The Trend of Economic Complexity in China: Based on Input-output tables from 1987 to 2007

Li Shantong¹ Wu Sanmang²

(1. Development Research Center of the State Council, Beijing 1000101 2. School of Humanities & Economic Management; China University of Geosciences; Beijing 100083; China)

Abstract: This essay is based on Average Propagations Lengths, using data of Input-output tables from 1987 to 2007, to measure complexity and change of China’s economy. The results showed that (1) during 1987 to 2007, complexity of China’s economy has enhanced apparently in general, industry chains have been expanding, complexity index raised 34.9% from 2.69 in 1987 to 3.63 in 2007; however, structural change brought by annexation and reorganization of state-owned enterprises (SOE) during 1987 to 2007 has caused slight drop of economic complexity; (2) the fundamental position of energy resources and minerals mining industries in China’s industry chain has been strengthened while marginal industries, such as wholesale and retail trade, real estate and social services have been having wider pulling effect on other industries; (3) differences have emerged among complexity and change of China’s different regions: economic complexity of eastern area including Guangdong, Zhejiang, Jiangsu provinces is apparently higher and with faster speed than mid-west area including Jiangxi, Hunan, Shanxi and Xinjiang provinces.

Key Words: Economic Complexity; Average Propagations Lengths; Production Chains

1. 
   Introduction
   

Researches on complexity in the west started in the 60s of 20^th century. Various kinds of indexes and methods to measure economic complexity were mentioned. Yan and Ames (1963) suggested

correlation measuring, Finn (1976) and Ulanovicz (1983) suggested cycling measuring and development, with the recent impact from globalization and adjustment of manufactures space layout, researches on economic complexity has once again become a new hot spot. For example, average propagations lengths by Dietzenbacher and Romero (2007), mutual dependence measuring by Amaral et al. (2007) and some other new measuring methods for economic complexity.

The various methods for measuring economic complexity suggested by western scholars are mainly based on a frame of input-output analysis. This is because input-output charts illustrate the mutual dependent relationships between departments (industries), which is the essential question in measuring economic complexity (J.Carlos Lops, Joao Dias and J.Ferreira do Amaral, 2008). Erik Dietzenbacher and Geoffteu J.D.Hewings（2008）provided representative researches on causes of economic complexity change. They took Chicago for instance, analyzed the change of economic complexity in developed areas and suggested that the increase and decrease of economic complexity in developed areas are determined by comparison of space and function separation of economic activities. If the space separation of economic activities is more obvious, economic complexity decreases; if the function separation is more obvious, economic complexity increases. Joao Dias and J.Ferreira do Amaral（2008）used many economic complexity measuring indexes to measure some OECD countries’ economic complexity and change from the 70s to 90s in 20^th century. The results showed that complexity of large economy is higher than small economy (for example, economic complexity of America and Japan is higher than the Netherlands and Denmark), closed economy is more complex than open economy, with the deepening of international division of labor, OECD countries’ moving industries (especially manufacturing industry) outwards, some economic activities’ (low side stages of manufacturing) outsourcing to developing countries, economic complexity of OECD countries started to show tendency of decreasing.

Since the reformation, China’s economy development has reached an apparent effect and increased quickly. At the same time, reformation also took place in economic structure and regional structure (Wu Sanmang, Li Shantong, 2010), which will change the mutual relationships between China’s industries. Under this circumstance, analyzing complexity and change of China’s economy is good for grasping China’s economy’s general operating condition, more importantly, it is helpful for ensuring general national economic strategy, making relevant industrial policies, improving national economy’s health, stability and sustainable development.

This essay consists 4 parts: the second part mainly explains economic complexity measuring methods and measuring data sources; the third part mainly analyzes economic complexity of the whole country and different industries’ positions in the industry chains; the forth part compares and analyzes economic complexity and change of Guangdong, Shanghai, Liaoning, Hebei, Jiangsu, Zhejiang, Jiangxi, Hunan, Shanxi and Xinjiang provinces; the fifth part is the conclusion of this essay and policy suggestions.

The economic complexity measuring methods employed by this essay is Average Propagations Lengths, suggested by Ditzenbacher et al（2005）， Dietzenbacher and Romero（2007）， Dietezenbacher and Temurshoev（2008）. Its main characteristic is to focus on one industry change having ultimate influence on average lengths of another industry change through affecting the whole producing process. Influences from one industry change on another surely can be analyzed from a forward angle (capital motivation) and backward angle (need drawing). Take backward angle analysis for example (forward angle analysis basically the same), suppose an economy has n industries, with input coefficient matrix A (illustration 1), , means the middle input need of industry i by total output of one unit of industry j. Take the impact on industry 1 from industry 3’s needs increasing 100 units into consideration, apparently, the most direct first impact is directly transmitted from industry 3 to industry 1, industry 1’s total output increased 100 units. Then take the second impact into consideration, the increased 100 units of industry 3 will obviously cause the total output of other industries, such as industry 2’s total output will increase 100 units, which will further cause industry 1’s total output increasing 100 units and so on (illustration 2). Therefore, the impact on industry 1’s total output from industry 3’s increasing needs is completed through several lengths, more lengths, stronger relevance between industry 3 and industry 1, same to other industries. Through calculating the Average Propagations Lengths between industries, it actually can show the relevance extent between industries within the economic system and length of industry chains, i.e. complexity within economic system.

<1 length path>

Sec 3 a13 Sec 1

<2 length paths>

Sec 3 a23 Sec 2 a12 Sec 1

Sec 3 a33 Sec 3 a13 Sec 1






Illustration 1 input coefficient matrix Illustration 2 impact wave & route

To specifically calculate the average lengths, we should start from the needs’ angle. Suppose X represents the vector formed by total output, A represents middle input matrix, y represents ultimate needs vector, hence . The answer to that formula is .

represents Leontief paradox matrix. If vector in the matrix remains the same, the ultimate need to increase will require the total output to increase .

According to Leontief paradox matrix, to expand with power series:

(1)

So the total increased output is:

(2)

Therefore, the ultimate need of industry j increasing one unit can be calculated, which will bring increased total output to industry i:

(3)

The first item on the right side of the above formula shows the direct impact, i.e. impact completed with one length; other items are indirect impacts, which shows impacts completed with multiple lengths. For example, includes all the impacts completed with two lengths.

Under circumstance, initial impact should be included, for an extra unit of ultimate need increasing will firstly cause its own total output increasing one unit. Therefore, industry j’s ultimate need for increasing one unit causes industry j’s total output increase, the amount is:

(4)

To sum up, Average Propagations Lengths (APL) can be derived with the following thinking:

If the ultimate need of industry j increases one unit, the total output of industry i will increase , among that, the proportion of was completed with one length; the proportion of was completed with two lengths, the rest may be deduced by analogy. The ultimate need of industry j will increase, which will cause the increase of industry i’s total output. The average length is:

(5)

Under circumstance, similar inferential thinking is also suitable. Yet the initial output increase is irrelevant to the production structure, it doesn't provide any information about dependence between two departments, so that it can be ignored. Therefore, the increase of the ultimate need of one unit of industry j will cause the increase of industry j’s total output through production process influence, the increased amount is :

(6)

Similarly, (7)

Suppose , then the numerator can be expressed through elements of H and .

（I-A）premultiplies H is

So from

Average propagations lengths can be deduced:

(8)

The foregoing is the APL deduced from backward angle (need drawing angle), other than that , an APL formula can also be deduced from forward angle (capital motivation angle).

Define an output vector , the proportion of directly used value as middle product of department j distributed by industry i among total output of industry i.

Hence:

(9)

The answer is:

(10)

Element in matrix G shows the general dependence of industry I on industry j. During the process of reasoning APL, in the same way, increasing one unit of industry i’s capital can also have impact on total output of industry j, as following:

(11)

The first item gives one length of direct impact; the second item is two lengths of indirect impact the rest may be deduced by analogy.

Therefore, the average propagation length of the impact from industry i’s capital increase on industry j’s total output is:

(12)

Suppose the numerator is , at the same time ,

(13)

which can prove that the APL values deduced from both forward and backward angles are the same. According to the definition of input-output coefficient, there is or ( is the diagonal matrix formed by elements from vector lining up on the main diagonal line).

Also

Because

Hence and

So

Definition:

(14)

gives the average propagations lengths of industry i to all the departments with forward capital motivation.

Definition:

(15)

gives the backward drawing average propagations lengths of industry j’s needs increasing to all the departments with backward drawing.

We can see that there are large FA value and small BA value, which means that movement of capital of this industry has impact on other departments with more average lengths while needs increasing has impact on other industries with less average lengths, which shows that this industry is at an advanced position among the industry chains; however, large BA value and small FA value means that movement of capital of this industry has impact on other departments with less average lengths while needs increasing has impact on other industries with more average lengths, which shows that this industry is at the end of the industry chain.

Speaking of the whole economic system, Complexity Index can be constructed as:

(16)

i.e. CI shows the average lengths of all industries’ capital raising having impact on other industries from a forward angle and the average lengths of all industries’ needs increasing having impact on other industries from a backward angle. Therefore, the stronger connections between industries, longer industry chain, the higher economic complexity and vice versa.

2. Data sources

The data sources this essay uses for analyzing economic complexity of China are from the input-output tables of China in 1987, 1992, 1997, 2002 and 2007; for analyzing economic complexity of each province are from the input-output charts of each province in 1987, 1992, 1997, 2002 and 2007. Due to the differences between input-output chart assortment and the amount of industries in 1987, 1992, 1997, 2002 and 2007, merging and rearrangement of each year’s input-output chart is necessary. Specifically, we combined coal exploiting industry and petroleum and natural gas exploiting industries of each year together to form energy exploitation industry; combine metallic ore extraction industry and nonmetallic extraction industries of each year together to form metallic/nonmetallic extraction industry; combine petroleum industry and coal and coal gas product industry of 1987 and 1992 together; combine petroleum processing and coking industry and coal gas producing and supply industry of 1997 together; combine petroleum processing, coking and nuclear fuel processing industry and gas producing and supply industry of 2002 and 2007 together to form petroleum processing and coal coking industry; combine mechanical devices mending industry and other industries of 1987, 1992 and 1997 together; combine waste materials industry and other manufacturing industries of 2002 and 2007 together to form other industries; combine electric power, vapor and hot water producing and supply industry and water producing and supply industry of 1997, 2002 and 2007 together to form power, heat and water producing and supply industry; combine freight and postal industry and tourists transportation industry of 1987 and 1992 together; combine freight, storage and postal industry and tourists transportation industry of 1997 together; combine public transportation and storage industry and postal industry of 2002 and 2007 together to form transportation and postal industry; combine food and drink industry and communal and resident service industry of 1987 and 1992 together; combine social service industry and real estate industry of 1997 together; combine leasing and business service, tourism, information transmission and computer service industry and software, real estate and other social service industry of 2002 together; combine leasing and business service, information transmission and computer service industry and software, real estate, resident service and other service industry of 2007 together to form real estate and social service industry; combine health and sports, social welfare and educational cultural art broadcasting television media industry and scientific research and general technique service industry of 1997 together; combine education, health, social insurance, social welfare, culture, sports, entertainment, scientific research industry and general technique service industry of 2002 together; combine leasing and business service, information transmission, computer service and software, real estate, resident service and other service, research and experiment development, general technique service, irrigation, environment and public devices management, health and social insurance industry and social welfare, culture, sports and entertainment industry of 2007 together to form cultural educational health and science industry while no change happened in other years; public management and social organizations are administrative departments in 1987, 1992 and 1997 while no change happened in other years. After merging and rearranging, there are 27 departments (industries) left, as chart 1.

Chart 1 Departments remained after merging and rearranging

Department	Code	Department	Code	Department	Code
Agriculture	1	Chemical industry	10	Other manufacturing	19
Energy exploitation	2	Nonmetallic mineral product	11	Power and water production	20
Metallic/nonmetallic extraction	3	Metal smelting and rolling processing	12	Architecture	21
Food manufacturing and tobacco processing	4	Metal product	13	Transportation and postal service	22
Textile industry	5	Devices with general and special use manufacturing	14	Real estate and social service	23
Clothing, leather, eiderdown and product	6	Transportation devices manufacturing	15	Scientific, educational, cultural and health industry	24
Lumber processing and furniture manufacturing	7	Electrical machines and devices manufacturing	16	Wholesale and retail trade	25
Papermaking, printing and cultural/educational appliance manufacturing	8	Communication devices, computer and other electronic devices manufacturing	17	Finance and insurance industry	26
Petroleum and coal gas	9	Apparatus, meters and machines with cultural and office use manufacturing	18	Public management and social organizations	27