Ownership and Productivity in Vertically-Integrated
Firms: Evidence from the Chinese Steel Industry
Loren Brandt1 , Feitao Jiang2 , Yao Luo1 , and Yingjun Su∗3
1
2
University of Toronto
Chinese Academy of Social Sciences
3
University of Pittsburgh
November 6, 2016
Abstract
We study productivity differences in vertically-integrated Chinese steel operations, using a
unique data set that provides plant-level information on material inputs and output in physical units and plant equipment for each of the three main stages in the steel value chain, i.e.,
sintering, iron-making and steel refining. We find that private vertically-integrated units are
more productive than provincial state-owned (SOEs) firms, followed by central SOEs. This
ranking lines up with our productivity estimates in the two downstream production stages, but
central SOEs outperform in sintering, most likely because of their superior access to higher
quality raw materials. The productivity differential favoring private firms declines with the
size of vertically-integrated operations, turning negative for units larger than the median. We
attribute this pattern to differences in the internal configuration of vertically-integrated units,
which reflect the greater constraints confronting expanding private sector firms. Increasing returns to scale within each stage of production partially offset these costs, and rationalize firms’
choice on larger vertically-integrated operations.
Key Words: Total Factor Productivity, Vertically-Integrated, Steel, SOEs, Private, China
∗
Corresponding author. Contact: Department of Economics, University of Toronto, 150 St.George Street, Toronto,
ON M5S 3G7. Email: [email protected]. We thank Victor Aguirregabiria, Garth Frazer, Frank Giarratani, Thomas
Rawski, David Rivers, participants at the University of Toronto CEPA Seminar for helpful comments. All errors are
our own.
1
Introduction
Increased productivity is an important source of economic growth for firms, industries and
countries. Researchers have documented sizable and persistent productivity differences across producers, even within narrowly-defined industries (Syverson (2011)).1 Understanding the sources of
these differences requires accurate measurement of productivity, a task hindered by various obstacles. First, in the estimation one must address the endogeneity issue generated by the relationship
between unobserved firm productivity and input choices. Second, the absence of producer-level
input and output prices leads to the estimation of revenue-based productivity measures that can
reflect aspects other than the true efficiency of the producer.2
Even if one accurately estimates productivity, identifying the sources of these observed differences is difficult because productivity studies are usually done at the aggregate firm level. In reality,
production often involves complicated processes that are carried out in multiple production units
within a firm. Aggregate data on inputs and output force researchers to treat the firm as a black
box, leaving as an important research agenda the link between a firm’s performance and its internal
configuration.
We examine one particular industry, China’s steel industry, for which we construct a new
data set that covers vertically-integrated steel operations and provides plant-level information on
production equipment and inputs and output in physical units for each stage in the value chain. The
richness of our data allows us to identify the physical efficiency of producers, and more important, to
decompose production performance into process- and equipment-level differences, thereby providing
new insight into the internal dimensions of complex industrial operations..
A recent literature has documented productivity differences between firms and sectors in China
that appear tied to ownership and the regulatory environment (Hsieh and Klenow (2009), Hsieh and
Song (2015), Brandt (2015), Berkowitz, Ma, and Nishioka (2016)). State-owned (SOEs) firms often
have better access to capital, technology, inputs and human resources, differences that may not be
easily captured by data used (e.g. Haggard and Huang (2008)). Given the importance of ownership
structure on firm performance in China, this paper focuses on the productivity differences between
SOEs and private firms.
In addition to identifying the underlying sources of productivity differences by ownership that
are of interest to a growing literature on resource misallocation and productivity dispersion, the
1
2
See for example, Syverson (2004) and Hsieh and Klenow (2009).
See the detailed discussion in De Loecker and Goldberg (2014).
2
study of China’s steel industry itself is important. The industry plays a key role in current proposals
for rebalancing of the Chinese economy. The sector produces half of the world’s steel, is the largest
iron ore importer in the world, and more recently has been at the center of a number of international
trade disputes. All of these issues necessitate a thorough understanding of Chinese steel producers’
performance.
Our estimation of production function for the steel sector builds on the control function approach
introduced by Olley and Pakes (1996) and Levinsohn and Petrin (2003), and closely follows Ackerberg, Caves, and Frazer (2015) and Gandhi, Navarro, and Rivers (2016). We allow for production
technology to differ in each stage of production and estimate production functions separately for
the three main stages in the value chain (sintering, iron making and steel making). We then follow
Domar (1961) to integrate productivity estimates from each stage into estimates for verticallyintegrated operations using as weights either the estimated elasticities of material inputs in iron
making and steel making or the value shares of sinter and iron out of steel.
We find that private firms are on average 6.2 percent more productive than central SOEs, and
2.3 percent relative to provincial SOEs. With value-added in the steel industry 25 to 30 percent
of the gross output, these observed productivity differences translate into sizable differences in
profitability. This ranking lines up with our productivity estimates in the two downstream production stages (iron making and steel making), but central SOEs outperform in upstream activity
(sintering), most likely because of central SOEs’ superior access to higher quality raw materials.
We also find that the productivity premium of private firms declines with the size of verticallyintegrated operations, turning negative for units larger than the median. This declining pattern
is tied up with the internal configuration of the private firms when they expand: they install
more plants of larger sizes, but plants that are smaller in size on average than those in SOEs.
This expansion pattern drives down relative productivity through two distinct mechanisms: First,
plant productivity drops most rapidly with plant size in each stage of production within private
vertically-integrated operations, mostly likely because of their difficulty in accessing better human
capital and the associated learning-by-doing effects. Second, the rising number of plants spreads
more thinly scarce managerial resources in private firms that are critical to the coordination of
multi-process production. Our study suggests that the premium of private firms in productivity
would be significantly higher if constraints were removed.
The remainder of the paper is organized as follows. Section 2 describes the data and presents
key facts that help guide the empirical analysis. We provide an empirical approach to identify
3
multi-stage productivity in section 3, followed by a discussion on productivity differences and the
underlying sources in section 4. We discuss potential biases resulting from measurement errors in
section 5 and conclude in section 6.
2
Data and descriptive evidence
2.1
Steel production technology
Vertically-integrated steel production involves a complex series of individual processes that use
coal as the primary energy source and iron ore as the basic raw material (Ahlbrandt, Fruehan, and
Giarratani (1996)). A steel firm integrates production in four major links along the production
chain: sintering, pig iron making, steel making and steel rolling (see Figure 1).3 The process
of sintering is basically a pre-treatment step of iron ore to produce from iron ore fines a high
quality burden called sinter for iron making facility - the blast furnace. The principle of sintering
involves the heating of iron ore fines along with flux and coke fines or coal to produce a semimolten mass that solidifies into porous pieces of sinter with the size and strength characteristics
necessary for feeding into the blast furnace. It is basically an agglomeration process achieved
through combustion.4 Sinter, together with coke, pulverized coal and limestone are then fed into
the top of a blast furnace, while a blast of hot air is blown into the lower section of the furnace
through a series of pipes, setting off a chemical reaction throughout the furnace as the material
moves downward.5 The molten pig iron from the blast furnace along with oxygen and fuel are then
fed into a basic oxygen furnace to produce steel, which is called primary steel making. Modern steel
making can also incorporate a secondary steel making process, which involves refining of the crude
steel. In this process, alloying agents are added, the level of dissolved gases in the steel is lowered,
and inclusions are removed or altered chemically to ensure that high-quality steel is produced.6
The semi-finished steel produced in vertically integrated firms is finally shaped into sheets, bars,
wire, and tube steel of desired thickness and uniformity through a metal forming process in rolling
mills.7
Technologically, larger blast furnaces incur smaller heat losses and enable installation of heat
3
We provide a detailed description of steel technology in the appendix.
http://ispatguru.com/the-sintering-process-of-iron-ore-fines-2/
5
https://en.wikipedia.org/wiki/Blast-furnace
6
Wikipedia http://en.wikipedia.org/wiki/Steelmaking
7
https://en.wikipedia.org/wiki/Rolling-(metalworking)
4
4
recovery equipment more cost effectively.8 However, larger furnaces are more demanding in the
grade of iron ore they use. The use of low-grade ore in larger blast furnaces increases energy
intensity, generates more waste, and even shorten the life expectancy of the blast furnaces.
2.2
Data
We construct a unique monthly-level data set on the production of vertically-integrated firms
in the Chinese steel industry from January 2009 to October 2011.9 Over this period, firms in our
sample produced sixty percent of the total steel output in China.10 The reported data are in the
form of equipment-level information on inputs and outputs in physical units for each of the three
major stages of production (sintering, pig iron making and steel making). Input information includes key material inputs, standardized energy consumption, number of workers, size of equipment
(capacity) and utilization rates.11 These data are supplemented by information on ownership, year
of establishment and location. In our analysis, a piece of equipment such as a blast furnace or basic
oxygen furnace is treated as a separate plant.
Our analysis centers on the first three major stages of production, i.e. sintering, pig-iron making
and steel making, and excludes steel rolling. We do so for several reasons. First, finished rolled
steel products can be highly differentiated, and differ in value added, final usage, and price. Output
however is only reported in physical terms. Second, we only have data on total production of rolled
products at the firm level rather than the product or the plant level. The input information is
similarly aggregated across products and plants. And third, while the main purpose of sintering
and pig iron making is to meet the immediate consumption needs of the next stage in the production
chain, firms often sell or hold inventory in semi-finished steel for later use. Therefore, between steel
making and rolling, there is a dynamic dimension to decision-making that is hard for our data to
capture. Despite this omission, we still capture a high percentage of the activity in the sector. In
an average steel firm, the total value-added generated by the three stages under our consideration
8
http://ietd.iipnetwork.org/content/blast-furnace-system
The underlying data are collected by the Chinese Iron and Steel Association (CISA) as part of regular data
collection efforts from all the firms in China with annual steel production over 1 million tons.
10
Our production data cover less firms than the total member firms of the CISA. They cover almost all the SOEs
and 24% of the total production by private firms. There are two sources of omissions for private firms: First, two
thirds of the omitted private production come from large- and medium-sized member firms of similar size to the
private firms present in the sample. For example, the notable omissions include big private firms such as Shandong
Rizhao Steel, with an annual production capacity of 10 million tons. Second, the rest omissions are small non-member
firms. Also excluded are plants ran by the headquarters of Baosteel, a central SOE that is generally acknowledged
to be the most technically advanced steel firm in China.
11
For steel rolling, we only have aggregate firm level information.
9
5
is more than double that of the rolling stage, or nearly seventy percent overall.12
Steel production in China is a highly vertically-integrated activity. Out of total of 81 firms
for whom we have production data, 70 undertake sintering, 71 are involved in pig-iron production
and 68 make steel. An individual firm may also operate more than one vertically-integrated unit.
At the sinter-iron-steel level, we compiled data on 136 fully vertically-integrated units (hereafter
VI), operated by 59 firms.13 Figure 2 provides an illustration of the typical make-up of a firm in
our sample. Each firm may operate multiple VI units; moreover, each stage of the VI may involve
production in multiple plants, i.e. sintering machines, blast furnaces or basic oxygen furnaces.
Ownership We categorize firms by three basic types of ownership: central SOEs, provincial
SOEs and private firms. Central SOEs are under the direct supervision of the State-owned Assets
Supervision and Administration Commission of the State Council (SASAC). We also define firms
that have been merged into central SOEs as central state-owned. Provincial SOEs are under the
direction of provincial or regional SASACs. Private firms in our sample include joint-ventures
(JVs), wholly owned foreign firms and privatized SOEs.14
China’s steel industry continues to be state dominated. Although it has declined significantly
the last decade, data at the national level for 2014 suggest that nearly half of steel production is
still by state-owned firms. Table 1 provides a breakdown for our sample, which is skewed in favor of
state-owned firms, of ownership at the plant level by stage of production and by VI units. In each
of the three stages of production, between seventy and eighty percent of all plants are state-owned.
State-owned firms are also consistently the source of eighty percent of total production, with the
remainder coming from private firms. Within the state sector, provincial SOEs dominate.
Size Steel firms span a wide range of sizes at both the plant and VI unit level. By industry
convention, we measure the size of a sintering plant by the effective area of a sintering machine;
size of a pig iron making plant as the effective volume of a blast furnace; and the size of a steel
making plant as the tonnage of a basic oxygen furnace. We define the size of a VI unit as the
total size of steel making plants within the VI unit. These size measures directly reflect production
capacity.
12
We base these calculations on a report by the Mingsheng Bank in China: Research on the steel industry and
suggestions on development strategy. October, 2015.
13
See Appendix for the detailed methodology that we used to link the plants across stages. We lose observations
from a small number of firms and VI because of missing data.
14
Privatized SOEs were the product of restructuring efforts in the state-sector in the late 1990s and early 2000s.
We compare private and privatized SOEs later in the paper.
6
Table 2 provides summary data on plant size for each stage of production by ownership. A clear
ranking emerges: On average, plants of central SOEs are the largest, followed by those of provincial
SOEs and then private firms. A typical plant of a private firm is only 60 percent of the size of
a central SOE. The average size of a private pig-iron furnace, for example, is 698 cubic meters
compared to 1230 for a furnace of a centrally owned SOE. Note also in columns (4) and (5) the
wide range of plant sizes within each ownership group. Table 3 provides comparable information
at the VI level. Central SOEs operate the largest VI units, which on average are more than twice
as large as those of the private VI units (301 versus 131), and a third larger than the VI units of
provincial SOEs (301 versus 227).
In Table 4, we break down VI units into size quartiles and report for each quartile the total
number of units by ownership and their respective shares of total steel production. Almost half of
the VI units in central SOEs are in the largest size quartile, which produce 13.3 percent of total
steel, and make up the largest share of total production by central SOEs. The number of VI units
of provincial SOEs is fairly evenly distributed throughout the quartiles, but those in the largest
size quartile play a dominant role in total steel production. In sharp contrast with the SOEs, only
a single private VI unit lies in the largest size group. Most private VI units are smaller in size than
the sample median. In terms of the total production of private firms however, the VI units in the
third quartile are the most important, and produce 37 percent of the steel by private firms.
Internal structure of VI As part of a single vertically-integrated unit, firms will typically
operate multiple plants, e.g. sintering machines, blast furnaces or basic oxygen furnaces, in each
stage of production. In Table 5 we report the average number of plants and their average size for
each stage of production by ownership and VI size. As before, we break down VI units into size
quartiles. As a general rule, the number of plants used in each stage increases with the VI quartile.
The increase however is less than proportional to the increase in the size of the VI unit, implying an
increase in average plant size with the size of the VI unit. For Central SOEs, the number of sinter
and pig-iron plants actually falls with VI size. For steel, they increase, but less rapidly than they
do in either provincial SOEs or private firms. This behavior gives rise to systematic differences in
the number of plants and plant size in each stage of production as the size of the VI unit increases.
In particular, central SOEs consistently operate the smallest number and largest plants in each
size category, followed by provincial SOEs and then private firms. Alternatively, as private firms
expand, they do so using more plants of smaller average size compared to SOEs.
7
3
Estimating total factor productivity of vertically-integrated firms
This section describes a framework to estimate total factor productivity of multiple stage pro-
duction systems. Section 3.1 discusses the timeline of firms’ decision. Section 3.2 presents the
theoretical framework and the methodology to construct aggregate productivity for VI units. Section 3.3 explains the details of our estimation procedure.
3.1
Description of firm decision
We now describe how firms make choices regarding investment and production. At the beginning
of each year, a firm observes its state, which includes observable variables that affect their input
access, output market and borrowing/regulation constraints. Based on its initial state, the firm
chooses its targeted level of total production to maximize current profit. This production must then
be allocated among vertically-integrated units (VI) and plants in each stage to minimize its total
production cost. After observing production, the firm is informed of its productivity. At the end
of the year, the firm decides on investment, which depends on the current state and productivity.
Moreover, the choice of investment (i.e., whether or not to vertically integrate, the size of the VI
unit, and its internal configuration) is limited by current regulations (mostly on minimum size of the
plants) and has dynamic implications: first, larger plants are less flexible on input and potentially
more costly to maintain, which affects the expected payoff when there is uncertainty in the input
market; second, larger plants enjoy the benefits of increasing returns to scale.
Since we have short panel data, we leave the investigation of the full industry dynamics for
future research. Instead, we focus on the monthly production at each VI unit. At the beginning of
each month, each firm observes its stock of capital and labor and then its individual productivity
of plants. Based on these observables, the firm chooses its intermediate input for each plant in
the last stage. Note that the firm obtains its last-stage intermediate input through a second-tolast stage production. Moving backward, the firm chooses its intermediate input for each plant in
the second-to-last stage. The process continues in this manner till the first stage of production.
As is convention, we assume that intermediate input choices are monotone with respect to the
corresponding productivity. At the end of this month, the firm decides on hiring/firing employees
for each of its plants and maintaining/utilizing certain plants in the next month.
8
3.2
A model of multiple-stage production
In each period t, a VI unit (unit “i”) engages in three major stages of production, i.e. sintering
(stage “1”), pig iron making (stage “2”) and steel making (stage “3”). Along this production chain,
output in each stage serves as the key material input for the production of subsequent downstream.
For simplicity, we assume that each stage involves a single plant.15 A complete production process
is described as below:
β1
Yi1t = min{eωi1t Lαi1t1 Ki1t
, γ1 Ri1t }ei1t ,
(1)
β2 γ2
Yi2t = eωi2t +i2t Lαi2t2 Ki2t
Ri2t ,
(2)
β3 γ3
Yi3t = eωi3t +i3t Lαi3t3 Ki3t
Ri3t
(3)
where
Yi1t = Ri2t ,
Yi2t = Ri3t
and Ri1t represents crude iron ore fine, Yi1t and Ri2t denote sinter, Yi2t and Ri3t pig iron, and Yi3t
denotes the final product steel. Our measurement of capital Ki·t is the capacity of the plant in this
stage, and Li·t is the corresponding number of employees. Productivity ωit is Hicks-neutral. While
each stage uses a different technology, Yi1t = Ri2t and Yi2t = Ri3t reflect the intrinsic linkage of the
multiple-stage steel production. As sintering is an agglomeration process that reshapes iron ore to
the size and strength necessary for pig iron making, this stage of production is assumed Leontief
in materials.16
Applying the Leontief first order condition for sintering, we proceed with the following (log)
15
We will deal with multi-plant production later.
Substitutability may exist between raw iron ore and labor (capital) mostly likely due to the quality of iron ores.
However, we don’t have information on the raw iron ores used in sintering.
16
9
production system:
yi1t = α1 li1t + β1 ki1t + ωi1t + i1t ,
yi2t = α2 li2t + β2 ki2t + γ2 ri2t + ωi2t + i2t ,
yi3t = α3 li3t + β3 ki3t + γ3 ri3t + ωi3t + i3t ,
yi1t = ri2t ,
yi2t = ri3t
One advantage of the above production system is that it allows intuitive aggregation of stage
productivity. In particular, we obtain such an aggregate for each VI unit by combining the above
(log) production functions for the three stages following Domar (1961):
yi3t = ωit + α1 γ2 γ3 li1t + α2 γ3 li2t + α3 li3t + β1 γ2 γ3 ki1t + β2 γ3 ki2t + β3 ki3t + it
where ωit ≡ ωi3t + γ3 ωi2t + γ2 γ3 ωi1t and it ≡ i3t + γ3 i2t + γ2 γ3 i1t are aggregate productivity
and aggregate noise, respectively. Intuitively, the aggregate productivity ωit reflects the sum of
productivity in each stage of production weighted by its importance in the production chain using
elasticities.
Alternatively, we can use the value shares of pig iron and sinter out of the total value of steel as
the corresponding weights. We assume that producers face perfect competition for sinter, pig iron
and steel, the price of which are P1 , P2 and P3 , respectively. We omit VI unit subscript and time
subscript t in the following illustration. Iron making (steel making) plants choose labor L2 (L3 ) and
intermediate material R2 (R3 ) to maximize profits, while capital K2 (K3 ) is predetermined.17 The
first order conditions with respect to material R2 and R3 and the inter-linkage equalities equations
Y1 = R2 and Y2 = R3 imply:
P 1 Y1
P2 Y2
P2 Y2
γ3 =
P3 Y3
γ2 =
Hence we obtain the alternative weights:
17
Labor could be a dynamic choice too. We examine this more fully in our discussion of the estimation approach.
10
P 2 Y2
P 3 Y3
P 1 Y1
γ2 γ3 =
P 3 Y3
γ3 =
(4)
(5)
In addition, for the VI units that have multiple plants in each link of the production chain,
before aggregation, we first construct a weighted average stage productivity using as the weight
either the share of deterministic components of production (K α Lβ Rγ ) or the share of plant size.
3.3
Estimation approach
For estimation, we adopt the control function approach developed by Olley and Pakes (1996)
and rely on firm’s choice on intermediate inputs to control for unobserved productivity (Levinsohn
and Petrin (2003)). A major advantage of our data is that it contains plant-level information on
inputs and output, which allows estimating production functions by stage and the calculation of
plant-level productivity estimates. A standard procedure has two steps.18
In the first step, we use energy input to control for unobserved TFP. For stage s ∈ {2, 3}, the
energy input is determined by predetermined capital and labor, as well as TFP:
eist = φst (kist , list , ωist ).
Following Ackerberg, Caves, and Frazer (2015), we assume that φst (·) is strictly monotone in ωist
conditioning on (kist , list ). This implies that the above relationship can be inverted:
ωist = φ−1
st (kist , list , eist ).
Therefore, we obtain our first step estimating equation in which the output y is a semiparametric
function of inputs (kist , list , eist , rist )
yist = αs list + βs kist + γs rist + φ−1
st (kist , list , eist ) + ist
18
We abstract from firms’ entry/exit decisions since they are not prominent in the data. At this stage, we do not
take into account monthly entry/exit decisions of plants, but this could be dealt with in a manner similar to Olley
and Pakes (1996). Effectively, we can estimate the probability a plant shuts down and use it as a control in our
estimation.
11
As usual, we collect the deterministic terms and denote them as Φst (kist , list , eist , rist ) ≡ αs list +
βs kist + γs rist + φ−1
st (kist , list , eist ). Note that for stage s = 1, the same analysis follows by leaving
out ri1t due to the Leontief technology.
Ackerberg, Caves, and Frazer (2015) argue that firms may take longer time to optimally install
capital and labor input than to purchase intermediate inputs, which includes materials and energy.
Since our data are on monthly basis and include large SOEs that face larger hiring and firing costs,
labor is likely to be fixed or quasi-fixed. Therefore, it is reasonable to assume that the demand for
intermediate input depends on productivity and the predetermined capital and labor input. The
advantage of using energy inputs as control variables is two-fold: first, energy input is measured
in terms of standardized coal, which addresses the issue of potential bias resulting from quality
differences in inputs; and second, using energy input for the control function throughout all three
stages keeps our estimation consistent. To simplify illustration, the subsequent analysis abstracts
from stage subscript s. We approximate Φt (kit , lit , eit , rit ) by a high order polynomial and use
OLS regression for estimation. We also include ownership dummies (Downership), time dummies
(Dt) and province dummies (Dprovince) in the regression. In pig iron making, we adjust material
input r by the percentage of pure ore content to control for quality difference. In steel making,
plants differ significantly in the share of steel that goes through secondary refining. A major goal
of secondary refining is to remove impurities from the molten steel, so the intensity of secondary
refining potentially reflects the quality of pig iron used in steel making. To control for input quality
in steel making, we also include in the first stage a dummy to capture whether plants carry out
secondary refining (Dsecondit ) and then the share of steel that goes through secondary refining
(secondit ).
In the second step, we estimate the parameters θ ≡ (α, β, γ) ∈ Θ by GMM which exploits a
Markov assumption on the TFP and the timing of input choices. In particular, we assume that
TFP follows a first-order Markov process:
ωit = g(ωi,t−1 ) + ξit
which says that the current productivity shock consists of an expected term predicted by productivity at t − 1 (ωi,t−1 ) plus a deviation from the expectation, often referred to as the “innovation”
component (ξist ). Note that ωit is identified up to θ from the first step after taking out measurement errors and unanticipated shocks from output. We regress ωit on a linear function of ωi,t−1 to
12
obtain g(ωi,t−1 ).19 Denote ωit (θ) ≡ Φ̂t (kit , lit , eit , rit ) − αlit − βkit − γrit . For a given θ, g(·) can be
estimated and thus ξist (up to θ) is obtained. The latter is used to contruct the moment conditions:

li,t−1







lit




E[(ξit (θ) + it ) 
] = 0.
kit






ri,t−1


Φi,t−1 (ki,t−1 , li,t−1 , ri,t−1 )
Since the capital stock is a state variable at t, it should be orthogonal to the innovation shock
on productivity at t. We use current labor (lit ) as an instrument for itself because of its dynamic
feature. We also include labor at t − 1 as an additional instrument. And we use lagged material
input ri,t−1 as an instrument for rit . As pointed out by Gandhi, Navarro, and Rivers (2016), the
use of ξit + it rather than ξit alone in the moment condition is more general. We search over the
parameter space Θ to find α̂, β̂ and γ̂ that minimize the above moment conditions.
We use the GMM procedure to identify separately production function coefficients for each
individual stage s, s = {1, 2, 3}. As is commonly done, we also add firms’ age to the production
function to control for potential systematic differences in technology resulting from the learning-bydoing process.20 In steel making, we allow the status of secondary refining (Dsecondi,t−1 ) and the
share of secondary refining (secondi,t−1 ) to enter the productivity evolution process since secondary
refining technology may potentially impact the law of motion of productivity.
Measurement errors Our use of measures of output and inputs in physical units introduces
measurement errors, which can bias our estimates. We do not capture potential quality differences
in output, or in the firm’s human capital. Similar issues arise in our use of equipment capacity
as our measures for a firm’s capital.21 The number of employees that we use to measure labor
abstracts from differences in workers’ skill level. We will discuss more the measurement errors and
provide robustness check for our estimates by taking into account output quality and installation
price of production equipment.22
19
The results are robust to higher order polynomials.
Ideally we want to use a plant’s age to capture this process. Lacking this information, we use a firm’ age.
21
We extract the information from a report by the Chinese Iron and Steel Association. August 2016.
22
We do not have information on labor quality.
20
13
4
Main results
4.1
Production function coefficients and returns to scale
Table 6 presents estimates of the production function for sintering, iron making and steel making, the three major production stages along the value chain for steel. For each stage of production,
we report results using both OLS and GMM. The GMM estimation corrects for any endogeneity
bias due to the potential relation between input usage and unobserved productivity. For sintering,
the coefficients are only provided for labor and capital, and not for materials, reflecting the Leontief
technology.
For individual production parameters, the differences between the OLS and GMM results are
relatively small. The elasticities are largest for materials, followed by that for capital and then
labor. Of the three stages, sintering is the most capital intensive, followed by pig iron and then
steel making. More important differences emerge with respect to estimates of return to scale. Most
notably, our GMM estimates imply increasing returns to scale, and thus falling long-run average
costs, in each stage of production.23 The sum of the input elasticity is largest for sintering (1.12),
followed by steel making (1.06), and then iron making (1.03). Our finding of increasing returns
to scale in steel firms is consistent with recent plant-level estimates of 1.03 of Collard-Wexler and
De Loecker (2015) for the US steel industry and estimates of 1.07 by Sheng and Song (2012) for
China. Sheng and Song (2012) also use GMM, but their estimates are at the firm level and based
on an aggregate revenue production function.24
4.2
Dispersion of productivity
We derive TFP (Total Factor Productivity) estimates for each stage of production using the
production function estimates above. In Table 7, we report two measures of plant-level dispersion
for productivity: the coefficient of variation, and the ratio of TFP of plants at the 90th percentile to
those at 10th percentile.25 Several things are noteworthy. First, dispersion declines as production
moves downstream. While sintering plants at the 90th percentile are more than twice as productive
as the plants at the 10 percentile, in pig iron the ratio is 30 percent, and in steel making, the 90th
23
We replicate the OLS and GMM estimation for a thousand bootstrapped samples, and find that the mean of
the returns to scale from GMM is statistically larger than the returns to scale from the OLS.
24
Our estimates are most comparable to Collard-Wexler and De Loecker (2015), who are able to construct firm-level
input and output deflators, and thus effectively estimate a production function in physical terms.
25
The 90:10 ratios for sintering, iron making and steel making are based on the average productivity of plants over
time.The ratio for VI is based on the average productivity of vertically-integrated units over time.
14
percentile plants are 25 percent more productive than the 10th percentile plants. At the level of
vertically-integrated units, the 90:10 ratio is 1.91. Second, these differences are much smaller than
estimates for Chinese manufacturing in 2005 by Hsieh and Klenow (2009), who find a 90-10 ratio
of 11.5, or six time our estimates at the VI level.26
4.3
Productivity differences by ownership at plant level
We are interested in the effect of ownership on plant-level productivity. In Table 8, we report
estimates of productivity by ownership for each stage of production. Estimates are obtained from
simple OLS regressions of the log of plant-level TFP on ownership dummies that also control for
the effect of seasonality with the use of monthly dummies. In these regressions, central SOEs are
our omitted category. In both pig-iron making and steel-making, private firms have a productivity
advantage over central SOEs, 5.2 percent and 5.8 percent, respectively. Premiums of private firms
in both stages are slightly smaller in comparisons with provincial SOEs. In sharp contrast, the
productivity ordering by ownership is reversed for sintering: Plants of central SOEs are 8.6 percent
more productive than private plants, and 10.2 percent more productive than plants in provincial
SOEs.
Estimates we reported in Table 2 suggest important differences in the size distribution of plants,
with central SOEs consistently running the largest plants, followed by provincial SOEs, and then
private firms. To identify the role of plant size in explaining productivity differences by ownership,
we add to the previous regressions an interaction term between plant size and our ownership
dummies and report the estimates in Table 9.27 Three findings emerge: First, the coefficient on
size suggests a decline in TFP as size expands in central SOEs, our reference group, in all three
stages. Second, TFP in private plants declines relative to central SOEs as size expands in all three
production stages, with the effect more pronounced (and statistically significant) in iron-making
and steel production. These results imply that in larger plants the premium of private plants over
SOEs disappears and turns negative. Finally, for provincial SOEs, the productivity gap with central
SOEs narrows in sintering and iron-making as plant size expands, but widens in steel.
What might help to explain the reversal in the productivity ranking in the case of sintering?
26
There are a number of possible explanations for these differences. First, Hsieh and Klenow (2009)’s estimates
also reflect productivity differences within industries, but their estimate is calculated over all industries. Second,
their estimates are based on a value-added rather than gross aggregate production function. As they point out in the
paper, the measure of productivity should reflect the quality and variety of a plant’s products, not just its physical
productivity.
27
Note that in these regression we may be picking up the systematic (and unobserved) correlation between the
size of the plant and overall number of plants the firm is running.
15
A regular supply of iron ore is critical to the running of sintering plants. SOEs, especially central
SOEs, typically enjoy privileged access to iron ore.28 Central SOEs source imported iron ore
through long-term contracts directly with the importers, which enable them to build up inventories
of iron ore when prices are relatively low. In principle, sourcing difficulties could force private firms
to operate their sintering plants at lower rates of capacity utilization, which then show up as lower
productivity. Data on capacity utilization reveal only modest differences by ownership in the case
of sintering.29 Sourcing difficulties related to private firms’ more limited access to higher quality
iron ore however might hold the key to the differences we observe in productivity.30
In general, the quality of domestic iron ore is much lower than that of imported ore. This is
reflected, for example, in the ore’s percentage of silica, a chemical substance that lowers the quality
of sinter and also adversely affects the production process. For domestic iron ore, the silica content
ranges from 6.5 to 12 percent. By contrast, imported iron ore is more homogeneous in pure ore
content, and contains only 4 percent of silica.31 Over the three-year period between 2009 and 2011,
steel firms of all ownership in China relied heavily on imported ore, however private firms used
two-thirds more domestic iron ore than did SOEs: 33.3 percent versus 20 percent.32 The gap with
central SOEs might also be even higher than that suggested by these figures.
Sintering is positioned at the very beginning of the value chain and entails the production of
high quality burden out of crude iron ore fines. The use of lower grade domestic iron ores by private
firms necessitates additional processing in order to produce the iron ore of the desired quality for
pig-iron production. This ties up the processing equipment longer and requires additional labor
inputs, both of which translate directly into the lower plant productivity we observe.33
4.4
Productivity differences in VI by ownership
Recall that we can use either elasticities of material inputs or value shares to integrate estimates
of stage TFP into an aggregate TFP at VI level. In Table 10 we report these two sets of weights
for each stage of production. These weights deliver two main messages. First, the importance of
production to the overall efficiency in the value chain increases from upstream to downstream. The
28
Interview with a steel consultant at Shanghai Securities Research Institute in December, 2014.
Capacity utilization is measured here as the ratio of operating days to total calendar days minus scheduled
maintenance days. Private firms actually operate slightly more intensively than central SOEs by 1.8 percentage
points.
30
Factors influencing sintering process. July 8, 2013. http://ispatguru.com/factors-influencing-sintering-process/
31
The information on iron ore fines is extracted from Yu (2004).
32
Data on iron ore are reported on an annual basis and cover two-thirds of the firms in the production data.
33
In iron- and steel-making, however, our production function estimation already factors in the quality of the key
material inputs. In fact, controlling for input quality changes only slightly the magnitudes of productivity differentials.
29
16
sintering productivity is halved when we take into account its importance to the entire verticallyintegrated units, while over 80 percent of the productivity in iron making is transmitted to the
VI units. Second, the two alternative weights are similar in magnitudes, which suggests that our
estimated elasticities are reasonable. The two sets of weights deliver similar estimates of TFP. The
subsequent analysis is based on the TFP estimates weighted by the elasticities.
We present estimates of aggregate productivity differentials by ownership in Table 11. Column
(1) shows that private VI units are on average 6.2 percent more productive than the VI units in
central SOEs, and are 2.3 percent more productive relative to provincial SOEs. Two main messages
emerge. First, the ordering of productivity by ownership at the VI level follows that found in iron
making and steel making. This implies that the sizable productivity disadvantage of private firms
in sintering is more than offset by their superiority in the two downstream stages of production.
Second, the magnitude of the private ownership premium in steel seems small by comparison with
Hsieh and Song (2015)’s recent estimate of 33 percent for 2007 for the manufacturing sector, but
more in line with Berkowitz, Ma, and Nishioka (2016), who find an average 8.2 percent productivity
premium of private firms relative to SOEs between 2003 and 2007.34
Care must be taken in interpreting our estimates however. First, in addition to the likely
productivity losses in sintering tied to sourcing difficulties, private firms may be facing other constraints that impact their productivity relative to SOEs.35 Below, we examine the role possibly
played by restrictions on how private firm expand. In a less constrained environment, the premium
of private firms might be even larger. Second, with value added in the steel sector 25-30 percent
of gross output, even modest productivity differences of the sort we have estimated translate into
significant differences in profitability by ownership, which have wider implications.
4.5
The larger, the better?
We documented systematic differences in the size of VI units by ownership: SOEs in general
operate much larger VI units. The scatter plot of TFP against VI size in Figure 3 demonstrates a
negative relationship between the two for the full sample, with the slope much steeper for private
34
Differences in these estimates may come from several sources: First, estimation of a value-added versus grossoutput production function. Although both value-added and gross-output based TFP indices provide a measure of
technological change, the two will not necessarily be the same (Balk (2009)). Second, differences in assumptions
relating to the underlying production technology, e.g. Cobb-Douglass versus CES versus translog, may result in
differences in estimated TFP and our productivity ranking. And third, some estimates may only reflect within-sector
variation, while others capture both within and between sector differences.
35
Back of the envelope calculations suggest that eliminating the premium of central SOEs in sintering would raise
the premium of private firms at the VI level by 2-3 percentage points.
17
firms than SOEs. To examine how TFP differs systematically with VI size by ownership, we run
regressions of TFP on VI size that also include interaction terms of ownership dummies with VI
size. Results are provided in Table 11 column (2) and confirm the results of Figure 3. For central
SOEs, size appears to have no significant effect on TFP. In sharp contrast, for private firms, and
slightly less so for provincial SOEs, productivity of VI units declines with size. The coefficient
on the interaction term for private firms implies that with a doubling in size, their productivity
declines by 13.6 percent relative to central SOEs.36 This has the effect of reducing the productivity
premium of these firms relative to central SOEs at larger sizes.
To further illustrate how the productivity premium differs by size, and explore any potential
nonlinear relationships, we once again divide our sample into size quartiles and estimate productivity differentials by ownership for each of the subsamples. Table 12 confirms that the productivity
advantage of private VI units declines remarkably with size. Private firms outperform central SOEs
by 32.7 percent and provincial SOEs by 7.9 percent when the VI size is below the 25th percentile.
These premiums are huge relative to the average premiums of 6.2 percent and 2.3 percent that
we presented earlier. Clearly, a pooled-sample regression conceals any heterogeneity that might
be tied to the size of VI units. The productivity premium of private firms remains positive but
declines considerably in the second quartile. For VI units between the median and 75th percentile,
the ranking of TFP completely flips: Central SOEs demonstrate an absolute advantage in this
quartile of 19.8 and 5.2 percent relative to central and provincial SOEs, respectively. In the largest
quartile, private firms once again exhibit a significant advantage in TFP over the SOEs, however
this is tied to the operations of a single private VI unit. With output in the third size quartile
nearly forty percent of the private sector’s total steel production, the low relative productivity of
these VI plants drags down considerably the private sector’s overall premium relative to the SOEs.
The internal configuration of VI units
A vertically-integrated unit consists of sets of sinter-
ing, pig-iron and steel making plants. As firms expand existing vertically-integrated units, or build
new ones, they have choice over the size of the equipment/plant they use in each stage to obtain
their desired output capacity. In pig-iron, for example, they may decide to use two 400 m3 blast
furnaces rather than a single 800 m3 blast furnace. Similar options are available in the choice of
sintering equipment and steel furnaces. Differences in how vertically-integrated units of private and
state owned firms are internally configured may help explain the systematic relationship we found
36
Since the productivity of central SOEs is not systematically related to size, this also implies an absolute decline.
18
between size and productivity of these two types of firms.
To examine this relationship more fully, we first regress the number of plants in a VI unit on
log size and log size interacted with our ownership dummies. Since the number of plants is a
count variable, we report results in Table 13 using Poisson regression. Two findings emerge. First,
when central SOEs expand, the absolute number of plants drops in sintering and iron making, but
increases in steel making. Second, doubling the size of VI units in private firms is associated with
more plants in all stages of production, both absolutely and relative to SOEs that expand at the
same rate. In Table 14, we report related results from the perspective of average plant size. They
tell a complementary story. As the size of the VI unit doubles, the average size of private plants
in each stage of production increases, but increases less rapidly relative to central SOEs by 13.3
percentage points in sintering, 27.4 percentages points in iron making and 17 percentage points in
steel making.
In short, as private firms try to expand their capacity, they install larger plants, but more of
them since their average plant size is smaller than SOEs. From the perspective of Table 5, this
difference is especially sharp in the third quartile for iron-making, exactly the quartile in which
private plants in iron-making, and as VI units, do most poorly relative to the SOEs.
Larger plant size
As suggested by Table 9, TFP in private plants declines relative to cen-
tral SOEs as size expands in all three production stages, with the effect more pronounced (and
statistically significant) in iron-making and steel production.
Ahlbrandt, Fruehan, and Giarratani (1996) argue in the context of the US steel industry that
for a given level of technology, the best performing plants are those with the most capable production workers. More generally, newer technology and human capital are highly complementary.
In the context of China’s steel sector, larger plants require managers and workers with compatible
capabilities to effectively conduct operation.37 Li (2011) points out, for example, that by design
larger blast furnaces are more advanced in their technology (e.g. energy saving and environmental
friendly), and also more demanding in how they are operated and in the role of advanced management systems. Compared to small furnaces, workers need to control more strictly the size, shape
and temperature of the burdens fed into large furnaces, thereby putting a premium on higher quality shop-floor workers. For example, in larger furnaces, the production process must be carefully
monitored and slag removed almost immediately because of the greater risk that it might clog the
37
Note that our measure on labor does not distinguish between high- and low-skilled employees. We also don’t
have information on managers. Therefore, our TFP estimates should incorporate the variations in these two aspects.
19
furnace as pressure inside the furnace increases (Yao (2014)). More important, large blast furnaces
require managers adopt modern management procedures, such as “PDCA”, i.e. Plan, Do, Check
and Action. Large blast furnaces also generate huge amounts of data, hence, management and analysis of data are critical for operating and control of large and modern blast furnace.38 In addition,
large furnaces require additional care and maintenance, creating more challenges to technicians. A
temporary breakdown lasting a single minute can result in substantial costs.
However, human capital is more of a scarce resource in private firms. In China’s steel sector,
while 18.7 percent of total employees in SOEs had a college diploma and above, the fraction in
private firms was only 7.2 percent. In addition, skilled labor made up 4.7 percent of total employees
in SOEs, in contrast, private firms had merely 2 percent.39 SOEs in general provide better wage and
non-wage benefits (housing, pensions, child care and health care, etc) than private firms do, so are
more attracted in the labor market when searching for better human capital. There is a vast body
of literature that document earning gaps between SOEs and non-state firms in urban China.40 Even
though the earning premium of SOEs over private firms declined over time, the premium remained
to be 24 percent in 2007 (Démurger, Li, and Yang (2012)). The decomposition of earnings suggests
that the observed differentials are not only attributed to endowment of workers, hours worked, but
are largely to incomplete labor market integration tied to the ownership structure.41 The lack of
compatible managers and qualified workers could be one source to induce the rapidly declining
TFPs in the larger plants. In addition, the declining TFP with plant size regardless of ownership
may also reflect the learning by doing process required to fully master the newly installed larger
plants in the industry. It is common that larger furnaces fail to reach their full production efficiency
due to the lack of operational experience. Li (2011) documents relevant cases in Baosteel, which is
widely accepted as China’s most advanced steel maker. And the disadvantage in existing human
capital in private firms likely prolongs the time needed to digest the new technology.
Coordination
To operate VI units, firms have to coordinate multiple plants both within the
same stage and across stages. Ahlbrandt, Fruehan, and Giarratani (1996) point out that integrated
plants can best be described as a series of processes, which must be compatible and coordinated
38
High Capacity Iron Making with Large, Modern Blast Furnaces. International Conference on Emerging Trends
in Metals & Minerals Sector. New Delhi, 5 September 2014.
39
The figures are based on the authors’ calculation using the 2004 Industrial Survey Data.
40
See for example, Zhao (2002), Chen, Démurger, and Fournier (2005), Démurger, Fournier, Shi, and Zhong (2007),
Démurger, Li, and Yang (2012), Ge and Yang (2010), Xia, Song, Li, and Appleton (2013).
41
The earning variable in these literature cover both wage and non-wage benefits and is adjusted by regional living
standards.
20
in order to achieve maximum efficiency and quality of product. However, coordinating changes in
the work environment can be challenging, as it involves a series of practices including coaching,
facilitation, training and team building, conflict resolution, motivation and communication. Better
management practice and capable managers would facilitate coordination and thereby reduce the
coordination cost. We saw in the previous section that private firms in general face constraints
on human capital. This situation may apply to managerial talents as well. The lack of skilled
managers likely induces additional coordination cost at the expense of efficiency. Even if private
firms have as good managers as SOEs, the rising number of plants as they expand spreads more
thinly the managerial resources in private firms, posing more challenges for coordination in the
multi-process production.
To investigate how well each of the production stages are coordinated with each other, we
construct TFP correlations between two consecutive links along the production chain for each VI
unit. In Table 15 we present TFP correlations by ownership and by VI size. Private firms display
the highest TFP correlation across stages when VI size is below median. However, when VI units get
larger, TFP correlation drops steadily in private firms. In sharp contrast, TFP tends to align much
better across stages in larger SOEs. In short, the failure of the private firms to align production
efficiencies across stages when they expand translates into a loss in aggregate TFP.
4.6
Why private firms have relatively small plants?
The strongest diminishing size effect on TFP at plant level in private firms also helps to understand their choice on relatively smaller plants in times of expansion. Private firms very likely face
a set of constraints when they make expansion plans. Under such circumstances, the decision on
relatively smaller plants could still be optimal. There are a variety of reasons for why private firms
expand as they do.
Capital constraints It takes considerable investment cost to install a vertically integrated steel
unit. The installation cost of a single large plant is substantially larger than multiple small plants
with equal capacity. In Table 16, we present the installation cost by plant size. Taking blast
furnaces for iron-making as an example, to install two 500m3 furnaces rather than a single furnace
of 1000m3 would save up to approximately 4.5 million US dollars, or 7-8% of total investment.42
In theory, the increasing returns to scale should provide a strong motive for firms to install larger
42
The figures are based on an internal report prepared by the Chinese Metallurgy Planning Institute in August
2016 for the authors.
21
plants. However, it is widely documented that private firms in China are discriminated against
in the credit market.43 Hence, private firms face the trade-off between enjoying lower long-run
average cost by bearing the immediate high investment cost and making less costly investment.
The financing constraints very likely distort the decision of private firms and steer them towards a
second-best choice of installing smaller plants.
Regulatory constraints Rapid expansion of China’s steel sector in the last two decades has
produced unexpected and unwelcome outcomes notably massive excess capacity. The Chinese
central government wants to cut excessive capacity, and more importantly, to cut small firms
and restructure the industry around a few giant state-owned firms under its direct supervision.
Consequently, government permission is essential for capacity expansion. Nevertheless, to obtain
approval for expansion projects is extremely harder for private firms than for SOEs. Despite the
central directive to refrain capacity, there are cases in which firms expand with tacit consent from
local governments, which promote massive investment in their locality to improve local tax bases
and economic growth. Nevertheless, private firms that undergo large scale expansion would all too
easily draw public attention and become a target of upper-level regulatory agencies. A well-known
example was Tieban steel, a private firm, the owner of which ended up being sent to prison for
carrying out a large capacity expansion project of 8 million tons against the will of the central
government. On the contrary, splitting large scale expansion into several smaller projects and
install smaller plants one by one would be a much wiser action to take advantage of the regulatory
loophole. Therefore, the regulatory constraints could play a role in limiting the size of facilities in
private firms.
Human capital constraints
A growing body of literature and stylized facts demonstrate the
effect of firm ownership on firms’ capability in accessing resources and capital. Garnaut et al. (2012)
base their work on a surveyed sample of private enterprises in China and argue that private firms
are not only financially constrained, but are also constrained in other areas such as human capital.44
Iskandar uses the World Bank 2012 survey data to provide evidence that private firms are human
capital constrained in terms of skilled and trained labor force. The steel industry is no exception.
As we presented before, while 18.7 percent of total employees in SOEs had a college diploma and
43
Among many others, Brandt and Li (2003); Poncet, Steingress, and Vandenbussche (2010); Guariglia, Liu, and
Song (2011); Cull, Li, Sun, and Xu (2015).
44
The four surveyed cities include Beijing, Chengdu, Chengde and Wenzhou.
22
above, the fraction in private firms was only 7.2 percent. In addition, skilled labor accounted for 4.7
percent of total employees in SOEs, in contrast, private firms had merely 2 percent.45 Therefore,
smaller facilities are more compatible with the managerial talent, organizational capabilities and
skill sets that private firms have. Larger facilities require more talented and experienced managers
as well as higher skill workers, which SOEs likely have in more abundance.46
Raw material constraints
As is evidenced in Figure 4, the iron ore that smaller furnaces
accept covers a wide range of grade while larger furnaces only go with high grade ore. Access to
only lower grade iron ores and greater flexibility of smaller furnaces with respect to iron ore choice
may predispose them towards smaller units. Larger furnaces are substantially more demanding in
the quality of raw materials due to their structural features. The difficulty of firms in sourcing high
quality raw materials keeps them from installing large furnaces.
Production flexibility
Smaller facilities allow private firms to adjust more quickly to changing
market demand. Steel production, in general, is very responsive to market changes. When economy
booms, steel price rises, firms tend to produce more and expand more rapidly to grasp the rising
demand. Large facilities entail an enormous amount of building time, hence are associated with
more uncertainties, which would pull down the expected gains from the booming market. On the
other hand, when economy slows down, steel price drops, firms with several small facilities can
cease operation gradually and timely. Large facilities, however, are hard to be fully adjusted in the
short run due to the high cost in shutdown and re-light. For example, since January 2016, the steel
price has experienced a remarkable increase after a downturn in 2015. By April 2016, 40-50 million
tons of steel capacity - mostly in private firms - were estimated to have resumed production, which
accounted for more than 70% of the idle capacity in 2015. Big SOEs, on the contrary, did not
catch this new round of price surge to resume idle capacity. It requires thorough re-examination
and replacement of key components before a large sized blast furnace could be safely restarted.
The entire process usually takes two to four weeks and incurs tremendous cost, which keeps the big
SOEs from adjusting production flexibly.
47
45
The figures are based on the authors’ calculation using the 2004 Industrial Survey Data.
Several studies have also shown that state-owned firms in China hold aside large human resource inventories
(e.g. Peng and Heath (1996); Tan (2003)).
47
http://news.cqcoal.com/a/xinwenzixun/jinriguanzhu/2016/0427/65557.html
46
23
5
Discussion
5.1
Measurement error in capital
Capacity alone may not fully capture the variations in capital, which could result in a bias
in our productivity estimates. Installation costs per unit of capacity, for example, increase with
plant size.48 The potential bias results from two sources. First, the positive correlation between
capacity and unit installation cost leads to an upward bias in capital coefficients. Second, estimated
productivity contains the unit price of capacity. Other things equal, the overestimate of the capital
stock in private firms would lead to a downward bias in the productivity differentials that we found
in iron making and steel making.
The following proof formalizes our argument. To simplify the exposition, we subsume stage
subscript s and time subscript t. Let us rewrite the production function using price-adjusted
capital k ∗ , consisting of unit capacity price p and capacity k, the capital measure that we use in
our baseline estimation.
yi = αli + βki∗ + γri + ωi + i
= αli + βki + γri + βpi + ωi + i
In our baseline model, we treat unit capacity price p as measurement error. First, unit capacity price
p is positively correlated with capacity k, which will lead to a potential upward bias in the estimated
parameter on capital β. Second, our measure of productivity (β̂pi + ω̂i ) includes the unobserved
unit capacity price, which would potentially bias the ownership differentials in productivity. Let us
consider the estimated productivity differential of private plants and central SOEs, i.e., β̂(pprivate
−
i
pcentral
) + (ω̂iprivate − ω̂icentral ). The first term reflects capacity price difference, and the second
i
measures the true difference in productivity. As private plants are systematically smaller than
central SOEs, unit capacity price of private plants are expected to be lower. Consequently, the
first term of the productivity differential turns negative, which gives rise to a downward bias in the
estimated productivity premium of private plants as opposed to central SOEs.
We use the price information on installation price of steel making plants in Table 16 to adjust
capital, and re-estimate the production function for steel using this adjusted capital measure. The
estimated coefficients are reported in Table 17. Compared to the baseline estimation, using the ad48
We extract the information on installation cost of steel plants from an internal report prepared by the Chinese
Metallurgy Planning Institute in August 2016 per the authors’ request.
24
justed capital generates a lower coefficient in capital, as we predicted. We report the corresponding
productivity differentials in Table 18. The productivity premium of private plants relative to central SOEs rises from 5.8 percent to 7.5 percent, when we base our estimates on the price-adjusted
capital, and increase in relative TFP of nearly thirty percent.
Independent of plant size, systematic differences may also exist in the costs per unit of capacity
between private firms and SOEs. In general, we expect private firms to be more cost sensitive, and
for them to be successful in finding ways to build plants of any size at lower cost, and thus enjoy
lower per unit cost of capacity relative to SOEs. This source of measurement error would further
underestimate productivity premiums of private firms. Similar to our discussion about the bias
generated by ignoring the increasing unit cost of capacity with plant size, there will be an effect
coming through our estimate of the elasticity for capital, and our estimate of the capital stock of
these private firms. Additional information on capacity cost by ownership is needed to estimate
the magnitude of this bias.
5.2
Measurement error in output
From Table 19 we know that private firms produce lower quality output consistently in each of
the production stages. As to output quality, we observe qualification rates of sinter, iron and steel.
In addition, sintering plants report stability rate of sinter. Iron making plants report the share of
premium iron. And the share of secondary steel making provides an important piece of evidence
on the quality of steel. Output is measured in physical units in our data set, therefore precludes
output quality differences between firms, which could bias the productivity estimates, as illustrated
below. To simplify the exposition, we subsume stage and time subscripts.
yi∗ (yi , Xi ) = f (li , ki , ri ) + ωi + i
(6)
where y ∗ measures the quality-adjusted output, defined as a function of the observed output y and
X, a vector of output quality measures. f is a general production function and is stage-specific but
time-invariant. Assume that y and the quality components are additively separable.
yi∗ = yi + δ(Xi )
25
(7)
Substitute (7) into (6) generates the baseline production function that we estimated.
yi = f (li , ki , ri ) + (ωi − δ(Xi )) + i
(8)
Hence the estimated productivity ω̂i also incorporates output quality.
To see how output quality affects productivity differentials by ownership, we re-estimate the
aggregate productivity differentials by controlling the quality of each output. Table 20 shows that
productivity premium of private firms relative to central SOEs slightly drops when we control for
output quality, from 6.2 percent to 5.7 percent. And the premium relative to provincial SOEs
experience a more pronounced change, declining from 2.3 percent to less than 1 percent. The
shrinking premiums suggest that SOEs produce higher quality output at the expense of productivity.
6
Conclusion and future work
This paper is one of the first to study the underlying sources of productivity differences by
firms’ ownership structure through the lens of firms’ internal configuration. The new data set that
we construct provides plant-level information on production equipment, and inputs and output in
physical units for each stage in the value chain of vertically-integrated operations. We find that
firms’ internal configuration plays an important role in understanding the sources of productivity
differences between firms, and in inferring potential constraints that firms face. In particular, private firms are on average 6.2 percent more productive than central SOEs, and 2.3 percent relative
to provincial SOEs. This ranking lines up with our productivity estimates in the two downstream
production stages, but central SOEs outperform in sintering, most likely because of their superior
access to higher quality raw materials. Moreover, private firms expand by adding more but smaller
plants, which potentially reflects various constraints that they are facing. As a result, the productivity advantage of private firms declines with the size of vertically-integrated operations, turning
negative for units larger than the median. This paper suggests that the productivity advantage of
private firms would be significantly higher if the constraints were removed.
We see the present paper as the start of a research agenda that may encompass several further
projects. In the current paper, we impose the assumption that in a vertically-integrated operation,
each production unit (i.e., equipment) operates independently both within and across stages. In an
immediate extension, we are working to relax this assumption by allowing for productivity shocks
to be correlated within and across stages. This full-fledged description of productivity goes one step
26
further to characterize the links of vertically-integrated firms’ internal activities. We will jointly
estimate production functions for the three stages in the value chain. This extension will make an
important contribution in methodology to the production function literature.
The second project focuses on China’s industrial policy in the steel industry. Beijing has been
struggling to restructure the industry around a few giant national champions through two major
policy tools: capacity reduction and M &A (merger and acquisition). We are working to examine
the consequences of these two aspects of policy. In one paper, we focus on firms’ decision-making
on investment under the policy influence of capacity reduction. On one hand, firms have strong
incentives to expand ex-ante to remain a significant player so as to avoid being shuttered or downsized. On the other hand, as suggested by the current paper, the government would likely cut
private firms, which are nevertheless the most efficient segments of the industry. Therefore, the
policy on capacity reduction may lead to unintended consequences. To understand the dynamic
implication of this policy, we will construct a dynamic structural model of firm investment on
steel capacity where SOEs and private firms expand under different borrowing/hiring/input constraints. We will estimate the model using manually assembled annual firm-level information on
output, steel capacity (capital), employees, wages, intermediate inputs and profits over 2000-2013
originating from the Chinese Iron and Steel Association. With the estimated model, we plan to
run counterfactual experiments of various capacity reduction schemes and study their impacts on
efficiency and welfare.
In another paper, we will explore the impact of M &A on firm efficiency and market power.
The central government has constantly promoted (and often imposed) consolidation during the last
15 years. We have constructed a timeline with details of annual M &A transactions from 2000 to
2013 in the steel industry. A particularly nice feature of our data is that firms report information
separately for subsidiary units both before and after such reorganizations. Therefore, the inputs
and detailed disaggregated output data by final product enable us to examine firms’ performance
with regard to productivity, product mix and markups before- and after-M &A.
We anticipate a series of papers that will generate policy implications to a globally important
industry at the center of China’s proposals for rebalancing of the economy. In addition, the implication of our work is not restricted to China’s steel industry. The analytic frameworks that we
propose should provide broad insights into future research on the performance of complex industrial
operations, and in particular, the industries under government regulation.
27
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30
Figure 1: Steel Technology of Vertically-Integrated Firms
31
Figure 2: Firm Structure of Vertically Integrated Firms
32
2
-2
0
aggregate tfp
2
0
-2
aggregate tfp
4
TFP and VI size (central)
4
TFP and VI size (full sample)
3
4
5
logsize
6
7
3
6
7
4
2
-2
0
aggregate tfp
2
0
-2
aggregate tfp
5
logsize
TFP and VI size (private)
4
TFP and VI size (provincial)
4
3
4
5
logsize
6
7
3
4
5
logsize
6
Figure 3: Aggregate TFP and Size of Vertically-Integrated Units
Notes: VI size is measured by the total size of steel making plants within the VI units.
33
7
60
Percentage of pure ore content
52
54
56
58
50
5
6
7
logsize
quality
lpoly smooth: quality
8
9
95% CI
Fitted values
Figure 4: Grade of Iron Ore and Size of Iron-Making Plants (Blast Furnace)
Notes: Blast furnace size is measured by the effective volume of the furnace in cubic meters (m3 ).
34
Table 1: Total Number of Plants and Production Share by Ownership
Panel A: Sintering
Number of Plants
Product Share
(1)
Full Sample
343
100%
(2)
Central
56
19.8%
(3)
Provincial
203
61.3%
(4)
Private
84
18.9%
Number of Plants
Product Share
Panel B: Iron Making
(1)
(2)
Full Sample Central
490
92
100%
19.3%
(3)
Provincial
249
59.4%
(4)
Private
149
21.3%
Number of Plants
Product Share
Panel C: Steel Making
(1)
(2)
Full Sample Central
342
68
100%
18.4%
(3)
Provincial
209
63.4%
(4)
Private
65
18.3%
(3)
Provincial
77
(4)
Private
33
(3)
Provincial
35
(4)
Private
15
Number of VI Units
Number of Firms
Panel D: VI Units
(1)
(2)
Full Sample Central
136
26
Panel E: Firm
(1)
(2)
Full Sample Central
59
9
35
Table 2: Summary Statistics of Plant Size by Ownership
Panel A: Sintering
Total
Central
Provincial
Private
(1)
Number
343
56
203
84
(2)
Mean
156
204
158
122
(3)
Std. Dev
127
161
127
84
(4)
Min
24
24
24
24
(5)
Max
853
853
550
360
(4)
Min
128
200
128
179
(5)
Max
5500
4038
5500
2680
(4)
Min
12
30
12
30
(5)
Max
300
260
300
180
Panel B: Pig iron making
Total
Central
Provincial
Private
(1)
Number
490
92
249
149
(2)
Mean
1016
1230
1127
698
(3)
Std. Dev
926
1046
1036
460
Panel C: Steel making
Total
Central
Provincial
Private
(1)
Number
342
68
209
65
(2)
Mean
95
123
93
72
(3)
Std. Dev
62
66
63
39
Notes: Sintering plant size is measured by the effective
areas of sintering machines in m2 ;iron making plant size
is measured by the effective volumes of blast furnaces in
m3 ; steel making plant size is measured by the tonnage
of basic oxygen furnaces.
36
Table 3: Summary Statistics of VI Unit Size by Ownership
Total
Central
Provincial
Private
(1)
Number
136
26
77
33
(2)
Mean Size
218
301
227
131
(3)
Std. Dev
185
212
190
96
(4)
Min
30
30
30
40
(5)
Max
990
840
990
540
Notes: VI size is measured by the total size of steel making
plants within the VI units.
37
Table 4: Number and Production Share of VI units by Size
Panel A: Size distribution of VI units
Central
Provincial
Private
Total
(1)
1st quartile
size<90
Number
3
16
13
32
(2)
2nd quartile
[90,160)
Number
6
21
11
38
(3)
3rd quartile
[160,300)
Number
5
18
8
31
(4)
4th quartile
size≥300
Number
12
22
1
35
(5)
Total
Number
26
77
33
136
Panel B: Output share by VI size
Central
Provincial
Private
Total
(1)
1st quartile
size<90
Output Share
0.8%
6.0%
4.3%
11.1%
(2)
2nd quartile
[90,160)
Output Share
1.5%
11.6%
4.6%
17.7%
(3)
3rd quartile
[160,300)
Output Share
2.9%
14.3%
6.7%
23.9%
(4)
4th quartile
size≥300
Output Share
13.3%
31.7%
2.4%
47.4%
(5)
Total
Output Share
18.5%
63.5%
18.0%
100.0%
Notes: VI size is measured by the total size of steel making plants within the VI units; the
size quartiles are calculated over the observations in the whole sample; output is measured by
steel.
38
Table 5: Internal Configuration of VI units
Sintering
(1)
Ownership
Central
Provincial
Private
Variables
Number of Plants
Average Size
Number of Plants
Average Size
Number of Plants
Average Size
Total
2.06
267
2.38
189
2.12
129
(2)
1st quartile
size<90
2.34
102
1.71
116
1.71
74
(3)
2nd quartile
[90,160)
2.38
95
2.22
141
2.31
147
(4)
3rd quartile
[160,300)
2.50
222
2.41
225
2.09
151
(5)
4th quartile
size≥300
1.66
393
2.87
248
5.00
360
(3)
2nd quartile
[90,160)
2.28
985
2.84
809
3.29
614
(4)
3rd quartile
[160,300)
2.13
1902
2.59
1770
3.56
826
(5)
4th quartile
size≥300
2.25
2840
2.94
2125
3.00
2680
(3)
2nd quartile
[90,160)
1.83
87
2.21
67
2.00
79
(4)
3rd quartile
[160,300)
2.26
94
3.09
81
2.69
84
(5)
4th quartile
size≥300
2.97
183
3.13
151
3.00
180
Iron Making
(1)
Ownership
Central
Provincial
Private
Variables
Number of Plants
Average Size
Number of Plants
Average Size
Number of Plants
Average Size
Total
2.27
2031
2.67
1406
2.82
707
(2)
1st quartile
size<90
2.71
475
1.99
613
1.85
482
Steel Making
(1)
Ownership
Central
Provincial
Private
Variables
Number of Plants
Average Size
Number of Plants
Average Size
Number of Plants
Average Size
Total
2.42
131
2.57
94
1.90
75
(2)
1st quartile
size<90
1.30
45
1.49
47
1.09
54
Notes: VI size is measured by the total size of steel making plants within the VI units; the size
quartiles are calculated over the observations in the whole sample; sintering plant size is measured
by the effective areas of sintering machines in m2 ; iron making plant size is measured by the effective
volumes of blast furnaces in m3 ; steel making plant size is measured by the tonnage of basic oxygen
furnaces.
39
Table 6: Production Functions
(1)
Variables
l
k
(2)
Sintering
OLS
GMM
0.212***
(0.0077)
0.812***
(0.0065)
0.215***
(0.0034)
0.901***
(0.00027)
0.000885***
(0.00028)
0.0006501
(0.00090)
7,630
0.808
YES
YES
YES
7,630
m
age
Observations
R-squared
Ownership FE
Province FE
Time FE
YES
YES
YES
(3)
(4)
Iron Making
OLS
GMM
(5)
(6)
Steel Making
OLS
GMM
0.119***
(0.0047)
0.298***
(0.0048)
0.594***
(0.0050)
0.000267*
(0.00014)
0.101***
(0.0013)
0.378***
(0.0011)
0.555***
(0.0049)
-0.000436*
(0.00024)
0.0602***
(0.0044)
0.155***
(0.0037)
0.746***
(0.0048)
-0.000305***
(0.00010)
0.0583***
(0.0021)
0.137***
(0.0029)
0.862***
(0.0019 )
-0.000522***
(0.00017)
10,087
0.921
YES
YES
YES
10,087
8,514
0.927
YES
YES
YES
8,514
YES
YES
YES
Note: Standard errors of GMM are computed via bootstrap of 1000 replications.
40
YES
YES
YES
Table 7: Dispersion of TFP
Variables
Sintering
Iron Making
Steel Making
VI
(1)
Std Dev
0.58
0.21
0.11
0.79
(2)
90:10 ratio
2.31
1.30
1.25
1.91
Notes: 90:10 ratios for sintering, iron
making and steel making are based on
the average productivity of plants over
time. The ratio for VI is based on
the average productivity of verticallyintegrated units over time.
41
Table 8: Ownership Premium in Productivity
Variables
Private
Provincial
Constant
Observations
R-squared
Time FE
(1)
(2)
(3)
Sintering
logtfp
Iron Making
logtfp
Steel Making
logtfp
-0.0855***
(0.0153)
-0.102***
(0.0133)
0.0395
(0.0293)
0.0515***
(0.00606)
0.0110**
(0.00558)
-0.0640***
(0.0122)
0.0576***
(0.00379)
0.00819***
(0.00315)
-0.0384***
(0.00721)
8,728
0.015
YES
11,837
0.020
YES
8,510
0.047
YES
Notes: Central SOEs are the omitted group. Private and
provincial indicate ownership dummies.
42
Table 9: Plant TFP and Plant Size by Production Stage
Variables
logsize
Private x logsize
Provincial x logsize
Private
Provincial
Constant
Observations
R-squared
Time FE
(1)
(2)
(3)
Sintering
logtfp
Iron Making
logtfp
Steel Making
logtfp
-0.160***
(0.0127)
-0.0104
(0.0184)
0.0609***
(0.0145)
-0.0981
(0.0887)
-0.426***
(0.0721)
0.814***
(0.0687)
-0.0443***
(0.00541)
-0.0460***
(0.00901)
0.0146**
(0.00623)
0.319***
(0.0595)
-0.0964**
(0.0431)
0.238***
(0.0391)
-0.0251***
(0.00440)
-0.0637***
(0.00656)
-0.0277***
(0.00481)
0.307***
(0.0292)
0.117***
(0.0227)
0.0772***
(0.0219)
8,728
0.070
YES
11,837
0.045
YES
8,510
0.157
YES
Notes: Sintering plant size is measured by the effective areas of
sintering machines in m2 ; iron making plant size is measured by
the effective volumes of blast furnaces in m3 ; steel making plant
size is measured by the tonnage of basic oxygen furnaces. Central
SOEs are the omitted group. Private and provincial indicate
ownership dummies.
43
Table 10: Weights for TFP Aggregation
Sintering
Iron making
Steel making
(1)
Weight 1
Elasticity
γ̂2 ∗ γ̂3
0.48
γ̂3
0.86
1
(2)
(3)
Weight 2
Value Share
Mean Std Dev
0.52
0.16
Mean Std Dev
0.82
0.05
1
Notes: γ̂2 is the estimated elasticity of material
input (iron ore) in iron-making production function. γ̂3 is the estimated elasticity of material
input (iron) in steel-making production function.
44
Table 11: Ownership Premium of Aggregate TFP
(1)
(2)
VI
logtfp
VI
logtfp
0.0622***
(0.0178)
0.0393**
(0.0156)
-0.0911***
(0.0341)
0.00715
(0.0164)
-0.136***
(0.0237)
-0.0809***
(0.0187)
0.707***
(0.122)
0.460***
(0.103)
-0.140
(0.0960)
3,440
0.018
YES
3,440
0.053
YES
Variables
logsize
Private x logsize
Provincial x logsize
Private
Provincial
Constant
Observations
R-squared
Time FE
VI denotes vertically-integrated units. VI size is
measured by the total size of steel making plants
within the VI units. Private and provincial are
ownership dummies.
45
Table 12: Ownership Premium of Aggregate TFP by VI Size
Variables
Private
Provincial
Constant
Observations
R-squared
Time FE
(1)
(2)
(3)
(4)
1st quartile
size<90
logtfp
2nd quartile
[90,160)
logtfp
3rd quartile
[160,300)
logtfp
4th quartile
size≥300
logtfp
0.327***
(0.0528)
0.248***
(0.0527)
-0.222***
(0.0822)
0.135***
(0.0464)
0.119***
(0.0421)
-0.141*
(0.0811)
-0.198***
(0.0277)
-0.0515**
(0.0257)
-0.0408
(0.0616)
0.195***
(0.0451)
-0.0223
(0.0175)
-0.101**
(0.0472)
748
0.082
YES
918
0.037
YES
802
0.107
YES
972
0.056
YES
VI size is measured by the total size of steel making plants within the VI
units. The size quartiles are calculated over the VI-month observations
in the pooled sample. Private and provincial are ownership dummies.
46
Table 13: Number of Plants and VI Size by Production Stage
Variables
logsize
Private x logsize
Provincial x logsize
Observations
R-squared
Owner FE
Time FE
(1)
(2)
(3)
Poisson
Sintering
Number
Poisson
Iron Making
Number
Poisson
Steel Making
Number
-0.246***
(0.0342)
0.603***
(0.0495)
0.508***
(0.0388)
-0.0652*
(0.0337)
0.436***
(0.0458)
0.192***
(0.0378)
0.370***
(0.0362)
0.133**
(0.0522)
-0.0426
(0.0403)
3,440
3,440
3,440
YES
YES
YES
YES
YES
YES
Notes: Number is simplified for number of plants. VI size is
measured by the total size of steel making plants within the VI
units. Private and provincial are ownership dummies.
47
Table 14: Average Plant Size and VI Size by Production Stage
Variables
logsize
Private x logsize
Provincial x logsize
Observations
R-squared
Owner FE
Time FE
(1)
(2)
(3)
Sintering
logsize
Iron Making
logsize
Steel Making
logsize
0.715***
(0.0323)
-0.133***
(0.0466)
-0.323***
(0.0368)
0.750***
(0.0281)
-0.274***
(0.0406)
-0.0850***
(0.0321)
0.617***
(0.0204)
-0.170***
(0.0294)
-0.00481
(0.0232)
3,440
0.337
YES
YES
3,440
0.538
YES
YES
3,440
0.594
YES
YES
Notes: VI size is measured by the total size of steel making
plants within the VI units. Sintering plant size is measured by
the effective areas of sintering machines in m2 ; iron making plant
size is measured by the effective volumes of blast furnaces in
m3 ; steel making plant size is measured by the tonnage of basic
oxygen furnaces. Private and provincial are ownership dummies.
48
Table 15: TFP Correlation by Ownership and by VI Size
Panel A: TFP correlation between sintering and iron making
Central
Provincial
Private
Mean
Std. Dev
Mean
Std. Dev
Mean
Std. Dev
(1)
1st quartile
size<90
(3)
2nd quartile
[90,160)
(5)
3rd quartile
[160,300)
(7)
4th quartile
size≥300
0.005
(0.0569)
0.337
(0.311)
0.573
(0.163)
0.188
(0.437)
0.327
(0.398)
0.535
(0.294)
0.411
(0.364)
0.422
(0.306)
0.257
(0.400)
0.396
(0.313)
0.487
(0.339)
0.240
Panel B: TFP correlation between iron making and steel making
Central
Provincial
Private
Mean
Std. Dev
Mean
Std. Dev
Mean
Std. Dev
(1)
1st quartile
size<90
(3)
2nd quartile
[90,160)
(5)
3rd quartile
[160,300)
(7)
4th quartile
size≥300
0.058
(0.0723)
0.225
(0.437
0.475
(0.229)
0.123
(0.447)
0.275
(0.383)
0.357
(0.373)
0.354
(0.301)
0.164
(0.491)
0.178
(0.480)
0.308
(0.341)
0.358
(0.314)
0.123
Notes: The correlation is calculated over the monthly TFP by verticallyintegrated units. VI size is measured by the total size of steel making plants within
the VI units. The size quartiles are calculated over the VI-month observations in
the pooled sample.
49
Table 16: Unit Cost of Plant Installation
Panel A: Blast Furnace (Iron Making)
Size (m3 )
450-1000
1000-2500
2500-4000
>4000
Unit cost( unit:1,000RMB))
360
390
415
475
Panel B: Basic Oxygen Furnace (Steel Making)
Size (tonnage)
≤50t
60-80
100-120
150-180
200-250
≤300
Unit cost(unit:1,000RMB))
2650
3350
4150
4650
5150
5750
Notes: Data Source: Chinese Iron and Steel Association. 1 US Dollar = 6.78 RMB.
50
Table 17: Production Function: Robustness Check
(1)
Variables
l
k
m
age
Observations
Ownership FE
Province FE
Time FE
(2)
Steel Making
Price-Adjusted Non-Adjusted
GMM
GMM
0.0598***
(0.0022)
0.117***
(0.0027)
0.870***
(0.0015)
-0.000629***
(0.00020)
0.0583***
(0.0021)
0.137***
(0.0029)
0.862***
(0.0019 )
-0.000522***
(0.00017)
8,514
YES
YES
YES
8,514
YES
YES
YES
Note: Standard errors of GMM estimation are
computed via bootstrap of 1000 replications.
51
Table 18: Ownership Premium of Productivity in
Steel Making: Robustness Check
Variables
Private
Provincial
Constant
Observations
R-squared
Time FE
(1)
(2)
Price-Adjusted
logtfp
Non-Adjusted
logtfp
0.0746***
(0.00402)
0.0179***
(0.00334)
-0.0459***
(0.00765)
0.0576***
(0.00379)
0.00819***
(0.00315)
-0.0384***
(0.00721)
8,510
0.056
YES
8,510
0.047
YES
Notes: Central SOEs are the omitted group.
Provincial and private are ownership dummies.
52
Table 19: Output Quality Differences by Ownership
Variables
Private
Provincial
Constant
Observations
R-squared
Time FE
(1)
(2)
(3)
(4)
(5)
(6)
Sintering
Qualification
Sintering
Grade Stability
Iron Making
Qualification
Iron Making
Premium Grade
Steel Making
Qualification
Steel Making
Secondary
-5.259***
(0.392)
-3.233***
(0.340)
95.52***
(0.750)
-10.35***
(0.814)
-2.195***
(0.707)
90.60***
(1.559)
-0.131**
(0.0586)
0.0819
(0.0539)
99.86***
(0.118)
-2.674***
(0.769)
-10.72***
(0.708)
70.06***
(1.544)
-0.101*
(0.0569)
-0.118**
(0.0473)
99.87***
(0.108)
-38.13***
(1.432)
-24.45***
(1.190)
55.36***
(2.729)
8,728
0.024
YES
8,728
0.026
YES
11,837
0.006
YES
11,837
0.031
YES
8,510
0.007
YES
8,510
0.081
YES
Notes: All quality measures are in percentage points. Secondary denotes the share of steel that goes through secondary
steel refining and provides an important piece of evidence on the quality of steel.
53
Table 20: Quality-Adjusted Ownership
Premium of Aggregate Productivity
Variables
Private
Provincial
Constant
Observations
R-squared
sinter quality
iron quality
steel quality
Time FE
(1)
(2)
logtfp
logtfp
0.0622***
(0.0178)
0.0393**
(0.0156)
-0.0911***
(0.0341)
0.0571***
(0.0185)
0.0490***
(0.0158)
0.120
(0.416)
3,440
0.018
NO
NO
NO
YES
3,440
0.050
YES
YES
YES
YES
Notes: Central SOEs are the omitted
group. Provincial and private are ownership dummies.
54
7
Appendix
7.1
Linkage of the vertically-integrated operations
Our data set reports information for each individual stage of the VI operations but does not
directly link the plants across stages within firms. The majority of firms in our sample own multiple
plants in each production stage, therefore firms could run several VI operations. And in practice,
within firms, VI operations are independent of each other. A subset of plants in the upstream
supplies intermediate materials only to certain plants in the downstream. The supply chain remains
fixed as the linkage is determined at the design stage to ensure that production capacity of each
individual stage should be in proportion to its immediate downstream. In the process of production,
sintering plants deliver sinter directly to blast furnaces that are tied to them through leather belts.
The iron making plants, in turn, are in charge of transporting smelted iron to the downstream basic
oxygen furnaces right after the iron leaves the blast furnaces. Production of each stage are strictly
aligned with one another, and output of each stage is transferred in time to the downstream stages.
Based on these features of the vertically-integrated firms, production of two consecutive stages in
the same periods should be a good criterion to identify linkage across stages, and we can ignore
inventory and also dynamic decisions, etc. As an industry convention, the ratio of iron production
to steel production is roughly 1 and that of sinter to iron is 1.25.49 The scatter plots in figure A1
and A2 provide convincing evidence to justify the linkage that we identified.
7.2
Algorithm
As discussed in Ackerberg, Caves, and Frazer (2015), the GMM estimation approach that we
take to the finite samples is subject to the convergence of local minimums. To address this concern,
we follow a flexible algorithm to set initial values for the objective function. We start from the
OLS estimates θols ≡ (αols , βols , γols ) (estimated elasticities for labor, capita and material input
respectively), and then we draw 100 random vectors v ≡ (vl , vk , vr ) from a uniform distribution
ranged from 0.8 to 1.2.50 We give perturbation to the OLS estimates using the random vectors v
and make 100 sets of initial values at θp ≡ θols · v 0 , p = 1, 2, ..., 100. For each set of initial values, we
obtain an optimal θ̂p , and we value the objective function using θ̂p . Finally we pick our estimates of
49
The information on the criterion of internal linkage in the steel value chain comes from a phone interview with
an engineer at the Design & Research Institute of Wuhan Iron & Steel Group in July 2016.
50
We relax the range to (0.7,1.3) and (0.9,1.1) too, and obtained robust estimates.
55
0
production of iron (unit: 10,000 tons)
100
200
300
θ̃ from the minimal values of the objective functions using these 100 different sets of initial values.51
0
100
200
production of sinter/1.25 (unit: 10,000 tons)
300
Figure A1: Linkage: Sintering-Iron Making
51
Ideally, one can expand the number of initial-value sets for robustness check. In our case, the convergence is
reached among these 100 sets of values.
56
100
production of steel (unit: 10,000 tons)
20
40
60
80
0
0
20
40
60
production of iron (unit: 10,000 tons)
Figure A2: Linkage: Iron Making-Steel Making
57
80
100