Polycentric urban development and economic productivity in China: A multiscalar analysis

Abstract

‘Urban polycentricity’ has become both a conceptual framework capturing emerging empirical realities and a spatial planning vision adopted in cities across Europe, USA, and, recently, also China. Despite the blossoming academic literature on polycentricity, only limited attempts have been made to explore whether and how polycentric urban development at different spatial scales affects the urban economy. In this paper, we empirically analyse whether and how urban polycentricity at different spatial scales in China is associated with urban economic performance. To this end, we extend the Cobb–Douglas production function and include measures of both inter-urban and intra-urban polycentricity to explain differences in labour productivity. The analysis links intra-urban monocentricity and inter-urban polycentricity with higher levels of labour productivity. In addition, the analysis points to an agglomeration spillover effect, as well as a potential weak positive interaction effect between intra- and inter-urban polycentricity. The paper concludes with policy implications for China’s spatial development.

Keywords

Polycentricity productivity multiscalar China polycentric urban development

Introduction

Plans for polycentric urban development have recently gained momentum in China’s spatial planning praxis, as the concept is being incorporated at different geographical scales (Cheng and Shaw, 2018; Liu et al., 2018). In 2015, the importance of the coordinated development of cities within urban regions was ‘officially’ recognized in the fourth Central Urban Work Conference, which was attended by top Chinese political leaders. Specific and highly publicized cases include the current development of two new towns near Beijing. The satellite town of Tongzhou was designated a ‘vice-administrative centre’ in 2015, with the hope of relocating the municipal government of Beijing and a range of ancillary sectors away from the city centre, which is thought to be ‘plagued’ by urbanization diseconomies (Liu et al., 2018). Meanwhile, approximately 150 km south of Beijing, an entirely new city, the Xiong’an new district, has been planned and under construction since early 2017. One of the goals in developing this new district is to achieve a more ‘balanced’ spatial economic pattern in the wider Beijing–Tianjin–Hebei region. More recently, the plan for the Guangdong–Hong Kong–Macao Greater Bay Area in southern China aims to develop the already quite polycentric urban region (Cheng and Shaw, 2018; Liu et al., 2018) into one that ‘is driven by poles, supported by axes and radiating to nearby areas, promote a rational division of labour and complementary positioning among large, medium-sized and small cities’ (State Council of China, 2019: 11).

These observations represent the latest episodes in what appears to be increasingly popular ‘polycentricity’ thinking. Indeed, the term ‘urban polycentricity’ has become both a theoretical model to conceptualize emerging urban forms and a spatial planning vision adopted across different places. Although Van Meeteren et al. (2016) have identified ‘polycentricity’ as a concept that is particularly prone to conceptual stretching (and, therefore, vagueness), in urban and regional studies the term is most commonly used to refer to the presence of multiple proximate ‘centres’ of roughly similar ‘importance’ in an area (Kloosterman and Musterd, 2001; Meijers and Lambregts, 2009). ‘Polycentric urban development’ is often linked with more competitive urban economies in which ‘the polycentric system’ is deemed to be more than the sum of its parts (cf. Meijers, 2005). Put differently, the combined agglomeration effects of a range of nearby centres is posited to be equal to and perhaps even exceeding that of an undifferentiated ‘large’ centre.

While the debate over the economic impacts of urban polycentricity is still inconclusive (Meijers and Burger, 2010; Zhang et al., 2017), it is further complicated by the fact that polycentricity has been conceived and pursued at multiple spatial scales. For example, the European Spatial Development Perspective has interpreted and pursued polycentricity at the intra-urban, inter-urban, and inter-regional levels (Brezzi and Veneri, 2015; Davoudi, 2003). Meanwhile, in US planning circles, polycentricity has been debated at both the intra-urban (e.g. the discussion on edge cities: see Lee, 2007) and inter-urban scales (e.g. the discussion on ‘megaregions’: see Harrison and Hoyler, 2015).

Therefore, extending from previous studies (for example, Liu et al. 2018; Sun and Li, 2016; Zhang et al., 2017) this paper aims to empirically analyse how urban polycentricity at different spatial scales in China is associated with urban economic performance. This general aim translates into two concrete contributions to the literature.

We enrich the literature by focusing on the Chinese case with its specific background in terms of economic development, the role of cities therein, and its specific political economy; and

We explicitly pay attention to the multiscalar nature of ‘urban polycentricity’ by incorporating different scalar dimensions and their (potential) interactions. In our analysis, urban-economic ‘performance’ will be approximated by measures of non-agricultural labour productivity.

We extend the Cobb–Douglas production function and include polycentricity measures at both intra- and inter-urban levels to explain differences in labour productivity. In the ‘Literature review’ section, we provide definitions of key terms and elaborate our conceptual framework, which culminates in a set of testable hypotheses. ‘Data and methods’ discusses our empirical research design, while ‘Results and discussions’ presents our empirical results with robustness checks. Finally, the ‘Concluding remarks’ section summarizes key findings and concludes with avenues for future research.

Literature review

Multiscalar polycentric urban development

In the context of an overall ‘lack of focus in dealing with polycentric urban phenomena’ (Kloosterman and Musterd, 2001: 624), a key aspect of the polycentricity debate has been the scale at which polycentric urban development unfolds (cf. van Meeteren et al., 2016). The academic literature dealing with ‘urban polycentricity’ commonly distinguishes between (a) intra-urban and (b) inter-urban patterns of the population and economic activities. (Intra-urban and inter-city are used interchangeably in this paper. Same applies to inter-city and inter-urban.). The former literature is exemplified by the debate in urban economics over whether a polycentric version of the monocentric Alonso–Muth–Mills urban land use model should be advanced (van Meeteren et al., 2016). While a centre in the original Alonso–Muth–Mills’s model often represents a pocket of employment, which is usually the central business district, a polycentric version explores the ‘optimal’ number and location of employment centres – for instance, in US cities (McDonald and McMillen, 2000; Wei and Knox, 2015). Meanwhile, the literature on inter-urban polycentricity is exemplified by research on ‘polycentric urban regions’. Here, the analyses of urban interactions in a region such as the Dutch Randstad would be representative for this line of research (e.g. Meijers, 2005; Van Oort et al., 2010).

This neat distinction between intra-urban and inter-urban polycentricity does not do justice to the empirical complexities and conceptual nuances in the literature (van Meeteren et al., 2016). Hall and Pain (2006) rightly note that an analysis of, say, ‘polycentricity in Southeast England’ is circumscribed by the territorial definitions of ‘London’ and ‘the Southeast’, the functional processes being captured, and the scales at which these processes unfold. In other words, what may appear to be a monocentric phenomenon at one geographic scale/for one function can be part of a polycentric phenomenon at another scale/for another function (Burger et al., 2014; Van Meeteren et al., 2016). Consequently, empirical evidence regarding the effects of polycentricity in different studies is often difficult to compare since they sometimes relate to different spatial scales (Davoudi, 2003; Van Houtum and Lagendijk, 2001).

Kloosterman and Musterd (2001) offer some rules of thumb regarding how to differentiate between intra- and inter-urban polycentricity. Intra-urban polycentricity appears to be an apt framework when ‘centres’ (a) are organized around a common public transport infrastructure, (b) reside under the same administrative unit, (c) are part of a generic and functional economic system, and/or (d) share the same cultural and historical identities. By the same token, the lack of integrated transport infrastructure, the presence of multiple social-cultural identities, and the lack of political authority can be seen as a sign that the inter-urban polycentricity language needs to be adopted. In reality, however, there is a scalar continuum of polycentricity that makes a neat scalar distinction perforce a difficult proposition. Nonetheless, it is possible to use the distinction as a useful heuristic in that it does have some analytical value. In the US context, for example, the distinction would imply that population and employment centres within individual metropolitan areas are to be interpreted through the lens of intra-urban polycentricity, while ‘megaregions’ that usually consist of multiple metropolitan areas are to be interpreted through the lens of inter-urban polycentricity (Harrison and Hoyler, 2015).

Urban spatial structure and economic performance at the intra-urban scale

The relationship between urban spatial structure and the economy is often interpreted in terms of the relative balance between agglomeration economies and diseconomies (Zhang et al., 2017). On the one hand, the clustering of people and economic activities in cities may facilitate labour pooling, input sharing, and knowledge spillovers, thus generating ‘agglomeration economies’ and improving economic productivity (Duranton and Puga, 2004). On the other hand, as cities become larger, agglomeration diseconomies may arise, for example, because of congestion and pollution. A polycentric city with multiple urban centres may alleviate this type of problem by reducing commuting distance, especially for long-distance commuters (Zhao et al., 2011). Meanwhile, the provision of additional housing in (sub)centres can potentially increase housing affordability and improve the job–housing balance, while polycentric urban patterns may leave more green spaces between centres to mitigate heat island effects and increase air quality (Wang et al., 2017). The effect of city size has, therefore, been extensively explored. For example, while Capello and Camagni (2000) argue that a network of smaller cities could better contain agglomeration diseconomies, recent research by Helsley and Strange (2014) suggests that the size of cities may not necessarily be conducive to economic agglomeration. Still, examining the association between city size and growth in 114 countries from 1960 to 2010, Frick and Rodríguez-Pose (2016) did not identify a universal positive relationship.

It is often posited that a polycentric urban structure can help achieve ‘optimal’ urban performance in that the negative impacts of urban concentration can be mitigated, while agglomeration economies are preserved (Fujita and Thisse, 2002; Krugman, 1993; Masip-Tresserra, 2016). The emergence of information and communication technologies, as well as falling transport costs, have facilitated the development of and interactions between (sub)centres in a city. The possible synergies arising from the interaction between individual (sub)centres can then produce agglomeration economies that are observed in a single urban core of a roughly similar size. Parr (2002) suggests that agglomeration diseconomies are often contained in individual (sub)centres. As a corollary, cities with a more balanced system of (sub)centres are theoretically expected to provide more productive and efficient environments. An analysis by Meijers and Burger (2010) associates a higher level of intra-city polycentricity with higher labour productivity in US metropolitan areas. Similarly, a positive association between urban polycentricity and economic productivity is found for Italian cities (Veneri and Burgalassi, 2012). However, empirical evidence sometimes points in other directions. For example, no evidence for an ‘efficient’ urban spatial structure concerning employment and population growth in US metropolitan areas was found in Lee and Gordon (2007). Given the positive relationship found within the American and European contexts, our first hypothesis is that a more polycentric urban structure at the intra-city scale is associated with greater urban economic performance.

Urban spatial structure and economic performance at the inter-urban scale

Although the effects of agglomeration and external economies were initially deemed to be largely ‘local’, the geographical scale at which agglomeration effects unfold seems to be expanding (Phelps, 2004). For example, Parr (2002) regards economies of agglomeration at the intra-city scale to be conventional ‘agglomeration externalities’ and considers economies of agglomeration at the inter-city scale to be ‘regional externalities’. The assumed benefits of ‘polycentric urban regions’ can be associated with Alonso’s (1973) notion of ‘borrowed size’ (cf. Burger and Meijers, 2016). The ‘borrowed size’ thesis argues that a group of functionally integrated small cities can exhibit ‘some of the characteristics of a larger city’ (Alonso, 1973: 200). Furthermore, while ‘growth pole’ theories predict economic spillovers from leading urban centres to smaller ones (Ke and Feser, 2010), small cities may, in turn, suffer from ‘agglomeration shadows’, as their opportunities for development may be captured and subsequently stifled by larger cities (Burger et al., 2015). Inter-urban polycentricity also resonates with Capello’s (2000) notion of ‘urban network externalities’, in which she argues that cities situated in a functional network will enjoy additional benefits through synergies and complementarities between cities. More recently, Meijers et al. (2018) presented a cross-sectional analysis of 117 European polycentric urban regions, highlighting that inter-city polycentricity is associated with urbanization economies. As both the ‘borrowed size’ thesis and the notion of synergies within an urban network suggest a positive relationship between inter-urban polycentricity and city performance, our second hypothesis is that inter-urban polycentricity is positively associated with greater economic productivity.

In addition, there are ongoing debates about whether ‘small’ cities benefit or suffer from being positioned in a polycentric urban region. For example, on the one hand, the interactions and synergetic effects between cities may generate something that is more than the sum of its parts (cf. Meijers, 2005), while Partridge et al. (2007) find that a small city’s proximity to major urban centres is positively related to its population growth. On the other hand, a recent study by Burger et al. (2015) finds that larger cities can take advantage of there being neighbouring smaller cities, thus potentially leading to agglomeration shadows for those smaller cities. Given this, we explore a third hypothesis focusing on if and how smaller cities benefit from being located in a polycentric urban region. Given conflicting evidence and arguments we have no clear-cut expectations regarding this hypothesis.

Potential interactions in a multiscalar urban spatial structure

The literature on the interaction between polycentricity at different spatial scales is patchy and has produced inconclusive results. However, somewhat paradoxically, it is exactly this patchiness and inconclusiveness alongside the fluidity of the polycentricity concept that makes polycentric urban development into an appealing spatial imaginary, in that policymakers can interpret polycentricity in line with their viewpoints and material interests (Granqvist et al., 2019). While previous studies often treat intra-urban and inter-urban polycentricity as two different ‘spheres’ of polycentricity (van Meeteren et al., 2016), scholars have identified the potential interactions between polycentricity at different scales (Davoudi, 2003).

Our discussion here within the Chinese context summarizes from and builds upon Liu et al. (2018), where a moderate positive relationship between intra-urban and inter-urban polycentricity is found for Chinese cities. The joint forces of decentralization and marketization processes allow city regions to develop more polycentric urban patterns (Hsing, 2010; Ma, 2002). At the intra-urban scale, land-based development resulted in the emergence of ‘development zones’ in the 1990s and university/new towns in the 2000s, which have been associated with urban economic development in urban peripheries (see for example, Wu and Phelps, 2011). Meanwhile, at the inter-urban scale, city regions in this area often have both centrally initiated plans and locally coordinated development platforms (e.g. the Pearl River and the Yangtze River Deltas). Marketization facilitates the conversion of rural land into urban counterparts, thereby further promoting the growth of the town and village enterprises (Wei, 2013). As a result, some small cities have emerged where town and village enterprises are clustered and where there used to be suburbs and rural counties. The decentralization process at the inter-city scale is also manifested by land-based municipal finance, allowing cities to provide additional investments in public goods such as infrastructure and amenities, which, in turn, boosts economic development (Lin, 2002; Hsing, 2010; Wu, 2015).

In contrast, primate urban systems in China’s economically lagging western provinces may also be conducive to economic performance, which is illustrated by monocentricity at both the intra-urban and inter-urban scales. Given the scarcity of resources, concentrating the population, business, and favourable policies within a major city, which is a common practice in many developing countries, contributes to economic efficiency (see for example, Wei, 2013). These major cities are usually the capital cities of different provinces, which are well endowed with infrastructure and (regional) development policies (Liu et al., 2018). They may have a better chance of upgrading their industry. Similarly, at the intra-urban scale, resources tend to be allocated to the most densely populated urban centres, which is also often the by-product of a socialist legacy (Li, 2014; Wu, 2015). Therefore, the fourth hypothesis we will explore is whether a positive interaction effect exists between polycentric spatial structures at intra-urban and inter-urban scales on urban economic performance. In other words, we hypothesize a polycentric city in a polycentric urban region or a monocentric city in a monocentric urban region to be associated with higher urban economic performance.

Based on this necessarily brief discussion, we propose the following set of working hypotheses:

H1: A higher degree of intra-city polycentricity is associated with higher labour productivity.

H2: A higher degree of inter-city polycentricity is associated with higher labour productivity.

H3: A small city may or may not exhibit higher labour productivity in a polycentric urban region.

H4: There exists a positive interaction effect between polycentricity at intra-urban and inter-urban scales on labour productivity.

Data and methods

Data sources and study area

Our analysis focuses on cities at the prefectural level and above in China. The geographical analysis of prefectural-level and above cities in China qualifies as Kloosterman and Musterd’s (2001) reading of intra-city polycentricity for the following reasons. First, a Chinese prefectural-level city is, in principle, a self-contained urban system consisting of a core urban area as well as its associated towns, counties, and districts. What is often considered to be a ‘city’ in the Chinese context is similar to a ‘metropolitan region’ in the USA (Liu and Wang, 2016). The political authority over these urban centres is often consolidated in the hands of a municipal government, which inter alia oversees the taxation, budgeting, and planning of all sub-units (Li, 2014). The remote centres rely on the core urban areas for higher-level goods and services. Second, the (sub)centres within a prefectural level city are usually well connected by means of local roads and public transit. Consequently, in our study, the intra-urban analysis will focus on the multiple centres within prefectural-level cities, while the inter-urban analyses address the regional clusters of neighbouring prefectural-level cities.

The LandScan™ High-Resolution Global Population Dataset for the year 2010 is used to measure both intra- and inter-urban polycentricity (Bhaduri et al., 2007). Importantly, the gridded population data are ideal for coherent multiscalar analysis. Socioeconomic data such as gross domestic product (GDP) and population were gathered from the 2010 Population Census Data and the 2011 China Statistical Yearbook. Due to data availability issues, our final sample included 270 out of 286 prefectural-level and above cities (approximately 94%; Figure 1).

Figure 1.

Cities included in this study.

The focus on population distribution entails a morphological approach to studying polycentricity. Our choice for this morphological approach rests on the following observations, which have been spelled out in more detail in Liu and Wang (2016). First, gridded population data enable consistent comparisons across multiple spatial scales (Liu et al., 2018). Second, a focus on population centres is relevant in the Chinese context. For example, shaping the spatial distribution of the population is still a major (if not the determining) planning goal. Per capita requirements of public service provisions and green space are adopted as key parameters in the urban planning targets of contemporary China (Liu and Wang, 2016). Nevertheless, we note that the method used here should be considered as one specific attempt to measure polycentricity. As a result, other analyses based on other types of urban centres, such as employment hotspots, may or may not arrive at the same conclusions.

Measuring inter- and intra-urban polycentricity

As previously mentioned, the intra-city polycentricity is explored through the spatial structure of population centres within individual Chinese cities, while the inter-city level analysis focuses on the spatial distribution of the population across nearby cities (Liu et al., 2018). A schematic diagram of our approach is shown in Figure 2. A higher degree of polycentricity is characterized by a relatively more balanced distribution of urban centres, while a lower degree of polycentricity points to a more hierarchical distribution of urban centres. Drawing on Brezzi and Veneri (2015), Liu and Wang (2016) and Meijers and Burger (2010), our method of measuring polycentricity consists of three consecutive steps.

Figure 2.

A conceptual diagram of polycentricity measures in this study (a relatively larger size of the solid circle indicates a larger number of people in the population centre (upper panel) or larger number of total people in all population centres within a city (lower panel)).

Identifying population centres

The first step is to determine the population centres within individual cities. We define population centres as a cluster of grids with substantively higher population densities than the surrounding grids. Adapting Liu and Wang (2016), we identify intra-city population centres from LandScan in the following three steps. First, for each city, the grids of the top 5% (of the population) are selected as candidate cells. Second, candidate cells that are adjacent to each other are combined to form candidate centres. Third, candidate centres covering at least 2 km² (i.e. comprising at least two grids in LandScan) are picked as the final population centres.

Measuring intra-urban polycentricity

Polycentricity focuses on how balanced the ‘importance’ is distributed amongst urban centres. As this study employs population centres, a city with more balanced distributed population centres has a higher degree of intra-urban polycentricity (Figure 2). The rank-size distribution based on the size of population centres provides information about such hierarchies and is, therefore, a reasonable measure of the degree of polycentricity (Burger et al., 2014; Meijers and Burger, 2010; Brezzi and Veneri, 2015). Consequently, we adopt this method, fit a rank-size distribution of intra-city population centres, and calculate the slope of the corresponding regression line. Following Meijers and Burger (2010), we construct three scenarios in which the largest two, three, and four centres are included in the rank-size distributions. The slope for each scenario is then calculated (Equation (1)) as follows:

IntraSlope (k) = \frac{\sum_{i = 1}^{k} \sum^{​} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sum_{i = 1}^{k} {(x_{i} - \bar{x})}^{2}}

(1)

where for the

i th

largest population centre,

x_{i}

\log_{10} (i), y_{i}

denotes the logarithm of the total population of the

i th

largest population centre with the base 10, and

\bar{x} = \frac{\sum_{i = 1}^{k} x_{i}}{k}

and

\bar{y} = \frac{\sum_{i = k}^{k} y_{i}}{k}

where k = 2, 3, and 4.

A flatter slope of a rank-size distribution suggests a more balanced distribution amongst different centres and thus points to a more polycentric system. Finally, the measure of intra-city polycentricity (IntraPoly) is constructed as per Equation (2), in which a higher value indicates larger levels of intra-city polycentricity:

IntraPoly = \frac{1}{3} \sum_{i = 2}^{4} | \frac{1}{IntraSlope (i)} |

(2)

Measuring inter-urban polycentricity

We calculate inter-city polycentricity in a similar way but focus on the size distribution among neighbouring cities. The more evenly distributed the cities are, the more polycentric the region is (Figure 2). For each city, the calculation of inter-city polycentricity starts with constructing its ‘neighbouring region’, which includes the following two categories of cities: (1) all cities that share borders with a given city are included; and (2) following Partridge et al. (2007), nearby cities within a 100 km radius of that city (but not necessarily sharing borders with the focal city) are included in the analysis. Second, the total population in the previously identified intra-city centres is calculated. Third, we consider the rank-size distribution of the largest two, three, and four cities within a city’s region. Similar to the measure of intra-city polycentricity, we calculate the slope in each scenario, as in Equation (3):

InterSlope (k) = \frac{\sum_{i = 1}^{k} \sum^{​} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sum_{i = 1}^{k} {(x_{i} - \bar{x})}^{2}}

(3)

where for the

i th

largest city in a city’s ‘neighbourhood’,

x_{i}

\log_{10} (i), y_{i}

denotes the logarithm of the summation of the population in all population centres of the

i th

largest city with base 10, and

\bar{x} = \frac{\sum_{i = 1}^{k} x_{i}}{k}

and

\bar{y} = \frac{\sum_{i = k}^{k} y_{i}}{k}

, where k = 2, 3, and 4.

The inter-city polycentricity (InterPoly) is computed as per Equation (4), in which a higher value indicates more pronounced levels of inter-city polycentricity.

InterPoly = \frac{1}{3} \sum_{i = 2}^{4} | \frac{1}{InterSlope (i)} |

(4)

Model formulation

Following Ciccone and Hall (1996) and Meijers and Burger (2010), we extend the Cobb–Douglas production function to evaluate the labour productivity in cities. While the original Cobb–Douglas production function presents the output that can be produced by two or more inputs (especially physical capital and labour), our empirical model starts from the following linear equation (Equation (5)):

\begin{matrix} \ln (LP) \sim \ln (CLR) + \ln (LLR) + \ln (HCLR) + \ln (GOV) + \ln (POP) + ln (PUD) \end{matrix}

(5)

where

LP

denotes labour productivity,

CLR

denotes the capital–labour ratio,

LLR

denotes the land–labour ratio,

HCLR

denotes the human capital–labour ratio, and

PUD

represents the effects of polycentric urban development as described in the previous section of this study, including the direct impact of intra-city polycentricity (H1), inter-city polycentricity (H2), the role of city size (H3), and the interaction effects between polycentricity at the two scales (H4).

For each city, the effects of $PUD$ are measured in terms of intra-city polycentricity $(IntraPoly)$ and inter-city polycentricity $(InterPoly)$ . The dependent variable, $LP$ , is operationalized by GDP in the secondary and tertiary sectors divided by the size of labour force in the secondary and tertiary sectors (Li et al., 2019). The $CLR$ is calculated as the capital stock divided by the size of labour force in the secondary and tertiary sectors. Capital stock data of Chinese cities are obtained from Ke and Xiang (2012), where the depreciation rates of 20 years for buildings/constructions and of 6.5 to 7.5 years for equipment are taken according to China’s Ministry of Finance. The $LLR$ is computed as the average built-up urban area per worker. The $HCLR$ is approximated by the average age of the permanent resident population. The total population ( $POP$ ; including both those in and out of the workforce) of individual cities is included. Considering the recent debates on variegated capitalism in China, local governments exert institutional power and adopt different market intervention strategies (Zhang and Peck, 2016). Therefore, governmental intervention $(GOV)$ is derived as the fiscal expenditure divided by GDP in each city in order to control for the heterogeneity of governments’ role on labour productivity (Sun and Li, 2016). We report the descriptive statistics in Table 1.

Table 1.

Descriptive statistics of variables (N = 270).

Variable^a	Min	Max	Mean	SD	Data source(s)
LP	9.667	12.802	11.148	0.515	China Statistical Year Book (2011)Population Census of China (2010)
CLR	8.194	12.208	10.300	0.818	China Statistical Year Book (2011)Ke and Xiang (2012)
LLR	2.649	6.243	4.093	0.632	China Statistical Year Book (2011)
HCLR	1.936	2.460	2.192	0.086	Population Census of China (2010)
POP	13.186	17.177	15.113	0.644	Population Census of China (2010)
GOV	–3.096	0.396	–1.908	0.421	China Statistical Year Book (2011)Population Census of China (2010)
IntraPoly	–2.195	3.740	–0.150	0.632	LandScan (2010)
InterPoly	–1.883	4.599	0.584	0.820	LandScan (2010)

SD: standard deviation; LP: labour productivity; CLR: capital–labour ratio; LLR: labour–land ratio; HCLR: human capital–labour ratio; POP: total population; GOV: governmental intervention; IntraPoly: intra-city polycentricity; InterPoly: inter-city polycentricity.

^aAll variables were log-transformed.

Estimation strategies

We estimate Equation (5) using an ordinary least square (OLS) estimator. We start by benchmarking our model with the standard Cobb–Douglas production function. Both the adjusted $R^{2}$ and the Akaike information criterion (AIC) are used to evaluate the model’s fit. OLS is the best linear unbiased estimator when the errors are independently distributed and homoscedastic. Therefore, before reporting our OLS results, we calculate a series of regression diagnostics regarding multicollinearity, autocorrelation, and heteroscedasticity. Importantly, an OLS estimator is only consistent when the regressors are exogenous to the model. Hence, we also checked the possible presence of endogeneity, which will be addressed in the following section.

Multicollinearity of regressors

A concern in any multivariate regression model is the potential of multicollinearity, where two or more exogenous variables are highly correlated such that one variable can be reasonably linearly predicted from other variables. Although the presence of multicollinearity neither affects the reliability nor adversely impacts the predictive power of a model, it may not produce a valid result regarding individual exogenous variables. Therefore, the variance inflation factor (VIF) for each additive independent variable is reported. Empirically, a VIF of 5 and above usually indicates the presence of multicollinearity, and a VIF over 10 suggests severe multicollinearity problems.

Autocorrelation and heteroscedasticity of the errors

An OLS producing ‘optimal’ results also relies on the errors being independently distributed and homoscedastic. Therefore, a Durbin–Watson statistic is applied to detect the presence of autocorrelation in the errors, and a Breusch–Pagan test is used to test if the variance of errors is constant (i.e. homoscedastic). In case of the presence of heteroscedasticity, the OLS is still unbiased, but it becomes inefficient as the coefficients associated with regressors may be either underestimated or overestimated.

Robustness check of endogeneity

Although the specification in Equation (5) implies that polycentricity affects labour productivity, the actual causality may in principle work in both directions. For example, areas with higher labour productivity may attract more firms and provide more employment opportunities, which, in turn, may lead to the creation of multiple population and employment centres (Meijers and Burger, 2010). Put differently, the presence of multiple population centres can be both the cause and consequence of labour productivity. If endogeneity is an issue, the OLS estimators will be biased.

Therefore, we apply a two-stage least square (2SLS) estimator with instrumental variables (IVs) to control for endogeneity. According to Wooldridge (2010), IVs are ideally related to endogenous variables (i.e. IntraPoly and InterPoly) and simultaneously unrelated to the dependent variable (i.e. LP). Geomorphological features such as mountains and water bodies significantly affect land uses and inevitably shape polycentric urban development (Zhang et al., 2017). Meanwhile, such topographical features are unlikely to be associated with the level of labour productivity. Consequently, we use the average value of the slope (i.e. the first-order derivative of a digital elevation model (DEM)) within a city (IntraSlope) as the IV for the degree of intra-city polycentricity (IntraPoly). Similarly, we use the standard deviation of the landform curvature (i.e. the second-order derivative of a DEM) across neighbouring cities (InterCurvature) as the IV for the degree of inter-city polycentricity (InterPoly). DEM data were acquired from the Global 30 Arc-Second Elevation Project of the US Geological Survey (GTOPO30; https://lta.cr.usgs.gov/GTOPO30). Given that GTOPO30 was completed in late 1996, a 15-year lag alleviates the possibility that recent topography might be related to economic development due to more active mountain exploitation in the developed area. Weak instrument tests are applied to examine whether the specifications of each IV is valid. Given the validity of all IVs, the Wu–Hausman test is further applied to determine whether the 2SLS is a more consistent and efficient estimator compared to the OLS. If regressors can be treated as exogenous variables, OLS should be preferred over 2SLS (Wooldridge, 2010). Table 2 reports the results of endogeneity tests and the summary of the first-stage regression of the 2SLS. The topographical profiles as instrument variables are valid at both scales, as the weak instruments tests are significant at the p<0.05 level. Importantly, both the Durbin–Wu–Hausman Chi-square statistic and the Wu–Hausman F-statistic are insignificant, suggesting that endogeneity is not a concern in our specifications.

Table 2.

First-stage regression results of 2SLS regressions on labour productivity.

	Intra-city polycentricity (IntraPoly)	Inter-city polycentricity (InterPoly)	Both
Instrument (t)	IntraSlope	InterCurvature	IntraSlope InterCurvature
Weak instrument (F-statistic of first-stage regression)
IntraPoly	11.86***		7.30***
InterPoly		4.05*	3.19*
Exogeneity
Wu–Hausman	0.01	0.05	1.13
N	270	270	270

***p < 0.001.

*p<0.05.

Results and discussions

Overall findings

Our discussion of the estimation results begins with a benchmarking of the standard Cobb–Douglas production by only including the exogenous factors of the CLR, LLR, and HCLR in Model 1. From Model 2 to Model 6, we employ a stepwise regression approach by gradually adding explanatory variables. In Model 2, we add the POP and the level of GOV as the baselines for estimating the effects of polycentric urban development. Model 3 and Model 4 represent two intermediate models, where intra-urban and inter-urban polycentricity are included, respectively. Model 5 includes the main effects of polycentricity at both intra-urban and inter-urban scales concurrently, which allows the testing of H1 and H2. Subsequently, Model 6 was developed to test the potential synergies, which is manifested by the role of population size (H3) and multilevel interaction effects (H4) on labour productivity. The regression results are reported in Table 3.

Table 3.

OLS regression results of labour productivity in 2010.

		Model 1		Model 2		Model 3		Model 4		Model 5		Model 6
	H	Beta	SE	Beta	SE	Beta	SE	Beta	SE	Beta	SE	Beta	SE
(Intercept)		23.289***	6.305	14.168*	6.409	12.976*	6.367	14.146*	6.330	12.948*	6.286	12.714*	6.285
CLR		0.400**	0.039	0.305***	0.038	0.305***	0.038	0.309***	0.038	0.309***	0.038	0.301***	0.038
LLR		–0.005	0.046	0.078	0.050	0.082	0.050	0.074	0.050	0.077	0.049	0.081	0.049
HCLR		1.454***	0.288	1.021***	0.298	0.962**	0.296	1.021***	0.294	0.962**	0.292	0.958**	0.293
POP				–0.045	0.032	–0.038	0.032	–0.049	0.032	–0.042	0.032	–0.061	0.034
GOV				–0.342***	0.049	–0.363***	0.049	–0.342***	0.049	–0.363***	0.049	–0.363***	0.049
IntraPoly	H1					–0.067*	0.027			–0.067*	0.027	–0.360	0.282
InterPoly	H2							0.057**	0.021	0.057**	0.020	–0.557*	0.251
POP × IntraPoly												–0.042	0.041
POP × InterPoly	H3											–0.091*	0.037
IntraPoly × InterPoly	H4											0.013	0.030
Adjusted $R^{2}$		0.657		0.708		0.714		0.715		0.721		0.725
F-statistic		173***		132***		113***		114***		100***		72.1***
Breusch–Pagan $(χ^{2})$		1.700		5.900		6.660		8.590		9.190		13.700
Durbin–Watson		1.879		2.034		2.044		2.058		2.065		2.085
Avg. VIF		2.451		2.435		2.217		2.198		2.046		N/A
AIC		124.66		83.012		78.884		77.262		72.889		71.382

SE: standard error; CLR: capital–labour ratio; LLR: labour–land ratio; HCLR: human capital–labour ratio; POP: total population; GOV: governmental intervention; IntraPoly: intra-city polycentricity; InterPoly: inter-city polycentricity; VIF: variance inflation factor; AIC: Akaike information criterion.

***p < 0.001.

**p < 0.01.

*p < 0.05.

The higher the value of IntraPoly, the greater degree of polycentricity at intra-city scale; the higher the value of InterPoly, the greater degree of polycentricity at inter-city scale. All variables are standardized.

The gradual increment in the adjusted $R^{2}$ along with a decrease in the AIC as we move from Model 1 to Model 6 indicates that our main effect model (Model 5) and full model (Model 6) improve the explanatory power. None of the four models leads to significant concerns of heteroscedasticity (insignificance of Breusch–Pagan tests) or autocorrelation (insignificance of Durbin–Watson tests), while adding more explanatory variables does not raise issues of multicollinearity (with an average VIF of around 2 and the VIF of all single covariates being less than 4).

Labour productivity and polycentricity at multiple scales

As suggested by Model 1, the effects of capital and human resources on productivity in Chinese cities are significant and positive. Most notably, a standard deviation increase in the average years of education increases labour productivity by about 1.5 standard deviations if everything else remains equal. Model 2 suggests that government spending tends to affect urban productivity negatively. A standard deviation increase in governmental spending decreases labour productivity by 0.34 standard deviations. The negative impact of government spending has two potential explanations (Zhang et al., 2017). On the one hand, economically lagging cities with low productivity tend to rely on transfer payments from the central government, and fiscal expenditures, therefore, account for a substantial portion of local GDP. More specifically, most cities with large GOV values in our sample are located in China’s mountainous inland. On the other hand, a high percentage of GDP in governmental fiscal expenditures may imply a strong local state in managing the economy. State involvement in the economy is often linked with unnecessary institutional costs and may, therefore, lead to stagnating urban economies (Huang, 2008). We note that our GOV variable is only one specific measure of government capacity and quality (see also Rodríguez‐Pose and Zhang, 2019).

The effects of polycentricity are highlighted in Models 5 and 6. Our discussion will focus on the impacts of geographies, economic development, and government policies (Liu et al., 2018; Wei, 2013; Wu, 2015). First, according to Model 5, when other covariates are held constant, a standard deviation increase in IntraPoly is associated with a 0.067 standard deviation decrease in labour productivity. Put differently, a higher level of monocentricity at the intra-city scale corresponds to a higher level of labour productivity. Our first hypothesis (H1) is, therefore, rejected. This is consistent with the observations in Li et al. (2019) as well as Li and Liu (2019) on dominant agglomeration economies in Chinese cities. Compared to polycentric cities, a monocentric one of similar size often has a larger central city, which is conducive to agglomeration economies (Li et al., 2019). Furthermore, in the Chinese context, such results may also be interpreted in the context of the literature on infrastructure sharing and agglomeration. Much of the urban construction in China has been concentrated in the central parts of cities (Wu, 2015). Consequently, the central part of a city often serves most urban functions. Usually, this is the densest area in a city, and many outlying (new) towns and districts have yet to grow into fully functional centres. Because city centres tend to be so densely populated, a city may entail a more hierarchical intra-city urban system despite the emergence of other population centres. This is in line with the significant agglomeration effects of city centres found in the American and European contexts (Agarwal et al., 2012; Rosenthal and Strange, 2003). Nevertheless, the polycentricity measure used in this study (Meijers and Burger, 2010) tends to pick up cities with fragmented and mountainous internal geographies. Again, such cities are more commonly seen in the economically lagging regions.

As for the effects of polycentricity at the inter-city level, a standard deviation increase in InterPoly is associated with a 0.057 standard deviation increase in labour productivity. Put differently, a higher level of polycentricity at the inter-city scale may be linked with a higher level of labour productivity, so H2 is accepted. Recent studies often find that the most developed city regions in China – the Pearl River Delta, the Yangtze River Delta, and Beijing-Tianjin-Hebei – are among the most polycentric ones (Chen et al., 2017; Li et al., 2018; Zhao et al., 2017). While these polycentric urban regions are often seen as the product of intensive economic decentralization, rapid marketization, and high economic productivity (Zhao et al., 2011), our results suggest that there is also a positive effect in the other direction. This can be related to concepts such as regional externalities (Parr, 2002) and regional innovation systems (Asheim and Isaksen, 2002). With emerging information and communication technologies and falling transportation costs, the scope and scale of agglomeration effects can be expanded (Partridge et al., 2007; Renski, 2011). For example, Fu (2008: 89) has observed that ‘regional innovation and technological capabilities have contributed further to regional economic growth in China’s coastal regions but not in the inland regions.’

In Model 6, the negative and significant coefficient associated with POP × InterPoly suggests that a small city may benefit from being in a more polycentric urban region (H3 is accepted). In more polycentric urban regions, smaller cities seem to benefit from positive spillovers, while they are less likely to become the ‘victims’ of the ‘agglomeration shadows’ in which smaller cities are exploited by nearby larger cities (See Burger et al., 2015; Dobkins and Ioannides, 2001). Along the same line, ‘non-leading cities’ in a monocentric urban region may suffer from the ‘primate regional urban system’ syndrome in the Chinese context. Our empirical findings are in line with the theories for ‘borrowed size’, which has been adopted as an organizing principle in many contemporary polycentric city-region discussions (Hesse, 2016). The results are also consistent with previous evidence from Yangtze River Delta (Sun and Ding, 2016); however, contradictory to the finding based on Beijing-Tianjin-Hebei region (Chen and Sun, 2017). Nevertheless, theories of ‘borrowed size’ should be interpreted with caution in the Chinese context, as a prefectural-level city in China is, in practice, comparable with a ‘metropolitan region’ in the US context (Li, 2014). Another caveat is that most of the literature derived from established theories of ‘borrowed size’ focuses on functional polycentricity, while here we adopt measures of morphological polycentricity. While there are often moderate positive correlations between both functional and morphological polycentricity and between different measures of morphological polycentricity in the Chinese context (Liu et al., 2018), our use of morphological polycentricity measures based on population centres may be influencing our findings. Nonetheless, this finding resonates with some recent empirical evidence from other countries. For example, Kaufmann and Meili (2019) demonstrate the contribution of small- and medium-sized towns to regional economies in Switzerland, while, based on a study of 117 European urban regions, Meijers et al. (2018) show that the development of a network of smaller cities is more conducive to urbanization economies than megacities are.

Finally, the coefficient associated with the interaction term between intra-city and inter-city polycentricity is insignificant, and H4 is, therefore, not accepted. One possible reason could be related to how the capital stock was calculated for Chinese cities. While this approach is widely adopted in Organisation for Economic Co-operation and Development countries to measure capital stock through perpetual inventory (Goldsmith, 1951), there are many theoretical concerns and technical difficulties to adopt the same empirical strategy for Chinese cities. For example, existing literature has not produced a clear answer regarding the base year for stock capital in China as well as a reasonable depreciation rate for the Chinese market. Furthermore, both administrative annexation and jurisdiction adjustment (Ma, 2002) pose further challenges to the accounting process. Therefore, as a supplement, we re-estimated Models 1 to 6 with an alternative measure of CLR, defined as the ratio of total fixed assets of enterprises above a designated size (i.e. legal industrial enterprises with annual primary business income of five million CNY or more) over the total labour of those firms (Table 4, Appendix 1).

In these alternative Models A1 to A6, all the previous interpretations still hold, but the LLR variable becomes significant. Besides, Model A6 suggests a weak positive interaction effect between intra-city polycentricity and inter-city polycentricity at the 0.1 level. This result might be interpreted in two ways in light of the other three hypotheses. On the one hand, our results imply that if a city is situated in a monocentric region, increasing its monocentricity through the densification of its urban core may lead to greater economic productivity. Cities in western and central China are often monocentric at both the intra-urban and inter-urban scales (Liu et al., 2018). City regions in these areas are often dominated by one leading city and, therefore, suffer from a ‘primate regional urban system’ syndrome (Henderson, 2002; Storper, 2013). While a primary city could theoretically serve as the growth pole and generate spillover effects (Richardson, 1976), leading cities usually capture more growth potential with their relatively better endowments of transport, telecommunication, and other infrastructure (Li et al., 2018). Examples that seem to entail such dynamics include provincial capitals and their surrounding city regions in western China, such as Guiyang and Nanning (the provincial capital of Guizhou and Guangxi, respectively). Guiyang has recently become known for its International Big Data Expo and information and communication technology industries. The province of Guizhou has strategized the big data industry and thus implemented preferential policies towards its capital. Nevertheless, in 2014 the State Council of China put forward Gui’An New Area (located outside Guiyang) as another economic growth pole for the region, leading to uncertainties in terms of the relationship between multiscalar polycentricity and economic productivity. Similarly, Nanning is not only the largest city but also the economic and culture hub of Guangxi. Furthermore, several recent national strategies have prioritized Nanning. For example, the China-Association of Southeast Asian Nations Exposition has been held annually in Nanning since 2004 (see for example, Cheng, 2013). In 2006, Guangxi Airport Group (the management entity of all airports in Guangxi) relocated from Guilin (the third largest city in Guangxi, about 350 km from Nanning) to Nanning itself. A year later, the Ministry of Railways of China decided to relocate the regional railway hub from Liuzhou (the second largest city in Guangxi, about 200 km from Nanning) to Nanning.

On the other hand, if a city is located in a more polycentric region, a balanced intra-city urban system may benefit the city more. This benefit is again in line with Liu et al.’s (2018) observation that China’s coastal city-regions are found to be polycentric at both the intra-city and inter-city levels. Due to the emergence of town and village enterprises in the 1980s, the ‘fever’ of establishing development/enterprising zones in the 1990s, and new town development in the 2000s, cities in the more developed coastal areas are usually polycentric at the intra-city level (Hsing, 2010; Lin, 2002; Wu and Phelps, 2011). Recent plans that may help capturing such dynamics include Guangdong–Hong Kong–Macao Greater Bay Area (officially approved by the State Council) and Greater Hangzhou Bay Area (currently under consideration by the National Congress; See also Cheng and Shaw, 2018)). It is worth mentioning that the Hangzhou Bay Bridge was opened about 10 years ago, shortening the travel time between Shanghai and Ningbo (a major city in Zhejiang province) from four to two hours. An improvement of road transport infrastructure in such already polycentric urban regions will likely further foster the increase of both the morphological and functional polycentricity of the greater Yangtze Delta River city region and boost economic development (See for example, Yue et al., 2010).

Nonetheless, the interaction term of intra-city and inter-city polycentricity is insignificant when accounting for CLR with capital stock via perpetual inventory, and becomes significant only at the 0.1 level when proxying CLR by capital flow. This is also the reason why we had to take an inductive approach to deconstruct such a possible interaction effect by means of an intuitive interpretation of well-established planning and policy examples along with our first-hand knowledge. We admit the limitations of such inductive approach, and expect this weak empirical evidence to be a starting point for future investigation of the mechanisms of possible interaction effects.

Concluding remarks

The concept of ‘urban polycentricity’ has attracted sizable interest in both academic and policy circles. It has been used not only as an ideal-typical theoretical construct to characterize the emerging urban landscape, but also normatively to set goals and visions in spatial plans. In this process, polycentricity has been conceived and pursued at different geographical scales. However, in general terms, the interaction between polycentricity at various urban spatial scales has been less well explored. Therefore, this paper aims to understand how polycentricity affects economic performance (expressed by labour productivity) at multiple scales.

Our results associate intra-urban monocentricity and inter-urban polycentricity with higher levels of labour productivity. These findings at the intra-city level are consistent with recent analyses (Li et al., 2019; Zhang et al., 2017), but here we extended these insights by framing them in and relating them to effects at other spatial scales. For example, we found that smaller cities tend to benefit more from regional agglomeration than larger cities do. Furthermore, while we did not find a significant synergy effect of intra-city and inter-city polycentricity when measuring CLR with capital stock, a weak synergy effect is found when measuring CLR with capital flow, where either a monocentric city situated in a monocentric urban region or a polycentric city located in a polycentric urban region is associated with better urban economic performance. Overall, the different effects of intra-urban and inter-urban polycentricity on labour productivity not only reconfirm the multiscalar nature of polycentric urban development but also emphasize the necessity to understand the scales at which agglomeration economies are achieved.

Some of the limitations of our study pave the way for future research. First, as one specific attempt, our study only examines morphological polycentricity from one measurement. Other measures of polycentricity may reflect different aspects (Vasanen, 2012), and sensitivity issues may occur when comparing different measures of polycentricity. Second, even though using population data in the Chinese context may be warranted, using fine-grained datasets detailing employment could lead to more nuanced and diverse analyses. Third, a longitudinal study may provide more robust results and reveal the nuanced spatiotemporal dynamics of polycentric urban development in China. Finally, future work can test polycentric urban development’s roles in other dimensions of urban performance.

Footnotes

Acknowledgments

The authors are very grateful for the insightful comments made by the Editor and anonymous reviewers. We would like to acknowledge all the participants of the RSA Research Network on ‘Polycentric Urban Regions’ (PURs) Workshop -- Conceptualising, Identifying and Analysing Polycentric Urban Regions at the Faculty of Architecture and the Built Environment, Delft University of Technology, the Netherlands, January 28--29, 2019, for their constructive comments.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This paper is supported by the Key Laboratory of Regional Sustainable Development Modeling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences (Grant No. KF2018-08), the tenure-track start-up package from the University of Twente, and Hong Kong Research Grant Council (ECS 27604016).

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