Received: 25 March 2020
DOI: 10.1111/grow.12430
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Revised: 28 July 2020
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Accepted: 11 August 2020
ORIGINAL ARTICLE
The heterogeneity of agglomeration effect: Evidence
from Chinese cities
Wenwen Wang1,2
1
School of Finance, Zhejiang University of
Finance & Economics, Hangzhou, China
2
School of Economics, Zhejiang
University, Hangzhou, China
Correspondence
Wenwen Wang, School of Finance,
Zhejiang University of Finance &
Economics, No. 18, Xueyuan Street,
Xiasha Higher Education Park, 310018
Hangzhou, China.
Email: wangwendy2018hi@gmail.com
Funding information
Research for this project was supported
by Zhejiang Institute of Social Science
and Technology Planning Office under
Grant (number19NDQN339YB) and
Management Office of the National
Statistical Scientific Research Organization
of China under Grant (number 2017LY06)
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1
Abstract
Using annual surveys of industrial firms in China from 1998
to 2007, this paper applies the non-linear least squares (NLS)
method based on a grid search to analyse the effect of city
size on firm total factor productivity (TFP). The results show
that overall, the agglomeration effects in large cities, but not
selection effects, significantly promote improvement in firm
TFP. The optimal agglomeration scales of different industries
differ as follows: those of capital- and technology-intensive
industries are larger than those of labour-intensive industries.
The agglomeration effects are also robust to different spatial areas without considering administrative boundaries. An
inverted U-shaped relationship exists between firm size and
agglomeration effects, while the relationship between firm
age and agglomeration effects is U-shaped. State-owned
firms experience weaker agglomeration effects than nonstate-owned firms. Cities higher in the administrative hierarchy and those with special economic zones have stronger
agglomeration effects. However, cities higher in the administrative hierarchy and those with a larger economic development zone index can provide more resources to increase the
survival rate of low-productivity firms; thus, selection effects
are not significant in Chinese cities.
IN T RO D U C T ION
Industrial agglomeration is regarded as the most important engine for industrial growth in developing
countries (Badr et al., 2019). Numerous studies have shown that industrial agglomeration contributes
to improvement in regional productivity (Andersson & Lööf, 2011; Badr et al., 2019; Ciccone, 2002;
392
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© 2020 Wiley Periodicals LLC.
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Growth and Change. 2021;52:392–424.
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Ke, 2010; Liang & Goetz, 2018). Scholars have found that co-agglomeration plays an important role
in economic spillover and promotes growth (Aleksandrova et al., 2020; Ellison et al., 2010). However,
the debate in the academic community regarding whether agglomeration effects are caused by intra-industry agglomeration (localization economies) or inter-industry agglomeration (urbanization
economies) has continued (Barufi et al., 2016; Cainelli et al., 2015; Fazio & Maltese, 2015; Glaeser
et al., 1992). In recent years, scholars have begun to emphasize the differences in agglomeration
effects among different industries and firms with different characteristics (Amara & Thabet, 2019;
Antonietti & Cainelli, 2011; Badr et al., 2019; Beaudry & Schiffauerova, 2009; Duschl et al., 2015;
Hartog et al., 2012; Hu & Liang, 2008; Kenney & Patton, 2005; Liang & Goetz, 2018; Neffke et al.,
2011; Tao et al., 2019). In addition, scholars have noted the heterogeneity of firms (Ottaviano, 2011)
and proposed that uncontrolled firm selection effects could cause endogenous problems and the overestimation of agglomeration effects (Ciccone, 2002; Henderson, 2003; Rosenthal & Strange, 2004).
Therefore, some studies combine agglomeration effects with selection effects and use data for empirical analyses (Arimoto et al., 2014; Baldwin & Okubo, 2006; Behrens et al., 2014; Cieślik et al., 2018;
Combes et al., 2012; Maré & Graham, 2013; Otsuka & Goto, 2015; Yu & Yang, 2014). However, few
existing studies comprehensively evaluate the heterogeneity of agglomeration effects while considering selection effects.
With fiscal decentralization and the economic growth-oriented promotion incentive institution
(Cao et al., 1999; Li & Zhou, 2005; Montinola & Jackman, 2002), local governments compete to
provide low-cost land and subsidize basic investment for manufacturing firms. Numerous industrial
parks and economic development zones have been constructed through the transfer of industrial land
at low prices. Areas with development zones have large advantages in attracting high-quality firms
due to the cheap land, tax relief, and credit support (Lu et al., 2019) and can form a scientific industrial
space layout in a targeted manner, affecting the agglomeration effects. However, many governmental
supports prolong the survival of a series of low-productivity firms, which, in turn, could negatively
affect the competition effects. In fact, there are numerous zombie firms in China (Wang et al., 2018).
The existence of such firms has seriously affected the market mechanism of the survival of the fittest.
Therefore, the development of agglomeration effects in China changes based on regional features, industry features, and firm features. These differences warrant further discussion. Based on the quantile
approach proposed by Combes et al. (2012), this paper uses the non-linear least squares (NLS) method
proposed by Yu and Yang (2014) to explore the influence of city size on firm TFP. By separating the
selection effects, it is found that the agglomeration effects significantly promote improvement in firm
TFP, while selection effects do not.
Subsequently, this paper divides industries into capital- and technology-intensive industries and
labour-intensive industries and finds that the optimal agglomeration scales of different industries differ. The agglomeration scales of capital- and technology-intensive industries are larger than those
of labour-intensive industries. An inverted U-shaped relationship exists between the firm size and
agglomeration effects, while a U-shaped relationship exists between the firm age and agglomeration
effects. The agglomeration effects of state-owned firms are weaker than those of non-state-owned
firms. Cities with higher administrative levels and cities with special economic zones have stronger
agglomeration effects. In addition, this article further analyses the reasons why the selection effects
are not significant.
The contributions of this paper are as follows. First, this paper uses the NLS method based on a
grid search to improve the quantile approach proposed by Combes et al. (2012), thereby reducing
the degree of non-linearity in the optimization objective function and improving the operating efficiency. Second, this article further examines the heterogeneity of agglomeration effects among different industries, firms with different characteristics and regions with different amounts of resources.
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Analysing the differences in agglomeration effects from various perspectives helps provide a comprehensive understanding of agglomeration effects. Third, this paper uses a web crawler to locate the
specific latitude and longitude of firms in a robustness test and uses ArcGIS to split space at different
units, thereby alleviating the interference of the modifiable areal unit problem (MAUP).
This paper proceeds as follows. Section 2 reviews the literature and proposes several hypotheses.
Section 3 introduces the theoretical model and methodology. Section 4 reports the data source and
variables. Section 5 reports the main regression results and several robustness checks. Finally, Section
6 draws the main conclusions.
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L IT E R AT U R E R E V IE W A N D RESEARCH HYPOTHESIS
As the data change from macro level to micro level, the discussion regarding agglomeration effects
changes from the regional level to firm level (Andersson & Lööf, 2011; Ciccone, 2002). Some scholars make a more detailed distinction between agglomeration effects and note that the benefits of
spillover depend on specific technical levels, business models, and indexes related to specific industries (Duschl et al., 2015).
Cities of different sizes have different forms of agglomeration effects; large cities have stronger
urbanization economies, while small cities have stronger localization economies (Glaeser et al., 1992).
Capital- and technology-intensive industries need technological support and capital requirements to
offset high risks. Industry development in each link in the industry chain in large cities is complete.
Firms can cooperate with scientific research institutions, financial institutions, public institutions, and
consulting agencies in large cities to gain financial, technical and informational support (Fu & Hong,
2008). Furthermore, capital- and technology-intensive industries have complex industrial chains and
require many intermediate products. Downstream capital- and technology-intensive industries benefit more from economies of scale in large cities’ intermediate product markets (Ke & Zhao, 2014;
Krugman & Venables, 1995). However, labour-intensive industries are still at the low end of technology, and firms in specialized markets can obtain production knowledge simply by imitating each other.
In addition, labour-intensive industries have a low need for intermediate goods, indicating that these
industries are less dependent on the economies of scale of intermediate goods markets in large cities.
Regarding firm characteristics, large firms have an advantage in seeking non-local intermediate
suppliers, which reduces the demand for local suppliers (Porter, 1998). In addition, large-scale firms
can provide better wages and attract more labour. Altogether, employment stability is high (Audretsch
& Thurik, 2001), and the labour pool cannot exert its role. In addition, regions with large firms hinder knowledge spillovers and foster a business culture, which, in turn, hinders innovation (Chinitz,
1961; Saxenian, 1994; Thurik & Carree, 1999). Finally, larger firms have a higher degree of vertical
integration, which prevents face-to-face communication (Enright, 1995) and hinders the formation of
agglomeration effects. The survival period of firms could also affect the agglomeration effects. As the
survival period of firms expands, firms can gain experience through “learning by doing” (Andersson
& Lööf, 2011; Thompson, 2005), thereby reducing its dependence on the external environment, but
firms with too long a lifespan may fall into a dilemma due to problems in the early part of their life,
such as vague ownership, and therefore be more dependent on the external industry chain for survival.
Regarding firm ownership, state-owned firms in China have a very important status for local governments, and thus, governments tend to protect the interests of state-owned firms and give them
more preferential policies (Bai et al., 2004). Therefore, the incentive of state-owned firms to reduce
transaction and production costs by linking with other firms is weak.
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Regarding regional characteristics, under the context of administrative decentralization and “promotion tournaments” (Li & Zhou, 2005), Chinese local governments adopt location preferences, such
as tax benefits, interest-free or low-interest loans and public subsidies, including energy, raw material,
land and technology subsidies, to promote urban economic development. Generally, cities higher in
the administrative hierarchy can obtain more state resources, such as physical and infrastructural inputs and financial supports (Chan & Zhao, 2002; Zhang & Zhao, 2001), and thereby attract targeted
firms to clusters (Haughwout et al., 2004; Koven & Lyons, 2002; Martin & Rogers, 1995). In cities,
local governments also allocate resources through providing land, public services, infrastructure and
subsidies to firms in economic development zones. The policy of attracting investment has led to the
concentration of industries in the economic development zones of the cities (Howell, 2019; Koster
et al., 2016; Lu et al., 2019). Local governments in cities with a higher administrative status and cities
with special economic development zones can attract firms in all positions of the industrial chain
through regionally targeted policies (Lu et al., 2019). Therefore, the industrial chain is more closed
through overall planning, and firm productivity is promoted through forward and backward spillovers
(Hu & Xie, 2014).
The above research findings only emphasize the impact of agglomeration effects. However,
there is heterogeneity among firms, and inefficient firms excluded from markets through competition could also improve the productivity of industrial agglomeration (Arimoto et al., 2014;
Behrens et al., 2014; Combes et al., 2012; Syverson, 2004). If only the agglomeration effects are
considered, the endogeneity problem between agglomeration and productivity could be severe
(Ciccone, 2002; Henderson, 2003; Rosenthal & Strange, 2004). To address such endogeneity,
several scholars use instrumental variables to address the endogeneity problem (Ciccone, 2002;
Ciccone & Hall, 1996; Henderson, 2003). However, the effects of agglomeration on productivity may still be overestimated without considering selection effects (Baldwin & Okubo, 2006).
Melitz and Ottaviano (2007) were the first to theoretically verify the existence of competitive
effects. Combes et al. (2012) integrated these two effects into a framework and tested this framework using French manufacturing data. The empirical evidence shows that the differences in the
productivity of French manufacturing firms are mainly derived from agglomeration effects and
that selection effects do not exist. In China, Yu and Yang (2014) noted that the method used by
Combes et al. (2012) has a high degree of non-linearity in optimizing the objective function and
that the bootstrap method runs at a slower speed in calculating the parameters. These authors
improved the regression method proposed by Combes et al. (2012) and used NLS based on a
grid search method to reduce the degree of non-linearity in the optimization objective function
and increase the running speed. The authors found that the productivity advantage of large cities
in China is derived from agglomeration effects rather than selection effects and that an S-type
relationship exists between city size and accumulated agglomeration effects.
Based on the above analysis, we propose the following four research hypotheses to guide our empirical analysis.
Hypothesis 1 Capital- and technology-intensive industries have a higher optimal city size than
labour-intensive industries.
Hypothesis 2 The agglomeration effects of smaller firms are stronger than those of larger firms.
Hypothesis 3 State-owned firms benefit less from agglomeration than non-state-owned firms.
Hypothesis 4 Cities with higher administrative levels and cities with special economic development zones have stronger agglomeration effects.
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3.1
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T H E O R E T ICA L MO D E L A ND M ETHODOLOGY
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Theoretical model
Drawing upon the theoretical model proposed by Combes et al. (2012), it is assumed that there are I
cities in a country and that the population of city i is Ni. The products of the consumer utility function
include numeraire and differentiated products. The production of numeraire assumes a constant return
to scale, while differentiated products are increasing returns to scale. According to first-order conditions, consumers’ demand functions for each differentiated product can be obtained. Moreover, the
price at which a certain consumer’s demand for a differentiated product in city i is exactly zero is the
cutoff price h−i , and products higher than the cutoff price will not be purchased. The demand function
can be expressed as a production function with a critical price and product prices. Firms that produce
a differentiated product need to pay s units sunk cost before entering the market, and only then will
the labour demand per unit of product, h, be known. Assuming wage is one unit, h is the marginal
cost of the firm. The draw of h is random, the probability density function is assumed to be g(h), and
the cumulative distribution function is G(h). Since the marginal cost and price under monopolistic
competition are equal, the threshold cost (cutoff) for any firm in a city to survive is also h.1 All firms
above this value have negative profits and cannot survive. At equilibrium, supply equals demand, and
the demand from city j to a firm in city i is the individual demand multiplied by city j’s size. In addition, the marginal cost of the firm is τijh, where τij is the iceberg cost of a unit of product transported
from city i to city j (when i = j, τij = 1, and when i ≠ j, τij > 1). The production cost for the threshold
of city j faced by a firm in city i is h−j ∕𝜏 ij. Then, we can determine the function of the profit of a given
firm in city i from city j with respect to price, namely, Πij = f(h−j , 𝜏 ij , h). Since firms are under monopolistic competition, entry and exit will end when the expected profits are zero. The expected operating
profit of a certain firm in each city of city i is the expected value of its profit, where the probability
density function of h is g(h); thus, the sum of the N expected profits in all cities and the sunk cost
can be balanced. By combining N equations, the critical threshold cost of city j can be expressed as
h−j = h(N1 , . . . , Nj , . . , 𝜏, . . . , s, g(h)).
The effect of agglomeration effects stems from the interaction between labour forces (Fujita &
Ogawa, 1982; Lucas & Rossi-Hansberg, 2002) under the assumption that the effective labour force
−(ln(di −1)
that a person in city i can provide
. ∑
∑ is ai h
Among them, ai = f1 (Ni , 𝛿 Nj ), di = g1 (Ni , 𝛿 Nj ) ai ≥ 1, 1 ≤ di ≤ e (when all cities have a scale
j≠i
j≠i
of 0, ai, di are both 1). The setting of δ is based on the interaction between cities, i.e., there will be
spatial decay within the city, i.e.𝛿 ∈ [0, 1]. In addition, h−(ln(di −1)) is set based on the difference in firm
costs, i.e., the effective labour that a person can provide depends on city size and the production cost
of the firm.
Therefore, the number of labourers to be employed by a certain firm in city i is the product of the
total output and the labour demand per unit of product divided by the unit effective labour that the
workers in the firm can provide, which can be derived as follows:
∑
li (h) = Qij (h) × h∕[ai h−(lndi −1) ]
j
Firm productivity is defined as the total output of a firm divided by the labour force employed;
∑
⎛ Qij (h) ⎞
⎜ j
⎟
thus, the efficiency of a firm can be expressed as 𝜙i (h) = ln ⎜
⎟ = Ai − Di ln(h).
⎜ li (h) ⎟
⎝
⎠
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Among them, Ai ≡ ln(ai ), Di ≡ ln(di ). In addition, all firms above the critical cost(of)city i will be
−
eliminated. Suppose Si is the share of a firm that is eventually eliminated Si ≡ 1 − G h
Therefore, A, D and S depict the degree of transformations of firm productivity in large cities relative to those in small cities. If A > 0, firm productivity in large cities is shifted to the right relative to
that in small cities, i.e., firms in large cities benefit more from agglomeration effects. D characterizes
the extent of dilation of firm productivity distribution in large cities relative to that of firm productivity distribution in small cities. If D > 1, the firm productivity distribution in large cities is dilated
relative to the firm productivity distribution in small cities. The difference between A and D is that the
former will cause all firms in the same city to receive the same degree of benefit, while the latter is
based on heterogeneous firm productivity. The degree of benefit due to the size of the city will change
according to firm productivity. High-productivity firms benefit more. S characterizes the truncation
degree of the firm productivity distribution in large cities relative to the firm productivity distribution
in small cities. If S > 0, the distribution of firm productivity in large cities has a left truncation relative
to that in small cities.
( )
̃
Referring to the study by Combes et al. (2012), let F(𝜙)
= 1 − G e−𝜙 be the potential cumulative
distribution of the density function of logarithmic firm productivity in the absence of agglomeration
and selection effects. The agglomeration effects cause a right shift and dilation of the distribution, while
selection effects imply left truncation. Therefore, the actual firm productivity distribution is obtained
by transforming the potential logarithmic firm productivity distribution. It can be proven that the cumulative distribution function Fi (Φ) of the logarithmic firm productivity in city i is given as follows:
⎧ ̃
⎪ F
Fi (𝜑) = max ⎨0,
⎪
⎩
�
𝜑−Ai
Di
�
⎫
− Si ⎪
⎬
1 − Si
⎪
⎭
(1)
As the cumulative distribution form of the logarithmic firm productivity is unknown, it is not feasible to directly obtain the parameters of different cities. Therefore, Combes et al. (2012) believe that
the relative parameters of cities can be estimated by comparing the cumulative distribution functions
of the logarithmic firm productivity in different cities. Therefore, the cumulative distribution function
Fj (Φ) of the logarithmic firm productivity of a similar city j can be expressed as follows2:
⎧ F̃
⎪
Fj (𝜑) = max ⎨0,
⎪
⎩
� 𝜑−A �
j
− Sj ⎫
⎪
⎬
1 − Sj
⎪
⎭
Dj
(2)
Let A = Ai–DAj, D = Di/Dj, and S = (Si–Sj)/(1–Sj). Assume city i is larger than city j. According to
the above description, it can be known that A, D, and S are the relative positions and left truncation of
the cumulative distribution function of the logarithmic firm productivity between cities. If agglomeration effects and selection effects can promote firm TFP, A > 0, D > 1, and S > 0.
When Si > Sj,
�
�
⎧
⎫
𝜑−A
⎪ Fj D − S ⎪
Fj (𝜑) = max ⎨0,
⎬
1−S
(3)
⎪
⎪
⎩
⎭
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When Si < Sj,
Fj (𝜑) = max
{
0,
Fi (D𝜑 + A) − S
}
(4)
−S
1 − 1−S
To obtain the parameter estimation formula, the cumulative distribution function of the logarithmic firm productivity is converted into a moment estimation represented by quantiles. First,
we transform (3) and (4) as follows: assume that the potential cumulative distribution function F̃ is
invertible; then, Fi and Fj are also invertible. Let 𝜆i (u) = F−1
be the quantile of Fi at probability
i (u)
−1
u and 𝜆j (u) = Fj (u) indicate the quantile of Fi at probability u. Through transformation, we obtain
the following:
m𝜃 (u) = 𝜆i (rs (u)) − D𝜆j (S + (1 − S)rs (u)) − A = 0, u ∈ [0, 1]
(5)
)
r̃s (u) − S
A
+ = 0, u ∈ [0, 1]
1−S
D
(6)
m
̃ 𝜃 (u) ≡ 𝜆j (̃rs (u)) −
1
𝜆
D i
(
} (
{
})
{
S
S
+ 1 − max 0, − 1−S
u, r̃s (u) = max {0, S} + (1 − max {0, S}) u.
where rs (u) = max 0, − 1−S
Combes et al. (2012) used the quantile approach to estimate the above model. Combes et al.
(2012)’s method is an extension of the generalized method of moments (GMM) method, which uses
continuous moments to estimate parameters under an infinite set.
To estimate the parameters of (5) and (6), Combes et al. (2012) transformed the moment condition of the theoretical quantile into the moment condition of the sample quantile; thus, the sample
estimation of λi and λj must be determined first. Using city i as an example, first, the logarithmic
firm productivity is listed in ascending order. Assuming that the value
of firm productivity is f, let
( )
( )
{
}
Φi = {𝜑i (0) , …, 𝜑i fi and 𝜑i (0) < … < 𝜑i (f); then, the quantile is 𝜆̃ i k = 𝜑i (k) , ∀k ∈ 0, …, fi , u ∈ (0, 1).
fi
The sample quantile estimation can be expressed as follows:
̂
𝜆i
𝜆i (u) = (k∗i + 1 − uEi )̂
(
k∗i
Ei
)
+ (uEi − k∗i )̂
𝜆i
(
k∗i + 1
Ei
)
(7)
where k∗i = int (uEi). For city j, the index of (7) is replaced with j. Then, Combes et al. (2012) estimated the parameter samples for solutions (5) and (6) by minimizing the following objective function:
̂
𝜃 = argmin M(𝜃)
(8)
1
1
̂̃ 𝜃 (u))2 du
where M(𝜃) = ∫ 0 (̂
m𝜃 (u))2 du + ∫ 0 ( m
∑
∑
1
1
K
Among them, ∫ m
̂̃ 𝜃 (u))2 du ≈ 1 Kk= 1 ( m
̂̃ 𝜃 (uk )2 +.
m𝜃 (uk )2 + m
̂ 𝜃 (uk−1 )2 )(uk − uk−1 ), ∫0 ( m
̂ 𝜃 (u)2 du ≈ 21 k = 1 (̂
0
2
̂̃ 𝜃 (uk−1 )2 )(uk − uk−1 )
m
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3.2
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399
Introduction to the NLS method based on a grid search
However, Yu and Yang (2014) noted that although the method approximates the number of quantile
rows linearly, the solution for obtaining parameters A, D, and S is still a very complicated and highly
non-linear function, rendering the solution process very complex.
Therefore, this paper adopts the non-linear least squares (NLS) method proposed by Yu and Yang
(2014) to estimate the regression results. This method is applicable when the explanatory variable and
dependent variable are non-linear. A typical non-linear regression model is listed as follows:
yt = xt (𝛽) + ut
yt is the explanatory variable, and β is the estimated parameter with k dimensions. Xt(β) is a non-linear regression function. Xt(β) indicates that the regression function will change with the observed
value mainly because Xt(β) depends on the explanatory variable.
NLS is widely used in the theory of industrial agglomeration. For example, some scholars use
the NLS method to estimate the exponential function to observe the spatial decay of agglomeration
effects based on the geographic distance (Ahlfeldt and Feddersen, 2018; Amiti and Cameron, 2007;
Andersson et al., 2004; Rice et al., 2006), and some scholars use NLS estimation models to measure
agglomeration and crowding effects (Ahlfeldt & Feddersen, 2018; Ciccone & Hall, 1996). The dependant variable and explanatory variables in the function in this paper also have a non-linear relationship; thus, the NLS method can be used for the regression estimation. The objective function of NLS
is as follows:
Q(𝛽) = SSR(𝛽) =
n
∑
(yt − xt (𝛽))2 = (y − x(𝛽))T (y − x(𝛽))
t=1
The key to NLS estimation is to find the β value that minimizes SSR(β).
Many algorithms can be used to minimize the smooth function Q(β). Most algorithms operate basically the same. The algorithm processes a series of iteration steps. In each iteration step, the algorithm
starts with a specific β and attempts to find a better estimation. The algorithm first selects the direction
for the search and then decides how far to proceed in that direction. After completing the operation,
the algorithm determines whether the current value of β is close enough to the local minimum value
of Q(β). If it is, the algorithm stops. Otherwise, the algorithm will choose another search direction and
repeat the process. The most common method used to estimate NLS is the Newton-Raphson method.
The following part provides a simple introduction to the Newton-Raphson method. Assuming that
Q(β) is twice continuously differentiable, given the initial value of β(0), the second-order Taylor expansion formula that is subsequently used is expanded around β(0) to obtain the approximate value of
Q(β) to Q*(β) as follows:
1
Q∗ (𝛽) = Q(𝛽 (0) ) + gT(0) (𝛽 − 𝛽 (0) ) + (𝛽 − 𝛽 (0) )T H(0) (𝛽 − 𝛽 (0) )
2
(9)
𝜕g
where g(𝛽) = 𝜕𝛽
is the gradient of Q(β), which is the column vector with dimension k, and H(β) is
2
the Hessian matrix of Q(β), which contains the elements 𝜕𝜕𝛽Q(𝛽)
, a matrix of order k×k. To simplify the
i 𝜕𝛽 j
notation, g(0) and H(0) represent g(β(0)) and H(β(0)), respectively.
It can be easily observed that the first-order condition for a minimum of Q*(β) with respect to β
can be written as follows:
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g(0) + H(0) (𝛽 − 𝛽 (0) ) = 0
Solving these equations will produce a new value of β, which we call β(1), as follows:
(10)
𝛽 (1) = 𝛽 (0) − H−1
g
(0) (0)
Equation (10) is the core of Newton-Raphson. If the quadratic approximation Q*(β) is a strictly
convex function, β(1) is the global minimum of Q*(β) if and only if the Hessian matrix H(0) is positive
definite. In addition, if Q*(β) is a good approximation of Q(β), β(1) should be close to ̂
𝛽 , and Q*(β) is
the minimum value of Q(β). The Newton-Raphson method involves repeatedly using Equation (10) to
find a series of values (β(1), β(2)…). When the original function Q(β) is a quadratic function that has a
global minimum at ̂
𝛽 , the Newton-Raphson method will obviously find ̂
𝛽 in the first step because the
quadratic approximation is then exact. When Q(β) is approximately quadratic, because all square sum
functions are close enough to their minimum values, the Newton method usually converges quickly.
Consequently, based on NLS, Yu and Yang (2014) proposed a simplified solution to estimate (8).
k ∈ [1, …, K], uk–uk–1 = b, where b is a fixed constant; thus, the objective function M(θ) of (8) can be
written as follows:
(11)
N(𝜃) = N1 (𝜃) + N2 (𝜃)
Among
them,
√
∑K
∑K
2 , a = 1, k ∈ [2, …, K], a = a = 1∕ 2.
̂
N1 (𝜃) = k = 1 (ak m
̂ 𝜃 (uk ))2 , N2 (𝜃) =
(a
(u
))
m
̃
k(
k
( (k = ))
( )) 1
(
( ))
1 k 𝜃 k
y1k (S) = ak ̂
𝜆i rs uk , x1k (S) = ak ̂
𝜆j S + (1 − S) rs uk , y2k (S) = ak ̂
𝜆j %̂rs uk ,
Let
( ( )
)
.
x2k (S) = (ak ̂
𝜆)i r̃s uk − S))∕ (1(− S)
)
̂
can
be
expanded
into
a
linear
function
as
ak m
̂ 𝜃 uk ( and
a
m
̃
u
k 𝜃
k
)
( )
̂̃ 𝜃 uk = y2k (S) − D−1 x2k (S) − D−1 Aak
follows:ak m
̂ 𝜃 uk = y1k (S) − Dx1k (S) − Aak , ak m
We define the following:
⎡ y11 (S) ⎤
⎢
⎥
Y1 (S) = ⎢ ⋮ ⎥ ,
⎢ y (S) ⎥
⎣ 1k
⎦
⎡ x11 (S) ⎤
⎢
⎥
X1 (S) = ⎢ ⋮ ⎥ ,
⎢ x (S) ⎥
⎣ 1K ⎦
⎡ y21 (S) ⎤
⎢
⎥
Y2 (S) = ⎢ ⋮ ⎥ ,
⎢ y (S) ⎥
⎣ 2k
⎦
⎡ x21 (S) ⎤
⎢
⎥
X2 (S) = ⎢ ⋮ ⎥
⎢ x (S) ⎥
⎣ 2K ⎦
The functions N1 (θ) and N2 (θ) can be converted as follows:
N1 (𝜃) = [Y1 (S) − DX1 (S) − Aa]� [Y1 (S) − DX1 (S) − Aa]
[
] [
]
1
A �
1
A
N2 (𝜃) = Y2 (S) − X2 (S) + a Y2 (S) − X2 (S) + a
D
D
D
D
(
)
Among them, a� = a1 , ⋯, aK .
[
]
[
]
[
]
[ ]
[ ]
Y1 (s)
X1 (s)
0k
a
0
We also define Y (S) =
, Z1 (S) =
, Z2 (S) =
, d1 =
, d2 = k .
0k
X2 (s)
a
Y2 (s)
0k
Then, (11) can be equivalently transformed as follows:
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400
|
401
⎧
⎫
N(𝜃) = 𝜀(S)� 𝜀(S)
⎪
⎪
1
A ⎬
⎨
Where
𝜀(S)
=
Y(S)
−
DZ
(S)
−
(S)
−
Ad
+
Z
d
1
1
⎪
D 2
D 2⎪
⎩
⎭
When S is a constant, (8) can be simplified to solve the non-linear LS estimation. Subsequently,
the Newton-Raphson iteration can be used to determine the parameter value.However, in this paper,
it may be difficult to converge by directly using the Newton-Raphson method to iteratively solve the
problem. Therefore, it is possible to use a grid search to determine the specific values of a certain
parameter and then use the Newton-Raphson method to perform the NLS estimation. A grid search is
a type of optimal algorithm. In the process of searching, the interval of the parameter is set first, and
then, the step is set. When the step is large, the accuracy is low. When the step is small, the accuracy is
high. If the search interval of X is [Xmin, Xmax], SX = (Xmax–Xmin)/KX is the step. For X, the Kth search
value is Xmin+(k–1)*SX, 0 ≤ k ≤ KX.
In this paper, the interval is divided into Q equal divisions with a certain accuracy in a given search
interval [c, d]. The parameter S uses the grid search method to divide any discontinuous points by the
above interval to calculate Y (S), Z1 (S), and Z2 (S) and uses the NLS estimation to solve parameters
A and D as follows:
Y(S) = DZ1 (S) +
A
1
Z (S) + Ad1 − d2 + 𝜀(S)
D 2
D
Then, the corresponding parameter S and non-linear estimation are determined according to the
corresponding minimum mean squared residual (MSR). Here, we define c = −0.5, d = 0.5, and Q =
100.
Furthermore, to ensure the robustness of the search results, we only use the moment conditions in
(5) and discard those in (6) to re-estimate the parameter when constructing the optimization objective
function. The objective function is simplified to N1 (θ). Meanwhile, the function is simplified to the
linear form of A and D, and the parameter value can be obtained by using the LS estimation. The corresponding linear equation is as follows:
Y1 (S) = DX1 (S) + Aa + 𝜀1 (S), where ε1 (s) is the corresponding error term.
4
4.1
|
DATA S OU RC E A N D VA R IABLES
|
Data source
The data used in this article are derived from annual surveys of industrial firms from 1998 to 2007.
The data are collected by corresponding regions and departments, which annually submit the data to
the State Statistical Bureau of China according to the country’s statistical scope, calculation methods,
statistical calibration, and reporting catalogues. The greatest feature of China’s industrial firm database is that it has many statistical indicators and a complete statistical scope. The statistical scope of
the Chinese industrial firm database contains large and above medium-sized manufacturing firms in
the region of mainland China, including state-owned firms, collectively run firms, stock-cooperation
ventures, joint ventures, limited liability firms, limited firms, private firms, other domestic firms,
Hong Kong firms, Macao- and Taiwan-invested firms, and foreign-invested firms. The industrial
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statistical indicators include the industrial added value, total industrial output value, industrial sales,
other indicators, financial cost indicators and employees’ wage.
The codes of the administrative divisions reported by the industrial firm database greatly vary
across different years. For the sake of comparison convenience, this article uses the administrative
division code issued by the National Bureau of Statistics on December 31, 2002 as the standard.
According to the national administrative division adjustment document announcement, we merge,
replace, delete or add the code of the administrative divisions of all years to unify the data to the standard in 2002. In addition, since China’s national economy industry classification system was revised
in 2002, the data classification of China’s industrial firms in 1999–2002 use the national economy
industry classification system GB/T4754-1994. To unify the industry calibration and allow the data to
be easily processed, this article adjusts the industry code from 1999 to 2002 according to the National
Economic Industry Classification GB/T4754-2002. Finally, it is inevitable that some flaws appear
during the survey and that some missing or unreasonable values of variables exist (such as negative
output) that are generated during actual production and operation; thus, we also exclude some samples. In addition, this article excludes firms whose operations have been discontinued, firms under
construction, firms that have been cancelled, firms under bankruptcy, and firms in other non-operational states and only uses data with an operating status code equal to 1. Finally, this article uses the
method proposed by Xie et al. (2008) and excludes samples with fewer than 8 employees or samples
in which the ratio of the added value to sale is less than 0 or greater than 1.
4.2
|
City size
We use the population of prefecture-level cities to measure city size. The data are derived from the
China Urban Statistical Yearbook. Due to the lack of data of some city indicators, only 213 of the 283
cities above the prefecture level remain after deleting the samples with missing values.
4.3
|
Firm productivity
We use the total factor productivity (TFP) to measure a firm’s productivity. When measuring a firm’s
TFP, simultaneity bias, selectivity and attrition bias exist. The former implies that a firm can partially
perceive its productivity information and change the factor input level to maximize profits, resulting
in endogeneity in the input factors; the latter occurs because the factor input of a firm determines its
survival probability in the face of exogenous shocks, biasing the capital estimation. This paper uses
the semi-parametric estimation method (referred to as the OP method) proposed by Olley and Pakes
(1996) to estimate firm TFP.3 This method makes investment decisions based on the current productivity of firms and uses the current investment of firms as an agent variable representing unobservable
firm productivity shocks to resolve the simultaneity bias.
Figures 1 and 2 show the geographical distribution of the city sizes and the corresponding average TFP of the firms. To a certain extent, the colour depth of the two variables in the figure shows
a corresponding relationship. Figure 3 shows the probability density distribution of the logarithmic
TFP of firms above the median city size and firms below the median city size. It can be found that
overall, the productivity probability density distribution function of urban firms above the median
city size is generally shifted farther to the right than that of urban firms below the median size.
Specifically, the average TFP of urban firms above the median city size is 3.56, and the average TFP
of urban firms below the median city size is 3.46. Subsequently, this article divides the industries
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402
FIGURE 1
|
403
Distribution of the mean urban population
into labour-intensive industries and capital- and technology-intensive industries and further characterizes the probability density distribution function of the logarithmic TFP of firms above and below
the median city size (see Figures 4 and 5). The average TFP of the capital- and technology-intensive
industries is 3.594 among those above the median city size and 3.496 among those below the median
city size. The average TFP of labour-intensive industries is 3.536 in cities above the median size and
3.411 in cities below the median size.
In addition, this article describes the probability density distribution of firms with different
ownership (Figures 6 and 7) as follows: the average TFP of non-state-owned firms in cities above
the median size is 3.656, while the average TFP in cities below the median is 3.573; the average
TFP of state-owned firms in cities above the median city size is 2.563, while the average TFP of
firms in cities below the median is 2.381. This article also characterizes the probability density
distributions of firms above and below the average firm size (Figures 8 and 9). When classifying
the sample according to the average firm size, we find the following: the average TFP of below-average sized firms in cities above the median city size is 3.605, the average TFP of below-average
sized firms in cities below the median is 3.541, the average TFP of above-average sized firms in
cities above the median city size is 3.628, and the average TFP of above-average sized in cities
below the median is 3.545.
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FIGURE 2
5
5.1
|
Distribution of the mean logarithmic total factor productivity
M A IN R E S U LTS
|
Basic regression
The main results obtained using the NLS estimation based on a grid search are presented in Table 1.
The results reflect 28 two-digit level manufacturing industries and all industries together using the
OP method.
Columns (1)-(5) in Table 1 include the estimation of A, D, and S, the corresponding standard
error and the regression’s R2. In Column (2), we can observe that D is larger than 1 in 18 of the 28
sectors and in the all-sector estimation. This finding shows that more than half of high-productivity
firms benefit more from being located in large cities. In addition, the estimated value of industry D in
all industries is 0.976, showing that the heterogeneity of the agglomeration effects is not significant
in the all-sector estimation. Using industries with industry code 18 (textile, clothing, shoe, and hat
industries) as an example, if the logarithmic TFP distribution in an area below the city size average is
shifted by 0.062, the firms will have a 9.63%, 10.1%, and 10.6% productivity advantage in the median,
second quartile and third quartile of the distribution, respectively. In Column (4), the estimated values
of A in 18 of the 28 sectors are significantly larger than zero, indicating that firms benefit more in
larger cities because of agglomeration effects. This result is consistent with the theory proposed by
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404
|
405
F I G U R E 3 Probability density distribution of the logarithmic total factor productivity of all industries in cities
above (solid) versus below (dashed) the median city size
F I G U R E 4 Probability density distribution of the logarithmic total factor productivity of labor-intensive
industries in cities above (solid) versus below (dashed) the median city size
Krugman (1991). In addition, if all industries are considered, the parameter of A is 0.821. This finding
shows that the average productivity of firms in large cities is e ^ 0.821-1 or 127% higher than that of
firms in small cities due to agglomeration effects. However, we find that regardless of whether we examine the whole sample or one sector, S remains zero or near zero, indicating that no selection effects
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F I G U R E 5 Probability density distribution of the logarithmic total factor productivity of capital technology
intensive industries in cities above (solid) versus below (dashed) the median city size
F I G U R E 6 Probability density distribution of the logarithmic total factor productivity of the non-state-owned
firm sample in cities above (solid) versus below (dashed) the median city size
exist in large cities in China, confirming the results reported by Combes et al. (2012). Column (6)
reports the R2 of the productivity distribution based on a grid search. The R2 of 15 of the 28 industries
are above 0.8. However, in some industries, the estimated value of A is negative, indicating that these
industries experience a congestion effect.
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406
|
407
F I G U R E 7 Probability density distribution of the logarithmic total factor productivity of the state-owned firm
sample in cities above (solid) versus below (dashed) the median city size
F I G U R E 8 Probability density distribution of the logarithmic total factor productivity of the below averagesized firms in cities above (solid) versus below (dashed) the median city size
5.2
|
Sensitivity analysis and robustness checks
To ensure the accuracy of the highest quality search and avoid possible local solutions for the nonlinear model optimization, we use LS estimation based on partial moments to calculate the parameters
in a grid search framework (see Table 1). It can be observed that the optimal solutions of the two
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F I G U R E 9 Probability density distribution of the logarithmic total factor productivity of the above averagesized firms in cities above (solid) versus below (dashed) the median city size
search methods are close, but the value of A estimated by LS is slightly larger than that estimated by
NLS, while the estimated value of D is smaller. Using industries with code 13 as an example, the A
and D estimations are 0.322 and 0.936, respectively, under the NLS estimation and 0.329 and 0.934,
respectively, under the LS estimation. Figure 10 reports the mean square residuals in which the overall
data are used to estimate the grid search under two moment conditions. It can be found that S = 0 is
the only minimum solution of the MSR.
To eliminate the bias caused by the OP method when estimating firm TFP, this article uses ordinary least squares (OLS), fixed-effect, and LP methods (Levinsohn et al., 2003) to re-estimate the
TFP of the overall sample (see Table 2). The parameters A, D and S estimated by the three methods
are basically similar to those estimated by the previous OP method. Because some determinants of
production are unobserved by econometricians but are observed by the firm, when using the OLS
method, an endogeneity problem exists. The fixed-effect model can only solve endogeneity problems
related to a time-invariant shock, which usually underestimates the coefficient of capital (Griliches &
Mairesse, 1995). The OP and LP method allow the optimal input decision to be converted into “observed” unobserved productivity shocks. Levinsohn et al. (2003) use a similar method but insert an
intermediate input demand function instead of an investment function to control for unobserved productivity shocks. The OP method requires data with zero investment to be discarded, while Levinsohn
et al. (2003) note that such data could sometimes account for a significant portion of the data. From
the result, we can find the OP method estimator A = 0.227 is the closest to the LP method estimator
A = 0.225 among 3 methods. The OLS method estimator D = 0.968 is the closest to LP method estimator D = 0.965 among 3 methods. S = 0 is still not significant in these three estimations. In general,
the estimated value of A under the fixed-effect model is the largest, followed by that estimated using
the OP method and finally that estimated by the OLS method.
Some evidence shows that spatial externalities will decrease as the distance increases (Békés &
Harasztosi, 2018; Briant et al., 2010). Fotheringham and Wong (1991) note that the MAUP renders
multivariate analysis results no longer stable. Rosenthal and Strange (2001) also note that the influence
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408
0
0
0
0.01
0
0
0.01
0
0.01
0
0
0
0
0
0
0.01
0
0
0
0
0
0
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
1.048
1.015
0.999
1.014
0.913
0.999
1.073
1.017
1.002
1.069
1.038
0.942
0.954
1.064
1.016
1.08
1.01
1.034
0.999
0.953
0.928
0.936
D
0.001
0.001
0.002
0.002
0.001
0.001
0.002
0.001
0.001
0.002
0.002
0.001
0.001
0.002
0.001
0.002
0.001
0.001
0.002
0.001
0.001
0.001
V(D)
0.095
0.346
0.433
0.322
−0.145
−0.059
0.014
0.06
0.4
0.08
−0.088
0.086
0.067
−0.219
−0.064
0.322
0.232
−0.205
0.033
−0.074
0.062
−0.002
A
0.004
0.003
0.008
0.006
0.005
0.004
0.006
0.003
0.003
0.006
0.007
0.005
0.004
0.006
0.004
0.008
0.003
0.004
0.01
0.005
0.003
0.005
V(A)
0.569
0.138
0.012
0.696
0.805
0.761
0.928
0.915
0.776
0.525
0.506
0.822
0.784
0.811
0.828
0.905
0.885
0.866
0.551
0.873
0.94
0.759
R
0
0
0
0
0
0
0.01
0
0
0
0
0
0
0.01
0
0.01
0
0
0.01
0
0
0
1.047
1.015
0.995
1.012
0.91
0.998
1.071
1.016
1.001
1.067
1.034
0.94
0.953
1.061
1.015
1.076
1.009
1.032
0.994
0.951
0.927
0.934
D
0.002
0.001
0.003
0.002
0.002
0.002
0.002
0.001
0.001
0.002
0.003
0.002
0.002
0.002
0.001
0.003
0.001
0.002
0.003
0.002
0.001
0.002
V(D)
(9)
0.065
0.002
0.117
0.353
0.436
0.329
−0.141
−0.056
0.031
0.068
0.408
0.084
−0.08
0.089
0.069
−0.211
−0.052
0.33
0.236
−0.196
0.036
−0.057
A
(10)
S
S
(8)
(7)
(5)
2
(4)
(6)
(3)
(1)
(2)
LS with partial moment condition
NLS with all moment condition
Basic regression results
0.006
0.005
0.012
0.008
0.007
0.005
0.008
0.005
0.005
0.009
0.01
0.007
0.005
0.009
0.005
0.012
0.005
0.006
0.014
0.007
0.005
0.007
V(A)
(11)
|
(Continues)
65,291
23,530
31,196
108,273
61,493
15,742
6,493
25,303
96,637
10,067
17,180
27,972
36,097
15,243
22,590
30,213
66,339
111,731
1,779
20,744
29,601
73,386
Observations
(12)
409
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Industry code
TABLE 1
WANG
0
0
0
0
0
0
36
37
39
40
41
All sectors
0.967
1.077
1.062
1
1.002
1.015
1.031
0.002
0.001
0.001
0.001
0.001
0.001
0.001
V(D)
0.034
0.091
0.113
0.045
0.217
−0.125
−0.06
A
0.005
0.003
0.005
0.004
0.005
0.004
0.005
V(A)
0.708
0.953
0.907
0.301
0.671
0.888
0.885
0
0
0
0
0
0
0
0.965
1.076
1.061
0.998
1
1.013
1.029
D
0.002
0.001
0.002
0.002
0.002
0.002
0.002
V(D)
0.038
0.097
0.118
0.051
0.225
−0.122
−0.055
A
(10)
0.008
0.005
0.007
0.006
0.007
0.006
0.007
V(A)
(11)
1,229,359
13,790
39,106
80,685
64,644
54,099
102,053
Observations
(12)
WANG
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Notes: A and D are the right shift and dilation degree of the potential cumulative distribution function of firm total factor productivity caused by agglomeration effects, and S is the probability that an
inefficient firm is excluded from the cities. V(D) and V(A) are standard errors of parameter D and A.
0
35
D
(9)
S
S
(8)
R2
(5)
(7)
(4)
(6)
(3)
(1)
(2)
LS with partial moment condition
NLS with all moment condition
(Continued)
|
Industry code
TABLE 1
410
FIGURE 10
|
411
Mean square residuals (MSR) of the grid search
of knowledge spillover has boundaries. To test whether the agglomeration effects are spatially stable,
this article uses programming to obtain the coordinates of the Baidu application programming interface (API) source based on the firm name and firm address and then uses ArcGIS to divide the area
into equal area squares. The specific steps are as follows. First, we use the Baidu Maps API to obtain
latitude and longitude information. Second, due to China’s policy restrictions, all domestic network
map service providers encrypt and shift map data. Thus, data from a map server cannot be directly
used for spatial analyses and require re-encoding into the international universal coordinate system
WGS1984. Third, we use ArcGIS analysis tools to divide the space into 100 km × 100 km, 200 km ×
200 km, and 400 km × 400 km squares (see Figures 11–13). Finally, based on the space boundaries of
the squares, the number of the firms in different squares is separately summed4. The results are shown
in Table 2. Although the values of the A estimators increase, which may be caused by the change in the
city size measurement, the direction of the estimators coincides with the previous results. It is found
that the results are still robust.
5.3
|
Heterogenous agglomeration effects
To further explore the heterogeneity of agglomeration effects in different industries, we divide the industries into capital- and technology-intensive and labour-intensive industries, separate the firm logarithmic TFP based on the city size into 19 groups in ascending order, and then use NLS based on a grid
search to determine the parameter estimation of each neighbouring group, including group 2-group 1,
group 3-group 2, and group 4-group 3, etc. It can be found that in the 19 groups, the estimated values
of A in 10 groups of capital- and technology-intensive industries are significantly greater than 0 and
those of D in 10 groups are greater than 1; the estimated values of A in 10 labour-intensive industries
are greater than 0 and those of D in 9 groups are greater than 1. In addition, this article describes the
trend in the cumulative value of parameter A, which depicts the change in the agglomeration effects
(see Figure 14). It can be found that as the size of the city increases, the cumulative agglomeration
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TABLE 2
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Robustness test
S
D
V(D)
A
V(i)
R2
Observations
0.002
0.213
0.005
0.702
1,147,993
Replacing the TFP measurement method
Tfp_OLS
0
0.968
Tfp_Fe
0
0.971
0.001
0.228
0.005
0.773
1,147,993
Tfp_LP
0
0.970
0.001
0.227
0.004
0.791
1,147,993
Re-estimation based on spatial scale adjustment
100 × 100
0
0.782
0.002
0.930
0.007
0.877
1,016,434
200 × 200
0
0.807
0.002
0.856
0.007
0.875
1,020,056
400 × 400
0
0.785
0.002
0.931
0.007
0.879
1,020,056
Regression results of different ownership firms
Sample of stateowned firms
0
1.005
0.001
0.065
0.004
0.806
113,349
Sample of nonstate-owned
firms
0
0.962
0.001
0.276
0.002
0.936
1,116,425
Regression results under different administrative interventions
Provincial city
sample
0
0.937
0.001
0.359
0.004
0.898
130,259
Sub-provincial
city sample
0
0.96
0.001
0.277
0.002
0.935
218,163
General city
sample
0
0.995
0.001
0.146
0.004
0.859
926,368
Sample of
Special
Economic
Zone Cities
0
0.893
0.001
0.553
0.004
0.931
38,525
Sample of
non-special
economic zone
cities
0
0.978
0.002
0.192
0.006
0.699
1,141,881
Notes: A and D are the right shift and dilation degree of the potential cumulative distribution function of firm total factor productivity
caused by agglomeration effect, and S is the probability that an inefficient firm is excluded from the cities. V(D) and V(A) are standard
errors of parameter D and A.
effects first increase and then decrease. The turning point of the inverted U-shaped curve of capitaland technology-intensive industries is even farther to the right than that of the labour-intensive industries. Capital- and technology-intensive industries experience the largest cumulative agglomeration
effect in groups 18-17, while the average city size in this group is 12 million. Labour-intensive industries achieve the largest cumulative agglomeration effect in groups 8-7, while the average city size is
4.8 million. This finding shows that capital- and technology-intensive industries generate the strongest agglomeration effects in mega cities, while labour-intensive industries can achieve the strongest
agglomeration effects in large cities.5 This conclusion coincides with hypothesis 1.
Subsequently, to test the heterogeneity of the agglomeration effects in firms of different sizes, this
article measures the size of the firm based on the average number of employees, arranges the average
number of employees in the firm in ascending order, separate all firms into 18 groups, and estimates
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412
FIGURE 11
100 km × 100 km
FIGURE 12
200 km × 200 km
|
413
parameters A, D, and S of the different groups. Then, we draw the trending figure of the agglomeration
effects based on the estimated value of parameter A (see Figure 15). It can be found that the agglomeration effects show an inverted U-shape, i.e., medium-sized firms benefit the most from agglomeration
effects, which is consistent with hypothesis 2.
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FIGURE 13
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400 km × 400 km
FIGURE 14
The relationship between the city size and cumulative agglomeration effects (A) in capital
technology-intensive industries (solid line) and labour-intensive industries (dashed line)
To examine whether there is a difference in the agglomeration effects of firms based on their survival time, this paper groups firms according to the firm age. To exclude outliers, this article removes
firms aged over 200 years or less than 0 years and then groups the remaining firms in ascending order
to examine the agglomeration effects and selection effects within different groups. As the age group
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414
FIGURE 15
|
415
The relationship between the firm size and agglomeration effects (A)
increases, the value of A decreases from 0.139 at the beginning to −0.056 in group 7 and then rises to
0.229 in group 18, indicating that the agglomeration effects show a U-shaped trend (see Figure 16).
This finding shows that as firms grow older, agglomeration effects initially weaken but later increase.
This paper also estimates the sample by dividing the firms into state-owned firms and non-stateowned firms (see Table 2). It can be found that the agglomeration effects experienced by state-owned
firms are significantly smaller than those experienced by non-state-owned firms, which is consistent
with hypothesis 3.
To test whether administrative intervention could influence the agglomeration effects, we divided
all cities into provincial cities, vice-provincial cities, and common cities to test whether the agglomeration effects vary among cities at different administrative hierarchical levels. As a result, we find that as
the administrative hierarchy decreases, the estimated value of A continues to decline (see Table 2). The
estimated value of A in provincial cities is 0.359, while that in common cities is only 0.146, indicating
that being higher in the administrative hierarchy does cause stronger agglomeration effects. In addition,
we conduct a regression after classifying the cities according to whether they have special economic
zones (SEZs). We can find that the agglomeration effects of cities with SEZs are significantly higher
than those of cities without special economic zones as follows: the parameter A of the former is 0.553,
which is almost double the parameter A of the latter, i.e., 0.192 (see Table 2). These findings are consistent with hypothesis 4.
5.4 | Why are selection effects not significant? An explanation from the
perspective of zombie firms
In this section, we further examine why the selection effects are not significant6 in China. The promotion of local officials in China is closely linked to the economic development of their jurisdiction (Li
& Zhou, 2005), and the bankruptcy of firms has a significant effect on the local GDP and employment rates (Min & Qun, 2012). To stabilize the economy, local officials may give higher subsidies to
firms with lower productivity or those that are “in the red”. In addition, to avoid defaults on bad loans
(Hoshi, 2006; Peek & Rosengren, 2005), banks continue to provide loans to these firms, preventing
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FIGURE 16
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The relationship between firm age and agglomeration effects (A)
inefficient firms from elimination (McGowan et al., 2017); these firms saved from elimination due to
government support are often called “zombie firms” (Caballero et al., 2008). Although zombie firms
do not produce benefits, the government invests production resources in these firms (Tan et al., 2016),
leading to a significant increase in their survival rate, a distortion in competition (Nishimura et al.,
2005) and chaotic market competition (Caballero et al., 2008).
Therefore, we use a semi-parametric Cox survival model to analyse the impact of government intervention on the survival risk of zombie firms and the reasons for the non-significant selection effects. We
use the actual profit method used by He and Zhu (2016) to identify zombie firms. We use the administrative hierarchy of the city(Rank) and economic development zone index(Zone_index) to measure the
resources in a city. We divide all cities into provincial cities, vice-provincial cities, and common cities as
follows: 2 represents provincial cities, 1 represents vice-provincial cities, and 0 represents common cities.
The construction of the economic development zone index is described in Démurger et al. (2002). By referring to the previous literature concerning the survival probability of firms and zombie firms (Agarwal
& Gort, 1996; Dimara et al., 2008; Doi, 1999; Du & Li, 2019; Evans, 1987; He & Yang, 2015; Jovanovic,
1982; Mata & Portugal, 1994; Olley & Pakes, 1996; Shen & Chen, 2017), we also input the logarithmic
firm scale (LnScale), capital density (Capitaldensity), industry concentration (HHI), whether to export
(Export_dummy), firm age (Firm_age), industry dummy variables (Industry_dummy), province dummy
variable (Province_dummy), and a time dummy (Year_dummy) as control variables in the Cox survival
model. The regression coefficients of the Rank and Zone_index are significantly negative at the 1% level,
indicating that firms in cities higher in the administrative hierarchy and those with a higher economic
development zone index have a higher probability of survival. This finding confirms that resources increase the survival of zombie firms. Subsequently, this article divides the sample into state-owned firms,
foreign-owned firms and private firms. The results are basically robust. The improvement in firm productivity originates from a transfer of resources from inefficient to efficient firms (Duranton et al., 2014).
Foster et al. (2006) use data of the US service industry and find that the productivity of exiting firms is
much lower than that of existing firms, but the productivity of new firms is higher than that of mature
firms. In fact, the existing “zombie firms” in China occupy the production factors invested by the government, significantly impeding patent applications and the TFP of normal firms (Tan et al., 2016). Over
time, this development model is not conducive to the upgrading of industrial clusters.
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416
6
|
|
417
CO NC LUSION S
Past studies have analysed the influence of agglomeration on productivity. However, few existing
studies have comprehensively evaluated the heterogeneity of agglomeration effects while considering
selection effects.
Therefore, this article uses data of Chinese industrial firms from 1998 to 2007 and finds that the
agglomeration effect is an important mechanism for improving firm TFP. However, agglomeration
effects are quite different across firms in different industries or of different ages, sizes or ownership or
in regions with different amounts of resources. By grouping the firms into capital- and technology-intensive industries and labour-intensive industries, we find that the optimal agglomeration scale for
capital- and technology-intensive industries is larger than that of labour-intensive industries. We also
find that the firm size and cumulative agglomeration effects have an inverted U-shaped relationship,
while a U-shaped relationship exists between firm age and agglomeration effects. State-owned firms
experience weaker agglomeration effects than non-state-owned firms. In addition, the agglomeration
effects are greater in cities higher in the administrative hierarchy and those with special economic
zones. Furthermore, we use a Cox survival analysis to analyse the influence of administrative intervention on zombie firms to explain why the selection effects are non-significant. We find that zombie
firms in cities higher in the administrative hierarchy and those with a higher economic development
zone index have a higher survival probability.
Therefore, this article provides the following policy implications. First, local governments should
consider industrial, firm and regional characteristics and rationally plan the industrial spatial layout
when implementing industrial policies. Second, to promote the healthy development of industrial
agglomeration, a market environment characterized by fair competition should be created for private
firms and foreign-owned firms. Third, local governments should allow the market to play a basic role
in allocating resources. Low-productivity firms should not be rescued by administrative means, as this
could hinder the entry of high-productivity firms and the exit of inefficient firms.
AUTHOR’ CONTRIBUTIONS
All authors contributed to the study conception and design. Material preparation, data collection, and
analysis were performed by Wenwen Wang. The first draft of the manuscript was written by Wenwen
Wang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
CODE AVAILABILIT Y STATEMENT
The code that support the findings of this study are available from the corresponding author upon
reasonable request.
ACKNOWLEDGMENTS
We would like to thank Professor Miaojun Wang, Professor Xiwei Zhu, Professor Xiangrong Jin, and
seminar participants at Zhejiang University. Our deepest gratitude also goes to editors and anonymous
reviewer(s) for their careful work and thoughtful suggestions.
CONFLICTS OF INTEREST
The authors declare that they have no conflict of interest.
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WANG
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DATA AVAILABILIT Y STATEMENT
The data that support the findings of this study are available from the corresponding author upon
reasonable request.
ORCID
Wenwen Wang
https://orcid.org/0000-0003-2758-6606
ENDNOTES
1
This is the cost for products only sold within its city. When products are sold outside the city, the transportation cost
should also be considered.
2
For the specific proof, refer to Combes et al. (2012).
3
We also use programs in the online appendix of Brandt et al. (2012) to match firms over the years.
4
The divided area’s city size cannot be measured in terms of previous urban populations. Li et al. (2019) believe that
the number of firms can be used as a proxy for the urban size. Therefore, this paper sums the number of firms in
different sub-regions to measure the scale of different space units.
5
In 2014, the State Council divided cities into five categories and seven tiers. Cities with a population greater than 10
million are considered mega cities; cities with a population of 5-10 million are considered super cities; cities with a
population of 3-5 million are considered type I large cities; cities with a population of 1-3 million are considered type
II large cities; cities with a population of 500,000 to 1 million are considered medium cities; cities with a population
of 200,000 to 500,000 are considered type I small cities; and cities with a population less than 200,000 are considered
type II small cities.
6
In addition, this paper also uses the method proposed by Arimoto et al. (2014), constructs an index to measure
market access, divides the sample into two groups according to the degree of market access, and further tests the
agglomeration and selection effects of prefecture-level cities with different market access levels to examine whether
market integration affected the significance of the selection effects. The indicator construction method is as follows:
∑Y
Market Potentialrt = d st Drs where Yst is the GDP of prefecture-level city s in year t, Drs is the distance between two
s rs
cities measured according to the prefecture-level city centre, and Drs captures whether r and s share a border. Because
China is a large country, geographical factors serve as a natural obstacle to market access in regions with very long
geographical distances. Therefore, the market potential here only considers access to neighboring prefecture-level
cities. However, this article did not find selection effects even in regions with low market integration, indicating that
market integration does not explain why the selection effects are not significant.
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How to cite this article: Wang W. The heterogeneity of agglomeration effect: Evidence from
Chinese cities. Growth and Change. 2021;52:392–424. https://doi.org/10.1111/grow.12430
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APPENDIX
TABLE A1
Industry name corresponding to the 2-digit industry code
2-digit industry code
Industry name
2-digit industry code
Industry name
13
Food Processing
27
Medical and
Pharmaceutical Products
14
Food Production
28
Chemical Fibers
15
Beverage Production
29
Rubber Products
16
Tobacco Processing
30
Plastic Products
17
Textile Industry
31
Non-metal Mineral
Products
18
Garments and Other Fiber
Products
32
Smelting and Pressing of
Ferrous Metals
19
Leather, Furs, Down, and
Related Products
33
Smelting and Pressing of
Nonferrous Metals
20
Timber Processing, Bamboo,
Cane, Palm Fiber, and Straw
Products
34
Metal Products
21
Furniture Manufacturing
35
Machinery and Equipment
Manufacturing
22
Papermaking and Paper Products
36
Special Equipment
Manufacturing
23
Printing and Record Pressing
37
Transportation Equipment
Manufacturing
24
Stationery, Educational, and
Sports Goods
39
Electric Equipment and
Machinery
25
Petroleum Processing, Coking
Products, Gas Production, and
Supply
40
Electronic and
Telecommunications
26
Raw Chemical Materials and
Chemical Products
41
Instruments, Meters,
Cultural, and Official
Machinery
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WANG
***p < .01; **p < .05; *p < .10.
−0.029***
0.000
4,713.85
20,479
YES
(−27.673)
2
0.000
671.8
4,091
YES
(−3.761)
−0.226
***
Stated-owned
3
−0.029***
0.000
759.7
3,756
YES
(−10.656)
4
0.000
929.61
10,831
YES
(−1.031)
−0.019
Foreign-owned
5
−0.031***
0.000
1,496.16
9,869
YES
(−21.398)
6
0.000
1,328.85
7,265
YES
(−2.999)
−0.158***
Private-owned
7
−0.028***
0.000
1,391.85
6,854
YES
(−12.289)
8
WANG
14682257, 2021, 1, Downloaded from https://onlinelibrary.wiley.com/doi/10.1111/grow.12430 by Zhejiang University, Wiley Online Library on [13/07/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
0.000
4,397.81
LR Chi2
Prob > Chi2
22,187
YES
(−2.098)
−0.058
Observations
Control variables
Zone_index
Rank
**
All samples
1
Further exploration of nonsignificant selection effects using cox survival analysis
|
TABLE A2
424