CityReads | Benefits of Big City largely Go to the Elite

楼市 2024-06-14 21:12 上海

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Benefits of Living in Big City largely Go to the Elite

Any theory attempting to explain urban scaling must address the tail differences that arise from varying city sizes.

Arvidsson, M., Lovsjö, N. & Keuschnigg, M. Urban scaling laws arise from within-city inequalities. Nat Hum Behav 7, 365–374 (2023).

Source:https://doi.org/10.1038/s41562-022-01509-1

Picture source:

https://liu.se/en/news-item/storstadslivets-fordelar-endast-for-eliten#:~:text=Because%20of%20the%20greater%20diversity,learning%20opportunities%20in%20larger%20cities

Over the past decade, the field of urban science has developed a theory of quantitative urbanism, indicating that despite the complexity, diversity of human behavior, and geographical differences in cities around the world, there exists a power law (scaling law) between the urban population size and various characteristics of urban life (see CityReads | Life in the City Is Essentially One Giant Math Problem; CityReads | Scale: Simple Law of Organisms, Cities, and Companies).

Urban scaling law discusses how the characteristics of urban life change with the increase or decrease in city size. The power law can be expressed with an exponential formula and can be categorized into three types based on the size of the exponent: First, if the exponent equals 1, it indicates a linear change, meaning that the characteristic of urban life changes at the same rate as the city size. For example, the relationship between water or electricity consumption and population size is linear. Second, if the exponent is less than 1, it indicates a sublinear change, meaning that the characteristic of urban life grows at a slower rate than the city size. Urban infrastructure generally falls into this category, such as the number of gas stations, total road area, and the total length of power grid cables in relation to population size are all sublinear. Third, if the exponent is greater than 1, it indicates a superlinear change, meaning that the characteristic of urban life grows at a faster rate than the city size. Most economic activities fall into this category. For instance, the relationship between GDP and population size is superlinear. If a city's population doubles, or if we compare a large city with another city half its size, the former's GDP is more than twice that of the latter. Similarly, the relationships between private R&D employment and population size, and the number of new patents and population size are also superlinear.

The superlinear relationship between urban socioeconomic activities and city size has garnered particular attention, as it corroborates the agglomeration and scale effects of cities. Agglomeration effects are also one of the essential characteristics explaining the emergence of cities (CityReads | What Is the Nature of Cities). The economic benefits of urban agglomeration can be understood as mechanisms of sharing, matching, and learning. The larger the city, the stronger the agglomeration effect. There are many studies on the benefits of large cities, such as enhancing social networks (CityReads | Do we all live in “urban villages”?), providing learning opportunities, improving human capital, and increasing income (CityReads | Learning Advantages of Working in Big Cities; CityReads | Big Cities & Working Women), among others.

Researchers from Linköping University in Sweden published a paper in 2023 in the journal Nature Human Behaviour titled "Urban scaling laws arise from within-city inequalities." The paper highlights a deficiency in existing urban scaling theories studies, which overlook the inequalities within cities, and proposes that the superlinear outputs of urban socioeconomic activities largely depend on the extreme outcomes of a few elites. Using micro-level data from Sweden, Russia, and the United States, the paper points out that urban life characteristics, represented by urban interconnectivity, productivity, and innovation, exhibit heavy-tailed distributions. This means that the highest tail disproportionately contributes to the majority of the city's totals. These tail differences can explain much of the superlinear relationship between urban socioeconomic activities and city size. The paper also proposes that a city-size-dependent cumulative advantage mechanism constitutes the channel through which tail differences emerge.

The theoretical contribution of the paper lies in pointing out that any theory explaining urban scaling must consider the causal processes of the city's heavy-tailed distribution. The practical and policy significance of the paper is in highlighting that the agglomeration effects of cities benefit urban elites the most, while the majority of city residents are at least partially excluded from the socioeconomic benefits of urban growth.

Problems with Urban Scaling theory

The paper first points out that the issue with urban scaling lies in its strong homogeneity assumption. It assumes that the residents of a city have roughly the same number of social network connections and that companies in specific urban industries have similar economic complexity, thereby possessing roughly the same productivity levels. Based on this assumption, empirical research uses city totals and averages to analyze and explain the effects of urban scale, focusing on the "average" resident or business. The implicit assumption is that as the urban population grows, the scale effects are driven by homogeneous changes across the entire city's distribution.

However, human networks and productivity exhibit heavy-tailed distributions, meaning that a very small fraction of highly connected or highly successful individuals contribute to the majority of the city's total. Power laws are extremely common in nature and society, not only manifesting as scaling laws between cities but also as highly skewed distributions within cities. Therefore, using totals and averages as metrics for measuring relevant urban quantities is often inappropriate and even misleading.

Within-City Tailedness

Within-city tailedness refers to the relative contribution of the top ten percentiles (≥90%) in a city, reflecting the inequality within the city. If the typical resident or company in a city can be represented by the 50th percentile, then the city's tailedness can be represented by the highest 90th percentile and above.

The paper attempts to answer the following theoretical questions: Does within-city tailedness systematically differ by city size? How much of the superlinear power law can be attributed to differences in city tails? How much of the scaling differences between different categories of cities can be explained by tail differences? If within-city tailedness is crucial to scaling between cities, what mechanisms lead to tail differences by city size?

Urban Life Exhibits Heavy-Tailed Distributions, Especially in Large Cities

The figure below shows that, contrary to the homogeneity assumption implied by urban scaling laws, the distributions of connectivity, productivity, and innovation indicators within cities are highly skewed. Their tails increase with city size, exhibiting heavy-tailedness.

a, Interconnectivity: the number of online friendships on the Russian social media platform VKontakte in larger and smaller cities, and the degree of companies in employee-mobility networks in Stockholm and Göteborg (>1 million) and in Sweden’s smaller labour market areas (<100,000). b, Productivity: company revenue per employee and annual wage in Sweden. c, Innovation: the number of patents filed per inventor and the sum of research grants (US dollars) awarded to researchers in larger and smaller US Metropolitan Statistical Areas.

The role of city tails for superlinear scaling

If superlinear scaling is driven by mass rather than the tail, then removing the influence of the city tail on estimating the exponent coefficient should be negligible. However, excluding the top 10% of the most connected social media users in Russian cities and the top 10% of the most connected companies in Swedish cities results in a 43% and 44% reduction in the connectivity index, respectively. Similarly, removing the top 10% of the highest productivity companies and the top 10% of the highest income earners in Sweden reduces the productivity index by 60% and 31%, respectively. Excluding the top 10% of the highest productivity inventors and the top 10% of the highest funded researchers in Sweden reduces the innovation index by 38% and 32%, respectively.

If we use a city's typical social media user, company, wage earner, inventor, or funded researcher, i.e., selecting the 50th percentile individuals and companies to represent the city's average level, thereby smoothing out the city tail differences, we find that the exponents of various city indicators decrease by 36-80%. Therefore, most of the differences in superlinear scaling between urban indicators can be explained by tail differences. Tail differences play a crucial role in explaining superlinear power laws.

But, not everyone can access the productive social environments that larger cities provide. Different returns from context accumulate over time which gives rise to substantial inequality.

Micro-Level Mechanisms Behind Within-City Inequality and Urban Scaling

There are three explanatory mechanisms for the relationship between tail differences in city size, within-city inequality, and urban scaling:

1.How individual productivity depends on the local social environment and how this dependency affects agglomeration effects: Due to the greater diversity, specialization, and matching in large cities, scarce skills are often concentrated there. Technicians and professionals in large cities are more likely to find other professionals whose skills complement their own, thereby enhancing the productivity of economic activities.

2.The dynamic benefits of living in large cities: Large cities provide more learning opportunities, leading to higher average wages compared to smaller cities. However, the learning effects in large cities vary based on the attributes of the local social environment in which city residents live.

3.The randomness and path dependency in individual life courses: For example, an individual's current position in the labor market can significantly affect their future opportunities. When processes are random and exhibit path dependency, small differences accumulate over time, resulting in severe inequality at the collective level.

For highly skilled and knowledgeable individuals, large cities offer 1) complementary social environments and new opportunities for personal learning and growth. However, 2) the availability of these opportunities varies among different individuals, and 3) due to the randomness and path dependency of the process, differences accumulate over time.

However, not everyone benefits from the productive social environment that large cities provide. For low-skilled and non-professionals, large cities offer fewer additional interaction opportunities. Over time, the different returns from the environment accumulate, leading to severe inequality.

In summary, these three mechanisms lead to a city-size-dependent cumulative advantage mechanism. Large cities provide new opportunities necessary for continued growth but distribute them unevenly, generating tail differences in city size, which account for a significant portion of the overall differences in urban outputs.

Using micro-level data from 1.4 million Swedish wage earners, the paper categorizes them into "tail income earners" with the highest early-career wages (≥ 90th percentile) or "median income earners" in the 40-60th percentiles. It tracks the wage growth and mobility patterns of all those aged 30 and over from 1990 to 2007 over ten years. It finds that as they age, tail income earners exhibit a stronger exponential growth coefficient than median income earners. Supported by the city-size-dependent cumulative advantage mechanism, those who initially succeed in large cities thrive even more, far surpassing the typical individuals in large cities and the tail individuals in smaller cities, while the wage growth trajectories of typical individuals in small and large cities remain almost the same.

How significant is this difference? Assuming that tail income earners' wage growth rates were the same as those of median income earners with similar education levels in their respective cities, by preventing the cumulative advantage effect over ten years, tail differences would be reduced by 33%.

Conclusions

The assumption of urban scaling is that residents and businesses within the same city have similar levels of connectivity, productivity, and innovation, which overlooks the inequality within cities.

Urban scaling does not account for the heavy-tailed distribution characteristic of urban life. The tails systematically grow larger with city size, and explaining the causal processes behind these heavy tails constitutes a key element of urban scaling. Any theory attempting to explain urban scaling must address the tail differences that arise from varying city sizes.

Urbanization is not a panacea for social inequality. On the contrary, agglomeration effects particularly benefit urban elites who dominate the city's hierarchical structure. Their social networks and wealth are more dependent on the social environment provided by large cities. Meanwhile, the higher-than-expected output of large cities largely relies on the tail outcomes of a few elite individuals. Ignoring this dependency could lead policymakers to overestimate the stability of urban growth, especially considering the high spatial mobility of urban elites, their tendency to move to "wealthy places," and their reliance on specific industries and the long-term growth of these industries.

The city-size-dependent cumulative advantage mechanism operating at the micro level results in a "rich-get-richer" process at the city level, whereby most urban residents are partially excluded from the socioeconomic benefits of growing cities. Considering the cost of living in large cities, many urban residents are actually worse off compared to residents with similar socioeconomic status living in smaller cities.

CityQuotes

1."In people's eyes, in the swing, tramp, and trudge; in the bellow and the uproar; the carriages, motor cars, omnibuses, vans, sandwich men shuffling and swinging; brass bands; barrel organs; in the triumph and the jingle and the strange high singing of some aeroplane overhead was what she loved; life; London; this moment of June." — Virginia Woolf, Mrs. Dalloway

2."Books are not only the arbitrary sum of our dreams, and our memory. They also give us the model of self-transcendence. Some people think of reading only as a kind of escape: an escape from the "real" everyday world to an imaginary world, the world of books. Books are much more. They are a way of being fully human."— Susan Sontag, Where the Stress Falls

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