# Sources of China’s Economic Growth: An Analysis Based on Nonparametric Accounting Method

## LiangYongmei(梁泳梅)andDongMinjie(董敏杰)

Abstract: This paper improves the slacks-based method for estimating inefficiency, derives the criteria for the selection of the weights of output and input inefficiencies in the objective function, and creates a new nonparametric method for accounting economic growth. Based on this method, the paper estimates the sources of China’s economic growth from 1978 to 2013. Our findings suggest that factor input and especially capital is a major source of economic growth for China as a whole and its major regions, and that economic growth in recent years is increasingly dependent on capital. For a rather long period of time before 2005, China’s northeast, central and western regions lagged behind the eastern region in terms of economic growth, and TFP and factor input are major reasons behind such regional growth disparities. Although other regions have narrowed their disparities with and even overtaken the eastern region in terms of economic growth, the key driver is the rapid increase in the contribution of factor input. Advanced technologies of eastern region should be utilized to promote TFP progress in other regions, which is vital to economic growth in these regions and China as a whole.

Keywords: TFP contribution, share of TFP contribution, slacks- based method for estimating inefficiency, data envelope analysis (DEA)

JEL Classification: O11, O39, O47, O53

1. Introduction

The sources of China’s rapid economic growth since reform and opening- up in 1978 have been under heated debate in academic community. While conclusions of existing studies on the pre- 1978 period are generally consistent, the results of studies on the post1978 period vary greatly ( see Table 1). Take the 1990s for instance, most studies found that total factor productivity ( TFP) in that decade contributed 20% to 30% of economic growth; Bosworth and Collins (2008) found this share to be as high as 54.7%. For the about two decades from around 1982 to 2000, most studies found

that the contribution of TFP to China’s economic growth is about 30%; the result of Bosworth and Collins ( 2008) reached nearly 50%, while Wu (2003) found this share to be no more than 20%.

Another important factor that led to the above- mentioned difference of conclusions i s the employment of different research methods. Existing methods of economic growth accounting mainly include parametric method,

stochastic frontier production function method and nonparametric method; of which, the first two methods require certain assumptions of the form of production function and error term. Nonparametric method can avoid the above presumptive specifications and is thus more appropriate for the estimation of TFP growth rate or its contribution to economic growth (Kumar and Russell, 2002; Unel and Zebregs, 2006). Specifically, most nonparametric methods first estimate the Malmquist Index before conducting further treatment to obtain the contributions of TFP and production factors to economic growth.

As pointed out by Liang and Dong (2012), a certain degree of deviation, though limited, may exist in the estimation results based on these methods. Hence, Liang and Dong (2013) derived a nonparametric method to estimate

the sources of China’s economic growth using provincial data. Nevertheless, the following two drawbacks may exist in this approach. First, for output inefficiency as the key variable in this method, the study has employed the output- based data envelope analysis ( DEA), which is actually a radial DEA model that may cause deviations in the result of estimation. Specifically, the circumstance where the factor input of observation unit has changed without the change of output inefficiency is likely to exist in reality. Following an output-based DEA method, the result of decomposition of output inefficiency and thus economic growth sources will not change as well. However, based on TFP’s definition, the change in factor input may also lead to the change of TFP. On the other hand, in estimating the output variations caused by factor input, the study failed to take into account factor efficiency. As to be mentioned in the following section of this paper, this may overestimate the contribution of factor input to economic growth and thus underestimate TFP’s contribution to economic growth.

This paper improves the slacks- based inefficiency (SBI) method for the estimation of inefficiency developed by Fukuyama and Weber (2009) to derive the criteria for the selection of the weights of output and input inefficiencies in the target function of the method and thus creates a new nonparametric accounting method for economic growth to compensate for the above- mentioned drawbacks of Dong and Liang’s (2013) method. Based on the new method, this paper estimates the sources of economic growth for China as a whole and its four major economic regions1 from 1978 to 2013 and discusses the reasons behind regional growth differences. The rest of this paper is structured as below: Part 2 introduces the accounting method of this paper; Part 3 offers data explanations; Part 4 reports the results of estimation; Part 5 is a summary of this paper and sheds light on the direction of future research.

2. Nonparametric Accounting Method

Given that inefficiency is the foundation for the accounting method of this paper, we first introduce the SBI estimation method, then elaborate the improvement of SBI and the accounting method employed in this paper, and finally offer a graphic illustration of the accounting method.

2.1 Estimation of Inefficiency: SBI Method

Various methods for estimating inefficiency exist under the framework of DEA method. In the early stage, output- based or input- based method is selected. The former calculates the maximum proportion by which output can be expanded under constant input, while the latter calculates the maximum proportion by which input can be reduced under constant output. Because the output- based or inputbased perspective needs to be selected, the two linear plans are referred to as the “angular DEA models”. Results of estimation under both models are generally inconsistent. Another method to avoid this problem is to introduce directional distance function approach ( DDF), i.e. it is assumed that input and output expand or reduce by the same proportion. However, since output expands and input reduces by the same proportion, DDF can be classified as a radial DEA model. Some researchers ( Tone, 2001, 2002; Färe and Grosskopf, 2010; Tone and Tsutsui, 2010) relaxed the assumption of the expansion of output and the reduction of input by the same proportion and developed a slack- based measure ( SBM). On the basis of the SBM method, Fukuyama & Weber ( 2009) further developed a slacks- based method for the measurement of inefficiency, whose general form can be written as follows:

1

Eastern region includes the provinces and municipalities of Beijing, Tianjin, Hebei, Shanghai, Jiangsu, Zhejiang, Fujian, Shandong, Guangdong and Hainan; Northeast includes three provinces of Liaoning, Jilin and Heilongjiang; Central region includes six provinces of Shanxi, Anhui, Jiangxi, Henan, Hubei and Hunan; Western region refers to ten provinces and autonomous regions including Inner Mongolia, Guangxi, Chongqing, Sichuan, Guizhou, Yunnan, Shaanxi, Gansu, Qinghai, Ningxia and Xinjiang.

Where, denotes the inefficiency of j for n production units during time t. The numbers of types contained in the output and input vectors are P and Q; and respectively denote the input and output of production unit j during period t; and respectively denote the directional vectors of input and output, which are normally substituted by and ; denotes the slack of input type p of production unit j during period t; denotes the slack of output q of production unit j during period t.

and respectively denote the inefficiencies of input type p and output type q; mp and mq respectively denote the weights of inefficiencies for input type p and output type q. denotes the weight vector that corresponds to various production units on the production frontier.

For the selection criteria of mp and mq, Fukuyama and Weber (2009) adopted mp= and mq= . This practice has been followed by many other forthcoming studies (Akther et al., 2013). This standard is actually the average values of the numbers of input and output indicators and lacks theoretical basis and significance in economics. In particular, in case the output contains undesirable output, the above drawback is likely to cause difficulty in the selection of weights.

2.2 Estimation of Inefficiency: an Improved SBI Method

Considering that inputs are labor l and capital k and output is y, P= 2 and Q= 1 in equation (1). For any production unit j, equation ( 1) can be specified as follows:

Under complete economic conditions, marginal factor output is equal to the return to factor and the level of output is the sum of the products of various factor inputs and marginal factor output. But in reality, due to the existence of non-complete competition factors such as monopoly, deviation may exist between return to factor and the effective marginal output of factor, and the level of output is the sum of the products of various factor inputs and the average return to factors, i.e.:

In reality, not all the production units are on the production frontier and the problems of insufficient output or redundant input exist in the inefficient production units. The reason is that the level of their production technology is relatively low compared with the effective production units on the production frontier. By mirroring inefficient production units on the production frontier, we may arrive at their corresponding effective production portfolio

. Where, Yt, Lt and Kt respectively denote effective yield and the effective inputs of labor and capital; Wtand Rt respectively denote effective return to labor and capital: if the effective production portfolio is in a fully competitive environment, return to factor is equal to the marginal output of factor; if the effective production portfolio is in an environment that is not fully competitive, deviations exist between the marginal output of factor and the return to factor, and Wtand Rt denote return to labor and capital measured by the income distribution mechanism of effective production units and technology level. Furthermore, effective yield Yt can be written as:

Relative to the original production units, effective production units can generate the same amount of an even greater yield with smaller factor input due to a higher level of technology in use. The slacks of labor, capital and yield are defined as follows:

Under the assumption of constant return to scale, the optimal yield corresponding to Wtand Rt when the factor input of production units is put into sufficient use is as follows:

By taking the difference between equation (8) and equation (4) and substituting equation (5) into equation (7), we may arrive at:

The above equation can be further arranged into the following:

The inefficiency of production unit j can be calculated through the following non-linear programming:

Compared with the linear programming of equation ( 2), the non- linear programming of equation (12) has the following two differences: first, production function. The weights of inefficiencies for the yield, labor and capital in equation ( 2) my, ml and mk can be specified in equation ( 12) as 1, and . Second, constraints: equation ( 12) has included two constraints on the basis of equation (2):

Here, the economic connotations of the two constraints are illustrated. and in the numerator denote the total return to labor and capital for production units referenced in the creation of production frontier, while

is the weight vector that corresponds to various production units in the creation of production frontier. Hence, and denote total return to labor and capital in the effective production portfolio. On the other hand, denominators and denote the labor and capital inputs of effective production portfolio. Their ratio denotes the effective return to labor and capital, which is equation (13). By solving equation (12), we may arrive at such variables as , , , , and

.

2.3 Growth Accounting

By definition, the contribution of TFP to output growth aggregate (“TFP contribution”) is the part of output growth aggregate that cannot be explained by factor input, i.e. the difference after deducting the contribution of factor input to output growth (“factor contribution”). Factor contribution refers to the output growth purely caused by change in factor input when other factors are constant. Take labor’s contribution for instance, it refers to the output growth caused by the change in labor input when labor efficiency and the return to labor are both constant. and

respectively denote the efficiency of labor and capital utilization:

If measured by the production technology and efficiency during period t, output growth caused by change in labor input is . If measured by the production technology and efficiency during period t+ 1, the output growth i s

. By taking the average value between the two as contribution of change in labor input to output growth (“labor contribution”) Lt, t+ 1, we arrive at:

By the same token, we may obtain the contribution of changing capital input to output growth aggregate (“capital contribution”) Kt, t+ 1:

The sum of labor contribution and capital contribution is factor contribution INPUTt, t+ 1:

denotes output growth from period t to period t + 1. The economic connotations of

, , and are illustrated in the following sections of this paper. In the DEA method, TFP contribution can generally be further divided into the following two parts: the contribution of efficiency change to output growth aggregate (“contribution of efficiency change”) and the contribution of technology progress to output growth aggregate (“contribution of technology progress”). In reference to the practice of Dong and Liang ( 2013), TFP contribution can be expressed as follows:

The first term to the right side of the equation is the contribution of efficiency change, denoted as EFFEt, t+ 1; the second term is the contribution of technology progress, denoted as TECHt, t+ 1. If the current-phase DEA method is followed, such a method of decomposition may cause the result of “technology retrogression”, i.e. the production frontier of the following phase is within the production frontier of a previous phase, causing technology progress to be negative. Hence, some studies have employed sequential DEA method in estimating inefficiency, i.e. not only is currentphase production portfolio included in creating the production frontier, but the production portfolios of various previous phases are included as well, which may cause production frontier to move outward relative to the scenario of current-phase DEA method.

Although this will avoid “technology retrogression”, it will also reduce the contribution of efficiency change. Hence, compared with the estimation result with the adoption of sequential DEA, the contribution of technology progress calculated using current DEA method is generally low, while the contribution of efficiency change is normally high. Given the trade- off between the contribution of efficiency change and the contribution of technology progress, we will mainly focus on TFP contribution in the following sections

of this paper and briefly report the decomposition result of the contribution of efficiency change and the contribution of technology progress. Because decomposing the contribution of efficiency change and the contribution of technology progress is helpful to understanding the graphic illustrations of the following accounting method, TFP contribution is still decomposed.

In summary of the above equations, output growth aggregate can be written as:

By dividing both sides of equation (25) by yt and denoting various terms as , tfpt, t+ 1, inputt, t+ 1, effet, t+ 1, techt, t+ 1, lt, t+1 and kt, t+ 1, we may arrive at: Where, , effet, t+ 1, techt, t+ 1, lt, t+ 1 and kt, t+ 1 respectively denote the output growth rates from period t to period t+ 1, contribution of efficiency change to output growth rate (“contribution of efficiency change”), contribution of technology progress to output growth rate (“contribution of technology progress”), contribution of labor to output growth rate (“contribution of labor”), as well as contribution of capital to output growth rate (“contribution of capital”). In this manner, the output growth rate from period t to period t+ 1 is decomposed into four terms, of which the sum of the first two terms is the contribution of TFP to output growth rate (“TFP contribution”) tfpt, t+ 1, while the sum of the last two terms is the contribution of factors to output growth rate (“factor contribution”) inputt, t+ 1. If the “share of contribution” of various terms to output growth is to be brought under attention, the various terms of equation (26) should be divided by to arrive at:

According to Dong and Liang (2013), after the estimation of output growth sources for various provinces, municipalities and autonomous regions, the sources of output growth for China as a whole and its various economic regions can be aggregated on the spatial dimension. Output growth rate for China as a whole and its various regions can be written as:

Where, is the regional gross product of province ( municipality or autonomous region) i during period t. N is China as a whole or the number of provinces ( municipalities or autonomous regions) contained in each region.

denotes the gross domestic product of China as a whole or the gross regional product of various regions contained in each region during period t.

On the temporal dimension, the contribution of various sources and the intertemporal cumulative values of the shares of contribution can be calculated. The output growth rate from period t to period t+T can be written as:

2.4 Graphic Illustration

Considering that production portfolio contains two types of input, it takes threedimensional graphics to fully demonstrate the above- mentioned accounting method. For the ease of demonstration and considering that TFP contribution is a major concern in economic growth accounting, we have employed a plane figure to illustrate variations in efficiency and the contributions of technology progress and factor input to output growth aggregate (Figure 1). In this manner, the production portfolio becomes one of single input and single output, while output is still denoted by y and input is denoted by x2.

In the figure, horizontal axis denotes output and vertical axis denotes input. Period t contains two production units and , and the variations in input and output for the two production units during period t+ 1 are expressed in the figure as

and respectively. For , the production frontier during period t is radial line , and the effective production portfolio of on is ; the production frontier in period t+ 1 is radial line

, and the effective production portfolio of on is .

The situation is a bit different for . If measured by production technology during period t, corresponds to the effective production portfolio of . Yet as is located within the production frontier ( i. e. the loss of factor efficiency exists), after factor input increases from xt to xt+ 1, the variation of output is AtBt, rather than . Hence, when xt increases, production frontier actually becomes a curve

. Similarly, measured by the production technology during period t+ 1, corresponds to the effective production portfolio of . But as

is located within the production frontier (i.e. the loss of factor efficiency exists), after factor input drops from xt+ to xt, the variation of output is , rather than . Thus, when xt+ 1 reduces, production frontier actually becomes a curve .

Based on definitions of equations (20)-(23), , , and respectively denote

, , and

. Namely, denotes the difference between optimal output and real output measured by the production frontier during period t with the factor

input during period t; denotes the difference between optimal output and real output measured by the production frontier during period t+ 1 with factor input during period t; denotes the difference between optimal output and real output measured by the production frontier during period t+ 1 with the factor input during period t; denotes the difference between optimal output and real output measured by the production frontier during period t+ 1 with the factor input during period t+ 1.

Furthermore, the difference between and denotes the contribution of efficiency variations to output growth aggregate, which is equivalent to the first item to the right side of equation (24). The difference between and

denotes the expansion of production frontier measured by the input level during period t; the difference between and denotes the expansion of production frontier measured by the input level during period t+ 1. Their average value denotes the contribution of technology progress to output growth aggregate, which is equivalent to the second item to the right side of the equation ( 24). and respectively denote the “real” growth volumes of optimal output caused by factor input variations measured by the production frontiers of t and t+ 1 periods. Their average value denotes the contribution of factor input to output growth aggregate, which is equivalent to equation (15) or equation (16).

3. Data Explanations

( 1) Output: Output indicator is the real regional GDP measured by the constant price of 1978, which is arrived at by multiplying the regional GDP of various provinces, municipalities and autonomous regions in 1978 and the regional GDP indices measured by the constant price of 1978 for various years, with data taken from China Statistical Yearbook and Collection of Statistical Information of the People’s Republic of China since 1949.

(2) Labor input: The number of employment for various provinces, municipalities and autonomous regions is used, with data taken from China Statistical Yearbook. Starting from 2011, the National Statistical Bureau (NBS) did not publish the employment figures for various provinces, municipalities and autonomous regions. The employment numbers for various provinces, municipalities and autonomous regions during 2011 and 2013 are estimated based on their share in 2010 in national total employment.

(3) Fixed assets inventory: Perpetual inventory method ( PIM) is generally used to calculated the fixed asset inventory of various provinces, municipalities and autonomous regions based on the following equation: . Where,

and Kt denote the fixed capital inventories during period t- 1 and period t; denotes depreciation rate during period t, It denotes new investment volume during period t, and Pt denotes the price index of investment goods. This equation involves four major variables as explained below:

a. Annual new investment volume: fixed assets formation is identified as the nominal investment volume for various provinces, municipalities and autonomous regions.

b. Price index of investment goods: The price deflator with the base period of 1978 is calculated based on the fixed assets formation price indices of various provinces, municipalities and autonomous regions between 1952 and 2004 provided by Historic Information of China’s GDP Accounting (1952-1995) and Historic Information of China’s GDP Accounting ( 1952- 2004), and indices as of 2005 are replaced by the fixed asset investment price indices of various provinces, municipalities and autonomous regions.

c. Capital stock of base period K0: the fixed capital stock of various provinces, municipalities and autonomous regions in 1978 is estimated with the ratio between the capital formation aggregate in 1978 and the average growth of fixed capital formation between 1978 and 1987.

d. Depreciation rate: Given the different specifications of depreciation rate in literature, this paper reports the calculation result when depreciation rate is 10.96%. Meanwhile, in conducting robustness test, the calculation results with depreciation rates at 9.6%, 4% and 7% respectively are reported.

( 4) Share and return of factor income:

Measured by the income approach, GDP includes labor wage, business surplus, fixed asset depreciation and net production tax. Based on existing studies, two methods can be followed in measuring the share of labor wage in GDP: the first method is the “share of labor income based on factor approach, i.e. the share of labor wage in the aggregate of labor wage, business surplus and fixed assets depreciation; the second method is the “share of labor income based on GDP approach”, which is the share of labor wage in the aggregate of labor wage, business surplus, fixed assets depreciation and net production tax. Despite a difference of around seven percentage points in the “share of labor income” calculated using the two methods, the tendency is more or less consistent. After the share of labor income is obtained, it is multiplied with GDP to calculate aggregate return to labor, which is divided by total employment to arrive at the net return to labor. The difference between GDP and aggregate labor income is aggregate return to capital, which is divided by total fixed capital stock in current year to obtain unit return to capital. Here, we report the results of calculation based on the first method and conduct robustness test using the second method. The itemized GDP data used for calculating the share of labor income are taken from the CEIC database and cei.gov.cn. Data for 2013, which are not available, are replaced with the data of 2012.

4. Results of Estimation

Based on the accounting method in Section 2, we estimated the economic growth sources for China as a whole and its four major economic regions between 1978 and 2013, as well as the shares of contribution for various sources. Here, we respectively report the estimation results for China as a whole and its four major economic regions and lastly report the results of robustness test.

4.1 Sources of China’s Economic Growth

It needs to be noted that similar to Dong and Liang ( 2013), the output growth rate in this paper involves three statistical scales: the first statistical scale is the aggregation of GRPs for various provinces, municipalities and autonomous regions; the second statistical scale is the one used in this paper, i.e. the aggregation of the contribution of efficiency variation, the contribution of technology progress, labor contribution and capital contribution; the third statistical scale is the national GDP growth after the output data of various provinces, municipalities and autonomous regions are adjusted by the NBS. The first two statistical scales both follow provincial data with generally consistent results. We have respectively adjusted the contributions of various sources to obtain the values corresponding to the third statistical scale based on the adjustment factor of the ratio between national economic growth rates calculated based on the third statistical scale and the second (or the first) statistical scale. In the following part of this paper, we will mainly report the contributions of various sources obtained on such a basis. Of course, such adjustment does not affect the calculation results of the shares of contribution of various sources.

From 1978 to 2013, China’s economy had grown by 25.1 times, with TFP, labor and capital contributions growing 5.4 times, 1.9 times and 17.8 times respectively, the share of TFP contribution is about 21.6%, and the shares of labor and capital contribution are 7.5% and 71.0% respectively. Without taking into account the impact of global financial crisis after 2008, China’s economy had grown by 14.6 times between 1978 and 2007, with TFP, labor and capital contributions growing 3.6 times, 1.1 time and 9.8 times respectively. The share of TFP contribution is about 24.8% and the shares of labor and capital contribution are 7.8% and 67.4% respectively. On the whole, TFP progress is a key driver of China’s economic growth. Yet the share of TFP contribution is far smaller than the share of capital contribution. Capital input is the most important engine of China’s rapid growth, which is consistent with the conclusions of most studies.

In terms of temporal trend ( Table 2), the share of TFP contribution had been generally negative before 1990 with wild swings but had been on the rise. After further reforms in the

1990s, the share of TFP contribution approached and even exceeded 50%, before stabilizing at 30% to 40%. Starting from 2005, the share of TFP dropped to around 20%, bottoming at 12.7% and 5.7% in the depth of global financial crisis in 2008 and 2009 respectively before rebounding to around 20% since 2010. In TFP contribution, the contribution of efficiency variations is negative in most years. The share of labor contribution was high at the beginning of China’s reform and

opening up and even exceeded 20% in certain years. After 1992, however, it plunged to less than 10% before rising to around 10% after China’s entry to the WTO in 2001 and falling steeply after 2010. The share of capital contribution provided the major source of growth in most years and had been generally on the decline between 1978 and 1991, on the rise after further reforms in the early 1990s, and generally above 70% after 2004. In most of the years after the eruption of global financial crisis, it even approached 80%. On the whole, China’s economic growth is increasingly

reliant on factor input and especially capital input.

4.2 Economic Growth Sources of the Four Major Economic Regions

Consistent with China’s overall situation, factor input and especially capital input provided the major source of economic growth across regions: from 1978 to 2013, the economy of China’s eastern, northeast, central and western regions grew by 46.0, 23.4, 31.4 and 31.6 times respectively, and TFP only contributed 11.5, 4.3, 6.4 and 4.6 times of growth respectively. Yet capital input contributed to growth by 30.6, 70.9, 23.0 and 25.0 times respectively, and the shares of capital contribution reached as high as 66.5%, 76.3%, 73.2% and 79.3% respectively.

The share of TFP contribution is the highest in China’s eastern region, reaching 25.0%, followed by central, northeast and western regions with 20.3%, 18.4% and 14.6% respectively. Although the shares of TFP contribution are still far below the shares of capital contribution for China’s northeast and western region, they are above the result of Dong and Liang (2013) that the share of TFP contribution is almost zero for the northeast and even negative for central and western region. Given the improvement in resource allocation since China’s reform and opening up and the spillover effect of technology progress in prosperous regions, the results that the share of TFP contribution is zero or even negative are very likely to have been caused by an underestimation of the share of TFP contribution. Such underestimation is mainly due to the following reason: factor efficiency is not taken into account in estimating the output variations caused by factor input variations, which is equivalent to the absence of labor

efficiency , in equation (15) and capital efficiency , in equation ( 16). As labor and capital efficiencies are positive numbers no greater than 1, such absence has caused overestimation in the shares of labor and capital contribution and thus underestimation in the share of TFP contribution. For central and western regions where factor efficiency is low, the extent of such underestimation is even greater.

Compared with other regions, the TFP contribution is relatively high for the eastern region, while the share of TFP contribution has little difference compared with other regions. The reason is the significant advantages of eastern region in terms of both TFP contribution and factor input contribution compared with other regions. From this perspective, both TFP and factor input are the major causes of economic growth disparities between eastern and western regions. In fact, based on the estimation result of this paper, TFP contribution accounts for almost 60% of the variance of economic growth rates for China’s provinces, municipalities and autonomous regions between 1978 and 2004, and factor input contribution is slightly above 40%. TFP contribution is only slightly above factor input contribution.

Throughout most of the years since reform and opening- up in 1978, China’s eastern region outstripped the three other regions in terms of economic growth ( Table 3). Before 1990, the advantage of eastern region was not very significant. However, since 1991, growth disparities began to widen, reaching five to nine percentage points in 1992 and 1993. Thereafter, the gaps began to narrow. Between 2005 and 2007, regional economic growth differences had been very small. Yet after 2008, the global financial crisis dealt a heavy blow to the exportoriented eastern region, resulting in its slower growth compared with other regions.

Although China’s northeast, central and western regions outpaced eastern region in terms of economic growth, further analysis of economic growth sources reveals that such “catch-up” benefits from rapid increases of factor contribution in these regions (mainly contributed by capital input): with the implementation of priority strategies to develop central and western regions and rejuvenate old industrial bases in the northeast since late 1990s, the gaps of capital contribution between other regions and central regions narrowed. As of 2005, in particular, capital contribution (and thus factor input contribution) in the northeast, central and western regions far exceeded that of eastern region. Contrary to capital contribution, the TFP

contribution of other regions remains significantly below that of eastern region with the tendency to expand in recent years.

4.3 Robustness Test

As mentioned above, the share of labor income and depreciation rate are subject to different statistical scales or selection criteria, which may lead to different estimation results. In order to test the robustness of this paper’s conclusions, we estimated China’s economic growth sources under different shares of labor income and depreciation rates. There are two methods for estimating the share of labor income and four options for depreciation rate, which in combination produce eight scenarios. Scenarios 1 through 4 follow the “share of labor income by factor approach” and depreciation rates of 10.96%, 4%, 7% and 9.6% respectively. Scenarios 5 through 8 follow the “share of labor income by GDP approach” and depreciation rates of 10.96%, 4%, 7% and 9.6% respectively. Although the estimation results of Scenario 1 are already reported above, they are still listed here

in order to compare with the estimation results of other scenarios.

Obviously, no matter which scenario is adopted, the contribution of each source shares a generally consistent tendency with the change in the share of contribution. For most of the years, the contribution of each source and the share of contribution are not sensitive to the change in depreciation rate. Change in the estimation approach for the share of labor income has a certain impact on the contribution of each source and the share of contribution, but the extent of such impact is very small. The same is true for the four major economic regions3.

Table 4 reports the output growth of China as a whole and its various economic regions from 1978 to 2013, TFP contribution and the share of contribution, labor input contribution and the share of contribution, as well as the cumulative values of capital input contribution and the share of contribution. As the figures suggest, change in the level of depreciation rate has a minimal impact on the estimation results. Change in the statistical scale for the share of labor income has major impacts on the contribution of each source and the share of contribution. Relative to the result of estimation based on “share of labor income by factor approach”, the share of TFP contribution estimated based on the “share of labor income by GDP approach” reduced by about 10 percentage points, the share of labor input contribution fell by around one percentage point, and the share of capital input contribution increased by about 10 percentage points. However, the magnitude of such changes does not affect this paper’s conclusions. On the whole, this paper’s conclusions are relatively robust.

5. Conclusions and Research Directions

This paper has improved the SBI method developed by Fukuyama and Weber ( 2009), derived the criteria for the selection of the weights of output and input inefficiencies in the target function of this method, and created a new nonparametric method for economic growth accounting on such a basis. Following this method, this paper has estimated the economic growth sources of China as a whole and its four major economic regions separately from 1978 to 2013 and discussed the reasons behind regional growth disparities. Our findings are as follows: production factor and especially capital input are major sources behind the economic growth of China as a whole and its various regions, and in recent years, the dependence of economic growth on capital has the tendency to further increase; during a rather long period of time, China’s northeast, central and western regions lagged behind the eastern region in terms of economic growth, and TFP and factor input are major reasons behind such regional economic growth disparities; although China’s northeast, central and western regions have narrowed their economic growth disparities with and even overtaken the eastern region in terms of growth rates, the key driver is the rapid increase in the contribution of factor inputs in these regions, while TFP contribution remains significantly smaller in these regions than in the eastern region and such gaps have the tendency to widen.

For more than 10 years from the early 1990s to the early 21st century, the contribution of TFP to China’s economic growth had been smaller than the contribution of capital but generally stayed above 30%. The implication is that TFP progress remains a major driver of China’s economic growth. However, we should also be aware that China’s economy is increasingly dependent on capital. From 2008 to 2013, capital contributed 70% to 80% of China’s economic growth; even without considering the impact of the recent global financial crisis, the contribution of capital to China’s economic growth reached around 70% from 2005 to 2007. In the context of persistent difficulties facing China’s economy, discussions on a new round of stimulus policy began to heat up. Balancing the speed and efficiency of economic growth is an important and long-term issue. Given the low contribution of TFP to economic growth in China’s northeast,

central and western regions, the advanced technologies of China’s eastern region should be fully utilized to promote TFP progress in these regions, which is vital to their economic growth. Existing studies have identified the following measures to achieve this objective: giving play to regional comparative advantage, promoting labor flow, enhancing market-based operation and urbanization, increasing industrial concentration, propelling SOE reform, and introducing advanced technology.

Although the conclusions are not significantly different from previous studies, this paper provides a new nonparametric accounting method for estimating economic growth. Limitations of this paper are twofold: first, although the nonparametric method can be used to conduct multi- input and multi- output productivity accounting and certain studies have taken environmental factor into account in TFP estimation or economic growth decomposition, this paper does not take environmental factor into account. Second, traditional nonparametric method does not require the configuration of the form of return to scale and only requires either constant or variable return to scale. In calculating the optimal output when the input of production factor is fully utilized (Equation 8), this paper creates the condition of constant return to scale, which to some extent delimits the scope of application for this paper’s method. How to include environmental factor and expand this method to the circumstance of variable return to scale is a direction of our further research.