Total factor productivity growth and technological change in the telecommunications industry

The fast growing telecommunications industry in China has been experiencing dramatic technological change and substantial productivity growth. The actual productivity growth pattern in the sector, however, need to be empirically examined. In this paper, using input and output data at the provincial level, we employ DEA-based Malmquist productivity index to estimate productivity change, technological change and relative efficiency change in China's telecommunications industry for the period spanning the years from 2011 to 2015. The results show that based on our sample, the productivity improved by 22.9% per annum, which was exclusively due to an average of 25.5% technological progress in the industry production function, while the average efficiency change is slightly negative. Our results also indicate that regions with relatively low levels of telecommunications (and economic) development have a greater chance and ability of enhancing telecommunications productivity growth through technological catch-up. In addition, we find that the industry experienced significantly higher productivity growth and technological progress in the later sample period between 2013 and 2015 than in the early period between 2011 and 2013.

1. Introduction. The telecommunications industry has been one of the most dynamic and fast growing industries over the past two decades in China. As of 2016, the penetration rate of mobile phone in China reached 96.2 per 100 persons, and the total business revenue of China's telecommunications industry achieved 3594.8 billion RMB in 2016 [30]. A well-developed telecommunications system plays a key role in the economic growth and development of a country [9,12]. And the development level of an industry can be measure by the productivity of this industry, although productivity is not the only determinant of economic growth, it does provide a measure of economic prosperity of an industry. Productivity analysis can provide valuable information about the effectiveness of economic policies and, thus, provide a useful tool in policy design to improve economic development and industry performance [23].
Since the early 1980s, there has been a growing interest in measuring the productivity of the telecommunications industry. In the early period, the focus was on measuring total factor productivity (TFP) growth, which is the growth in output not accounted for by the growth in inputs. The pioneering studies include Nadiri and Schankerman (1979) and Denny, Fuss, and Waverman (1981), they used an adjusted Divisia TFP index to estimate the TFP growth of the telecommunications sector in the United States and Canada, respectively [10,31]. Some subsequent studies applied the conventional growth accounting and econometric approaches to measure TFP change in telecommunications, such kind of studies include [24,33,38]. More recently, production frontier approaches such as data envelopment analysis (DEA) and the Malmquist index have become popular in measuring the productivity performance of the telecommunications industry. Madden and Savage (1999) conducted a panel study to examine the telecommunications productivity, innovation and technological catch-up in 74 countries for the period 1991 to 1995. Using the Malmquist productivity change index, they found that TFP growth was highest for the subsample of industrialized countries (10.2% per annum) and was negative for countries in Africa (3.7% per annum) and the Western Hemisphere (10.2% per annum). They also found that developing countries could enhance telecommunications productivity through technological catch-up [27]. Giokas and Pentzaropoulos (2000) also applied the DEA approach to investigate the regional productive efficiency of public telecommunications organizations in Greece in 1998, their studies indicated that out of a total of 36 telecommunications centers, 15 of them were found to be efficient (with a maximum score of one) [17]. Uri (2000Uri ( , 2001 examines productivity change, technical progress, and efficiency improvement in the U.S. wireline telecommunications industry, and he found that productivity increased by about 5.0 percent per year, and the growth was due primarily to technology innovation rather than improvements in relative efficiency [36,37]. Using a representative sample of 16 firms in the mobile wireless industry in the United States, Banker et al. (2010) examined the productivity growth of the U.S. mobile wireless industry over the period 2000 to 2002, and found that the industry experienced a significant growth of 13% in productivity, which was primarily due to an average technological progress of 9.9% in the industry [2]. Hisali and Yawe (2011) employed the Malmquist TFP index to measure TFP change of the telecommunications industry in Uganda over the period 2001 to 2006, and the results indicated that there was TFP growth in Ugandas telecommunications industry, which was mainly due to technical or technological progress as opposed to technical efficiency [19].
The previous literature primarily focused on the traditional fixed-line telephone market in the United States or the European countries. Despite the significant expansion of China's telecommunications sector over the last few years, there has been a lack of quantitative studies on the productivity performance of China's telecommunications in the 3G/4G era. From a regulatory perspective, it is important to provide insights into the drivers of the productivity growth in China's telecom industry as well as how efficiently this sector have used the various inputs during the expansion process. Based on this, our study contributes to the existing literature in production economics by examining the drivers of productivity change, and by providing new empirical evidence on productivity growth and technological change in a fast growing hi-tech sector of China.
The purpose of this paper is to measure the productivity performance of China's telecommunications industry and examine the drivers of productivity in this industry for the period spanning the years from 2011 to 2015 at the provincial level. The Malmquist productivity change index based on DEA approach is used in the productivity measurement. Economic theory postulates that productivity improvements in industries can arise from technological progress generated by an upward shift in the production possibilities set as well as relative efficiency improvement on the part of inefficient firms in the industry because they catch up with the efficient firms over time [32]. The telecommunications industry is a high-tech industry driven by continuous technological progress [18,22]. Based on this argument and the existing empirical studies listed above, we argue that productivity growth in Chinas telecom industry is mainly due to industry-wide technological progress rather than efficiency improvement on the part of the inefficient firm. Based on this, in this study, we examine the relative contribution of these two effects to understand the drivers of productivity change in China's telecom industry. In addition, we also analyze the trend in productivity improvements in the telecom industry over time. We hope that the results from this productivity analysis can provide some economic and policy implications for subsequent infrastructure development of the telecommunications industry in China.
The rest of the paper is structured as follows. Section 2 provides a discussion of the methodology and the sample data we use for this study. Section 3 contains empirical analysis of the relationship between productivity growth and its components. Section 4 concludes the whole study and discusses the policy implications of this study for China's telecommunications reform.
2.1. Total factor productivity (TFP). TFP is defined as the ratio of aggregate output to aggregate input, with outputs and inputs generally aggregated according to revenue and cost share weights, respectively. When all inputs in the production process are accounted for, TFP growth can be thought of as the amount of growth in real output that is not explained by the growth in inputs. This is why Abramovitz (1956) described the TFP residual as a "measure of our ignorance" [1]. It is a relative concept with comparisons either being made across time or between different production units. For example, if it is possible to produce more output in period t + 1 when using the same amount of inputs that were used in period t, then productivity is said to have improved. In other words, productivity is higher in the second period compared to the first.
2.2. DEA-based Malmquist productivity change index. TFP growth is often calculated using the Törnqvist index [11]: where ε T is TFP growth calculated by Törnqvist index, ∆ represents time differences (proxied by log differences), r i are output revenue shares, y i are outputs, c j are input cost shares, x j are inputs and ln is the natural logarithmic operator. Equation  1 shows that TFP growth is the weighted sum of output growth rates less input growth rates, where the weights are the average output revenue shares and average input cost shares.
One of the problems in conducting a productivity analysis of China's telecommunications industry is a lack of detailed cost data on the industry. As the industry has long been under state control, service prices, labour wages and capital costs are not based on market values and are all regulated by the government. Hence, due to data availability, it is not possible to apply productivity analysis which requires the use of detailed cost data to China's telecommunications industry. In view of this, when detailed cost or revenue share data are not available, the non-parametric DEA approach, which does not require the use of cost share data, can be used to calculate productivity growth [5,14].
Based on this, this paper employs the Malmquist TFP change index -a DEAbased approach. Besides measuring technical efficiency, it is crucial to assess the evolution of TFP and efficiency through time in order to examine whether a change in the production frontier has occurred. The growth of TFP is defined as the change in output due to technological change and technical efficiency change over time. Technological change is represented by a shift in the production frontier between periods t and t + 1, whereas efficiency change is represented by the movement of a decision making unit (DMU) closer or further from the present and past frontiers. Technological change and technical efficiency change cannot be measured accurately using trends in annual average efficiency scores because the average scores are based on separate frontiers estimated for each year over the study period.
In 1953, Malmquist proposed a quantity index for use in consumption analysis [29]. Although it was developed in a consumer context, the Malmquist quantity index has recently enjoyed widespread use in a production context, in which multiple, but cardinally measurable outputs replace scalar-valued but ordinally measurable utility. In production analysis, Malmquist productivity change index is obtained by constructing quantity indexes as ratios of distance functions, which are functional representations of multiple-output-multiple-input technology which require only input and output quantity data [4,14,29].
Malmquist indexes have a number of desirable features. They are easy to compute, as Färe, Grosskopf, and Roos (1995) have demonstrated [15]. Under certain conditions they can be related to the superlative Törnqvist and Fisher ideal quantity indexes, as Caves, Christensen, and Diewert (1982) as well as Färe and Grosskopf (1992) have shown [4,13]. Another attractive feature of the Malmquist productivity index is that it decomposes total factor productivity growth into technical efficiency change and technological change (shifts in the frontier technology). Färe et al.(1994) showed that the technical efficiency change index of the geometric mean of adjacent-period Malmquist productivity indexes, derived under the assumption of constant returns to scale, can be expressed as the product of an index of pure technical efficiency change, an index of scale efficiency change and an index of technological change [14]. The value of each of these decompositions is that they provide insight into the sources of productivity change.
The output distance function is defined for time period t as [35,16]: where x t denotes the input vector, y t denotes the output vector, and S t denotes the production technology set that models the transformation of inputs, x t , into outputs, y t .
To define the Malmquist, it is necessary to define distance functions with respect to two different time periods such as This distance function measures the maximum proportional change in outputs required to make (x t+1 , y t+1 ) feasible in relation to the technology in period t. Analogously, it is possible to define a distance function that measures the maximum proportional change in output in order to make (x t , y t ) feasible in relation to the technology in period t + 1. This is denoted as D t+1 o (x t , y t ). Thus, to calculate output-oriented Malmquist productivity change index we must calculate the four component distance functions, which will involve four LP problems.
We begin by assuming constant to scale (CRS) technology, that is, The remaining three LP problems are simple variants of this: In order to avoid selecting an arbitrary reference (benchmark) technology, the output-oriented Malmquist productivity change index between periods t and t + 1 is specified as the geometric mean of two Malmquist productivity indexes: where D t o (x t , y t ) is the output distance function at time t, and x t and y t represent the input and output quantities of DMUs at time t, respectively. This represents the productivity of the production point (x t+1 , y t+1 ) relative to the production point (x t , y t ). A value greater than one will indicate positive TFP growth from period t to period t+1. Following Färe et al. (1995), the Malmquist productivity change index can be rewritten as [15]: In the empirical application of this approach that follows, the Malmquist productivity index is calculated using nonparametric programming techniques. Assume that there are k = 1, 2, , K DMUs using n = 1, 2, , N inputs at each time period, x nkt . These inputs are used to produce m = 1, 2, , M outputs, y mkt . All inputs and outputs are strictly positive and the number of DMUs remains constant for each time period.
The production frontier in period t is defined to be z kt y mkt (m = 1, 2, ..., M ); z kt x nkt (n = 1, 2, ..., N ); which exhibits constant returns to scale and strong disposability of inputs and outputs. The assumption of constant returns to scale may be relaxed to allow nonincreasing returns to scale by adding the following constraint: where z kt denotes an intensity variable indicating at what intensity a particular activity may be employed in production. Thus, as opposed to the Törnqvist index, an interesting feature of the Malmquist TFP index is that it allows productivity growth to be decomposed into technological change or technological innovation (shifts in the frontier technology) (T echCh) and changes in technical effciency (Ef f Ch). By calculating DEA-based Malmquist productivity change index, changes in total factor productivity over time can be attributed to three separate explanations [17,3]. First, the technical efficiency of an individual DMU may change, at a given scale of operation. Second, the efficiency of the DMU may change in response to a change in the scale of operation. Finally, the underlying technology may change, thereby inducing a shift in the production frontier, which will affect the efficiency of all DMUs. The Malmquist index provides estimates of each of these effects by calculating separate distance functions in each period and by varying the assumption about the available technology.  Table 1 shows the operating environments of these 31 DMUs in 2015. As is shown in Table 1 , per capita income in the eastern region was much higher than that in the other two regions in 2015. And the penetration rates of internet services and telephone services (both in terms of fixed-line and mobile services) were also much higher in the eastern region, which means that the eastern region of China has a relatively higher level of telecommunications (and economic) development.
Data about the outputs and inputs of the telecommunications sector are required to measure the productivity of the sector. Telecommunications output is measured by the total revenue, and the input variables include capital and labor.
In the telecommunications sector, the appropriate variable to measure output is not obvious. Some previous studies used the number of subscribers, the total number of calls (in minutes), total revenue or turnover to measure output. Kiss (1983) argued that by using total revenue to measure telecommunications output, changes in the quality of services and the increased number of connected parties could be reflected in telecommunications charges [21]. This study follows Kisss approach by using the total business revenue (in RMB or Yuan) derived from the provision of telecommunications services as a measure of output. Several other previous studies also used revenue as a proxy for the output of telecommunications [2,25,26,27].
Capital and labour are the two major inputs used in providing telecommunications services. For the capital input data, different kinds of equipment and physical assets are needed in the provision of telecommunications services. Based on data availability, four major capital assets are used to measure capital input. They are the length of optical cable lines (in kilometres), the capacity of long-distance telephone exchanges (in circuits), the capacity of local office telephone exchanges (in exchange lines), and the capacity of mobile telephone exchanges (in subscribers). The capital inputs that we select is consistent with some previous studies on the telecom industry [25,26,27,28]. For the labour input, it is more difficult to obtain reliable data. The official data about the number of staff in the telecommunications industry at the provincial level is combined with that in the postal industry and transportation industry. Thus, we estimate the number of staff in the telecommunications sector at the provincial level according to the proportion that telecommunications employees accounted for the employees of those industry. The telecommunications industry is a representative knowledge-embedded service industry [20], so the estimated labour input will not affect the accuracy of the outcomes largely. Table 2 shows the descriptive statistics for the outputs and inputs used for constructing the DEA Malmquist models in China's telecommunications industry.
3. Empirical results. The output-oriented formulation is used to compute the Malmquist productivity change index to measure the change in productivity of China's telecommunications industry over the period 2011 to 2015. Table 3 reports the annual averages for the Malmquist productivity change index and the associated decompositions, including technological change (TechCh), efficiency change (EffCh), pure efficiency change (PEffCh) and scale efficiency change (SEffCh) 1 .
A value greater than one for TFP and its components represents an improvement in performance, whilst a value less than one represents declining performance. As in shown in Table 3, the average productivity growth rate in China's telecom industry Note: DMU = Decision-making unit, GRP = Gross regional product, Pr1 = Fixedline penetration rate(per 100 persons), Pr2 = Mobile penetration rate(per 100 persons), Pr3 = Internet penetration rate(%). Source: China Statistical Yearbook 2016.  The results indicate that, during the study period, technological innovation exclusively contributed to productivity improvements in the telecom industry by significantly expanding the production possibilities set. That is to say, productivity growth in China's telecom industry was driven by industry-wide technological progress rather than improvements in efficiency between 2011 and 2015.
Of the 31 provinces in the sample, 11 provinces showed a slight improvement in efficiency throughout the 2011-2015 period, while 16 provinces declined and 4 provinces operated just efficiently. Technological change among provinces showed considerable variability over the period, ranging from a high of 43.9% per annum (Qinghai) to a low of 11.0% per annum (Beijing). Examination of individual province also shows that the highest productivity growth rates occurred in the western and central region, Qinghai (50.1% per annum), Anhui (41.5%) and Chongqing (36.1%). On average, TFP growth is highest for the subsample of western region (28.7% per annum), while the growth rate for the eastern region is the least (17.7% per annum). These results indicate that regions with relatively low levels of telecommunications (and economic) development have a greater chance and ability of enhancing telecommunications productivity growth through technological catch-up.  Table 4 reports the Malmquist TFP index summary of annual averages during 2011 to 2015 and Figure 1 show the Malmquist TFP index trend versus technological change and efficiency change during this period. Note that 2012 in Table 4 refers to the change between 2011 and 2012, similarly hereinafter, and in Figure 1, 2011 represents the base year and equals the value of unity. As is shown in Figure 1, Malmquist TFP index (TFPCh) and technological change index (TechCh) roughly followed the same synchronized rising trajectory, while technical efficiency index (EffCh) basically remained stable around one during the period 2011 to 2015. This graph demonstrates more clearly that total factor productivity growth is driven exclusively by technological innovation rather than technical efficiency.
Then, the DEA-based Malmquist productivity index and its decompositions are calculated for the data of the period 2011 to 2013, and 2013 to 2015 separately. The comparison results of productivity change, technological progress and relative efficiency between these two period are reported in Table 5. We observe that China's telecom industry experienced on average an extra 21.1% improvement in productivity and an extra 16.5% in terms of technological progress per annum during the period 2013 to 2015 than 2011 to 2013, which means that the bulk of the productivity improvement and technological change during our sample period occurred during the latter half. This result is due to the fact that more emerging technologies such as 4G deployed and developed in China in the latter part of our sample period, technological progress directly led to the great improvement in industrial productivity. In addition, that means telecom operators have been able to tap into increased demand for their services over time due to network effects [28]. Our study provides new empirical evidence on productivity growth and its drivers in the telecom industry during a period when the industry experienced substantial changes in technology. The empirical results show that China's telecom industry has experienced substantial productivity growth and technological progress during the study period. Based on our sample, the productivity improved by 22.9% per annum, which was exclusively due to an average of 25.5% technological progress in the industry production function, while the average efficiency change is slightly negative. Our results also indicate that regions with relatively low levels of telecommunications (and economic) development have a greater chance and ability of enhancing telecommunications productivity growth through technological catch-up. In addition, we find that the industry experienced significantly higher productivity growth and technological progress in the later sample period between 2013 and 2015 than in the early period between 2011 and 2013. The importance of technological progress on industry performance shows that telecom regulators need to employ incentive regulation which can promote technological innovations to propel the sustainable development of telecommunications industry. Even if efficient and creative in matching supply and demand, market is usually incapable of organizing the risky, long-term and complex R&D processes which are necessary for creating radical technological innovations [6]. Market is inherently flawed in stimulating technological innovation. More importantly, technological progress in telecommunications not only plays a key role in the productivity growth of the telecommunications industry, but also can strongly promote the development of other industries and help produce huge externalities to the overall productivity [8,9,34]. From this standpoint, the government should create an environment that is conductive to technological innovation and adopt regulatory policies that stimulate technological innovations. Telecommunications regulators need to realize that technological innovation is the only essential way to reduce the costs and improve the service quality of telecommunications services, in the condition where technical level is not mature enough, relying solely on structural control to restructure the industry and promote competition, or using price regulation to influence the competitive relationship and profitability of operators cannot help to promote the efficient development of telecommunications industry.
As government regulation is the institutional condition of technological innovation, which is the fundamental driving force for the development of the telecommunications industry, government should play its own important role in promoting technological innovation in the telecommunications industry, eliminating factors that may hinder the pace of technology progress and establishing incentive systems that are conducive to technological innovation in an effort to promote the continuous development of telecommunications technology. As such, the overall productivity of the telecommunications service industry can be improved constantly.