Are Chinese Cities Really Too Small?

Transcription

1 March, 2014 Are Chinese Cities Really Too Small? Chao Li and John Gibson Department of Economics, Private Bag 3105, University of Waikato, Hamilton 3240 New Zealand ( Department of Economics, Private Bag 3105, University of Waikato, Hamilton 3240 New Zealand ( Corresponding author: (ph), (fax).

2 Acknowledgements: We are grateful to Scott Rozelle for helpful suggestions and to Geua Boe-Gibson for help with the GIS. All remaining errors are those of the authors.

3 Are Chinese Cities Really Too Small? Abstract The inverted U-shaped relationship between real output per worker and city scale in China is re-examined. About 80% of Chinese cities are close to their estimated productivity-maximizing employment scale, with productivity losses from sub-optimal scale typically below 10%. The remaining 20% of under-scale cities employ few workers. These findings challenge the often repeated claim that China has too many small cities and foregoes agglomeration-based productivity gains as a result. Keywords: Agglomeration, Cities, Population, Productivity, China JEL: R12, O15

4 1. INTRODUCTION It is often claimed that a legacy of China s command economy era, and especially its hukou restrictions on migration, is that Chinese cities are too small to maximize productivity benefits from agglomeration effects (Au and Henderson, 2006; Xu 2009). This paper reprises the issue of how far Chinese cities are from productivity-maximizing scale, and the associated question of how big are the productivity losses from sub-optimal scale. A fresh look is needed because the data used by previous studies inaccurately measured city scale (e.g. Xu, 2009) and employment (e.g. Au and Henderson, 2006). It is only since China s 2010 population census that accurate city-level estimates of the urban population and of total employment are available. The problem with the existing evidence is that it relies on data that ignore the permanent residents of cities whose hukou registration is elsewhere. For example, Xu (2009) uses a panel of 155 urban cores (hereafter, cities ) over , with city scale measured using the local hukou registered population. 1 In the mid-1990s the stock of non-hukou migrants was already around 100 million (Chan, 2012), with many more in coastal cities than inland cities, so substantial error in measured city scale is likely to bias estimates of the size-productivity relationship. Au and Henderson (2006) use employment data from 205 cities in 1997 to show an inverted U-shaped relationship between output per worker and city scale, noting that most Chinese cities are below the size for peak productivity. But their measure of employment seems to exclude workers in private sector firms, and since the private sector employment share varies across cities, this data feature also may bias the size-productivity relationship. 2 1 The urban core is made up of districts (shiqu) of a prefectural city, and most closely corresponds to a city proper. 2 Au and Henderson use City Statistical Yearbook (CSY) data, where private sector employment in the 1998 issue is titled as self-employed (which has a very low share of the total). Comparing total and sector-level employment in the long form 2010 census with CSY data for the same year shows a substantial undercount in the CSY. Consistent reporting conventions are maintained in the CSY; for example, it continues to report only the local hukou registered (and non-agricultural hukou) population rather than the resident (or urban) population. It is likely therefore that the 1997 data were also an undercount, by omitting employees in private sector firms. 1

5 Even simple descriptive claims about China having too many small cities are undermined by using registered population. Au and Henderson (2006) note that in 2000 China had nine metro areas with populations over 3 million and another 125 with populations in the 1-3 million range; a ratio of large to small cities of 0.07 compared to a global average of But if 2000 census data are used to recalculate this ratio, with cities measured by their residents, China had 20 large cities and 89 cities of 1-3 million, giving a ratio of 0.23 just below the global average. Yet using the hukou registered population for each city in 2000 as a measure of scale, China seemingly had only 15 cities with more than 3 million people versus 88 cities of 1-3 million, giving a ratio of large to small cities of The bias from using the hukou population count grows with the scale of non-hukou migration. For example, in the 2010 census, 38 cities had a resident population exceeding 3 million and 97 cities were of 1-3 million, giving a large-to-small ratio of 0.39, but if the hukou counts are (wrongly) used the ratio is just The issue of optimal city size is timely in China. The early reform era saw continuation of policies to constrain growth of big cities and favor small ones. For example, the 1990 City Planning Law (Zhonghua Renmin Gongheguo Chengshi Guihua Fa) mandated strictly controlling the size of large cities and developing medium-sized and small cities and most new cities in this era were simply relabeled counties. Many of these were poor sites for agglomeration and this county-to-city upgrading system was abandoned in More recently, large cities have been allowed to expand area by converting adjacent counties into urban districts, and planning laws now omit the phrase controlling the size of large cities (Fan et al, 2012). 3 The ratio using the registered population differs from that reported by Au and Henderson (2006), who did not use census data for China (which are the only reliable source of city population estimates for that time). Instead they use 1998 values that appear to be from the World Urban Prospects issued by the United Nations, which are extrapolated to 2000 using growth rates (see p.10 of worldcitiesdocumentation1003.doc, downloaded from on October 7, 2013). 4 This may be why the small cities most violate Zipf s Law in China (Anderson and Ge, 2005; Chen et al, 2013). 2

6 2. DATA AND MODEL SPECIFICATION The sample is 286 cities in 2010, which come from prefectures containing 97% of China s GDP and 93% of the population. 5 Our data are at the same spatial level as Au and Henderson (2006) and Xu (2009) but cover more of China. Full details on the sample and data sources can be found in Li and Gibson (2014), who show agglomeration effects occur in these cities but not in the county-level cities. 6 Thus even though studies of the city size distribution include county-level cities (Anderson and Ge, 2005; Chen et al, 2013), we ignore them here, which also serves to maintain comparability with Au and Henderson (2006) and Xu (2009). The dataset is compiled from two main sources: the China City Statistical Yearbook (CSY) (NBS, 2011) and the 2010 Population Census (NBS, 2012). 7 The CSY reports city-level GDP and counts of those with local hukou but not the resident population. Non-hukou residents now number around 200 million so the CSY gives a misleading measure of city scale, despite many studies using these data. Moreover, employment data in the CSY omit the private sector. We therefore use more reliable population and employment data from the 2010 Population Census long form, which is given to 10% of households to obtain details on occupations and employment, which we gross to city-level totals by multiplying by ten. A complete description of data sources and variables is in Appendix Table 1. We follow Au and Henderson (2006) and use a flexible functional form to relate output per worker, GDP/N to city scale, N, industrial structure (msgdp), capital, and other covariates: 8 ln ln. (1) Specifically, GDP/N is non-agricultural GDP per worker. The industrial structure variable msgdp 5 Au and Henderson (2006, p.558) note that GDP data at prefecture-level in China are of extremely high quality. 6 Moreover, Fan et al (2012) show that county-level cities did not grow faster than counties that were not relabeled. 7 To construct an instrumental variable we also use the 2001 yearbook on registered (hukou) population of the Ministry of Public Security (MPS, 2001) and the 2001 edition of the CSY. 8 Au and Henderson (2006) also estimate a structural model but their main results are for a flexible functional form. 3

7 is the ratio of GDP in the secondary sector to the tertiary (services) sector, and this is needed because the peak scale is higher in more service-intensive cities. 9 Capital/N is industrial fixed assets per worker, and the vector of control variables, X includes population-weighted distance to all other places to proxy for domestic market potential, distance to the ten largest ports to proxy for foreign market access, average years of schooling to proxy for labor quality, and the output of foreign-affiliated firms relative to domestic firms to proxy for technology. These capture similar concepts to the control variables used by Au and Henderson (2006) although details of their construction differ (e.g. we use GIS while they hand-measured from a map). The estimate of productivity-maximizing employment (the peak point ) for the k th city calculated from the results of equation (1) follows Au and Henderson (2006) and is: (1a) While letting city industrial structure (as proxied by msgdp) shift the inverted U is better than forcing a single peak over different types of cities (e.g., Xu, 2009)), the msgdp ratio ignores some variation in city structure (Figure 1). First, not just large cities are service intensive, with small and large cities often having the same msgdp ratio. Second, the primary sector is ignored but most small cities have non-trivial values for gdp1 (the ratio of primary sector GDP to total GDP). One cannot treat cities as service intensive based purely on msgdp since for equal msgdp, services are more important the lower is gdp1, and peak employment is thus higher. To fully capture local economic structure for the purpose of determining the shape of the inverted U, it is better to include both msgdp and gdp1 in the regression. Thus, equation (1) becomes: ln 1 ln (2) The calculation of the peak point for the k th city based on equation (2) is as follows: 9 Au and Henderson call this the manufacturing-to-service ratio, but secondary GDP also includes mining, utilities and construction sectors. We will call this variable msgdp for ease of comparison but note its wider definition. 4

8 (2a) While we provide estimates for equations (1) and (2), a problem with these functional forms is that the estimated peak points for some cities are negative. This is less of a problem when using a Generalized Leontief specification: ln ln (3) which was the preferred functional form of Au and Henderson since it let them calculate peak points for more cities. With this specification, peak size is found from equation (3) as follows:.. (3a) When N k is less than the 95% confidence interval surrounding * N k a city is deemed under-sized, otherwise it is over-sized. If N k is outside * N k it is considered significantly under- or over-sized. The final issue before turning to the results concerns the direction of effect between city scale and productivity. Firms and workers may be more productive in a bigger city, or being more productive for whatever reason causes a city to grow. In other words, the quantity of labor may be endogenous. Li and Gibson (2014) study this issue using as instrumental variables the planned size of cities from the command economy era, with no significant bias found from using OLS. The same approach is used here, but only on a linear model, using either N or N because the coefficients on higher order terms become insignificant when instrumented and so the inverted U-shaped relationship disappears (results available from the authors). 10 The same sensitivity occurs if a wider set of control variables than those of Au and Henderson (2006) are used, so we employ just their controls to focus on the reappraisal of peak points. 10 Similarly, using the employment data from the 2011 edition of the CSY (which excludes private sector workers), the U-shaped relationship disappears. 5

9 3. RESULTS The results in the first three columns of Table 1 consider the endogenous quantity of labor issue. As in Li and Gibson (2014), instrumenting for city scale with size in the command economy era makes no difference to the results. 11 Therefore OLS is used to estimate the remaining models. The results for the Taylor series flexible functional form are in columns (4) and (5) and for the Generalized Leontief in columns (6) and (7). For both specifications, including gdp1 adds explanatory power, and without this variable the results in columns (4) and (6) do not yield an inverted U, given the statistical insignificance of the ˆ 2 coefficient from equation (1). The importance of fully controlling for industrial structure using both msgdp and gdp1 is also shown in Figure 2, which uses ten cities to illustrate some features of the scale-productivity relationship implied by the Generalized Leontief model in column (7) of Table 1. The ten cities chosen are the smallest, largest, and closest to the mean in terms of scale, N and structure (msgdp and gdp1), along with one city where msgdp=1, which is a case that Au and Henderson particularly focus on. The curves are in terms of net output per worker, which links to the dependent variable in the Table 1 regressions using the transformation: 12 ln ln (4) A further feature of these curves is that to focus on the shape, and where actual city scale lies relative to the peak, the curves are normalized with values on the y-axis peaking at the same value as for Shenzen (257,000 yuan per worker per year). A similar normalization is used by Au and Henderson in their illustration of the impact of differing industrial structure. 11 The Hausman test results for the model in column (1) versus (2), and column (1) versus (3) are 2.05 and 1.29, with p=1.00 for both. The models in columns (1) to (3) were also re-estimated using N instead of N (and similarly changing instruments), with other variables unchanged. The OLS result for N was (0.024)*** and the IV results were: (0.027)*** and (0.027)*** with the Hausman tests again statistically insignificant. 12 Net output is also used by Au and Henderson (2006, p. 553) and is defined by them as city output (valued added or GDP) less borrowing costs (rental cost of capital). 6

10 Just controlling for the ratio of GDP in the secondary sector to the tertiary sector (msgdp) is not sufficient for dealing with variation in industrial structure. For example, the msgdp ratio for Chaozhou is nearly six times that of Hohhot but the two cities have the same inverted U pattern, which is co-determined by variation in gdp1. Conversely, Jingzhou has almost the same msgdp ratio as Chaozhou but its output-scale curve is shifted well to the left because of a higher gdp1 ratio. Karamay is an outlier, in terms of an enormous secondary sector GDP share (msgdp=9.2), but rather than this shifting the peak left it shifts it to the right, beyond the largest city in the sample (Shanghai N=11.9 million). In terms of other outliers, the three cities with N * k 0 (Suizhou, Lincang and Suihua) all have a large primary sector share, showing that the higher the gdp1 ratio, the further the inverted U shifts to the left. One feature of the curves in Figure 2 that is consistent with Au and Henderson is that the slope to the left of the peak is steeper than to the right, implying a bigger loss for under-sized cities than for over-sized cities. For example, employment in Shenzhen is more than three million above the peak point and the predicted output loss from being too big is just over 10%. But if Shenzhen was three million below peak employment the predicted loss would be over 30%. Note that in the figure, the predicted output at actual city scale is shown by the diamondshaped marker on each curve and in many cases this is near to the peak point. The percentage output loss from operating away from the peak point is calculated as: 13 ln ln (5) According to this calculation, the losses from cities being away from peak scale are much smaller than Au and Henderson find. Table 2 reports the details of using equation (5), with cities 13 This compares predicted output at actual and peak scale, so model errors cancel (unlike comparing actual output to predicted output). These calculations exclude the 20 cities with negative employment at the peak.

11 divided along two dimensions: scale relative to peak point and the size of the output loss from not being at the peak point. Four scale groups are used: significantly under-sized (N k below the * lower bound of the 95% confidence interval of N ), under-sized (N k below k * N k but above the lower bound confidence interval), over-sized, and significantly over-sized if employment is * above the upper bound of the confidence interval of N. There are slightly more cities outside the 95% confidence intervals for k * N k than inside the intervals, with the significantly under-sized group the biggest (Figure 3). But using employment shares (indirectly shown by the marker size in Figure 3), the biggest group is the significantly over-sized cities (home to 31% of workers). In terms of the output loss from not being at peak point, the modal category in Table 2 is for a 0-5% loss, which has 44% of the cities (with 42% of the workers). The median loss from a city not being at peak point is 7%, and even allowing for the skew from a few small cities in the % loss category, the un-weighted mean loss is just 16%. In contrast, Au and Henderson (2006) report a mean loss from cities not being at their peak point of 30% and a median loss of 17%; both being about twice as large as the losses estimated in Table 2. These differences persist throughout the distribution, except at the very extreme tail of the highest losses. Specifically, for cities at the 75 th, 90 th, 95 th and 100 th percentiles of the loss distribution, the losses are 22%, 42%, 66% and 242%, with equivalent values from Au and Henderson of 38%, 69%, 103% and 229%. It is also apparent from Table 2 that not only do few cities have large output losses from being too small they also employ an even smaller share of workers. Hence, a focus on the number of cities can be misleading because of the asymmetries in city size. Specifically, 21% of cities have large (>25%) output losses from being under-sized compared with just 1.5% of cities having similar losses from being over-sized. But once the focus turns to the number of workers the pattern is reversed; while 8% of workers are in under-sized cities with large (>25%) output 8

12 losses, twice as many (17%) are in over-sized cities that suffer equivalent-sized losses. It is hard to deduce from this pattern that the problem for China is one of under-sized cities. Indeed, almost two-thirds of workers in the sector of urban China considered here (that is, the core urban districts that also are what Au and Henderson (2006) and Xu (2009) study) are in cities where output losses from being away from peak points are below 10%. 4. CONCLUSIONS This paper reappraises the claim that Chinese cities are too small. Using more complete data on employment and including the primary sector share of GDP in the regression models, we find Chinese cities are closer to their peak scale and have smaller losses in net output per worker from being away from the peak point than is suggested by Au and Henderson (2006). Moreover, cities far from their peak tend to be the smallest cities in the urban hierarchy, which are the home to only a small share of the urban population. Evidently, the reshaping of China s economic geography by the movements of hundreds of millions of non-hukou migrants is producing an urban system that does not have productivity losses that are as large as previously thought. 9

13 References Anderson, G., & Ge, Y. (2005). The size distribution of Chinese cities. Regional Science and Urban Economics, 35(6), Au, C. & Henderson, V. (2006). Are Chinese cities too small? Review of Economic Studies 73(3): Chan, K.W. (2012). Internal Labor Migration in China: Trends, Geography and Policies. In Population Distribution, Urbanization, Internal Migration and Development: An International Perspective, United Nations Population Division, New York: pp Chen, Z., Fu, S., & Zhang, D. (2013). Searching for the Parallel Growth of Cities in China. Urban Studies, 50(10), Fan, S., Li, L., & Zhang, X. (2012). Challenges of creating cities in China: Lessons from a shortlived county-to-city upgrading policy. Journal of Comparative Economics, 40(3), Li, C. & Gibson, J. (2014). Agglomeration Economies in China: Locations and Effects. Working Paper 02/14. Department of Economics, University of Waikato. Ministry of Public Security (MPS). (2001). Population Statistics of the People s Republic of China by County 2000 (Zhonghua Renmin Gongheguo Quanguo Fenxianshi Renkou Tongji Ziliao 2000 Nian). Beijing: Qunzhong Press. National Bureau of Statistics (NBS). (2011). China City Statistical Yearbook 2011 (Zhongguo Chengshi Tongji Nianjian 2011). Beijing: China Statistics Press. National Bureau of Statistics (NBS). (2012). Tabulation on the 2010 Population Census of the People s Republic of China by County (Zhongguo 2010 Nian Renkou Pucha Fenxian Ziliao). Beijing: China Statistics Press. Xu, Z. (2009). Productivity and agglomeration economies in Chinese cities. Comparative Economic Studies, 51(3),

14 Figure 1. Variation in City Industrial Structure ln(gdp1) ln(msgdp) Notes: The marker size is proportional to city scale (employment). The variables are in logarithms to enable easy visualization of patterns. In original units, msgdp ranges from 0.33 to 9.20 and gdp1 ranges from to

15 Figure 2. Effects of City Industrial Structure on the Relationship between Scale and Net Output Net Output per Worker (thousand yuan) Karamay (9.20, 0.005) Shenzhen (0.90, 0.001) Shanghai (0.73, 0.006) Mianyang (1.67, 0.068) Chaozhou (1.42, 0.066) Hohhot (0.25, 0.017) Jingzhou (1.44, 0.121) Suzhou (1.00, 0.189) Lincang (0.53, 0.235) Suihua (0.33, 0.586) N (million) Notes: Numbers in ( ) are the msgdp and gdp1 ratios for each city. The predicted output at actual scale is shown by the diamond-shaped marker on each curve. 12

16 Figure 3. Comparison of Actual City Scale and Peak Points N* (million) Sig under-sized Sig over-sized Under-sized Over-sized 45 degree line N (million) Notes: Markers are proportional to the actual scale (employment) of each city. 13

17 Table 1. Determinants of Urban Productivity, Allowing for Endogenous Quantity of Labor and Flexible Functional Forms (n=286) Flexible Functional Form Specifications Endogenous Quantity of Labor Taylor Series variables in [ ] Generalized Leontief (1) (2) (3) (4) (5) (6) (7) Scale and industrial structure variables N (0.048)*** (0.054)*** (0.053)*** [N 2 ] or N (0.009)** (0.010)*** (0.068) (0.070)*** [N] or N (0.074) (0.079)*** (0.217) (0.236)* [N msgdp] or N msgdp (0.043)** (0.041)** (0.114)*** (0.110)*** [N gdp1] or N gdp (1.122)*** (0.400)*** Control variables Capital/N (0.023)*** (0.022)*** (0.022)*** (0.025)*** (0.025)*** (0.027)*** (0.027)*** Market Potential (Pop-Weighted Distance) (0.319) (0.299) (0.299) (0.316) (0.302) (0.316) (0.303) Average Distance to 10 Largest Ports (0.281) (0.263) (0.263) (0.280) (0.270) (0.278) (0.270) Average Years of Schooling (0.243)*** (0.238)*** (0.237)*** (0.248)*** (0.269)** (0.249)*** (0.290)* Foreign-Domestic Industrial Output Ratio (0.037) (0.035) (0.035) (0.037) (0.036) (0.037) (0.035) Constant (1.639) (1.536) (1.534) (1.670) (1.618)* (1.613) (1.562) Adjusted R-squared Cragg-Donald Wald test a Sargan test p-value b Notes: The dependent variable is (log) non-agricultural GDP per worker. Variables in italics are in logarithms. Each regression also includes 29 province-level fixed effects. Standard errors are in parentheses; * significant at 10%; ** at 5%; *** at 1%. Models in columns (2) and (3) use instrumental variables (the square root of the (log) number of non-agricultural hukou in 2000 for each city, plus in (3) a dummy for cities with higher registered non-agricultural population than resident urban population in 2010) and all other models are estimated with OLS. a First-stage F statistic for the instruments. b Over-identification test. 14

18 Table 2. Number of Cities and Workers in Terms of the Size of the Net Output Loss per Worker From Scale Not Being at the Peak Point % Loss in Net Output per Worker from being away from peak point 100%-250% Number of Cities (% of total) Millions of Workers (% of total) Sig undersized Undersized Oversized Sig oversized Total Sig undersized Undersized Oversized Sig oversized % 1.5% 0.6% 0.6% Total 50%-100% 25%-50% 10%-25% 5%-10% 0%-5% % 0.8% 5.3% 1.6% 11.2% 12.9% % 0.8% 15.8% 6.1% 5.7% 11.9% % 0.4% 0.4% 0.8% 18.8% 8.8% 0.2% 0.2% 7.4% 16.6% % 4.1% 1.5% 1.5% 15.0% 4.9% 3.7% 1.3% 6.7% 16.5% % 25.9% 14.7% 43.6% 2.5% 23.6% 15.5% 41.6% Total % 30.5% 16.5% 3.8% 100% 24.5% 27.5% 17.0% 31.0% 100% Notes: Calculation of the net loss is based on equation (5) in the text. Significantly under-sized and over-sized cities are those outside the 95% confidence interval for their peak point, while under-sized and over-sized cities are above or below their peak point but within the 95% confidence interval. The sample size is 266 because 20 cities with negative peak points are omitted. 15

19 Appendix Table 1. Variable Definitions and Summary Statistics Variable Definition Mean Std. Dev. Min Max Dependent GDP/N Secondary and tertiary sector GDP per worker (in thousand yuan) Independent N Secondary and tertiary sectors employment (census long form 10, in million) msgdp Ratio of secondary sector GDP to tertiary sector GDP gdp1 Primary sector share of GDP Capital/N Industrial fixed assets per worker (in thousand yuan) Market Potential (Pop-Weighted Distance) Population-weighted average distance to all other districts and counties (kilometers) Average Distance to 10 Largest Ports Port capacity weighted average distance to China s ten largest ports (kilometers) Average Years of Schooling Ratio of total education years to total residents Foreign-Domestic Industrial Output Ratio Industrial output of foreign invested firms over that of domestic firms Instrument 2000 Non-Agricultural hukou 2000 non-agricultural population (in million) Notes: Employment (workers by sectors) is from 2010 population census long form ( 10). Resident population is from 2010 population census. Average year of schooling is from 2010 population census. Market potential and port access are calculated based on Haversine formula and using latitude and longitude data from a GIS map of China. All other variables are either directly from or calculated (ratios, per worker/resident variables) using data in China City Statistical Yearbook 2011 together with employment and population data from 2010 population census Non-agricultural hukou is from China City Statistical Yearbook 2001 and Population Statistics of the People s Republic of China by County Number of observation is 286. Sources: MPS (2001); NBS (2011, 2012). 16