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Spatial frictions

People spend years of their lives shuffling from city to city and countless amounts of money sending goods along similar journeys – a result of so-called ‘spatial frictions’. This columns asks whether these frictions matter for the size distribution of cities, the sizes of individual cities, and the productivity of cities. The short answers are: no, yes, and it depends.

As of 2008, for the first time in history, more than half of the world’s populations live in cities. Understanding urbanisation and its affect on living standards is key for policymakers looking to make informed decisions in the years to come.

One issue for city dwellers is ‘spatial frictions’. The world is full of spatial frictions, as revealed by the costs of moving goods and people across space. These frictions influence where consumers and firms locate and how they interact. Trade frictions for shipping goods across cities induce consumers and firms to spatially concentrate to take advantage of large local markets.

At the same time, such a spatial concentration generates urban frictions within cities: people spend a lot of time on commuting – because of congestion and long commuting distances – and they pay high land rents.

Economists have studied these fundamental tradeoffs for decades, analysing how firms and workers choose their locations depending on the magnitudes of – and changes in – spatial frictions (Fujita et al 1999; Fujita and Thisse 2002). Still, little is known to date about how important urban and trade frictions are in shaping the urban structure of a country and in determining our standards of living.1 For example:

  • What would the US urban system look like if there were no spatial frictions?
  • Do spatial frictions matter for the size distribution of cities?
  • Do they affect the sizes of individual cities?
  • Do they contribute to the productivity advantage of large cities and to the nature of competition in cities?

Answering those questions is certainly a challenging endeavour, and it requires a consistent modelling approach that allows us to keep track of the complex interactions that arise in an urban system.

How do we go about it?

To address these questions, we develop and quantify a novel model of a system of cities that features both urban frictions and trade frictions, and in which city sizes, wages, as well as firms’ productivities and markups are all endogenously determined. Using data for 356 US metropolitan statistical areas (MSAs) in 2007, we structurally estimate the model’s parameters and conduct two counterfactual experiments. These two experiments aim at shedding some light on the quantitative importance of spatial frictions.

One important aspect of our rich multi-city framework is that it features multiple margins of adjustment. Given the distribution of population, changes in spatial frictions directly affect the productivity advantage of cities and the nature of competition in cities. Such changes in productivity and competition, in turn, induce changes in wages, rents, and prices, thereby affecting individual location decisions. Put differently, shocks to spatial frictions are absorbed into: productivity and competition, as in the recent trade literature; and population movements, as in the urban economics and new economic geography literatures. Putting those aspects together, our model provides an ideal laboratory for evaluating how changes in spatial frictions affect the size distribution of cities, the sizes of individual cities, productivity, and competition.

We would have little faith in our counterfactual predictions were our model a poor approximation of reality. We thus devote particular attention to consistently checking to what extent our framework can reproduce some of the empirical features observed at the MSA and firm levels. Overall, we find that our model fits the data quite well. For example, it replicates fairly well the observed patterns of aggregate land rents that are linked to urban frictions. It also replicates reasonably well the distribution of average wages across MSAs. Last, it goes quite a long way in matching available micro-evidence on the spatial structure of US firms' shipments (Hilberry and Hummels 2008; Holmes and Stevens 2010) that are linked to trade frictions, as well as the observed US size distribution of establishments in our 356 MSAs.

What are our key findings?

In our counterfactual analyses, we first explore what would happen in a first hypothetical scenario where commuting within cities is costless (no urban frictions). We then analyse a second hypothetical scenario where consumers face the same trade costs for local and nonlocal products (no trade frictions).

Our first question is: How important are those spatial frictions for the size distribution of cities? As shown in Figures 1 and 2, we find that neither type of frictions significantly affects the US city-size distribution. Even in a world without urban or trade frictions, that distribution would follow the rank-size rule – a strong empirical regularity – fairly well.2

Second, as depicted in Figures 3 and 4, we find that removing spatial frictions would change the sizes of some individual cities quite substantially within the stable distribution. Figures 3 and 4 further tell us that, without urban frictions, large congested cities like New York or cities close by (eg New Haven-Milford, CT) would gain population, while small isolated cities (eg Casper, WY) would lose population. In contrast, without trade frictions, large cities would shrink compared to small cities as good access to a large local market no longer matters in a world where shipping goods is basically costless. In total, about 4 million people would move across cities in the former and around 10 million people would move across cities in the latter case.

Figure 1. Rank-size rule, observed and counterfactual (no urban frictions)

Figure 2. Rank-size rule, observed and counterfactual (no trade frictions)

Figure 3. Changes in MSA populations and initial size (no urban frictions)

Figure 4. Changes in MSA populations and initial size (no trade frictions)

Last, turning to productivity and competition, Figures 5-8 summarise the changes in productivity and markups across cities for the two counterfactual scenarios. Eliminating trade frictions would lead to a whopping aggregate productivity gain of 68% and markup reductions of 40%, both of which are quite unevenly distributed across MSAs (see Figures 7 and 8). More remote US areas, in particular those outside the densely populated regions of New England and California, are those enjoying the largest productivity gains. The reason is that lower costs of shipping goods across space intensify competition and lead to the exit of the least productive firms. Eliminating urban frictions would generate smaller aggregate productivity gains of less than 1%, but still lead to a notable markup reduction of about 10%. The reason is that lower urban costs imply less resource waste for intra-city commuting, which in turn supports more firms in all cities even though these firms need not be, on average, more productive. The changes are again unevenly distributed across MSAs and follow a rich spatial pattern (see Figures 5 and 6). The most populated areas of the East and West coasts (LA, Seattle, New York, and Philadelphia) benefit the most.

Figure 5. Spatial distribution of productivity changes (no urban frictions)

Figure 6. Spatial distribution of markup changes (no urban frictions)

Figure 7. Spatial distribution of productivity changes (no trade frictions)

Figure 8. Spatial distribution of markup changes (no trade frictions)

What have we learned?

In a nutshell, spatial frictions do not matter for the size distribution of cities, they do matter for individual city sizes, and they do matter for productivity and competition to a different extent depending on the type of frictions we consider. Our findings have clear-cut implications, both for spatial theory and for economic policy. From a theoretical perspective, as far as the city-size distribution is concerned, our results suggest that we can abstract from either urban or trade frictions without loss of generality. The recent modelling strategies taken by eg Gabaix (1999), Eeckhout (2004), Duranton (2007), and Rossi-Hansberg and Wright (2007), where trade frictions are assumed away, therefore seem to provide good approximations. However, to explain the rise and fall of individual cities within the stable distribution requires a model that takes both types of spatial frictions into account. Our results also suggest that such a model may be needed to understand productivity and markup differences across cities, both of which loom large in the policy debate. Last, our framework is flexible enough to be brought to data for different countries and to be simulated for different scenarios such as investments in transportation infrastructure or urban mass-transit systems.


Behrens, K, G Mion, Y Murata, and J Südekum, "Spatial frictions", CEPR Discussion Paper 8572.

Combes, P-Ph and M Lafourcade (2011), “Competition, market access and economic geography: Structural estimation and predictions for France”, Regional Science and Urban Economics, forthcoming.

Desmet, K and E Rossi-Hansberg (2010), “Urban accounting and welfare”, CEPR Discussion Paper 8168, Centre for Economic Policy Research.

Duranton, G (2007), “Urban evolutions: the fast, the slow, and the still”, American Economic Review, 98:197-221.

Eeckhout, J (2004), “Gibrat's law for (all) cities”, American Economic Review, 94: 1429-1451.

Fujita, M, PR Krugman, and AJ Venables (1999), “The Spatial Economy: Cities, Regions and International Trade”, MIT Press.

Fujita, M and J-F Thisse (2002), “Economics of Agglomeration – Cities, Industrial Location, and Regional Growth”, Cambridge University Press.

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

Hanson, G (2005), “Market potential, increasing returns, and geographic concentration”, Journal of International Economics, 67:1-24.

Hillberry, R and D Hummels (2008), “Trade responses to geographic frictions: A decomposition using micro-data”, European Economic Review, 52:527-550.

Holmes, TJ and JJ Stevens (2010), “Exports, borders, distance, and plant size”, NBER Working Paper 16046, National Bureau for Economic Research.

Redding, SJ (2010), “The empirics of New Economic Geography”, Journal of Regional Science, 50:297--311.

Redding, SJ and D Sturm (2008), “The costs of remoteness: Evidence from German division and reunification”, American Economic Review, 98:1766-1797.

Rossi-Hansberg, E and M Wright (2007), “Urban structure and growth”, Review of Economic Studies, 74:597-624.


1 Our quantitative analysis contributes to both the recent empirical new economic geography and urban economics literatures. Although the former has made some important progress recently (eg Hanson 2005; Redding and Sturm 2008; Redding 2010; Combes and Lafourcade 2011), new economic geography models have still been confronted with data mostly in a reduced-form manner. It is fair to say that few attempts have been made to conduct comprehensive counterfactual experiments. One notable exception in the urban economics literature is the recent paper by Desmet and Rossi-Hansberg (2010).

2 The rank-size rule, also known as Zipf’s law, states that the size of a city is inversely proportional to its rank (in terms of population). For example, in the 2000 US Census, New York had 8,008,278 inhabitants, roughly twice as much as the second-ranked city Los Angeles (3,694,820 people), and roughly thrice as much as the third-ranked city Chicago (2,896,016 people).


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