The competitiveness and development strategies of provinces in China: a data envelopment analysis approach

Abstract

This paper explores the development strategies of Chinese provinces by synthesizing the dimensions of a competitiveness index and the Data Envelopment Analysis model. After documenting the close relationship between real GDP per capita and competitiveness, we introduce a production approach to study competitiveness and develop various possible strategies facing a province. In particular, while coastal provinces should consider innovating new technologies and institutions to improve competitiveness, western provinces may adopt a proportional development strategy that simultaneously enhances every aspect of its competitiveness. Further, the proportional development strategy for competitiveness is found to reduce regional disparity. The policy implications from our framework could not have been achieved had the analysis been solely based on the conventional methods of studying the competitiveness index.

1 Introduction

China’s rapid economic growth of more than 8 % per year in recent decades has not been equally shared among provinces, with Guizhou and Tibet, in particular, lagging behind the rest in economic development and per capita income growth. Uneven development causes social and political instability (Lee 2007; Wang and Hu 1999). Hence, the mechanism through which provinces, especially less developed ones, can advance their economies, is imperative for China’s sustainable development in the future.

This paper broaches the development strategies of provinces in China from the perspective of competitiveness. Though controversial, the concept of competitiveness explores more aspects of an economy than a narrow focus on GDP and factor inputs (Krugman 1996).¹ We postulate that the long-term growth of a province’s income per capita depends on such factors as institutions, market structure, production inputs and technology. These factors can be summarized by a competitiveness index. Thus a more competitive province is expected to have a higher productivity. A competitiveness index has many dimensions. Treating these dimensions as outputs in a production process, we exploit the notion of productive efficiency to extract information for policy makers, which cannot be otherwise obtained from conventional studies on the competitiveness index alone.

Our framework also examines regional disparity from the perspective of competitiveness, an issue noticed by Chinese government officials since 1999 when then Party Secretary Jiang Zemin initiated a Western Development Program (WDP) to counteract the exacerbating regional disparity. In 2004, the central government advanced the concept of a Pan-Pearl River Delta region to promote economic growth in southern and southwestern China (Sun and Fan 2008). Academic studies on regional disparity usually focus on income disparity or output and consumption inequality (Chen and Zheng 2008; Cheng 1996; Lam and Liu 2011; Tsui 1996; Yao and Liu 1998). By decomposing multiplicative inequality indices (Cheng and Li 2006), we use the production approach to obtain new insights into the inequality of competitiveness among provinces.

The paper proceeds as follows. Section 2 discusses the relation between competitiveness and GDP per capita. Section 3 describes the modified model borrowed from the literature of efficiency and productivity analysis. Section 4 applies the model to provincial competitiveness of China, thereby yielding policy implications presented in Sect. 5. Section 6 investigates regional disparity in competitiveness. Section 7 concludes.

2 Competitiveness and GDP per capita

We adopt the view similar to the World Economic Forum (Schwab 2013) that provincial competitiveness is the set of institutions, policies, and factors that determine the level of productivity of a province. Thus, competitive provinces are expected to be more productive and have larger potential to attract capital to sustain and enhance economic growth. This implies that a more competitive economy should have a higher per capita income, leading to our first question:

Question 1

Does a higher level of competitiveness generate a higher real GDP per capita of a province?

The annual reports on overall competitiveness of China’s provinces (Li et al. 2007–2009) contain a comprehensive source of data on the provincial competitiveness of China.² We extract the competitiveness index data from these reports for the period 2005 to 2008. These reports have nine main dimensions of provincial competitiveness for 31 provincial level administrative units.³ Table 9 in the Appendix contains information of all dimensions. In addition, we derive provincial real GDP per capita (rgdppc) at the 2005 constant price using the China Stock Market and Accounting Research Database (CSMAR) developed by Shenzhen GTA. The descriptive statistics of the provincial competitiveness index and its nine dimensions are provided in Table 1 below.

Table 1 Descriptive statistics of the provincial data

In the above table, rgdppc is the provincial real GDP per capita, y is the competitiveness index, and y _i is the ith dimension of y, i = 1, …, 9. The average scores of the nine dimensions remain roughly at the same level during our sample period.

Extant studies of China’s development typically focus on real GDP per capita, by connecting it with structural break (Smyth and Inder 2004), geographic factors (Bao et al. 2002) and capital deepening, labor deepening, and productivity growth (e.g. Zhu 2012). Here we investigate how provincial competitiveness may move with GDP per capita. Specifically, the correlation coefficient between provincial competitiveness index (y) and GDP per capita is as high as 0.85, which is consistent with Cho et al. (2008) who find national competitiveness is highly correlated with GDP per capita.

We regress the logarithm of rgdppc on the logarithm of y to obtain a fixed-effect equation whose parameter estimates are statistically significant at α = 0.01 (Table 2).

Table 2 The effect of competitiveness on real GDP per capita

This equation uses dummy variables to control for time, regional and administrative differences. The variables y2006, y2007, y2008 are time dummies with reference to year 2005; noneast is a regional dummy with reference to the eastern region⁴; dcm is a dummy for direct-control municipalities⁵ and ar for autonomous regions.⁶ The estimated coefficient of ln(y) is highly significant and positive, yielding our first result:

Result 1

Provincial competitiveness affects provincial real GDP per capita positively.

Based on Result 1, competitiveness improvement is beneficial to an economy. However, exactly how the improvement can be achieved is not immediately obvious. There are three possible scenarios. First, the competitiveness of a province is already at the maximum. In other words, no further improvement on any dimension is possible without introducing new institutions and technologies. Second, the competitiveness improvement of a province can be realized by tradeoffs among dimensions. Finally, all dimensions of competitiveness can be increased simultaneously. As the policies under each scenario can greatly vary, studying the competitiveness index and its dimensions alone may not provide the necessary information useful for policy development. Our proposed remedy borrows the insights provided by the literature of efficiency and productivity analysis.

3 The conceptual framework

A competitiveness index is a weighted average of some selected dimensions. Suppose the overall competitiveness of an economy has M dimensions,⁷ denoted by y _m for m = 1, …, M. Each dimension measures an aspect of the economy believed to link to its competitiveness. The value of a dimension indicates the respective level achieved by an economy. When two vectors of dimensions are proportional to each other, they are said to have the same dimension mix; otherwise they are said to have different dimension mixes.

To improve its competitiveness, a province may strengthen all dimensions proportionally without changing the dimension mix. We refer to this kind of policy as the proportional development strategy. Alternatively, the province can increase some particular dimensions at the expense of others during the process of competitiveness enhancement. This kind of policy will alter the dimension mix and therefore we refer to it as the disproportional development strategy. In some circumstances, a province can emphasize some dimensions while all dimensions are expanded simultaneously. This strategy is called a hybrid development strategy. The second research question thus arises:

Question 2

Under what conditions is a particular strategy appropriate?

Conventional studies on competitiveness do not answer this question. We propose treating the dimensions of competitiveness as outputs in a production process, thus establishing a framework for analyzing economic development strategies in general and, as detailed below, for China in particular.

3.1 The production approach to competitiveness

Given the limited knowledge and resources of a province, there exists a maximum proportion that can be achieved by a province along each dimension mix. Once the maximum has been achieved, further improvement can only be realized by allowing tradeoffs among various dimensions. Thus each province is like a firm that produces multiple outputs. Each dimension is akin to an output, implying that modeling the competitiveness of a province is similar to the modeling of production technology of a firm. This allows us to construct a frontier of competitiveness dimensions. When a province has the potential to raise all competitiveness dimensions, we can treat it as operating under inefficient production.

Let $y = \left( {y_{1} , y_{2} , \ldots , y_{M} } \right)\in{\Re }_{ + }^{\text{M}}$ be the vector of M dimensions of competitiveness, where y _m is the mth dimension of competitiveness. Assuming a “technology” plays a governing role behind these dimensions, a province can increase all dimensions proportionally up to this technology’s limit. The set of all feasible vectors of dimensions is defined as S = {y: y is a vector achievable by a province}.⁸ Since the dimensions are mainly ratios, the absolute size of a province is immaterial and “inputs” are not included.

For illustration, consider Fig. 1 that portrays only two competitiveness dimensions, y ₁ and y ₂. The curve ZZ′ represents the “efficient frontier” for the generic province in terms of feasible maximum dimension mixes. Any combination of these two dimensions lying on the frontier has the highest possible level of competitiveness, given the ratio of these two dimensions. The feasible set S is the area between ZZ′ and the positive portions of horizontal and vertical axes.

Fig. 1

Frontier of competitiveness dimensions

Consider point A inside the set S. A proportional development strategy could be signified by a movement from A to B along a given ray. In contrast, if point C is the target, then moving from A to C will involve a non-proportional increase in both dimensions under a disproportional development strategy. In addition, moving from point A to point D is also a disproportional development strategy that pushes the dimension y ₂ at the expense of dimension y _1.

Let $y^{0} = (y_{1}^{0} ,y_{2}^{0} )$ be the competitiveness vector of any generic province. If the province does not lie on the frontier, the overall competitiveness can be improved through a proportional development strategy. Any possible proportional increase, however, is bounded by the set S. We measure the potential improvement in competitiveness through proportional development as:

$$ E_{p} = max_{\theta } \left\{ {\theta \hbox{:}\,\theta y^{0} \in S} \right\} $$

The measure $E_{p}$ is called the efficiency of proportional competitiveness. As $y^{0} \in {\text{S}}$ and θ = 1 is a possible solution, we have $E_{p}$ ≧ 1. When $E_{p}$ = 1, no further proportional development is possible and improvement must be achieved by an outward shift of the frontier. When $E_{p}$ > 1, 100 × (E _p  − 1) is the potential percentage increase in the competitiveness index. If the province is operating at point A in Fig. 1, $E_{p}$ measures the ratio of OB to OA.

3.2 Changing dimension mixes in the production approach

The dimensions’ weights are analogues of output prices in production theory. Increasing competitiveness is comparable to increasing total revenue. We use w _m to denote dimension m’s weight in the overall competitive index, C, so that $C = \sum\nolimits_{m} {w_{m} y_{m} }$. The observed competitiveness for the province that operates at y ⁰ is therefore $C^{0} = \sum\nolimits_{m} {w_{m} y_{m}^{0} }$. Let $y^{1} = E_{p} y^{0}$ be the dimension vector of the maximum expansion of $y^{0}$, and $C^{1} = \sum\nolimits_{m} {w_{m} y_{m}^{1} }$, the corresponding competitiveness. Thus $E_{p} = C^{1} /C^{0}$, the ratio between the competitiveness index of maximum proportional expansion on all dimensions and the observed overall competitiveness index.

Assuming the weights correctly reflect a policy-maker’s preferences, then the target of the policymaker is to find a feasible combination of dimensions to maximize the competitiveness index. The maximum value of C is

$$ C^{*} = max_{\varvec{y}} \left\{ {\sum\limits_{\text{m}} {{\text{w}}_{\text{m}} {\text{y}}_{\text{m}} \hbox{:}\,y \in {\text{S}}} } \right\} = \sum\limits_{m} {w_{m} y^{*}_{m} } \;{ \geqq }\sum\limits_{m} {w_{m} y_{m}^{1} = C^{1} } $$

(1)

where $y^{*}$ denotes the optimal solution for attaining C*. The potential for increasing the observed competitiveness may then be measured by:

$$ O_{c} = \frac{{C^{*} }}{{C^{0} }}{ \geqq }\frac{{C^{1} }}{{C^{0} }} = E_{p} \;{ \geqq }\;1. $$

(2)

We call $O_{c} \;{ \geqq }\;1$ the overall efficiency of competitiveness. While $O_{c}$ = 1 implies that a province has already attained its highest possible level of competitiveness, compared to other provinces, $O_{c}$ > 1 implies that 100 × ($O_{c}$ − 1) % of the competitiveness index can be increased via the dimension vector y*. It can be easily deducted that:

$$ O_{c} = \frac{{C^{*} }}{{C^{1} }} \cdot \frac{{C^{1} }}{{C^{0} }} = \frac{{C^{*} }}{{C^{1} }} \cdot E_{p} . $$

(3)

Let $E_{d} = \frac{{C^{*} }}{{C^{1} }}$ so that $O_{c} = E_{d} \cdot E_{p}$. It naturally follows that E _d  ≧ 1.

The index $E_{p}$ measures the increase in the degree of competitiveness by proportional expansion along the given dimensions, and $E_{d}$ measures the gain in competitiveness by moving from $y^{1}$ to $y^{*}$. If $E_{d}$ > 1, then the change must be achieved by a disproportional change in the given dimension mix of $y^{0}$ and a disproportional development strategy is necessary to attain the maximum degree of competitiveness. We call $E_{d}$ the efficiency of dimension mix competitiveness. This model is similar to the output-oriented technical efficiency of a firm.⁹ As shown in Fig. 1, $O_{c} = OC^{{\prime }} /OA$ and $E_{d} = OC^{{\prime }} /OB$. For all the three measures above, a larger value means a worse performance in competitiveness, mirroring more room for improvement.

The answer to Question 2 leads to our second result:

Result 2

All provinces fall into the following four mutually exclusive and exhaustive cases:

(a) When E _p  > 1 and E _d  = 1: A proportional development strategy is appropriate.

(b) When E _p  = 1 and E _d  > 1: a disproportional development strategy is appropriate.

(c) When E _p  > 1 and E _d  > 1: A hybrid development strategy is appropriate.

(d) When E _p  = 1 and E _d  = 1: For the most competitive province, innovation is required.

3.3 The uncontrollable nature of the dimensions of competitiveness

There is a major difference between the technology of production and the technology of competitiveness. Similar to production technology, the technology of competitiveness models the substitutability among dimensions. Unlike outputs in production, however, a desired level of each dimension is a policy target, not always under full control of the government.

In the case of a firm, once inefficiency is identified, the firm owner, in principle, can hire an appropriate manager to eliminate that inefficiency. Thus for a given input vector, the output vector can be chosen directly by the firm within the restriction of the technology.

In contrast, the dimensions of competitiveness of a province are partially controlled by the provincial government only. The feasibility set S indicates the achievable limits of competitiveness dimensions. The dimensions are policy targets, rather than what can be fully determined by any organization. To be sure, the government can influence these dimensions. Dimension 5 (competitiveness in knowledge-based economy) is a good example to illustrate this idea. In this dimension, technology factors include R&D expenditure, number of patents, added value in high-tech industry, etc. The amount of R&D expenditure can be determined by the government that can mobilize public resources in this area. The number of patents and added value in high-tech industry are not directly controllable. Nevertheless, they can be influenced. For example, ensuring sufficiently high income level and comfortable accommodations of researchers by public funding can stimulate the number of patents. Tax reliefs encourage the establishment of high-tech firms. Whether a certain level of a competitiveness dimension can be achieved depends on the efforts of the government and the economic interactions within the province.

In conclusion, the efficiency of proportional competitiveness (E _p ) and the efficiency of dimension mix competitiveness (E _d ) help identifying a strategy of policy directions for the government, but not policy outcome.

4 Empirical findings on provincial competitiveness

Consider K provinces, each with the dimension vector $y^{k}$, k = 1, …, K. Following the general Data Envelopment Analysis (DEA) convention in Charnes et al. (1978) and Farrell (1957), the empirical set of feasible dimensions of competitiveness is constructed by the convex disposal hull of the observed data as in (4).

$$ S = \left\{ {y\hbox{:}\,\sum\limits_{k = 1}^{K} {z_{k} y^{k} \;{ \geqq }\;y} ,\quad \sum\limits_{k = 1}^{K} {z_{k} = 1} ,\quad z_{k} \;{ \geqq }\;0,\quad k = 1, \ldots ,K} \right\} $$

(4)

The set S in (4) is similar to the empirical variable-returns-to-scale technology set in the DEA literature. The dimensions of competitiveness are treated as outputs of provinces. The scores of the nine dimensions are expressed as ratios or have been adjusted for size so that information along the lines of the inputs in the production process is not needed. An output-oriented DEA model without input is equivalent to an output-oriented DEA model with a single constant input (Kao et al. 2008; Lovell and Pastor 1999). The corresponding “efficiency” of proportional competitiveness for province j can be found by solving the following standard linear programming problem,

$$ E_{p}^{j} = max_{\theta } \left\{ {\theta \hbox{:}\,\sum\limits_{k = 1}^{K} {z_{k} y^{k} \;{ \geqq }\;\theta y^{j} } , \quad \sum\limits_{k = 1}^{K} {z_{k} = 1} ,\quad z_{k} \;{ \geqq }\;0, \quad k = 1, \ldots ,K} \right\} $$

(5)

The weights for dimensions used in our data are generated by applying the well-established Delphi method to minimize subjectivity (Li et al. 2007–2009). Under each dimension, there are different numbers of indicators, and weights are also generated form the Delphi method, but their weights are independent of weights for the nine dimensions. By doing so, the number of indicators under each dimension will not affect the integrating process at different levels. During their investigation, the Questionnaire of Experts’ Opinion on the Weighting system of Chinese Provincial Competitiveness Index was distributed to experts from academic circles and government bodies. All experts were required to answer the questionnaire independently. The final weights for these nine dimensions are determined by incorporating all survey results. We have also presented these weights in Table 9 in the Appendix. Given these weights $w_{m}$, m = 1, …, M, the maximum value of the objective function is given in (6) below:

$$ C^{j*} = max_{y} \left\{ {\sum\limits_{m = 1}^{M} {w_{m} y_{m} \hbox{:}\,\sum\limits_{k = 1}^{K} {z_{k} y^{k} \;{ \geqq }\;y} ,\sum\limits_{k = 1}^{K} {z_{k} = 1,\quad z_{k} \;{ \geqq }\;0,\quad k = 1, \ldots ,K} } } \right\} $$

(6)

The overall efficiency of competitiveness and efficiency of dimension mix competitiveness are then

$$ O_{c}^{j} = \frac{{C^{j*} }}{{\sum\nolimits_{m = 1}^{M} {w_{m} y_{m}^{j} } }},\quad E_{d}^{j} = \frac{{{\text{O}}_{c}^{j} }}{{E_{p}^{j} }} $$

(7)

The linear programming problems and equations of (5), (6) and (7) are applied to the data of all provinces in each of the years between 2005 and 2008. We use the software GAMS to implement the above linear programs, thereby answering our next question:

Question 3

What characteristics do different provinces have according to their performance in $O_{c}$, $E_{p}$ and $E_{d}$ ?

We compute the overall efficiency of competitiveness for each province over the period 2005–2008. The geometric means of these efficiency scores by year are summarized in Table 3 to shed light on the general pattern, yielding the following observations. First, with the exception of 2007, the average score of overall competitiveness, $O_{c}$, declined from 1.98 to 1.79. This implies that on average a province could have raised its competitiveness index by 98 % to catch up with the best province in 2005, but the potential gain fell to less than 80 % by 2008. In other words, during these 4 years, China had improved its overall competitiveness. Second, the average score of the efficiency of dimension mix competitiveness, $E_{d}$, also shows an improvement, whereas the average score of the degree of proportional competitiveness, $E_{p}$, is basically unchanged. Thus, the fall in $O_{c}$, or improvement in overall competitiveness, is mainly attributed to $E_{d}$. Third, in each year the average value of E _d exceeds that of $E_{p}$.¹⁰ This implies that, in China, on average, a larger portion of improvement in competitiveness can be achieved from changes in the dimension mix, via a disproportional development strategy.

Table 3 Average efficiency of competitiveness index and its decomposition

To further explore our findings’ policy implications, provinces are categorized according to their average values of $E_{d}$ and $E_{p}$ over the four sample years. The results are presented in Table 4. For easy exposition, the diagonal cells are shaded. In this table, moving from left to right across the row signals deterioration in dimension mix competitiveness, and moving down the column means deterioration in proportional competitiveness. Thus, the cells in the lower right corner of the table have low competitiveness, whereas the cells in the upper left corner have high competitiveness.

Table 4 Categorization of provinces

The four cells in the lower right corner of the table call attention to the least competitive provinces that mostly are Western provinces. In particular, Gansu, Guizhou and Tibet are the least competitive with $E_{d} > 1.6$ and $E_{p} > 1.6$. By contrast, the two cells in the upper left corner indicate the most competitive provinces, with Shanghai, in particular, being the most competitive.

We summarize the patterns in the above table as follows:

• 1. Most efficient provinces: E _d  = E _p  = 1

Shanghai is the only province in this group. Since the feasibility set constrains the relation between competitiveness and the dimensions, further improvement in competitiveness is possible only through the “technological” changes necessary to expand the feasible set. For further improvement in competitiveness, Shanghai can either learn from other advanced cities like New York and London or it can originate new technologies to upgrade its development. In 2003, the Mainland and Hong Kong Closer Economic Partnership Arrangement (CEPA) is established, transforming the economic and trade cooperation between Shanghai and Hong Kong from trading in manufactured goods to high-end services at an annual growth rate of approximately 20 % since 2004 (Horesh 2013). However, Horesh (2013) also observed that despite Shanghai’s faster pace of development between 1992 and 2012 as compared to Hong Kong, Shanghai is still widely seen as less global and entrepreneurial. For further internationalization, Shanghai can learn from Hong Kong to diversify its services sector and improve its capacity for innovation and global reach. To become world cities such as New York, London, Tokyo, Paris, Shanghai should further focus on economic liberalization, strengthening market institutions, building regional linkages and creating production new space for industrial consolidation and investment promotion (Yusuf and Wu 2002). Openness, combined with policy measures that induce competitiveness, will most likely lead to outcomes that are in Shanghai’s long-term interests.

• 2. Frontier provinces: E _p  = 1, E _d  > 1

All are eastern coastal provinces. It is not feasible for these competitive provinces to enhance all aspects simultaneously. Disproportional development strategy is appropriate. Since they are already on the frontier of the feasibility set, they should pay attention to innovating new technology to push the frontier outward. Since 2004, Zhejiang and Guangdong have reconsolidated their industrial structure. The Zhejiang government promoted replacing traditional agriculture with ecological and dedicated agriculture, as well as industries of high input, high cost and high emission with industries that produce high quality and environment friendly output. Similarly, Guangdong province moved its labor-intensive industries from the Pearl River Delta to the Eastern, Western and the Northern mountain areas. Meanwhile, high-quality personnel are attracted to work in developed areas. In short, Guangdong and Zhejiang are adopting the disproportional development strategies by specifically giving priority to a knowledge-based and coordinated development path.

• 3. Inefficient but close to frontier provinces: 1 < E _p  ≦ 1.3, E _d  > 1.3

Both proportional and disproportional development strategies can improve competitiveness. Since these provinces are relatively close to the frontier, they should focus on disproportional development strategy.

• 4. Highly inefficient provinces: E _p  > 1.3 and E _d  > 1.3

Most are western provinces with vast room for improvement through proportionally expanding all dimensions in the short run and changing the dimension mixes in the long run. Since China launched its WDP, western regions have received support from the central government. For example,the fiscal transfer from the central government up to 2004 in western region rose from 28 to 34.4 %. Local governments also heavily invest in infrastructure (y ₆) and improve the efficiency of government policies (y ₇). For example, during 2005–2008, e-government was widely promoted in Guangxi and Chongqing, Ningxia strengthens social security system to cover retirement pension, medical care, unemployment, etc. (Yao and Ren 2009). Using our terminology, the western provinces have adopted the disproportional development strategy in the China Western Development. As to be discussed in Sect. 5.2, such strategy is inferior to the proportional development strategy.

Several observations emerge from the preceding discussion. First, in terms of provincial competitiveness, Western China lags far behind Eastern China. From the Central Government point of view, China may need to choose appropriate policies to remedy the regional unbalance. Second, coastal provinces, like Beijing, Jiangsu, Zhejiang, Guangdong, and Shandong are on the frontier though relatively efficient in dimension mix. Although they can improve competitiveness through changing dimension mixes, long-run improvement must involve innovations of new technologies. Finally, our model derives different provincial development directions, which is not possible in the conventional methods that study the competitiveness index and its dimensions alone. These observations form our answer to Question 3:

Result 3

Shanghai is the most competitive province and western provinces lag far behind eastern provinces in terms of competiveness and its efficiency components.

5 Boosting GDP per capita through competitiveness improvement

This section explores the relations among efficiency of competitiveness, GDP per capita and the development strategies of a province. To identify these relations, we define the real GDP gap per capita:

$$ \delta^{kt} = rgdppc_{max}^{t} /rgdppc^{kt} . $$

where rgdppc ^kt is the real GDP per capita in RMB of province k in year t, and rgdppc ^t _max is the highest provincial real GDP per capita in RMB in year t among all provinces. Thus δ ^kt measures the potential difference between the real GDP per capita of a province and that of its maximum peer province. For instance, δ ^kt = 1.1 means that should a province attain the maximum level, its real GDP per capita can be increased by 10 %.

5.1 Efficiency components

Recall that a larger value of efficiency score in E _p or E _d means a larger potential to increase the competitiveness index. As competitiveness affects real GDP per capita positively, we expect that δ ^kt can be explained by the efficiency of proportional competitiveness E _p and the efficiency of dimension mix competitiveness E _d . We ask the following question:

Question 4

Which component of the overall efficiency of competitiveness has a larger impact on real GDP gap per capita?

To derive our answer, we estimate the following regression:¹¹

$$ \ln (\delta ) = \beta_{0} + \beta_{1} \ln (E_{p} ) + \beta_{2} ln(E_{d} ) + \beta_{3} noneast + \beta_{7} dcm + \beta_{8} ar + \varepsilon ; $$

where dummy variables are defined as before. We expect β ₁ and β ₂ to be positive, as confirmed by the estimates reported in Model 1 of Table 5:

Table 5 The potential impacts of various development strategies

The estimates of β ₁ and β ₂ are positive at any meaningful level of significance and $\hat{\beta }_{1}$ is greater than $\hat{\beta }_{2}$ at 5 % level of significance.¹² Since the real GDP gap per capita (δ) reflects potential losses due to low competitiveness, increasing E_p by 1 % will raise the potential losses by 1.22 %. Said equivalently, eliminating 1 % of the inefficiency of proportional competitiveness will reduce the potential losses by 1.22 %.

Therefore, the answer to Question 4 is:

Result 4

While improving both efficiency of proportional competitiveness (i.e., reduce the value of E _p to 1) and efficiency of dimension mix competitiveness (i.e., reduce the value of E _d to 1) brings the per capita real GDP gap of a province closer to its potential maximum (i.e., a smaller value of δ), the impact on per capita real GDP gap of E _p is larger than that of E _d .

Result 4 suggests that expanding all dimensions proportionally should be done with priority in a hybrid development strategy.

5.2 Boosting GDP per capita through changing the dimension mix

When changing dimension mix can improve competitiveness, which directions should a province go? To simplify discussion, the nine dimensions are further classified into three groups in Table 6,¹³ with each group reflecting a particular type of policy, thereby answering the next question that attracts policy makers’ attention:

Table 6 Group categorization

Question 5

Which dimensions should be emphasized in the disproportional development strategy?

To answer this question, we first assess the impacts of the above three groups on the competitiveness index in the disproportional development strategy and define the following three variables:

$$ \begin{aligned} g_{1} & = \frac{{E_{p} \cdot y^{0} + \sum\nolimits_{m = 2,3,6} {w_{m} \left( {y_{m}^{*} - E_{p} y_{m}^{0} } \right)} }}{{E_{p} \cdot y^{0} }} \\ g_{2} & = \frac{{E_{p} \cdot y^{0} + \sum\nolimits_{m = 1,4,8} {w_{m} \left( {y_{m}^{*} - E_{p} y_{m}^{0} } \right)} }}{{E_{p} \cdot y^{0} }} \\ g_{3} & = \frac{{E_{p} \cdot y^{0} + \sum\nolimits_{m = 5,7,9} {w_{m} \left( {y_{m}^{*} - E_{p} y_{m}^{0} } \right)} }}{{E_{p} \cdot y^{0} }} \\ \end{aligned} $$

Using g ₁ as example, E _p ·y ⁰ is the vector of dimension on the frontier when all observed dimensions are expanded proportionally. y* is the vector when the maximum value of the competitiveness index is attained. A disproportional policy is needed for a province to shift from E _p ·y ⁰ to y*. The corresponding values of competitiveness at E _p ·y ⁰ and y* are $\sum\nolimits_{m = 1}^{9} {w_{m} (E_{p} y_{m}^{0} )}$ and $\sum\nolimits_{m = 1}^{9} {w_{m} y_{m}^{*} }$, respectively. The potential increase in the value of competitiveness from the disproportional development strategy is equal to $\sum\nolimits_{m = 1}^{9} {w_{m} (y_{m}^{*} - E_{p} y_{m}^{0} )}$. The term Σ_m=2,3,6 w _m (y ^* _m  − E _p y ⁰ _m ) equals the change of value of overall competitiveness due to the disproportional variations of the dimensions in group 1. The value of g _i thus measures the percentage change of the competitiveness when the dimensions in group i = 1, 2, 3 are changed.¹⁴ For instance, if g _i  = 1.1, the contribution of the dimensions in group 1 in the disproportional development strategy is 10 % increase in the value of the competitiveness index.

Based on the definitions of the components of each group, we can call these components, factor-driven (g ₁), structure-driven (g ₂) and government-driven (g ₃), which can be increased by policies of injecting more resources, improving the structure of the economy, and improving the functions of the government, respectively. By comparing their effects on real GDP per capita, different policy emphases can be addressed under the disproportional development strategy.

The three components of each province are listed in Table 10 in the Appendix for the years 2005 and 2008. It is found that $g_{1}$ is the smallest component for all provinces, implying that factor-driven category is the least important for raising real GDP per capita because it has the least potential in increasing provincial competiveness. Thus boosting investments in industries, infrastructure and general education is ineffective to raise China’s income per capita. In comparison, the structure-driven component, g ₂, dominates in determining competitiveness improvement in both years whereas the government functioning, g ₃, is the second largest component.

Each of the three components can be larger or smaller than one. A value larger than one means the increase in this category can potentially increase the competitiveness index, and therefore increase real GDP per capita. Conversely, a value smaller than one means this category has currently been over emphasized and reallocating resources from this group to other groups can increase competitiveness. Using Beijing in 2008 as an example, the values of factor-driven, structure-driven, and government-driven component are 1.02, 1.04 and 0.98, respectively. Thus shifting resources from the government-driven sector to the structure-driven sector may raise the competitiveness of Beijing and therefore its real GDP per capita.

To reach a more general conclusion, the logarithm of δ is regressed on the logarithm of $E_{p}$ and these three components, along with the previously defined dummy variables. The estimated results are presented under Model 2 in Table 5. All estimated coefficients of ln(g ₁), ln(g ₂)and ln(g ₃) are significant at α = 0.05. However, an F-test indicates the hypothesis that these three coefficients are equal cannot be rejected at α = 0.10. Model 3 in Table 5 presents the estimated regression equation that restricts these three coefficients to be equal. We now state the answer to Question 5:

Result 5

All three groups of dimension mix components have significant impacts on real GDP gap per capita. Since their impacts are statistically equal, the group of dimensions to choose depends on the position of a province in the feasibility set.

We summarize our findings as below:

• 1. When E _p  > 1 and E _d  = 1, adopting the proportional development strategy can narrow the gap between the real GDP per capita of a province and the maximum level.

• 2. When E _p  = 1 and E _d  > 1, the disproportional development strategy is desirable. All factor-driven, structure-driven, and government-driven policies are equally effective to raise real GDP per capita, as long as they can raise the overall competitiveness. Which one to choose depends on the position of a province in the feasibility set.

• 3. When E _p  > 1 and E _d  > 1, the hybrid development strategy is appropriate. Since the estimated coefficient of ln(E _p ) is significantly higher than that of ln(E _d ), the proportional development strategy is more effective to raise the real GDP per capita. A province should pay more attention to all dimensions of competitiveness before its potential has been exhausted.

5.3 Comments on two policies

The financial Tsunami in 2008 hit many sectors of the Chinese economy, with ensuing efforts by the central government and local authorities in China to revive the economy. This section analyzes two policies from the competitiveness point of view to illustrate the usefulness of our framework introduced herein.

This first policy is the big push from the central government. In 2008, Premier Wen Jiabao announced that four trillion RMB would be injected to the economy. This policy greatly increased fixed investment of the whole economy. Two consequences of this policy on the Chinese economy ensue:

• Consequence 1: Fixed investment drastically increased.

• Consequence 2: The share of state-owned enterprises in the whole economy increased.¹⁵

Consequence 1 means resources are allocated into the factor-driven category which has been shown to be least important in improving competitiveness. Consequence 2 actually means more loans of local governments and lower level of marketization. This lowers the value of the structure-driven category. Thus resources are used inefficiently, at the expense of harming the highest potential of improving competitiveness. In short, the four trillion RMB investment was an ineffective competitiveness policy.¹⁶

The second policy is the “Empty out the cage of old birds for new ones [teng long huan niao]” policy in the Guangdong province. For simplicity, we call this policy “new bird policy”. The purpose of this policy is to replace low-end, labor-intensive and polluting manufacturing enterprises with high-tech production and research and development centers. From Table 4, Guangdong’s efficiency scores are E _p  = 1 and E _d  > 1. Without technological progress, changing the dimension mix along the frontier, rather than proportionally expanding all dimensions, is necessary to improve competitiveness. The new bird policy means enhancing Group 3 by increasing resources to develop a knowledge-based economy (y ₅) and sacrificing Group 1 by decreasing emphasis in macroeconomic conditions (y ₁). In Table 10, the three components of competitiveness for Guangdong are 0.99 for s ₁, 1.02 for s ₂, and 1.05 for s ₃. This implies that the Guangdong authority should reduce the factor-drive group (Group 1) in favor of the other two groups. In particular, the government-driven group (Group 3) has the highest potential to improve competitiveness. Hence the new bird policy can be justified from the point of view of improving competitiveness.

6 Regional competitiveness disparity

The previous section demonstrates that raising competitiveness can raise real GDP per capita. What we do not know is whether proportional or disproportional development strategy is more suitable to reduce regional disparity. Section 4 shows that, on average, the losses due to inefficient dimension mix (E _d ) are larger than that of inefficient proportional competitiveness (E _p ). The following question naturally emerges:

Question 6

Is inequality in E _d the main source of overall competitiveness inequality?

6.1 Decomposing the inequality of overall competitiveness

To examine the disparities in competitiveness among China’s regions, we use the entropy-based Theil index. Let x denote an N-dimensional vector of observations, $x_{i}$, with mean $u = \frac{1}{N}\sum\nolimits_{i = 1}^{N} {x_{i} }$. One version of Theil’s measure of inequality (Cheng and Li, 2006), among these N observations is:

$$ T\left( x \right) = \frac{1}{N}\sum\limits_{i = 1}^{N} {ln\left( {\frac{u}{{x_{i} }}} \right)} . $$

The closer is the index to zero, the greater is the equality among observations. This index is zero if and only if the value of $x_{i}$ is the same for all. In our present application, x denotes one of the vectors of O _c , E _d and E _p over the N = 31 provinces.

The method developed by Duro and Esteban (1998) and Cheng and Li (2006) enables us to decompose the inequality of O _c in terms of the inequalities of its multiplicative components, E _d and E _p . Let the means of O _c , E _d and E _p be O _cu , E _du , and E _pu . The decomposition of the inequality O _c is as follows:

$$ \begin{aligned} T\left( {O_{c} } \right) & = \frac{1}{N}\sum\limits_{i = 1}^{N} {ln\left( {\frac{{O_{cu} }}{{O_{ci} }}} \right)} \\ & = \frac{1}{N}\sum\limits_{i = 1}^{N} {ln\left( {\frac{{E_{du} }}{{E_{di} }} \cdot \frac{{E_{pu} }}{{E_{pi} }} \cdot \frac{{O_{cu} }}{{E_{du} E_{pu} }}} \right)} \\ & = T\left( {E_{d} } \right) + T\left( {E_{p} } \right) + ln\left( {\frac{{O_{cu} }}{{E_{du} E_{pu} }}} \right) \\ \end{aligned} $$

(8)

In (8), the interaction term, $ln\left( {\frac{{O_{cu} }}{{E_{du} E_{pu} }}} \right)$ is a residual indicating the correlation between $E_{d}$ and $E_{p}$. Specifically, the interaction is positive (negative) when $E_{d}$ and $E_{p}$ are positively (negatively) correlated. When this term is zero, $E_{d}$ and $E_{p}$ are uncorrelated. The measure T(x) is always positive and a larger number will indicate greater inequality.

The general interprovincial competitiveness inequality is summarized in Table 7. Except for 2006, the values of interprovincial inequality of overall efficiency of competitiveness are falling, thus suggesting a lower degree of inequality. While inequality in E _d has been increasing until 2007, inequality in E _p has been decreasing, with the interaction component remaining almost unchanged. Therefore, the improvement in inequality mainly stems from the lower inequality of $E_{p}$ among provinces.

Table 7 Interprovincial competitiveness index and its decomposition

The inequality of efficiency of proportional competitiveness T(E _p ) is larger than the inequality of efficiency of dimension mix T(E _d ) each year in the sample period.¹⁷ Since changes in $E_{p}$ involve proportional development strategy, the finding of T(E _p ) > T(E _d ) implies that a development strategy with due consideration to all aspects is more effective to alleviate the inequality of competitiveness among provinces. To sum up, we have the following result:

Result 6

The main source of competitiveness disparity is the inequality in the efficiency of proportional competitiveness (E _p ).

6.2 Inter-regional versus intra-regional inequality of competitiveness

Based on Shorrocks (1982) and Tsui (2007),we investigate the source of inequality from the perspectives of inter-region and intra-region. In view of the finding that the provinces in some regions are more inefficient than provinces in other regions, the following question arises:

Question 7

Does inter-regional competitiveness inequality dominate intra-regional competiveness inequality?

Suppose there are G regions and the number of provinces in the gth region is $N_{g}$. Let $O_{cu}^{g}$ and $T^{g}$ be the sample mean of overall efficiency of competitiveness ($O_{c}$) and the value of Theil’s measure of region g, respectively. The formula of Shorrocks (1982) and Tsui (2007) is:

$$ T\left( {O_{c} } \right) = T_{b} \left( {O_{c} } \right) + T_{w} \left( {O_{c} } \right) $$

where $T_{b} \left( {O_{c} } \right) = \sum\nolimits_{g = 1}^{G} {\frac{{N_{g} }}{N}{ \ln }\left( {\frac{{O_{cu} }}{{O_{cu}^{g} }}} \right)}$ is the inter-region inequality and $T_{w} \left( {O_{c} } \right) = \sum\nolimits_{g = 1}^{G} {\frac{{N_{g} }}{N}T^{g} }$ is the intra-region inequality. The finding in Sect. 4 that highly inefficient provinces concentrate in the western area leads us to postulate that the inter-region inequality of competitiveness is higher.

The inequality of overall efficiency of competitiveness and its components are computed for each year in 2005 to 2008. The scores are summarized in Table 8. Generally, competitiveness inequality tends to decline over the 4 years with exception in 2006. The source of improvement coming from the intra-region inequality T _w (O _c ), continuously drop from 0.0213 in 2005 to 0.0172 in 2008. In contrast, the inter-region inequality in competitiveness T _b (O _c ) is larger than the intra-region inequality T _w (O _c ) in each year. Thus, we have:

Table 8 Inter-region and intra-region competitiveness inequality

Result 7

The main source of inequality of competitiveness is the inter-region inequality of competitiveness in China.

7 Conclusions

This paper is based on the premise that the knowledge of human beings imposes maximum values of the dimensions of competitiveness along each dimension mix. The feasibility set of competitiveness reflects this constraint. By incorporating the weights of the dimensions of competitiveness into the feasibility set, we decompose the improvement of competitiveness into proportional change in all dimensions and alternatively, a change in the dimension mix. This enables us to extract more policy implications from existing competitiveness index than what conventional studies of competitiveness can do.

We have found statistical evidence for the link between competitiveness and real GDP per capita in China. Borrowing the DEA methodology in the productivity and efficiency analysis literature, we identify three possible cases of improving competitiveness: expanding all dimensions at the same time, expanding some dimensions at the cost of shrinking others, and a combination of both. Our production framework of competitiveness provides important implications for policy makers.

We also found that provincial real GDP per capita is significantly affected by the efficiency of proportional competitiveness E _p and the efficiency of dimension mix E _d . In the case of changing dimension mix, our analysis shows that structure-driven and government-driven dimensions are more effective in raising real GDP per capita. Using pre-1997 data, Fan et al. (2003) conclude that structural changes have provided the main momentum for China’s economy from the productivity perspective. In sympathy, we have shown that structural changes are also essential for enhancement in competitiveness.

In addition, we find that the proportional development strategy should dominate the disproportional development strategy before reaching the frontier of competitiveness for central and western provinces in China. There are three reasons: First, these provinces are far from reaching the frontier. Expanding all dimensions simultaneously is still possible and desirable. Second, when a province is inefficient in proportional competitiveness and dimension mix, the proportional development strategy can be more effective to increase its competitiveness. Finally, the inequality of efficiency of proportional competitiveness account for a larger portion of the inequality of overall provincial competitiveness. In summary, the proportional development strategy can better increase provincial real GDP per capita while controlling the inequality of competitiveness than the disproportional development strategy.

Appendix

See Tables 9 and 10.

Table 9 Information about dimensions

Table 10 Values of three components for provinces in 2005 and 2008