derve the optmal soluton. Therefore, we can estmate these unknowns by mnmzng the followng quantty: N J d 1 1 I ( exp RD 2000, ) / ( 2000, ) J 1 j0 q jd 1 (1 r) jd j 2 (6), n whch N s the total duraton of data. In practce N s a large number relatve to J + d and therefore multple least squares should be summed over n Equaton (6). Mnmzng Equaton (6) s therefore the same as least squares fttng between the model and the data. As the functonal form s nonlnear, the calculaton needs to be carred out numercally, and n ths study the downward smplex method s appled. In each numercal search of the optmal soluton of and 2000, several sets of start values are tred to ensure the stablty of the soluton. In ths study we use a 2-year gestaton lag, whch s consstent wth the fndng n Pakes and Schankerman (1984) who examned 49 manufacturng frms across ndustres and reported that gestaton lags between 1.2 and 2.5 years are approprate values to use. As mentoned prevously, we set the value of to 20 (for pharmaceutcals we use 25 due to the longer product lfe cycle n ths ndustry) to derve δ for all the combnatons of d and. 12

13 The estmated value of constant δ s ± 0.73 % for the pharmaceutcal ndustry, ± 1.00 % for the IT hardware ndustry, ± 1.78 % for the semconductor ndustry, and ± 1.89 % for the software ndustry. These results ndcate that the rankng of R&D deprecaton rates across ndustres n a descendng order s: IT hardware, software, semconductor, and pharmaceutcal ndustres. Snce the technologcal and competton envronments change over tme, the R&D deprecaton rates are expected to vary through the 20 years of nterval covered by our database. Therefore we need to calculate ndustry-specfc and tme-dependent R&D deprecaton rates. The tme-dependent feature of was obtaned by mnmzng Equaton (6) wth subsets of data. Instead of usng all years of data, we performed least squares fttng over a fve-year nterval each tme, n addton to the fve pror years used for sales forecasts. Three more subsets of data are examned n the same way, each wth a step of 3 years n progresson. As a result there are four subsets of data where the datamodel ft s carred out, and the estmated deprecaton rates are the md-years of tme wndows, whch are years 1995, 1998, 2001, and The man data for carryng out the data-model ft are the ndustry average sales and R&D nvestment data between 1989 and 2008 from Compustat. The BEA annual return rates to all assets for non-fnancal corporatons are used for the values of I Ω and r. We use (d, J) = (2, 20) for all ndustres except pharmaceutcals. When we alter the value of these parameters we obtan qualtatvely smlar results. The best-ft tme-varyng R&D deprecaton rates for the studed four ndustres show that the rankng order the deprecaton rates s n general mantaned over tme (See 13

14 R&D Deprecaton Rate [%] Prelmnary verson. Please do not crculate. Fgure 2). The vertcal and horzontal error bars are the standard devaton of the estmated R&D deprecaton rate resultng from the errors assocated wth sales forecasts Hardware Semconductor Software Pharmaceutcals Year Fgure 2. Deprecaton rates for four R&D ntensve ndustres The results of the tme-varyng R&D deprecate rates ndcate that (1) R&D resources n pharmaceutcals are more approprable than n other ndustres due to effectve patent protecton and other entry barrers; (2) Compared wth other ndustres, the IT hardware ndustry has been adopted a hgher degree of global outsourcng to source from few global supplers and the module desgn and effcent global supply chan management has made the ndustry products ntroduced lke commodtes, whch have shorter product lfe cycle. Therefore, the IT hardware ndustry has the hghest R&D deprecaton rate; (3) The R&D deprecaton rate of the semconductor ndustry has 14

15 slghtly declned snce early Ths s consstent wth the ndustry s consensus that the rate of technologcal progress n the mcroprocessor ndustry has slowed down after Table 2 compares the constant R&D deprecate rates estmated by ths study wth those obtaned from other recent studes. The comparson ponts to several favorable features of our model. Frst, the derved ndustry-specfc R&D deprecaton rates fall wthn the range of recent research estmates based on commonly-adopted producton functon and market valuaton approaches (Bersten and Mamuneas, 2006; Hall, 2007; Huang and Dewert, 2007; Warusawtharana, 2008). Also, the results are consstent wth those of recent studes, whch ndcate that deprecaton rates for busness R&D are lkely to vary across ndustres due to dfferent competton envronments each ndustry faces, and are hgher than the tradtonal 15% assumpton derved usng the data of the 1970s (Bersten and Mamuneas, 2006; Corrado et al., 2006; Hall, 2007; Huang and Dewert, 2007; Warusawtharana, 2008; Grllches and Maresse, 1984). 4. Concluson R&D deprecaton rates are crtcal to calculatng rates of return to R&D nvestments and captal servce costs, whch are mportant for captalzng R&D nvestments n the natonal ncome accounts. Although mportant, measurng R&D deprecaton rates s extremely dffcult because both the prce and output of R&D captal are generally unobservable. As of now, measurng R&D deprecaton rates remans an unresolved problem. Gven that no good soluton s avalable, BEA has adopted two smplfed methods based on exstng studes to temporarly resolve the problem of 15

16 Table 2. Summary of studes on R&D deprecaton rates Study δ: R&D Deprecaton Rate Approach Data Lev and Souganns Scentfc nstruments: 0.20 Amortzaton 825 U.S. frms over the (1996) Electrcal equpment: 0.13 perod of ; Ballester, GarcaAyuso, and Lvnat (2003) Knott, Bryce and Posen (2003) Bersten and Mamuneas (2006) Hall (2007) Hall (2007) Huang and Dewert (2007) Warusawtharana (2008) Chemcal: 0.11 Scentfc nstruments: 0.14 Electrcal equpment: 0.13 Chemcals: 0.14 Pharmaceutcals: Electrcal equpment: 0.29 Chemcals: 0.18 Computers and scentfc nstruments: 0.05 Electrcal equpment: 0.03 Chemcals: 0.02 Computers and scentfc nstruments: 0.42 Electrcal equpment: 0.52 Chemcals: 0.22 Electrcal equpment: 0.14 Chemcals: 0.01 Chps: Hardware: Medcal Equpment: Pharmaceutcal: Software: Ths study Semconductor: ± IT hardware: ± 0.01 Software: ± Pharmaceutcal: ± Amortzaton Producton functon Producton functon Producton Functon Market valuaton Producton functon Market valuaton R&D nvestment Model Compustat dataset 652 U.S. frms over the perod of for preferred specfcaton; Compustat dataset 40 U.S. frms over the perod of ; Compustat dataset U.S. manufacturng ndustres over the perod of U.S. frms over the perod of ; Compustat dataset U.S. frms over the perod of ; Compustat dataset U.S. manufacturng ndustres over the perod of U.S. manufacturng ndustres over the perod of ; Compustat dataset 1167 U.S. frms over the perod of ; Compustat dataset measurng R&D deprecaton rates n ts 2006 Research & Development Satellte Account (R&DSA) and 2007 R&DSA. BEA chose the rates followng two rules: Frst, the rates were close to tradtonal 15% assumpton. Second, the overall rankng of the rates suggested by the lterature was preserved. The methods, however, mplctly assume that all studes are equally vald and that future deprecaton patterns wll be dentcal to those n the study perod. Moreover, the most recent studes conclude that 16

17 deprecaton rates for busness R&D are lkely to be more varable due to dfferent competton envronments across ndustres and hgher than the tradtonal 15% assumpton. To ncorporate the effect of ndvdual ndustry technologcal and competton envronment, as well as gestaton lags, I develop an R&D nvestment model to derve ndustry-specfc R&D deprecaton rates. The premse of my model s that a busness R&D asset deprecates because ts contrbuton to a frm s proft declnes over tme. Wthout any problematc assumptons adopted by other methods, ths model contans very few parameters and allows us to utlze Compustat data on sales and R&D nvestments. Unlke prevous studes, t does not rely on the captal accumulaton formula, thus avodng the problem of gnorng productvty gan from R&D nvestments. My research results hghlght several promsng features of my model: Frst, the derved constant ndustry-specfc R&D deprecaton rates fall wthn the range of estmates from prevous studes. The tme-varyng results also capture the heterogeneous nature of ndustry envronments n technology and competton. In addton, the results are consstent wth conclusons from recent studes that deprecaton rates for busness R&D are lkely to be more varable due to dfferent competton envronments across ndustres and hgher than tradtonal 15% assumpton (Bersten and Mamuneas 2006, Corrado et al 2006, Hall 2007, Huang and Dewert 2007 and Warusawtharana 2008). Our analyss can be expanded to all thrteen R&D ntensve ndustres, as well as the comparson wth the results calculated wth Compustat and BEA-NSF datasets. In addton, to capture the dynamc nature of ndustry technology and competton envronments over tme, t requres BEA to buld a longer tme-seres data set wth both 17

18 R&D nvestments and ndustry outputs based on a consstent ndustry classfcaton method. BEA currently has NAICS-based R&D nvestment and ndustry output data from 1987 to 2008 and SIC-based ndustry output data from 1977 to However, n order to captalze R&D nvestments nto the natonal ncome accounts, t s mportant for us to establsh the dataset of R&D nvestments and ndustry output wth a longer tme seres. References Azcorbe, A., Moylan, C., and Robbns, C. Toward Better Measurement of Innovaton and Intangbles, Survey of Current Busness, January 2009, pp Copeland, A., & Fxler, D. Measurng the Prce of Research and Development Output, U.S. Bureau of Economc Analyss Workng Paper, October, Corrado, C., Hulten, C., & Schel, D. Intangble Captal and Economc Growth, Natonal Bureau of Economc Research workng paper 11948, January Grlches, Z R&D and Productvty: The Econometrc Evdence, Chcago: Chcago Unversty Press. Hall, B. Measurng the Returns to R&D: The Deprecaton Problem, Natonal Bureau of Economc Research Workng Paper 13473, October Huang, N. and Dewert, E Estmaton of R&D Deprecaton Rates for the US Manufacturng and Four Knowledge Intensve Industres, workng paper for the Sxth Annual Ottawa Productvty Workshop held at the Bank of Canada, May 14-15, Jorgenson, D. and Grlches, Z The Explanaton of Productvty Change, Revew of Economc Studes, 34 (July):

19 Mead, C. R&D Deprecaton Rates n the 2007 R&D Satellte Account, Bureau of Economc Analyss/Natonal Scence Foundaton: 2007 R&D Satellte Account Background Paper, November Mlls, T. C Tme Seres Technques for Economsts. Cambrdge: Cambrdge Unversty Press. Robbns, C., and Moylan, C Research and Development Satellte Account Update: Estmates for , New Estmates for Industry, Regonal, and Internatonal Accounts, Survey of Current Busness, October Slker, B R&D Satellte Account Methodologes: R&D Captal Stocks and Net Rates of Return, Bureau of Economc Analyss/Natonal Scence Foundaton: R&D Satellte Account Background Paper, December Sumye, O., Robbns, C., Moylan, C., Slker, B., Schultz, L., and Matalon, L. BEA s 2006 Research and Development Satellte Account: Prelmnary Estmates of R&D for Effect on GDP and Other Measures, Survey of Current Busness, December 2006, pp Warusawtharana, M. Research and Development, Profts and Frm Value: A Structural Estmaton, Federal Reserve Board workng paper, December