4.2. Robustness Tests
The endogeneity of polycentricity in relation to better economic performance or to the omission of key variables are salient concerns and have the potential to significantly bias the coefficients. First, urban spatial structure and labor productivity are potentially related in two directions. The positive correlation between them may stem from the fact that cities with higher productivity are more likely to be decentralized and clustered. Second, although we included as many relevant control variables as possible and used a two-way fixed-effects model to control for unobservable time and city effects, some relevant variables may still be missing from the regressions.
Ordinary least squares (OLS) can suffer from the potential bias caused by reverse causality and omitted variables. TSLS estimation is a common method for reducing this potential bias. Therefore, we conduct a TSLS estimation by using an instrumental variable that is correlated with the potentially endogenous urban spatial structure but not with labor productivity.
Inspired by previous related research [
36], topographic data could be a valid source of instruments for urban spatial structure. Thus, we use the SRTM 90-m resolution DEM elevation data gathered by the National Aeronautics and Space Administration (NASA) and the National Imagery and Mapping Agency (NIMA) to obtain the average slope of each postal code area in each Chinese city proper.
However, rather than directly adopting the average slope of terrain roughness, we designed a group of more relevant instruments. Generally, firms prioritize building in areas where the slope is less steep. In contrast, areas with steep inclines have high construction and usage costs; thus, they have a lower potential for becoming centers of employment concentration. Therefore, a less steep postal code area, i.e., a postal code area with a lower average slope, could probably attract more employment. We use (90°—the average slope of each postal code area) as a measure of potential employment to replace the actual employment in the corresponding postal code area. Then, based on the formulas for the urban spatial structure indices, we replace actual employment with each location’s potential employment (90°—average slope) and then use these new indices as instrumental variables (IVs) for the urban spatial structure. A higher value for these IVs could be positively related to a higher level of centralization or concentration. The IVs are also time-variant, as the locations of the CBDs change over time.
Regarding the validity of the instruments, the slope of the surface is a natural feature and thus highly exogenous in relation to economic activities. Furthermore, we use topographic data from 2000, which are very unlikely to have been influenced by economic development after 2004; in addition, because of the height measurements taken by the SRTM 90-m resolution DEM elevation instruments are precise to approximately 16 meters (approximately the height of a five-story building), we can conclude that our slope measurements are unlikely to be affected by the built environment.
In
Table 4, the Cragg–Donald F statistic shows that our instruments are relevant in most of our models. However, limited information maximum likelihood (LIML) estimation, which is less sensitive to weak IVs, is used in
Table 5 to reduce the negative impact of weak IVs.
Table 5 confirms the results that we obtained from the OLS model. As the spatial structure variables are not shown to be endogenous by Durbin–Wu–Hausman tests, we conclude that the OLS estimations are more efficient. However, we present the TSLS results here as a robustness test.
In addition, we also find that the results are mostly robust to alternative urban spatial structure indices (
Table 6).
4.3. Discussion
The estimates suggest that the interactions between urban spatial structure and labor productivity are heterogeneous with respect to population size. Most models support the idea that in large cities, a decentralized and clustered structure performs better, which confirms that the relation between economic performance and polycentricity depends on the urban population size. Recalling our second hypothesis, there are two potential mechanisms for the larger economic influence of polycentric structures: decentralization diminishes the negative externalities of agglomeration, and reclustering in subcenters re-establishes the positive externalities through “borrowed size”. Our results confirm both mechanisms. With the growth of the city population, whether employment is more clustered or dispersed matters just as much to urban economic performance as whether clustering occurs near the CBD.
To put our findings into context and enrich the academic and practical guidelines on the evolution of urban spatial structure, we provide the following discussion.
4.3.1. Discussion 1: Comparing Our Results with Those of Previous Studies
To the best of our knowledge, this paper is the first to verify the theoretical predictions at the city proper scale that polycentric structure improves economic performance more in larger cities. Referring to the previous works on a comparable scale, some argue that the effects of polycentricity on economic performance do not depend on city size [
4,
12], while others raise conclusions opposite ours [
2].
First, one of the reasons for the different results could be the methods used. Due to data availability, we adopt panel data models instead of the cross-sectional models, as were used in previous works. The cross-sectional models are not as reliable as panel models because they are more likely to be biased.
Second, the different context of the study case could also affect the results. Our results contrast with those obtained by Meijers and Burger (2010) [
2], who argued and empirically showed that polycentricity resulted in better economic performance in small metropolitan areas than in large metropolitan areas. They explained that the functional connections between urban subcenters in small metropolitan areas were denser than those in larger areas. This inconsistency may originate from differences in the developmental stages of the samples. Metropolitan areas in the United States are already mature; therefore, the influence of agglomeration economies and diseconomies is more balanced. Since the 1970s, American metropolitan areas have evolved toward polycentric spatial structures that are functional rather than morphological. In contrast, China is in the midst of fast-paced urbanization, and the share of the urban population has only recently surpassed that of the rural population. At this stage, the urban morphological spatial structure is evolving rapidly, and the surplus between agglomeration economies and diseconomies plays an important role in labor productivity.
Nevertheless, our results are in line with some findings on larger scales [
10,
20,
29].
4.3.2. Discussion 2: City Size Threshold for a Positive Influence from Polycentricity
We attempt to find the city size threshold at which the economic influence of polycentricity changes from negative to positive. We specify the interactions between the urban spatial structure (centralization and clustering) and urban population size to capture potential heterogeneity (Model 5 in
Table 3). We then calculate the marginal effect of lnSTU’s contribution to economic performance as
. As
and
are opposite in sign in all our models, the sign of lnSTU (
) changes from negative to positive or from positive to negative as the population grows (see
Figure 5). Simply put, when we set the estimated coefficient for lnSTU (i.e.,
) equal to zero, we obtain the critical point for this change. As
Table 7 and
Figure 5 show, centralization and dispersion (monocentricity) better facilitate economic performance only in small cities with fewer than approximately 600,000 residents. However, decentralization and clustering (polycentricity) are better structures for cities with more than 700,000 residents. Furthermore, the city size threshold for centralization is lower than that for clustering, which implies that for better economic performance, decentralization should occur before clustering in the urban structure evolutionary process.
According to a study on “ghost towns” using nighttime light data, unsuccessful new towns appear quite frequently around small-sized cities, such as Jiayuguan, Zhangye, Jiuquan, and Fangchengang [
37]. We find that the populations of these cities are usually below 600,000 residents, which coincides with our findings. Thus, polycentricity strategies are planned too far ahead for small cities. Instead, monocentricity (centralization and clustering) could be better choice for these small cities.
4.3.3. Discussion 3: Optimal City Size Constrained by Different Spatial Structures
By adding the quadratic form of lnPOP and the interaction terms between lnPOP and the urban spatial structure variables, we can calculate the peak population point (P*, henceforth) that represents the optimal city size, as constrained by different spatial structures. Maximizing GDP per worker and holding the other control variables constant gives a peak size of
As the mediating effect of city size on centralization is negative and that on clustering is positive, the peak size is larger for decentralized and clustered cities. Calculated on the basis of the estimates from Model 5 in
Table 3, the results presented in
Table 8 and
Figure 6 support our hypothesis and indicate the peak points where GDP per worker is maximized for each quartile of the spatial structure indices in 2013. The peak population size increases as cities become more decentralized and clustered. To simplify the comparison, we define two hypothetical cities. The first is polycentric with a MWI value in Q1 and a DELTA value in Q3 (decentralized and clustered). The second city is monocentric and has its MWI value in Q3 and its DELTA value in Q1 (centralized and dispersed). The optimal population size in the polycentric city, under the chosen specifications, is twice as large as that in the monocentric city (584.13/253.86 ≈ 2.3).
As a validation of our results, we collect the estimated Chinese optimal city size raised by early works (
Table 9). These numbers are very close to our findings.
4.3.4. Discussion 4: The Economic Significance of Urban Spatial Structure
Based on the results from Model 5 in
Table 3, we aim to calculate the economic significance of urban spatial structure transformation, namely, how much profit is accrued when cities become more decentralized (a decrease in MWI) and more clustered (an increase in DELTA). Thus, we choose the following five Chinese cities with different population sizes as our study cases: Jiayuguan (200,000), Suizhou (500,000), Weinan (1 million), Wuhan (5 million), and Tianjin (8 million).
Table 10 confirms that the economic performance that results from the transformation of the urban spatial structure varies based on the urban population size. In small cities such as Jiayuguan (200,000), each 1% reduction in centralization results in a 1.1 thousand yuan decrease in GDP per capita, and a 1% increase in clustering also results in a 2.6 thousand yuan decrease in GDP per capita. In Suizhou (500,000), the loss values are 0.04 and 0.2 thousand yuan per capita, respectively, which are both smaller than those in Jiayuguan. However, in larger cities, the decentralization and clustering processes create an increase in economic benefits, and larger cities earn more. The effects of both the 1% decrease in centralization and the 1% increase in clustering in Tianjin (8 million) are double those in Wuhan (5 million). These values are all of economic significance and thus cannot be ignored. These economically significant outcomes are also confirmed when we consider a change of one standard deviation.