Economic activity is highly unevenly distributed across space, as reflected in the existence of cities and the concentration of economic functions in specific locations within cities, such as Manhattan in New York and the Square Mile in London. The strength of the agglomeration and dispersion forces that underlie these concentrations of economic activity is central to a range of economic issues. The delicate balance between these two sets of forces helps to determine, for example, the incomes of mobile and immobile factors, the magnitude of investments, and both city and aggregate productivity. The impact of public policies differentiated by location (‘place-based policies’), and of transport infrastructure investments, local taxation and land regulation, is crucially determined by how these policies affect the equilibrium balance between these centripetal and centrifugal forces.

The complexity of modelling spatial interactions between agents has meant that the theoretical literature on economic geography (as synthesised in Fujita et al. 1999) has traditionally focused on stylised settings – such as a small number of symmetric locations – that cannot easily be taken to the data. More recent research has developed quantitative models of the spatial distribution of economic activity. These models are rich enough to incorporate first-order features of the data, such as large numbers of locations with heterogeneous geography, productivity, amenities, and local factors, as well as trade and commuting costs. They are also able to incorporate key interactions between locations such as trade in goods, migration, and commuting. Yet at the same time these models are sufficiently tractable as to enable quantitative counterfactuals to evaluate empirically meaningful policies and counterfactual scenarios. In recent work, we review this recent body of research that we group under the name ‘quantitative spatial economics’ (Redding and Rossi-Hansberg 2016). We highlight the key new theoretical and empirical insights, and discuss remaining challenges and potential areas for further research. We provide an extensive taxonomy of the different building blocks of quantitative spatial models used in the literature and discuss their properties.

A distinguishing feature of the study of economic geography relative to the study of international trade is that economic agents are typically assumed to be geographically mobile. Early theoretical research on ‘new economic geography’ concentrated on providing a fundamental theoretical explanation for the emergence of an uneven distribution of economic activity even on a featureless plain of ex ante identical locations. This theoretical literature highlighted the potential for multiple equilibria in location choices, in which each agent’s location choice depends on those of other agents in a mutually reinforcing process of cumulative causation. However, the complexity of these theoretical models limited the analysis to stylised spatial settings like a few locations, a circle, or a line. Therefore, the extent to which theoretical results for these stylised spatial settings would generalise qualitatively and quantitatively to more realistic environments was unclear.

Research in quantitative spatial economics shares many similarities with the earlier theoretical literature on economic geography. The mechanisms are typically the same, although there is greater scope to combine multiple mechanisms within a single framework. The broad questions are also largely the same. For example, how important is physical geography (e.g. mountains, coasts) versus economic geography (the location of agents relative to one another)? What is the impact of reductions in transport costs on the spatial distribution of economic activity? However, there are three key differences relative to the earlier theoretical research.

• First, this new research connects in a meaningful way with the observed data, and hence provides quantitative rather than qualitative answers to these questions.
  

The emphasis is therefore on combining, measuring and quantifying existing theoretical mechanisms. In contrast to the previous theoretical work, this research does not aim to provide a fundamental explanation for the agglomeration of economic activity, but instead aims to provide an empirically relevant quantitative model to perform general equilibrium counterfactual policy exercises. Agglomeration in these models is simply the result of exogenous local characteristics, augmented by endogenous economic mechanisms. These frameworks can accommodate many asymmetric locations that can differ from one another in terms of their productivity, amenities, and transport and mobility connections to one another.

• Second, this work identifies the key structural parameters that need to be estimated to undertake such quantification.
• Third, the meaningful connection with the data permits specificity in addressing counterfactual questions of interest to policymakers.
  

For example, if a railroad is built between these cities in this country at this time, what is the quantitative effect on these particular regions, sectors, and factors of production? This specificity not only can address important policy questions, but the ability to contrast the model’s predictions with real-life policy allows us to gauge the empirical importance of different theoretical mechanisms.

On top of the quantitative evaluation of specific counterfactuals and policy exercises, the existing research on quantitative spatial models has yielded two main general sets of insights relative to the earlier literature on economic geography. The first set of general insights are methodological. These include an improved understanding of the conditions for the existence and uniqueness of equilibrium in economic geography models (see in particular Allen and Arkolakis 2014), the conditions under which these models can be inverted to separate out the contributions of physical and economic geography to the observed spatial distribution of economic activity, and methods for undertaking counterfactuals to evaluate comparative statics with respect to changes in the model’s parameters. Perhaps even more important is that the literature has provided a set of model ‘components’ that allow us to introduce, in a unified theoretical framework, a large variety of agglomeration and congestion forces in a simple and practical way. Together these insights facilitate the quantification and measurement that is at the heart of this body of research.

The second set of general insights is substantive in terms of the quantitative importance of theoretical mechanisms.

• First, market access is an empirically relevant causal determinant of the spatial distribution of activity. Following the division of Germany after the end of the WWII, this mechanism can account for the observed decline in the relative size of West German cities close to the new border with East Germany of around one third (Redding and Sturm 2008). Changes in market access through goods trade can also explain the observed impact of the large-scale expansion of the railroad network in 19th century India (Donaldson 2016). Through the same mechanism, the removal of all railroads constructed up to 1890 in the US would have reduced the value of agricultural land by around 60% (Donaldson and Hornbeck 2016).
• Second, canonical models of urban economics (as in Lucas and Rossi-Hansberg 2002) can account quantitatively for the observed gradients of economic activity within cities (as in Ahlfeldt et al. 2015). The estimated parameter values imply substantial and highly localised agglomeration externalities, both for production and residential choices.
• Third, the local incidence of economic shocks is shaped in an important way by spatial linkages in goods and factor markets, which give rise to heterogeneous treatment effects of changes in the local economic environment (Monte et al. 2015) as well as heterogeneous aggregate implications of local shocks (Calando et al. 2014).
• Fourth, the distribution of economic activity across cities and regions is shaped in a quantitatively important way not only by productivity and amenity differences, but also by a number of other spatial frictions, such as local infrastructure and governance (e.g., Desmet and Rossi-Hansberg 2013, Behrens et al 2014).
• Fifth, the distribution of economic activity shapes the dynamics of local innovation and growth by determining the market size of firms.
  

This link is quantitatively relevant for understanding the evolution of the spatial distribution of economic activity over time (e.g. Desmet and Rossi-Hansberg 2014) and for the counterfactual dynamic response of the economy to global migration and trade policy changes, as well as global shocks such as climate change (e.g. Desmet and Rossi-Hansberg 2015, Desmet et al. 2016).

The literature on quantitative spatial economics has already achieved much. Nonetheless, there remain many areas where further research is needed. First, most research has continued to be concerned with the production and trade of goods, whereas much economic activity today is concentrated in services, whether tradable or non-tradable. Second, most of the main frameworks in the literature are static and abstract from the effect of spatial frictions on the evolution of the spatial distribution of economic activity and growth. Third, although there have been several influential studies of the sorting of heterogeneous workers and firms across geographic space, there remains scope for further work. Fourth, the economic analysis of the geography of firm and worker networks remains under-explored. We expect much progress along these and other dimensions over the coming years.

Ahlfeldt, G M, S J Redding, D M Sturm and N Wolf (2015) “The economics of density: Evidence from the Berlin Wall”, Econometrica, 83(6): 2127-2189.

Allen, T and C Arkolakis (2014) “Trade and the topography of the spatial economy”, Quarterly Journal of Economics, 129(3): 1085-1140.

Behrens, K, G Mion, Y Murata and J Südekum (2014) “Spatial frictions”, DICE Discussion Papers 160, Heinrich-Heine-Universität Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).

Caliendo, L, F Parro, E Rossi-Hansberg and P-D Sarte (2014) “The impact of regional and sectoral productivity changes on the US economy,” NBER, Working Paper 20168.

Desmet, K and E Rossi-Hansberg (2013) “Urban accounting and welfare”, American Economic Review, 103(6): 2296-2327.

Desmet, K and E Rossi-Hansberg (2014) “Spatial development”, American Economic Review, 104(4): 1211-1243.

Desmet, K and E Rossi-Hansberg (2015) “On the spatial economic impact of global warming”, Journal of Urban Economics, 88: 16-37.

Desmet, K, D K Nagy and E Rossi-Hansberg (2016) “The geography of development”, Princeton University, mimeograph.

Donaldson, D (2016) “Railroads of the Raj: Estimating the impact of transportation infrastructure?”,American Economic Review, forthcoming.

Donaldson, D and R Hornbeck (2016) “Railroads and American economic growth: A ‘market access’ approach”, Quarterly Journal of Economics, forthcoming.

Eaton, J and S Kortum (2002) “Technology, geography, and trade”, Econometrica, 70(5): 1741-1779.

Fujita, M, P R Krugman and A J Venables (1999) The Spatial Economy: Cities, Regions and International Trade, Cambridge: MIT Press.

Lucas, R E and E Rossi-Hansberg (2002) “On the internal structure of cities”, Econometrica, 70(4): 1445-76.

Monte, F, S J Redding and E Rossi-Hansberg (2015) “Commuting, migration and local employment elasticities”, NBER, Working Paper 21706.

Redding, S J and E Rossi-Hansberg (2016) “Quantitative spatial economics”, CEPR Discussion Paper 11500.

Redding, S J and D M Sturm (2008) “The costs of remoteness: Evidence from German division and reunification”, American Economic Review, 98(5): 1766-1797.