Archive for the ‘Economic geography’ Category

“Large cities” in the EU and US, redux

12 October 2012

The Economist is six months late to the party, but the latest print edition has a piece on that McKinsey comparison of American and Europe cities. I have some quibbles, again.

I don’t understand the piece’s opening, though it has little to do with what follows. It begins:

AMERICA is full of vast, empty spaces. Europe, by contrast, seems chock-a-block with humanity, its history shaped by a lack of continental elbowroom. Ironically, Europe’s congestion partly reflects the fact that its large cities suck up relatively few people.

Moving people across cities wouldn’t change the (unweighted) average population density of the US or EU, so what does this comparison mean? Europe is going to be full of humanity because the land area of the EU is roughly half that of the continguous US (1.7m vs 3.1m square miles). Since larger cities are generally denser, the population-weighted density of Europe would rise if its large cities had higher population shares.

Never mind the elbowroom. The Economist continues:

Although America and the euro zone have similar total populations, America’s 50 largest metropolitan areas are home to 164m people, compared with just 102m in the euro area. This striking disparity has big consequences.

Differences in metropolitan populations may help explain gaps in productivity and incomes. Western Europe’s per-person GDP is 72% of America’s, on a purchasing-power-parity basis. A recent study by the McKinsey Global Institute, the consultancy’s research arm, reckons that some three-quarters of this gap can be chalked up to Europe’s relatively diminutive cities. More Americans than Europeans live in big cities: there is a particular divergence in the size of each region’s “middleweight” cities, those that teem just a little less than the likes of New York and Paris (see chart). And the premium earned by Americans in large cities relative to those in the countryside is larger than that earned by urban Europeans.

As I explained back in April, the MGI report does not say Europeans would reach American prosperity levels if the population shares of their large cities reached American levels:

The gap in per capita GDP between the US and Europe is about 35%, according to the MGI figures in Exhibit 2. The “large city” premia in the United States and Europe of 34% and 30% are virtually the same. That means that the difference in per capita income attributable to the difference in “large city” population shares is the large city premium (~30pp) times the difference in large city population shares (22pp). The six to seven percentage points explained by this difference in population shares is at best one-fifth of the 35% gap between US and EU incomes. You can confirm this quick calculation by studying the decomposition in MGI’s Exhibit 2. Moving more people into large cities wouldn’t meaningfully reduce the US-EU per capita income gap.

Look at Exhibit 2 for yourself:

The Economist mentions the big-city population share and big-city premium components. They neglect that 53 of those 74 percentage points are strictly attributable to the difference in average income. Differences in metropolitan populations are not at the heart of the story.

After citing all the advantages of cities, the Economist considers two reasons why European cities aren’t as large as US cities: regulatory barriers and incomplete integration. While the former might matter, I put a lot of stock in the latter. As I explained in my prior post, Zipf’s law holds at the country level. Since no European state has a population close to 300 million, we should not expect any European city to approach the size of NYC or LA. Until intra-European mobility looks anything like intra-US mobility, I think we should expect Zipf’s law to hold at the country level. And since MGI used a common cutoff of population > 150,000 for defining a “large city”, it’s not at all surprising that a larger share of the US population lives in its large cities. I wrote before:

Given the UK population, increasing the fraction of UK residents who live in “large cities” with populations greater than 150,000 would require the emptying out of smaller metropolitan areas. While such migration is entirely possible, it would violate the expected city size distribution… If you know the populations of New York and London and are familiar with Zipf’s law, then it’s not at all surprising that a greater fraction of the US population is found in metropolitan areas above some common population threshold. I don’t think that tells us much about the economic mechanisms determining the role of US cities in the global economy.

Update: Related to my comparison of US and UK city-size distributions, see Henry Overman on the details of Zipf’s law for UK cities.

Changes in urbanisation and income

3 October 2012

from the Economist:

Cross-country comparisons of large cities

20 April 2012

A number of people have highlighted a new McKinsey Global Institute report on US cities in the global economy.

Here’s the MGI summary:

In a world of rising urbanization, the degree of economic vigor that the economy of the United States derives from its cities is unmatched by any other region of the globe. Large US cities, defined here as those with 150,000 or more inhabitants, generated almost 85 percent of the country’s GDP in 2010, compared with 78 percent for large cities in China and just under 65 percent for those in Western Europe during the same period. In the next 15 years, the 259 large US cities are expected to generate more than 10 percent of global GDP growth—a share bigger than that of all such cities in other developed countries combined.

I find this definition of a “large city” to be puzzling. I’ve searched the report for the word “150,000″ and the authors don’t seem to have provided an explanation for this measurement choice. That’s unfortunate, because using this cutoff for cross-country comparisons has big implications that may lead readers astray. But before we get into those measurement details, let’s just make clear what the report’s executive summary does and doesn’t say.

At Ezra Klein’s place, Brad Plumer says:

The report’s authors argue that the city gap between the United States and Europe account for about three-quarters of the difference in per capita GDP between the two. In other words, the United States appears to be wealthier than Europe because it has a greater share of its population living in large, productive cities.

That second sentence isn’t plausible. Look at Exhibit 1 in the McKinsey report, which I’ve reproduced here:

 

The gap in per capita GDP between the US and Europe is about 35%, according to the MGI figures in Exhibit 2. The “large city” premia in the United States and Europe of 34% and 30% are virtually the same. That means that the difference in per capita income attributable to the difference in “large city” population shares is the large city premium (~30pp) times the difference in large city population shares (22pp). The six to seven percentage points explained by this difference in population shares is at best one-fifth of the 35% gap between US and EU incomes. You can confirm this quick calculation by studying the decomposition in MGI’s Exhibit 2. Moving more people into large cities wouldn’t meaningfully reduce the US-EU per capita income gap.

Over at Atlantic Cities, Nate Berg summarizes Exhibit 1 as “though cities all over the world are responsible for major contributions to the global gross domestic product, the concentration of large – and especially semi-large – cities in the U.S. outperforms them all.” He quickly notes that “the sheer number of large cities in the U.S. is clearly a major part of the difference, especially with about 80 percent of the country’s population concentrated in these metropolitan regions.” In fact, it’s more than a major part of the difference – it’s basically all of it.

“Large city” economic output is a larger share of total economic output in the United States because “large city” population is a larger share of population in the United States. US “large cities” have 80% of the US population and produce 84% of US output. European “large cities” have 58% of their population and produce 64% of their output. If “large cities” are more important to GDP in the United States (or in Plumer’s interpretation the US “derives more economic benefit from its cities than any other country on the planet”), it’s because a larger fraction of the population lives there.

This is a statistical artifact created by using the same population cutoff to define “large cities” in countries with quite different national populations. It’s not clear that telling us that a greater share of Americans live in metropolitan areas with populations greater than 150,000 than Europeans tell us that these economies operate differently.

The typical country’s city size distribution is decently characterized by a power law, Zipf’s law, which implies a log-linear relationship between a city’s size and its rank in the size distribution. Zipf’s law doesn’t hold for the entire distribution, but we know from Rozenfeld, Rybski, Gabaix & Makse (AER 2011) that it’s a decent approximation for places with more than 10,000 or so people in both the US and UK.

I’ve displayed the city size distributions for both the US and UK in the figure below. The US distribution stops around 10.8 because only 280 (consolidated) metropolitan areas were defined in 2000. Rozenfeld et al have shown that it’s safely to linearly extrapolate down to something like 9.4.

 

 

Given the UK population, increasing the fraction of UK residents who live in “large cities” with populations greater than 150,000 would require the emptying out of smaller metropolitan areas. While such migration is entirely possible, it would violate the expected city size distribution. We don’t see such top-heavy city size distributions in economies with a decent number of cities (of course, city-states like Singapore violate Zipf’s law). If you know the populations of New York and London and are familiar with Zipf’s law, then it’s not at all surprising that a greater fraction of the US population is found in metropolitan areas above some common population threshold. I don’t think that tells us much about the economic mechanisms determining the role of US cities in the global economy.

Addendum: The MGI report compares Western Europe to the United States, but Zipf’s law holds at the country level. Using Western Europe, which has an aggregate population akin to that of the US, doesn’t give us reason to expect  a similar share of the population to live in cities with populations exceeding 150,000. There is no Western European city the size of Los Angeles or New York. [Thanks to @ptitseb for suggesting this clarification.]

Moretti – “The New Geography of Jobs”

17 April 2012

Enrico Moretti has written a book that’ll be released in about a month. It’s titled The New Geography of Jobs.

The distribution of Chinese city sizes

28 September 2010

The Economist‘s Economics Focus column looks at Chinese cities and manages to discuss the distribution of city sizes while avoiding the phrase “Zipf’s law”.

China makes a habit of bending the rules of economics. Do its cities obey the rank-size rule? The fit is not perfect. China’s small cities are too dispersed and its big cities are too even in size…

Messrs Xu and Zhu show that China’s cities became more equal during the 1990s, especially in the first half of the decade…

China’s small cities exploded in number. But its biggest metropolises conspicuously failed to explode in size. As BCG notes, only 27m Chinese live in cities of more than 10m, compared with 58m Indians and 32m Brazilians. Shanghai may have sprouted dozens of skyscrapers and Beijing may boast half a dozen ring roads, but China’s big cities are still surprisingly small.

This partly reflects a conscious policy. Although China’s rulers have embraced urbanisation, they still seem wary of mega-cities…

China’s economy would benefit from a stretching out of the distribution of its cities, argue Ting Jiang of Hong Kong University of Science and Technology and co-authors. But how might such a divergence come about? It might, they speculate, happen as an unintended consequence of the government’s push to expand higher education. Since the bigger cities have the most universities, their expansion will draw youngsters from the hinterland to the metropolis. And with a degree (and a job), their graduates should win permission to stay.

Xu and Zhu, “Urban Growth Determinants in China“, Chinese Economy, 2008.

[HT: Alejo]

Glaeser: Triumph of the City

18 September 2010

Ed Glaeser has a book coming out in February titled Triumph of the City: How Our Greatest Invention Makes Us Richer, Smarter, Greener, Healthier, and Happier.

What border effect?

15 January 2010

Hillberry & Hummels “Trade responses to geographic frictions: A decomposition using micro-data” (European Economic Review, 2008):

The highly non-linear effect of distance on trade may help explain some results in the ‘‘home bias’’ literature. While our estimates on 3-digit zip code data reveal that intra-state shipments are significantly higher than cross-state shipments, this effect disappears entirely when shipment distances are measured more accurately using 5-digit zip codes. We instead find that the ‘‘borders’’ between 5-digit zip codes represent a sizeable barrier to trade. We consider these zip-code effects the reductio ad absurdum of the home bias literature. While one can imagine many barriers to trade that operate at national borders, it is harder to conceive of what barriers plausibly operate at state borders, and harder still to imagine those associated with 5-digit zip codes. Our results suggest that ‘‘home bias,’’ at least in state borders, is an artifact of geographic aggregation. Since shipments drop off extraordinarily rapidly over very short distances, attempts to measure border effects on larger geographical groupings are nearly certain to ascribe the non-linear effects of distance to ‘‘home bias’’ dummy variables.

Measuring distance

11 November 2009

Neat:

The CEPII has built and made available two datasets providing useful data for empirical economic research including geographical elements and variables. A common use of these files is the estimation by trade economists of gravity equations describing bilateral patterns of trade flows…

Distance calculation requires information on geographical coordinates of at least one city in each of the country. The simplest measure of geodesic distance considers only the main city of the country, reported here with the English and French names, latitude and longitude. In most cases, the main city is the capital of the country. However, for 13 out of the 225 countries, we considered that the capital was not populated enough to represent the “economic center” of the country. For these countries, we propose the distances data calculated for both the capital city and the economic center…

There are two kinds of distance measures: simple distances, for which only one city is necessary to calculate international distances; and weighted distances, for which we need data on the principal cities in each country. The simple distances are calculated following the great circle formula, which uses latitudes and longitudes of the most important city (in terms of population) or of its official capital. These two variables incorporate internal distances based on areas provided in the geo_cepii.xls file. The two weighted distance measures use city-level data to assess the geographic distribution of population inside each nation. The idea is to calculate distance between two countries based on bilateral distances between the largest cities of those two countries, those inter-city distances being weighted by the share of the city in the overall country’s population.

Distance and internet communication

21 October 2009

Jacob Goldenberg & Moshe Levy:

while technology has undoubtedly increased the overall level of communication, this increase has been most pronounced for local social ties. We show that the volume of electronic communications is inversely proportional to geographic distance, following a Power Law. We directly study the importance of physical proximity in social interactions by analyzing the spatial dissemination of new baby names. Counter-intuitively, and in line with the above argument, the importance of geographic proximity has dramatically increased with the internet revolution.

Via Free Exchange.

Trade costs between cities

6 July 2009

Ed Glaeser is pretty blasé about some intranational trade costs in this paragraph:

The national high-speed rail agenda is being pushed with claims that these trains will jump-start economic growth. No serious evidence supports such claims. When new transportation does affect local economies, it generally does so by moving activity from one place to another, not by creating nationwide benefits.

Better intercity transit shifts economic activity with no gains from economic reorganization? That’s not what economists usually expect from falling trade costs. Professor Glaeser is an expert on economic geography and urban economics, so there’s probably some research or theory behind that claim – I wish he wrote link-filled blog posts rather than Boston Globe columns.

Hat tip: Avent.


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