Hi-Sa Discussion Paper Series No.229 Esimaing Producion Funcions wh R&D Invesmen and Edogeney Young Gak Kim December 2007 Hosubashi Universy Research Un for Saisical Analysis in Social Sciences A 21s-Cenury COE Program Insue of Economic Research Hosubashi Universy Kunachi, Tokyo, 186-8603 Japan hp://hi-sa.ier.h-u.ac.jp/
Esimaing Producion Funcions wh R&D Invesmen and Endogeney YoungGak Kim Graduae School of Economics Hosubashi Universy December 2007 ABSTRACT This sudy analyses he producion funcion esimaion when here is an unobservable idiosyncraic producivy shock and he series of he producivy shock follows a firs-order endogenous Markov process which is conrolled by R&D invesmen. The producion funcion approach, in general, suffers from endogeney problems when here are deerminans of producion which are no observed by he economerician bu are observed by he manager of a firm. To conrol for his problem, recenly developed economeric mehods are applied o he producion funcion esimaion. The resuls show ha here is a possibily ha oher esimaion mehods such as OLS esimaion and fixed effec esimaion underesimaes he conribuion of capal. The resuls also sugges ha he rae of reurn o R&D varies considerably across indusries and whin an indusry. JEL Classificaion Numbers: D24, O32
1. Inroducion In he leraure, here are wo main approaches o he valuaion of R&D, ha is, he producion funcion approach and he marke value approach. In he producion funcion approach, he producion funcion is ypically esimaed in a parameric way wh he R&D sock which is he accumulaed value of R&D expendure afer depreciaion. This approach was originaed by Griliches (1981), and is ofen called he knowledge-capal model. In conras, he marke value approach is based on he heorem ha under he assumpions of linear homogeneies of he producion funcion and he adjusmen cos funcion, he value of a firm is equivalen o he weighed sum of each asse of he firm. 1 By regressing he marke value of a firm on he asses which he firm has, one can obain he coefficiens on he asses which show how he marke values each asse. The marke value approach also uses he R&D sock o gauge he rae of reurn of R&D. Alhough hese wo approaches have a long hisory and have been used in many sudies, boh suffer from some common problems. Here, wo of hem are singled ou. The firs is he endogeney problem in he esimaion. As Marschak and Andrews (1944) and many oher scholars afer hem have poined ou, here is a possibily ha he decisions ha a firm makes depend on he producivy which is unobservable o he economerician. If his is he case, OLS esimaes are biased, no maer wheher he producion funcion or of marke value approach are chosen. 2 A few soluions o his problem have been developed and used in he leraure. Two of he earlies soluions are insrumenal variables (IV) esimaion and fixed effecs esimaion. For he las fifeen years, wo new echniques have been developed. One of hem is dynamic panel esimaion. 3 The oher is he echnique developed by Olley and Pakes (1996) and Levinsohn and Perin (2003). The second problem is relaed wh how o consruc he R&D sock daa. In his leraure, many sudies calculae accumulaed R&D expendures (wh appropriae depreciaion) o obain he R&D sock. However, his procedure requires he cerainy assumpion (i.e., all of he R&D expendure is accumulaed wh 100 percen cerainy) and assumpions wh regard o he depreciaion rae (i.e., R&D sock depreciaes wh a cerain fixed rae). However, he firs assumpion ignores he uncerainy surrounding R&D, which is one of he mos characerisic aspecs of R&D invesmen. As for he second assumpion, mos sudies simply assume an arbrary rae of depreciaion, which has been radionally 15 percen. If one ries o use only flow informaion on R&D o esimae he producion funcion, anoher srong assumpion is required, namely ha he raio of R&D expendure o R&D sock is very sable, which may no be he case in realy. This paper focuses on addressing hese wo problems aking he producion funcion approach. 1 See Wildasin (1984). 2 The marke value esimaion is basically equivalen o he invesmen funcion esimaion which is well known o suffer from he endogeney problem. 3 See Arellano and Bover (1995) and Blundell and Bond (2000). 1
The esimaions in his paper are designed for solving he endogeney problem, and are based on he esimaion model developed by Olley and Pakes (1996) and Levinsohn and Perin (2003). Boh hese sudies propose a similar srucural esimaion, bu differ in which variable o use o proxy he firm-specific producivy shock. Their approaches have been adoped and exended in a large number of sudies. 4 Ye, mos of hese sudies do no explicly include R&D acivy as an inpu. As for his poin, Buener (2005) showed ha endogenizing he producivy process and incorporaing R&D expendures ino he dynamic invesmen model of Olley and Pakes is difficul. However, Doraszelski and Jaumandreu (2007) ried o solve his problem using labor inpu o proxy he producivy shock and obained reasonable resuls. The esimaion model of Doraszelski and Jaumandreu (2007) is closes o he model in his paper. The esimaion model in his paper uses only informaion on R&D expendure, no R&D sock. Insead, R&D expendure is assumed o conribue o he enhancemen of he producivy. One of he advanages of his model is ha here is no need for srong assumpions wh regard o he R&D acivy, such as assumpions of a fixed rae of depreciaion and he linear and cerain accumulaion of knowledge. This paper found ha here are poenial esimaion biases and ha he possible origins of he biases are unobservable producivy shocks (endogeney problem) and ignoring he conribuion of R&D acivy. The biases are especially prominen in he esimaes of he coefficien on capal. Besides, he relaionships beween reurns on R&D invesmen and firm s characerisics are examined in deail. The paper sars by describing he basic model in he nex secion. In Secion 3, he sraegy for conrolling for he endogeney is described in deail. Secion 4 provides some explanaion on he daa used in his paper. In Secion 5, he resul of he basic esimaion is repored and compared wh he resuls of oher esimaion mehods, while Secion 6 focuses on he relaionship beween producivy and R&D expendure. 2. The opimal behavior of a firm This secion describes he basic model used in his paper. The model considers he opimal behavior of a firm in a general seing. A he beginning of each period, he firm makes four inpu decisions, ha is, how much inermediae inpu o use for he producion of ha period, how much o inves as capal for he producion of he nex period, how much o expend on R&D acivy o enhance he producivy of nex period, and how many people o employ for he producion of nex period. These assumpions mean ha inpu decisions wh regard o capal, labor, and R&D should be made one year ahead. In mos sudies, labor inpu is considered as a variable inpu. In realy, however, and 4 According o Ackerberg, Caves, and Frazer (2006), hese wo sudies are ced direcly in more han 800 papers. 2
especially in Japan, labor mobily is relaively low, meaning ha labor is more akin o a fixed inpu. Mos lised companies decide heir employmen levels a leas one year ahead. Given his suaion, he only variable inpu is inermediae inpu. Invesmen in angible capal, R&D acivy, and employmen decisions may involve adjusmen coss. An opimizing firm maximizes he discouned presen value of fuure profs. The producion funcion of such a firm is Y = F A, K, L, M, ω, ε ), (1) ( where K, L, and M are he capal inpu, labor inpu, and inermediae inpu respecively. A is he common echnology level a ime. Boh ω and ε are producivy shocks experienced by he firm, bu differ in he sense ha he former are observable o he manager of he firm bu no o he economerician whereas he laer are unobservable o and unpredicable by boh he manager and he economerician. Each period, he manager of he firm decides he level of producion (Y ), of inermediae inpus (M ), of invesmen in capal for producion in he nex period (I ), of expendure on R&D acivy for producion in he nex period (R ), and of addional employmen for producion in he nex period (E ) afer observing he firm s producivy (ω ). These assumpions mean ha akes a full period for new invesmen in capal o be ordered and insalled and addional employees o be hired and rained and o be ready for producion. New invesmen and new employees add o he fuure capal sock and labor force respecively in a deerminisic way: K + + 1 = (1 δ ) K I ( 2) L = L + E +1 (3) Invesmen in R&D acivy does no show up in he producion funcion because is assumed here ha he firm invess in R&D acivy o enhance he producivy level. The producivy shock in he nex period is assumed o be a funcion of he producivy level and he R&D expendure in he curren period: 5 5 In his paper, is assumed ha he producivy shock is he only unobservable variable. R&D acivy conribues o producion only hrough he producivy process. An alernaive approach would be o assume here are wo unobservable variables: a producivy shock and he knowledge capal generaed by pas R&D invesmen. However, his approach would require much more 3
ω = G( ω, R ) + 1 (4) Funcion G is assumed o include a sochasic erm and o be expecable by he manager. In much of he leraure on knowledge capal, he funcional form of G is assumed o be deerminisic and linear. Here, however, his assumpion regarding he funcional form is no imposed. Olley and Pakes (1996) and Levinsohn and Perin (2003) assume an exogenous firs-order Markov process for equaion (4) which excludes R. This issue will be discussed in greaer deail below. The opimizaion problem he firm faces can be expressed by he following Bellman equaion: V ( K, L, ω ) = P K { K max { P I, E, R + C K ( I Y F( A, K, K )} P, L L { L, M + C, ω, ε ), ω ) P 1 + Ε[ V ( K+ 1, L+ 1, ω+ 1) K, L, ω, I, E, R ]} 1+ ρ (5) L ( E, L )} P C R R ( R M M C K, C L, and C R represen he adjusmen cos of capal invesmen (invesmen in angible capal, I ), labor (new employmen, E ), and R&D acivy (R&D expendure, R ). P Y is he oupu price and P K, P L, P M, and P R are he facor prices of capal, labor, inermediae inpu, and R&D. ρ is he discoun rae. Adjusmens in inermediae inpus do no incur any coss, so ha he firm can flexibly change inermediae inpu levels as required. The opimizing behavior can be described wh a se of firs order necessary condions. The condion wh respec o inermediae inpus is simples: F = M P P m y (6) The firs order necessary condions wh respec o capal and capal invesmen resul in a simple Euler equaion: complicaed funcions and involve a greaer burden of compuaion. This ask is lef for fuure work. 4
P K C I K 1 = Ε P 1+ ρ Y + F K C 1 P + 1 1+ K + 1 K K + 1 (7) Similarly, he Euler equaion for labor inpu and employmen is: P L C E L 1 = Ε P 1+ ρ Y + F L C 1 P + 1 1+ L + 1 L L + 1 (8) On he oher hand, he equaion for he producivy level and R&D expendure akes a slighly differen form: P R C R R 1 = Ε P 1+ ρ Y + 1 F ω + 1 P R + 1 C ω R + 1 G R (9) As can be seen, he decisions regarding inpus, M, and invesmen, I, E, and R, are funcions of he sae variables K, L, and ω. Moreover, unless producion funcion F akes a special form, he decision rules are also funcions of variable inpu and exogenous variables. 3. Esimaing he producion funcion The discussion now urns o he more concree sep of he esimaion of he producion funcion. The producion funcion in he previous secion ook an absrac form. Here, following he radion of he leraure on producivy, a Cobb-Douglas producion funcion is assumed, which, moreover, makes possible o compare he resuls obained in his paper wh hose in oher sudies. The producion funcion is assumed o ake he following form: Y = A K β k L βl M e β m ω e ε (10) y = β 0 + β l + β k + β m + ω + ε (11) l k m where he lower case indicaes he logarhm of he corresponding variable. This is a very simple and sandard funcional form. If ω = ω i, his is jus a simple fixed effec model wh a sochasic elemen. If ω is consan over ime and he error erm, ε, has auoregressive srucure, is a sandard form of 5
a Blundell and Bond (2000) regression. Their GMM regression (he so-called sysem-gmm ) is hough o be a soluion o his kind of problem. However, his soluion requires he assumpion ha producivy is consan over ime. Here, is assumed ha producivy is governed by a conrolled firs-order Markov process wh ransion probabilies P(ω ω -1, r -1 ). This assumpion is described in he following equaion, [ ω Info ] + ξ = E[ ω ω 1, r 1] + ξ = g( ω 1, r 1) ξ ω E + = 1 (12) where Info -1 is he informaion se in period -1. This means ha realized producivy of firm i in period can be decomposed ino wo pars, ha is, producivy expeced from he informaion se a -1, g(ω -1, r -1 ) and a random shock, ξ, so ha ξ is independen of r -1. 6 As is well known, if he producion funcion conains deerminans (ω ) which are no observed by he economerician bu observed by he manager of he firm, and if he observed inpus are chosen as a funcion of hese deerminans, hen an endogeney problem is presen and OLS esimaes of he coefficiens on he observed inpus are biased. To conrol for his, Olley and Pakes (1996) used invesmen as a proxy for producivy shocks. More recenly, Levinsohn and Perin (2003) have suggesed using inermediae inpu as a proxy for producivy shocks insead. One of he reasons ha hey prefer inermediae inpu as a proxy is ha inermediae inpu suffers less from he inveribily problem which is caused by he possible lumpiness of invesmen or zero invesmen. This paper follows he mehodology adoped by Levinsohn and Perin, ha is, inermediae inpu is employed as a proxy. However, he approach here differs from Levinsohn and Perin s mehodology wh respec o he assumpion of he producivy process. Their sudy assumes ha producivy ω follows an exogenous Markov process. Typically, however, firms srive o enhance heir producivy, ofen hrough R&D acivies. To ake his aspec ino accoun, he producivy level is assumed o evolve according o he conrolled firs-order Markov process described in (12). This assumpion differs from hose generally adoped in he leraure in several respecs. Firs of all, invesmen in R&D is assumed o raise producivy only in he nex period. In he leraure on knowledge capal, he invesmen in R&D in his period has a direc effec on he producion in fuure periods. In his paper, invesmen in R&D in his period (r ) has a direc effec on he producion in he nex period (ω +1 ), bu no on he producion in he following period or hereafer 6 A random shock o producivy may be considered as he realizaion of he uncerainy relaed wh producivy self plus he uncerainies inheren in he R&D acivy. In his sense, he shock is expeced o be correlaed wh R&D expendure in period 1 in s variance. Discussion in his paper requires only he mean independency. 6
(ω +2, ω +3, ). Alhough he invesmen in R&D in his period (r ) conribues o producivy in period +2 hrough he enhanced producivy in +1, 7 he effec of he invesmen in R&D in (r ) on producivy in +2 (ω +2 ) is no a direc one and canno be idenified. Tha is, his effec of r on ω +2 is no disinguished in a qualaive way from he behavior of he producivy process self, ha is, he effec of ω +1 on ω +2. However, his may no reflec he realy. Typically, firms engage in R&D employing a long ime horizon, argeing profs hree or five years ahead. To capure such a longer-erm effec beyond period +1, second or higher-order Markov processes should be inroduced. Accommodaing his idea is no impossible, bu requires much more compuaion, so ha his ask is lef for fuure work. Second, he conribuion of invesmen in R&D o producivy follows a sochasic process. As is well known, in he knowledge capal model, R&D expendure is assumed o be accumulaed in a deerminisic way o become R&D sock. There is no uncerainy in his process. Third, here is no need o consruc R&D sock. In general, o consruc reliable daa on sock values, long ime series of flow daa are essenial. However, long ime-series daa for R&D are rarely available. Because of he lack of daa, many sudies in he leraure on knowledge capal herefore assume ha he growh rae of R&D flow is equal o ha of R&D sock. In addion, in he general knowledge capal model, he depreciaion rae of knowledge is simply assumed o be a cerain fixed level, such as 15 percen a year. Bu as he model in his paper uses only daa on R&D expendure, no R&D sock, here is no need for such assumpions. The discussion now urns o he esimaion process. The firs sep for he esimaion is o choose which variable o use o proxy he unobserved producivy shock. As described above, in he esimaion process of Levinsohn and Perin (2003), inermediae inpus are used o proxy he producivy shock. Levinsohn and Perin showed ha under cerain condions, a firm s inermediae inpu has a monoone relaionship wh he firm s producivy level, jus as Olley and Pakes (1996) proved he monoone relaionship of invesmen in capal wh he producivy level. Once he proxy variable is shown o be a monoone funcion of he producivy level, one can inver his funcion o express a firm s producivy level as a funcion of he capal sock and he proxy variable, wheher he proxy variable is inermediae inpu or capal invesmen. Since in Levinsohn and Perin (2003) and Olley and Pakes (1996) labor inpu is a variable inpu, and is no used as a proxy, is hough ha he esimae of he coefficien of labor is no biased. For his reason, he firs sep in boh papers is he esimaion of he coefficien on labor by OLS esimaion. 7 In oher words, he invesmen in R&D in his period (r ) enhances he enhanced producivy in he nex period (ω +1 ), and he producivy in he nex period enhances he producivy in he period afer nex (ω +2 ). 7
Bu as Ackerberg, Caves, and Frazer (2006) poin ou, here is a possible collineary problem. If labor inpu is a funcion of inermediae inpu, or if labor inpu is a fixed variable such as in he model in his paper, labor inpu shows up in he invered producivy funcion. If his is he case, he coefficien on labor inpu is no idenified because labor inpu shows up boh in he invered funcion and ouside of he funcion. This is called he collineary problem in his paper. To make clear his problem of he unobservable producivy shock and inpu choice, consider he opimizaion condion of he Cobb-Douglas producion funcion of equaion (10). The firs-order necessary condion wh respec o inermediae inpu wh E(ε )=0 gives he demand for inermediae inpu. By invering his demand funcion, he producivy of he firm can be wren as a funcion of capal, labor, inermediae inpu, and price of inermediae inpu: ω h( k, l, m, p = β ln β + (1 β ) m 0 m m ) m β l l β k k + p m. (13) m m where p = ln P ln P. The price indexes do no have idenificaion subscrips because perfec compeion in facor markes is assumed. Using equaion (13), producion funcion (11) can be rewren as 8 y = β + β l + β k + β m + h( k, l, m, p ) + ε 0 l k m m (14) Here, is assumed ha maerial is he only variable inpu. If labor is also assumed o be a variable inpu, as in mos of he leraure, equaion (13) can be rewren as follows using a firs-order necessary condion wh respec o labor: m l ω = λ + (1 β β ) m β k + (1 β ) p + β p, 0 l m k l l (15) where p w = ln P ln P, w p m m = ln P ln P, and 8 Noe again ha boh funcions g in (12) and h in (14) do no have subscrip for ime, which means ha boh funcions are assumed o be ime-invarian. 8
λ 0 = β0 lnβm βl ( lnβl lnβm). In his case, equaion (11) can be rewren as y = β +, m l 0 + βll + βkk + βmm h( k, m p, p ) + ε (16) If he invered facor demand funcion (13) or (15) is insered ino equaion (11), he producion funcion is ransformed ino a simple opimizaion condion wh he inpu erms being cancelled ou. This equaion means ha he opimizaion condions in a parameric esimaion do no conribue o idenificaion in his seing. Anoher possibily is o esimae equaion (14) or (16) by assuming funcion h in equaion (14) or (16) as an unknown funcion. Forunaely, equaion (16) can be esimaed o obain an esimae of he coefficien on labor. Bu as can be easily seen, esimaion of (14) does no idenify any coefficien of inpu because all of he inpus show up boh in funcion h and ouside of. Excep for such special cases, he producion funcion canno be esimaed wh invered facor demand funcion h. As menioned above, in his sep, Olley and Pakes (1996) and Levinsohn and Perin (2003) esimae he coefficien on variable inpu because in heir model, funcion h does no include labor, l. Bu as shown here, in mos cases esimaing he coefficien on labor in he firs sage is problemaic. In his paper, he coefficien on labor is no esimaed in he firs sage bu in he second sage, as suggesed by Ackerberg, Caves, and Frazer (2006). 9 The purpose of his sage is o cancel ou he random disurbance o obain: Φ = β 0 + β l + β k + β m + h( k l k m, l, m, p m ). (17) In his esimaion, funcion h is hough o be an unknown funcion, because, as described above, opim izaion condions do no conribue o he idenificaion of he coefficiens. One of he general ways o approximae an unknown funcion is o use a series esimaor made up of a complee se of polynomials. 10 A series esimaor of polynomials of degree hree is used in his esimaion. 11 9 In his paper, labor is assumed as a fixed inpu in he sense ha is decided a leas before he curren period begins. Laer, in he esimaion, his assumpion of he fixy of labor is relaxed. 10 When one uses an unknown funcion h(u, v) of wo variables u and v, a complee se of polynomials of degree x means a se of all polynomials of he form u a v b, where a and b are nonnegaive inegers such ha a+b x. See Judd (1998). 9
~ ~ ~ To recover he implied ξ s for any candidae value of he parameers ( β, β, β ), he implied ~ ~ ~ producivy shock ω β, β, β ) is compued as follows: ( k l m k l m ~ ω = Φˆ ~ β l l ~ β k k ~ β m m (18) Under he assumpion of a conrolled firs-order Markov process in equaion (12), regressing ~ ω on a series esimaor of polynomials of ω 1 ~ and r 1 provides he implied ξ s. ~ ξ ~ ω g( ~ ω, r ) (19) = 1 1 The assumpions regarding he iming of he inpu decision yield he momen condion, k k E ξ + ε l = E v l = 0 (20) m 1 m 1 where v = ξ + ε. Noe ha again, he capal sock and labor inpu are decided a ime -1 so ha hey do no respond o he innovaion in producivy, and ha las period s inermediae inpu decision should be uncorrelaed wh he innovaion in producivy in he curren period. The sample analogue o he above momen condion is 1 T 1 N i k l m 1 v 1 1 ( β ) = z v ( β ) (21) T N i where β. = ( β β k, βl, m) 11 Previous sudies show ha polynomials of higher degree han four usually provide lle more informaion on he original funcion. 10
Then, as described in Wooldridge (2002), he objecive funcion can be wren as follows: min β 1 N 1 z v( β ) W z v( β ), (22) N where W is he weighing marix, z is he marix of z, v(β) is he marix of v (β), and N is he number of firms during he period. The weighing marix used in he firs sep for a consisen esimaor is W 1 = z z N 1. The second sep uses he weighing marix W 1 1 = z v( ˆ) β v( ˆ) β z (23) N where βˆ is he coefficien vecor acquired in he firs sep. Funcion (23) is also used for he overidenificaion creria. 4. Daa The main daa se used in his paper is he daa se of financial repors of lised firms compiled by he Developmen Bank of Japan (he DBJ daa se ). Mos deflaors used here for convering curren values o real values are aken from he Japan Indusrial Producivy Daabase 2006 (JIP 2006). A deailed descripion of he daa consrucion is provided in he appendix. The daa used in his paper cover he period from 1999 o 2005. Even hough mos inpu and oupu daa ses of firms are available since 1970, early R&D daa appear highly unreliable, hus confining his sudy o a much shorer period. Only he accouning rules for R&D expendure were changed in 1998, did daa on R&D become much more reliable in Japan. This sudy does no cover he enire economy because mos R&D acivy is concenraed in manufacuring indusry. According o he Whe Paper on Science and Technology, unil 2000, R&D expendure in service indusries was less han 10 percen of he oal and even in 2006, R&D expendure in service indusries was no more han 12.6 percen of oal R&D expendure in Japan. 11
5. Esimaion Resuls for he Producion Funcion 5.1. Esimaion equaion Given he se of assumpions spelled ou above, he producion funcion o be esimaed is as follows: y = β ) + 0 + βll + βkk + βmm + g( h 1, r 1 + ξ ε (24) where h = y β l β k β m (25) l k m In his non-parameric esimaion, funcion g is unknown. In his paper, as described above, a series esimaor made up of a complee se of polynomials of degree hree is used o esimae funcion g. Anoher poin o be noed here for he esimaion of funcion g is ha some firms do no perform R&D. A simple and common soluion o ake his ino accoun is o use he following funcional form: g( h 1, r 1) = 1( r 1 = 0) g0( h 1) + 1( r 1 > 0) g1( h 1, r 1) (26) where g 0 ( h 1) = g00 + g01( h 1), g1( h 1, r 1) = g10 + g11( h 1, r 1), (27) (28) and 1(.) is he indicaor funcion wh he condion in he parenhesis. As described above, funcions g 01 and g 11 are esimaed wh polynomials of up o degree hree. One can easily see ha he consans β 0, g 01 and g 11 are no esimaed separaely. Thus, in he esimaion process, no β 0 is esimaed bu β 0 + g 01 and β 0 +g 11. 5.2. Insrumenal Variables 12
According o equaion (20), available insrumens are curren fixed inpus, K and L, one-period lagged variable inpu, M, and he lagged values of K, L, and M. 12 These values are used as insrumen variables. Overidenificaion is esed wh he crerion funcion (23). 5.3. Esimaion Resuls To compare he resuls wh hose in he leraure, several radional producion funcions are also esimaed. The producion funcions esimaed for comparison basically ake he following funcional form: y = β l k m n ) + u 0 + βl + βk + βm + κ( (29) κ ( n ) = γ 1( n = 0) + 1( n > 0)( γ1 + γ nn 0 ) (30) wher e κ is a funcion relaed o knowledge inpu and n denoes he R&D sock. This funcional form wh he R&D sock follows he radional knowledge capal model. R&D sock daa are consruced as he accumulaed value of R&D expendure wh a depreciaion rae of 15 percen. To ake non-r&d-performing firms ino accoun, wo dummy variables are added, one for R&D-performing and he oher for non-r&d-performing firms. Depending on he assumpions regarding he error erm, u, he mos commonly used esimaion mehods are OLS and fixed effec esimaion (FXE henceforh). Here, boh esimaions were conduced, once wh he funcion κ and once whou. 13 Table 1 shows he resuls. Columns (1) and (3) do no include he erm relaed o R&D. Columns (2) and (4) add he funcion κ relaed o R&D inpu o he producion funcion elemens. Finally, for furher comparison, column (5) shows he resul of he esimaion using Levinsohn and Perin s approach (LP). Their esimaion model does no include R&D as an inpu. As described above, heir esimaion scheme is well known as a way o conrol for endogeney in he producion funcion using maerial inpu as a proxy for producivy shocks. 12 The producs of he insrumens menioned above and he producs of polynomials of he insrumens are also available. How much addional informaion is available from hese insrumen variable series should be esed, bu his ask is lef for fuure work. In his paper, he simples ools are adoped. 13 Random effec esimaion was no performed here because he purpose is o compare coefficiens. Wha maers is consisency, no efficiency. 13
Looking a he resuls in Table 1, he mos noable poin is ha he esimaes of he coefficien on capal are more significan in he esimaion approach developed in his paper (labeled ENDOG) han in he alernaive approaches. In many cases, using FXE, he resul for he coefficien on capal is no significan or significan bu negaive, and in some insances, his is also he case using OLS. In conras, using ENDOG, he coefficien is posive and significan in many cases. These resuls require some elaboraion. In mos case, LP esimaion did no obain posive and significan esimaes for he coefficien on capal. This may be inerpreed as indicaing ha he differences of he esimaes for he coefficien on capal arose from he differences in he wo approaches, ENDOG and LP. As menioned above, he differences are wheher R& D is included and how o esimae he coefficien on labor. To deermine he origin of he difference in he coefficien esimaes, wo differen esimaions are conduced. The esimaion labeled ENDOG1 (column (6) in Table 1) assumes ha labor is a variable inpu, whereas ENDOG2 assumes ha is a fixed inpu. As he coefficien values show, he wo resuls are almos idenical. This demonsraes ha he difference in he esimaion resuls does no seem o be aribuable o he fixy of labor. The remaining possible origins of his difference herefore are he inclusion of R&D or he collineary problem described in Secion 3. Comparing he resuls of he esimaion using he mehod of LP and ENDOG shows ha boh facors are responsible for he difference. A possible reason is ha in he LP esimaion, he labor coefficien is esimaed in he firs sage, so ha he coefficien value has nohing o do wh R&D inpu. If he difference is mosly aribuable o he R&D inpu, hen he coefficien value of labor in ENDOG should be idenical or similar o ha of he LP esimaion. Bu as seen in Table 1, he labor coefficien values of he ENDOG esimaion are que differen from ha of he LP esimaion. Taking ino accoun wha Ackerberg, Caves, and Frazer (2006) poin ou, boh collineary and he absence of R&D inpu are likely o be he main causes of he difference in he capal coefficien esimaes. A final issue o be considered here are daa problems relaed o R&D. The main daa se used in his paper conains five ems relaed o R&D expendure. Two ems concern he cos expended for research acivies, wo refer o he cos of developmen acivies, and he fifh em is he aggregaed valu e. Accouning rules regarding R&D expendure changed in 1998. Before ha year, was no compulsory o repor R&D expendure and, consequenly, only some firms repored. To migae his problem, he producion funcion was esimaed again using only daa of firms ha eher repored R&D expendure in all years or ha repored no R&D expendure in all years hroughou he observaion period (i.e., firms ha repor R&D expendure in some years, bu no in ohers, were excluded). The resuls, employing again he LP esimaion and he wo ENDOG 14
esimaions wh labor reaed as a variable inpu in he firs and as a fixed inpu in he second are shown in Table 2. The resuls are essenially he same as he main resuls repored in Table 1. 6. Producivy and R&D Invesmen 6.1. Producivy comparison This secion examines he characerisics of he producivy index calculaed using he resuls of he main esimaion and he relaionship of he index wh R&D invesmen. In he conex of his paper, he producivy of each firm ( ωˆ ) is defined as follows: 14 ˆ ω = y ˆ β l ˆ β k ˆ β m (31) l k m For he comparison, wo indexes of oal facor producivy are calculaed for each firm every year. The firs of hese indexes is calculaed employing he mehodology developed by Good, Nadiri, and Sickles (1997) and Aw, Chen, and Robers (2001). This index basically measures he disance of a firm s producivy from he average producivy of he indusry in he base year (1981 in his paper), 15 and is labeled as lntfp1 in his paper. The second index measures he disance of a firm s producivy from he indusry average in he curren year and is denoed as lntfp2 hereafer. 16 The summary saisics of he TFP indexes w, lntfp1, and lntfp2 are shown in Table 3, while he correlaion beween hem is presened in Table 4. The laer indicaes ha he main producivy index is significanly correlaed wh hose used for comparison. The purpose here is o examine he origin of he difference beween he indices if any significan differences exis focusing on he relaionship beween lntfp1 and ω. To his end, is assumed for he ime being ha ω is he rue index for oal facor producivy and he biasedness of a producivy index is defined by comparing he index wh ω. A simple way o do his is as follows. Afer regressing lntfp1 on ω, he prediced value for each ω is calculaed. The case where he ˆ ω + ˆ ε 14 Sricly speaking, he righ-hand side of (30) corresponds o. However, for noaional simplicy is simply expressed as ωˆ. ω whou he subscrips is used when no ambiguies arise as a resul. 15 Daa used for he esimaion covers from 1999 o 2005. Bu he limaion is because of he credibily of R&D daa. Oher daa has much longer coverage. TFP is calculaed wh daa from 1981 o 2005. 16 A more deailed explanaion of he indexes of TFP is found in he appendix. 15
acual lntfp is greaer han he prediced one is defined as an upward bias and he oppose as a downward bias. Table 5 repors he resuls. Columns (1) and (2) show he means of he producivy ω of he wo groups, he upwardly-biased and he downwardly-biased group. The wo groups are expeced o have he same mean and Table 5 shows his. Looking a he resuls for each indusry, -ess for comparing he means of he producivy of he wo groups indicae ha here are no significan differences in he producivy levels in five of he seven indusries. The wo indusries in which he differences are significan are he wholesale and reail indusry and he chemical indusry, bu he acual magnudes of he differences are raher small. Comparing he ways producivy of ω and lntfp1 are measured, he bigges difference is wheher cos shares of each inpu are esimaed or calculaed. This issue is examined more closely in columns (3) o (14). The cos shares in columns (3), (7), and (11) which are used o calculae lntfp1 differ in a leas hree respecs from he coefficien esimaes, β s, in columns (4), (8), and (12) which are used o calculae ω. The firs is ha he cos shares are calculaed based on how much is expended for he inpu facors, so ha he cos shares are no immune o he endogey problem, whereas he coefficien esimaes are expeced o be. The second is ha he cos share is based on consan reurns o scale so ha he cos shares sum up o 1. The hird is ha cos shares may differ by firm because hey use individual firm s cos srucure of labor, capal, and inermediae inpu, whereas coefficiens of he inpus are esimaed by indusry, by assuming ha he coefficiens on each inpu are he same fall all firms in an indusry. In general, one can see ha he cos share of labor in column (3) is overesimaed, whereas he cos share of capal in column (7) seems o be underesimaed. In he case of inermediae inpu, is no clear which is he case. If he cos-based share is overesimaed, wha kind of bias is caused? Columns (5) and (6) compare he averages of he cos share of labor beween he downwardly-biased and he upwardly-biased group. In mos cases, he downwardly-biased group has a higher cos share of labor, meaning ha he lntfp1 underesimaes he producivy of more labor-inensive firms. As for he cos share of capal, comparing columns (9) and (10) does no reveal as clear a relaionship beween he cos share of capal and he direcion of bias as in he case of cos share of labor. Alhough lntfp1 underesimaes he cos share of capal, he effec of he bias differs depending on he indusry. In he general machinery, elecrical and elecronic machinery, and ransporaion machinery indusries, he producivy of more capal inensive firms ends o be downwardly biased, whereas in he oher indusries, he producivy of capal inensive firms ends o be downwardly biased. 16
6.2. R&D invesmen and producivy From he definion of he producion funcion in (11), he simples way o define he reurns o R&D invesmen is as follows: 17 y r 1 11 1, 1) = g ( h 1, r 1) g = r ( h r 1 1 1 r (32) As described above, he values of h -1 and r -1 differ by firm and year, so ha he value in (32) also differs by firm and year. Table 6 shows he disribuion of R&D reurns by indusry. Reurns vary widely no only from indusry o indusry, bu even whin an indusry. This means ha some firms enjoy higher R&D reurns han ohers. This raises he quesion: wha deermines he reurns on R&D invesmen? To analyze his, R&D reurns are regressed on firm characerisics, ha is, firms size, reurn on asses (ROA), deb raio, and ownership srucure. Table 7 shows he resuls. In four indusries of he seven, R&D reurns urn ou o be correlaed wh firms size as measured by he volume of sales. In oher words, he bigger a firm is, he greaer are he benefs from R&D acivy. Figure 2 shows hese relaionship beween R&D reurns and firms size by indusry. 18 Anoher poin o noe is ha R&D reurns are posively correlaed wh ROA. In five of he seven indusries, his correlaion is clear and srong, meaning ha more profable firms enjoy higher reurns from heir R&D invesmen. R&D reurns seem o be negaively correlaed wh he deb raio and he raio of shares owned by he governmen (labeled GOV in he able 7). On he oher hand, R&D reurns are posively correlaed wh he raio of shares owned by foreign firms (labeled FRN in he able 7) and he raio of shares owned by privae invesors ( labeled PER in he able 7), even hough hose relaionship is weak. Anoher poin of ineres is how R&D reurns are viewed by he sock marke. Table 8 shows ha, in general, Tobin s q is posively correlaed wh R&D reurns. 19 Reurn on asses (ROA) is included as a conrol variable. ROA is hough of as a main facor 17 This definion is differen from ha in he knowledge capal leraure. Esimaion of he reurns o R&D in he knowledge capal model capures he rae of reurn o R&D sock, no R&D flows, whereas in his paper, he main esimaion capures he reurns o R&D flow. R&D sock is no defined here. 18 In he chemical indusry, wo disinc clusers can be observed. A possible reason is ha his indusry includes heerogeneous sub-indusries, such as pharmaceuicals and non-pharmaceuicals. However, even when ploing he chars for pharmaceuicals and non-pharmaceuicals separaely, as shown in he figure, he same clusering is observed. 19 The definion and mehod of consrucing Tobin s q are described in deail in he appendix. 17
affecing he share price. This resul shows ha even when conrolling for he effec of ROA, R&D reurns end o significanly affec he share price. Variables represening firm size, such as sales and he number of employees, are no included in his regression because when hey were included, heir coefficiens were generally insignifican. 7. Concluding remarks This paper aemped o apply recenly developed economeric mehods o conrol for he endogeney problems and esimaion biases arising from missing variables. The idiosyncraic producivy shock ha causes he endogeney problem beween he inpus and oupu is replaced wh an invered inermediae inpu demand funcion as in Levinsohn and Perin (2002). Bu as Ackerberg, Caves, and Frazer (2006) suggesed, he invered demand funcion is hough o be an unknown funcion and he coefficien on labor is esimaed in he second sage. Firms are assumed o conduc R&D o enhance he producivy of he nex period, and he producivy process follows a conrolled firs-order Markov process. This paper found ha here are esimaion biases and ha he possible origins of he biases are unobservable producivy shocks (endogeney problem) and ignoring he conribuion of R&D acivy. The biases are especially prominen in he esimaes of he coefficien on capal. Calculaing he reurns on R&D invesmen using he esimaion resuls, was found ha R&D reurns are posively correlaed wh firm size (measured by sales) and ROA (reurn on asses), and ha markes ake ino accoun his R&D reurn in heir valuaion of firms. 18
Appendix This appendix provides a deailed descripion of how he daa se was consruced. Oupu For oupu, sales afer adjusing for invenory are used. For he wholesale and reail indusry, purchases of merchandise are subraced from sales. The price index for oupu and inpu is aken from he JIP2006 daa base. 20 Price of Capal Goods Capal goods consis of he following six ypes of asses: (1) nonresidenial buildings; (2) srucures; (3) machinery; (4) ransporaion equipmen; (5) insrumens and ools; and (6) land. The price index used for deflaing (1) and (2) is ha for consrucion maerials in he corporae goods price index (CGPI). For machinery, he weighed average of he following hree CGPI componens was used: general machinery and equipmen, elecrical machinery and equipmen, and precision insrumens. As he (fixed) weigh, he capal formaion marices for 1985, 1990, 1995, and 2000 rearranged by he Research Insue of Economy, Trade and Indusry (RIETI) by indusry are used. The same procedure is employed o consruc he price index for insrumens and ools. The price index for insrumens and ools is he weighed average of five CGPI componens: meal producs, general machinery and equipmen, elecrical machinery and equipmen, precision insrumens, and oher manufacuring indusry producs. Again, he capal formaion marices are used as he fixed weigh. The ransporaion equipmen componen of he CGPI is adoped as he price index for ransporaion equipmen. Finally, for land, he index of urban land prices compiled by he Japan Real Esae Research Insue is used. The index for commercial areas is adoped for non-manufacuring firms, whereas ha for indusrial areas is adoped for manufacuring firms. Nominal invesmen The following noaions are used in he calculaion of nominal invesmen: KGB : book value of gross capal sock a he end of he period; KNB : book value of ne capal sock a he end of he period; 20 The JIP2006 daa base provides deflaors up o 2002. They were exended here up o 2004 using SNA deflaors. 19
AD : book value of accumulaed depreciaion ; DEP : accouning depreciaion during he period. The definion of nominal invesmen is: NOMI = KNB KNB 1 + DEP. (A.1) Since DEP is no available unil 1977, 21 (AD - AD -1 ) was used as a weigh o disribue oal depreciaion beween he five kinds of capal goods excluding land. Capal sock The perpeual invenory mehod is used o calculae real capal sock: NOMI K + = ( 1 δ ) K 1 (A.2) PK where PK is he price index for he capal asse. The inial year chosen for he calculaion based on he perpeual invenory mehod is 1970, because accumulaed depreciaion is only available since 1969. In he main regressions, capal sock does no include land. However, o consruc Tobin s q, land sock is calculaed. To conver he book value of land o he marke value, a somewha complicaed procedure was adoped. Using he book value of land sock a he end of each period and he acquision of land during he year, is possible o calculae he acquision value of he land acquired during he period. However, he saisics do no allow o discern when he land sold during his period was acquired, so ha is no clear how o apply he price index for land o he land value sold during he period. For his reason, he las-in-firs-ou principle is assumed for land. Tha is, when firms sell land, is assumed ha hey sell he land which was acquired las. Accumulaed ne purchases are calculaed backward and is assumed ha he land sold during his period was acquired during he period when he accumulaed ne purchase firs urns posive. Here is an example. Year Bough Sold acc1998 acc1999 1991 100 400 220 1992 120 300 120 1993 160 30 180 0 21 Depreciaion by asse is only available afer 1978. Before 1977, he sum of he depreciaion for all asses is repored. 20
1994 110 50-130 1995 170 100 160-20 1996 80 90-90 1997 100 10-170 1998 90-90 -270 1999 180-180 Variable acc1998 is he accumulaed value of land which is bough in he curren period (in his example 1998) or has been bough in he pas (in his example 1997, or earlier) from he curren period o he pas. Land which is sold is added o he sum as a negaive value. Thus, his variable should be read from he curren o he pas. This variable, herefore, shows how many periods ago he land was bough which is sold in he curren period. Variable acc1999 is defined in he same way. The land sold in 1998 (90 uns of land) was bough in 1997. When one looks a acc1998 and reads from 1998 backwards, firs urns posive in 1997. In 1999, 180 uns of land were sold. Under he las-in-firs-ou principle, he land sold in 1999 includes he land which was bough in 1997, 1996, 1995 and 1993. In his case, he price index of land in 1993 is applied o he land which is sold in 1999. Depreciaion rae The JIP2006 provides fixed capal formaion marixes aggregaed o 39 asses by JIP2006 indusry classificaion and corresponding depreciaion raes. Aggregae depreciaion raes for he five capal goods are calculaed using he indusry weighs from he fixed capal formaion marix. The average depreciaion raes are (1) 8.31297%, (2) 2.25949%, (3) 12.77375%, (4) 17.12287%, and (5) 12.45546%. 22 Capal sock aggregaion A Divisia index or Tronqvis index should be applied here. However, once he base year is se, he producivy of firms which did no exis in ha year canno be calculaed. For his reason, he capal sock is aggregaed by summing up he marke value of each ype of capal good. Capal cos Capal cos is measured as follows: c k 1 z p& k = pk{ λ r + (1 u)(1 λ) i + δ ( )} (A.3) 1 u p k 22 For comparison, Hayashi and Inoue (1991) use depreciaion raes of (1) 4.7%, (2) 5.64%, (3) 9.489%, (4) 14.70%, and (5) 8.838%. 21
where z is he expeced presen value of ax savings due o depreciaion allowances on a yen of invesmen in capal goods, u is he efficien corporae ax rae, λ is he own-capal raio (=1-deb/oal asse), r is he long-erm bond rae, i is he prime rae, δ is depreciaion, and p k is he price index. z is calculaed as follows: z = ( u δ )/[{ λr + (1 u)(1 λ) i} + δ ]. (A.4) Tax saving, z, is no calculaed for land sock because land has no depreciaion. Thus, capal cos for land, c land, is slighly differen from he one for oher capal goods for he same reason. Capal cos is calculaed by muliplying c by he capal sock. Labor coss and maerial coss are obained from prof/loss ables. Effecive corporae ax rae Following Hayashi and Inoue (1991), he effecive corporae ax is calculaed as follows: ( u + v )(1 + r ) = (A.5) (1 + r + v ) where u is he corporae ax rae, v is he enerprise ax rae, and r is he shor-erm ineres rae. Labor inpu Man-hours are used here as labor inpu. Labor hour daa are aken from he JIP2006 daa base and exended up o 2004 using he Monhly Labor Survey. Indusry average man-hours are applied o each firm classified in ha indusry because firm daa for labor hours are no available. Inermediae inpu Inermediae inpu is calculaed as follows: Sales cos + Selling, general and adminisraive expenses Depreciaion Increase of produc Increase of goods in process For he reail and wholesale secor, purchases of merchandise are subraced from his inermediae inpu. The price index for inermediae inpu is aken from he JIP2006 daa base. 23 23 The JIP2006 daa base provides deflaors up o 2002, which were exended up o 2004 using SNA deflaors. 22
Calculaing TFP Following Good, Nadiri, and Sickles (1997) and Aw, Chen, and Robers (2001), he TFP level of firm f in year in a cerain indusry is calculaed in comparison wh he TFP level of a hypoheical represenaive firm in year 0 in ha indusry by lntfp1 + f, s= 1 = (lnq (lnq s f, lnq lnq ) s 1 ) n i= 1 s= 1 = 1 1 ( Si, f, + Si, )(ln X i, f, ln Xi, ) 2 n 1 ( Si, s + Si, s 1)(ln X i, s ln X i i, 2 s 1 )] (A.6) where Q f,, S i,f,, and X i,f, denoe he gross oupu of firm f in year, he cos share of facor i for firm f in year, and firm f s inpu of facor i in year, respecively. Variables wh an upper bar denoe he indusry average of ha variable. Consan reurns o scale are assumed. As facor inpus, capal, labor and real inermediae inpus are aken ino accoun. The represenaive firm for each indusry is defined as a hypoheical firm whose logarhmic value of gross oupu as well as he logarhmic value of inpus and cos shares of all producion facors are idenical wh he indusry averages. The firs wo erms on he righ-hand side of equaion (A.6) denoe he gap beween firm f s TFP level in year and he represenaive firm s TFP level in ha year. The hird and fourh erm denoe he gap beween he represenaive firm s TFP level in year and he represenaive firm s TFP level in year 0. Therefore, lntfp f, in equaion (A.6) denoes he gap beween firm f s TFP level in year and he represenaive firm s TFP level in year 0. Cross-secional TFP (lntfp2) is defined in a simpler way: n 1 ln TFP2 f, = (lnqf, lnq ) (,,, )(ln,, ln, ) i = S 1 i f + Si X i f X i (A.7) 2 TFP is calculaed using equaions (A.6) and (A.7), wh 1980 used as he base year. Observaions whose deviaion of lntfp1 from he indusry average of lntfp1 in a year is greaer han hree imes he indusry sandard deviaion of lntfp1 in ha year is hough o be ouliers and are discarded. Then lntfp1 and lntfp2 are calculaed again wh re-calculaed values of he indusry averages of inpus, oupu, and cos shares. Tobin s q 23
Tobin s q is defined as he sum of he marke value of equy and deb divided by he replacemen cos of capal. The marke value of equy is calculaed as he number of socks issued muliplied by he sock price. The sock price is a he firs ransacion day of he monh following he financial repor. If no price informaion for ha day is available, he price for he earlies dae following he financial repor is used. Deb includes only liabilies wh ineres. The replacemen cos of capal is calculaed as he sum of he marke value of aggregaed capal above and he oal sum of asses minus he book value of angible fixed asses. 24
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