Maitha, J. K.

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(a) UNIVERSITY OF NAIROBI 
(b/) Institute for Development Studies 
Working papers 
TIME - SERIES PRODUCTION FUNCTIONS AND 
TECHNOLOGICAL PROGRESS IN KENYAN INDUSTRY 
By 
J.K. Maitha 
WORKING PAPER NO. 217 
INSTITUTE FOR DEVELOPMENT STUDIES 
UNIVERSITY OF NAIROBI 
P.O. Box 30197 
NAIROBI, KENYA 
LIBRARY 
1 ° FEB 2011 
INSTITUTE OF 
DEVELOPMENT STUDIES 
June, 1975 
Views expressed in this paper are those of the author. They should 
not be interpreted as reflecting the views of the Institute for 
Development Studies or of the University of Nairobi. 
RAJ 3 2,2 Z I 
IDS 
095291 
TIME-SERIES PPODfJCTION FUNCTIONS AND TECHNOLOGICAL 
PROGRESS IN KENYAN INDUSTRY* 
By 
J.K. Vtaitha 
The slow rate of growth of employment in the modern sector 
of the economies of the LDCs has stimulated great interest in the 
elasticities of substitution between capital and labour in these countries 
The main reason for this interest in the elasticities of substitution 
is the determination of the degree of substitutability between capital 
and labour. From this knowledge we can deduce some useful results 
concerning growth, employment and distribution of income. Technological 
progress could also be another explanation of this slow growth of 
employment in LDCs but very few studies has attempted to estimate the 
nature of technological progress in LDCs. In this paper we attempt to 
estimate both elasticities of substitution and technological progress 
in the main sectors of the Kenyan economy. 
In the case of Kenya a number of studies have appeared on 
2 
employment and productivity mainly in the manufacturing sector. 
However, very few of these studies have directly estimated the elasticity 
of substitution although some reject the capital-labour hypothesis 
even without direct evidence. Host of these studies assume constant 
returns to scale and to our knowledge, very few attempts have been made 
to estimate returns to scale. Our knowledge about technological progress 
in Kenya is meagre and there are no estimates available due to paucity 
of data. 
THE. fttDEL. 
Our estimates of the elasticity of substitution are based on 
the constant elasticity of substitution (CES) production function. 
In this study we are also interested in estimating the extent of 
technical progress in Kenya's economy. If we assume the Hicks-Neutral 
technological progress, the CES production function can be written: 
Q = AeXt|6 k ' £ + ( H ) L " V i (1) 
- 2 -
where 0, ¥ and L are value added3 capital and labour. xs 63£ and 
v are technology, distribution. substitution n^d homogeneity parameters. 
Due to lack of data on capital,, we cannot estimate (1) directly. 
However, if we assume constant returns to scale and further that factor can 
and product markets are competitive, then we /estimate the elasticity 
of substitution and technical progress from data on value added;, wages 
for 
and labour. Thus Cv =1, the following regression equation can be 
derived from (1)''. 
log q = aQ + a-jlog wt + a2t (2) 
where q = value added per man (Q/j) 
w = the wage rate O'Vj) 
t = trend term 
The economic parameters are estimated or calculated, from, the 
regression coefficients as follows: 
* = ax 
X = a2/(l-a3) 
where A is the elasticity of substitution and X is the technological 
progress parameter. 
celebrated 
Equation (2) is the L • ACS | | formulation for estimating 
the elasticity of substitution and has been widely used. However, 
estimates of c from it are characterized by some problems of identification 
and specification.^  If the constant returns to scale assumption is 
dropped, then another equation can. be derived, to estimate the elasticity 
of substitution, technical progress and the returns to scale parameter.^  
From (1)s the marginal product for labour is given by: 
90 = k 0 1+Ca/v)L-l-a 
aL 
where k = A e rt(l» 6) A ert 
By eo.u^ ^^ r-g tht; .marginal "product witli the-wage rate and after 
some rearrangement, we have the following estimating equation. 
- 3 -
log Qt = b^ +b-jlog wt + b? log + b^t. (3) 
where A = b-,/b~ 
A " h3/(l-b2) 
1 - b v 
Equations (2) and (3) are our basic estimating equations. 
Empirical Pesults: 
Equations (2) and (3) were fitted to time-series data covering 
7 
eight sectors over the period 1956 •• 72. The eight sectors are large 
scale Agriculture, Mining and Quarrying, Manufacturing, Transport and 
Conrounications, Building and construction, Commerce, services and the 
public sector. Fouation (2) fitted the data better than equation (3). 
In equation (3) employment (L) is included to pick up dramatic and 
sudden changes in value added (0). Thus the L variable should explain 
qualitative changes in 0 that do not follow ? smooth growth pattern, 
over time. Fquation (3) did not fit the data. The coefficient of 
L was insignificant post of the time and L was highly correlated 
with the wage rate. Hence equation (3) was dropped, in favour of 
equation (2). 
There are three possible explanations as to why equation (3) 
fails to fit our data. First, the sectors considered in this paper 
may not be characterized hy increasing returns to scale. Second, the 
period covered by the data could be relatively short and hence equation 
(3) inappropriate. Third, there were no significant dramatic and 
sudden changes in value added during the period 1956 - 72. 
The results of equation (2) are shovm in table 1 below, 
- 4 -
TABLE 1 
ESTIMATE? OF E-OUATIOM 2 (1956 - 1972) 
Sector Constant log w Time 
1. Agriculture .780 1.045 .044 .980 
(.500) (.027) 
2. Mining » Quarrying 9.966 1.001 .177 .971 
(.638) (.025) 
3. Manufacturing 6.07 2 .755 .086 .987 
'(.171) (.013) 
4. Transport & Communications 7.093 .028 .062 .979 
(.038) (.007) 
5. Building ft Construction 5.349 .815 .065 .949 
(.246) (.019) 
6. Commerce 2.697 .784 .003 .954 
(.192) (.012) 
7. Services 5.065 .118 .018 .248 
(.149) (020) 
8. Government 2.6 76 .218 .087 .993 
(.333) (.016) 
The numbers in brackets are standard errors of the coefficients. 
Equation (2) oroduced insignificant results in three sectors, namely 
transport and communications, services and. government. Services had the 
poorest results and only the trend term coefficient was significant in 
transport and communications and the public sector. The wape rate 
coefficient in mining and quarrying is significant at the ten per cent 
level. All the other coefficients are significant at least at the five 
per cent level. The estimated economic parameters from the sectors with 
significant results are shown below. 
TABLE 2 
ESTIMATED FCOmOVTC ?/tJ^ METFP-c-
A A Sector a X 
Agriculture 1.05 -0.98 
Mining a Quarrying 1.01 -0.18 
Manufacturing 0.76 0. .35 
Building ?•> Construction 0 = 82 0.35 
Commerce 0.78 0.01 
In the four sectors the estimated elasticity of substitution 
8 
is not significantly different froro. unity." This implies that 
capital-labour substitution is not as limited as calimed in some 
quarters, Thus increasing the level of wages can he expected to 
impede employment creation through capital substitution for the 
expensive labour. 
The estimated coefficient for technoh -'foal progress suggests 
that there was technological retregression in Agriculture and, 
Mining and Quarrying during the period 1956 72. This agrees with 
other economic indicators in these two industries. In agriculture 
employment has declined considerably during this period and the rate 
of capital formation has been very low. In Mining and Quarrying, 
both employment and capital formation have been declining during 
this period. Manufacturing and building and Construction show 
reasonable rates of technological progress and Commerce shows the 
least technological progress. 
All the coefficients of the technological progress parameters 
are consistent with T~-icks-neutral or labour augmenting technological 
change. Hicks-neutral technological progress in a CPS production 
function is determined according to table .3 below. 
- 6 -
TABLP 3 
KICK5-WHJTHAL TBQM)LQGICAI P&XaJBSS IN A CES 
PRODUCTION FACTION 
g < 1 
If b2 > 0 
X > 0 
- p X < 0 
g > 1 
If b2 > 0 
X < 0 
-p X < 0 
FOOTNOTES 
I would like to thank ILO for financial support but any 
errors are vry responsibility. 
1. See for example, C.K., "Capital Substitution in Manufacturing 
in Underdeveloped Countries, ' Econometrica" Vol.37, (July 1969), 
in A.D. witto. Alternative Estimates of Capital-Labour 
Substitution in Manufacturing in Developing Economies: Consents 
On Professor Clague,'" Fconometrica, Vol.39 No.6 (November, 1971) 
J.P., Behram, "Sectoral Elasticities of Substitution between 
capital and Labour in a Developing Economy. Time series .Analysis 
in the Case of Post-war Chile," Econometrica, Vol.40, Ho.2 
C^ arch, 1972), K.A. Oyelabi, 'Tests of Factor Substitution in 
Nigeria's Manufacturing Sector5, Eastern Africa Economic Review, 
Vol.3 No. 1 (June, 1971) and J.Y.I haitha, ' Capital-Labour 
Substitution in Manufacturing in a Developing Economy: The Case 
of Kenya, " Eastern .Africa Economic Peview, Vol.5. No.2 (December, 
1973). 
2. See J.P.. Harris and >f.P. Todaro, ''^ ages, Industrial Employment 
and Labour Productivity'', Eastern. Africa Economic Peview, Vol.1 
Mo.l (June, 1969), J.7?. King, 'T'*ages, Employment and Productivity 
in Kenya: A Comment' , Eastern Africa Economic Peview, Vol.4 Mo.2 
(December, 1972) and W.J. House, "Wages, Employment and Productivity 
in Kenya: Some further Evidence-'s Fastern Africa Economic P.eview, 
Vol.5 No.l (June, 1°73) J.K. Maitha, op.cit. 
3. W.J. House, op.cit. tried to estimate the elasticity of 
substitution using the Arrow, et.al, ;.*<odel and. obtained, 
elasticities slightly larger than unity. However., using the 
same model, the author, op.cit. finds that for most of Kenyan 
manufacturing industries, the elasticity of substitution tends 
to be unity. 
4. For the original derivation, see, Arron, K.J., H«B. Chenery, 
B.S. Finhas and P.M. Solow,''Capital-Labour Substitution and. 
Economic Efficiency," Peview of Economics and. Statistics, 
August (1961). 
5. For example, see, J.P. Mbroney, ''Identification and Specification 
Analysis of Alternative Equations for Estimating the Elasticity 
of Substitution," Southern Economic Journal, Vol.XXXVI (january, 
1970) 
6. See for examole, C.E. Ferguson, "Substitution, Technical Progress 
and Returns to Scale,'" American Economic Peview, Vol.LV, (May,1965) 
7. The data for value added, wages and employment were obtained 
from the Statistical .Abstracts 1962 - 1973. 
This result agrees with other estimates of the elasticity of 
substitution by the author. 


Time-series production functions and technological progress in Kenyan industry

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Time-series production functions and technological progress in Kenyan industry

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