Analyzing the Sources of Misallocation in
Indian Manufacturing: A Gross-Output
Approach
Sujana Kabiraj∗

It is well established that misallocation of factor resources lowers productivity.
in questo documento, I use data from both formal and informal firms to study
distortions in input and output markets as sources of misallocation in the
Indian manufacturing sector. My work extends the seminal work of Hsieh and
Klenow (2009). I consider output, capital, raw material, energy, and service
sector distortions in a monopolistically competitive framework to measure
the aggregate dispersion in total factor revenue productivity (TFPR). I also
decompose the variance in TFPR and show that raw material and output
distortions play a major role in defining aggregate misallocation.

Keywords: distortion, Indian manufacturing, misallocation, productivity
JEL codes: E10, O41, O47

IO. introduzione

According to the World Bank, the per capita income of the United States
(US) era 30 times that of India in 2017. Explaining such differences is one of the
fundamental problems in growth economics. Klenow and Rodriguez-Clare (1997)
and Hall and Jones (1999) demonstrate that the disparity in total factor productivity
(TFP) is the primary source of cross-country income differences. In this context,
another debate is about the sources of TFP differences among rich and poor nations.
Banerjee and Duflo (2005), Restuccia and Rogerson (2008), and Hsieh and Klenow
(2009) argue that in poor countries, some TFP differences are generated from a
misallocation of resources across firms. in questo documento, I follow the aforementioned
notion that resource misallocation is a primary source of variation in TFP. I include
intermediate inputs such as raw materials, energy, and services into the model of
Hsieh and Klenow (2009) to obtain the extent of misallocation that originates from
factor market distortions in a developing country such as India.

∗Sujana Kabiraj: University of Wisconsin-Stevens Point, stati Uniti. E-mail: skabiraj@uwsp.edu. I am grateful to
Jenny Minier of the University of Kentucky for providing the data used for the empirical analysis. I thank Areendam
Chanda and other members of the faculty at Louisiana State University for their valuable comments as well as the
managing editor and anonymous referees for helpful suggestions. The Asian Development Bank recognizes “China”
as the People’s Republic of China and “Bangalore” as Bengaluru. The usual ADB disclaimer applies.

Asian Development Review, vol. 37, NO. 2, pag. 134–166
https://doi.org/10.1162/adev_a_00152

© 2020 Asian Development Bank and
Asian Development Bank Institute.
Pubblicato sotto Creative Commons
Attribuzione 3.0 Internazionale (CC BY 3.0) licenza.

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Analyzing the Sources of Misallocation in Indian Manufacturing 135

When measuring physical TFP, one can adopt either of the two known
approaches to measuring a firm’s output: value added or gross output. The former
excludes intermediate inputs, whereas the latter includes them. The difference
between the two measures of TFP is more pronounced at the firm or industry
level rather than in aggregate output. Gullickson and Harper (1999); van der Wiel
(1999); Hulten, Dean, and Harper (2001); and Cobbold (2003) have demonstrated
the benefits of the gross-output approach over the value-added method. IL
productivity manual published by the Organisation for Economic Co-operation and
Development (2001) concludes that the gross-output approach is more appropriate
for productivity measurement because it reduces productivity measurement bias.
Based on these findings, I extend the Hsieh–Klenow model to measure productivity
using the gross-output approach by including raw material, energy, and service
sector intermediate inputs as factors of production.1 The inclusion of these factors
separately into the production process enables a more detailed representation of
factor misallocation. Inoltre, the decomposition of factor market distortions
by considering each factor input distortion separately provides a way to distinguish
the level of misallocation in each factor market and to identify the corresponding
potential gain from reallocation. I find that distortions in the output market and raw
material market explain the lion’s share of the variation in productivity.

TFP is a residual in the production process and is not observed directly.
Inoltre, it is difficult to measure firm-level TFP as the unit of production varies
across firms. Therefore, I measure the variation in total factor revenue productivity
(TFPR), which by definition is the product of output price and the physical TFP of
a firm. In the absence of any factor market misallocation, TFPR should be equal
for all firms within an industry. The intuition behind this claim is as follows: if a
firm has a high TFP, the marginal cost as well as the output price for that firm
will be proportionally lower compared to a low-TFP firm in a particular industry,
thus equalizing TFPR. Based on this intuition from Restuccia and Rogerson (2008)
and Hsieh and Klenow (2009), I build my empirical results by using data from
both formal and informal manufacturing sector firms in India for the survey year
2005–2006. In such a developing country, the informal sector plays an extensive
role in shaping the economy. The informal manufacturing sector in India consists of
around 17 million firms that provide 82% of total employment in that sector. Hence,
it seems appropriate to include informal sector data in the empirical analysis.

My work has the closest resemblance to the paper by Chatterjee (2011). IO
extend the paper by including service sector inputs and energy inputs in the model
separately. There exists a severe distortion in tariff rates in India’s energy sector. For
esempio, during 1999–2000, the industrial sector paid a tariff on electricity almost

1The KLEMS gross-output approach decomposes the factors of production into capital (K), labor (l), energy
(E), materiali (M), and services (S). The use of the KLEMS approach facilitates a decomposition of sources of growth
in the production of firms as well as the inputs used in such production.

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136 Asian Development Review

15 times higher than that paid by the agriculture sector and 2.1 times higher than
that paid by the domestic sector (Thakur et al. 2005). Although the Electricity Act of
2003 worked toward the reduction and gradual elimination of cross subsidies, come
distortions may have some impact on the cost of energy usage for small and large
firms as well as in formal and informal sectors. Besides, small firms often have to
use other electricity sources (such as generators), which in turn may impact resource
allocation differently in smaller firms as compared to their bigger counterparts.
Additionally, liberalization in the service sector in the early 1990s has resulted in
significant growth in the sector. According to Chanda and Gupta (2011), service
sector reforms along with external market linkages led to substantial growth in
the most liberalized service sectors such as business services, banking, insurance,
formazione scolastica, medical and health, and others. There is evidence in the literature that
can link service sector reform to productivity in the manufacturing sector. For
esempio, Arnold, Javorcik, and Mattoo (2011) demonstrate a positive relationship
between service sector reform and the performance of manufacturing firms in the
Czech Republic. In India, the cost share of service inputs is around 10% and that
of energy is around 7% for the manufacturing sector. Exclusion of these factor
inputs might lead to misleading measurements of output and productivity. I also
include distortions in the energy and service sectors to verify whether some of the
variation in firm-level TFPR is attributed to these factors. I find that there is very
little variation in TFPR due to energy input distortions and that misallocation in
service inputs is more pronounced in the dispersion of TFPR. D'altra parte, IO
find output and raw material distortions are the primary sources of misallocation in
the manufacturing sector. Another interesting result is that the distortions, Quando
taken from several factor markets, together reduce the variation in TFPR. Questo
surprising result will be the subject of further research.

The rest of the paper is organized as follows. Section II discusses the relevant
literature. In section III, I present a theoretical model to show how TFPR is affected
by firm-level distortions. Section IV describes the data, and section V analyzes the
empirical results and the decomposition of the variance of TFPR. Section VI sheds
some light on the misallocation among different groups of industries within the
manufacturing sector. In section VII, I construe some relationship between firm
size and misallocation in factor markets. Finalmente, I conclude in section VIII.

II. Literature Review

My work is related to a large body of literature that has accumulated over
the last few decades. Hsieh and Klenow (2009) argue that in a monopolistically
competitive framework, misallocation in factor markets can result
in large
differences in TFP and in output among firms within an industry. Per esempio, UN
capital market distortion caused by the disparity in access to cheap credit will result
in differences in the marginal product of capital among firms. Hsieh and Klenow

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Analyzing the Sources of Misallocation in Indian Manufacturing 137

argue that in such a situation, the aggregate economy will be better off by allocating
more capital to the firm with the higher marginal product of capital. Using firm-
level data from India and the People’s Republic of China (PRC), they calculate
the TFP gain from reallocating capital, equalizing TFPR within the industry, to be
30%–50% in the PRC and 40%–60% in India. I follow the same intuition in
this paper. I include raw materials, energy, and service sector inputs as factors of
production and find the effect of distortions in all those inputs on firm-level TFPR.
The goal is to find the empirical measurement of distortions in individual factor
markets on aggregate TFPR.

Restuccia and Rogerson (2008) demonstrate the effect of factor distortion
on TFP. They state that different taxes and policies across firms create disparities
in prices and lead to a 30%–50% decrease in output and TFP in developing
countries. Midrigan and Xu (2014) argue that financial frictions cause variations
in TFP across firms through two channels. In particular, financial frictions distort
entry decisions and technological adoption of producers. Inoltre, they create
disparities in return to capital among producers. Fernald and Neiman (2011)
deviate from the standard setup of monopolistic competition. They show that, in un
two-sector economy with heterogeneous financial policies and monopoly power,
TFP measured in terms of quantities and real factor prices can diverge.

There is a body of literature based on Hsieh and Klenow’s framework.
Camacho and Conover (2010) use Hsieh and Klenow’s methodology to measure
productivity differences through misallocation in resources for Colombian
industries. Taking the US as the benchmark economy, they find a wide TFPR
distribution for Colombia, which implies large resource misallocation across firms.
They also calculate that the reallocation of labor and capital among firms will
improve aggregate TFP by 47%–55%. Another paper by Kalemli-Ozcan and
Sørensen (2014) measures TFP dispersion through capital misallocation for 10
African countries using the World Bank enterprise survey data. They argue that
access to finance is one of the main sources of substantial capital misallocation.
Dia, Marques, and Richmond (2016) extend the Hsieh–Klenow model to include
intermediate inputs and measure TFP disparity using firm-level data from Portugal.
They consider data from all sectors of the economy. Consequently, the endogenous
intermediate inputs in their model take into account goods produced by all sectors.
They find huge misallocation across industries. According to their results, in the
absence of misallocation within industries, there would have been a 48%–79%
gain in value-added output during 1996–2011. In India, it is rather difficult to find
firm-level data for sectors other than manufacturing; hence, I take aggregate input
produced by other sectors as exogenously given in the model.

The most closely related work to my research is the paper by Chatterjee
(2011), which extends the Hsieh–Klenow framework for both formal and informal
manufacturing sectors in India. Chatterjee also includes intermediate input market
distortions in the model as a source of variation in TFP. She assumes that the
economy has an intermediate input, aggregated from a fraction of total production

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138 Asian Development Review

by each existing firm. The data used in Chatterjee’s paper was obtained from
the Annual Survey of Industries (ASI) for formal firms and the National Sample
Survey Office (NSSO) for informal sector firms, as in the case in my paper.
Since both of these surveys primarily focus on manufacturing sector firms, IL
aggregated intermediate input produced from these firms will take into account only
manufacturing sector products. Consequently, Chatterjee ignores inputs from other
sectors such as energy and services in her model. D'altra parte, I consider
aggregated energy and service inputs as exogenously given in the model apart from
the combined raw materials produced by the existing firms. In the next section, IO
extend Hsieh and Klenow’s model to measure the degree of misallocation in the
economy.

III. Model

I consider a static one-period model without uncertainty, used by Hsieh and
Klenow (2009). I assume that the economy consists of J manufacturing industries
indexed as j = 1, 2, … , J. Each industry consists of Nj monopolistically competitive
firms indexed as i = 1, 2, … , Nj. Each firm produces differentiated products and
thus has substantial market power. The firms have heterogeneous productivity Aij
as exogenously given and an endowment of capital Kij, labor Lij, raw material Mij,
energy Eij, and service sector input Zij. Firms combine the factors to produce a
good using a Cobb–Douglas production function. The firm’s production function is
come segue:

Yi j = Ai jK
(cid:2)

Dove

S

αK j
i j L
αS j

αM j
i j E

αL j
αZ j
αE j
i j M
i j Z
i j
= 1 and S ∈ {K, l, M, E, Z}.

I consider only manufacturing sector firms in the model because I could
find data only for the manufacturing sector in India, which I use for the empirical
analysis. For the sake of simplicity, I assume that all raw materials coming from
the manufacturing sector are aggregated into a single raw material M, whereas all
energy inputs and service sector inputs are aggregated into factor inputs E and Z,
rispettivamente. A fraction of the output produced by manufacturing firms considered
in the model is aggregated as the manufacturing input M and used by the same
firms; hence, the price of M is taken as endogenously determined. D'altra parte,
since service and energy inputs that are produced by firms in their respective sectors
are not considered in the model, I take the output prices of such firms as exogenous.
Some manufacturing products may also be used by service and energy sector firms
as intermediate inputs; these products are considered as part of consumption goods
in the model. I further assume that all firms in an industry have the same cost share
of factor inputs αS j , but there is a variation in factor shares between industries.

in questo documento, I measure the misallocation in resources that affects firm-level
TFPR. Distortion in an input or output market does not always uniformly increase

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Analyzing the Sources of Misallocation in Indian Manufacturing 139

(or decrease) the marginal product of the factors of production (MPF) for all firms.
As firms equalize price with the marginal product of factor inputs, a firm that faces
taxes will have higher MPF for service inputs than the firms facing subsidies. IL
intuition behind the entire literature based on Hsieh and Klenow (2009) originates
from the hypothesis that aggregate productivity will be higher if factors can be
reallocated from lower MPF firms to higher MPF firms.

I assume several types of factor market distortions in the model. Some
elements that change the MPF for all inputs by the same proportion are called
output distortions (τYi j ). Tax on the output of a firm affects all inputs proportionally
and can be identified as an example of an output distortion. Inoltre, if the
distortion creates a discrepancy in only the marginal product of capital, I call it
capital distortion (τKi j ) in accordance with Hsieh and Klenow. Similar remarks
hold for raw material distortion (τMi j ), energy distortion (τEi j ), and service sector
input distortion (τZi j ). Per esempio, differentiation in electricity price between small
and large businesses is perceived as an energy distortion as it affects only the
marginal product of energy. Note that labor distortion is not considered separately
but that every other distortion affects the respective MPF, relative to the marginal
productivity of labor.

Each firm produces a single good Yi j that is used both as a final consumption
good and as an intermediate raw material. Ci j and Xi j denote final consumption
good and intermediate raw material, rispettivamente, which are produced by the ith firm
from the jth industry. Firms face a downward sloping demand schedule that resulted
from the assumption of a differentiated product environment in a monopolistically
competitive market. Hence, the industry’s final good appears to be a constant
elasticity of substitution aggregation of all firms’ final goods represented as

⎛

⎞

ρ
ρ−1

Yj =

⎝

N j(cid:5)

i=1

ρ−1
ρ

⎠

Yi j

where ρ > 1 is the elasticity of substitution. For simplicity, I assume the elasticity
of substitution is the same for all industries. This assumption follows from the
literature. Each industry’s output is sold as consumption good C j and intermediate
raw material X j as was the case with firm-level output. I further assume that the
markets for consumption goods and raw materials, produced by each industry,
is perfectly competitive. Hence, the final consumption good is aggregated from
industry-level consumption goods by a Cobb–Douglas production function:

C =

J(cid:8)

j=1

θ j
j

C

Dove

J(cid:5)

j=1

θ j = 1

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140 Asian Development Review

The intermediate raw material is produced endogenously by aggregating each
industry’s production of raw materials, again using a Cobb–Douglas production
function:
J(cid:8)

M =

λ j
j

X

j=1

Dove

J(cid:5)

j=1

λ j = 1

In the above two equations, θ j and λ j are the factor shares of each industry
in total consumption and total intermediate raw materials production, rispettivamente.
Each firm chooses intermediate raw materials from the aggregated M according to
their productivity. The aggregate quantity of other inputs such as energy E and
services Z are exogenous in the model. Hence, each firm chooses the optimal
amount Ei j and Zi j based on its production function. The industry aggregates E j
and Z j are given by the sum over each firm’s use of energy and services in that
industry.

I will now solve the model for optimal factor resources and output by
maximizing profit for the firm, industry, and economy. I assume that total factor
resources are limited in the manufacturing sector by the aggregate use of factor
resources of the firms in the sector.

For each S ∈ {K, l, M, E, Z}, we can write the aggregate factor resources as

S =

J(cid:5)

N j(cid:5)

j=1

i=1

Si j

and solve for the equilibrium to identify the effects of distortion on productivity.

UN.

Equilibrium Analysis

In this section, I present a comprehensive equilibrium structure for firms,
industries, and the economy. The equilibrium consists of the quantities of the
consumption good and the intermediate raw materials produced at the level of the
firm, industry, and aggregate economy. It also takes into account the optimal amount
of capital, labor, raw materials, energy, and services used by each firm. The input
markets and final goods markets clear at equilibrium. I now solve the optimization
problems for each market.

1.

Final Goods Problem

I assume a representative firm produces a final good Y that is used in
consumption C and in raw material M for further production. C is produced using

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Analyzing the Sources of Misallocation in Indian Manufacturing 141

consumption good C j produced by the industries. I assume C to be a numeraire
commodity with unit price P. Likewise, Pj represents the price of the fraction of
output or final good produced by each industry Yj. I do not distinguish between price
of final good C j and raw material X j, produced by each industry, on the assumption
that both are of the same good and are subject to the same cost and market
structure. Hence, the optimization problem for the final consumption good is given
by

PC −

max
C j

J(cid:5)

j=1

PjC j

subject to

C =

J(cid:8)

j=1

θ j
j

C

2.

Intermediate Raw Materials Problem

The fraction of output used as the intermediate raw material (M) È
constructed by the representative firms aggregating the produced raw materials (X j)
from each industry. The price of the aggregated intermediate raw material M is
given by pm. The representative firm optimizes the production of M as follows:

J(cid:5)

j=1

PjX j

pmM −

max
M j

subject to

M =

J(cid:8)

j=1

λ j
j

X

(3)

(4)

We can solve the final goods problem from equations (1) E (2) and the
intermediate raw materials problem from equations (3) E (4) to find the prices set
by representative firms. The market clearing price of the final good is

P =

(cid:9)

J(cid:8)

j=1

(cid:10)θ j

Pj
θ j

= 1

and the intermediate raw material’s price is

pm =

(cid:10)λ j

(cid:9)

J(cid:8)

j=1

Pj
λ j

(5)

(6)

(1)

(2)

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142 Asian Development Review

The second equality in equation (5) follows from the assumption that C is a
numeraire good. Both prices are functions of the industry price (Pj) and the share
of each industry in producing the same good (θ j and λ j, rispettivamente).

3.

The Industry’s Problem

The final goods produced by each industry Yj are used as both final
consumption good C j and intermediate raw material X j. I assume that C j and X j
are fractions of the same good, hence they face the same optimization problem.
Inoltre, Ci j and Xi j are fractions of a firm’s output Yi j; Perciò, I assume that
they are produced using the same production function and that they also incur the
same marginal cost. It is safe to assume that the firms charge the same price Pi j for
both parts of their output. I represent the industry’s problem as

J(cid:5)

j=1

Pi jYi j

PjYj −

max
Yj

subject to

⎞

ρ
ρ−1

ρ−1
ρ

⎠

Yi j

⎛

⎝

N j(cid:5)

i=1

Yj =

The market clearing industry price is
⎛

⎞

ρ
ρ−1

Pj =

⎝

N j(cid:5)

i=1

1−ρ

⎠

Pi j

(7)

(8)

(9)

4.

The Firm’s Problem

To allow for factor misallocation in the input and output markets, I consider
several types of distortions. I assume that there exists an output distortion (τYi j ) Quello
affects the marginal product of each factor of production by the same proportion.
I also consider capital distortion (τKi j ), raw material distortion (τMi j ), energy
distortion (τEi j ), and service sector input distortion (τZi j ) that affect the marginal
product of capital, raw materials, energy, and service inputs, rispettivamente, relative to
the marginal product of labor.2 Each firm solves the following profit maximization

2Since all distortions are measured relative to the labor market, I do not explicitly use labor distortion

= 0).

(τLi j

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Analyzing the Sources of Misallocation in Indian Manufacturing 143

problem to choose the optimized level of capital, labor, raw materials, energy, E
service inputs:3

max
Yj

Pi jYi j

− pe

(cid:12)

(cid:11)
1 − τYi j

(cid:12)

(cid:11)
1 + τEi j

subject to

− wLi j − r
(cid:11)

Ei j − pz

(cid:11)

1 + τKi j
(cid:12)

1 + τZi j

Yi j = Ai jK

αK j
i j L

αL j
i j M

αM j
i j E

αZ j
αE j
i j Z
i j

Solving firm i’s problem yields
(cid:11)
(cid:9)

(cid:10)

(cid:12)

K∗
i j

=

L∗
i j

=

M ∗
i j

=

E∗
i j

=

Z∗
i j

=

ρ − 1
ρ

(cid:10)

(cid:10)

(cid:10)

(cid:10)

(cid:9)

(cid:9)

(cid:9)

(cid:9)

ρ − 1
ρ

ρ − 1
ρ

ρ − 1
ρ

ρ − 1
ρ

αK j

αL j

αM j
(cid:11)

αE j

αZ j

(cid:12)

1 − τYi j
(cid:11)
1 + τKi j
(cid:12)
1 − τYi j
w

(cid:11)

(cid:12)

(cid:11)
1 − τYi j
(cid:12)
1 + τMi j
(cid:11)
1 − τYi j
1 + τEi j
(cid:11)
1 − τYi j
(cid:11)
1 + τZi j

(cid:12)

(cid:12)

(cid:12)

(cid:11)

(cid:12)

Pi jYi j
R

Pi jYi j

Pi jYi j
pm

Pi jYi j
pe

Pi jYi j
pz

(cid:12)

Ki j − pm

(cid:11)
1 + τMi j

(cid:12)

Mi j

Zi j

(10)

(11)

(12UN)

(12B)

(12C)

(12D)

(12e)

Optimal quantities of factor inputs contain both output distortion and
distortion in their respective factor markets. By combining equations (12UN)–(12e)
with the firm’s objective function in equation (10), we can find the market clearing
price for each firm:

(cid:10) (cid:11)

(cid:12)αK j

1 + τKi j

(cid:11)
(cid:12)αM j
1 + τMi j
(cid:11)
1 − τYi j

(cid:11)
1 + τEi j
(cid:12)
Ai j

(cid:11)

(cid:12)αE j

(cid:12)αZ j

1 + τZi j

(13)

(cid:10) (cid:9)

(cid:9)

ρ − 1
ρ

MC
(cid:7)

Pi j =

Dove

(cid:7) =

(cid:8)

S

α

αS j
S j

MC = r

αK j wαL j pm

αM j pe

αE j pz

αZ j

3It

is important

to note that, although the price of aggregated raw materials (M) produced in the
manufacturing sector is determined using the profit maximization problem in section III.A.2, firms may consume
different combinations (Mi j) of such raw materials for their production; hence, they take the price (pm) as exogenously
given.

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144 Asian Development Review

Note that the firm-level price in equation (13) comprises the marginal cost of
production, markup, distortions, and the reciprocal of firm-level productivity. Given
the assumption that firms in an industry have the same factor shares and input costs,
I can infer that in the absence of distortions, the price of each firm in an industry
would have been inversely proportional to the TFP of the firm. This inference is
in line with my conjecture that all firms in an industry will have the same revenue
productivity in the absence of any misallocation in factor resources.

I define firm-level total revenue productivity as TFPRi j = Pi jAi j. Solving

TFPRi j from equation (13) yields
ρ − 1
ρ

TFPRi j =

MC
(cid:7)

(cid:10) (cid:11)

(cid:10) (cid:9)

(cid:9)

1 + τKi j

(cid:12)αK j

(cid:11)
1 + τMi j
(cid:11)

(cid:11)
1 + τEi j
(cid:12)

(cid:12)αM j
1 − τYi j

(cid:11)

(cid:12)αE j

(cid:12)αZ j

1 + τZi j

(14)

Revenue productivity given by equation (14) is a measure of firm-level
distortion. Variation in TFPRi j gives us the degree of misallocation in input and
output markets. I build my empirical findings on this intuition and try to measure the
extent of variation in firm-level revenue productivity in the presence of distortions.
I define the marginal revenue products of factor inputs for an industry as the
weighted average of the value of firm-level marginal revenue products, dove il
weights are calculated as a share of a firm’s output in the industry:

MRPS j =

(cid:2)N j
i=1

(cid:13)

PS
1−τYi j
(cid:13)
1+τSi j

(cid:14)
Pi jYi j
(cid:14)
PjYj

(15)

Recall that S consists of all factor inputs such as K, l, M, E, and Z. PS
denotes the corresponding factor prices r, w, pm, pe, and pz, rispettivamente, and τSi j
indicates the corresponding factor distortions relative to labor.

I define industry-level total factor revenue productivity (TFPR j) to be
proportional to the geometric average of the average marginal revenue products
of factor inputs in the industry (given in equation [15]):
αK j ⎡

⎤

⎡

⎤

TFPR j =

⎡

⎢
⎢
⎢
⎣

(cid:9)

(cid:10) (cid:9)

(cid:10)

ρ − 1
ρ

MC
(cid:7)

⎢
⎢
⎢
⎣

(cid:2)N j
i=1
⎡

αM j

⎤

(cid:14)

1
(cid:13)
1−τYi j
(cid:13)
1+τKi j

Pi jYi j
(cid:14)
PjYj

⎥
⎥
⎥
⎦

⎢
⎣

(cid:2)N j
i=1
⎡

αE j

⎤

αL j

⎥
⎦

Pi jYi j

(cid:14)

1
(cid:13)
1−τYi j
PjYj

(cid:2)N j
i=1

1
(cid:13)
1−τYi j
(cid:13)
1+τMi j

(cid:14)
Pi jYi j
(cid:14)
PjYj

⎥
⎥
⎥
⎦

⎢
⎢
⎢
⎣

(cid:2)N j
i=1

1
(cid:13)
1−τYi j
(cid:13)
1+τEi j

(cid:14)
Pi jYi j
(cid:14)
PjYj

⎥
⎥
⎥
⎦

⎢
⎢
⎢
⎣

(cid:2)N j
i=1

1
(cid:13)
1−τYi j
(cid:13)
1+τZi j

(cid:14)
Pi jYi j
(cid:14)
PjYj

αZ j

⎤

⎥
⎥
⎥
⎦

.

(16)

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Analyzing the Sources of Misallocation in Indian Manufacturing 145

B.

Allocation of Factors in the Industry

I now solve for the allocation of factor resources for each industry. IO
aggregate factor resources used by all firms in an industry using their marginal
products to get the following:

S j =

N j(cid:5)

i=1

Si j = S

(cid:2)

αS j
J
j=1

θ j/MRPS j
αS j

θ j/MRPS j

(17)

(cid:2)

Recall that S ∈ {K, l, M, E, Z}. and S =

J
j=1 S j are aggregate supplies of
factor inputs in the economy. Also recall that θ j is the share of each industry
in producing the final consumption good. Note that factor accumulations in each
industry are affected by factor distortions only through the corresponding marginal
revenue products. This result is due to the Cobb–Douglas aggregation at the
industry level. Combining industry-level factor inputs (17) and revenue productivity
(16), we can derive
αK j
PjYj = TFPR jK
j L

αL j
j M

αM j
j E

αE j
j Z

(18)

αZ j
j

Combining industry price Pj from (9) and firm’s price Pi j from (13) together

with firm-level revenue productivity from (14), we can simplify

⎡

Pj =

N j(cid:5)

⎣

i=1

(cid:10)

(1−ρ )

(cid:9)

TFPRi j
Ai j

1
1−ρ

⎤

⎦

Equating (18) E (19), we get

Yj = TFP jK

αK j
j L

αL j
j M

αM j
j E

αE j
j Z

αZ j
j

Dove

TFP j =

⎡

N j(cid:5)

⎣

(cid:9)

i=1

Ai jTFPR j
TFPRi j

(cid:10)

(ρ−1)

1
1−ρ

⎤

⎦

(19)

(20)

(21)

Hence, the total factor productivity of each firm is a function of the
firm-level TFP, TFPR, and industry-level revenue productivity. Now, we can write
the final consumption outcome of the economy as follows:

C∗ =

J(cid:8)

(cid:13)

TFP jK

j=1

αK j
j L

αL j
j M

αM j
j E

αE j
j Z

αZ j
j

(cid:14)θS

and the intermediate good of the economy as

M ∗ =

J(cid:8)

(cid:13)

j=1

TFP jK

αK j
j L

αL j
j M

αM j
j E

αE j
j Z

αZ j
j

(cid:14)λS

(22)

(23)

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146 Asian Development Review

Following Hsieh and Klenow (2009), I now assume that TFP (Ai j) E
revenue productivity (TFPRi j) are jointly log-normally distributed to depict the
effect of firm-level distortion on the productivity of an industry. By this assumption,
the logarithm of industry-level TFP can be expressed as

⎛

⎞

log TFP j = 1

1 − ρ log

N j(cid:5)

⎝

i=1

(ρ−1)

⎠ −

Ai j

(cid:11)
log TFPRi j

(cid:12)

Var

ρ

2

(24)

Equazione (24) shows that factor distortions reduce overall productivity of
an industry through the variance of firm-level TFPR. On the basis of this finding,
I will now proceed to show how factor distortions contribute to firm-level TFPR
variation. Note that I assume that the number of firms are unaffected by factor
market distortions. This assumption is elaborated in more detail in Hsieh and
Klenow (2009).

IV. Data

This study uses data on the formal manufacturing sector from the Annual
Survey of Industries (ASI) collected by the Central Statistical Office of India. ASI
is the primary source of industrial statistics in India, which covers all factories
as defined in the Factories Act of 1948. ASI data is an annual survey of formal
manufacturing firms with more than 50 workers and a random one-third sample
survey of firms with more than 10 workers (with electricity) or firms with more
di 20 workers (without electricity). I use the 62nd round of ASI data collected in
the survey year 2005–2006.

I also take into account data for the unorganized manufacturing sector
collected by the National Sample Survey Office (NSSO) of India for the survey
year 2005–2006. The NSSO collects firm-level data for the informal manufacturing
sector in India every 5 years. The dataset includes small manufacturing firms along
with some service sector firms and some unincorporated proprietary firms. These
firms are not registered under the Factories Act of 1948; hence, they are not included
in the ASI data. The data for the informal sector consists of a large number of
firms that use one or two workers. These firms have missing values for most of the
variables I take into consideration. Also, they contribute a very small percentage of
total value added.

Tavolo 1 summarizes the distribution of informal firms and the corresponding
cumulative percentages of contributions to total value added, according to the
number of employees. There are over 30,000 one-employee firms that contribute
only 1.6% of total value added and almost none of them have data for labor and
capital in the corresponding dataset. In my analysis, I do not include such firms. IO
only consider informal firms that have at least six employees, a cutoff set on the
basis of these firms’ substantial market share. To keep the two datasets comparable,

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Analyzing the Sources of Misallocation in Indian Manufacturing 147

Tavolo 1. Informal Firms Distribution

No. of Employees No. of Firms

Cumulative % Di
Value Added

1
2
3
4
5
6
7
8
9
10
11–20
21–30
31– 50
51–100
More than 100

31,874
23,734
9,468
4,658
2,601
1,948
1,349
1,054
732
648
1,712
342
190
92
61

1.6
4.4
6.9
9.1
11.6
17.8
21.8
26.0
31.0
37.0
57.4
62.8
73.0
95.0
100.0

Fonte: National Sample Survey Office (NSSO) survey of
unorganized manufacturing enterprises, 2005–2006.

Tavolo 2. Distribution of Firms: Annual Survey of Industries
versus National Sample Survey Office

ASI Data

NSSO Data

No. of Employees No. of Firms No. of Employees No. of Firms

1–10
11–20
21–50
51–100
101–500
More than 500

4,663
6,818
6,771
3,719
7,648
2,254

6–10
11–20
21–50
51–100
101–500
More than 500

3,512
1,194
397
77
31
5

ASI = Annual Survey of Industries, NSSO = National Sample Survey Office.
Sources: Government of India, Ministry of Statistics and Programme Implementation
(2005–2006a and 2005–2006b).

I only consider manufacturing industries that are covered in both the ASI and NSSO
datasets. The literature in the field (La Porta and Shleifer 2008) argues that informal
sector firms are small and highly unproductive compared to formal sector firms. IL
assumption of monopolistic competition among firms in the model allows for firms
with different levels of productivity to coexist in the market.

Tavolo 2 shows the distribution of firms in the analysis. There are around
31,000 formal sector firms taken from the ASI data, whereas the number of informal
sector firms from the NSSO data is around 5,000. For this analysis, I had to drop
some observations from both sectors due to missing data. Formal firms consist of
all sizes, while informal firms are mostly small. To simplify the analysis, I use
2-digit industry-level data developed in the National Industrial Classification (NIC)

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148 Asian Development Review

system. I consider 23 different industries, including food and beverage, machinery
and equipment, legna, paper, publishing, computing machinery, and others (Vedere
Tavolo 3).

Hsieh and Klenow (2009) use the value-added method to measure
productivity and distortion in capital and output. They did not incorporate raw
materiali, services, or energy inputs in the production function. I first replicate their
results using the value-added method and then extend the model to incorporate
intermediate inputs as factors of production. This extension will adopt
IL
gross-output method. I use nominal revenue of the firm as the output variable.

Aside from firm revenue, the variables that I use for this analysis are the
firm’s industry (2-digit NIC), labor compensation, net book value of fixed capital
stock, rent on capital, intermediate input costs, and fuel and energy costs. I assume
that service input cost is the same as the residual cost. I use labor compensation
including wages, bonuses, and benefits as proxy for labor input. Capital is measured
by the average of net book value of capital at the beginning and end of the year.
I deviate from Hsieh and Klenow (2009) and Chatterjee (2011), as well as other
previous works based on the measurement of the rental cost of capital. Existing
literature in this field uses an exogenous percentage of capital as rental cost, whereas
I measure the same by variables such as rent on machinery, building, and land,
interest paid on loans, and other miscellaneous capital cost, which are taken from
the ASI data for the formal sector.

Tuttavia, for informal firms, the NSSO data do not explicitly provide rent
on capital. I measured rental cost from the residual of value added after subtracting
total labor cost. The costs of raw materials and energy are calculated explicitly
from the cost of inputs of production. Service input costs consist of transport
and communication costs, insurance charges, license costs, and other operative
expenses.

The elasticity of substitution (ρ) is assumed to be constant in the model.
Based on the literature in this field, I assume the value of ρ to be 3. In most of my
empirical analysis, I use factor shares from industries in the US as a benchmark
to identify the effect of distortion on productivity. The factor shares data are from
the KLEMS measures found in the National Income and Product Accounts industry
database (2005) provided by the US Bureau of Labor Statistics.

V. Empirical Analysis

My identification strategy is similar to that of Hsieh and Klenow (2009)
and Chatterjee (2011). I established identification of distortions based on the
rationale that, in the absence of distortions, revenue factor shares of output will
be proportional to the parameters αK j, αL j, αM j, αE j, and αZ j in a market with
monopolistic competition. Because I assume distortions in factor markets, IL

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Analyzing the Sources of Misallocation in Indian Manufacturing 149

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150 Asian Development Review

revenue shares will give a biased estimation of the parameters. We can validate
this from the first-order conditions of the firms:
(cid:11)
1 + τSi j
(cid:11)
1 − τYi j

ρ
ρ − 1

PSSi j
Pi jYi j

αS j =

(25)

(cid:10)

(cid:9)

(cid:12)

(cid:12)

where αS j = {αK j, αL j, αM j, αE j, αZ j} and the respective PS = {R, w, pm, pe, pz}.4
Recall that S consists of all factor inputs and τSi j denotes corresponding distortions
relative to the labor market. In the presence of distortions, I cannot distinguish
the misallocation in resources from the bias in the parameters. Following Hsieh
and Klenow (2009), I take into account US factor shares. The strategy is based
on the assumption that US factor markets are less distorted than in India and the
technology used in the industries is the same for both countries. A more detailed
discussion on the assumptions are presented in Chatterjee (2011). Factor shares for
both countries, described in Table 3, represent the average of the cost share for each
factor in each industry.

Figura 1 illustrates the bias in factor shares in Indian industries with
respect to benchmark US industries. Any deviation from the 45-degree line shows
misallocation in the corresponding factor markets in India. I find a similar pattern
in capital, labor, and raw material shares presented in Chatterjee (2011). È
evident from the figure that cost shares of capital, labor, and service inputs are
significantly higher in the US than in India, whereas shares of raw materials and
energy are higher in India. Prossimo, I analyze within-industry variation in average
revenue product of labor. Figura 2 illustrates the distribution of the logarithm of
firm-level average revenue product of labor (APRL) relative to the industry mean,
log (APRLi j/APRL j ). I trim 1 percentile from both ends to avoid outliers. IL
horizontal axis shows log (APRLi j/APRL j ), whereas the vertical axis measures the
density of firms. There is a substantial variation in average revenue product of labor
within an industry with a variance of 3.76.

UN.

Value-Added versus Gross-Output Approach

The goal in this section is to measure the variation in firm-level TFPR as
an indicator of misallocation in factor markets. The variable of interest is the
logarithm of firm-level TFPR relative to the industry TFPR, log (TFPRi j/TFPR j ).
I depict both value-added and gross-output approaches to measure TFPR. Primo, IO
replicate the results from Hsieh and Klenow (2009) using the value-added approach.
They estimate the distribution of TFPR using formal manufacturing sector data for

4The assumption of common factor prices is a hypothetical frictionless situation, which allows me to identify
the factor allocation distortion apart from any exogenous variation that may affect factor prices. As long as distortions
exist, firms pay different factor prices, and the dispersion in distortions provides us with a sense of how much firms
actually deviate from the equilibrium.

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Analyzing the Sources of Misallocation in Indian Manufacturing 151

Figura 1. Factor Shares for the United States and India

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US = United States.
Fonte: Author’s calculation based on the Annual Survey of Industries and the National Sample Survey Office of
the Government of India, Ministry of Statistics and Programme Implementation (2005–2006a, 2005–2006b); E
KLEMS measures from the National Income and Product Accounts of the US Bureau of Labor Statistics (2005).

1987–1988 and 1994–1995. I repeat their method using 2005–2006 data for both
formal and informal sectors. I also illustrate the TFPR distribution using the
gross-output method using the same data. Cobbold (2003) presented the formal
relationship between value-added and gross-output TFP as
TFPVA = G
VA

× TFPGO

152 Asian Development Review

Figura 2. Distribution of the Logarithm of Average Revenue Product of Labor

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Fonte: Author’s calculation based on the Annual Survey of Industries and the National Sample Survey Office of the
Government of India, Ministry of Statistics and Programme Implementation (2005–2006a, 2005–2006b).

where G and VA represent nominal values of total revenue and total value added,
rispettivamente.

Several studies, such as Oulton and O’Mahony (1994) and van der Wiel
(1999), show that productivity growth measured using value added is much higher
than the measurement considering all inputs. It naturally follows from the above
equation that given G and VA, TFP as well as TFPR measured using the value-added
approach will be larger than if measured by the gross-output approach.

Before calculating the variance, I trim 1% tails of log (TFPRi j/TFPR j ) A
get rid of outliers. Figura 3 plots the distributions of the logarithm of TFPR relative
to the industry mean. The dashed line shows the value-added TFPR distribution
whereas the solid line shows the distribution using the gross-output approach. IL
variation in value-added TFPR is much higher than the variation in gross-output
TFPR. Tavolo 4 presents the TFPR dispersion statistics in firm-level TFPR. Standard
deviation (SD) in value-added TFPR is around 0.99 compared to 0.47 using the
gross-output approach. The difference in both methods is more pronounced when
the variation in TFPR is estimated at higher percentiles.

Tavolo 5 shows the dispersion in the logarithm of TFPR in Hsieh and Klenow
(2009) using the value-added approach and the same variable in Chatterjee (2011)
using the gross-output approach. The results display a larger value-added SD than

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Analyzing the Sources of Misallocation in Indian Manufacturing 153

Figura 3. Distribution of the Logarithm of Total Factor Revenue Productivity

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kdensity = kernel density, TFPR = total factor revenue productivity.
Fonte: Author’s calculation based on the Annual Survey of Industries and the National Sample Survey Office of the
Government of India, Ministry of Statistics and Programme Implementation (2005–2006a, 2005–2006b).

Tavolo 4. Dispersion of the Logarithm of Total Factor
Revenue Productivity

Statistics

Value Added

Gross Output

Standard deviation
75th to 25th percentiles
90th to 10th percentiles

0.99
1.23
2.45

0.47
0.51
1.08

Note: The variable is log (TFPRij/TFPRj).
Fonte: Author’s calculation based on the Annual Survey of Industries and
the National Sample Survey Office of the Government of India, ministero
of Statistics and Programme Implementation (2005–2006a, 2005–2006b);
and KLEMS measures from the National Income and Product Accounts
of the US Bureau of Labor Statistics (2005).

Tavolo 5. Dispersion of the Logarithm of Total Factor Revenue Productivity
in the Literature

Statistics

Hsieh–Klenow (1994–1995) Chatterjee (2004–2005)

Standard deviation
75th to 25th percentiles
90th to 10th percentiles

0.67
0.81
1.60

0.49
0.56
1.19

Notes: Column 2 shows dispersion of total factor revenue productivity estimated by Hsieh and
Klenow (2009) for 1994–1995 data using the value-added approach. Column 3 depicts the same
variable estimated by Chatterjee (2011) for 2004–2005 data using the gross-output approach.
Sources: Hsieh and Klenow (2009) and Chatterjee (2011).

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154 Asian Development Review

in Hsieh and Klenow (2009), who use the same approach with formal sector data
from 1994 A 1995. This might be the consequence of an increase in overall level of
misallocation in the last decade or inclusion of the informal sector in my analysis.
Inoltre, I find comparable results (shown in Table 4) with those of
Chatterjee (2011) in the dispersion of gross-output TFPR. After including energy
and service sector distortions, the SD in firm-level TFPR in my study dropped by
0.02 from an overall 0.49 as shown by Chatterjee using 2004–2005 data. The gap
between the results is more conspicuous in the 75th to 25th percentiles and 90th to
10th percentiles.

B.

Decomposing the Misallocation in Factor Markets

I now turn to separating the effect of each component attributed to the
variance of firm-level TFPR. Moving forward, only the gross-output approach will
be considered. I take into account several types of distortions in input and output
markets. The calculation for each type as a function of total revenue, cost of inputs,
and factor shares is derived from first-order conditions of a firm as

1 − τYi j

=

1 + τKi j

=

1 + τMi j

=

1 + τEi j

=

1 + τZi j

=

(cid:9)

(cid:10)

ρ
ρ − 1
αK j
wLi j
αL j rKi j
wLi j
αM j
αL j pmMi j
wLi j
αE j
αL j peEi j
αZ j
wLi j
αL j pzZi j

wLi j
αL j Pi jYi j

(26UN)

(26B)

(26C)

(26D)

(26e)

where all input market distortions are measured relative to the labor market. IL
intuition behind equations (26B)–(26e) is that, in the presence of distortions, input
costs relative to labor compensation will be lower than given by the output elasticity.
Equazione (26UN) demonstrates that a deviation of labor share from output elasticity
with respect to labor will result in an output distortion.

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To give a more elaborate presentation of the above result, I now find
the variance of log (TFPRi j/TFPR j ). The total misallocation is measured by the
following variance:

(cid:21)

Var

log(TFPRi j/TFPR j

(cid:12)
] = Var (DK + DL + DM + DE + DZ − DY )

(27)

Analyzing the Sources of Misallocation in Indian Manufacturing 155

Tavolo 6. Variance Decomposition

Component

Variance or Covariance

0.0472
0.0119
0.3490
0.0048
0.0345
1.1203
0.0030
0.0346
0.0029
0.0082
0.0727
–0.0026
0.0001
0.0001
0.0067
0.0129
0.0533
0.5716
0.0034
0.0302
0.1110
0.2194

Var(DK )
Var(DL)
Var(DM )
Var(DE )
Var(DZ )
Var(DY )
Cov(DK , DL)
Cov(DK , DM )
Cov(DK , DE )
Cov(DK , DZ )
Cov(DK , DY )
Cov(DL, DM )
Cov(DL, DE )
Cov(DL, DZ )
Cov(DL, DY )
Cov(DM , DE )
Cov(DM , DZ )
Cov(DM , DY )
Cov(DE , DZ )
Cov(DE , DY )
Cov(DZ, DY )
Var[log(TFPRi j/TFPR j )]
TFPR = total factor revenue productivity.
Note: The table shows variances and covariances of the
components of log TFPR, where DS (S ∈ {K, l, M, E, Z}) E
DY are given by equations (28) E (29).
Fonte: Author’s calculation based on the Annual Survey of
Industries of the Government of India, Ministry of Statistics
and Programme Implementation (2005–2006a); and KLEMS
measures from the National Income and Product Accounts of
the US Bureau of Labor Statistics (2005).

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Dove

⎡
(cid:11)
⎣
1 + τSi j

DS = αS j log

DY = log

(cid:12)

(cid:11)
1 − τYi j

(cid:12) N j(cid:5)

i=1

(cid:11)

(cid:12)

1 − τYi j
(cid:11)
1 + τSi j

Pi jYi j
(cid:12)
PjYj

⎤

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(28)

(29)

Recall that S consists of all factor inputs such as K, l, M, E, and Z. αS j
denotes the corresponding factor shares, and τSi j indicates the corresponding factor
distortions. Also recall that I measure factor distortions relative to the labor market,
implying τLi j to be 0. In the above equations, DS can be inferred as components
of each factor input in the variance of TFPR. Tavolo 6 describes the variance and
covariances of each of the above components.

156 Asian Development Review

The variance of the components of equation (16) depict the contribution of
factor distortions in explaining the variation in firm-level TFPR. Since I measure
distortions in factor markets relative to the labor market in my analysis, IL
variance of DL measures the variation in industry TFPR in the presence of only
output distortions, multiplied by the cost share of labor. Inoltre, the variance
of DY determines the variation in firm TFPR attributed to only output distortion.
Dispersions in DY and DM are very high compared to the overall variance of
log(TFPRi j/TFPR j ), implying that misallocation is highest in output and raw
materiali.

Overall variance in log (TFPRi j/TFPR j ) includes the pairwise covariance
between the components of equation (16) anche. It is interesting to note that the
covariance between output and raw material distortions is the highest (0.5716). Questo
result may follow from the fact that in my framework, raw materials are endogenous,
thus the output of one firm is used as raw materials in another.

Prossimo, I examine the distinct effect of each distortion on the logarithm of
TFPR relative to the industry mean. In Figure 4, the solid lines illustrate the
distribution of the variable of interest, taking one factor distortion at a time. IL
dashed line represents the actual firm-level TFPR distribution taking all distortions
together. The top panels of Figure 4 show TFPR distributions taking either output
or capital distortion. Allo stesso modo, the middle panels and bottom panel depict scenarios
with only raw material, energy, or service input distortions, rispettivamente.

In the absence of any distortion, I expect the TFPR of all firms to equalize,
which should reflect in a distribution that shows a vertical line in a graph centered
at 0. Any deviation from such a line shows signs of distortion. Taking one factor
distortion at a time facilitates the comparison between the contribution of each
factor input distortion toward the overall distortion in the market.

Since higher dispersion in the distribution shows higher distortion, it is
perceptible from Figure 4 that output and raw material distortions play the main
role in the overall distortion within an industry. Capital and service input distortions
contribute a modest share in the measurement of misallocation. Energy distortion
is almost negligible. These results emphasize the findings in Table 6.5

The intriguing observation from Figure 4 is that the misallocation in TFPR is
lower when all factor market distortions are considered than when considering only
output distortion or only raw material distortion. Such findings imply that factor
input distortions offset each other’s effects in describing total misallocation. This is
an area I would like to work on in the future in order to understand the underlying
intuition.

5Since the distortion in other markets are measured relative to the labor market, I cannot estimate the
magnitude of the distortion in the labor market. The Appendix shows factor market distortions in different sectors
similar to Figure 4, relative to the energy input market.

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Analyzing the Sources of Misallocation in Indian Manufacturing 157

Figura 4. Distribution of Firm-Level Total Factor Revenue Productivity Taking One
Distortion at a Time (relative to the labor market)

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TFPR = total factor revenue productivity.
Note: All TFPR distributions are in logarithm and relative to the industry average.
Fonte: Author’s calculation based on the Annual Survey of Industries and the National Sample Survey Office of the
Government of India, Ministry of Statistics and Programme Implementation (2005–2006a, 2005–2006b).

C.

Formal versus Informal Sectors

Since I use data from both formal and informal sector firms in my empirical
analysis, it is important to examine if there is any inherent difference in the pattern
of input and output distortions between these two sectors. Figura 5 illustrates the

158 Asian Development Review

Figura 5. Distribution of Firm-Level Total Factor Revenue Productivity in Formal and
Informal Sectors

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