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# OAR Box 1669 Prepped by Charmelle Mathews



## Document

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### COWLE S FOUNDATIO N

FO RRESEARC H I

N ECONOMIC S A T YAL E UNIVERSIT Y

Bo x2125 , Yal e Statio n Ne w Haven , Connecticu t 0652 0

COWLE S FOUNDATIO N

DISCUSSIO N

PAPE RNO . 82 8

Note : Cowle s Foundatio nDiscussio nPaper s ar e preliminar y material s circulate dt o stimulat e discussio nand critica l comment . Request s fo r singl e copie s o f a Pape r wil l befille db y th e Cowle s Foundatio nwithi n the limit s o f th e supply . Reference s inpublication s t o Discussio nPaper s (othe r thanacknowledgmen t tha t a write r hadacces s t o suc hunpublishe dmaterial ) shoul db e cleare dwit hth e autho r t o protec t th e ten tativ e characte r o f thes e papers .

MEASURIN GMARKE T POWE RI N U.S . INDUSTR Y

Matthe w D . Shapir o Apri l 198 7

/P. 3

MEASURINGMARKE T POWE RI N U.S . INDUSTRY

& " Matthe w D . Shapir o Yale Universit y

an dNationa l Burea uo f Economi c Researc h

Octobe r 198 6 Revise dMarc h198 7

I a m gratefu l fo r helpfu l discussio nwit hErns t Berndt , Timothy Bresnahan , Zv i Griliches , R . Glen nHubbard , N . Gregor y Mankiw , Whitne y

Newe y andparticipant s i nseminar s a t MIT , NBER , Northwestern , NYU , Princeton , an d Yale ; fo r financia l suppor t fro m the NS F andNBER-Oli nFellowship ; and fo r researc hassistanc e by Mic o Loretan .P. 4



### Measuring Marke t Powe r i n U.S . Industr y

ABSTRAC T

?; , 

### Non-competitiv e conduc t ca n b e assesse d b yestimating the siz e o f the marku p o r Lerne r index achieve d i n a market . Th e marku p implie s a pric e elasticit yo f deman d face d b

yth e representative firm . Fo r a give n markup , non-competitiv e conduc t i s greate r the mor e elasti c i s the marke t elasticit y o f demand . Th e rati o o f the firm' s t o the marke t elasticit yi s a measur e o f non-competitiv e conduc t tha t i s insensitive t o th e valu e o f the monopoly . T o implemen t thi s measure , bot h the firm' s an d th e marke t elasticitie s o f deman d mus t b e estimated . Hal l show s ho wt o estimat e the markup , an d henc e th e elasticit yface d b ythe firm , fro

mthe cyclica l behavio r o f productivity . T o estimat e the marke t elasticity , a n instrumenta l variable s procedur e exploiting a covarianc e restrictio n betwee n productivit yshock s an d deman d shock s i s used . Result s fo r broa d sector s o f privat e industr y an d fo r non-durabl e manufacturing industrie s displa ya wid e rang e o f monopol ypower .

Matthe wD . Shapir o Cowle s Foundatio n fo r Researc h i n Economic s Yal e Universit y Bo x 212 5 Yal e Statio n Ne wHaven , C T 06520-212 5 tel . 20 3 432-371 6P. 5

"• r-),- •••.?m. 

## fit 1 . Introductio n

Thi s pape r present s som e new estimate s o f the degre e o f marke t powe r i n U.S . industry . Non-competitiv e outcome s ca nb e assesse dby comparin g pric e
andmargina l cost . Usin g price-cos t margin s alon e t o asses s marke t powe r i s problemati c becaus e they fai l t o tak e int o accoun t the valu e o f th e monopoly . A

monopol y

wil l comman

da greate r margi nthe mor e inelasti c i s the deman dfo r the good . Difference s i nelasticit y o f demandshoul db e take nint o accoun t i ncomparin g conduc t acros s markets . Th e measur e i nthi s pape r doe s s o by

normalizin g the estimate dmarkupb y the elasticit y

o f demand . I na recen t serie s o f papers , Rober t Hal l suggest s tha t many U.S . industrie s ar e no t competitive . Thi s resul t i s base do na simpl e and elegan t reinterpretatio no f the well-know nfac t tha t productivit y varie s pro-cyclically . The reasonin g i s a s follows : A s outpu t expand s i nthe troug ho f a recession , labo r increase s les s tha ni s warrante db y a standar d productio nfunction . Hence , pric e exceed s margina l cost . Pu t differently , whe noutpu t i s low , price doe s no t fal l enoug ht o allow the sal e o f good s tha t ca nb e produce da t ver y lo w margina l cost . Hal l reason s tha t thi s findin g i s onl y

consisten t wit ha hig hdegre e o f monopol y power . Ther e i s littl e evidenc e o f substantia l profit s i nU.S . industry ; h e reason s tha t th e monopol y

profit s ar e dissipate dby chroni c exces s capacity . 

# h, al l (1986a , b , c ) 

# MP. 6

I nthi s paper , I exten dHall' s framewor k t o yiel da nindependen t
measure o f th e degre e o f monopol y powe r i na nIndustry . Hal l take s perfec t competitio na s hi s nul l hypothesi s an dthe nmeasure s departure s fro m pur e competition . I nth e formulatio ni nthi s paper , th e pola r hypothesi s o f pur e monopol y

ca nbe studied . More importantly , i f th e industr y i s neithe r perfectl y

competitiv e no r perfectl y monopolistic , a measur e o f th e degre e o f marke t powe r ca nb e calculated . Th e markupimplie s a nelasticit y o f deman d face db y

th e representativ e fir m i nth e industry . Th e rati o o f th e marke t elasticit y

o f deman dt o tha t implie dby th e marku pi s a measur e o f marke t power . I nthe pola r cas e o f perfec t competition , i t equal s zero . I nth e opposit e pola r cas e o f perfec t monopoly , i t equal s one . I nth e intermediat e rang e betwee nzer o andone , i t measure s non-competitiv e conduct . T o implemen t thi s measur e i t i s necessar y t o estimat e bot hthe marke t elasticit y

o f deman dan dth e implie dby th e marku pratio . I follow Hal l i n estimatin g the latte r fro m th e cyclicalit y

o f productivity . T o estimat e th e marke t elasticit y o f demand , I exploi t th e covarianc e restrictio nbetwee n th e productivit y

shock andth e disturbanc e i nth e deman d equation . B y definition , anindustr y productivit y

shoc k i s uncorrelate dwit hthe deman d disturbance . Th e restrictio nserve s t o identif y th e pric e elasticit y o f demand . Thi s covarianc e restrictio nha s a ninstrumenta l variable s interpretation . The productivit y shoc k i s a vali dinstrumen t fo r th e pric e variabl e i nth e deman dequation . Thi s approac ht o estimatin g th e elasticit y
o f deman dshoul dhav e wid e applicatio nbeyon dit s us e her e i nmeasurin g marke t power . 

# 6~,_JL2
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ie 

### "Mi.

V.

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2 . Theoretica l Framewor k fo r Measurin g Marke t Powe r I nthi s sectio no f th e paper , I review

Hall' s measur e o f non competitiv e behavio r anddevelo pa furthe r measur e o f th e degre e o f monopol y power . Unde r assumption s o f constan t return s t o scal e andcompetitio nSolo w (1957 ) show s tha t th e tota l facto r productivit y residua l (the "Solo w residual" ) wil l measur e technologica l chang e i na productio nfunction . Thi s residua l i s define da s


### (1 ) Ac t -Ay t - Ak t - « t (An t - Ak t )

wher e A

y , A k , $nd Anequa l the percen t chang e i noutput , capital , an d labor , an da equal s the shar e o f labo r incom e i nnomina l output . The shar e i s measure da s a - W N / P Ywher e W

, N , P , andYar e the level s o f the nomina l wage , labor , the nomina l pric e level , andrea l output . Equatio n(1 ) applie s equall y

wel l t o the aggregat e econom y o r t o a nars»wl y define d 2 industry . Solow' s derivatio nrequire s tha t the technolog y b e constan t return s t o scal e an dtha t technologica l chang e b e disembodied . Solow' s derivatio nals o require s tha t market s ar e competitiv e andlabo r i s variabl e
Variable s andparameter s shoul dal l be though t o f a s subscripte db y i fo r industry . Thi s subscrip t i s suppresse dexcep t wher e i t i s neede di na particula r context . Productivit y ha s a drif t s o Ac t i s no t mea nzero . Henc e the equation s i nAc. hav e constant s tha t ar e suppresse dfo r notationa l convenience . I nth e estimates , a constan t i s include di nal l th e regression s s o the estimate dAc ar e mea nzer o i nthe sample .

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withi nth e period , s o labo r i s pai dit s margina l product . Capita l nee dno t b e pai dit s margina l produc t s o i t ca nb e fixe di nadvance . A simila r relationshi phold s unde r imperfec t competition . Defin e Xt o b e margina l cost . Solow' s derivatio nhold s i f pric e doe s no t equa l margina l cost , bu t i nequatio n(1 ) labor' s shar e i noutpu t shoul db e replace dby labor' s shar e i ncost . Denot e labor' s shar e i ncos t a s a - W N / XYan

d denot e the tru e productivit y shoc k a s A

c . The nthe tru e productivit y shoc k i s give nb y

(!' ) 

### A

c * - Ay t - Ak t - « ° (An t - Ak t )
Margina l cos t is , however , unobservable , Hal l suggest s assumin g tha t H - P^/ Xi s a constant . The n(1 ) and (1' ) ca nbe combine dt o yiel d


### (2 ) Ac t - (/i-l)a t (An t - Ak t ) + Ac t

where A c i s th e measure dSolow residual , wher e A c i s th e tru e productivit y

shock , an d wher e n i s a nunknow nparamete r t o b e estimated . Hall' s strategy

i s the nt o estimat e th e marku prati o / xan d t o tes t the hypothesi s tha t i t equal s one . Fo r a wide rang e o f industrie s h e i s abl e t o rejec t th e nul l o f perfec t competition . Th e marku pdoe s no t provid e a natura l metri c fo r th e degre e o f monopol y powe r i na nindustry . Fo r example , a monopol y facin g relativel y inelasti c deman dwil l hav e a large r marku ptha na monopol y facin g mor e elasti c demand . Moreover , i t ma y b e desireabl e t o rank industrie s accordin g t o thei r degre e o f non-competitiv e 

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conduc t rathe r tha nsimpl y t o categoriz e the m a s competitive o r no t competitive . I conside r a measur e o f monopol y powe r tha t take s int o accoun t the elasticit y

o f demandi nth

e industry . Th e measur e nest s the specia l
case s o f perfec t competitio nan dperfec t monopoly . The marku pca nbe expresse di nterms o f th e elasticit y o f deman dface d by the representativ e fir m i nthe industry . Hence ,



### (3 ) *



### A

### -

i f the representativ e fir m act s a s i f i t face s a nelasticit y o f demandequa l * 3 * t o 0 . Th e valu e -1// 3 i s the Lerne r inde xo f marke t power . Denot e the marke t elasticit y o f demanda s 0. I f the industr y i s monopolized , o r i f it s firm s collud e effectivel y t o duplicat e th

e monopol y

outcome , the n0 wil l equa l 0. Give nestimate s o f bot hparameters , i t i s possibl e t o tes t the natura l nul l hypothese s o f monopol y (0 - 0 ) a s wel l a s tha t o f perfec t competitio n(0 - - « or , equivalently , y. - 1) . Attentio nnee dno t be confined , however , t o thes e pola r cases . Th e rati o o f the marke t t o the firm' s elasticitie s i s a natura l measur e o f

Thi s formul a i s a simpl e rearrangemen t o f the firs t orde r conditio n fo r the one-perio dprofi t maximizatio nproblem . I t wil l als o aris e fro m a discounte dpresen t valu e maximizatio nproblem a s lon g a s sale s today d o no t affec t deman di nthe future .monopol y power . Defin e thi s rati o a s P.1 0



### (4 ) 

## 6-0/0


## .

Th e coefficien t ha s a natura l interpretation . Unde r competitio n8 equal s
zero ; unde r monopol y i t equal s one . I f the industry function s a s a Courno t oligopoly , th e reciproca l o f 8 measure s the numbe r o f equally-size dfirms . Bresnaha n(1987 ) argue s persuasivel y tha t th e rati o 6 i s a ninterestin g
measur e o f conduc t fo r model s where Courno t behavio r i s no t maintained . I t normalize s th e departur e o f price fro m margina l cos t b y the elasticit y

o f demand . Th e interpretatio na s the reciproca l o f the numbe r o f firm s i na Courno t oligopol y provide s a usefu l metri c fo r marke t outcome s eve nunde r differen t model s o f fir m behavior .

3 . Identificatio nandEstimatio n The strategy

i s t o estimat e the marku prati o n an dthe pric e elasticit y
o f deman d0 an

dthe nt o comput e the inde xo f marke t powe r 8. I nthi s section , I conside r instrumenta l variable s procedure s fo r estimatin g thes e parameters . T o estimat e th e marku pratio , j» . Hal l make s th e crucia l identifyin g if assumptio ntha t th e tru e productivit y shock Ac ha s n o aggregativ e
4 * The distinctio nbetwee n0 an d0 ha s bee ndiscusse da t leas t sinc e Chamberlain . I t i s develope dby Bresnaha n(1982 ) an danalyze di ndetai l b y Bresnaha n(1987) . 

# °lP.1 1



### •t y ?

r 

### 8$ . 

## If


## t - 7 -

component . Thi s assumptio ni s specificall y a t varianc e wit hsom e theorie s
o f the busines s cycle . Specifically , Kydlandan dPrescot t (1982 ) rel y o nan aggregat e productivit y shoc k a s the onl y drivin g variabl e i nthe busines s cycle . (I t i s importan t t o note , however , tha t som e implementation s o f rea l busines s cycl e theories , notabl y tha t o f Lon g andPlosse r (1983) , generat e cycle s wit hshock s tha t ar e independen t acros s sectors. ) Hence , Hall' s formulation , a s he i s carefu l t o acknowledge , ca nshe dn o ligh t o ntheorie s tha t requir e a naggregativ e productivit y shoc k a s a nessentia l ingredien t i n aggregativ e fluctuations . Unde r Hall' s assumption , aggregat e GNP growt hi s a vali dinstrumen t fo r
a (A n- A k ) i nequatio n(1 ) o nindustr y data . Som

e recen t wor k o f m y ow n call s int o questio nHall' s assumptio ni nthi s data . I nparticular , fo r many industrie s i t i s difficul t t o rejec t tha t margina l cos t move s consistentl y wit hobserve dproductivit y unde r th e hypothesi s tha t observe dproductivit y i s tru e productivit y (Shapiro , 1987) . I nthi s case , Hall' s procedur e i s invalid . O nthe othe r hand , I nabou t hal f the non-durabl e manufacturin g industries--result s fo r whic hI wil l highligh t here--m y earlie r tes t reject s th e nul l tha t observe dproductivit y i s tru e productivity . Moreover , i t i s
commo npractice i nindustria l organizatio nt o assum e tha t year-to-yea r change s i naggregat e outpu t com e fro m demand . Hence , i t seem s bes t t o remai nagnostic ; I presen t result s base do nHall' s elegan t solutio no f usin g aggregat e GN P growt ha s a ninstrumen t i nthe marku pequation .



### b y Usuall y identificatio ni s no t achieve db y disaggregatio nalone . I n thi s case , a t leas t approximately , disaggregatio ndoe s lea dt o identificatio nbecause o f th e rol e o f the aggregat e demandshock . Se e the Appendi xfo r details . 

# toP.1 2

Thi s agnosticis m

nee dno t b e nihilism . I t ther e ar e trul y exogenou s variable s tha t ar e correlate dwit hmovement s i nlabo r input , thes e ca nb e
use da s instruments . Vali destimate s ca nb e offere dwithou t takin g a stand
o nwhethe r o r no t ther e i s a macroeconomi c componen t t o tru e productivit y growth . Oi l price s andgovernmen t purchase s (especiall y militar y

purchases )
ar e candidate s fo r instruments . Estimate s tha t use thes e wil l als o b e

6 presented . Althoug hon e onl y need s t o estimat e th e elasticit y o f deman dt o estimat e 8, i t i s helpfu l t o writ e dow nthe entir e deman dequation . Conside r th e followin g deman dequatio ni npercen t chang e for m fo r a give n industry : 

### (5 ) Ay t - /?Ap t + Z t 7 + A» t

Here , A

y i s th e growt hrat e o f output , A p i s the growt hrat e o f the relativ e price , th e Z ar e deman dshif t variables , andtAv i s a tast e shock . T o estimat e the elasticit y o f demand , i t i s necessar y t o overcome a difficul t simultaneit y problem . Th e ofte nintractabl e identificatio n problem

ha s a straightforwar dsolutio ni nthi s context . Conside r the

Hal l (1987 ) take s th e agnosti c positio nanduse s simila r instrumen t lists . Bu t se e Hal l (1986a , b , c) .

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followin g identifyin g assumptions :

• Th e productivit y shoc k A

c i s uncorrelate dwit haggregat e deman d
o r othe r aggregat e demandshifter s suc ha s militar y expenditur e o r oi l prices . ie

• The productivit y shoc k A

c i s uncorrelate dwit hthe tast e shoc k At/ an dwit hothe r variable s tha t shif t demand .
The firs t o f thes e assumption s ha s alread y bee ndiscussed . I t i s use dby Hal l t o identif y

p. i nequatio n(2) . Fo r aggregat e demandt o b e a vali d instrumen t fo r <

* Anthe naggregat e demandmus t be on e o f the demand shifter s Z . Fo r a ninstrumen t t o b e vali di t mus t bot hb e uncorrelate d wit hthe disturbanc e an dcorrelate dwit hthe endogenou s variable . Th e secondassumptio nfollow s virtuall y by definitio no f a productivit y shock . Independen t movement s i ntechnology shoul dbe uncorrelate dwit h change s i ntaste . Th e identifyin g assumptio nI s a covarianc e restrictio n rathe r tha nthe mor e conventiona l exclusio nrestriction . ^.Suc ha covarianc e restrictio nha s a ninstrumenta l variable s interpretatio n(Hausma nand Taylor , 1983) . Th e estimate ddisturbanc e A c i s a vali dinstrumen t fo r pric e i nth e demandequatio n(5) . I t i s certainl y correlate dwit hpric e movements , i t i s b y constructio nuncorrelate dwit hthe aggregat e deman d componen t o f Z , an di t is , by

assumption , uncorrelate dwit hth e tast e shock s Ai/ . Implici t i s the assumptio ntha t the productivit y shoc k i s

%. 

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### 1 0

uncorrelate dwit hth e othe r exclude dvariables , whic har e throw nint o th e
erro r term . Th e two-ste pestimato r wher e the residual s fro m (2 ) ar e use da s instrument s fo r (5 ) i s consisten t asymptoti c norma l andi s efficien t (se e Hausman , Newe y

andTaylo r (1987)) . Indeed , sinc e the deman dequatio nI s just-identified , th e instrumenta l variable s estimato r i s numericall y identica l t o maximu m likelihood . Yet , the covarianc e matri xprinte dou t b y standar dcompute r package s i s incorrect . Th e tru e covarianc e matri xi s a functio no f nuisance parameters . I comput e andrepor t th e correc t estimates . Se e th e Appendi xfo r detail s o f the computation . One possible exclude dvariable , futur e pric e changes , coul ddefea t identification . I f good s ar e durable , thi s variabl e i s relevan t fo r demand
and coul dwel l b e correlate dwit hthe productivit y shock . Th e result s fo r th e durable s ar e suspec t i nan y cas e becaus e the flow deman dcurv e i s completel y

inadequat e fo r them . Developin g a complet e theor y o f suppl y

an d deman dfo r durable s unde r imperfec t competitio ni s wel l beyon dthe scop e o f thi s paper . Th e result s fo r durable s ar e include d onl y fo r completeness . Before presentin g th e estimates , furthe r consideratio no f the parameterizatio no f the demandequatio ni s i norder . A s note dabove , onl y th e paramete r o f th e relativ e pric e wil l b e estimated . The omitte d variable s ar e orthogona l t o the instrument , s o thi s procedur e yield s consisten t estimates . Nonetheless , i t i s worthwhil e thinkin g abou t the
Unde r th e identifyin g assumptions , instrumenta l variable s estimatio n o f /3.i s consisten t eve ni f al l the Z ar e omitted. . Efficienc y coul dbe gained , however , b y includin g som

e i t they

ar e observable . O f course , i f the y ar e endogenous , on e woul dnee dinstrument s fo r them . 

# AP.1 5

- 1 1 -

omitte dvariables . I nparticular , aggregat e deman di s omitted . Not e the instrumen t i s orthogona l t o thi s omitte dvariabl e no t jus t i ntheory bu t by constructio na s lon g a s aggregat e GN P i s use da ninstrumen t i nth e marku p equation . Yet , omittin g thi s crucia l demandshifte r lead s t o a n inefficiency . On e wa y t o includ e i t withou t havin g t o estimat e anothe r paramete r i s t o estimat e a homogenou s demandsystem . I nthi s case , the lef t han d sid e o f (5 ) become s industry outpu t growt hminu s aggregat e outpu t growth . Hence , the demandequatio nbecome s

(5' ) Ay t - Aq t - /JA P( ; + Z ^ + A ^

wher e A

y , A p , andAi/ are , a s before , the industry outpu t growth , relativ e pric e growth , an ddemandshock ; wher e A q i s aggregat e outpu t growth ; and wher e Z . ar e demandshifter s excludin g aggregat e outpu t growth . Al l the element s o f Z. . excep t th e constan t ar e subsume dint o the erro r ter m s o onl y 0 an dth e intercep t ar e estimated . Not e tha t the orthogonalit y o f aggregat e outpu t growt ht o the instrument s implie s tha t the estimat e o f 0 wil l be numericall y

th e sam

e whethe r (5 ) o r (5' ) i s estimated . Th e standar derror s will , however , be affected . Th e demandequatio nactuall y estimate di s (5' ) wher e al l o f th e deman dshifter s (excep t the constant ) ar e subsume dint o the disturbance .

Gros s outpu t versu s value adde d The dat a use dt o estimat e bot hthe markupandth e demandequatio nwil l be o na value-adde drathe r tha na gros s pric e basis . Hence , th e estimate d 

# MP.1 6



### 1 2

parameter s ar e no t comparabl e t o conventionall y estimate dones . Hal l (1986a ) give s the formul a t o conver t the value-adde dmarku pt o the rati o o f gros s price t o margina l cos t (ji) . I f 7 i s the shar e o f material s i ngros s outpu t andmaterial s ar e use di nfixe dproportion s wit hgros s output , the n Jt. - p/(l+(/i-l)7) . Hubbar d(1986 ) andDomowitz , Hubbard , an dPeterse n (1987 ) stres s ho w

Hall' s empirica l result s o nthe value-adde dmarkup s ar e substantiall y

large r tha nth e gross-outpu t markups . * Th e firm' s andth e marke t elasticitie s o f demand(0 and0) als o ar e estimate do na value-adde dbasis . Agai nunde r the assumptio ntha t material s
ar e use di nfixe dproportion s wit hgros s output , i t i s possibl e t o calculat e the elasticitie s o na gros s price/gros s outpu t basis . Specifically , the gros s price/gros s outpu t elasticitie s ar e 0- 0 /(I-7 ) and0 - 0/(l-i). Not e tha t the correctio nfo r bot hthe firm' s an dth e marke t elasticitie s ar e
g Usin g th e value-adde ddeflato r rathe r tha nthe gros s outpu t pric e inde xi nthe deman dfunctio nals o add s a multipl e o f the growt hi nrea l material s price s t o th e disturbanc e o f th e deman dfunction . Thi s componen t o f the disturbanc e i s orthogona l t o the productivit y shoc k instrument . Change s i nmaterial s price s wil l no t bia s th e measur e o f tota l facto r productivit y

a s lon g a s material s ar e use di nfixe dproportion s (the assumptio nmade here ) o r value-adde di s measure da s a Divisi a inde x(Bruno , 1978 , Theorem

2) . The GN P dat a ar e double-deflated , no t Divisi a indexes . (The U.S . nationa l income an dproduc t account s ar e rebase dever y te nyears , no t continually. ) The bia s i nusin g th e double-deflate d dat a instea do f a Divisi a calculatio ni s ver y smal l eve ni nthe fac e o f material s pric e change s o f the siz e see ni nth e 1970s . (Brun o andSachs , 1985 , p . 58) . Finally , i nthe estimate s wher e oi l pric e change s ar e include da s instrument s fo r th e marku pequation , th e instrumen t i nth e deman dequatio n i s orthogona l b y

constructio nt o thi s majo r componen t o f material s pric e changes . 

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### r e 

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*..- • •:& •

- 1 3

th e same . Henc e the measur e 8 nee dno t b e correcte dfo r the material s share . Dat a ar e availabl e fo r material s shar e i s manufacturing . Result s o na gros s outpu t basi s ca nhenc e b e reported .

4 . Dat a an

dResult s Th e marku pequatio n(2 ) an dthe demandequatio n(5' ) ar e estimate do na pane l o f al l U.S . privat e industries . Estimate s ar e presente dfo r bot h
t broa d sector s an

dfo r tw

o digi t industries . Th e tw o digi t industrie s hav e the narrowes t definition s provide di npublishe dNationa l Incom e andProduc t Account s (NIPA ) data . Th e dat a reflec t the comprehensiv e revision s o f th e NIP A tha t wer e publishe di nDecembe r 198 5 an dar e revise da s o f Jul y 1986 . Detail s ar e provide di nth e Appendix . Th e dat a ar e availabl e fro m 194 7 t o 198 5 excep t fo r the labo r data , whic hbegi ni n1948 . Th e sampl e perio di n thu s 194 9 t o 198 5 t o allo w fo r computin g the changes . Thes e dat a ar e a t a highe r leve l o f aggregatio ntha ni s ofte nuse di nstudie s <£ f marke t power . Consequently , the estimate s wil l be average s o f sometime s disparat e markets . Th e advantag e o f thes e dat a ove r accountin g dat a i s that , a t leas t i n theory , th e NIP A

measure s the appropriat e economi c concepts . Th e markup s equatio n(2 ) andthe demandequatio n(5' ) ar e estimate dby th e instrumenta l variable s procedure s discusse di nth e previou s section . Th e elasticit y

face dby

the firm , 0 , andthe rati o o f the marke t t o firm' s elasticity , 8, ar e compute dfro m the estimate dp. and0. Th e standar derror s * o f the estimate d0 and8 ar e compute dusin g the first-orde r Taylo r serie s 

## i / *

### 1 4 -

approximation , whic h I s vali d asymptotically . The covarianc e betwee n th e * estimate dp an

d0 i s zer o i nthe sampl e becaus e o f the covarianc e restrictio no nth e disturbance s o f the equation . Basi c Result s Tabl e 1 present s result s fo r broa dsectors . Th e estimate s ar e base do n poole drathe r tha nth e dat a fo r the tota l sector . Dat a fo r the tw o digi t industrie s ar e poole dunde r the correspondin g sector . The tw o digi t industrie s ar e give ni nthe Appendix . Construction , Wholesal e Trade , and Retai l Trad e hav e n o two-digi t sub-industrie s i nthes e data . The poolin g procedur e i s a s follows . Th e marku pequatio n(2 ) i s estimate dby instrumenta l variable s o neac hsectora l pane l o f industries . Withi nthe panels , eac htw

o digi t industr y

ha s a differen t intercep t bu t th e same slop e coefficien t (p-1) . Th e residual s fro m thes e equation s ar e use da s

9 instrument s fo r pric e i nth e demandequatio n(5') . Again , eac hdeman d equatio nha s a differen t intercep t bu t a commo nslop e coefficient . Fo r bot h equations , I repor t the system tw o stag e leas t square s standar derrors . Th e reporte dDurbin-Watso nstatistic s ar e the averag e fo r thos e o f the tw o

Th e residual s fro m th e unrestricte destimate s o f equatio n(2 ) wher e p varie s acros s industrie s ar e use da s the instruments . Thi s procedur e assure s tha t the covarianc e restrictio nhold s i nth e sampl e fo r eac h industry .

Th e standar derror s thu s ar e consistentl y estimate di nligh t o f the clea r heteroskedasticit y acros s the tw

o digi t industries .



# '7P.1 9

*5

-



### 1 - 1 5

digi t equations . The pooling ha s tw o advantage s ove r estimate s carrie d
ou t o nth e tota l dat a fo r eac hsector . First , the estimate s ar e mor e efficient . Second , i t i s possibl e t o remov e a fixe deffec t fo r eac h industry . 1 2 Th e result s o f the poole destimate s ar e presente di nTabl e 1 . Th e firs t thre e column s give th e estimate dmarkupcoefficients , the standar d
error s o f estimates , an dth e Durbin-Watso nstatistic s fo r Hall' s marku p equatio n(2) . Th e standar derror s o f the coefficien t estimate s ar e give ni n parentheses . Th e markup s ar e essentiall y zer o i nagriculture , construction , an dservices . I ndurabl e an dnon-durabl e manufacturin g andi nfinance , the markup s ar e moderatel y size dbu t strongl y significant . I nmining , transportation , communication s andutilities , an dtrade , the markup s ar e
ver y large . Al l the markup s ar e estimate s wit ha moderat e t o ver y fin e degre e o f precision . Th e nex t thre e column s give the estimate s fo r the deman dequation . Th e result s o f th e instrumenta l variable s estimatio ni s highl y satisfactory . Excep t fo r mining , al l the estimate delasticitie s ar e negative . Excep t fo r minin g andfinance , the elasticitie s ar e precisel y estimate dt o b e value s bounde dawa y

fro m zero .
Th e distributio nacros s industrie s o f the Durbin-Watso nstatistic s fo r non-durable s ar e give ni nth e nex t table . The distributio no f th e statistic s acros s the industrie s i s consisten t wit hth e hypothesi s o f n o seria l correlation . Result s fo r othe r sector s ar e similar . 1 2 Fo r completeness , Tabl e 1 report s result s fo r durabl e goods . Thes e shoul db e discounte dbecause , a s note dabove , the for m o f the deman d functio ni s inappropriat e fo r them .


### / «- 1 6 

# w

Th e nex t tw

o column s give the value s o f the implie delasticit y * * 0 - p/(l

'p) an

do f the measur e o f marke t powe r 8 - 0/0 . Ther e i s a one - * to-on e relationshi pbetwee np and0 . Industrie s wit hhig hmarkup s hav e lo w implie delasticities . Th e measur e o f marke t powe r 8 give s a somewha t differen t rankin g o f the competitiv e tha nd o the markup s alone . Minin g an d financ e hav e estimate dmarke t elasticitie s tha t ar e essentiall y zero . Consequently , they appea r t o be competitiv e base do nth e 8 measur e regardles s o f the markup . Industrie s wit hnon-degenerat e estimate s o f the marku pals o displa y interestin g difference s i nranking . Fo r example , transportatio nan dretai l trad e hav e simila r estimate dmarkups . Th e industrie s fac e differen t elasticitie s o f demandan dhenc e ca nbe ranke d i n term s o f degre e o f marke t power . The assumptio ntha t the slop e coefficient s i neac ho f the sub industrie s ar e equa l underlie s the poolin g o f equation s (2 ) and(5') . Fo r al l industrie s excep t fo r durables , on e canno t rejec t thes e hypothese s usin g conventionally-size dtests .

, Estimate s fo r th e individua l non-durabl e manufacturin g industrie s ar e presente di nTabl e 2 . Th e estimatio nprocedur e i s the sam e a s fo r th e result s i nTabl e 1 excep t ther e i s n o pooling . I nsevera l o f the industrie s (food , textiles , apparel , andprintin g an dpublishing) , the estimate d markup s ar e insignificantl y differen t fro

m zero . Thes e industrie s als o hav e smal l markups . Othe r markup s ar e significantl y differen t fro

m zero . Rubbe r
andleathe r hav e relativel y smal l markups ; paper , chemicals , andpetroleu m hav e intermediat e markups ; tobacc o ha s a ver y larg e markup .P.2 1

«

v e
e r - 1 7

Th e estimate dmarke t elasticitie s al l li e betwee n-1. 0 and-1.8 . Mos t
ar e estimate dver y precisely . Usin g th e innovatio ni nindustrie s productivit y

a s a ninstrumenta l variabl e is ' a promisin g approac hfo r estimatin g elasticitie s o f demand . * Th e las t tw

o column s o f Tabl e 2 give the implie destimate s o f 0 an d8 . The estimate s o f 8 display interesting dispersio nandyiel dranking s a s t o marke t powe r tha t ar e differen t fro m thos e implie s by th e marku palone . A s i nTabl e 1 , al l o f the poin t estimate s o f 8 fal l withi nth e admissibl e rang e betwee nzer o andone . Tobacco , paper , an dchemical s al l hav e value s o f 8 insignificantl y

differen t fro

m th e monopol y

outcome anda t leas t thre e standar ddeviation s differen t fro m the competitiv e outcome . Al l thre e industrie s ca nbe characterize da s monopolize ddespit e thei r ver y differen t estimate dmarkups . Appare l an dleathe r hav e value s o f 8 o f 0. 3 an d0. 5 respectively . Moreover , eac hestimat e ha s standar derro r suc htha t bot hthe competitiv e andmonopolize doutcome s ca nb e rejected . Foo dan dtextile s hav e smal l estimate d8. Thes e industrie s appea r t o b e competitive , althoug h the poin t estimate s ar e imprecise . Finally , th e standar derror s fo r printin g andpublishing , petroleum , andrubbe r ar e larg e enoug ht o make i t difficul t t o rejec t an y hypothesis .

Alternativ e Instrument s The previou s result s ar e base do nthe perhap s incorrec t assumptio ntha t yea r t o yea r change s i naggregat e outpu t ar e unrelate dt o productivit y shocks . T o provid e estimate s tha t ar e robus t t o failur e o f thi s assumption , I presen t estimate s base do nalternativ e instruments . These instrument s 

# 20

### 1 8

shoul db e strictl y exogenous . Th e instrument s use dar e growt hi noi l price s 1 3 andmilitar y

employment . Oi l price s have bee ndetermine dlargel y b y force s independen t o f th e U.S . busines s cycle . Thes e includ e the Sue z crisis , the OPE C pric e increase s afte r the Yom Kippu r wa r an

dafte r th e fal l
o f th e Sha ho f Iran , impor t quotas , an ddomesti c pric e regulations . Change s i nmilitar y

employmen t ar e largel y determine db y

wars , whic hagai nar e no t
cause db y

U.S . busines s cycles . O nthe othe r hand , oi l pric e change s and
war s effec t th e busines s cycle . Therefore , the y ar e likel y

t o b e adequat e instruments . The result s fo r the poole dmanufacturin g dat a wit hthe alternativ e instrumen t list s ar e presente di nTabl e 3 . The firs t lin e repeat s th e result s fro

m Table 1 fo r eas e o f reference . Th e nex t thre e line s show the result s fo r th e combination s o f th e alternativ e instruments . Th e fina l line show s th e resul t wit hal l thre e instruments . Wit heithe r oi l pric e o r militar y

employmen t growt halon e o r jointl y a s instruments , 8 i s estimate d t o b e 0. 1 o r 0.2 . Wit han y o f thes e combination s o f instruments , the estimate s o f p. andhenc e o f 8 ar e ver y imprecise . B

y comparin g the estimate s o f th e las t tw o lines , i t i s potentiall y possibl e t o judge whethe r th e use o f aggregat e GN P growt ha s a ninstrumen t i s a vali dover-Identifyin g

1 4 restriction . Th e poin t estimate s o f marke t powe r wit hthe alternativ e instrument s ar e smalle r tha nwit haggregat e GN P growt ha s a ninstrument . 

### 1 3 Se e th e Appendi xfo r source s o f thes e data . 1 4 A forma l Hausma nspecificatio ntes t compute do nthe las t tw o estimate s o f th e marku panddemandequation s i nTable 3 doe s no t rejec t th e overidentifyin g restriction .

### 19

Yet , thos e estimate s ar e s o imprecis e tha t i t i s impossibl e t o rejec t th e hypothesi s tha t us e o f aggregat e GNP growt hi s a ninstrumen t i s a vali d overidentifyin g restriction .

5 . Discussio n alternativ e Estimate s o f th e Markup I t i s interestin g t o compar e thes e estimate s o f marke t powe r wit hthos e obtaine db y

othe r techniques . Th e marku pca nb e estimate dfro m a cos t functio nrathe r tha nfro m th e cyclicalit y

o f productivity . Appelbau m (1982) , fo r example , estimate s 8 usin g the marku pfro m th e derivativ e o f a n estimated , parametri c cos t function . H e examine s thre e non-durabl e manufacturin g industries : textiles , rubber , andtobacco . Hi s finding s fo r textile s andtobacc o agre e qualitativel y wit hmine . Textile s ar e essentiall y

competitiv e an

dtobacc o ha s stron g marke t power . He find s rubbe r i s essentiall y competitive wherea s I findtha t industr y t o be clos e to th e monopol y

outcome , albei t wit ha nimprecis e poin t estimate . Appelbau

m estimate s les s monopol y powe r tha nd o I becaus e he find s smalle r markups . I t i s fairl y straightforwar dt o explai nwh y Appelbaum' s implementatio no f th e cos t functio nyield s systematicall y lowe r markup s tha n doe s Hall' s non-parametri c approac htha t I follow i nthi s paper . Appelbau m
use s a constan t return s t o cos t functio nwhere labor , materials , an dcapita l
The underlyin g estimate s fo r mos t o f th e individua l industrie s usin g onl y oi l andmilitar y employmen t growt hhav e larg e standar derrors . Note tha t rubbe r i s a ver y concentrate dindustr y (se e below) . 

# P2 -- 2 0

ar e al l fre e t o var y withi nth

e period . Thus , he constrain s margina l cos t t o equa l averag e cost . I f a nindustry show s littl e profi t i nexces s o f th e require drat e o f retur no ncapital , a s do mos t industries , thi s approac h wil l yiel da smal l markup . Hall' s procedur e admit s the possibilit y o f highe r markup s i nsuc hindustrie s becaus e Solow' s formulatio nallow s margina l cos t t o be belo w averag e cost . I nthe Solo w calculation , capita l
ca nb e quasi-fixe d (a s i t surel y is) , s o the margina l cos t curv e ca nhav e upwar dslope .

Measure s o f Marke t Powe r Compare d I t i s usefu l t o compar e the measure s o f marke t powe r presente di nthi s pape r wit hothe r measures . Befor e doin g so , i t i s necessar y t o pu t the
measure s o na nequa l basis . A s discusse dabove , p, 0 , and0 ar e o na value-adde dbasis . Tabl e 4 present s the estimate s fro m Tabl e 2 converte dto 1 8 a gros s outpu t basis . A s Hubbar d(1986 ) andDomowitz , Hubbard , and Peterse n(1987 ) stress , th e gros s outpu t base dmarku pi s substantiall y lowe r tha nthe value-adde dbase dones . Moreover , the ranking^o f the markup s change s dependin g o nth e material s intensit y o f the industries .
U.S . manufacturin g industrie s hav e lo w price-cos t margins . Domowitz , Hubbard , an dPeterse n(1986 , Tabl e 1 ) findtha t profit s pe r outpu t i s onl y abou t 3 5 percen t i nth e mos t concentrate dindustrie s an d2 6 percen t overall . Sinc e thei r calculatio no f profi t include s norma l retur nt o capital , thei r figure s imply , lowe r markup s tha nthos e include di nthi s paper . An y calculatio ntha t i s base do naverag e cos t mus t similarl y yiel dlo w

markups . 1 8 Th e gros s outpu t elasticitie s shoul db e interprete dwit hcautio n becaus e th e shar e o f material s ma y have shif t ove r time . r 

## i <2 1 -

Tabl e 5 compare s a numbe r o f measure s fo r the non-durabl e manufacturin g industries . The y ar e th

e markupcoefficien t a s estimate di nTabl e 2 (p) ; the marku pAdjuste dt o a gros s outpu t basi s (£) ; th e implie delasticit y o f demandfro

m Tabl e 2 (0 ) ; the impliedelasticit y o na gros s outpu t basi s (0 ) ; th e inde xo f marke t powe r fro m Tabl e 2 {8); anda measur e o f averag e 1 9 concentratio n(CR,) . Th e cross-sectiona l standar ddeviatio nan dsimpl e
an dran k correlation s o f thes e measure s ar e give ni nTable 5 . Th e simpl e correlation s amon g al l th e variable s ar e quit e high . Particularl y strikin g I s th e fairl y

stron g correlatio no f th e concentratio nrati o wit hthe othe r
measures . Concentratio nratio s migh t b e ver y misleadin g a s t o marke t powe r i ncase s wher e th e othe r measure s ma y not . Thi s i s especiall y true i f marke t powe r arise s becaus e o f monopolizatio no f loca l markets . Th e ran k correlation s o f the measure s wit hconcentratio nar e substantiall y weaker . Muc ho f th e leverag e fo r the correlation s come s fro m the extreme observatio n
o f tobacco . Excludin g tobacco , the correlatio no f Ji andthe concentratio n
measur e fall s t o 0.4 0 an dtha t o f 8 an

dthe concentratio nmeasur e fall s t o 0.49 . Figure s 1 and2 give a scatte r o f the observation s fo r Jian d8 versu s concentration . Th e importan t correlatio nbetwee nth e measure s clearl y emerge s fro

m the Figures . Asid e fro m petroleum , th e scatte r diagram s ar e qualitativel y

quit e similar . Th e estimate s o f marke t powe r i nthi s pape r give a simila r pictur e o f the degre e o f monopolizatio no f U.S . non-durabl e manufacturin g industrie s tha nd o the concentratio nratios .

I^J Y 1 9 Th e measur e i s the sale s rati o averag e o f fou r fir m concentratio n ratio s base do nthe fou r digi t dat a i nRotember g an dSalone r (1986) . 

# 3H

### 2 2 . $ .

Conclusio n I nthi s paper , I discus s estimatio no f demandelasticitie s by exploitin g the restrictio ntha t demandshock s an dtechnologica l shock s ar e independent . Althoug hthi s techniqu e ma y hav e broa dimplications , i t i s
use d her e t o compar e marke t demandelasticitie s wit hthos e implie db y pric e - margina l cos t margins . Th e price-margina l cos t rati o i s not , pe r se. a
measure o f monopol y power . I f a nindustr y ha s a price-margina l cos t rati o tha t differ s significantl y fro m unity , on e ca nrejec t th e hypothesi s o f pur e competition , bu t on e ca nsa y nothin g els e abou t th e degre e o f monopolizatio n i nth e industry . A give nprice-margina l cos t rati o wil l impl y mor e monopol y powe r th e mor e elasti c i s demand . Monopol y powe r mus t b e stron g i norde r t o extrac t hig hprice s i na nindustry wit helasti c demand . Th e estimate dmeasure s o f marke t powe r correspondt o a wid e rang e o f conduct . Th e poin t estimat e fo r tobacc o an dchemical s i s tha t they achiev e the monopol y

outcome . Pape r i s als o clos e t o the monopol y outcome . O nthe othe r hand , fo r appare l an dleather , bot hthe monopol y andcompetitiv e outcome s ca nb e decisivel y rejected . Finally , thi s pape r show s ho w t o estimat e the pric e elasticit y o f deman db y

exploitin g th e covarianc e restrictio nbetwee nproductivit y shock s
anddeman dshocks . Thi s covarianc e restrictio ni s a nimportan t ste pi n overcomin g the difficult y i nidentifyin g the deman dcurv e becaus e o f th e lac k o f vali dinstruments . Thi s techniqu e fo r estimatin g th e elasticit y o f deman dshoul dhave importan t application s beyon dthe measuremen t o f marke t power .

### er e
o n i y t o 

### 2 3

APPENDI X 1 . Dat a Th e dat a use di nthi s pape r ar e describe di nthi s Appendix . Excep t fo r th e dat a o nthe capita l stock , they ar e fro

m the Nationa l Incom e andProduc t Account s (NIPA) . Th e dat a ar e annua l an dar e availabl e
a t th e tw

o digi t leve l o f disaggregation . Th e NIP A wer e rebenchmarke d i n Decembe r 1985 . A t th e sam e time , th

e bas e yea r fo r the constan t dolla r calculation s wa s change dt o 1982 . Th e dat a incorporat e the Jul y 198 6 revision s an dwer e extracte dfro m BEA compute r tapes . Th e industry 

### * definition s ar e base do nthe 197 2 standar dindustria l classification . I ndetail , th e NIP A dat a ar e a s follows . Tabl e numbe r refe r t o thos e i nthe NIP A a s publishe di nth e Jul y Surve y

o f Curren t Business . outpu t ( y

) : Rea l value-adde di n198 2 dollar s (Tabl e 6.2) . deflato r ( p ) : Value-adde ddeflato r (Table s 6.1 , 6.2) . I nthe demand equatio nestimates , th e relativ e pric e i s calculate da s the rati o o f th e industr y

value-adde ddeflato r t o the aggregat e GN P deflator . manhour s ( n) : Hour s o f full-tim e andpart-time employee s (Tabl e 6.11) . Th e industr y leve l manhour s dat a ar e onl y availabl e a t the sectora l level . T o construc t hour s fo r the tw o digi t industries , the hour s fo r th e sectora l tota l ar e divide damon g th e appropriat e tw

o digi t industrie s i n proportio nt o the tw o digi t industry' s shar e i nfull-time equivalen t employmen t (Tabl e 6.7 ) i nthe sector . compensation : Compensatio n(Tabl e 6.4 ) i s use di nth e calculatio no f th e labor' s share , a . I t include s wage s andsalaries , employers ' contribution s t o socia l insurance , andothe r labo r income , bu t no t 

# 96?

### 2 4

proprietors ' income . Th e shar e a i s calculate da s a Divisi a index , tha t is , i t i s a movin g averag e o f th e shar e a t tim

e t andtim

e t-1 . The capita l stoc k dat a ar e als o base do nthe rebenchmarke d NIP A data . The y ar e publishe di nthe Survey o f Curren t Busines s (Augus t 1986 , fo r example ) wer e obtaine dfo r thi s stud y fro m compute r tape . The capita l stoc k i s constan t dolla r ne t capita l stoc k o f equipmen t plu s structures . The dat a fo r the instrument s i s a s follows : aggregat e GN P i s fro m the NIP A Tabl e 6. 2 andi s measure di nconstan t 198 2 dollars . Oi l price s ar e
measure da s th e rati o o f the produce r price inde xfo r crud e oi l (PPI561 ) t o th e GN P deflator . Militar y employmen t i s ful l time equivalen t Federa l militar y

employmen t (NIP

A Tabl e 6.6) . Al l instrument s ar e annua l andlo g differenced . The tw o digi t industrie s poole di nthe estimate s i nTabl e 1 fo r the respectiv e sector s ar e a s follows . Th e numbe r o f tw o digi t industrie s i s give ni nparentheses . Agricultur e (2) : Farms ; Agricultura l services , forestry , and fisheries . Minin g (4) : Meta l mining ; Coa l mining ; OlT andga s extraction ; Non-metalli c minerals , excep t fuels . Constructio n(1) . Durabl e manufacturin g (11) : Lumbe r andwoo dproducts ; Furnitur e and fixtures ; Stone , clay , andglass ; Primar y meta l industries ; Fabricate d meta l products ; Machinery , excep t electrical ; Electri c andelectroni c equipment ; Moto r vehicle s andequipment ; Othe r transportatio n equipment ; Instrument s andrelate dproducts ; Miscellaneou s manufacturin g industries . Non-durabl e manufacturin g (10) : Foo dan d kindre dproducts ; Tobacc o manufactures ; Textil e mil l products ; Appare l 

# 1 7P.2 9

- 2 5

andothe r textil e products ; Pape r an dallie dproducts ; Petroleu m an d
coa l products ; Rubbe r an dmiscellaneou s plasti c products ; Leathe r an d leathe r products . Transportatio n(7) : Railroa dtransportation ; Loca l
andinterurba npassenge r transit ; Truckin g andwarehousing ; Wate r transportation ; Transportatio nby air ; Pipelines , excep t natura l gas ; Transportatio nservices . Communication s an dUtilitie s (3) : Telephon e
andtelegraph ; Radi o andtelevisio nbroadcasting ; Electric , gas , an d sanitar y

services . Wholesal e trad e (1) . Retai l trad e (1) . Finance . insurance , an

drea l estat e (6) : Banking ; Credi t agencie s othe r tha n « banks ; Securit y

an dcommodit y

brokers , andservices ; Insuranc e carriers ; Insuranc e agent s an dbrokers , andservices ; Rea l estate . Service s (10) : Hotel s an dothe r lodging places ; Persona l services ; Busines s services ; Aut o repair , services , an dgarages ; Miscellaneou s repai r services ; Motio npictures ; Amusemen t andrecreatio nservices ; Healt hservices ; Lega l services ; Educationa l Service s

2 . Econometri c Issue s „ Disaggregatio nan dIdentificatio n Aggregat e outpu t growt hwil l no t i ngenera l be a vali dinstrumen t fo r estimatin g the marku pequatio n(2 ) o ndisaggregat e data . Disaggregatio n alon e typicall y

doe s no t yiel didentification . I f ther e i s a nImportan t aggregat e deman dshock , equatio n(2 ) wil l be approximatel y identified . Say aggregat e GN P growt h(denote dA q) evolve s a s

A q - Av

+ Zjfa^A

c * i-i-'i t 

# 2Z- 2 6

where A

v i s a naggregat e demandshoc k an dw . i s th e shar e o f industr y i i n the aggregate . (The share s ar e constan t onl y fo r notationa l convenience. ) Th e inconsistenc y i nestimatin g p. tha t arise s because the aggregat e i s the
som e o f th e industrie s i s

(Al ) pli m

T" 1 (M i - P L ) - u> ±Var(Ac it ) / Cov(a it (An lt -Ak lt ) , Aq t )

Th e usua l problem wit hidentificatio nby disaggregatio ni s tha t a s Var(A v ) vanishes , th e inconsistenc y i s o f orde r one . O nthe othe r hand , i f the variance o f th e deman dshoc k i s no t small , the inconsistenc y i s o nthe orde r
o f w. , whic hi s small .

Instrumenta l Variable s Estimato r an dCovarianc e Restriction s Conside r estimatio no f tw o equation s analogou s t o the marku pequatio n
and th e deman dequation . Dat a ar e availabl e o na pane l o f industries . Denot e the

m —

(A2 ) 

### 7kr

### -*,J. 

### + V

i t "i t 1 

### i

t

where k - 1, 2 indexe s equations , where i - 1, M indexe s indvistrles , andwher e t - 1, T indexe s time . I nmatri xnotatio nw e have

(A3 ) y k- X k « k+ v kP.3 1



### c e - 2 7 -
k k wher e th e y

andv

ar e stacke dvector s o f observation s an ddisturbance s an

d k k X- diag(X.) . Firs t conside r identificatio no f the parameters . Suppos e tha t th e firs t equatio n(k-1 ) i s a t leas t just-identifie da s i s the cas e o f markupequation . I t ca nb e estimate db y standar dinstrumenta l variable s techniques . Suppos e tha t the secon dequatio nha s tw o righ t han dsid e variables . (I nth e demandequatio nthey the constan t andthe pric e term. ) Th e equatio nI s under-identifie d b y conventiona l means . Tha t is , n o instrumen t i s available . Suppos e tha t the disturbance s o f the tw o equation s 1 2 ar e independen t Indu s try-by-industry . Tha t is , E( v v. ) - 0 . Thi s * restrictio ni s sufficien t t o just-identif y the parameter s o f the ' second equation . Moreover , i t ha s a ninstrumenta l variable s interpretation . Th e residua l fro

m th e firs t equatio nca nb e use da s a ninstrumen t fo r the second equation . Thi s procedur e yield s consistent , asymptoti c norma l estimate s and , becaus e the secondequatio ni s jus t identified , i s equivalen t t o maximu m likelihoo d(se e Hausman , Newey , andTaylo r (1987)) . The covarianc e matri xprinte db y the compute r fo r the secondequatio n wil l no t be correct . Th e correc t on e depend s o nthe estimate dparameter s
an d th e dat a fro

m th e firs t equatio nbecaus e the fitte dvalue rathe r than the tru e value o f v i s use da s th

e instrument . Le t Z , be the instrument s fo r th e secon dequatio nfo r the i equatio nan dwher e Z - diag(Z.) . (I n thi s paper , Z , ha s tw o columns , the constan t andthe residual s fro m th e A 2 firs t equation. ) The instrumenta l variable s estimato r o f 5 . i s suc htha t

(A4 ) " 2 2 2-1 2



### S\ - S\ + 

### (Z.'X^ ) \>v\


## m&. 

# BO- 2 8 -

Not e tha t the secondter m o f the righ t han dsid e o f (A4 ) wil l hav e a n

2 1 A 1 elemen t involvin g th e correlatio no f v andXS becaus e Z i s dependen t o n th e estimate d valu e o f S . Thi s ter m wil l ad dt o the covarianc e o f the estimat e 6 Defin e a matri xQ tha t ha s element s

A 2 1 A l A l 1 A 2 (A5 ) Wi j - v£'xJ'cov(Sj,«j)XjV ^
Thi s ter

m i s the covarianc e betwee nthe residua l fro m th e secondequatio n 1 A 1 and X6

. Le t £ b e th

e Mx M covarianc e matri xo f th e disturbance s o f th e 2 2 secon dequation s (Indu s try -by - industry ) . Tha t is , E( v v ' ) - 2381 . Le t 

# -[i°x ]

be a matri xtha t select s element s o f Z . correspondin g t o th e fitte d instrument . Th e correc t variance-covarianc e matri xo f the syste m 2 instrumenta l variable s estimato r o f S i s the n

(A6 ) V(* 2 ) - (Z'X 2 )" 1 Z'(2»I)Z(X 2 'Z)" 1 + (Z 2 'X)" 1 Z'(0®S)Z(X 2 'Z)" 1

Th e firs t ter

m i s th e standar dsyste m instrumenta l variable s covarianc e matrix . Th e secon di s the correctio nterm . Th e resultin g standar derror s
ar e strictl y

greate r tha nthe one s printe db y th e standar dcompute r program . I nthi s application , th e correctio nadd s te nt o twent y percen t t o the standar derrors . 

# St.j^f*4** s i'^" ' 

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vv o c o o UIU I tov o H U J U J ui to o P~u

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### a


## j^rrmr^t\(%rim''-'irmmm^^ ij-fiTTiritJ i

O P c oP.3 5

- 3 1

Tabl e 3 Elasticitie s Impliedan dEstimate d Poole dNon-durabl e Manufacturin g Industrie s Alternativ e Instrument s fo r Marku pEquatio n



# w Instrument s Marku pEquatio n DemandEquatio n Implie d


# w & '

ft f. l growt hin : GNP oi l price s militar y

employmen t oi l price s and militar y

employmen t GNP , oi l prices , and militar y

employmen t 0. 4

(0.1 ) 0. 1 (0.3 ) 0. 2 (0.3 ) 0. 2 (0.3 ) 0. 3 (0.1 ) 

### se

e 5. 0
14. 4
97. 3 

### 6. 0 4. 9 d

w 1. 9 1. 8 1. 7 1. 9 1. 9 

## P -1. 3 (0.1 ) -1. 2 (0.2 ) -1. 2 (0.2 ) -1. 2 (0.2 ) -1. 3 (0.1 ) 

### se

e 6. 9 6. 7
22. 5
10. 6 

### 7. 4 d

w 1. 9 1. 8 1. 9 1. 9 1. 9 

## 0 -3. 4 (0.6 ) -8. 6 (17.3 ) -5. 9 (7.1 ) -7. 6 (U.3 ) -3. 9 (0.9 ) 8

0. 4 (0.1 ) 0. 1 (0.3 ) 0. 2 (0.2 ) 0. 2 (0.2 ) 0. 3 (0.1 )



# 3* .

### 3 2 -

Tabl e 4 Value-Adde

dan d Gros s Output Parameter Estimate s

Foo d Tobacc o Textile s Appare l Paper Printin g Chemical s Petroleu

m Rubber Leathe r P-l

0. 4 4. 0 0. 3 0. 3 1. 5 0. 4 2. 0 1. 3 0. 7 0. 8 valu

e adde d * -3. 8 -1. 3 -4. 7 -4. 1 -1. 7 -3. 2 -1. 5 -1. 7 -2. 3 -2. 3 

## A

-1. 0 -1. 3 -1. 5 -1. 1 -1. 5 -1. 8 -1. 5 -1. 5 -1. 8 -1. 2 

## £- 1

0. 2 0. 5 0. 1 0. 1 0. 4 0. 3 0. 6 0. 2 0. 3 0. 3 gros s output

" *
-7. 1 -2. 9 -11. 2 -8. 4 -3. 5 -4. 7 -2. 8 -5. 3 -4. 4 -4. 8 

## fi

-2. 0 -2. 9 -3. 6 -2. 3 -3. 1 -2. 6 -2. 8 -4. 6 -3. 4 -2. 5 7

0.46 6 0.56 6 0.58 2 0.51 0 0.52 2 0.31 4 0.45 5 0.67 1 0.46 2 0.51 9

Note : Th

e estimate

dfi, 0 , an

d 0 ar e fro m Tabl e 2 . Th

e gros s output base d estimate s ar

e derive

daccordin

g t o th e formula s Ji- /i/(l+(p-l)7 ) (Hall , 1986a) , " * * * 

### 0 - 0 /(1-7) . an

d 0 - 0/(l-i). Th

e material s share s (7 ) ar e fro m Hubbar d (1986) .



# 5S" ,P.3 7



### 3 3

Tabl e 5 Alternativ e Measure s o f Marke t Powe r Non-durabl e Manufacturin g Industrie s

||| | standard deviatio n 1.1 4 0.1 6 

## fi

1.2 1 

### 2. 7 0.3 0 

### CR ,

0.1 9 

### §g ; simpl e correlatio n with :

IT':- * 

### 13. " 

## fi

CR , 1.0 0 

### 0.8 3 1.0 0 0.7 6

0.8 5 1.0 0 0.6 5

0.8 7 0.9 2 1.0 0 0.8 0

0.8 8 0.9 4 0.8 4 1.0 0 0.6 8

0.5 9 0.5 1 0.4 4 0.6 2 1.0 0



# m ran

k ' correlatio n with : A * P 

# f Y
8 CR , 1.0 0 

### 0.7 7 1.0 0 1.0 0

0.7 7 1.0 0 0.7 7

1.0 0 0.7 7 1.0 0 0.8 6

0.7 7 0.8 6 0.7 7 1.0 0 0.1 7

0.1 7 0.1 7 0.8 6 0.2 5 1.0 0


# 3 bP.3 8 

## Figur e 1

c o



### _ • o c 6 o u. o -
0. 7 -
0. 6 -
0. 5 -
0. 4 -
0. 3 -
0.2 - •»«Kttl«

_ -»oo d

•appare l •rubbe r

.pqp« r

•tooHta r •printin g an d publishin g •ahamtoolf t

0. 1 - 1 — 0. 2 —T— 0. 4 -~r— o. e Marku p (gros s prfoa/marglna l aosr ) 

## Figur e 2

• o c o U u. o -
0. 7 -
0. 6 -
0.5 -
0. 4 -
0 J - 0_2 - /

•foodr«tl|«

_

•opport i

i i •rubbe r

•leathe r

•printin g an d publishin g

III I -

•petroleu m •pape r

i •tabooo c

•ahamla c

T1 *:>. "



# I

0. 2 0. 4 0. 6 0. 6 Thet o -34 -

### 3 5

REFERENCE S

I Appelbaum , Elie , "The Estimatio no f th e Degre e o f Oligopol y Power, " Journa l o f Econometric s 1 9 (1982 ) 287-299 .
Bresnahan , Timoth

y F. , "The Oligopol y Solutio nConcep t i s Identified, " Economic s Letter s 1 0 (1982 ) 87-92 .
Bresnahan , Timoth

y F. , "Empirica l Studie s o f Industrie s wit hMarke t Power, " Handboo k o f Industria l Organization . Richar dSchmalense e andRober t Willig , eds. , forthcomin g (1987) .

J s ,

V \ & Bruno , Michael , "Duality , Intermediat e Input s an dValue-Added, " i n Productio nEconomics : A Dua l Approac ht o Theor y andApplications . vol . 2 , MelvynFus s andDanie l McFadden , eds . Amsterdam : North-Holland , 1978 .
Bruno , Michae l an

dJeffre y

D . Sachs , Economic s o f Worldwid e Stagflation . Cambridge , Mass. : Harvar dUniversit y Press , 1985 . Domowitz , Ian , R . Glen nHubbard , an dBruc e C . Petersen , "Busines s Cycle s and the Relationshi pbetwee nConcentratio nandPrice-cost«Margins, " Rand Journa l o f Economic s 1 7 (1986 ) 1-17 . Domowitz , Ian , R . Glen nHubbard , an dBruc e C . Petersen , "Marke t Structur e andCyclica l Fluctuations, " unpublishe dpaper , Northwester nUniversit y (1987) .
Hall , Rober t E. , "Th e Relatio nBetwee nPric e an dMargina l Cos t i nU.S . Industry, " unpublishe dpaper , Hoove r Institutio n(1986a) .



### I * 

# I Hall , Rober t E. , "Chroni c Exces s Capacit y i nU.S . Industry, " Nationa l Burea u o f Economi c Researc hWorkin g Pape r No . 1973 , Cambridge , M A (1986b) . 

# 3&- 3 6

Hall , Rober t E. , "Marke t Structur e an dMacr o Fluctuation, " Brooking s Paper s o nEconomi c Activit y (2:1986 ) 285-32 2 (c) .
Hall , Rober t E., "Productivit y an dth e Busines s Cycle, " Carnegie-Rocheste r Conferenc e o nPubli c Policy , forthcomin g (1987) .
Hausman , Jerr y

A . andWillia

m Taylor , "Identificatio ni nLinea r Simultaneou s Equation s Model s wit hCovarianc e Restrictions : A nInstrumenta l Variable s Interpretation, " Econometric a 5 1 (1983 ) 1527-49 .
Hausman , Jerr y

A. , Whitne y

Newey , an

dWilliam

Taylor , "Efficien t Estimatio n andIdentificatio no f Simultaneou s Equation s wit hCovarianc e Restrictions, " Econometric a (1987) , forthcoming .
Hubbard , R . Glenn , "Discussion, " Brooking s Paper s o nEconomi c Activit y (2:1986 ) 238-336 . Kydland , Fin nE . andEdwar dC . Prescott , "Tim e t o Buil dandAggregat e Fluctuations, " Econometric a 5 0 (1982 ) 1345-1370 . Long , Joh nB. , Jr . andCharle s I . Plosser , "Rea l Busines s Cycles, " Journa l o f Politica l Econom y 9 1 (1983 ) 39-69 . Rotemberg , Juli o J . andGart hSaloner , " A Supergame-Theoreti c Mode l o f Pric e War s durin g Booms, " America nEconomi c Revie w 7 6 (1986 ) 390-407 . Shapiro , Matthe w

D. , "Ar e Cyclica l Fluctuation s i nProductivit y Du e Mor e t o I ! Suppl y Shock s o r DemandShocks? " America nEconomi c Revie w Proceeding s 7 7 (1987 ) 118-124 . Solow , Rober t M. , "Technica l Chang e andthe Aggregate Production . Function, " Revie w o f Economic s an

dStatistic s 3 9 (1957 ) 312-320 . 

# •3 7 j