Productive Capacity of Capital Stock: Problems of Measurement

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

PRODUCTIVE C A P A C I T Y O F C A P I T A L STOCK : PROBLEMS O F MEASUREMENT

A l e x a n d e r A. P o d u z o v

S e p t e m b e r 1 9 8 3 C P - 8 3 - 4 7

CoZZaborative Papers report work which has not been performed solely at the International Institute for Applied Systems Analysis and which has received only

limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organi- zations supporting the work.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS

A-236

1 Laxenburg, Austria

FOREWORD

T h i s C o l l a b o r a t i v e P a p e r is o n e o f a series embodying t h e o u t c o m e o f a w o r k s h o p a n d c o n f e r e n c e o n E c o n o m i c S t r u c t u r a l Change: A n a l y t i c a l I s s u e s , h e l d a t IIASA i n J u l y a n d A u g u s t o f 1983. T h e c o n f e r e n c e a n d w o r k s h o p f o r m e d p a r t o f t h e c o n t i n u i n g IIASA p r o g r a m o n P a t t e r n s of Economic S t r u c t u r a l C h a n g e a n d I n d u s t r i a l A d j u s t m e n t .

S t r u c t u r a l c h a n g e w a s i n t e r p r e t e d v e r y b r o a d l y : t h e t o p i c s c o v e r e d i n c l u d e d t h e n a t u r e a n d c a u s e s o f c h a n g e s i n d i f f e r e n t s e c t o r s o f t h e world economy, t h e r e l a t i o n s h i p b e t w e e n

i n t e r n a t i o n a l m a r k e t s a n d n a t i o n a l e c o n o m i e s , a n d i s s u e s o f o r g a n i z a t i o n a n d i n c e n t i v e s i n l a r g e e c o n o m i c s y s t e m s .

T h e r e is a g e n e r a l c o n s e n s u s t h a t i m p o r t a n t e c o n o m i c

s t r u c t u r a l c h a n g e s are o c c u r r i n g i n t h e world economy. T h e r e are, h o w e v e r , s e v e r a l a l t e r n a t i v e a p p r o a c h e s t o m e a s u r i n g t h e s e

c h a n g e s , t o modeling t h e p r o c e s s , a n d t o d e v i s i n g a p p r o p r i a t e r e s p o n s e s i n t e r m s o f p o l i c y m e a s u r e s a n d i n s t i t u t i o n a l r e d e s i g n . O t h e r i n t e r e s t i n g q u e s t i o n s c o n c e r n t h e role o f t h e i n t e r n a t i o n a l e c o n o m i c s y s t e m i n t r a n s m i t t i n g s u c h c h a n g e s , a n d t h e m e r i t s o f a l t e r n a t i v e m o d e s o f e c o n o m i c o r g a n i z a t i o n i n r e s p o n d i n g t o s t r u c t u r a l c h a n g e . A l l o f t h e s e i s s u e s w e r e a d d r e s s e d by p a r t i c i p a n t s i n t h e w o r k s h o p a n d c o n f e r e n c e , a n d w i l l b e t h e f o c u s o f t h e c o n t i n u a t i o n o f t h e r e s e a r c h p r o g r a m ' s work.

G e o f f r e y H e a l A n a t o l i S m y s h l y a e v

E r n o Zalai

PREFACE

When studying t h e "economic growth" o f a country, one must be c a r e f u l t o i d e n t i f y it w i t h processes t h a t occur i n r e a l economic l i f e . It i s n e i t h e r adequate nor c o r r e c t t o define it merely i n terms o f t h e growth o f a p a r t i c u l a r s t a t i s t i c a l i n d i c a t o r such as r e a l GNP o r n a t i o n a l income. B u t when dealing w i t h r e a l growing economies, one a c t u a l l y has only two possible courses o f action, namely, t o s t u d y e i t h e r t h e growth o f aggregate value

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^however

it i s defined

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o r t h e growth o f t h e aggregate use value. The l a t t e r option means studying t h e growth o f t h e aggregate u t i l i t y o f a l l goods and s e r v i c e s produced during t h e period concerned. I believe t h a t aggregate value has l i t t l e o r nothing t o do with any u s e f u l d e f i n i t i o n o f economic growth, whereas aggregate use value i s p r e c i s e l y what should be kept i n mind i n any such studies.

Having adopted t h i s d e f i n i t i o n o f economic growth, however, t h e problem o f measurement immediately arises. To measure t h e growth o f aggregate u t i l i t y adequately, i t i s necessary t o measure b o t h t h e growth i n t h e q u a n t i t y o f goods and s e r v i c e s produced and t h e improvements i n t h e i r quality. My f e e l i n g i s t h a t t h e p r e s e n t s t a t e o f t h e a r t i n measuring t h e q u a l i t y

component o f economic growth i s such t h a t almost nothing d e f i n i t e can be said about t h e a c t u a l r a t e o f economic growth o f a given country. Escept one thing: i t must be higher than t h e r a t e o f growth o f r e a l GNP.

Therefore, t h i s paper does n o t s e t o u t t o examine t h e measurement o f economic growth per se. Rather, it i s concerned with t h e measurement o f one o f t h e f a c t o r s o f economic growth, namely, c a p i t a l input, which i s a t l e a s t more o r l e s s observable.

Several estimates o f t h e r a t e o f growth o f t h e productive

capacity o f c a p i t a l stock have already been published, mainly by US economists such as Robert Gordon o f Northwestern University, Dale Jorgenson o f Harvard, and others.

One v e r y noticeable f e a t u r e o f t h e available estimates i s t h a t t h e y r e f l e c t d i f f e r e n t f a c e t s o f economic r e a l i t y , and do n o t d i r e c t l y correspond t o one another. Therefore, t h e f i r s t purpose o f t h i s paper i s t o arrange and systematize them

somewhat. The second purpose i s t o provide a rough estimate o f t h e growth r a t e o f t h e productive capacity o f c a p i t a l stock f o r t h e US economy: t h i s i s chosen purely a s an i l l u s t r a t i v e example.

It i s c l e a r t h a t t h e problem i t s e l f i s o f a general, u n i v e r s a l nature. The need t o assess t h e c o n t r i b u t i o n o f

increased c a p i t a l stock p r o d u c t i v i t y t o n a t i o n a l economic growth e x i s t s i n a l l countries, even though perceptions o f i t s r e l a t i v e importance may d i f f e r from one c o u n t r y t o another.

Alexander Poduzov

PRODUCTIVE CAPACITY OF CAPITAL STOCK: PROBLEMS OF MEASUREMENT*

Alexander A. Poduzov

I n s t i t u t e o f U S A a n d C a n a d a S t u d i e s , A c a d e m y o f S c i e n c e s o f t h e U S S R , H o s c o w , U S S R

The extensive growth i n t h e physical volume o f c a p i t a l goods i s nowadays only one o f t h e reasons behind increases i n t h e productive capacity o f f i x e d c a p i t a l stock. The o t h e r major

f a c t o r t h a t can enable c a p i t a l t o produce an even g r e a t e r f i n a l o u t p u t i s t h e r i s e i n t h e q u a l i t y o f producers' durable equipment and s t r u c t u r e s , which increasingly embody t h e l a t e s t

technological achievements.

This can be i l l u s t r a t e d by t h e following example. Numerically c o n t r o l l e d machine t o o l s appear t o be much more productive than those t h a t they replace. Real value added i n t h e US i n d u s t r i e s using machine t o o l s grew 16% over t h e period 1973-1978 while t h e t o t a l number o f machine t o o l s f e l l by 14% (AM 1978). Another

example: t h e t o t a l number of g r a i n combines i n t h e United S t a t e s f e l l from 938,000 i n 1961/6S t o 655,000 i n 1975

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a drop o f 30%

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as a r e s u l t o f t h e s h i f t toward new, general-purpose combines;

over t h e same period, t h e t o t a l planted acreage was expanded by 20% (IT 1978).

However, t h i s phenomenon cannot be e a s i l y studied using o f f i c i a l s t a t i s t i c s , l a r g e l y due t o t h e way i n which t h e

productive capacity o f c a p i t a l stock i s measured. According t o numerous economists, t h e o f f i c i a l s e r i e s f o r aggregate c a p i t a l published i n many c o u n t r i e s mainly r e f l e c t t h e extensive growth o f accumulated c a p i t a l goods, whereas t h e q u a l i t y o f t h e c a p i t a l goods i s taken i n t o account only p a r t i a l l y , i f a t all. Thus these s e r i e s present a d i s t o r t e d p i c t u r e o f t h e phenomenon; they r e c o r d only a p o r t i o n o f t h e a c t u a l change i n c a p i t a l stock, and leave unobserved t h e o t h e r

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no l e s s important

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component o f t h e movement. The annual percentage r a t e o f change o f a more adequate series, which took i n t o account b o t h q u a n t i t a t i v e growth and

q u a l i t a t i v e improvement of c a p i t a l goods, might be expected t o be s u b s t a n t i a l l y higher than those o f t h e varioas o f f i c i a l series.

'"I would l i k e t o express m y appreciation t o David Bradford and Joe Peck f o r t h e i r helpful comments on an e a r l i e r d r a f t .

1. PROPERTIES OF TRfiDITIONhL SERIES

When assessing the movement o f c a p i t a l accumulated i n a

c e r t a i n country one usually s t a r t s by considering t h e time s e r i e s o f gross c a p i t a l stock measured i n constant prices. Out o f t h e d i f f e r e n t published s e r i e s r e l a t i n g t o fixed c a p i t a l t h i s one generally conforms best t o the notion o f physical volume of available c a p i t a l goods. It i s calculated by t h e perpetual inventory method according t o t h e following formula:

t

~ ( t ) =

1

g(t-m)~(m) (1)

m=

-a

where I(m) i s t h e r e a l gross c a p i t a l investment i n year m, gtt-m) i s the f r a c t i o n o f t h e c a p i t a l goods introduced during year m and s t i l l i n use i n t h e c u r r e n t year t, and t - m i s the age o f these c a p i t a l goods. Thus K t t ) i s t h e cumulative physical volume o f c a p i t a l goods introduced during a l l previous years and s t i l l available i n year t.

To evaluate t h e c u r r e n t value o f c a p i t a l investment i n constant prices s t a t i s t i c a l agencies use price indexes. Any

e r r o r s i n t h e calculation of the price indexes a r e automatically t r a n s f e r r e d t o t h e r e a l c a p i t a l investment and r e a l c a p i t a l stock s e r i e s where they produce corresponding biases b u t i n t h e

opposite direction t o the original errors. The Bureau o f Economic hnalysis of t h e US Department o f Commerce calculates price

indexes f o r new construction and takes wholesale price indexes f o r producers' durable equipment from t h e Bureau o f Labor S t a t i s t i c s o f the US Department o f Labor. US economists have repeatedly acknowledged t h a t both these indexes have important shortcomings.

Theoretically, such price indexes should take i n t o account only "pure" p r i c e increases, which a r e mainly due t o inflation.

But t h e r e l i a b l e e x t r a c t i o n o f t h i s type o f "pure" price movement o u t o f t h e t o t a l price increase

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which also includes the r i s e i n the cost o f c a p i t a l goods due t o t h e i r improved technical l e v e l

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presents substantial d i f f i c u l t i e s . Clccordingly, i t i s widely accepted i n the United S t a t e s t h a t t h e dynamics o f the o f f i c i a l price indexes r e f l e c t both pure price increases and a major p o r t i o n of t h e p r i c e increases due t o the r i s i n g quality o f c a p i t a l goods.

According t o Business Week tBW 19791, Robert Gordon o f Northwestern University has constructed an a l t e r n a t i v e "quality adjusted" d e f l a t o r f o r producers' durable goods t h a t takes i n t o account quality changes such as increased energy efficiency and increased machine output per dollar o f c a p i t a l cost. Gordon's index has increased by only 23% since 1947, while t h e o f f i c i a l BEA d e f l a t o r has moved up 286% over the same period. I n other words, t h e o f f i c i a l d e f l a t o r has grown 12.5 times as f a s t as Gordon's index. Even i f these estimates exaggerate the a c t u a l difference between the o f f i c i a l and "ideal" price indexes, t h e very order o f magnitude o f the difference highlights the p o s s i b i l i t y o f significant d i s t o r t i o n i n the measurement o f c a p i t a l growth

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a p o t e n t i a l l y substantial underestimation o f t h e t r u e r a t e o f c a p i t a l growth.

Although t h e o f f i c i a l US gross c a p i t a l stock series does r e f l e c t the changing q u a l i t y o f c a p i t a l goods, t h i s r e f l e c t i o n i s

f a r from complete: and one o f t h e main reasons f o r t h i s l i e s with t h e p r i c e indexes. Because o f t h e shortcomings i n h e r e n t i n these indexes, even those q u a l i t y changes t h a t a r e i n p r i n c i p l e

measurable and i d e a l l y should be r e f l e c t e d i n c a p i t a l stock

s e r i e s a r e i n p r a c t i c e f a r from f u l l y taken i n t o account. A t t h e same time, it must be emphasized t h a t t h e measurable q u a l i t y changes o f c a p i t a l goods r e p r e s e n t only p a r t o f t h e t o t a l increase i n t h e i r q u a l i t y o v e r a given period. The magnitude o f t h e d i f f e r e n c e between t h e p r i c e s ( a l l reduced t o t h e same base year) o f interchangeable modifications o f producers' durable equipment depends p r i m a r i l y on t h e d i f f e r e n c e between t h e c o s t s involved i n t h e production o f these modifications. This

d i f f e r e n c e i s n o t equal t o t h e d i f f e r e n c e between t h e productive capacities o f t h e v a r i o u s modifications.

The buyers' preference f o r t h e newer v e r s i o n s o f equipment obviously i n d i c a t e s t h a t t h e equipment's u t i l i t y m u s t have

increased more than i t s price. This means t h a t a c e r t a i n p a r t o f t h e t o t a l q u a l i t y improvement i n c a p i t a l goods cannot, i n

principle, be r e f l e c t e d i n t h e s t r a i g h t f o r w a r d r a t i o o f

comparable prices. This component cannot be r e f l e c t e d i n t h e dynamics o f gross c a p i t a l stock, even i f t h e measurable p a r t o f t h e q u a l i t y improvement i s f u l l y taken i n t o account. F o r t h i s reason it i s r e f e r r e d t o a s "unmeasured" q u a l i t y change.

The r e l a t i o n between t h e growth r a t e s o f an o f f i c i a l index o f c a p i t a l i n p u t and t h e s o r t o f index t h a t I would r e g a r d a s more comprehensive and appropriate i s shown i n Figure 1. The height o f t h e lower r e c t a n g l e up t o t h e bold l i n e corresponds t o t h e growth r a t e o f t h e o f f i c i a l l y published g r o s s c a p i t a l stock. It includes a more o r l e s s adequately measured q u a n t i t a t i v e component o f c a p i t a l growth a s well a s a r e l a t i v e l y small f r a c t i o n o f t h e q u a l i t a t i v e component. The height o f t h e upper r e c t a n g l e (above t h e bold line) corresponds t o t h e remaining, major p a r t of t h e q u a l i t a t i v e component o f t h e growth r a t e o f c a p i t a l input: it c o n s i s t s o f two subcomponents, representing t h e "measured" and

"unmeasured" p a r t s o f t h e q u a l i t y component.

Growth rate o f capital input

t

"Unmeasured"

quality

component

Measured quality

Growth rate

Quantity of official

component index

+

t

FIGURE 1 Components o f t h e growth r a t e o f c a p i t a l input.

Previous a t t e m p t s by economists t o c o n s t r u c t a s e r i e s t h a t would r e f l e c t q u a l i t y changes i n c a p i t a l goods t o a g r e a t e r e x t e n t than t h e o f f i c i a l s e r i e s have followed t h r e e main directions: we w i l l now b r i e f l y review each i n turn.

2. USE O F THE PRtlDUCTION FCINCTION

Robert Solow and h i s c o l l a b o r a t o r s concentrated on one v e r y important aspect o f q u a l i t y improvement r e l a t e d t o c a p i t a l goods, namely, t h e growth i n t h e productive capacity o f t h e goods. They proceeded from t h e assumption t h a t t h e r e q u i r e d s e r i e s can be c o n s t r u c t e d by means o f econometric processing o f t h e e x i s t i n g macroeconomic s e r i e s o f i n p u t s and o u t p u t s o f production. With t h a t end i n view, i n s t e a d o f t h e t r a d i t i o n a l index o f c a p i t a l stock (see eqn. 11, a new index o f c a p i t a l productive capacity was introduced:

A s compared w i t h eqn. (11, t h e m u l t i p l i e r (1+AIrn i s

introduced i n t o each item o f eqn.

(2)

t o take i n t o account t h e additional p a r t o f t h e q u a l i t y improvement o f c a p i t a l goods t h a t i s n o t r e f l e c t e d i n t h e o f f i c i a l s e r i e s f o r c a p i t a l investment Urn). According t o (21, f i x e d c a p i t a l stock i s represented by a vintage s t r u c t u r e with each vintage corresponding t o gross

c a p i t a l investments o f d i f f e r e n t y e a r s l e s s discards. A s a r e s u l t o f technological progress, c a p i t a l goods o f any given vintage a r e assumed t o be more p r o d u c t i v e than those o f any p r e v i o u s vintage and l e s s p r o d u c t i v e than those o f any subsequent vintage.

A l l t h e q u a n t i t a t i v e estimates o f A available f o r t h e US

economy ⁽

1

i s r e f e r r e d t o as t h e r a t e o f embodied technical progress (ETP)) a r e obtained by means o f i n d i r e c t econometric methods within t h e framework o f an aggregate production function, which can be w r i t t e n i n t h e simplest case as

where Y i s r e a l GNP and L i s l a b o r input, i n most cases measured as unweighted man-hours worked during a year. The e l a s t i c i t y o f o u t p u t with r e s p e c t t o c a p i t a l a, t h e r a t e o f disembodied

technical progress Y, and t h e scale m u l t i p l i e r A a r e unknown parameters t h a t might be estimated by t h e l e a s t squares method.

But, t o do t h a t , one m u s t have a t l e a s t preliminary calculated s e r i e s o f J (t), i.e. one m u s t know t h e magnitude o f A. The simplest way o u t o f t h i s s i t u a t i o n i s t h e following. Several values f o r A a r e a r b i t r a r i l y s e t within a s u f f i c i e n t l y wide range, and using (21, s e r i e s f o r J A ( t ) a r e calculated f o r each A . Then a l l these s e r i e s a r e p u t i n t o eqn. (3) i n t u r n and each time t h e parameters

a,

y, and A a r e estimated anew by l e a s t squares.

A s a r e s u l t , a combination o f a l l t h e parameters (including A ) i s

chosen t h a t ensures t h a t t h e a c t u a l d a t a on Y ( t ) during t h e observation period a r e v e r y c l o s e l y approximated by t h e f i g u r e s obtained from (3). This i s t h e way i n which most o f t h e available estimates o f A were obtained.

Table 1 presents, i n chronological order, estimates published i n t h e United S t a t e s o f t h e r a t e s o f ETP (see column 2).

Corresponding estimates o f t h e o t h e r i n t e n s i v e f a c t o r s o f

economic growth a r e given i n columns 3 and 4. Columns 5-8 contain information concerning t h e contribution o f individual f a c t o r s and groups of f a c t o r s t o t h e r a t e o f US economic growth. Average annual r a t e s o f US economic growth i t s e l f are given i n column 9.

According t o Solow's estimate, t h e average annual r a t e o f ETP over the period 1929-1961 was 4%. The d i s t i n c t i v e f e a t u r e of t h i s estimate stems from an a p r i o r i assumption developed by Solow t h a t ETP was the only intensive f a c t o r o f economic growth. I n other words, it was assumed from the very beginning t h a t Y = 0. I n addition, the index of t o t a l unweighted man-hours was taken as a labor input. But under these conditions X= 4% seems t o be a

substantial underestimate (see Jorgenson 1966, p.1). A more r e a l i s t i c result, though f o r a s l i g h t l y d i f f e r e n t i n t e r v a l o f observation, was obtained by Jorgenson: h i s estimate i s X = 10.1%.

The estimates o f I n t r i l i g a t o r , Thurow, and Srakolczai and Stahl a r e f r e e o f the a r t i f i c i a l assumption made by Solow.

Perhaps f o r t h i s reason, the r e s u l t s obtained by these economists are t o a great extent comparable t o one another. The r a t e o f ETP i s estimated as between 4% and 5%, and t h e r a t e o f disembodied technical progress plays a substantial r o l e i n a l l t h r e e cases, varying from 1.2% t o 1.7%. The extremely low r e l i a b i l i t y of these estimates i s t h e i r most important shortcoming, and t h i s i s

conceded by a l l the authors. The f a c t i s t h a t t h e model described by eqn. (3) f i t s t h e i n i t i a l s t a t i s t i c a l data almost equally well f o r a wide range of combinations of X and y. Therefore the choice o f an optimal combination of these parameters can be a r a t h e r a r b i t r a r y process. The work of Berglas proceeded along very similar lines. Although Berglas' f i n a l estimates are i n sharp c o n t r a s t with the r e s u l t s obtained by I n t r i l i g a t o r and the others, the r e l i a b i l i t y o f h i s estimates i s s t i l l very low.

I n the face of these d i f f i c u l t i e s US economists have

attempted t o improve t h e s t a t i s t i c a l methods of estimating t h e parameters o f production function (3). We w i l l n o t go i n t o the d e t a i l s o f the new methods b u t w i l l r e s t r i c t ourselves t o t h e following observation. Although Wicken's estimate of t h e r a t e o+

ETP i s d e f i n i t e l y nonzero ( i n fact, 2.21, he nevertheless writes:

"we can find no evidence t o support the embodiment hypothesis"

(Wickens 1970, p. 192). The r e s u l t s obtained by You a r e o f a more d e f i n i t e character. His estimate f o r the r a t e o f ETP i s zero.

Commenting on t h i s conclusion he writes: "However our f a i l u r e t o detect the embodiment e+fect leads us t o believe t h a t t h e

embodiment question may, a f t e r all, be unimportant." (You 1976, p. 127).

Thus, on t h e one hand, the postwar period appears t o have been one o f rapid technical progress, which has been r e f l e c t e d f i r s t o f a l l i n a radical renewal o f fixed c a p i t a l stock. The

quality o f capital goods has been improved rapidly as a r e s u l t of the embodiment o f the l a t e s t technological achievements: and t h i s conclusiort i s beyond a l l question. On the other hand, various econometricians, a f t e r more than twenty years o f intensive e f + o r t s t o obtain a q u a n t i t a t i v e estimate o f the r a t e o f ETP, have come t o the conclusion t h a t t h i s r a t e i s evidently equal t o zero. So we face a paradox which has certainly not been clearly resolved i n the economic l i t e r a t u r e . Meanwhile it i s r e l a t i v e l y easy t o observe t h a t t h e very methodology t h a t underlies the approach under consideration i s inherently contradictory. The authors o f the estimates discussed above implemented the ETP hypothesis i n a way t h a t assumed t h a t the c a p i t a l goods

ThBLE 1 Estimates of the rate of technical progress and its contribution to the rate of growth in the private business sector of the

US

economy. Source Period Rate of Rate of Rate of Contributions to 6NP growth rateb (percentage points) Rate of erbodied growth of diserb.

--

potential technical labor technical Erbodied technical Quality of

intensive

Extensive 6NPb growth progress qua1 i ty progress progress labor factors factors (7)+(8) (1) (1) (1) (4)+(5)+(6) Solow (1962) Intriligator (1965) Bergla5 (1965) Jorgenson (1966) Thurow (1960) Szakolczai and Stahl Yickens (1970) You (1976) 'Rpproxirate estirates by the author. bHypothetical 6NP under the as~urption that the unerployrent rate is 41,

c o n t r i b u t i n g t o t h e product a r e o f approximately i n v a r i a b l e

q u a l i t y and can be adequately measured by gross c a p i t a l formation i n constant prices. B u t t h e s e same goods, forming a component o f c a p i t a l stock, were characterized by progressively higher l e v e l s o f quality, and were t h e r e f o r e measured i n terms o f an aggregate o f use values.

The most r e c e n t estimates by US economists shown i n Table 1 avoid t h i s contradiction. They i n d i c a t e t h a t t h e model o f eqn.

(3) i s n o t s e l f - c o n t r a d i c t o r y only i n t h e case o f = 0. This

means t h a t even though ETP ( i n t h e sense formulated above) i s one o f t h e most important f a c t o r s o f r e a l economic growth, considered a s t h e growth o f aggregate u t i l i t y , it hardly has any e f f e c t on e x i s t i n g indexes o f o u t p u t such as GNP o r n a t i o n a l income ( f o r d e t a i l s see Poduzov 1980, pp. 146-158). Thus, u n t i l o u t p u t

indexes a r e l i m i t e d t o q u a n t i t a t i v e aspects o f r e a l economic growth, any a t t e m p t s t o estimate t h e growth r a t e o f t h e q u a l i t y o f fixed c a p i t a l stock by t h e simple use o f production functions would seem t o be fruitless.'

3. USE O F f7LTERNATIVE PRICE INDEXES

f7s pointed o u t e a r l i e r , c e r t a i n important shortcomings i n o f f i c i a l l y published p r i c e indexes lead t o a s i g n i f i c a n t

underestimation o f improvements i n t h e q u a l i t y o f c a p i t a l goods i n t h e gross c a p i t a l stock index. The basic method used by

economists attempting t o c o n s t r u c t a l t e r n a t i v e p r i c e indexes f r e e o f these shortcomings has been known since t h e end o f t h e

t h i r t i e s (Court 1939). However, i t s widespread adoption f o r

economic r e s e a r c h purposes began only i n t h e sixties, mainly due t o t h e work o f Zvi Griliches and h i s followers. The immediate problem t o be solved with t h e help o f t h i s method c o n s i s t s i n calculating a h y p o t h e t i c a l p r i c e movement f o r commodities (including producers' durable goods) t h a t r e f l e c t s only improvements i n t h e q u a l i t y o f t h e commodities. The p r i c e increase caused by i n f l a t i o n and o t h e r f a c t o r s n o t associated with improved q u a l i t y o f goods and s e r v i c e s i s calculated a s t h e difference between t h e a c t u a l and h y p o t h e t i c a l prices.

Since i n any given year t h e g r e a t m a j o r i t y o f commodities appear on t h e market i n a wide v a r i e t y o f versions t h a t d i f f e r from each o t h e r b o t h i n q u a l i t y and i n price, it i s possible t o examine t h e n a t u r e o f t h e interdependence between p r i c e and q u a l i t y c h a r a c t e r i s t i c s f o r a given t y p e o f equipment without introducing f u r t h e r complications by stepping outside t h e base year. f7ssuming t h a t t h e p r i c e d i f f e r e n c e between v a r i o u s

versions o f a given t y p e o f equipment i n t h e base y e a r i s caused by t h e d i f f e r e n c e i n q u a l i t y o f t h e d i f f e r e n t versions a s well a s b y p e c u l i a r i t i e s i n t h e marketing s t r a t e g y o f t h e f i r m s involved, economists w r i t e down t h e r e l a t i o n s h i p i n t h e form o f a

regression equation. S t a t i s t i c a l l y estimated parameters o f t h i s equation show t o what e x t e n t a given improvement i n t h e equipment

"Note t h a t t h i s comment applies s t r i c t l y t o consideration o f t h e e n t i r e n a t i o n a l economy. I f t h e approach i s applied t o individual s e c t o r s o r i n d u s t r i e s t h e inherent c o n t r a d i c t i o n disappears and t h e approach may well y i e l d worthwhile r e s u l t s . This p o i n t was brought t o my a t t e n t i o n by Joe Peck.

influences i t s price. Having q u a n t i t a t i v e estimates o f such

parameters f o r t h e base year, one can then use them as a system o f fixed weights f o r subsequent years.

The importance o f these parameters l i e s i n t h e f a c t t h a t they allow the calculation o f t h e hypothetical prices o f c a p i t a l goods with a specified l e v e l o f u s e f u l properties t h a t was absent i n the base year b u t was achieved i n subsequent years. The price change caused by a given change i n t h e technical l e v e l o f c a p i t a l goods can then be calculated i n t h i s way f o r any subsequent year.

To obtain the p r i c e index f o r use as a t o o l f o r deflating t h e c u r r e n t value o f producers' durable equipment, the price increase associated with q u a l i t y improvement i s subtracted from the actual price increase o f the equipment f o r each year. The difference thus calculated increases over time because o f i n f l a t i o n and

other f a c t o r s t h a t have nothing t o do with the increasing q u a l i t y o f fixed c a p i t a l stock.

Table 2 presents average annual percentage r a t e s o f change i n r e a l investment i n producers' durable equipment calculated using both o f f i c i a l and a l t e r n a t i v e price indexes and published by Gordon i n 1980. From these estimates one can see t h a t the

magnitude o f t h e difference between the growth r a t e s given by the o f f i c i a l and t h e a l t e r n a t i v e series i s o f the same order as t h e r a t e o f growth o f t h e o f f i c i a l s e r i e s i t s e l f . Gordon believes t h a t t h i s great discrepancy i s due t o a large bias inherent i n the o f f i c i a l wholesale p r i c e indexes. Besides "pure" price

increases, these indexes also take i n t o account t h e major p a r t o f the price increase associated with constructive improvements i n equipment

--

c u t t i n g operational costs, increasing efficiency, r e l i a b i l i t y , and safety, and so on. But t h i s l a t t e r component o f p r i c e increase has essentially nothing t o do with p r i c e indexes:

rather, it indicates t h a t t h e q u a l i t y o f equipment i s improving and, as can be seen from Table 2, when t h i s measured q u a l i t y i s taken i n t o account i n t h e dynamics o f r e a l investment t h e

o f f i c i a l growth r a t e o f investment i n equipment almost doubles.

The o f f i c i a l index o f US c a p i t a l investment, including both producers' durable equipment and structures, grew a t an average annual r a t e o f 3.6% over t h e period 1947-1970. Even i f one makes t h e u n r e a l i s t i c assumption t h a t t h e technical l e v e l o f s t r u c t u r e s introduced during t h a t period did n o t change, t h i s f i g u r e m u s t be increased t o 5.8% t o take i n t o account j u s t t h e q u a l i t y

improvements i n producers' equipment. I n other words, accumulated c a p i t a l stock i n t h e United States grew over the period 1947-1970 a t an average annual r a t e o f no l e s s than 6%, when t h e measured q u a l i t y o f c a p i t a l goods i s taken i n t o account.

TABLE 2 Annual percentage r a t e s o f change o f r e a l investment i n producers' durable equipment:

p r i v a t e business s e c t o r o f the US economy, 1947-1970.

S e r i es 1947-57 1957-70 1947-70

O f f i c i a l N I A 2.9 4.6 3.9 New a l t e r n a t i v e 6.7 7.7 7.2 New

-

o f f i c i a l 3.8 3.1 3.3 SOURCE: Usher (1980, p.159).

When surveying t h e r e s u l t s obtained by Gordon and others we should n o t ignore t h e f a c t t h a t t h e method employed f o r

calculating t h e a l t e r n a t i v e price indexes i s i t s e l f n o t e n t i r e l y f r e e o f drawbacks. F i r s t o f all, t h e method i s purely empirical:

i t s users make no claim t h a t it i s adequately founded i n economics (Terleckyi 1975). Next, t h e method does n o t produce stable, reproducible results. It o f t e n happens t h a t f i n a l

estimates d i f f e r substantially from one investigation t o another.

Finally, by comparison with t h e methods generally used i n US government s t a t i s t i c a l agencies, t h e a l t e r n a t i v e method requires much more information about the prices o f d i f f e r e n t versions of commodities, and t h i s information i s highly expensive t o collect and process.

4. USE OF CAPITAL SERVICES

Gordon's estimates given i n Table 2 do not completely r e f l e c t t h e r i s i n g quality o f US producers' durable equipment. They take i n t o account only t h e measured p a r t pf t h e quality improvement, i.e. the quality change r e f l e c t e d i n t h e difference i n prices o f successive versions o f c a p i t a l goods. They do not, however, take i n t o account t h e so-called "unmeasured" quality change t h a t

occurs over and above t h e simple price difference. The US economists Jorgenson, Christensen, and o t h e r s believe t h a t a r e l a t i v e l y complete r e f l e c t i o n o f t h e quality changes (both measured and unmeasured) o f c a p i t a l goods can be achieved i f these goods are widely rented and i f the corresponding r e n t a l payments are incorporated i n t o the measurement system. I n other words, they propose t o construct a new index o f t h e amount o f current productive services provided by a l l accumulated c a p i t a l goods.

This approach has both supporters and opponents among economists. The well-known US economist Edward Denison i s one o f i t s most consistent opponents. His position (SCB 1982, pp. 96, 97) i s as follows. Weighting the c a p i t a l goods according t o t h e i r r e l a t i v e r e n t a l values would mean t h a t unmeasured quality

differences between the goods would be taken i n t o account. But the very term "unmeasured" means t h a t such an approach cannot be implemented. The major d i f f i c u l t y i s that, although leasing has become an established practice i n t h e United States, especially during t h e postwar period, rented capital as a f r a c t i o n o f t o t a l c a p i t a l stock i s s t i l l insignificant. Even i f appropriate

s t a t i s t i c a l data were collected, i t s amount would s t i l l be i n s u f f i c i e n t t o undertake t h e necessary calculations.

Denison believes, then, t h a t an aggregate index of c a p i t a l goods weighted i n proportion t o r e n t a l values should n o t be calculated a t all, even i f a l l the necessary data were available.

Such a weighting system would cause the index of c a p i t a l t o r i s e more over time than the present procedure, and would represent any gains achieved by t h e improved design o f capital goods not as advances i n knowledge b u t simply as capital. This would n u l l i f y t h e concept of a r i s e i n the efficiency of c a p i t a l and would make it impossible t o analyze advances i n knowledge as a separate cause of growth (SCB 1982, p. 97).

I n contrast, Dale Jorgenson and others who are opposed t o the ideas o f Denison believe t h a t the calculation o f an aggregate

index of c a p i t a l services would substantially expand the

p o t e n t i a l i t i e s of economic analysis. These economists regard t h e

quality changes t h a t Denison describes as "unmeasurable" n o t only as measurable but as changes t h a t p o s i t i v e l y need t o be measured f o r a b e t t e r understanding o f the phenomenon (SCB 1982, p. 111).

According t o Jorgenson, the present practice o f using the

o f f i c i a l l y published gross stock o f fixed c a p i t a l as an aggregate index o f c a p i t a l goods introduces u n j u s t i f i a b l e asymmetry i n t o the treatment o f c a p i t a l and labor as f a c t o r s o f production. I n h i s opinion, an index o f c a p i t a l input should be constructed i n the same way as an index o f labor input. J u s t as a

quality-adjusted index o f labor input i s constructed from the quantities o f each labor service, using as weights t h e r e l a t i v e shares o f the income o f each labor service i n the t o t a l income o f a l l labor services, t h e quality-adjusted index o f c a p i t a l input should be constructed from the quantities o f each type o f c a p i t a l service, using as weights t h e r e l a t i v e shares o f t h e r e n t a l value o f each c a p i t a l service i n the t o t a l r e n t a l value o f a l l c a p i t a l services

(SCB

1982, p. 84).

The major obstacle faced by Jorgenson and o t h e r s when constructing quality-adjusted indexes o f c a p i t a l input was t h e lack o f s t a t i s t i c a l data on r e n t a l values f o r leased c a p i t a l goods. As already mentioned, leasing f o r production purposes i s n o t a widespread practice i n t h e United States (Hamel 1968). The major p a r t o f a l l c a p i t a l goods a r e owned by t h e i r users: as f a r as these goods a r e concerned, r e n t a l values a r e c l e a r l y

meaningless. The only possible way o u t o f t h i s s i t u a t i o n i s t o calculate t h e implicit r e n t a l value o f each type o f c a p i t a l service, i.e. t h e value t h a t would be received by t h e owners o f the c a p i t a l stock i f i t were r e g u l a r l y rented. This was t h e procedure followed by Jorgenson (Jorgenson and Griliches 1967, Christensen and Jorgenson 1969).

The most recent o f Jorgenson's estimates covers the US p r i v a t e domestic economy f o r t h e period 1948-1976. T o t a l c a p i t a l stock i s separated i n t o 46 i n d u s t r i a l sectors. Within each s e c t o r c a p i t a l stock i s disaggregated by f o u r legal forms o f

organization

--

corporate business, noncorporate business, p r i v a t e households, and nonprofit i n s t i t u t i o n s

--

and by six types o f asset

--

producers' durable equipment, consumers' durables, tenant-occupied r e s i d e n t i a l and nonresidential

structures, owner-occupied r e s i d e n t i a l structures, inventories, and land. The r e s u l t i n g estimates are shown i n Table 3.

The aggregate index o f the productive services o f accumulated c a p i t a l goods i s presented i n column 2. I n c o n t r a s t t o t h e

t r a d i t i o n a l index, which assesses items o f c a p i t a l stock i n r e l a t i v e prices (see column 11, t h i s index i s based on t h e

assessment o f c a p i t a l goods according t o t h e i r implicit r e n t a l values- This "capital services" index increases annually by half as much again as t h e t r a d i t i o n a l index and t h a t i s t h e main

r e s u l t o f Jorgenson's calculations. The f a c t t h a t t h e growth r a t e o f the c a p i t a l services index i s much higher than t h a t o f the physical volume o f c a p i t a l goods can only be due t o t h a t p a r t o f t h e t o t a l quality change which i s unmeasured i n t h e physical volume index b u t which appears t o be measured i n the c a p i t a l services index. This i s i n f a c t the i n t e r p r e t a t i o n given by Jorgenson (see column 3 o f Table 3).

It must be emphasized t h a t the growth r a t e s o f "unmeasured"

q u a l i t y change o f c a p i t a l goods presented i n Table 3 do n o t merely duplicate Gordon's estimates o f measured quality change.

Rather, Jorgenson's and Gordon's estimates complement one

TABLE 3 Average annual percentage r a t e s o f change o f r e a l c a p i t a l stock and r e a l capital services i n the United States, 1948-1976.

P e r i o d C a p i t a l C a p i t a l "Unmeasured"

s t o c k s e r v i c e s c a p i t a l qua1 i t y

( 1 ( 2 ( 3 )

Source: Furstenberg (1980).

another. Jorgenson proceeded from the assumption t h a t t h e amount o f productive services obtained from a c e r t a i n type o f capital goods i s s t r i c t l y proportional t o t h e accumulated physical stock o f these goods. This means t h a t h i s index o f productive services f o r any more o r l e s s narrow type o f asset taken as homogenous does n o t r e f l e c t any q u a l i t y changes other than those already r e f l e c t e d i n the o f f i c i a l index. Thus, the growth r a t e s o f

capital quality presented i n Table 3 r e f l e c t only s h i f t s i n t h e composition o f capital stock. They show t h a t over t h e postwar period a noticeable s h i f t took place i n t h e composition o f US c a p i t a l stock i n f a v o r o+ those types o f assets f o r which

implicit r e n t a l values per dollar o f (comparable base-year) price are r e l a t i v e l y higher. I n particular, t h e s h i f t i n t h e

technological s t r u c t u r e o f capital stock i n favor o f producers' durable equipment was apparently o f considerable importance. '

The shortcomings inherent i n Jorgenson's estimates a r e t h e following. First, i n s p i t e o f t h e f a c t t h a t calculations a r e based on a r a t h e r detailed decomposition o f c a p i t a l stock by industries and by legal forms o f organization, t h e o v e r a l l degree o f disaggregation does n o t appear t o be very high. I f t h e

nonproductive sphere i s excluded from the analysis, then within each o f t h e remaining industries Jorgenson d i f f e r e n t i a t e s between only f o u r types o f assets

--

producers' durable equipment,

nonresidential structures, inventories, and land

--

each o f which i s i t s e l f considered homogenous. Further decomposition within the types o f assets would probably give s t i l l higher estimates f o r t h e "unmeasured" q u a l i t y o f capital stock.

Second, Jorgenson's procedure o f weighting the elements o f capital stock by r e n t a l values i s based on neoclassical

investment theory, which proceeds from a number o f highly a r t i f i c i a l assumptions. I n p a r t i c u l a r it i s assumed t h a t the competition among firms i s perfect, t h a t a l l markets are i n a s t a t e o f equilibrium, t h a t firms are able t o foresee the expected demand f o r and p r i c e of t h e i r output with accuracy, and so on.

This theory does n o t give any helpful answer t o the question o f whether the weighting procedure takes "unmeasured" quality change i n t o account f u l l y o r only partially. Re-Ferences t o the necessity

o f calculating t h e index f o r c a p i t a l i n p u t i n t h e same way a s t h a t f o r labor, which i s based on t h e assessment and measurement o f each t y p e o f labor according t o i t s wages and salaries, a r e n o t f u l l y convincing because i n t h e case o f l a b o r i n p u t t h e idea i s t o t a k e account o f measured q u a l i t y change, i.e. q u a l i t y

r e f l e c t e d i n t h e p r i c e of a s p e c i f i c commodity

--

^labor.

Third, Jorgenson's estimates cannot be o f v e r y high r e l i a b i l i t y . Even i f t h e procedure o f weighting each t y p e o f c a p i t a l according t o i t s r e n t a l value allows us t o t a k e f u l l account o f "unmeasured" q u a l i t y change (which i s doubtful), t h e estimates presented i n Table 3 a r e f a r from perfect. One o f t h e main reasons f o r t h i s i s t h e following. Because leasing i s n o t a widespread p r a c t i c e i n t h e United S t a t e s and t h e r e i s a lack o f d i r e c t s t a t i s t i c a l d a t a on a c t u a l r e n t a l payments, t h e estimates were obtained by indirect, roundabout methods r e q u i r i n g sizeable preliminary c a l c u l a t i o n s o f i m p l i c i t r e n t a l values f o r each t y p e o f asset.

S t r i c t l y speaking, Gordon's and Jorgenson's estimates a r e n o t comparable because o f t h e d i f f e r e n c e i n t h e i r scope. Gordon

l i m i t e d himself t o producers' durable equipment, which i s only a p a r t

--

although c e r t a i n l y t h e most important p a r t

--

o f US c a p i t a l stock. A s f o r Jorgenson, he a c t u a l l y studied t h e dynamics o f t o t a l n a t i o n a l wealth, whose composition i s s u b s t a n t i a l l y

wider than t h a t o f c a p i t a l stock alone. Under these conditions, any judgments about t h e magnitude o f t h e postwar r i s e i n t h e technical l e v e l o f US c a p i t a l stock m u s t i n e v i t a b l y be

approximate. A s pointed o u t e a r l i e r , Gordon's estimates suggest t h a t US c a p i t a l stock, a f t e r measured q u a l i t y improvements i n c a p i t a l goods a r e taken i n t o account, grew o v e r t h e period 1947-1970 a t an average annual r a t e o f no l e s s t h a n 6% (it was assumed t h a t t h e q u a l i t y o f nonresidential s t r u c t u r e s did n o t improve over t h i s period). Assuming f u r t h e r t h a t Jorgenson's estimates f o r t h e "unmeasured" q u a l i t y change i n t o t a l n a t i o n a l wealth remain v a l i d when applied t o c a p i t a l stock alone, one

concludes t h a t o v e r approximately t h e same period, 1948-1969, t h e average annual r a t e o f "unmeasured" q u a l i t y change o f c a p i t a l stock was about 1.4%. This means t h a t f o r an approximate b u t f a i r l y r e a l i s t i c estimate o f t h e lower l i m i t o f US c a p i t a l i n p u t growth r a t e one should add 1.4% t o 6%. The r e s u l t i n g 7.4% i s twice a s high as t h e 3.7% annual growth r a t e i n t h e o f f i c i a l l y published gross c a p i t a l s t o c k index over t h e period under

consideration. (The author's rough estimate o f t h e t o t a l q u a l i t y improvement i n US c a p i t a l stock over t h e period 1947-1973 i s 5%

p e r year, and f o r c a p i t a l i n p u t 8.5% p e r year: see Poduzov 1980, p. 156.)

5. CONCLUSIONS

Three main conclusions may now be drawn.

F i r s t , o f f i c i a l l y published indexes o f t h e physical volume o f c a p i t a l stock do n o t give a complete p i c t u r e o f t h e a c t u a l r i s e i n t h e p o t e n t i a l o f accumulated c a p i t a l goods t o c o n t r i b u t e t o t h e production o f f i n a l o u t p u t and n a t i o n a l economic growth.

Although t h e y adequately r e f l e c t t h e process of q u a n t i t a t i v e , extensive growth o f c a p i t a l stock, t h e y ignore f o r t h e most p a r t changes i n i t s quality, i.e. t h e growth i n i t s productive

capacity. These t r a d i t i o n a l indexes would have been f a i r l y

adequate i n d i c a t o r s o f c a p i t a l i n p u t during t h e e r a preceding t h e i n d u s t r i a l revolution, i.e. a t a time when c a p i t a l stock grew on t h e whole i n terms o f quantity, whilst q u a l i t y improvements, i f any, occurred r e l a t i v e l y slowly. However, t h e usefulness o f such indexes i s diminishing g r e a t l y nowadays as t h e q u a l i t y and

e f f i c i e n c y o f c a p i t a l goods become increasingly decisive factors.

Second, economists have developed two complementary approaches t o c o n s t r u c t i n g indexes o f c a p i t a l input. One i s

concerned with t h e improvement o f t h e o f f i c i a l indexes o f c a p i t a l stock by taking more account o f t h e so-called "measured" q u a l i t y change, i-e. t h a t change which t h e o r e t i c a l l y should be accounted f o r b u t nevertheless i s n o t r e f l e c t e d i n t h e indexes because o f important shortcomings inherent i n t h e p r i c e d e f l a t o r s used i n t h e calculations. The o t h e r approach i s concerned with t h e measurement o f t h e so-called "unmeasured" q u a l i t y change, i-e.

t h a t p a r t o f t h e t o t a l increase i n technical l e v e l o f c a p i t a l stock which i s n o t i n p r i n c i p l e r e f l e c t e d i n t h e r e l a t i v e p r i c e s o f c a p i t a l goods b u t which leads t o a r e d u c t i o n i n t h e p r i c e per u n i t o f productive capacity.

Third, approximate estimates o f t h e "measured" and

"unmeasured" components o f t o t a l q u a l i t y change i n US c a p i t a l stock obtained by US economists i n d i c a t e t h a t t h e r o l e o f t h e increasing technical q u a l i t y o f c a p i t a l goods

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associated with c o n s t r u c t i v e improvements i n equipment, c u t t i n g o f operational costs, increasing efficiency, r e l i a b i l i t y , safety, and so on

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i s comparable i n importance with t h a t o f t h e extensive growth o f c a p i t a l stock. One can see from t h e s e estimates t h a t , over t h e period 1947-1970, t h e average annual r a t e o f growth o f c a p i t a l taken a s an aggregate o f use values i s l i k e l y t o have been a t l e a s t twice as g r e a t a s t h e 3.7% annual growth r a t e i n t h e o f f i c i a l l y published index o f gross fixed c a p i t a l stock. Even an index t h a t took i n t o account only one aspect o f t h e t o t a l q u a l i t y change o f c a p i t a l goods, namely t h e growth i n t h e i r productive capability, would a l s o be expected t o have grown much f a s t e r than t h e o f f i c i a l index.

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