Measurement of the Rate of Technical Progress

NOT FOR QUOTATION WITHOUT THE PERMISSION OF THE AUTHORS

MEASUREMENT O F THE

RATE

OF TECHNICAL PROGRESS

OLeg Ezsmont H e r m a n n R o s s

December 1985 WP-85-95

Working P a p e r s are interim r e p o r t s o n work of t h e I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems Analysis a n d h a v e r e c e i v e d only limited review. Views o r opinions e x p r e s s e d h e r e i n d o n o t n e c e s s a r i l y r e p r e s e n t t h o s e of t h e I n s t i t u t e o r of i t s National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS ANALYSIS 2361 L a x e n b u r g , A u s t r i a

PREFACE

In t h e beginning of 1985 IIASA s t a r t e d j o l n t l y w i t h t h e U n i v e r s i t y of Bonn a s t u d y on t h e World Economic Model under t h e l e a d e r s h i p of P r o f . Wilhelm K r e l l e . The s t r u c t u r e of t h e model was developed by Prof.

K r e l l e and d i s c u s s e d a t t h e IIASA Conference on t h e Analysi's and Fore- c a s t i n g of Economic S t r u c t u r a l Change i n May 1984. S h c e t h e n a team of s c h o l a r s from both E a s t and West has Been c o l l e c t i n g t h e n e c e s s a r y d a t a and e s t i m a t i n g t h e p a r a m e t e r s of s ~ o d e l s t o Be l i n k e d , a t a l a t e r d a t e , w i t h i n t h e framework of t h e g l o b a l model. The f l r s t quantitative r e s u l t s of t h i s e f f o r t were d i s c u s s e d i n t h e Workshop on Economic Growth and S t r u c t u r a l Change, h e l d i n Lodz, Poland, December 9-10, 1985.

T h i s paper p r e s e n t s t h e r e s u l t s of t h e e s t i m a t i o n s of p r o d u c t i o n f u n c t i o n s f o r OECD c o u n t r i e s and was wri'tten i n s m e r 1 9 8 5 , d u r i n g t h e v i s i t of D r . 0. Eismont, USSR, t o t h e U n i v e r s i t y of Bonn.

Anatoli: %yshlyaev Acting Leader

"Economic S t r u c t u r a l Change"

MEASUREMENT Ow

THE

RATE OF TECHNICAL

PKOGRESS

Oleg E i s m o n t * a n d H e r m a n n Ross**

*

Institute f o r Systems Studies of t h e USSR Academy of Sciences

(VNIISI), Moscow.

**

Institut f u r Gesellschafts- und Wirtschaftswissenschaften

d e r Universitat Bonn, Bonn-IIASA Research P r o j e c t o n Economic Growth and S t r u c t u r a l Change.

In t h e joint Bonn-IIASA R e s e a r c h P r o j e c t on Economic Growth and S t r u c t u r a l Change t h e r a t e of technical p r o g r e s s in e a c h country i s t a k e n a n exogenous t o t h e c e n t r a l model (Krelle, 1985) and should b e explained within t h e framework of t h e country models. The f i r s t problem comprises measuring t h e rate of technical pro- g r e s s of e a c h country in t h e r e f e r e n c e period. T h e r e is a n extensive l i t e r a t u r e o n t h e identification and measurement of technical p r o g r e s s (see, f o r example, Abramovitz, 1956; Brown, 1966; Fabricant, 1954; Kendrick, 1956; Kennedy and Thirlwall, 1972, Schmookler, 1952; Solow, 1957; Tinbergen, 1942; Valavanis-Veil, 1955). The a p p r o a c h e s d i f f e r considerably. This is largely due t o d i f f e r e n t con- c e p t s associated with t h e notion of technical p r o g r e s s . Thus, p r i o r t o t h e m e a - surement of t h e rate of technical p r o g r e s s w e must define what w e mean by t h i s no- tion.'

Let ^T b e a l a t e n t v a r i a b l e t h a t d e s c r i b e s t h e amount of productive knowledge embodied in l a b o r and used o n t h e a v e r a g e . This knowledge can only change slowly and continuously (we d o not consider c a t a s t r o p h e s of any kind). Thus 7 ( t ) should b e a continuous function of time. The r a t e of technical p r o g r e s s i s

he

f o l l o w i n g i d e a s a r e b a s e d on s o m e unpublished n o t e s o f P r o f e s s o r W. K r e l l e .

and i s also a continuous function of time.' For simplicity, w e assume a l i n e a r func- tion

Of c o u r s e , t h i s t y p e of function c a n only b e used f o r a limited time span.

By definition, T should b e linked with l a b o r , i.e., w e assume a Harrod-neutral technical p r o g r e s s . F o r simplicity w e consider only two f a c t o r s of production, la- b o r and capital. W e use t h e g r o s s domestic product Y (minus i n d i r e c t t a x e s plus subsidies) at constant p r i c e s a s a measure of production. W e assume t h e e x i s t e n c e of a neoclassical production function of t h e form

where L i s l a b o r (measured in man h o u r s ) and

K

i s c a p i t a l (measured in machine hours).

Assuming p e r f e c t competition and c o s t minimization, w e obtain

Y

i

^K

-

=

a - + ( 1 - a ) ~ a w , + ,

Y L

where a i s l a b o r income a s a p r o p o r t i o n of t o t a l income and ( 1

-

a ) i s c a p i t a l in- come a s a p r o p o r t i o n of total income. Total income is defined as t h e G D P minus in- d i r e c t t a x e s plus subsidies a t c u r r e n t p r i c e s .

Unfortunately, existing s t a t i s t i c s provide d a t a only f o r t o t a l capital,

KS

, and f o r t h e employed l a b o r f o r c e ,

L S ,

and d o not account f o r t h e i r utilization r a t i o s . So, l a b o r ,

L ,

in t h e production function, being t h e amount of productive s e r v i c e s r e n d e r e d by t h e employed l a b o r f o r c e , is a l a t e n t v a r i a b l e . The s a m e applies t o capital,

K ,

which is a l s o a l a t e n t variable. If w e introduce l a b o r and c a p i t a l utili- zation r a t i o s dL and bK, r e s p e c t i v e l y , w e obtain from equation (3)

W e defined w , a s t h e r a t e of change of productive knowledge t h a t i s actually used on t h e a v e r a g e ( o r t h a t i s normally used in society), not of productive knowledge t h a t i s o f f e r e d a t exceptional times. In this c a s e w e c a n assume t h a t w dL and w ^bK ' ~ e n e r a l l ~ , in t h i s paper w,: = 2/z defines the growth rate of the variable ^{1 .}

have z e r o means

Next w e t u r n t o t h e problem of estimating t h e l a b o r s h a r e a. Labor in t h e production function means t h e t o t a l l a b o r , i.e., t h e l a b o r of employed and self- employed persons. The s t a t i s t i c a l d a t a f o r t h e compensation of employees d o not include l a b o r income of t h e self-employed, but w e have t o use l a b o r income s h a r e s t h a t include t h i s . W e estimate i t by assuming t h a t t h e a v e r a g e l a b o r incomes of wage e a r n e r s and of t h e self-employed are t h e same. The number of self-employed can b e calculated from t h e available s t a t i s t i c s , see OECD Labor Force S t a t i s t i c s (various y e a r s ) . With t h e s e c o r r e c t i o n s w e obtain t h e values of a given in t h e second column of Table 1.

Table 1. Average s h a r e of l a b o r income, 1960-1982.~

Country Not including Including

self -employed self -employed U S

FRG Japan France UK Italy

The Netherlands Belgium-Luxembourg Canada

Source: OECD Labour Force S t a t i s t i c s ( v a r i o u s y e a r s ) ; OECD M a i n Economic Indi- c a t o r s ( v a r i o u s y e a r s ) ; OECD N a t i o n a l A c c o u n t s ( v a r i o u s y e a r s ) .

a Own c a l c u l a t i o n s ; t h e v a l u e s i n p a r e n t h e s e s a r e t h e standard d e v i a t i o n s .

It is worth noting t h a t after c o r r e c t i o n s t h e l a b o r s h a r e s are similar f o r all OECD countries.

W e now define t h e notional area of technical p r o g r e s s ,

G T n t ,

in y e a r t by:

This national rate includes t h e e f f e c t s of changing t h e d e g r e e s of utilization of la- b o r and capital and is not what w e want t o measure. But considering equation (5) w e see from equation (4) t h a t t h e rate of technical p r o g r e s s , w , , i s determined by t h e t r e n d of $ ^{7 , t .} Thus, w , i s determined by

Following equation ( I ) , w e assume a l i n e a r t r e n d . Because of equation (7), t h e un- known p a r a m e t e r s a . and a l in equation (1) are estimated by o r d i n a r y l e a s t s q u a r e s , t h e r e g r e s s i o n being:

where E i s a s t o c h a s t i c v a r i a b l e with z e r o mean.

The r e s u l t s of t h e estimations f o r OECD c o u n t r i e s are p r e s e n t e d in Table 2 and plotted in Figure 1 (see Appendix). The high s t a n d a r d e r r o r s and t h e sometimes small R$,,, should not i r r i t a t e t h e r e a d e r since w e have estimated t h e growth rates and a r e i n t e r e s t e d in explaining t h e t r e n d and not t h e business cycle.

Table 2 Trend function f o r technical p r o g r e s s :

6, =

a .

+

a l t

Country

DW

_SEE R c o r r ²

us

FRG J a p a n F r a n c e U K Italy

The Netherlands Belgium-Luxembourg Canada

DW, Durbin-Watson s t a t i s t i c s ; SEE, standard e r r o r o f e s t i m a t i o n s ; v a l u e s i n parentheses a r e t - s t a t i s t i c s ; t h e e s t i m a t i o n period w a s 1961-1982;

t

i s a t i m e t r e n d w i t h t l g 6 0

=

0

.

The r e s u l t s are quite remarkable: all rates of technical p r o g r e s s have de- clined during t h e l a s t 20 y e a r s , in t h r e e ways. The f i r s t consists of t h e c o u n t r i e s Japan, Italy, and The Netherlands, who s t a r t e d with v e r y high r a t e s , but t h e s e de- clined more t h a n those of t h e o t h e r countries. The second g r o u p comprises F r a n c e , Belgium, and t h e F e d e r a l Republic of Germany. with smaller, but l e s s de- clining r a t e s . The t h i r d g r o u p consists of t h e U S , Canada, and t h e U K with small r a t e s of technical p r o g r e s s t h a t d o not decline s o much (with t h e exception of Ca- nada).

To t e s t t h e plausibility of t h e s e r e s u l t s w e compared them with t h e r a t e of technical p r o g r e s s t h a t would b e o b s e r v e d if t h e economy moved according t o t h e long-term equilibrium growth path. Because of t h e l i n e a r homogeneity of F in equation (2) w e may write equation (1) a s

where k

=

- K is t h e capital-labor r a t i o , with l a b o r measured in efficiency units;

TL

k is constant on t h e equilibrium growth path. Thus, if t h e economy stayed on t h e equilibrium growth p a t h , we obtain from equation (8):

Of c o u r s e , t h e economy does not follow t h e equilibrium path exactly, but may fluc- t u a t e around it. In t h a t c a s e t h e function w ,

=

a.

+

a l t should follow t h e t r e n d of t h e growth r a t e w y I L of l a b o r productivity.

In Figures 2-10 (see t h e Appendix) t h e growth r a t e s of l a b o r productivity and t h e estimated r a t e s of technical p r o g r e s s a r e plotted f o r OECD countries (data a r e given in Table 3). The f i t i s quite satisfactory. In some c a s e s t h e t r e n d of growth r a t e s f o r l a b o r productivity is somewhat higher t h a n t h e corresponding r a t e s of technical p r o g r e s s as estimated using equation (7). This is easily explained since t h e equilibrium growth p a t h s a r e not constant in time. In t h a t c a s e i t follows from equation (8) t h a t

If k i s a n increasing function with time, we obtain w y I L

>

w , . These r e s u l t s can also b e i n t e r p r e t e d in t h e s e n s e t h a t t h e assumptions of a Harrod-neutral technical p r o g r e s s and of a growth t r e n d t h a t coincides with t h e equilibrium path a r e not far from reality.

Table 3. Growth rates of labor productivity, ~ ' ~ a b . ~

W f Y L O 1 , Growth rate of YfLABO1 W'YLO4, Growth rate of Y'LAB04 W'YLO7, Growth rate of YfLAB07 W'YLOZ, Growth rate of YfLAB02 WfYL05, Growth rate of Y'LAB05 WfYL08, Growth rate of YfLAB08 W'YL03, Growth rate of Y'LAB03 WfYL06, Growth rate of YfLAB06 WfYL09, Growth rate of YfLAB09 P e r i o d W f Y L O 1 W'YLOZ WfYL03 W'YL04 W'YL05 WfYL06 WfYL07 WfYL08 WfYL09

1960 1.360 7.884 9.119 5.665 3.930 7.068 6.996 5.759 1.930

1961 2.615 5.237 13.939 5.198 3.704 13.065 6.774 4.906 1.975

1962 3.760 5.725 7.310 5.573 0.862 7.169 2.101 4.517 2.202

1963 2.156 5.085 10.290 3.934 2.704 7.025 2.138 3.097 2.969

1964 3.194 5.610 12.231 4.800 4.244 5.022 7.354 6.220 2.647

1965 3.148 5.909 5.093 4.929 2.956 6.470 4.556 3.419 2.318

1966 3.740 4.146 8.122 3.764 3.110 5.150 2.101 -0.949 3.489

1967 2.313 5.470 8.675 5.530 4.090 5.451 7.563 6.369 1.906

1968 2.465 6.187 11.153 4.723 4.127 6.431 5.529 6.934 2.966

1969 0.481 6.916 12.929 5.162 1.000 11.311 4.846 5.602 1.778

1970 0.330 4.981 10.658 6.052 3.923 5.040 7.661 6.910 4.576

1971 2.719 4.249 5.028 5.975 5.145 5.490 4.665 2.229 4.749

1972 1.554 5.511 9.475 5.351 1.464 7.242 5.282 8.062 1.095

1973 2.176 5.480 7.059 4.329 3.971 9.881 6.357 0.027 3.000

1974 -1.569 3.956 3.062, 4.052 0.097 4.718 6.007 5.686 0.104

1975 1.515 3.284 4.686 4.288 1.862 0.087 2.195 4.299 0.997

1976 1.452 4.258 2.784 4.840 3.586 1.703 4.463 3.267 3.700

1977 1.789 5.129 3.853 3.588 0.020 -0.746 1.650 2.819 1.263

1978 0.848 3.403 3.238 4.394 2.883 2.057 1.728 ^' 2.909 -0.059

1979 -0.247 . 3.875 3.262 3.564 0.682 3.029 1.140 0.776 -1.199

1980 0.421 1.712 1.604 1.194 0.151 5.273 -1.153 9.307 0.077

1981 2.172 1.700 3.181 1.417 3.141 -1.084 -0.400 -0.265 1.101

a 01, U S ; 02, FRC; 03, Japan; 04, France; 05, UK; 06, Italy; 07, The Netherlands; 08, Belgium-Luxembourg; 09, Canada.

REFERENCES

Abramovitz, M. (1956), Resource and output in t h e United S t a t e s s i n c e 1870, Ameri- c a n Economic R e v i e w , P a p e r s a n d Proceedings, 46, 5-23.

Brown, M. (1966), Dn t h e Theory a n d Measurement of Technological Change (Cam- bridge University P r e s s , Cambridge).

Fabricant, S. (1954), Economic Progress a n d Economic Change, 34th Annual Re- p o r t of t h e National Bureau of Economic R e s e a r c h (NBER, N e w York).

Kendrick, J.W. (1956), Productivity t r e n d s : capital and labour, Review of Econom- i c s a n d S t a t i s t i c s , 38, 248-257.

Kennedy, Ch. and Thirlwall, A.P. (1972), Surveys in applied economics: technical p r o g r e s s , The Economic J o u r n a l , 82, 11-72.

Krelle, W. (1985), The World Model in Detail, 2nd version, mimeo (Bonn University, Bonn).

OECD (various y e a r s ) , Labour Force S t a t i s t i c s (OECD, Paris).

OECD (various y e a r s ) , Main Economic I n d i c a t o r s : Historical S t a t i s t i c s (OECD, P a r i s ) .

OECD (various y e a r s ) National Accounts: Main Aggregates (OECD, P a r i s ) .

Schmookler, J. (1952), The changing efficiency of t h e American Economy 1869-1938, Review o f E c o n o m i c s a n d S t a t i s t i c s , 3 4 , 214-231.

Solow, R.M. (1957), Technical change and t h e a g g r e g a t e production function, Re- v i e w o f E c o n o m i c s a n d S t a t i s t i c s , 39, 312-320.

Tinbergen, J. (1942), Zur Theorie d e r langfristigen Wirtschaftsentwicklung ,' Weltwirtschagtliches A r c h i v , 511-549.

Valavanis-Veil, S. (1955), An econometric model of growth, USA 1869-1953, Ameri- c a n Economic Review, P a p e r s a n d Pl'oceedings, 45.208-221.

APPENDIX

The Appendix comprises Figures 1-10 on t h e following pages.

W 'TRUO 1 GROWTH RRTE OF TECHN. PROGRESS

---

W ' T A U 0 5 GROWTH R R T E OF TECHN. PROGRESS

--- ---

0 W ' T A U 0 9 GROWTH R A T E OF TECHN. PROGRESS

l-

-

m - - - *

--

Third group

0

f-

.- -

I-

z -

W

uo

E m

' - -

^Canada

w -~

eq60

^{1 1}

^{1 6 [ 1}

^{1 I}

1 6 b

^{I I 1 7 $ I l 7 L I}

' ~ b '

W ' T R U 0 2 GROUTH R R T E OF T E C H N . PROGRESS

---

H ' T R U O U GROWTH R R T E OF 7 E C H N . PROGRESS

---

_W ' T R U 0 8 GROWTH R A T E OF TECHN. PROGRESS

Secondgroup

0

1

Belgium-Luxembourg

+ -

zo

t ? ' ~

I l 6 L 1 I

1 6 b 1

" 7 1 ' I

7 6 I I I I 1

B 0 YEAR

U ' T R U 0 3 GROWTH R R T E OF TECHN. PROGRESS

---

H ' T R U O S ^, GROWTH R R T E OF TECHN. PROGRESS

- - -

W ' T A U 0 7 GROWTH R A T E OF TECHN. PROGRESS

-

First group

+ -

The Netherlands

t ? ' ~

zo

E a 6 0 1 ¹ l 6 L 1 I I 6 B 1 I I 7 b 1 I I 7 b 1 I I B ~ '

n

^{'I E fiR}

Figure 1. The results of estimated progress, clustered in three groups of similar development.

W ' Y L O 1 GROWTH R R T E OF Y ' L R B O I

- A - W ' T A U 0 1 GROWTH R A T E O F TECHN. P R O G R E S S

I-

-

z

E y 6 0 1

I

1 6 b 1

^I l 6 b 1 I ' 7 b 1 I ' 7 k ' I I B

'

^{0 I I}

L YERR

-

USfl

Figure 2. Comparison

-

US.

W ' Y L 0 2 GROWTH R R T E O F Y 'LRB02

0

---

U 'TFIUO2 GROHTH R R T E O F T E C H N . P R O G R E S S

YERR

-

F R G

Figure 3. Comparison

-

Federal Republic of Germany.

U ' Y L 0 3 GROWTH R A T E O F T'LRB03

---

0 W ' T R U 0 3 GROWTH R R T E OF T E C H N . P R O G R E S S

0

-

LO

-

0 0

-

0)

I- Z

-

W

2 g

W .

~ ~ 6I ' 6 4 0 I I

6 8 1 1 1 1 1 1 1 1 1 1 1 1 1

72 76 8 0

YERR

-

JFlP

Figure 4. Comparison

-

Japan.

W ' Y L O U G R O U T H R R T E OF Y ' L f l B O U

----

0 il 'TRUOY GROWTH R A T E OF TECHN. PEJLiiES5

0

W . / 1 I I

O60 6

\r

^{' 6 b 1 ' 7 2 I} I l l , b l I l e b l l Y E A R

- ^{F R}

Figure 5. Comparison

-

France.

W ' Y L O S GROWTH R R T E OF Y ' L R B O S

--

^{W ' TRUOS} GROWTH R R T E OF TECHN. P R C G R E S S

0 0

-

4

I-

-

z : !

E o 6 0 ' ' 6 4 ' I I I I I I I I 1 1 1 1 1 1 1 1

6

a

7 2 7 6 8 0

a ^{Y E R R}

-

^UK

Figure 6. Comparison

-

^UK.

W ' Y L 0 6 G R d U T H R f l T E OF Y 'LflBO6

0

--

W ' T R U O 6 G R d U T H R A T E OF TECHN. P R O G E E S 5

0 4

.-I

0 0

-

CD

I-

z -

W

gg

W .

a 7 6 0 ' " 6

" ' "

^{11 6 B i l l7 2 l l l i 76 l I I 8 ID I I}

YEFIR

-

I

Figure 7. Comparison

-

^Italy.

W ' Y L 0 7 GROWTH R R T E OF Y ' L R B D 7

---

W ' T A U 0 7 G R O U T H R A T E OF TECHN. P R O G R E S S

0 0

-

4

I-

-

z : ;

_{I I I I I I I l i l}

72 76 8 0

fi:6a'

^{' 6 1 ' I} 1 6 b 1 I I I Y E R R

-

^NL

a

Figure 8. Comparison

-

The Netherlands.

-. W ' Y L O 8 GROWTH R A T E OF Y ' L R B 0 8

---

0 W ' T A U 0 8 GROWTH R R T E OF T E C H N . F R O G R E S S

0

z g

W e

a 7 6 0 ' ' 6 1 ' I I 6 b ' 7 b i " 7 6

Y E R R

-

^{B L}

"---&-

Figure 9. Comparison

-

Belgium- Luxembourg.

W 1 Y L O 9 G R O U T H R R T E OF Y ' L R B D 9

---

0 W 'T R U O 9 GROWTH R R T E OF T E C H N . P R O G R E S S

0

-

(D

0 0

-

N

I- Z

-

W 0 0

& a -

W . ; I I I I I I I I I I I 1 I I I 1 I I I I I I

a

7 6 0 64 68 72 76 80

Y E R R

-

^{C R N}

Figure 10. Comparison

-

Canada.