Productivity growth of Indian manufacturing: panel estimation of stochastic production frontier.

AuthorRoy, Prasanta Kumar
PositionReport - Statistical data

Along with technological progress, changes in technical efficiency, scale effect and changes in allocative efficiency can also contribute to productivity growth. The present study used the stochastic frontier production approach to decompose sources of TFPG of organized manufacturing into technological progress, changes in technical efficiency, scale effect and changes in allocative efficiency during 1981/ 82-2010/11. According to the results, technical inefficiency, though exists, is time invariant and technological progress (TP) became the main contributor to TFPG of the sector during 1981/82-2010/11. Furthermore, TFPG of organized manufacturing in most states in India declined during the post-reform period due to the decline in technological progress.


Most of the studies relating to productivity growth in Indian manufacturing considered technological progress to be the unique source of total factor productivity growth (TFPG) and it can be shown by the shift in production possibility frontier over time. However, some recent studies (Aigner, Lovell & Schmidt, 1977; Meeusen & Van den Broeck, 1977) have used a stochastic frontier production model that allows decomposing TFPG into two components: technological progress (TP) and change in technical efficiency (TE). Later, studies by, among others, Nishimizu and Page (1982), Kumbhakar (1990), Fecher and Perelman (1992), Domazlicky and Weber (1998) have been focusing on decomposition of TFPG using Stochastic Frontier Approach. Some studies have extended their analyses to deal with the issues of scale effect and allocative efficiency effect. By applying a flexible stochastic translog production function, Kumbhakar and Lovell (2000), Kim and Han (2001) and Sharma et al (2007) decomposed TFPG into four components: changes in technological progress, changes in technical efficiency, economic scale effect and changes in allocative efficiency.

In the present study we have used the stochastic production frontier approach to decompose TFPG of the total organized manufacturing industries in India and fifteen major industrialized states assuming that manufacturing industries in the states are not able to fully utilize the existing resources and technology because of various non-price and organizational factors that might have led to technical inefficiencies in production. Using panel data of the organized manufacturing industries of the states as well as all-India over a period from 1981-82 to 2010-11, pre-reform period (1981-82 to 1990-91), post-reform-period (1991-92 to 2010-11) and also during the two decades in the post-reform period (1991-92 to 2000-01 and 200102 to 2010-11], we have decomposed TFPG of the organized manufacturing sector into technological progress, changes in technical efficiency, scale effect and allocative efficiency effect. This decomposition of TFPG of Indian manufacturing has also been made for the pre-and post reform periods, and also for different decades in order to examine the trend and variations in the TFPG and its different components, during these sub-periods.

Decomposition of TFPG

Stochastic frontier model was first developed by Aigner, Lovell and Schmidt (1977) and Meeusem Van den Broeck (1977) and it was later extended by Pit and Lee (1981), Schmidt and Sickles (1984), Kumbhakar (1990) and Battese and Coelli (1992) to allow for panel data regression estimation in which technical efficiency and technological progress vary over time and across different production units. Here we discuss the methodology used in the efficiency literature for estimating stochastic production frontier and the decomposition of TFPG. We start with a standard stochastic frontier model that can be estimated using panel data. The model is written as:

[] = f([], [beta], t) exp ([] - [])--(1)

where [] represents the output of the i-th production unit (i=1 ... N) at time t (t=1 ... T); f(x) denotes the production frontier of the i-th production unit at time 't'; [] is the input vector used by the i-th production unit at time 't'; [beta] is the vector of technology parameter; 't' is the time trend serving as a proxy for technological change; [],s are symmetric random error terms independently and identically distributed with mean zero, and variance [[sigma].sup.2.sub.v], used to capture random variations in output due to external shocks like weather, strikes, lock-out etc. []'s are non-negative random variables associated with technical inefficiency of production, which are assumed to be independently distributed, such that []'s are obtained by truncation at zero of the normal distribution with mean i and variance [[sigma].sup.2.sub.u].

Taking logs of equation (1) and totally differentiating it with respect to time give the growth rates of output at time't' for the i-th production unit as shown below:


The first and second terms on the right-hand side of equation (2) measure the change in frontier output caused by technological progress (TP) and change in input use respectively. From the formula of output elasticity of input 'j', [[epsilon].sub.j] = [partial derivative]1nf ([],[beta],t)/ [partial derivative]n[x.sub.jt] the second term can be expressed as [[summation].sub.j][[epsilon].sub.j][[??].sub.jt]. where a dot over a variable indicates its rate of change. Thus, equation (2) can be written as


Thus, the overall productivity change is not only affected by TP and changes in input use, but also by changes in technical inefficiency. TP will be positive if the exogenous change in technology shifts the production frontier upward and it will be negative if it shifts the production frontier downward. On the other hand, if d[]/dt is negative, TE improves and if d[]/dt is positive, TE deteriorates over time; and -d[]/dt can be interpreted as the rate at which an inefficient producer catches up with the production frontier.

To examine the effect of TP and a change in efficiency on TFPG, let us express TFPG as output growth unexplained by input growth:


where [S.sub.j] denotes the observed expenditure share of input 'j'.

By substituting equation (3) into equation (4), we get


where [??][[summation].sub.j] = [[epsilon].sub.j] denotes the measurement of returns to scale (RTS) and [[lambda].sub.j]=[[summation].sub.j]/[epsilon]. The last component in equation (5) measures inefficiency in resource allocation resulting from the deviation of input prices from the value of their marginal products. Thus, in equation (5), TFP growth is decomposed into: i) TP that measures the shift in production frontier over time; ii) technical efficiency change (-d[]/dt) that measures the shift in production towards the known production frontier; iii) effect of scale change [([??]-1) [[summation].sub.j][[lambda].sub.j], [[??].sub.jt]] which shows the amount of benefit a production unit can derive from economies of scale through access to a larger market and iv) the allocative efficiency change denoted by [[summation].sub.j]([[lambda].sub.j]-[S.sub.j])[[??].sub.jt]. This last component captures the impact of deviations of inputs' normalized output elasticities from their expenditure shares (Kumbhakar & Lovell, 2000).

Model Specification

In our empirical analysis, we opt for a parametric approach by considering the time varying stochastic production frontier, originally proposed by Aigner, Lovell and Schmidt (1977) and Meeusen and Van den Broeck (1977), in translog form as


In equation (6), [] is the observed output, 't' is the time variable and 'x' variables are inputs, subscripts j and k index of inputs. The efficiency error, [], accounting for production loss due to unit-specific technical inefficiency, is always greater than or equal to zero and assumed to be independent of the random error; [], the random error which is assumed to have the usual properties (~iidN(0, [[sigma].sup.2.sub.v])).

The translog production frontier as specified in equation (6) is rewritten for two inputs--labor (L) and capital (K) in the following form:


where [], [] and [] are respectively the value added, labor input, and capital input for the aggregate manufacturing industry in state 'i' at time 't'; The distribution of technical inefficiency effects, [], is taken to be non-negative truncation of the normal distribution N([mu], [[sigma].sup.2].sub.u]), following Battese & Coelli (1992), to take the form as

[] = [[eta].sub.t][u.sub.i] =[u.sub.i] exp(-[eta][t-T]), i= 1, ..., N; t=1, ..., T--(8)

Here, the unknown parameter q represents the rate of change in technical...

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