Measurement and Convergence in Development Performance of China’s High-tech Industry

Abstract

In China’s high-tech industry development, there exist regional scale and regional performance differences, of which the latter will influence resource allocation in regional high-tech industry and upgrading process of industrial structure.¹ Hence, the article conducts a systematic research of measurement and convergence analysis in development performance of China’s high-tech industry. The article contains two main research parts. First, in terms of measurement, by adopting the Malmquist index methods, the article measures the comprehensive performance of China’s high-tech industry development. Second, to conduct convergence analysis, it studies agglomeration patterns characteristics, absolute β convergence and its converging mechanism of China’s provincial high-tech industry development performance from 2001 to 2013 by adopting a spatial autoregressive (SAR) panel data model. The results indicate distinct absolute β convergence in China’s high-tech industry development performance is due to technology diffusion. In addition, convergence rates of different regions vary.

Introduction and Literature Review

General Background and Significance

Under China’s independent national innovation strategy from the beginning of the twenty-first century, high-tech industry has become the priority of a regional development policy which aims to accelerate economic transformation and upgrade industrial structures. However, due to regional economic disparities, regional differences can be seen in two aspects of high-tech industry development. The first aspect embraces quantitative differences, or differences in the scale of existing regional development. And the second aspect is qualitative differences, or differences in the performance of existing regional structures. The latter will directly influence the allocation of national innovation resources and the transition paths of regional economic development models. Thus, further analysis on the dynamic variations in China’s high-tech development performance and to grasp its dynamic evolutionary mechanisms is significant in driving the effective upgrading of regional industrial structures and ensuring the collaborative growth of regional economies.

Literature on Performance Measurement

When studying high-tech industry development, the measurement on performance must be the initial focus. Currently, estimation methods mainly adopt data envelopment analysis (DEA; Alexandra, Loannis & Aggelos, 2016; Babkin, Lipatnikov, & Muraveva, 2015; Kou et al., 2016) and stochastic frontier analysis (SFA; Jan, 2016; Su & Chen, 2015; Wang & Song, 2011). Wang and Yang (2010), using a three-stage DEA method, proved that environmental factors had important impacts on the operational efficiency of high-tech industry and concluded that China’s high-tech industry operational efficiency was basically congruent with regional economic development levels. Combining SFA and spatial econometric methods, Yu and Wu (2010) concluded institutional factors, scale factors and expenditure on technology had positive influences on high-tech R&D efficiency, along with the finding that government policy and corporation management performance did not have obvious influences on R&D efficiency. With the wide application and popularisation of panel data, the efficiency estimation approach based on panel data has been constantly enhanced; meanwhile, the factors influencing high-tech industry innovation performance have also been constructed and revealed. That high-tech industry agglomeration development patterns determine spatial factors is an important dimension when investigating high-tech industry development performance. Yao (2004) concluded Beijing and Shanghai had the greatest innovation ability by combining regional innovative ability with high-tech industrial space.

Comments and Theoretical Framework

The existing literature has analysed the development efficiency of China’s high-tech industry in different periods adopting methods from industrial and provincial perspectives; empirical studies have also been undertaken on the coordinated regional development path of China’s high-tech industry. However, there is no research combining these two aspects. Unfortunately, the regional agglomeration of high-tech industries will lead to spatial correlations, which will have particular and differing influences on the internal and external dynamics of China’s high-tech industrial development. Additionally, despite China’s regional economic development convergence (Tsun & Wu, 2013), provincial high-tech industries are not the same in scale; however, they converge spatially in development performance. Nevertheless, the current literature seldom focuses on the issue of spatial convergence in high-tech industry development performance, and there is a gap in the understanding of the mechanisms underlying performance convergence. Thus, the article will pay attention to the spatial evolution of China’s high-tech industry development performance. It employs spatial statistics and spatial panel econometric methods to analyse spatial correlation features and the convergence of China’s high-tech industry development, to find the mechanisms underlying performance convergence.

The article proceeds as follows. The next section studies measurement of high-tech industry development performance. The third section presents the analysis of performance spatial convergence by adopting an SAR model. The final section concludes. Table 1 offers an overview of equations and indicators for the following sections.

Measurement of High-tech Industry Development Performance

Model Introduction

High-tech industry development is a process of technological innovation and industrialisation led by creative agents. Therefore, high-tech industry development performance should reflect both economic and technical advantages. From the value chain perspective (Feng, Zhang, & Gao, 2011; Yu, 2009), the production process of high-tech industry embodies both technological creation and economic production. Technology output is just an intermediate output in the overall process. Thus, this article divides the measurement of high-tech industry development performance into two stages. The first stage is the measurement of technology system efficiency, which includes R&D investment expenditure, human resources, patents as R&D output and non-patent tacit technology; the second stage is the efficiency calculation of the economic system, including the technical output investment of the first stage and fixed-asset investment and human resource investments in the production process. All of these factors contribute directly to the economic growth of high-tech industry. In terms of comprehensive performance measurement, Guan and He (2009) directly adopted input in the first stage and output in the second stage as an input–output index to calculate efficiency. Yu (2009) multiplied the efficiency of the two stages to represent comprehensive performance. In my opinion, these two methods cannot fully accommodate the role of technology outputs as semi-finished products in the overall production process. Hence, this article adopts weights to multiply the efficacy coefficient of R&D efficiency value in each province per year from the first stage by the economy efficiency value from the second stage; the result is regarded as the comprehensive performance of high-tech industry development. This avoids not only the complete neglect of R&D efficiency but also the exaggeration of its role in comprehensive performance.

Table 1

Overview of Equations and Indicators

Categories	Explanations	Sector
Equations
$K_{i t}^{R} = E_{i t}^{R} + (1 - δ) K_{i t - 1}^{R}$	R&D fund stock	2(1)
$P R_{i t} = [L_{i t} / (L_{i t} + F_{i t})] \times C P I_{i t} + [F_{i t} / (L_{i t} + F_{i t})] \times F I I_{i t}$	R&D deflator	2(2)
$K_{i 0}^{R} = E_{i 0}^{R} (1 + g) / (g + δ)$	R&D stock in the base period	2(3)
$P_{i t} = p_{i t - 2} + (1 - ρ) p_{i t - 1} + {(1 - ρ)}^{2} p_{i t}$	Patent stock	2(4)
$G_{i t} = [R_{i t} - \min_{t} (R)] / [\max_{t} (R) - \min_{t} (R)]$	Coefficient of R&D efficiency	2(5)
$y_{i t} = G_{i t} \times E_{i t}$	High-tech industry development performance	2(6)
$M o r a n ’ s I = (\frac{n}{\sum_{i = 1}^{n} \sum_{j = 1}^{n} W_{i j}}) \times {[\sum_{i = 1}^{n} \sum_{j = 1}^{n} W_{i j} (x_{i} - \bar{x}) (x_{j} - \bar{x})] / \sum_{i = 1}^{n} (x_{i} - \bar{x})}$	Moran’s I	3(7)
$W_{i j} = {\begin{matrix} Q_{i j} / d_{i j}^{2}, i \neq j \\ 0, i = j \end{matrix}$	Dynamic economic spatial weight matrix	3(8)
$\ln (y_{i, t + τ} / y_{i t}) = α_{0} + β \ln ( y_{i t}) + u, u ~ N (0, σ^{2} I_{n})$	Standard efficiency convergence equation	3(9)
$\ln (y_{i, t + 1} / y_{i t}) = α_{0} + β \ln ( y_{i t} ) + η_{i} + γ_{t} + u, u ~ N (0, σ^{2} I_{n})$	Parameter estimation based on panel data	3(10)
$v = - \ln (1 + β)$	Convergence rate	3
$\ln (\frac{y_{i t + 1}}{y_{i t}}) = α_{0} + β \ln y_{i t} + ρ W \ln (\frac{y_{i t + 1}}{y_{i t}}) + {(I - λ W )}^{- 1} ξ + η_{i} + γ_{t} + u, u ~ N (0, α^{2} I_{n})$	General spatial autoregressive model (GSAM)	3(11)
$g = α_{0} + ρ W_{1} g + β \ln (y_{0}) + α k + ξ$	A spatial econometric model, incorporating spatial Factors and the convergence mechanisms of both Neoclassical school and new growth theory school	3(12)
$\begin{matrix} \ln g_{i t} = α_{0} + α_{1} k_{i (t - 1)} + β_{1} \ln y_{i (t - 1)} + β_{2} d_{e a s t} \ln y_{i (t - 1)} + β_{3} d_{m i d} \ln y_{i (t - 1)} + \\ β_{4} d_{w e s t} \ln y_{i (t - 1)} + ρ W \ln g_{i t} + η_{i} + γ_{t} + ξ \end{matrix}$	Model fitting the convergence mechanism of China’s high-tech industry development performance	3(13)
$D = {\begin{matrix} d_{e a s t} = 1, d_{m i d} = d_{w e s t} = 0; y_{i .} m e a n s c i t i e s i n e a s t e r n r e g i o n \\ d_{m i d} = 1, d_{e a s t} = d_{w e s t} = 0; y_{i .} m e a n s c i t i e s i n c e n t r a l r e g i o n \\ d_{w e s t} = 1, d_{m i d} = d_{e a s t} = 0; y_{i .} m e a n s c i t i e s i n w e s t e r n r e g i o n \\ d_{e a s t} = d_{m i d} = d_{w e s t} = 0; y_{i .} m e a n s c i t i e s i n n o r t h e a s t e r n r e g i o n . \end{matrix}$	Dummy variable D	3(14)
Variables
$K_{i t}^{R}$	R&D stock	2(1)
$E_{i t}^{R}$	Current R&D expenditure	2(1)
PR	R&D deflator	2(2)
L	Labor expense	2(2)
F	Equipment expenditure	2(2)
CPI	Consumer price index	2(2)
FII	Price index of investment in fixed assets	2(2)
P_it	Patent stock	2(4)
p_it	Patent amount of province i in time t	2(4)
G_it	Coefficient of R&D efficiency in province i in the year t	2(5)
R_it	R&D efficiency value of province i in the year t	2(5)
min_t(R)	Minimum values of R&D efficiency in the year t	2(5)
max_t(R)	Maximum values of R&D efficiency in the year t	2(5)
y_it	Comprehensive performance value of high-tech industry in province i in the year t	2(6)
E_it	Economic efficiency of high-tech industry in province i in the year t	2(6)
x_i	Observed value of province i	3(7)
w_ij	Component elements of the spatial weight matrix	3(7)
Q_ij	Per capita GDP of high-tech industry employees in the year t	3(8)
d_ij	Geographical distance	3(8)
y_it	Comprehensive performance in area i in the year t	3(9)
g	Average growth rate of GDP per unit labor	3(12)
y ₀	Initial GDP per unit labor	3(12)
k	Growth rate of capital stock per unit labor	3(12)
W ₁	Spatial weight matrix based on neighbor relationships	3(12)
g_it	Growth rate of high-tech industry comprehensive performance in region i in the year t	3(13)
k_it	Investment growth rate of high-tech industry comprehensive performance in region i in the year t	3(13)
y_it	Comprehensive performance of high-tech industry comprehensive performance in region i in the year t	3(13)
Predetermined Variable
g	Average growth rate of expenditure K	2(3)
ρ	Depreciation rate of knowledge	2(4)
τ	Time interval	3
Parameters
δ	Depreciation rate	2(1)
i	Province	2(1)
t	Time	2(1)

Source: Authors’ own.

Index Selecting and Processing

Input–Output Index of the Technology System

In output index selection, patent count is widely used to measure R&D efficiency, as in Chen & Liang (2010), Oto and Martina (2015) and Wang (2007). In China, patents include invention patents, utility model patents and appearance design patents, among which the invention patent represents the most advanced technology. This article, therefore, chooses invention patent as the output of technology innovation systems. As the tacit achievement of non-patent technology cannot be quantified, it is not considered here.

In index selection, R&D expenditure and human resource input are the well-known input indices (Claudio, Cristina, & Teresa, 2013; Gao & Chou, 2015). In terms of fund inputs, this article chooses internal expenditure on high-tech industry R&D as the index. As Griliches (1990) pointed out, since the influence of R&D activities on knowledge production should be a continuous process, R&D stock should be chosen to replace current revenue. According to the methods of Goto and Suzuki (1989), the equation for R&D fund stock is

K_{i t}^{R} = E_{i t}^{R} + (1 - δ) K_{i t - 1}^{R}

(1)

where $K_{i t}^{R}$ represents R&D stock, $E_{i t}^{R}$ is current R&D expenditure, δ is the depreciation rate, and i and t represent province and time, respectively.

To measure R&D capital stock, the article implements deflation from the base period on R&D input and calculations of stock. As for R&D input deflation, most of the literature selects the proportion of labour expense and equipment expenditure in R&D input as the R&D input deflator (Li et al., 2011; Zhu & Xu, 2003; 2006). However, these researchers assume that the R&D deflator of each province per year is the same, while the author believes that there are obvious regional differences in China’s economic development. The CPI and the price index of investment in fixed assets of each province are also different. The final equation for the R&D deflator used in this article is constructed as follows:

P R_{i t} = [L_{i t} / (L_{i t} + F_{i t})] \times C P I_{i t} + [F_{i t} / (L_{i t} + F_{i t})] \times F I I_{i t}

(2)

where PR is the R&D deflator, L represents labour expense, F is equipment expenditure, CPI is the consumer price index and FII is the price index of investment in fixed assets, while i denotes the province and t denotes the year.

As for the measurement of R&D stock $K_{i 0}^{R}$ , this article chooses the year 2000 as the base period. According to the existing literature (Artis & Boriss, 2016), assuming that the average growth rate of expenditure K before 2000 is g, the equation for R&D stock in the base period is

K_{i 0}^{R} = E_{i 0}^{R} + (1 + g) / (g + δ)

(3)

To fix g, a rate of 5 per cent is adopted (Cheng, Sun, & Wang, 2011). The depreciation rate of R&D stock is usually set at 15 per cent or 25 per cent. Given that a rate of 25 per cent is mainly determined by patent data, and that the range of items covered by patent data in China is different to that in other major countries,² this article sets the depreciation rate of R&D stock as 15 per cent.

Human resource input selects the full-time equivalent of R&D personnel, which reflects the summed workload of full-time R&D personnel (the cumulated working hours of stuff who are full-year engaged in R&D activities for 90 per cent or more of their working time) plus the workload of part-time personnel, which is converted into actual working hours.

Input–Output Index of Economic System

During the technology transfer process, there are technology inputs, fund inputs and human resource inputs, along with fixed-asset inputs into the technology industrialisation process. The technology input selected is the one measured in the first stage, namely, invention patents. Considering that there exist both time lags and degeneration before knowledge input actually influences output, this article chooses invention patent stock as the technology input. According to Guan and Liu (2005), there is a delay of 2 years before technology input yields output, which means the influence of the input of a given year will become obvious in the third ensuing year. Therefore, the equation of patent stock in this article is

P_{i t} = p_{i t - 2} + (1 - ρ) p_{i t - 1} + {(1 - ρ)}^{2} p_{i t}

(4)

where p_it represents the patent amount of province i in time t, P_it is patent stock, and ρ is the depreciation rate of knowledge. Due to a lack of related measurements of the depreciation rate of knowledge in the current literature, this article presumes that ρ is 12.5 per cent (Cheng, Sun, & Wang, 2011; Guan & Liu, 2005).

In terms of fund input, the focus should be on technology industrialisation inputs. The technological industrialisation process requires fixed-asset inputs such as new plant, new equipment and so on; in particular, specialised production equipment is needed in the industrialisation of new technologies. Hence, this article adopts new increases to fixed assets to reflect the fixed-asset input of high-tech industry. The smoothing coefficient of this index is the fixed-asset investment price index of each province per year; the fixed price point is the year 2000.

In terms of human resource input, this article chooses employee numbers in provincial high-tech industry as the index. Although there are obvious differences in the development scales of China’s regional high-tech industries, the number of employees in high-tech industry provides a measure of the scale of high-tech industry.

In terms of output, given that industry technology innovation involves production and that the value of new products is the result of “R&D-production” innovation, which can enhance the overall value of technology, this article chooses new product value as the variable indicating economic output.³ Meanwhile, to eliminate the influence caused by price fluctuations, the new product output value still need to be deflated. Referring to the principle of new product development and the investment index, this article adopts the producer price index (PPI) of each province as a deflator; the base period is also the year 2000.

Empirical Analysis of Efficiency Measurement

In choosing a method to measure efficiency, considering that we focus on R&D efficiency in the first stage and economic efficiency in the second stage—and, moreover, that economic efficiency evaluation criteria are codetermined by the allocation and utilisation of resource elements—this article chooses the total factor productivity index to represent the economic efficiency of high-tech industry. Total factor productivity means ‘the efficiency of production in a certain time’. It is a productivity index that represents the total yield of unit total input, namely, the ratio of total productivity to all factors input. This article adopts the CCR model (based on Charnes, Cooper, & Rhodes, 1978) employing DEA and the Malmquist index to measure both R&D and economic efficiency in the two stages of high-tech industry. These are mature methods, the details of which can be found in many studies and are omitted here.

Considering the existence of unparalleled development of China’s high-tech industry, in accordance with regional economic theory and using the relevant statistical standards available since 2010, China is divided into four regions in the article, namely, the eastern, central, western and northeast regions, thirty provinces and cities of China form the basic unit in this article. Region division can be referred in Table 2. To ensure the same statistical standard, the data are all drawn from the China Statistics Yearbook on High Technology Industry (2001–2014), the China Statistics Yearbook on science and technology (2001–2014) and the China Statistical Yearbook (2001–2014). Since China has, from the beginning of the twenty-first century, implemented the Western China Development Drive, the Northeast Old Industrial Base Revitalization, the Rise of Central China and other national development plans, this article chooses to investigate the period from 2001 to 2013.

Table 2

Region Division

Regions	Eastern Regions	Central Regions	Western Regions	Northeast Regions
Provinces and cities	Beijing	Shanxi	Inner Mongolia	Hei Longjiang
	Tianjin	Anhui	Shaanxi	Jilin
	Hebei	Jiangxi	Qinghai	Liaoning
	Shanghai	Henan	Ningxia
	Jiangsu	Hubei	Xinjiang
	Zhejiang	Hunan	Gansu
	Fujian		Sichuan
	Shandong		Chongqing
	Guangdong		Guizhou
	Hainan		Yunnan
			Guangxi

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on Science and Technology (2001–2014), China Statistical Yearbook (2001–2014).

Note: Due to a lack of data, Tibet is excluded, while Hong Kong and Macao are not considered due to their social systems.

As derived from the calculation and equation previously stated, the dynamic variation of China’s high-tech industry R&D efficiency and economic performance from 2001 to 2013 can be seen in Figures 1 and 2.

Figure 1

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on science and technology (2001–2014), China Statistical Yearbook (2001–2014).

Figure 2

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on science and technology (2001–2014), China Statistical Yearbook (2001–2014).

In Figure 1, it can be seen that the R&D efficiency of China’s high-tech industry is low in four regions. The eastern region ranks first, followed by the central region, northeast region and western region in mean order, all with the same variation tendency, which matches the conclusions reached by other scholars (Wang & Yang, 2010; Yu & Wu, 2010). Figure 2 shows that the economic efficiency of China’s high-tech industry in these four regions fluctuates violently, with totally different variation tendencies; the northeastern region ranks first, followed by the central region, western region and eastern region in mean order. By decomposing the Malmquist index further, it can be seen that the technical progress indices of northeast China and western China are obviously higher than that of eastern China, demonstrating that a series of industrial transfer policies implemented by the Chinese government not only contributed to economic development in the northeast and western regions but also drove industrial technology upgrading in these two regions.

Comprehensive Performance Measurement of High-tech Industry Development

Referring to the previous approach, the equation for the coefficient of R&D efficiency is

G_{i t} = [R_{i t} - \min_{t} (R)] / [\max_{t} (R) - \min_{t} (R)]

(5)

where G_it represents the coefficient of R&D efficiency in province i in the year t, R_it is the R&D efficiency value of province i in the year t, and min_t(R) and max_t(R), respectively, represent the minimum and maximum values of R&D efficiency in the year t. In order to make the value of G greatly more horizontally comparable, the range of R will not take into consideration the R&D efficiency value across the whole of China’s eastern, central, western and northeastern regions.

The calculation equation of high-tech industry development performance is

y_{i t} = G_{i t} \times E_{i t}

(6)

where y_it and E_it, respectively, represent the comprehensive performance value and the economic efficiency of high-tech industry in province i in the year t.

Using Equations (5) and (6), the comprehensive performance values of high-tech industry in China’s thirty provinces and cities from 2001 to 2013 are calculated; their descriptive statistics can be seen in Table 3.

Table 3

Descriptive Statistics for thirty Cities of China’s Provincial High-tech Industry Comprehensive Performance from 2001 to 2013

	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010	2011	2012	2013
Mean	0.142	0.220	0.340	0.376	0.159	0.084	0.212	0.211	0.409	0.342	0.412	0.355	0.407
Variance	0.137	0.079	0.601	0.140	0.059	0.021	0.287	0.151	0.109	0.077	0.081	0.101	0.079
Median	0.021	0.127	0.149	0.245	0.073	0.028	0.046	0.062	0.341	0.304	0.321	0.311	0.318
Skewness	3.254	2.598	4.936	1.462	2.521	2.827	3.941	3.379	0.755	1.357	1.251	1.301	1.016
Kurtosis	10.055	6.892	25.849	1.491	6.118	7.556	17.042	12.628	–0.128	2.371	2.213	2.175	3.431

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on science and technology (2001–2014), China Statistical Yearbook (2001–2014).

Spatial Convergence Analysis of High-tech Industry Performance

As previously analysed, the variation difference of China’s regional high-tech industry comprehensive performance displays a certain fluctuation. To determine whether this fluctuation follows a law, whether it is consistent in the long run, and which factors are driving it, can help us to understand the evolution of China’s regional high-tech industry development performance and help local government to create specific development policies. Indeed, to answer such questions requires a convergence analysis of China’s provincial high-tech industry development performance. The traditional efficiency convergence approach is to adopt the absolute or conditional convergence equation of economics in order to make the calculation (Pan, Liu, & Peng, 2015). As spatial analysis techniques mature, more and more scholars have focused on the influence of spatial dependence on regional efficiency. Yu & Wu (2010) argued that China’s high-tech industry has shown a certain spatial clustering not only with regard to R&D factors but with R&D efficiency as an outcome of the clustering of R&D factors. Based on spatial dependencies in technological development, Yu and Lee (2009) conducted an empirical analysis of the regional convergence of technology efficiency and its influencing factors. In line with their approach, in this section a spatial panel econometric model is adopted to launch a further empirical analysis of China’s regional high-tech industry development performance convergence.

Exploratory Spatial Data Analysis on Characteristics Agglomeration Patterns of High-tech Industry Development Performance

Exploratory spatial data analysis (ESDA) is used to measure global spatial autocorrelation and local spatial autocorrelation. This includes the use of Moran’s I, which can be taken to reflect the general characteristics of high-tech industry development performance agglomeration patterns. The relevant equation is

\begin{matrix} M o r a n ’ s I = (\frac{n}{å_{i = 1}^{n} å_{j = 1}^{n} w_{i j}}) \times {[å_{i = 1}^{n} å_{j = 1}^{n} w_{i j} (x_{i} - \bar{x}) (x_{j} - \bar{x})] / \\ å_{i = 1}^{n} (x_{i} - \bar{x})} \end{matrix}

(7)

In this equation, x_i stands for the observed value of province i, while the w_ij are component elements of the spatial weight matrix. The value of Moran’s I generally is set between −1 and +1. When Moran’s I < 0, it means a negative spatial correlation; when Moran’s I = 0, it means no spatial correlation; when Moran’s I > 0, it means a positive spatial correlation. The greater the absolute value, the stronger is the correlation of the spatial distribution; this means that a more strongly aggregated distribution exists in space.

To set the spatial weighted matrix, methods in common use include the adjacency matrix method (Helen & Paul, 2016), the geospatial weight matrix method (Liu & Zhang, 2009), the economic spatial weight matrix method (Harry & Gianfranco, 2014) and so on. However, there are still certain shortcomings to the above methods.

First, it is obvious that economic weights based on adjacency relations do not consider the gradients of China’s high-tech industry development. For instance, there is no doubt that links exist between Jiangsu’s and Hubei’s high-tech industries. Second, a deterministic economic index does not match the laws of dynamic change in China’s industry development; the adoption of panel data and a fixed weight matrix would affect the findings. To avoid these flaws, this article adopts a dynamic economic spatial weight matrix, defined as follows:

w_{i j} = {\begin{matrix} Q_{i j} / d_{i j}^{2}, i \neq j \\ 0, i = j \end{matrix}

(8)

where Q_ij is the per capita GDP of high-tech industry employees in the year t, d_ij represents geographical distance, and the spatial weight matrix is standardised by row when calculated.

In Figure 3, it depicts Moran’s I index value for China’s high-tech industry development performance. With the exception of 2001, the Moran’s I statistical value for all years passed the significance test at the 5 per cent level, meaning that high-tech industry development performance shows an intensely positive spatial correlation. This is an obviously biased estimation even without considering the correlation estimation of spatial effects. The positive Moran’s I value indicates that the clustering trend appears in both high-tech development performance and high-tech industry development growth patterns. Additionally, regions with high performance are geographically close to one another, because high-tech industry clustering tends to be of a pole-axis aggregating mode—an interactive development within a region that starts from one or several leading enterprises that form pivots for its industrial chain. The competitiveness of high-tech industry products indeed provides a comprehensive competitiveness comparison of industrial chains. Therefore, it is not hard to understand why high-tech development performance shows convergence. From a dynamic perspective, Moran’s I shows certain fluctuations, which means that the spatial dependence of high-tech industry development performance presents as unstable in that it alternates from enhancing to weakening.

Figure 3

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on science and technology (2001–2014), China Statistical Yearbook (2001–2014).

Spatial Econometric Analysis for Comprehensive Performance β Convergence of High-tech Industry

Introduction to the Absolute Convergence Equation

In economics, convergence means that backward areas will have much higher economic growth rates than developed areas, a process that will gradually eliminate the economic gap between regions and contribute to a steady state of economic development. Referring to convergence studies in economics, the standard efficiency convergence equation is constructed as

\ln (y_{i, t + τ} / y_{i t}) = α_{0} + β \ln (​ y_{i t}) + u, u ~ N (0, σ^{2} I_{n})

(9)

where y_it is comprehensive performance in area i in the year t; if the regression result shows that β < 0, then there exists absolute convergence in regional industry comprehensive performance; and vice versa, if β ≥ 0, then there is no absolute convergence.

In choosing the time interval τ, no standard has yet been established for the convergence equation. Cellini (Yuan, 2009) believed that a longer time interval would cause heavy loss of information and suggested that annual intervals should be chosen in convergence analysis. Thus, this article assumes that τ = 1. The time effect dummy variable will therefore not be considered in the calculation of this model; estimation of the convergence equation thus becomes a parameter estimation based on panel data. The relevant equation here is

\ln (​ y_{i, t + 1} / y_{i t}) = α_{0} + β \ln (​ y_{i t}) + η_{i} + γ_{t} + u, u ~ N (0, σ^{2} I_{n})

(10)

The residual decomposing terms of the panel data model can be divided into fixed-effect and random-effect components. In line with Hausman’s conclusion that the p-value in the standard efficiency convergence Equation (10) is almost close to 0, the fixed-effect model is appropriate for the analysis of Equation (10).

The convergence rate is ν = –ln(1 + β) and the convergence proceeds as a negative exponential decay with v as its parameter. The term H indicates that the degree of convergence has reached 1/2; this means that the end state of high-tech industry development performance is related to a half logarithm correlation of the initial high-tech industry development performance. Similarly, Q and N stand for quantile convergences of 3/4 and 9/10, respectively, which indicates a higher degree of convergence (Hong, Hu, & Li, 2010).

In order to introduce spatial factors into the traditional econometric model, the general practice is to set a spatial lag factor. The most common such approaches include the spatial error model (SEM) and the SAR model. The former reflects the spatial spillover impact of regional random error, which will affect the whole industry system; neighbouring regions will also deviate from equilibrium. The latter approach implies that trends in regional industry performance are affected both by the development level and by the performance of adjacent regions. This article constructs the general spatial autoregressive model (GSAM) as

\begin{matrix} \ln (\frac{y_{i t + 1}}{y_{i t}}) = α_{0} + β \ln y_{i t} + ρ W \ln (\frac{y_{i t + 1}}{y_{i t}}) + {(I - λ W)}^{- 1} ξ + η_{i} + \\ γ_{t} + u, u ~ N (0, α^{2} I_{n}) \end{matrix}

(11)

when λ = 0, Equation (11) is the SAR convergence equation, and when ρ = 0, Equation (11) becomes the SEM convergence equation.

Estimation Methods of Parameters

Since the development of regional innovation performance displays spatial correlation, OLS (ordinary least squares) estimation is biased and invalid. In order to make the estimation results more comparable, a fixed-effect spatial panel convergence model is retained in convergence Equation (11),⁴ In order to construct an appropriate model, this article extends the spatial weight matrix to NT × NT dimensions and adopts Lagrange multiplier error (LM-Error) statistics, LM-Lag statistics and their spatial correlation robustness tests. If the statistics of LM-Error and LM-Lag are not significant, the general panel data regression model will be adopted; if LM-Lag (or LM-Error) is statistically significant and LM-Error (or LM-Lag) is not, the spatial lag model (or spatial error model) will be adopted. If the statistics of both LM-Error and LM-Lag are significant, Robust LM-Lag will be compared with Robust LM-Error; if the values of Robust LM-Lag (or Robust LM-Error) are much more statistically significant, the spatial error model (or spatial lag model) will be adopted (Elhorst, 2009).

The estimation of dynamic spatial panel data is generally divided into two types. One is the traditional dynamic panel data estimation approach, such as generalised least square (GLS), generalised method of moments (GMM) and so on, while the other is unconditional maximum likelihood (ML) estimation. The latter uses the first difference to eradicate fixed effects and then adopts ML estimation methods to obtain the first difference model. As long as the cross-sectional number is big enough, the estimation of the parameter vector has the characteristic of consistency (Zhang & Xie, 2012). Due to the fact that the range of the traditional dynamic panel data estimation method cannot be strictly limited within the constraint space of spatial panel data estimators, there will exist some invalid estimators.⁵ Compared with traditional dynamic panel estimation, the consistent estimation of the parameter vector from dynamic spatial panel unconditional maximum likelihood estimation is more asymptotically efficient. Hence, this article adopts this approach to conduct parameter estimation for the performance convergence model.

Empirical Analysis

According to the previous estimation methods, parameter tests and the estimation of corresponding econometric equations are conducted using MATLAB 7.0 software and program source code⁶ provided by Elhorst, with appropriate modifications. Table 4 presents the spatial dependence results obtained from OLS residual and spatial dependence tests based on a hybrid model residual. In the former method, LM-Lag and LM-Error all passed significance tests at the 1 per cent significance level, as did R-LM-Lag and R-LM-Error, with LM-Error > LM-Lag and R-LM-Error > R-LM-Lag. Meanwhile, in the latter method, the significance of LM-Error is greater than that of LM-Lag; therefore, the SAR model is thought to be the optimal parameter estimation model.

The estimated value based on the SAR model can be seen in Table 5. By analysing the data in Table 5, it is found that values of R-squared (0.2451) and log-likelihood (685) in spatial fixed effects are greater than those of time fixed effects and time-spatial double fixed effects. Even though log-likelihood (705) with no fixed effects is greater than that of spatial fixed effects, the fact that the influence of ρ (−0.1315) with no fixed effects is negative is not obviously logical, which means that the model is inadvisable. Therefore, the optimal choice is the spatial fixed-effect model. That spatial fixed effects exist in the spatial convergence model of performance means that changes in high-tech industry development performance are mainly affected by location, including regional economic structure, natural resource endowment and so on. This is congruent with the high-tech industry comprehensive performance calculation result of this article, which found that although the performance of developed areas is better than that of backward areas, there is no obvious dynamic law underlying comprehensive performance fluctuations, which also illustrates the advisability of a spatial fixed-effect model. In the spatial fixed-effect model, β = –0.0372 and passes the 1 per cent significance test. This means that there exists absolute β convergence in China’s high-tech industry comprehensive performance in the twenty-first century with a convergence rate of 0.038; the convergence periods of the three convergence degrees of H, Q and N are, respectively, 18 years, 37 years and 61 years.

Table 4

Spatial Correlation Test of Standard Efficiency Convergence Equation

OLS Residual Estimate		Hybrid Model Residual Estimate
Lmlag	6.1279***	Lmlag	5.9255**
Lmerr	14.299***	Lmerr	14.429***
R-Lmlag	45.164***	R-Lmlag	22.839***
R-Lmerr	53.466***	R-Lmerr	31.343***

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on Science and Technology (2001–2014), China Statistical Yearbook (2001–2014).

Note: ** denotes significance at the 5% level and *** denotes significance at the 1% level.

Table 5

Estimators of Spatial Convergence of China’s High-tech Industry Development Performance, Based on SAR Model

	None Fixed Effect	Spatial Fixed Effect	Time Fixed Effect	Time-spatial Double Fixed Effect
α ₀	0.8655***
β	0.5127***	−0.0372***	0.0611***	0.0475
ρ	−0.1315**	0.1965*	−0.045	−0.1014
σ ²	10.722	9.3659	9.803	8.32
Log-likelihood	705	691	685	669
R-squared	0.1315	0.2451	0.2096	0.2301
1/w_min	−0.171	−0.171	−0.171	−0.171
1/w_max	1	1	1	1

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on Science and Technology (2001–2014), China Statistical Yearbook (2001–2014).

Note: * denotes significance at the 10% level and ** denotes significance at the 5% level and *** denotes significance at the 1% level.

The Convergence Mechanism Analysis of High-tech Industry Development Performance

Currently, research into the mechanisms of economic convergence divides into two main schools, that is, the neoclassical school and the new growth theory school. The former believes that the economic convergence mechanism depends on diminishing capital returns, while the latter argues that it depends on technology diffusion. Dowrich and others (Zhang & Xie, 2012) combine these two mechanisms into one model; however, this model is relatively weak in explaining and expressing the spatial processes of technology diffusion. The spatial econometric method allows us to explain the spatial path of technology diffusion. Hong, Hu & Li (2009) adopted a spatial econometric model, incorporating spatial factors and the convergence mechanisms of both neoclassical school and new growth theory school in one model, defined as follows:

g = α_{0} + ρ W_{1} g + β \ln (y_{0}) + α k + ξ

(12)

where g, y₀, k and W₁ stand, respectively, for average growth rate of GDP per unit labour, initial GDP per unit labour, growth rate of capital stock per unit labour and the spatial weight matrix based on neighbour relationships. If it can be shown clearly that α < 1, the neoclassical convergence mechanism will be active; if β < 0 is clearly demonstrated, the convergence mechanism of new growth theory will be active.

The convergence mechanisms of regional efficiency, an important part of regional economic systems, still include diminishing capital returns and technology diffusion. In fact, diminishing capital returns indicate production efficiency differences caused by regional differences in industry investment levels, while the technology diffusion mechanism represents the learning processes created by interregional talent flows and resource exchanges. This learning mechanism is affected by several factors, such as regional geographical distance and regional economic development level, but also soft power, including management level, industry development environment, talents and skills, knowledge structures and so on. The impacts of geographical distance on the technology diffusion mechanism and the regional economic development level can be measured by the economic weight matrix. The industry development comprehensive performance directly demonstrates the soft power factors of regional industry development. In conclusion, according to the research aims of this article and convergence mechanism theory, and combining model (12), the econometric model is here constructed to fit the convergence mechanism of China’s high-tech industry development performance:

\begin{matrix} \ln g_{i t} = α_{0} + α_{1} k_{i (t - 1)} + β_{1} \ln y_{i (t - 1)} + β_{2} d_{e a s t} \ln y_{i (t - 1)} + β_{3} d_{m i d} \ln y_{i (t - 1)} \\ + β_{4} d_{w e s t} \ln y_{i (t - 1)} + ρ W ​ \ln g_{i t} + η_{i} + γ_{t} + ξ . \end{matrix}

(13)

In this equation, g_it, k_it and y_it are, respectively, growth rate, investment growth rate and comprehensive performance of high-tech industry comprehensive performance in region i in the year t. The parameters and equations of g and y may be referenced from previous constructions. K is the investment growth rate of provincial high-tech industry in each year. The investment values in each year are first smoothed, using the fixed-asset investment price index of each province per year as the smoothing coefficient. The constant price period is the same as in previous constructions, that is, the year 2000. In considering the lag effect of investment, a one-year lagged investment growth rate is adopted. W is the economic spatial weight matrix; its equation is model (8). Due to the major differences in China’s regional development patterns and technology diffusion mechanisms, many scholars tend to choose the eastern, central and western regions of China for analysis (Chen, 2015; Cheng et al., 2011). In fact, the northeastern region has its own regional features, which can be seen from China’s special plans that aim at revitalising the northeast region; its technology diffusion mechanism therefore cannot be classified along with the eastern and central regions. Therefore, the dummy variable D is built to capture these regional features. The equation is as follows:

D = {\begin{matrix} d_{e a s t} = 1, d_{​} = d_{w e s t} = 0; y_{i} . m e a n s c i t i e s i n e a s t e r n r e g i o n \\ d_{m i d} = 1, d_{e a s t} = d_{w e s t} = 0; y_{i} . m e a n s c i t i e s i n c e n t r a l r e g i o n \\ d_{w e s t} = 1, d_{m i d} = d_{e a s t} = 0; y_{i} . m e a n s c i t i e s i n w e s t e r n r e g i o n \\ d_{e a s t} = d_{m i d} = d w e s t = 0; y_{i} . m e a n s c i t i e s i n n o r t h e a s t e r n r e g i o n . \end{matrix}

(14)

From the model structure, the maximum likelihood estimation method of an SAR model based on panel data is adopted to obtain the parameter estimation, with the results displayed in Table 6.

Table 6

Parameter Estimation of China’s High−tech Industry Development Performance Convergence Mechanism

	Stochastic Effect	None Fixed Effect	Spatial Fixed Effect	Time Fixed Effect	Time-spatial Double Fixed Effect
α ₀	−0.2892	−0.2633
α ₁	0.0471	0.0442	0.1101	−0.1002	−0.016
β ₁	0.2637*	0.2681**	−0.0396*	−0.0372**	−0.0536*
β ₂	−0.1756	−0.1738	−0.3305	−0.1910	−0.3792
β ₃	−0.6163***	−0.6074***	−1.376***	−0.6217***	−1.332***
β ₄	−0.1511	−0.1471	−0.4959	−0.1629	−0.6353*
ρ	0.2915	0.2935***	0.2305**	−0.0534	−0.1535
R-squared	0.2141	0.2080	0.4369	0.2691	0.2947
σ ²	5.953	5.994	5.128	5.584	4.740
Log−likelihood	626.4	626.4	624.7	615.3	593.6
Hausman	−49.93***
1/ω_min	−0.171	−0.171	−0.171	−0.171	−0.171
1/ω_max	1	1	1	1	1
Spatial correlation test of residual	significant correlation	significant correlation	uncorrelated	uncorrelated	uncorrelated

Source: China Statistics Yearbook on High Technology Industry (2001–2014), China Statistics Yearbook on Science and Technology (2001–2014), China Statistical Yearbook (2001–2014).

Note: * denotes significance at the 10% level and ** denotes significance at the 5% level and *** denotes significance at the 1% level.

In analysing the effectiveness of the estimation models, given that the Hausman test is significant at the 1 per cent level and that the SAR model with random effects is not a perfect fit, it appears that the SAR model with fixed effects is a better choice. However, the residual of the SAR model with no fixed effects has a significant spatial correlation, which means that its cross-sectional data still have a significant spatial correlation and its estimate is not unbiased, which makes the model inappropriate. Among the three econometric models with spatial fixed effects, time fixed effects and time-spatial double fixed effects, given that the values of R-squared (0.4396) and log-likelihood (624.7) are the largest with spatial fixed effects, the SAR model with spatial fixed effects is therefore chosen in this article as the main interpretative object in the convergence mechanism analysis.

Analysing from the parameter estimation, α₁ < 1, but does not pass the significance test; β₁ < 0 and passes the 10 per cent significance test. This implies that China’s high-tech industry development performance operates under the new growth theory convergence mechanism, not the neoclassical school convergence mechanism. The findings also indicate that the equalisation of China’s regional investments may promote the coordination of regional economic development levels, but such equalisation cannot with certainty promote the coordination of regional economic development efficiency, which can be seen from the fact that China’s high-tech industry development performance displays no obvious law of capital diminishing returns. Pearson correlation analysis is next performed on the comprehensive performance of China’s high-tech industry development and on the growth rate of investment. The correlation coefficient is 0.085 and does not pass the significance test. This insignificant weak positive correlation indicates that investment growth does not obviously help to improve regional high-tech industry development performance; a more extensive development pattern appears to be driven by investment in China’s regional high-tech industry development. The value of β₁ in the spatial fixed effects SAR model is −0.0396. The rate of convergence is 0.0404, and the convergence times for the three convergence degrees H, Q and N are, respectively, 7.5 years, 35 years and 58 years. Compared with the convergence times of absolute β convergence, these periods do not obviously shorten, which proves again that the growth rate of investment makes a limited contribution to high-tech industry development performance convergence; and that technology diffusion plays a dominant role in China’s regional industry development performance.

Analysing the differences in regional technology diffusion mechanisms, the technology diffusion parameters of both the eastern and western regions are negative, but they do not all pass the significance test, thus failing to confirm that the technology convergence rates of eastern and western regions are faster than that of other regions. The technology diffusion parameter of the central region is −1.376 and passes the significance test at the 1 per cent level, which indicates that the technology performance convergence rate of the central region’s high-tech industry is faster than that of the other regions; and that the construction of soft environments and learning mechanisms in the central region’s high-tech industry development is stronger than that in other regions. While high-tech industry in the eastern region leads in technology, human resources and comprehensive ability, its convergence rate is not obviously faster than that of other regions; it is thus clear that high-tech industry in this region does not play a leading role and its supporting effects in convergence are not outstanding.

Analysing the interaction coefficient ρ of representative regions, its value is 0.2315 and it passes the 5 per cent significance test. Referring to the economic significance of W, we can say that geographical distance is still the most vital mechanism of technology diffusion. In fact, due to the obvious negative correlation between the technology diffusion effect and geographical distance (Rosina, 2012; Xiang & Cai, 2008), the central region, as a transfer station of technology diffusion, benefits most from the technology spillover effects of the eastern and western regions, which may be the reason why the convergence rate of central China is faster than that of other regions.

Conclusion and Suggestion

Conclusion

From a spatial view and applying spatial panel econometric models and related methods, this article, focusing on China’s provinces and municipalities, studies measurement and convergence issue of China’s high-tech industry development performance from 2001 to 2013 and concludes the following.

First, according to Malmquist index in the second section, although the R&D efficiency of China’s regional high-tech industry is not ideal, it has maintained a stable tendency under China’s eleventh five-year plan. Regional high-tech industry economic efficiency shows no obvious law of fluctuation. Generally, the technology progress index values of northeastern and western China are obviously higher than that of eastern China, which demonstrates a series of strategies for harmonious interregional development indeed plays a definite role in driving the development of regions with weaker high-tech industrial foundations.

Second, with the application of ESDA and Moran’s I index in the third section, it is found that there exists a significant positive correlation in the comprehensive performance of China’s high-tech industry development. This indicates not only that there exist obviously positive diffusion effects and cluster development modes in China’s high-tech industry development but also that OLS method should not be applied simply in researching convergence issues of high-tech industry development performance and that spatial factors must be considered. The correlation estimations of spatial econometric methods should be utilised; otherwise, the conclusions will not be robust.

Third, the spatial econometric diagnosis model indicates the optimal approach in studying high-tech industry development performance convergence is a spatial fixed-effect SAR model and that the related influencing factor of China’s high-tech industry comprehensive performance convergence is location, not time. The result of measurement demonstrates that the development performance of China’s high-tech industry has a significant absolute β convergence from 2001 to 2013.

Fourth, while a series of strategies to promote regional high-tech industry development implemented by China’s central and local governments since 2000 did in fact promote the development scale of regional high-tech industry, the convergence mechanism indicates that it did not bring forth the coordinated promotion of regional high-tech industry development performance. Simple incremental resource investment contributes little to the coordinated development of regional high-tech industry and is not a sustainable development model. Technology diffusion is the main regional convergence mechanism of China’s high-tech industry development performance over the years 2001–2013; and geographical distance is the core factor affecting the technology diffusion effect.

Policy Suggestion

According to the convergence evolution law of China’s regional high-tech industry development performance, feasible policies that may accord with the coordinated development of China’s regional high-tech industry include the following:

First, the barriers to regional technology flows should be further decreased. Technical exchanges and industrial cooperation should be encouraged between eastern and western China; a high-tech industry culture that is good for sharing the resource and achievement should be formed to drive the simultaneous advance of high-tech industry scale and performance in western China.

Second, the overall regional high-tech industry development policy should be further refined. Regional policies with their own unique characteristics should be created according to each region’s high-tech industry development foundations and hard and soft environments, thus making it possible to form a coordinated operating regional division system.

Third, the technology and industry transfers from eastern China should be speeded up. High-tech industry in eastern China should be encouraged to set up research, manufacturing and marketing centres in central, western and northeast China. The economic strategy that sees the more advanced industry and dominant technology of eastern China supporting the more backward regions should be implemented practically.

Footnotes

Notes

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