China’s inefficiently small cities: Perhaps Not?

John Gibson, Chao Li 23 July 2015

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A claimed legacy of China’s command economy era, and especially the hukou restrictions on labour mobility, is that there are too many cities with too few people. Important economic effects follow from this claim. For example, there seem to be larger gains from concentrating economic activity over space in China than in developed countries (Combes et al. 2013). Thus, China’s policymakers may have an incentive to try to manipulate the city size distribution so as to maximise benefits from urban agglomeration.

The costs of China’s inefficiently small cities appears high. The seminal paper by Au and Henderson (2006) estimated that the average city in China in the late 1990s lost 30% of net output per worker due to being smaller than the productivity-maximising peak size. The costs of being undersized were much greater than the costs of being oversized. 

Yet these previous studies may mislead because they use the wrong data to measure cities. Most studies on China measure cities by how many people have hukou household registration for that place, and not by who actually lives there. Recent urban arrivals without local hukou registration increasingly congregate in a few larger cities, so the count of local hukou holders wrongly makes cities seem too small and too evenly sized. Other studies measure city size by employment (such as Au and Henderson 2006), but do not note that employment data in the City Statistical Yearbooks that they use omit most private sector workers. These two errors are likely related since new urban residents without local hukou status are more likely to work in the private sector than in the state sector.

It is only since China’s 2010 population census that reliable city size estimates are available. In a recent paper, we use these more reliable measures to estimate the relationship between output per worker and city scale (Li and Gibson 2015). We report results for the urban districts (shiqu) of 286 prefectural cities – districts are the typical spatial unit studied by urban economists working on China, but we cover far more of the country than prior studies by including every prefectural city in the 2010 census except for Lhasa, which has incomplete data.

Do the data stand up to scrutiny?

A starting point to show effects of the errors in the previously used data is a log-log plot of city employment against city rank, using City Statistical Yearbook data (used in previous studies) and census data (Figure 1). The city rank-size distribution follows Zipf’s Law (which implies a slope of -1) more closely if the census is used, with a coefficient of -0.962 compared with ‑0.936 if the City Statistical Yearbook data are used.1 Zipf’s Law provides one benchmark for an efficient city size distribution (Gabaix 1999) so the closer fit using census data suggests that inferences about China’s apparently inefficient city size distribution may have been affected by errors in the data used. It is clear that the rank-size curve is shifted left if data from the City Statistical Yearbook are used – the employment estimates from this source average just 43% of the census record in the same year for the same cities.

Figure 1 Rank-size plots for China’s cities in 2010

Another feature apparent from Figure 1 is that it is the tails of very small and very large cities that diverge most from the linear fit of log rank on log size. To check that results are not due just to cities in the tails, the econometric estimates are weighted by city employment.

A generalised Leontief specification is used to relate non-agricultural output per worker to city scale, city industrial structure (the GDP share for the primary sector and the ratio of the share for the secondary sector to the share for the tertiary sector), capital per worker, and a vector of control variables that includes population-weighted distance to all other cities (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 labour quality), and the output of foreign-affiliated firms relative to domestic firms (to proxy for technology).

Rather than larger cities being more productive, it may be that causality goes the other way – being more productive, for whatever reason, causes a city to grow. The planned size of cities from China’s command economy era is a valid instrumental variable, and using this we find no significant endogenous quantity of labour bias. Therefore ordinary least squares is used to estimate the generalised Leontief model.

The econometric model allows the scale of each city to be compared with the estimated productivity-maximising scale, which is the peak point on a fitted inverted-U shaped relationship between output and scale. For most cities, the slope to the left of the peak is steeper than to the right, implying a bigger loss for undersized cities than for oversized cities. For example, employment in the city of Dongguan is 3 million over its peak point with a predicted output loss from being too big of just over 10%, while at 3 million below the peak the predicted output loss would be almost 50%.

We consider cities that are significantly over- or undersized according to whether the actual city scale is outside the 95% confidence interval surrounding the estimated scale that would maximise output per worker. There are roughly as many workers in significantly oversized cities as in significantly undersized cities, with 29% and 32% of workers in these two groups when using the weighted results, and 31% in the significantly oversized cities and 25% in the significantly undersized cities if using the unweighted results.

When city-level employment is measured using census data, we find a median loss of 8% in terms of net output per worker from a city not being at the peak point. The mean loss is 15%. These estimates are only half as large as those calculated by Au and Henderson (2006), who used the defective City Statistical Yearbook data that do not give a full count of employees. These differences in the estimates of net output loss per worker due to sub-optimal city scale persist throughout the distribution, as shown in Figure 2.

Figure 2 Comparing losses from sub-optimal city scale

Whether or not the results are weighted by city employment does not alter the key finding about the small size of losses due to sub-optimal city scale. In the weighted results, the modal loss category is 0-5%, which covers 37% of cities with 45% of workers. In the unweighted results, the 0-5% loss category has 44% of the cities with 42% of workers. A useful takeaway from these results is that four-fifths of cities are close to their productivity‑maximising scale, with net output losses of less than 25%, and these cities are home to over 80% of urban China’s workers.

Conclusions

The size of cities in China, and the effects of city size on productivity, are important topics for urban economists. But the data used in many previous studies do not stand up to scrutiny because they omit many workers. Using more comprehensive data on city employment from China’s 2010 census, we find no strong evidence to suggest that China has inefficiently small cities. Most cities are close to their productivity-maximising scale. In the cities that are not near their peak point, there are roughly as many workers in those that are too big as in those that are too small. China’s millions of new urban residents, who are not being tracked by statisticians (except in the census), seem to be reshaping the economic geography in ways that are reasonably consistent with productivity maximisation.

References

Au, C. and V. Henderson (2006), “Are Chinese cities too small?”, Review of Economic Studies 73(3), 549-576.

Combes, P. P., S. Démurger and S. Li (2013), “Urbanisation and Migration Externalities in China”, VoxEU.org, 9 July. 

Gabaix, X. (1999), “Zipf’s law for cities: an explanation”, The Quarterly Journal of Economics 114(3), 739-767.

Li, C. and J. Gibson (2015), “City scale and productivity in China”, Economics Letters 131, 86‑90. 

Endnotes

1 The difference is statistically significant at the p<0.001 level

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Topics:  Development

Tags:  China, cities, SEZs

Professor, Department of Economics, University of Waikato

PhD student, Waikato Management School, University of Waikato

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