Evidence on allocative efficiency and elasticities of substitution in the manufacturing sector of Pakistan.
Zafar, Sohail ; Ahmed, Eatzaz
I. INTRODUCTION
Lack of effective competition in factor markets often produces
allocative or price inefficiencies in the manufacturing sector of
developing countries like Pakistan. Such inefficiencies are common due
to distortion in factor markets leading to the use of inappropriate
factor proportions Lau and Yotopoulos (1971, 1972), Yotopoulos and Lau
(1973), Burki, et al. (1997), Khan (1998), Ahmed (1999), Zafar (2000).
Pakistan is also one of the country where labour is abundant but capital
and raw material are scarce. Our finding undermine estimates of
elasticities of demand and substitution based on classical assumption
that factor markets are perfectly competitive i.e. Kazi, et al. (1976),
Kemal (1981), Battese and Malik (1987, 1988, 1993), Malik, et al.
(1989), Mahmood (1989, 1992), Zahid, et al. (1992) and Khan and Rafiq
(1993). In order to discuss the cost structure of the manufacturing
sector we will estimate well behaved translog cost function.
II. THE MODEL
To estimate underlying technology one can use either production or
associated cost function. The choice between them is a matter of
statistical convenience. As a firm may not be able to have optimal
combination of inputs due to imperfection in decision-making and
imposition of distortionary government regulations. The role of these
potential sources of misspecification in a firms behaviour slither
introducing concept of shadow prices Lau and Yotopoulos (1971), Atkinson
and Halvorsen (1980, 1984), Burki, et al. (1997), Burki and Mahmood
(2004). The concept of shadow prices here after represented by
[p.sup.*.sub.i] = f ([[tau].sub.i][p.sub.i]). Where [[tau].sub.i] is
inefficiency parameter. The firms dual total shadow cost function is
defined as [c.sup.s] = [c.sup.s] ([tau]p,y). Where [tau]p is vector of
input specific shadow price. We can derive actual input demand function
with the help of shadow cost function by applying Shepherd's lemma [partial derivative][c.sup.a]/[partial
derivative][[[tau].sub.i][p.sub.i] = x. The firm's total actual
cost is given by [c.sup.a] = [3.summation over (i=1)]
[p.sub.i][x.sub.i]. If [[tau].sub.i] = [[tau].sub.i] [[for all].sub.ij]
firm's total actual cost function reduces to total shadow cost
function. Hicks own and cross price elasticities of demand for input i
with respect to its market price turns out
[[sigma].sup.h.sub.ij] = [k.sub.i]([k.sub.i] - 1) +
[[beta].sub.ii]/[k.sub.i] [[for all].sub.i] [not equal to] j
[[sigma].sup.h.sub.ij] = ([k.sub.i][k.sub.j] +
[[beta].sub.ij])[k.sub.i] [[for all].sub.i] [not equal to] j
The Allen partial elasticities of substitution turns out
[[sigma].sup.a.sub.ij] = (1 + [[beta].sub.ij]/[k.sub.i] [k.sub.j])
[[for all].sub.i] [not equal to] j
III. DATA
The Census of Manufacturing Industries (CMI) is the only major
source of data on different aspects of manufacturing industries in
Pakistan. All data in CMI are on aggregate level and on groups of
industries. Most of the data are taken from its sixteen most recent
publication (1969-71, 1970-71, 1975-76 through 1987-88 and 1990-91).
Some supplementary information is collected from Monthly Statistical
Bulletin and Economic Survey of Pakistan.
Value of production consist of value of finished products and by
products receipts for repairs and maintenance, value of electricity
sold, receipt for work done for others, value of the sale goods
purchased for resale, wastes and used goods, the net increase in the
value of working capital, and value of processed and fixed assets produced by establishment for its own use. Valuation is made at
ex-factory prices, which include indirect taxes and exclude transport
cost outside the factory gate.
To estimate unit labour cost we divide employment cost with average
daily persons engaged. The data on employment cost and average daily
persons engaged are given in Census of Manufacturing and Industries. The
most appropriate price of capital for our purpose is user cost of
capital calculated as follows [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE
IN ASCII]. Where [p.sub.k] is user cost of capital and [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] is price index of capital goods r
is real rate of interest [delta] is capital depreciation rate and
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. It is rate of
growth in price index of capital. Thus user cost of capital increases
with an increase in price of capital real rate of interest and capital
depreciation. On the other hand user cost decreases with appreciation in
value of capital due to increase in rate of growth in capital price. The
price index of machinery is taken from Monthly Statistical Bulletin and
is used as proxy for price index of capital both for Punjab and Sindh.
The rate of interest is average schedule banks rate on long term
advances for manufacturing sector. These information are available in
Monthly Statistical Bulletin Depreciation rate is calculated by dividing
total depreciation amount with value of fixed assets at the beginning of
the year. Total depreciation amount and value of fixed assets at
beginning of the year are available in CMI.
The quantity of capital is calculated by dividing value of capital
by price index of machinery. Finally multiplying quantity of capital by
user cost marks out total user cost of capital. Total cost is obtained
by summing up value of capital stock total employment cost and value of
raw material whereas input shares are obtained by dividing cost of each
input with total costs.
We estimate parameters of translog cost function along with share
equations in a system of equations. We use Iterative Zullner Efficient
(IZEF) method for seemingly unrelated regression equations. Since shares
satisfy adding up restriction it means all shares sum equal to one. To
solve the problem of singularity one of these equations is dropped
Christensen and Jorgenson (1969), Berndt and Christensen (1973), Barren (1969) showed maximum likelihood estimates are independent of the
equation omitted. We drop share equation of raw material and recover its
parameters with the help of adding up restrictions. Since IZEF
estimation converages to Maximum Likelihood Estimate which are unique it
follows that IZEF estimates are invariant to the choice of equation
dropped.
IV. EMPIRICAL FINDINGS
Our results show that estimated cost shares at each point of data
set are positive confirming monotonicity, while curvature condition also
holds i.e. the mean shares of capital labour and raw material are 0.06,
0.09 and 0.85. We have tested homotheticity condition for translog cost
model using the [X.sup.2] test. The calculated value of statistic is
74.99 which exceeds critical value at 5 percent level of significance.
Thus homotheticity does not hold in the estimated model. It follows that
underlying production function is not homogenous either. Parameters of
translog cost are reported in Table 1. It can be seen that most of the
parameter estimate are statistically different from zero at conventional
level of significance. The coefficient of price output interaction
variable [[beta].sub.iy] interpret change in input intensity as level of
output increase. It measures change in cost share of input i with
respect to increase in output with price of inputs held constant. Value
of [[beta].sub.iy] would be (negative) positive if intensity of input i
(decrease) increase with the level of output.
The estimated value of [[beta].sub.ly] is -0.04 which is
statistically different from zero, implying that intensity of labour is
lower at higher levels of output. On the other hand [[beta].sub.ky] is
0.01 and [[beta].sub.my] is 0.03 showing that intensities of capital and
raw material are higher at higher level of output however rate of
increase in capital, intensity with level of output is statistically
insignificant. In any case this pattern of factor intensities confirms
our result that underlying production structure is non-homothetic and
there exist biases in use of factor inputs.
Allen and Hicks price elasticities of demand, based on estimates of
translog cost share equations are calculated for each input pair and are
shown in Table 3. The Allen elasticity of substitution for combination
of capital and labour is negative, but the estimated value is
statistically insignificant where as cross price elasticities
[[sigma].sup.h] < 0 between labour and raw material and between
capital and raw material.
The results of Hicksian cross price elasticities of factor demand
are in agreement with the results of Allen partial elasticities of
substitution. As one should expect the magnitudes of Hicksian
elasticities are smaller than the corresponding Allen elasticities. This
is a natural result as Hicksian cross-price elasticity of factor demand
is obtained by Allen (1938) multiplying Allen partial elasticity of
substitution with average input share that is a positive fraction. Thus
effect of change in price of one input on demand for another input is
high if cost share of first input is large. This explains for example,
why elasticity of capital with respect to price of raw material is
larger than elasticities of raw material with respect to capital.
Hicks own price elasticities are of correct sign [[sigma].sup.h]
< 0 showing with an increase in price of an input the utilisation
decreases. The results show that raw material and labour are
substitutes. This means that when wage relative to price of raw material
increase firms will increase raw material intensity relative to labour.
This result is quite consistent with observed factor prices and factor
intensities within our sample. Over the years unit labour cost has risen
taster than users cost of raw material as a result raw material
utilisation has increased substantially. Measure of Hicks elasticity of
capital with respect to labour is -0.07 showing a complemetary
relationship but the value is statistically insignificant and is in no
harmony with factor prices and factor intensities within the sample.
The translog cost function along with share equations allows
allocative inefficiency, estimated with iterative Zellner efficient
technique. The function satisfies the monotonicity condition where as
the curvature condition does not hold. The test of homotheticity is
rejected implying that homotheticity does not hold either. The results
of parameters along with their t-statistic are reported in Table I. The
results show that about half of the estimates are statistically
different from zero at 5 percent level of significance. The estimated
value of [[beta].sub.ly] is -0.11 hence intensity of labour is lower at
the higher levels of output. On the other hand [[beta].sub.ky] is 0.02
and [[beta].sub.my] is 0.09 showing intensities of capital and energy
are higher at higher output levels. These results are qualitatively
similar to ones obtained without allowing allocative inefficiency.
We attain relative price efficiency equalise [[tau].sub.k] =
[[tau].sub.l] = [[tau].sub.m]. The actual cost and cost shares are
homogeneous of degree zero for all x therefore we cannot estimate the
values of [tau] for each input. The values shown in Table 2 exhibit that
[[tau].sub.k[not equal to]] [[tau].sub.m] while all other inputs are
relatively equally price inefficient.
Relative to labour raw material is inefficiently utilised. In
particular raw material is over used in relation to labour. We also find
that capital is inefficiently utilised as compared to labour and raw
material but the t-statistic indicate that the extent of inefficiency is
insignificant. This result is consistent with the findings of Burk, et
al. (1997) that capital and raw material are over utilised relative to
labour. The effects of relative price inefficiency on cost of production
can be evaluated by comparing actual total cost with the cost when
relative price efficiency has been attained. The efficient level of cost
is estimated by imposing restriction [[tau].sub.k] = [[tau].sub.m] = 1.
A comparison with fitted total cost indicates that at the mean
values of data over the period of our analysis relative price
inefficiency increases total cost by 0.62 percent, It implies that
allocative inefficiency increase cost of production or reduces
profitability of production units beneath full potential.
The results of own and cross-price elasticities of demand at
average values of variables along with t-statistics are shown in Table 3
we can observe that qualitative nature of our results are same as in
shadow cost in particular signs of all elasticities are same as before.
However in quantitative terms there is a significant change in the
magnitudes of elasticities compared with results without controlling
inefficiency. The absolute magnitude of the Allen elasticity has
increased for capital and labour but the degree of complementaries
[[sigma].sup.a] < 0 has remained statistically insignificant. Like
wise Hicks own elasticities of capital and labour have increased.
The cross-price elasticity also indicates an increase in magnitude
for labour with respect to capital while that of raw materiel with
respect to labour has decreased.
V. CONCLUSION
This study has been an attempt to investigate nature of allocative
inefficiencies in Pakistan's large scale manufacturing sector using
pooled provincial level time series data for Punjab and Sindh. The
nature of allocative inefficiencies here after focus distortion effect
in standard translog cost function. We estimated two models that are
generated by appropriate adjustments in globally known translog cost
function to explain substitutability of different inputs. In first model
we simply take translog cost function without introducing allocative
efficiency and then we include distortion parameters to represent
allocative inefficiency in the cost structure.
The relative price efficiency between each pair of inputs provide
evidence that raw material is over utilised as compared to labour while
other inputs are equally efficiently utilised. It turns out capital and
labour are complement in use while both of these inputs are
substitutable with raw material. However complementarities or
substitutability relationship are weak. Capital and labour are found to
be complement in analysis where manufacturing sector is treated as a
whole.
Hicks own price elasticities are of correct sign depict with
increase in price of an input utilisation decrease further raw material
and labour are substitutes. This means that when wage relative to price
of raw material increase firm will increase raw material intensity. This
result is quite consistent with observed factor prices and factor
intensities within our sample. Further comparative analysis is useful to
observe how estimate of substitution elasticities affect due to
conventional assumption that firms at disaggregates are able to minimise
cost in the light of observed input prices.
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Sohail Zafar is based at the Department of Economics. Universite of
Laval, Quebec, Canada. Eatzaz Ahmed is Professor and Chairman.
Department of Economics, Quaid-i-Azam University. Islamabad.
Table 1
Results of Translog Cost Function
Shadow Cost Actual Cost
Estimate t-statistic Estimate t-statistic
[[alpha].sub.o] -0.04287 * -1.99084 -0.17871 ** -1.68223
[[alpha].sub.k] 0.054163 * 9.03673 0.069541 ** 1.68227
[[alpha].sub.l] 0.113966 * 34.775 0.254508 * 3.65572
[[alpha].sub.m] 0.83187 * 107.352 0.675951 * 7.7462
[[beta].sub.kk] 0.036264 * 5.93955 0.038917 0.598841
[[beta].sub.ll] 0.020921 * 2.30363 0.063863 * 2.22854
[[beta].sub.mm] 0.038497 * 2.60915 0.06632 ** 1.69725
[[beta].sub.kl] -9.34E-03 * -2.81302 -0.01823 -0.71517
[[beta].sub.km] -0.02692 * -3.2527 -0.02069 -0.49398
[[beta].sub.lm] -0.01158 -1.17085 -0.04563 -1.38047
[[beta].sub.y] 0.798442 * 14.3678 0.77331 * 11.3929
[[beta].sub.ky] 9.03E-03 1.26604 0.016801 0.662313
[[beta].sub.ly] -0.03866 * -5.30534 -0.10473 * -3.95765
[[beta].sub.my] 0.029626 * 2.59179 0.087926 * 2.50531
[[beta].sub.yy] 0.284274 * 4.158 0.293844 * 3.81874
[[tau].sub.k] 0.326372 0.547926
[[tau].sub.m] 0.248006 * 2.27675
[[tau].sub.l] 1
* Significant at 5 percent level of significance.
** Significant at 10 percent level of significance.
Table 2
Relative Efficiency Test
Hypothesis t-statistic Ratios Estimates
[[tau].sub.l] = 1.13 [[tau].sub.l] / 3.07
[[tau].sub.k] [[tau].sub.k]
[[tau].sub.l] = 2.28 [[tau].sub.l] / 4.03 *
[[tau].sub.m] [[tau].sub.m]
[[tau].sub.m] = 0.13 [[tau].sub.m] / 0.08
[[tau].sub.k] [[tau].sub.k]
* Significant at 5 percent level of significance.
Table 3
Results of Elasticities of Substitution
Shadow Cost
Allen Elasticities
Estimate t-statistic
[[sigma].sup.a.sub.kl] -0.74101 ** -1.17445
[[sigma].sup.a.sub.km] 0.442952 ** 1.76429
[[sigma].sup.a.sub.lm] 0.85531 * 5.58513
Hicks Elasticities of
Substitution
[[sigma].sup.h.sub.kk] 0.30613 * -3.88458
[[sigma].sup.h.sub.ll] -0.6838 * -28.5823
[[sigma].sup.h.sub.mm] -0.10585 * -4.35944
[[sigma].sup.h.sub.kl] 0.06985 -1.2833
[[sigma].sup.h.sub.lk] -0.04219 -1.15216
[[sigma].sup.h.sub.km] 0.375977 ** 1.70158
[[sigma].sup.h.sub.mk] 0.025219 1.43918
[[sigma].sup.h.sub.lm] 0.725987 * 4.83761
[[sigma].sup.h.sub.ml] 0.080626 * 2.76234
Actual Cost
Allen Elasticities
Estimate t-statistic
[[sigma].sup.a.sub.kl] -2.3764 -0.38798
[[sigma].sup.a.sub.km] 0.57503 0.600408
[[sigma].sup.a.sub.lm] 0.428584 0.960245
Hicks Elasticities of
Substitution
[[sigma].sup.h.sub.kk] -0.94263 * -55.2265
[[sigma].sup.h.sub.ll] -0.22733 * -1.96296
[[sigma].sup.h.sub.mm] -0.15149 * -4.79984
[[sigma].sup.h.sub.kl] -0.22366 -0.40998
[[sigma].sup.h.sub.lk] -0.13799 -0.43703
[[sigma].sup.h.sub.km] 0.487921 0.610938
[[sigma].sup.h.sub.mk] 0.032989 0.517381
[[sigma].sup.h.sub.lm] 0.36366 0.956618
[[sigma].sup.h.sub.ml] 0.040337 0.888283
* Significant at 5 percent level of significance.
** Significant at 10 percent level of significance.
