A Decomposition of Total Factor

Productivity Growth : A Regional

Analysis of Indian Industrial
Manufacturing Growth


Surender Kumar

2
A Decomposition of Total Factor
Productivity Growth : A Regional
Analysis of Indian Industrial
Manufacturing Growth


Surender Kumar
*



Abstract


Total factor productivity (TFP) growth in industrial manufacturing
is measured for 15 major Indian states for the period 1982-83 to 2000-01
using non-parametric linear programming methods. TFP growth is
decomposed into efficiency and technological changes and also
measure for the bias in technical change. The resulting information is
used to examine whether the post-reform period shows any improvement
in productivity and efficiency in comparison to the pre-reform one.
Findings of the present exercise indicate the improvement in TFP. The
recent change in TFP is governed by the technical progress in contrast
to similar gain caused by the improvement in technical efficiency in the
pre-reform regime. The technological progress in state manufacturing
exhibited a capital using bias during the study period. Regional
differences in TFP persist, although the magnitude of variation has
declined in the post-reform period. Moreover, it is also found that there is

Fellow, National Institute of Public Finance and Policy, 18/2 Satsang Vihar Marg, Special
Institutional Area, Near JNU, New Delhi 110067 India. E-mail: surender@nipfp.org.in
surenderkumarbansal@hotmail.com
Acknowledgements: The author wishes to thank Professors B. N. Goldar and Gopinath
Pradhan for encouragement and for their comments and suggestions on the earlier version
of this paper. However, the disclaimer applies.
3
a tendency of convergence in terms of TFP growth rate among Indian
states during the post-reform years and only the states that were
technically efficient at the beginning of the reform remain innovative.
4
A Decomposition of Total Factor
Productivity Growth : A Regional
Analysis of Indian Industrial
Manufacturing Growth


Introduction



Since 1980, India's rate of GDP growth has more than
doubled, rising from 1.7 percent in 1950-80 to 3.8 percent in 1980-
2000. Such a development is ascribed to liberalisation of the
economy by many experts working in the area. It is pointed out that
until 1991, India had been one of the most over-regulated and closed
economies in the world. Up to this point the Central Governments
control over industrial development was maintained through public
ownership and license-permit-quota system. Planned industrialisation
took place in a highly protected environment, which was maintained
by high tariff, non-tariff barriers and controls on foreign investment,
together forming a set of policy tools that impeded rather than
facilitating the growth process of the economy. The New Industrial
Policy introduced in 1991 is considered a watershed event for the
Indian economy that shattered this old order. Trade liberalisation and
deregulation became the central elements. Here it should be noted
that the pickup in India's industrial growth precedes the 1991
liberalisation by a full decade. Even a cursory glance at the industrial
growth record shows that India's rate more than doubled during
1980s, with very little discernible change in trend after 1991. During
the first half of 1980s the government's attitude towards business
went from being outright hostile to supportive, which was further
reinforced, in a more explicit manner, in the second half of 1980s.
Rodrik and Subramanian (2004) have characterised the policy
changes of 1980s and 1991 as pro-business and pro-market reforms,
respectively. The former focuses on raising the profitability of the
established industrial and commercial establishments. It tends to
favour the incumbents by erasing restrictions on capacity expansion,
5
removing price controls, and reducing corporate taxes. A pro-market
orientation, in contrast, removes the bottlenecks to markets and aims
to achieve this through economic liberalisation by favouring new
entrants and consumers.

Looking into the underlying forces responsible for the
changed growth process, the recent works by Burgess and Venables
(2003) and Foster and Rosenzweig (2003) show that it is non-
agricultural productivity that appears to be the driver of aggregate
outcomes at state levels. A number of studies also have argued that
manufacturing experienced a surge in productivity in 1980s
(Ahluwalia, 1995; Unel, 2003; RBI, 2004). For example, Unel shows
that under the assumption of perfect competition, the average annual
growth rate of total factor productivity (TFP) is 1.8 percent and under
the assumption of a constant labour elasticity of 0.6, it is 3.1 percent
over the period of 1979-80 to 199798. However, there is another set
of studies, which contains evidence on the declining TFP growth in
the post-reform years (see for example, Das, 2003; Goldar, 2004).
The role of TFP, estimated from manufacturing sector in the spurt of
growth of the Indian economy, therefore, remains an unresolved
problem.

Studies on TFP estimation by far are based on average
production function and growth accounting methodology. They
assume that a firm is operating on its production frontier. Moreover,
TFP is treated analogous to technical change. Such an interpretation
is prone to serious limitations as several restrictive assumptions, such
as constant returns to scale and allocative and technical efficiency
have to be made.

In contrast to the approach adopted by growth accounting
and econometric studies, Ray (2002) uses non-parametric linear
programming techniques to construct the Malmquist productivity
index. In measuring the annual rates of change in productivity and
technical efficiency in manufacturing for individual states in India, he
uses the data for the period 1986-87 to 1995-96. Results of this study
show that, on average, the annual rate of productivity growth has
been higher in the 1990s in comparison to the 1980s. It has also been
pointed out that some states have actually experienced a slowdown
or even productivity decline in the 1990s. However, Rays
decomposition of Malmquist productivity index contains no index
6
reflecting the contribution of productivity change of biased technical
change.

The present paper extends the work of Ray (2002) not only
by including more number of years but also by further decomposition
of the technical progress into pure technical progress, input-biased as
well as output-biased technical progress. In the process it succeeds
in determining whether during the reform period technical progress
was either labour or capital deepening.

In the last two decades, the productivity growth measurement
literature has been extended from the standard calculations of TFP
employing production function framework towards more refined
decomposition methods. To overcome the shortcomings of growth
accounting approach and to identify the components of productivity
change, techniques have been developed that are based on the
decomposition of TFP index. A method of measuring productivity with
growing popularity is the use of Malmquist index. After its use from a
non-parametric perspective by Caves, Christensen and Diewert
(1982), who developed it as a way of measuring output produced per
unit of input, Fare, et.al. (1994) went further and employed Shepherd
output distance functions and a non-parametric linear programming
approach to measure productivity change for OECD countries.

The Malmquist index has several features, which make it an
attractive approach. First, it is a TFP index (Fare and Primont, 1995).
Second, it can be constructed using distance functions, which are
primal measures based only on input and output quantities rather
than price. Third, the index can be decomposed into technical
efficiency change, technical change and scale effect components.
Efficiency change can be further decomposed into pure efficiency
change and scale components. The technical change component can
also be decomposed into pure technical change, input-biased as well
as output-biased technical change components. As efficiency and
technical changes are analogous to the notions of technological
innovation and adoption respectively, the dynamics of the recent
growth observed in the manufacturing sector of the Indian economy
can be appreciated better. Finally, assumptions do not need to be
made with regards to objectives of firms or regions in terms of, say,
cost minimisation or profit maximisation objectives, which could be
inappropriate in certain situations.
7
The remainder of the paper is structured as follows: Section II
outlines the methodological issues related to the measurement of
TFP. Empirical results derived from these models and discussions are
presented in Section III. The present analysis, therefore, allows us to
present the efficiency and productivity scores and factors explaining
the productivity. The final section summarises the findings of the
study.


II. Methodology



We use linear programming techniques to construct the
Malmquist productivity index for the major states of India. Our
analysis is confined to the measurement of TFP growth in
manufacturing sector, which is decomposed into efficiency and
technological changes with an isoquant serving as reference
technology. Such a method also allows determination of the nature of
technological change, either capital or labour deepening, in the
Hicksian sense.

As noted above, to measure TFP in state manufacturing, we
use non-parametric linear programming (LP). The LP approach has
two advantages over the econometric one in measuring productivity
change (Grosskopf, 1986). First, it compares the states to the best
practice technology rather than average practice technology as is
done by econometric studies. Second, it does not require the
specification of an ad hoc functional form or error structure. In the
process, the LP approach allows recovery of various efficiency and
productivity measures in an easily calculable manner. Specifically, it
is able to answer questions related to technical efficiency, scale
efficiency, and productivity change.

We employ input distance function to construct the various
measures of efficiency and productivity, which allows estimation of a
multiple output, multiple input production technology. It gives the
maximum proportional contraction of all inputs that still allows a state
to produce a given level of manufacturing output. It is the reciprocal of
input-based Farrell measure of technical efficiency and provides the
theoretical basis for the Malmquist productivity index.

8
Let ( = x denote an input vector at period t
with i=1,2,,N inputs and an output vector at
period t with j=1,2,,M where and y . The
technology can be represented by the input requirement set as
follows:
) ,...., ,
2 1
t
N
t t t
x x x
(
t
= y ) ,.... ,
2 1
t
M
t t
y y y
N t
+
x
M t
+


T t S L
t t t t t t
,......, 1 }, ) , ( : { ) ( = = y x x y (1)

where can produce is the technology
set at period t. The input requirement set provides all the feasible
input vectors that can produce the output vector. The input distance
function requires information on input and output quantity and is
independent of input prices as well as behavioural assumptions on
producers. Figure 1 illustrates the input distance function for a two
input case. The frontier technology is given by piecewise linear
isoquant, . Efficient production activities occur at the extreme
points of the convex hull of the frontier (B and C). The vertical and
horizontal segments of the frontier lines indicate the strong (free)
disposability of inputs. Production activities inside the input
requirement set indicate the presence of inefficiency in those
activities. For example, production activity c is inside the input
requirement set and therefore inefficient. Ob/Oc gives the technical
efficiency of production activity c in terms of input distance function at
period t. When the observation falls on the efficient range, the value
of input distance function is equal to one.
t t t t
S x y x : ) , {( =
)
t
y
}
t
y
(
t
L

Let there be k=1,2,..,K
t
firms that produce M outputs
using N inputs , at each time
period t=1,.,T. A piecewise linear requirement set at period t is
defined as:
M m y
t k
m
,...., 1 ,
,
= N n x
t k
n
,..., 1 ,
,
=

9
K} ..., 1,........ k 0 z
N .., 1,........ n z
M .., 1,........ m : { ) (
t
k
K
1 k
t
k
1
=
=
= =

=
=
t
n
t
kn
K
k
t
m
t
km
t
k
t t t
x x
y y z x y L
(2)

where indicates intensity level, which makes the activity of
each observation expand or contract to construct a piecewise linear
technology (Fare, Grosskof, and Lovell, 1994). The constraint >0
implies constant returns to scale (CRS). By controlling the intensity
variable with additional constraints, i.e., and

in
the linear programme, variable returns to scale (VRS) and non-
increasing returns (NRS) to scale can be imposed (Afriat, 1972).
t
k
z
t
k
z
1

=
=
K
k
t
k
z
1
1
=
K
k
t
k
z
1

Let us define as Shephards input distance
function at period t with strong disposability of inputs assumption as:
) , (
t t t
i
D y x

(3) )} ( ) / ( : max{ ) , (
t t t t t t
i
L D y x y x =

Where estimates the maximum possible
contraction of and can be termed as a measure of overall
technical efficiency (OTE). OTE can be further decomposed into a
product of pure technical efficiency (PTE) and input scale efficiency
(ISE). That is, OTE
) , (
t t t
i
D y x
t
PTE
x
. ISE = Pure technical inefficiency is due
to overemployment of inputs, while scale inefficiency is due to the
states not operating in the range of CRS. The value of input distance
function under VRS provides the measure of PTE. Input scale
efficiency is then equal to PTE / OTE ISE = (Fare et al., 1994).

The Malmquist productivity index (MALM) yields a convenient
way of decomposing TFP change into technical change (TECH) and
overall technical efficiency change (OTEC). In order to estimate the
10
Malmquist productivity index from period t to t+1, additional distance
functions required are:

(4) )} ( ) / ( : max{ ) , (
1 1 1 1 + + + +
=
t t t t t t
i
L D y x y x
(5) )} ( ) / ( : max{ ) , (
1 1 t t t t t t
i
L D y x y x
+ +
=
and
(6) )} ( ) / ( : max{ ) , (
1 1 1 1 1 1 + + + + + +
=
t t t t t t
i
L D y x y x

The cross period distance function, , indicates
the efficiency measure using the observation at period t+1 relative to
the frontier technology at period t, and shows the
efficiency measure employing the observation at period t relative to
the frontier technology at period t+1. In Figure 1, the input
requirement set for period t+1 is given by L
) , (
1 1 + + t t t
i
D y x
) , (
1 t t t
i
D y x
+
) , (
1 1 1 + + + t t t
i
y x
t+1
(y
t+1
), and
and are given by Oe/Of and Oc/Oa
respectively. Cross period distance functions take values of less than,
equal to, or more than one. Similarly, is given by
Oe/Od.
) , (
1 1 + + t t t
i
D y x ) , (
1 t t t
i
D y x
+
D

The MALM consists of four input distance functions to avoid
choosing arbitrary base period and the geometric mean of two input
based technical efficiency indices is taken to form:


5 . 0
1 1
1
1 1 1
) , (
) , (
) , (
) , (

=
+ +
+
+ + +
t t t
i
t t t
i
t t t
i
t t t
i
D
D
D
D
MALM
y x
y x
y x
y x
(7)

The MALM can be decomposed into OTEC and TECH as:


5 . 0
1 1 1
1 1
1
1 1 1
) , (
) , (
) , (
) , (
) , (
) , (
4 4 4 4 4 3 4 4 4 4 4 2 1 4 4 3 4 4 2 1
TECH
t t t
i
t t t
i
t t t
i
t t t
i
OTEC
t t t
i
t t t
i
D
D
D
D
D
D
MALM

=
+ + +
+ +
+
+ + +
y x
y x
y x
y x
y x
y x
(8)
11
A
B
C
D
d
e
f
a
b
c
Lt(yt)
xt
xt+1
Lt+1(yt+1)
X2 input
X1
input
Figure 1. Input-Oriented Distance Function and the Malmquist Productivity Index
O


12
Where the first term defines the changes in OTE from period t
to t+1, i.e., moving closer to the isoquant or 'catching up'. The second
term, i.e., the geometric mean (GM) in parenthesis, represents
changes in technology, i.e., a shift in the frontier from period t to
period t+1. Recall that OTE . ISE PTE = Therefore, OTEC can be
further decomposed into pure technical efficiency change, PTEC, and
input scale efficiency change, ISEC, where
and . The MALM can
be written as:
t t
ISE ISEC
+
=
t
PTE PTE PTEC /
1 +
=
t
ISE /
1

TECH ISEC PTEC MALM = (9)

In the input-oriented case all the indices can be interpreted as
progress, no change, and regress, when their values are less than
one, equal to one, and greater than one respectively. Following Fare,
Grifell-Tatje, Grosskopf, and Lovell (1997), the TECH can be
decomposed into a product of output-biased technological change
(OBTECH), input-biased technological change (IBTECH) and the
magnitude of technological change (MATECH). Thus,

TECH MATECH IBTECH OBTECH = (10)



where

5 . 0
1
1 1
1 1 1
1 1
) , (
) , (
) , (
) , (

=
+
+ +
+ + +
+ +
t t t
i
t t t
i
t t t
i
t t t
i
D
D
D
D
OBTECH
y x
y x
y x
y x



5 . 0
1 1
1 1
) , (
) , (
) , (
) , (

=
+ +
+ +
t t t
i
t t t
i
t t t
i
t t t
i
D
D
D
D
IBTECH
y x
y x
y x
y x

and

) , (
) , (
1 t t t
i
t t t
i
D
D
MATECH
y x
y x
+
=

Since, we are considering only one output in the present
study, there will be no output-biased technological change, i.e.,
OBTECH=1, and equation (10) reduces to
13
MATECH IBTECH TECH = (11)

IBTECH measures the shift in the isoquant from period t to
t+1 due to changes in technology holding the level of output constant
at . The definition of Hicks' neutral, capital- or labour-deepening
technological change depends on, under constant capital-labour ratio,
the marginal rate of substitution of labour for capital (MRS
t
y
(
1
2
+ t
1 + t
LK
)
remaining constant, decreasing, or increasing (see Binswanger,
1974). Following Fare, Grosskopf, and Lee (1995) and Weber and
Domazlicky (1999) IBTECH is independent of outputs under CRS
when states produce a single output. Figure 2 describes how the
value of IBTECH and change in the capital-labour (K/L) ratio can be
used to identify the capital- or labour-deepening character of
technological change. Assume y=1, x
1
=labour (L) and x
2
=capital (K).
Let L
t
(1) represent the period t isoquant and , , and
Hicks' neutral, Hicks' labour-deepening (or capital-saving),
and capital-deepening (or labour-saving) from period t to t+1. A state
is observed to use the input vector in period t and
in period t+1 so that ( . If
IBTECH= 1, then . In
this case Oa=Of/Od, indicating Hicks' neutrality, since MRS
) 1 (
1 + t
n
L
) ,
t t
K
t
L) /
1 +
/ ) 1 ,
1 + t
x
) 1 (
1
1
+ t
L
L K ) / (
, (
1 + t t
i
D x
) 1 (
1
1
+ t
L
) 1 L
( = x
(
t
L = x
K
(
1 +
=
t
i
D
) ,
1 1 + + t t
K L
D
t
<
) 1 ) 1 , ( / ) 1 , (
1 + t t
i
t t
i
D x x
) 1 (
1
2
+ t
L
LK
does
not change. If the technology shifts instead to , then
(Ob/Oa)<(Of/Oc) and IBTECH<1. In this case, IBTECH<1 coupled
with the increase in the K/L ratio, indicates a capital-deepening (or
labour-saving) technological bias and decrease in the K/L ratio
indicates a labour-deepening technological bias. Finally, if the
technology shifts to , then (Ob/Oa)>(Of/Oe) and IBTECH>1.
Therefore, IBTECH>1 coupled with the increase in the K/L ratio
indicates a labour-deepening (or capital-saving) technological bias. In
other words, when the K/L ratio increases from period t to period t+1,
IBTECH<1 indicates a capital-deepening technological bias and
IBTECH>1 indicates a labour-deepening technological bias. Table 1
summarises the various kinds of input biased technological changes
that may occur.



14

Table 1: Input Biased Technical Change Direction

IBTECH>1 IBTECH= 1 IBTECH<1
t t
L K L K ) / ( ) / (
1
>
+

Labour-
deepening
Neutral Capital-
deepening
t t
L K L K ) / ( ) / (
1
<
+

Capital-
deepening
Neutral Labour-
deepening





Figure 2. Input Biased Technological Change
O
X1=Labour
X2=Capital
L2
Ln
L1
Lt
x t
x t+1
Lt(1)
L2,t+1(1)
Ln,t+1(1)
L1,t+1(1)
a
b
f
c d
e


15
III. Data and Discussion of Results



We calculate productivity and its components for fifteen major
Indian states
1
over the period of 1982-83 to 2000-01. The period up to
1990-91 is considered as pre-reform while the subsequent period is
regarded as post-reform. The data used in this study for calculating
productivity and its various components come from the Annual Survey
of Industries (ASI) for the relevant years. The manufacturing sector is
modelled as an industry producing a scalar output measured by the
gross value added at constant prices by employing the factor inputs,
labour and capital. Using gross value added at constant prices is a
common practice in the Indian empirical literature (e.g., Unel, 2003;
Ahluwalia, 1991; Balakrishnan and Pushpangadan, 1994; and Goldar,
1986). One advantage of using the gross value added rather than
gross output is that it allows comparison between the firms that are
using heterogeneous raw materials (Griliches and Ringstad, 1971).
The use of gross output in place of gross value added necessitates
the use of raw materials, which may obscure the role of labour and
capital in the productivity growth (Hossain and Karunaratne, 2004).
Another advantage is that use of gross value added accounts for
differences and changes in the quality of inputs (Salim and Kalirajan,
1999).

The input-output data covered by the ASI for individual states
are the aggregates of all establishments in the state. The number of
establishments covered by the Census varies widely across the
states. Therefore, following Ray (1997 & 2002), state level input-
output quantity data for the 'representative establishment' are
constructed by dividing the state-level aggregate values of the
variables by the number of establishments covered in the state. The
advantage of using the state level average data is that it imposes
fewer restrictions on the production technology.
2
Moreover, such kind
of averaging reduces the effects of random noise due to
measurement errors in inputs and outputs.

Except for the labour input, which is measured by the total
number of persons engaged in an average establishment, ASI reports
fixed capital stock and gross value added data in value terms.
Nominal values of gross value added were deflated by the wholesale
price index for manufactured goods. Fixed capital stock was deflated
16
by the price index for new machinery and transport equipment. Both
of these variables are measured at 1981-82 prices at all-India level.
3

Measuring the capital stock input is rather problematic. In many
studies capital stock is measured by the book value of fixed assets
while in others its flow is measured by summing rent, repairs, and
depreciation expenses or perpetual inventory created from annual
investment data. Needless to point out that each of these measures
has its own shortcomings. For example, the book value and perpetual
inventory methods do not address the question of capacity utilisation,
whereas the flow measure may be questioned on the ground that the
depreciation charges in the financial accounts may be unrelated to
actual depreciation of hardware. Thus following Ray (2002) in the
present study, capital stock is measured by the book value of fixed
assets. But to the extent that the true capital input is distorted, it is
distorted uniformly in all the states. Therefore, the relative
performance of states should not be affected seriously by this
shortcoming.

Contemporaneous CRS, VRS, and NRS technology sets
were constructed from the state level input-output data for each year.
Own period input distance functions were computed for each year
under the CRS, VRS, and NRS assumptions. Similarly, cross period
input distance functions were also computed for every pair of
adjacent years. Yearly MALM and its components were computed for
all the states in adjacent years.

Technical Efficiency Estimates

Since the basic components of Malmquist index is related to
measures of technical efficiency, we first report these results. Values
of unity imply that the state is on the isoquant in the associated year
while those exceeding unity imply that it is above the isoquant or
technically inefficient. Table 2 provides the geometric means of the
components of OTE for the 15 states. On average, inputs employed
in state manufacturing could have been contracted by 26.6 percent=(
1-1/1.362)100, 28 percent and 25 percent in the overall, pre-reform
and post reform
4
periods respectively. The average output loss due to
pure technical inefficiency was 13 percent, 16 percent and 11
percent, and the output loss due to scale inefficiency was 33 percent,
35 percent and 32.5 percent respectively for all the three periods. It
implies that the pro-market reform has helped in increasing the
technical efficiency of Indian states.
17
The state-wise results of technical efficiency are presented in
Table 3. Maharashtra, which is known to be industrially developed, is
the most efficient among the states under consideration. It was on the
isoquant during the pre-reform era and experienced only 1.2 percent
overall technical inefficiency during the post-reform era and all the
inefficiencies were due to input scale inefficiency. The table also
reveals that the most inefficient states in terms of overall technical
efficiency were Punjab in the pre-reform period, West Bengal in the
post-reform period, and Andhra Pradesh over the entire period of
study. Except for six states (Assam, Kerala, Madhya Pradesh,
Maharashtra, Tamilnadu and West Bengal), all others experienced
gains in OTE in the post-reform period in comparison to the pre-
reform years. Here it should be noted that the inefficiency in majority
of the states is due to scale.

Table 4 reports the states operating in the range of CRS,
decreasing returns to scale (DRS) and increasing returns to scale
(IRS) year-wise. To determine the scale of returns a state operates in,
following Grosskopf (1986), we estimate technical efficiency under
CRS (T
CRS
), VRS (T
VRS
) and NRS (T
NRS
).
5
In our study most of the
states were operating in the range of IRS. Maharashtra operates in
the range of CRS in 15 out of 19 years, while Assam operates in the
same range in the pre- and post-reform years. Thus the operation of
most of the states in the range of IRS helps to explain the cause of
inefficiency observed.

Total Factor Productivity Estimates

Next we calculate the Malmquist productivity index along with
its components for each state. Instead of presenting the year-wise
disaggregated results, we turn to a summary description of the
average performance of all states.
6
Recall that if the value of
Malmquist index or any of its components is greater than unity, then it
denotes regression or deterioration in performance between any two
adjacent years. Also it may be necessary to note that these measures
capture the performance relative to the best practice one.

Table 5 reports the annual average values of Malmquist index
along with those obtained from its decomposition. It can be seen from
the table that the Malmquist index does not show a steady upward
trend. On the contrary, it indicates productivity decline in 1983-84,
1987-88, 1989-90, 1991-92, and again in 2000-01. In the midst of
18
such variations, however, the average annual rate of productivity
growth is higher during the post-reform period than in its preceding
regime. The TFP has increased by 1.7 percent and 3.0 percent per
annum during pre- and post-reform years respectively. On average,
the improvement can be ascribed to technical progress (TECH) (0.4
percent and 2.8 percent respectively) and efficiency improvement
(OTECH) (1.2 percent and 0.2 percent respectively). Further
decomposition of technical progress indicates that during these two
periods the magnitude of pure technical progress (MATECH) was -0.2
percent and 1.6 percent whereas that of IBTECH was 0.6 percent and
1.2 percent. A decomposition of efficiency improvement reveals that
in the pre-reform years, the efficiency improvement was governed by
the gain in pure technical efficiency (PTEC) (1.7 percent), while in the
subsequent period, the improvement in scale efficiency (ISEC) and
pure technical efficiency change equally influenced the gain in the
overall efficiency change. In nutshell, it can be said that in the pre-
reform period, three-fourth of improvement in the total factor
productivity was governed by the technical efficiency improvement,
whereas in the post-reform years it was the technical progress that
governed the growth in total factor productivity.

Results of the present study confirm those of Ray (2002). Ray
found that TFP increased from 0.17 percent per year during the pre-
reform era (upto 1990-91) to 1.45 percent per year during the post-
reform years. Although the rates of growth in TFP obtained by Ray
(2002) are different from the ones in the present study, direction of
change in both is found to be same, that is, positive growth in the
decades of 1980s and 1990s. Another feature common to both the
studies is higher growth rate of TFP in the post-reform period
compared to its preceding period. The difference in magnitude of
estimated growth rates in TFP might be due to difference in
orientation of the methodology. While Ray used the output orientation
in the measurement of Malmquist index, the present study employed
input distance functions for that purpose.

The performance of TFP in each state is given in Table 6 as
average annual rates of growth over the period 1982-83 to 2000-01.
The table also contains the TFP growth rates for the pre- and post-
reform periods. As it is difficult to summarise the disaggregated
results, we include some of their general features. The disaggregated
results reveal widespread regional variation in productivity changes.
In the study period, 9 out of 15 states experienced productivity
19
improvement. While in the pre-reform period 11 states witnessed
growth in TFP, the corresponding number was 10 in the post-reform
years. In the pre-reform period four states (Orissa, 9.8 percent;
Rajasthan, 7.8 percent and Uttar Pradesh, 7.1 percent) witnessed the
growth in TFP more than 5 percent per year, whereas in the post-
reform years six states (Gujarat, 10.3 percent; Rajasthan, 9.8 percent;
Madhya Pradesh, 9.7 percent; Orissa, 6.5 percent; Uttar Pradesh, 5.9
percent and Maharashtra, 5.04 percent) registered more than 5
percent annual change in TFP. The table reveals that the variation in
TFP has decreased in the post-reform period in comparison to its
preceding years. The coefficient of variation in its growth rate among
the states was 301.7 percent and 187.5 percent during the pre- and
post-reform periods.

The most significant factor behind the improvement in TFP
during period of study could be found in technical progress as evident
from the positive rates of technical change in eight states. Here it
should be noted (see, Table 6) that in the pre-reform era, nine states
exhibit technical regress, whereas in the post-reform period only the
states of Andhra Pradesh (-1.4 percent), Assam (-4.8 percent),
Karnataka (-1.9 percent), Kerala (-4.4 percent), Punjab (-0.09
percent), Tamilnadu (-1.35 percent) and West Bengal (-1.7 percent)
exhibited technological regression. Also during the decade of 1980s
the contribution of OTE improvement was substantial. But in the
1990s, it was technical progress that contributed significantly to the
TFP progress. During both the decades, the progress in TFP in
Punjab was only due to the presence of catch-up effect while it was
due to innovation in Maharashstra.

Table 7 shows the decomposition of overall technical
efficiency change (catch-up effect). During the entire period, out of 15
states, 11 exhibit the presence of catch-up effect (positive change in
OTECH). In four states the contribution of change in PTE was zero,
while in another two this effect was negative. The remaining 9 states
witnessed a positive change. In the pre-reform period, the highest
catch-up effect was in Orissa, whereas in Andhra Pradesh it was
noticed during the post-reform years. In Orissa, the change in scale of
production and improvement in PTE equally contributed to the
positive effect, while in Andhra Pradesh the positive changes were
due to improvement in scale effects only.

20
Table 8 provides the decomposition of technical change into
pure and input-biased changes. The table also provides the annual
average estimates of change in capital-labour ratio. During the pre-
reform period, Uttar Pradesh exhibits the highest growth in the pure
technical change (3.2 percent) followed by Orissa (1.7 percent) and
Rajashtan (1.7 percent). It is Assam which records the highest
negative change in the magnitude of pure technical change during the
decade of 1980s. In the decade of 1990s, Orissa (9.3 percent),
Rajasthan (8.7 percent), Madhya Pradesh (8.2 percent), Uttar
Pradesh (8 percent), Gujarat (6.1 percent) and Bihar (4.6 percent)
had the highest growth rates in pure technical progress. During this
decade, seven states witnessed a negative change in pure technical
progress, while Maharashtra and Punjab, experienced stagnation.

Recall that if capital-labour ratio increases and IBTECH<1,
then it implies capital-using technical bias. On the other hand,
IBTECH>1 implies labour-using technical bias. If the capital-labour
ratio decreases, then IBTECH<1 indicates labour-using bias and
IBTECH>1 shows capital-using technical bias. In the present analysis
except for 1991-92, 1997-98 and 2000-01, capital-labour ratio has
increased over its previous year (Table 5). During the pre-reform era,
the average annual change in the capital ratio was 6.2 percent,
whereas it was 9.4 percent during the post-reform period. Moreover,
during both of the periods, the value of IBTECH was less than unity
implying the presence of capital using technical bias in Indian
manufacturing. This finding concurs with the finding of Pradhan and
Barik (1999). Pradhan and Barik also finds the absence of labour-
using technical progress in Indian manufacturing. Moreover, the
manufacturing sector exhibits neutral technical bias for two years
(1987-88 and 1994-95) and labour-using technical bias for four years.
But we do not observe any consistent trend in input biased technical
change either in favour of capital or labour (Table 5).

State-wise picture of the change in technical bias can be
judged from Table 8. The table reveals that all the states witnessed
an increase in average capital-labour ratio. In the post-reform era, all
except Kerala, exhibit capital-using technical bias. In Kerala the
technical bias was almost neutral. The finding on capital-using
technical bias of the 1990s is a significant departure from the
preceding decade when seven out of 15 states (Karnataka, Kerala,
Madhya Pradesh, Orissa, Punjab, Rajasthan and West Bengal)
exhibited almost neutral technical progress. In one of the states (Uttar
21
Pradesh), however, technical progress was slightly in favour of
labour.

Innovative States and Convergence

It should be noted that the technical progress change index
for any particular state between two adjacent years merely depicts
the shift in the isoquant at the output level observed for that state. A
value of technical change index less than unity does not necessarily
imply that the state under consideration did actually push the overall
isoquant inward. Thus in order to determine the states that were
shifting the frontier or were 'innovators' (see Fare et al., 1994), the
following three conditions are required of various input distance
functions for a given state k:

(a) ; 1
1
<
+ t
t
TECH
(b) ( ) 1 ,
1 1
<
+ + t t t
i
D y x ;
(c) ( ) 1 ,
1 1 1
=
+ + + t t t
i
D y x .

The condition (a) indicates that the isoquant shifts in case of
fewer inputs for the given level of output. With a given output vector,
in period t+1 it is possible to decrease input bundle relative to period
t. This measures the shift in the relevant portions of the isoquant
between periods t and t+1 for a given state. The condition (b)
indicates the production in period t+1 that occurs outside the isoquant
of period t (i.e., technical change has occurred). It implies that the
technology of period t is incapable of producing the output vector of
period t+1 with the input vector of period t+1. Hence the value of input
distance function ( )
1 1
,
+ + t t
y x relative to the reference technology of
period t is less than one. The condition (c) specifies that the state
must be on the isoquant in period t+1.Table 9 shows the states that
were innovator. Out of 18 two-year periods, Maharashtra and Assam
shifted the isoquant five times each, while Bihar achieved the feat
thrice and Gujarat twice.

In a recent study Aghion et al. (2003) finds that pro-market
reform give rise to larger increase in productivity in the states that
were closer to the frontier when the reforms were initiated. So, the
growth enhancing effect should be smaller for the representative firm
22
in the state that is farther from the frontier. On the other hand, the
convergence theory could be restated in terms of the relationship
between productivity and technical inefficiency. Such a relationship
would state that the states that were near the production frontier
would record a lower level of productivity growth than those farther
away. Therefore, the positive relationship between productivity level
and lagged technical inefficiency would indicate the presence of
convergence hypothesis (Lall et al., 2002).

In the present exercise we find that the states that were
closer to the frontier in the efficiency estimation at the beginning of
post-reform are not having the higher growth rate in TFP index. The
correlation coefficient between the technical efficiency scores in
1991-92 and cumulative Malmquist index in 2000-01 (assuming that
the value of Malmquist index is unity in 1991-92) is 0.22, which is
statistically significant at 95 percent level of confidence interval.
Moreover, we find that the states that were farther from the frontier in
1991-92 have gained not only due to increase in technical efficiency
but also have experienced the higher growth rate of technical
progress. This indicates that there is a tendency towards
convergence in the productivity growth rates across states. This
finding concurs with Ray (2002) and does not conform to Aghion et al.
Here, it should be noted that if a state is technically efficient and is on
the production frontier, then it is maximising its productive potential
and there is little to be gained from adopting technology or knowledge
from elsewhere. But only the states that were technically efficient
were innovative in the sense that they were able to shift the isoquant
inwards (see Table 9). It implies that although there is a tendency of
convergence in manufacturing productivity growth among Indian
states during the post-reform period, only those that are efficient at
the beginning of the reform remain innovative.


23
IV. Conclusions


In this paper we use state level data on manufacturing from
the Annual Survey of Industries for the years 1982-93 through 2000-
01 to measure the Malmquist index of productivity growth. The index
is also decomposed into technical change and efficiency change. The
efficiency change is further decomposed into pure technical efficiency
and input scale efficiency changes. The technical change is
decomposed into magnitude of pure technical change and input-
biased technical change. Such a decomposition of technical change
helps in identifying the directions of biases in favour of labour or
capital.

We found that in the pre-reform period TFP had grown at the
rate of 1.7 percent per year while in the post-reform era the
corresponding growth rate was 3 percent. While pre-reform periods
growth rate in TFP was due to gains in technical efficiency, in the
post-reform era it was influenced by the technical progress. Another
interesting result of the present exercise is the nature of technical
progress in Indian manufacturing. It was seen that the capital intensity
of Indian firms is increasing in the recent years.

Although regional differences in TFP persist, it appears that
the variation has declined in the post reform period. Majority of the
states tried to be nearer to the isoquant in post-reform era in
comparison to the pre-reform years. Most of the states are also
operating under the increasing returns to scale and the gain in TFP in
the post-reform era was due to gain in technical progress. In contrast,
in the pre-reform period it was due to efficiency improvement. During
the 1990s, capital intensity of the manufacturing sector seemed to
have increased as the technical progress was in favour of capital. The
states which were exhibiting either neutral or labour-using technical
bias in the pre-reform period also show capital-using technical
change during the post-reform era. It is also found that although there
is a tendency of convergence in terms of TFP growth rate among
Indian states during the post-reform era, only those that were
technically efficient at the beginning of the reform remained
innovative.

24
Beyond measuring of state TFP growth rates, the present
analysis demonstrates the richness of linear programming technique
that allows for an investigation of important research questions on the
underlying processes that influence TFP growth. Notwithstanding the
striking feature of the techniques used here, data limitations involved
in estimation remains an important factor. It is, therefore, necessary to
be cautious while applying these results to policy formulation.
25
References



Afriat, S. N. 1972. "Efficiency Estimation of Production Function",
International Economic Review, 13: 568-98.
Aghion, P., R. Burgess, S. Redding, and F. Zilibotti, 2003. "The
Unequal Effects of Liberalization: Theory and Evidence from
India", Unpublished, London School of Economics, London.
Ahluwalia, I.J. 1991. Productivity and Growth in Indian
Manufacturing, New Delhi: Oxford University Press.
Ahluwalia, I.J. 1995. India: Industrial Development Review, The
Economist Intelligence Unit and UNIDO.
Balakrishnan, P., and K. Pushpagandan, 1994. Manufacturing
Industry: A Fresh Look, Economic and Political Weekly,
October: 2028-35.
Binswanger, H. 1974. "A Cost Function Approach to the
Measurement of Elasticities of Factor Demand and
Elasticities of Substitution", American Journal of Agricultural
Economics, 56: 37786.
Burgess, R., and A. J. Venables, 2003. Towards a Microeconomics
of Growth", London School of Economics, London (mimeo).
Caves, D.W., L.R. Christensen, and W.E. Diewert, 1982. The
Economic Theory of Index Numbers and the Measurement of
Input, Output, and Productivity, Econometrica, 50: 1993-40.
Das, D. K. 2003. Quantifying Trade Barriers: Has Trade Protection
Declined Substantially in Indian Manufacturing, Working
Paper No. 105, Indian Council for Research on International
Economic Relations, New Delhi.
Fare, R., E. et.al., 1997. "Biased Technical Change and Malmquist
Productivity Index" Scandinavian Journal of Economics, 99:
119-27.
Fare, R., S. Grosskopf, C. A. K. Lovell, 1994. Production Frontiers.
Cambridge: Cambridge University Press.
Fare, R., et.al., 1994. "Productivity Growth, Technical Progress, and
Efficiency Change in Industrialised Countries" American
Economic Review, 84(1): 66-83.
Fare, R., S. Grosskopf, and W.F. Lee, 1995. "Productivity and
Technical Change: The Case of Taiwan", Southern Illinois
University (mimeo).
26
Fare, R. and D. Primont, 1995. Multi-Output Production and Duality:
Theory and Applications. Boston: Kluwer Academic
Publishers, Boston.
Foster, A. D., and M.R. Rozenzweig, 2003. Agricultural
Development, Industrialization and Rural Inequality,
unpublished, Harvard University, Cambridge, Massachusetts.
Goldar, B. N. 1986. Productivity Growth in Indian Industry. New Delhi:
Allied Publishers.
Goldar, B. N. 2004. "Productivity Trends in Indian Manufacturing in
the Pre and Post Reform Periods," Working Paper No. 137,
Indian Council for Research on International Economic
Relations, New Delhi.
Griliches, Z. and V. Ringstad, 1971. Economies of Scale and Form of
the Production Function. Amsterdam: North-Holland
Publishing Company.
Grosskopf, S. (1986) "The Role of the Reference Technology in
Measuring Productive Efficiency", The Economic Journal, 96:
499513.
Hossain, M. A. and N. D. Karunaratne, 2004. "Trade Liberalization
and Technical Efficiency: Evidence from Bangladesh
Manufacturing Industries" The Journal of Development
Studies, 40(3): 87-114.
Lall, P., A.M. Featherstone and D.W. Norman, 2002. Productivity
Growth in the Western Hemisphere (1978-94): the Caribbean
in Perspective, Journal of Productivity Analysis, 17: 213-231.
Pradhan, Gopinath and K. Barik, 1999. "Sustainability of Output
Growth in Indian Manufacturing: A Decomposition Analysis of
Selected Industries", Paper presented at the 1999 Annual
meeting of the Australian Econometric Society, University of
Technology, Sydney.
Ray, S.C. 1997. "Regional Variation in Productivity Growth in Indian
Manufacturing: A Non-parametric Analysis", Journal of
Quantitative Economics, 13: 73-94.
Ray, S.C. (2002) "Did India's Economic Reforms Improve Efficiency
and Productivity? A Non-parametric Analysis of the Initial
Evidence from Manufacturing", Indian Economic Review, 37:
23-57.
RBI 2004. Report on Currency and Finance, 2002-03, New Delhi.
Rodrik, Dani and Arvind Subramanian, 2004. "From 'Hindu Growth' to
Productivity Surge: The Mystery of the Indian Growth
Transition", IMF Working Paper WP/04/77, International
Monetary Fund, Washington DC.
27
Salim, R.A. and K. P. Kalirajan, 1999. "Sources of Output Growth in
Bangladesh Food Processing Industries: A Decomposition
Analysis" The Developing Economies, 37: 355-374.
Unel, B. 2003. Productivity Trends in Indias Manufacturing Sectors
in the Last Two Decades, IMF Working Paper, WP/03/22,
International Monetary Fund, Washington DC.
Weber, W.L. and B. R. Domazlicky, 1999. "Total Factor Productivity
Growth in Manufacturing: A Regional Approach Using Linear
Programming" Regional Science and Urban Economics, 29:
105-122.
28
Table 2: Efficiency Results, Geometric Means (yearwise)

Year Overall
Technical
Efficiency
Pure
Technical
Efficiency
Input Scale
Efficiency
1982-83 1.448 1.257 1.317
1983-84 1.273 1.160 1.235
1984-85 1.310 1.130 1.289
1985-86 1.507 1.176 1.498
1986-87 1.348 1.150 1.340
1987-88 1.338 1.125 1.310
1988-89 1.437 1.179 1.417
1989-90 1.422 1.131 1.407
1990-91 1.414 1.105 1.374
1991-92 1.296 1.079 1.281
1992-93 1.391 1.120 1.346
1993-94 1.505 1.149 1.505
1994-95 1.369 1.132 1.346
1995-96 1.282 1.102 1.274
1996-97 1.282 1.103 1.281
1997-98 1.343 1.071 1.332
1998-99 1.316 1.154 1.310
1999-00 1.361 1.145 1.343
2000-01 1.275 1.089 1.249
Pre-reform 1.387 1.156 1.352
Post- reform 1.340 1.114 1.325
Overall 1.362 1.134 1.338
29
Table 3: Efficiency Results, Geometric Means (statewise)

Overall Technical Efficiency
______________________
Pure Technical Efficiency
____________________
Input Scale efficiency
____________________
States
Overall Pre-
reform
Post-
reform
Overall Pre-
reform
Post-
reform
Overall Pre-
reform
Post-
reform
Andhra Pradesh 1.840 1.917 1.773 1.032 1.011 1.052 1.824 1.917 1.744
Assam













1.037 1.002 1.070 1.017 1.000 1.033 1.035 1.002 1.066
Bihar 1.120 1.126 1.114 1.074 1.029 1.117 1.068 1.048 1.086
Gujarat 1.218 1.264 1.173 1.042 1.069 1.017 1.217 1.262 1.173
Haryana 1.371 1.445 1.301 1.209 1.252 1.168 1.361 1.435 1.292
Karnataka 1.196 1.286 1.112 1.097 1.134 1.062 1.194 1.282 1.112
Kerala 1.376 1.364 1.429 1.127 1.204 1.061 1.365 1.352 1.429
Madhya
Pradesh
1.303 1.278 1.329 1.190 1.164 1.216 1.203 1.169 1.237
Maharashtra 1.019 1.013 1.025 1.000 1.000 1.001 1.012 1.000 1.025
Orissa 1.482 1.548 1.419 1.352 1.388 1.318 1.413 1.480 1.350
Punjab 1.775 1.935 1.629 1.105 1.119 1.090 1.775 1.935 1.629
Rajasthan 1.501 1.568 1.438 1.158 1.305 1.027 1.490 1.544 1.438
Tamil Nadu 1.354 1.281 1.432 1.052 1.078 1.027 1.354 1.281 1.432
Uttar Pradesh 1.527 1.690 1.379 1.265 1.406 1.138 1.520 1.676 1.379
West Bengal 1.642 1.482 1.819 1.476 1.302 1.674 1.541 1.315 1.805


30
Table 4: Returns to Scale in States

Year Constant
Returns to
Scale
Decreasing Returns to
Scale
Increasing Returns to Scale
1982-83 TN BIH, GUJ, HAR, KAR,
KER, MP, MAH, ORI,
RAJ, UP, WB
AP, ASS, PUN,
1983-84 ASS, BIH, MAH,
TN
MP, WB AP, GUJ, HAR, KAR, KER, ORI,
PUN, RAJ, UP
1984-85 ASS, MAH WB AP, BIH, GUJ, HAR, KAR, KER,
MP, ORI, PUN, RAJ, TN, UP
1985-86 ASS, MAH - AP, BIH, GUJ, HAR, KAR, KER,
MP, ORI, PUN, RAJ, TN, UP, WB
1986-87 ASS, MAH - AP, BIH, GUJ, HAR, KAR, KER,
MP, ORI, PUN, RAJ, TN, UP, WB
1987-88 ASS, MAH BIH, MP, WB AP, GUJ, HAR, KAR, KER, ORI,
PUN, RAJ, TN, UP
1988-89 ASS, GUJ BIH, MP, MAH, ORI AP, HAR, KAR, KER, PUN, RAJ,
TN, UP, WB
1989-90 ASS, MAH BIH, ORI AP, GUJ, HAR, KAR, KER, MP,
PUN, RAJ, TN, UP, WB
1990-91 ASS, MAH MP, ORI AP, BIH, GUJ, HAR, KAR, KER,
PUN, RAJ, TN, UP, WB
1991-92 BIH, KAR, MAH ORI AP, ASS, GUJ, HAR, KER, MP,
PUN, RAJ, TN, UP, WB
1992-93 KAR, MAH MP, ORI AP, ASS, BIH, GUJ, HAR, KER,
PUN, RAJ, TN, UP, WB
31
Year Constant
Returns to
Decreasing Returns to
Scale
Increasing Returns to Scale
Scale
1993-94 ASS, BIH - AP, GUJ, HAR, KAR, KER, MP,
MAH, ORI, PUN, RAJ, TN, UP, WB
1994-95 KAR, MAH MP AP, ASS, BIH, GUJ, HAR, KER,
ORI, PUN, RAJ, TN, UP, WB
1995-96 ASS, MAH MP AP, BIH, GUJ, HAR, KAR, KER,
ORI, PUN, RAJ, TN, UP, WB
1996-97 BIH, GUJ, KAR KER, MAH, ORI AP, ASS, HAR, MP, PUN, RAJ, TN,
UP, WB
1997-98 BIH ORI AP, ASS, GUJ, HAR, KAR, KER,
MP, MAH, PUN, RAJ, TN, UP, WB
1998-99 ASS, BIH, GUJ,
MAH
ORI AP, HAR, KAR, KER, MP, PUN,
RAJ, TN, UP, WB
1999-00 ASS, MAH BIH AP, GUJ, HAR, KAR, KER, MP,
ORI, PUN, RAJ, TN, UP, WB
2000-01 MAH BIH, MP AP, ASS, GUJ, HAR, KAR, KER,
ORI, PUN, RAJ, TN, UP, WB
Note: Andhra Pradesh (AP), Assam (ASS), Bihar (BIH), Gujarat (GUJ), Haryana (HAR), Karnataka,
(KAR), Kerala (KER), Madhya Pradesh (MP), Maharashtra (MAH), Orissa (ORI), Punjab (PUN),
Rajasthan (RAJ), Tamilnadu (TN), Uttar Pradesh (UP) and West Bengal (WB)


32
Table 5: Malmquist Productivity Index and its Decomposition, Geometric Means (yearwise)

Year OTE-CH PTEC ISEC IBTE-CH MATE-CH TE-CH MALM (K/L)
T+1
/
(K/L)
T

1983-84 0.879 0.923 0.938 1.005 1.155 1.161 1.021 1.131
1984-85
















1.029 0.974 1.044 0.987 0.980 0.967 0.995 1.105
1985-86 1.151 1.040 1.163 0.996 0.851 0.847 0.975 1.065
1986-87 0.894 0.978 0.895 0.989 1.076 1.064 0.952 1.092
1987-88 0.992 0.978 0.978 1.001 1.014 1.016 1.008 1.059
1988-89 1.074 1.048 1.082 0.989 0.841 0.831 0.893 1.015
1989-90 0.990 0.959 0.993 0.993 1.024 1.017 1.006 1.012
1990-91 0.994 0.977 0.977 0.988 0.978 0.967 0.961 1.116
1991-92 0.917 0.976 0.932 0.995 1.149 1.144 1.048 0.972
1992-93 1.073 1.038 1.050 0.979 0.945 0.925 0.993 1.079
1993-94 1.082 1.026 1.119 0.983 0.900 0.884 0.957 1.101
1994-95 0.910 0.985 0.894 1.001 1.096 1.097 0.998 1.048
1995-96 0.936 0.974 0.946 0.993 1.054 1.047 0.980 1.161
1996-97 1.000 1.001 1.005 0.999 1.001 1.000 0.999 1.074
1997-98 1.048 0.971 1.040 0.996 0.931 0.927 0.971 1.121
1998-99 0.980 1.077 0.983 0.988 1.001 0.989 0.969 0.973
1999-00 1.034 0.992 1.025 0.958 0.799 0.766 0.792 1.435
2000-01 0.937 0.951 0.929 0.991 1.183 1.173 1.098 0.927

33

Year OTE-CH PTEC ISEC IBTE-CH MATE-CH TE-CH MALM (K/L)
T+1
/
(K/L)
T

Pre-reform 0.988 0.983 0.997 0.994 1.002 0.996 0.983 1.062
Post-reform

0.998 1.001 0.997 0.988 0.984 0.972 0.970 1.094
Overall 0.993 0.992 0.997 0.991 0.993 0.984 0.977 1.078
Note: OTECH: Overall technical efficiency change index; PTEC: Pure technical efficiency change
index; ISEC: Input scale efficiency change index; IBTECH: Input biased technological
change index; MATECH: Magnitude of pure technological change index; TECH:
technological change index; MALM: Malmquist productivity index; (K/L)
T+1
/(K/L)
T
: Change
in capital-labour ratio over previous year.
34
Table 6: Decomposition of Malmquist Index: Average Annual Percentage Changes (statewise)

Overall
____________________________
Pre-reform
_________________________
Post- reform
_____________________
States

OTECH

TECH

MALM

OTECH

TECH

MALM

OTECH

TECH

MALM
Andhra Pradesh 0.662 -0.809 -0.142 -4.666 -0.214 -4.890 5.719 -1.409 4.391
Assam









-1.360 -3.511 -4.918 -0.204 -2.210 -2.418 -2.529 -4.828 -7.479
Bihar 0.663 3.599 4.238 2.838 1.686 4.477 -1.561 5.475 3.999
Gujarat 1.224 4.504 5.673 -0.618 1.392 0.783 3.031 7.518 10.321
Haryana 0.071 1.063 1.133 -0.251 0.656 0.407 0.391 1.469 1.854
Karnat-aka -0.043 -1.096 -1.139 2.376 -0.310 2.073 -2.522 -1.887 -4.457
Kerala 0.635 -2.137 -1.488 -0.003 0.089 0.086 1.270 -4.412 -3.086
Madhya Pradesh 1.602 5.371 6.887 2.413 1.653 4.026 0.785 8.949 9.663
Maharashtra 0.472 2.757 3.217 0.943 0.425 1.363 0.000 5.035 5.035
Orissa 2.584 5.693 8.130 8.188 1.734 9.780 -3.362 9.492 6.449
Punjab 2.475 -0.080 2.397 3.218 -0.072 3.148 1.727 -0.088 1.640
Rajasthan 3.440 5.522 8.772 6.201 1.664 7.763 0.598 9.228 9.771
Tamil Nadu -1.217 -1.667 -2.905 -3.363 -1.987 -5.417 0.884 -1.349 -0.453
Uttar Pradesh 0.954 5.610 6.511 4.741 2.477 7.101 -2.983 8.642 5.917
West Bengal -1.726 -1.072 -2.817 -4.488 -0.480 -4.990 0.963 -1.667 -0.689
Note: OTECH: Overall technical efficiency change index; TECH: Technological change index;
MALM: Malmquist productivity index.
35
Table 7: Decomposition of Efficiency Change Index, Geometric Means (statewise)

Overall
_____________________
Pre-reform
_____________________
Post- reform
______________________
States
OTECH PTEC ISEC

OTECH PTEC ISEC OTECH PTEC ISEC
Andhra Pradesh 0.993 0.995 0.993 1.047 0.990 1.047 0.943 1.000 0.943
Assam 1.014 1.008 1.014 1.002 1.000













1.002 1.025 1.016 1.025
Bihar 0.993 1.000 1.000 0.972 1.000 1.000 1.016 1.000 1.000
Gujarat 0.988 0.983 0.989 1.006 0.969 1.008 0.970 0.998 0.970
Haryana 0.999 0.998 1.003 1.003 0.999 1.009 0.996 0.996 0.996
Karnataka 1.000 0.997 1.001 0.976 0.978 0.978 1.025 1.016 1.025
Kerala 0.994 0.983 0.994 1.000 0.976 1.001 0.987 0.991 0.987
Madhya Pradesh 0.984 1.000 1.000 0.976 1.023 1.027 0.992 0.977 0.974
Maharashtra 0.995 1.000 1.000 0.991 1.000 1.000 1.000 1.000 1.000
Orissa 0.974 0.980 0.983 0.918 0.923 0.923 1.034 1.042 1.046
Punjab 0.975 0.978 0.975 0.968 0.965 0.968 0.983 0.990 0.983
Rajasthan 0.966 0.961 0.973 0.938 0.928 0.952 0.994 0.996 0.994
Tamil Nadu 1.012 1.000 1.012 1.034 1.000 1.034 0.991 1.001 0.991
Uttar Pradesh 0.990 0.978 0.995 0.953 0.949 0.961 1.030 1.009 1.030
West Bengal 1.017 1.019 1.026 1.045 1.054 1.054 0.990 0.986 0.998
Note: OTECH: Overall technical efficiency change index; PTEC: Pure technical efficiency change index;
ISEC: Input scale efficiency change index.
36
Table 8: Decomposition of Technological Change, Geometric Means (statewise)

Overall
____________________________
Pre- reform
______________________________
Post-reform
_____________________________
States
IBTECH MATECH TECH (K/L)
T+
1
/(K/L)
T

IBTECH MATECH TECH (K/L)
T+1
/
(K/L)
T

IBTECH MATECH TECH (K/L)
T+1
/
(K/L)
T

Andhra Pradesh 0.994 1.015 1.008 1.092 0.994 1.008 1.002 1.165 0.993 1.021 1.014 1.023
Assam










0.961 1.077 1.035 1.128 0.965 1.060 1.022 1.150 0.958 1.094 1.048 1.106
Bihar 0.994 0.970 0.964 1.048 0.998 0.985 0.983 1.050 0.989 0.956 0.945 1.046
Gujarat 0.986 0.969 0.955 1.120 0.987 1.000 0.986 1.121 0.985 0.939 0.925 1.119
Haryana 0.985 1.004 0.989 1.094 0.993 1.001 0.993 1.118 0.978 1.008 0.985 1.070
Karnataka 0.998 1.013 1.011 1.103 1.002 1.001 1.003 1.092 0.994 1.025 1.019 1.115
Kerala 1.002 1.020 1.021 1.067 0.997 1.002 0.999 1.093 1.006 1.038 1.044 1.042
Madhya
Pradesh
0.995 0.951 0.946 1.041 0.998 0.985 0.983 1.071 0.992 0.918 0.911 1.012
Maharashtra 0.963 1.010 0.972 1.094 0.977 1.020 0.996 1.126 0.949 1.001 0.950 1.063
Orissa 0.999 0.944 0.943 1.099 1.000 0.983 0.983 1.167 0.997 0.907 0.905 1.035
Punjab 0.998 1.003 1.001 1.064 0.997 1.003 1.001 1.122 0.998 1.002 1.001 1.010
Rajasthan 0.997 0.947 0.945 1.066 1.000 0.983 0.983 1.084 0.995 0.913 0.908 1.049
Tamil Nadu 0.994 1.023 1.017 1.097 0.989 1.031 1.020 1.136 0.998 1.016 1.013 1.060
Uttar Pradesh 1.000 0.944 0.944 1.077 1.008 0.968 0.975 1.116 0.993 0.920 0.914 1.039
West Bengal 0.996 1.014 1.011 1.077 1.003 1.002 1.005 1.125 0.990 1.027 1.017 1.030
Note: IBTECH: Input biased technological change Index; MATECH: Magnitude of pure technological change index; TECH:
Technological change Index; MALM: Malmquist productivity index; (K/L)
T+1
/(K/L)
T
: Change in capital-labour ratio
over previous year.
37
Table 9: States Causing Inward Shift in Isoquant Over the
Previous Year
Year States
1983-84 -
1984-85 Maharashtra
1985-86 Assam, Maharashtra
1986-87 -
1987-88 Assam
1988-89 Assam, Gujarat
1989-90 -
1990-91 Maharashtra
1991-92 -
1992-93 Maharashtra
1993-94 Bihar, Assam
1994-95 -
1995-96 -
1996-97 Gujarat, Bihar
1997-98 Bihar
1998-99 Assam
1999-00 Maharashtra
2000-01 -



















38
Endnotes



1
The fifteen major states are Andhra Pradesh (AP), Assam (ASS), Bihar
(BIH), Gujarat (GUJ), Haryana (HAR), Karnataka (KAR), Kerala (KER),
Madhya Pradesh (MP), Maharashtra (MAH), Orissa (ORI), Punjab (PUN),
Rajasthan (RAJ), Tamilnadu (TN), Uttar Pradesh (UP) and West Bengal
(WB). These fifteen major states account for approximately 95 percent of
population and industrial output in the country and are therefore
representative.
2
The firm level input-output pairs are feasible, although not individually
reported. Therefore, by the assumption of convexity, the average input-output
bundle will always be feasible. The aggregate input-output bundle will be
feasible only under the condition of additivity of technology (Ray, 2002).
3
To the extent that price indices at the state levels deviate from the All-India
indices, the non-labour variables for individual states will be distorted. But
non-availability of price indices at the individual state level precluded a more
refined construction of data.
4
The terms pre-reform and pro-business reform are used synonymously as
they refer to same period in the present study. Like that the terms post-reform
and pro-market are used synonymously in the present study.
5
If T
CRS
=T
VRS
the state operates in the range of constant returns to scale
(CRS). If T
CRS
T
VRS
=T
NRS
the state operates in the range of decreasing
returns to scale (DRS). Finally, if T
CRS
=T
NRS
<T
VRS
the state operates in the
range of increasing returns to scale (IRS).
6
The disaggregated results for each state and year can be had from the
author on request.
39