ESTIMATION OF ELASTICITIES OF SUBSTITUTION FOR CES AND VES PRODUCTION FUNCTIONS USING FIRM-LEVEL DATA FOR FOOD-PROCESSING INDUSTRIES IN PAKISTAN George E. Battese and Sohail J. Malik No.27 - May 1986 Typist: Val Boland ISSN 0157-0188 ISBN 0 85834 6273
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Estimation of Elasticities of Substitution for CES and VES Production Functions
This paper presents estimates of elasticities of substitution based upon data obtained from a survey of large-scale firms in the wheat flour milling, rice husking, sugar refining and edible oil processing industries in Pakistan.
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ESTIMATION OF ELASTICITIES OF SUBSTITUTIONFOR CES AND VES PRODUCTION FUNCTIONS USING
FIRM-LEVEL DATA FOR FOOD-PROCESSINGINDUSTRIES IN PAKISTAN
George E. Battese and Sohail J. Malik
No.27 - May 1986
Typist: Val Boland
ISSN 0157-0188
ISBN 0 85834 6273
Estimation of Elasticities of Substitution for CES and VES
Production Functions using Firm-Level Data for
Food-Processing Industries in Pakistan
George E. Battese and Sohail J. Malik
i. Introduction
The difficulties associated with estimation of elasticities of
substitution, using aggregative data for firms within specified asset-size
categories, are discussed in Battese and Malik (1986a,b). In order to
identify and estimate the elasticity of substitution for CES and VES
production functions, defined in terms of firm-leval data, it is necessary
that values of inputs of production be the same for firms within specified
categories. Further, there is a problem associated with the interpretation
of an elasticity of substitution for a product that is defined in a highly
aggregative form. For example, the aggregate two-digit-level industry, Food,
consists of twenty-eight quite diverse components, such as meat preparation,
ice cream, fish canning, vegetable and fruit canning, bakery products and
salt refining. An aggregate estimate for its elasticity of substitution does
not necessarily imply that the elasticities for all of the component
industries are the same. Moreover, given the heterogeneous nature of the
products involved, it is quite possible that the aggregate elasticity of
substitution measures, not only the substitution of labour for capital to
produce a given homogeneous product, but also the substitution of one product
for another.
The above discussion suggests the desirability of estimating elasticities
of substitution for well-defined products using firm-level data. This paper
presents estimates of elasticities of substitution based upon data obtained
from a survey of large-scale firms in the wheat flour milling, rice husking,
sugar refining and edible oil processing industries in Pakistan. These four
industries are responsible for nearly ninety per cent of the value-added in
the aggregate two-digit-level industry, Food [based upon Government of
Pakistan (1983)]. The output of the firms in each of these industries is
fairly homogeneous, although rice husking and edible oil processing produce
a wider variety of products and by-products than flour milling and sugar
refining. Rice husking produces a range of different quality rice with the
output composed of varying proportions of fine, broken and powered rice and
bran, while edible oil processing produces cottonseed, rapeseed and mustard
and sesamum oils, cakes and meal. Flour milling produces a fairly standard
quality of flour and bran, while sugar refining produces only white sugar and
mollasses.
2. Data on Food-Processing Firms
During 1980-81, the Pakistan Institute of Development Economics carried
out a survey of large-scale firms within manufacturing industries in Pakistan.
This survey was designed primarily to study the effective rates of protection
within manufacturing industries. From the list of large-scale firms available
for the Census of Manufacturing Industries, firms were selected in this survey
according to the following criteria:
(a) all firms in a particular three-digit-level category if their
number was less than forty; or
(b) twenty-five per cent of the firms in a particular category if
their number was more than forty.
Of the 822 firms selected in the survey, there were sixty-eight firms
(about eight per cent) in the flour milling, rice husking, sugar refining
and edible oil processing industries. Firms with these four industries are
3o
estimated to comprise about six per cent of the total number of large-scale
firms covered by the Census of Manufacturing Industries. The percentages of
sample firms within the four food-processing industries were 25.0, 30.9, 16.2
and 27.9 for flour milling, rice husking, sugar refining and edible oil
processing, respectively. For the 1976-77 Census of Manufacturing Industries
the percentages of food-processing firms within these four food-processing
industries were 39.9, 2.2, 11.2 and 46.6, respectively [Government of Pakistan
(1982, p.l)]. While there may have been changes in the relative percentages of
firms within the different food-processing industries, between the 1976-77
Census and the 1980-81 Survey, the significant differences between the two
sets of percentages are likely to be due to the criteria by which the sample
firms were selected. It is also noted that information supplied to the census
is voluntary and the number of firms reported therein does not necessarily
represent the true proportions of firms in the total population. For example,
it was reported that in the 1976-77 Census only sixty-five per cent of the
tota! number of large-scale firms on the census lists actually completed the
census [Government of Pakistan (1982, p.ix)].
In the 1980-81 Survey, information was obtained on the value of output,
value of input, changes in stocks, employment costs and the number of persons
employed. Of the sixty-eight firms within the four food-processing
industries, two firms reported data such that value-added was negative and
four firms reported employment costs that were greater than value-added.
Since this situation could arise only in the very short-run or have resulted
from reporting, or recording errors, these six firms are omitted from our
analyses. Data on the book value of different types of capital equipment
were obtained for only forty-two of these firms because the remaining firms
did not complete the questions on capital assets in the survey. Summary1
statistics for selected variables are presented in Table i.
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For the seventeen firms in rice husking, the sample mean wage rate,
5,410 Rupees and the sample mean value-added, 836,000 Rupees, are the lowest
among the four industries considered. For the eleven sample firms in sugar
refining the sample mean of value-added, 80,600,000 Rupees, is the highest.
The overall sample mean of the wage rate is 11,280 Rupees, the highest
being in edible oil processing, 17,230 Rupees. The sample mean of employment
is highest in sugar refining and its coefficient of variation is significantly
lower than those for the other three industries. The coefficients of
variation for the wage rate and the number of persons employed are much lower
in sugar refining and flour milling than for rice husking and edible oil
processing.
3. Analyses Involving CES Production Functions
We first assume that, for the observations on individual firms, the
stochastic constant-returns-to-scale CES production function [cf. Arrow, et al.
(1961)],
-l/p u.y. = y{SK7p + (I-61L7p} e , i=l,2,...,n, (11
1 1
¯ represent value-added, book-value of capitalapplies, where Yi’ Ki and L1
equipment and total number of persons employed for the i-th sample firm;
y, ~ and p are the efficiency, distribution and substitution parameters;
and the random errors, UI, U2,...,Un, are assumed to be independently and
identically distributed as normal random variables with means zero and
d~; and n represents the number of sample firms involved.variances,
Given the assumption of perfect competition in the factor and product
markets, the elasticity of substitution for the CES production function (1)t
-id = (l+p) , can be estimated from the indirect form:
Labor Substitution and Economic Efficiency", Review of Economics and
Statistics, XLIII, 225-250.
Battese, G.E. and Malik, S.J. (1986a), "Identification and Estimation of
Elasticities of Substitution for Firm-Level Production Functions Using
Aggregative Data", Working Papers in Econometrics and Applied Statistics~
No.25, Department of Econometrics, University of New England, Armidaleo
Battese, G.E. and Malik, S.J. (1986b), "Estimation of Elasticities of
Substitution for CES Production Functions Using Aggregative Data on
Selected Manufacturing Industries in Pakistan", Working Papers iz
Econometrics and Applied Statistics, No.26, Department of Econometrics,
University of New England, Armidale.
Behrman, J.R. (1982), "County and Sectoral Variations in Manufacturing
Elasticities of Substitution Between Capital and Labor" in Krueger, A.
(ed.), Trade and Employment in Developing Countries, Vol.2, University
of Chicago Press, Chicago, 159-191.
Brown, M. and de Cani, J.S. (1962), "Techno!ogical Change and the Distribution
of Income", International Economic Review, 4, 289-309.
Government of Pakistan (1982), Census of Manufacturing Industries, 1976-77,
Statistics Division, Karachi.
Government of Pakistan (1983), The Pakistan Economic Survey, 1982-83,
Finance Division, Islamabad.
Lu, Y.C. and Fletcher, L.B. (1968), "A Generalization of the CES Production
Function", Review of Economics and Statistics, L, 449-452.
Yeung, P. and Tsang, H. (1972), "Generalized Production Function and Factor-
Intensity Crossovers: An Empirical Analysis", The Economic Record, 48,
387-399.
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Estimation of Elasticities of Substitution for CES and VES ProductionFunctions Using Firm-Level Data for Food-Processing Industries inPakistan. George E. Battese and Sohail J. Malik, No.27 - May 1986.