<!-- class: inverse, center, title-slide, middle --> class: center, middle <style> g { color: rgb(0,130,155) } r { color: rgb(174,77,41) } y { color: rgb(177,148,40) } </style> # Lecture 08: Geospatial Data Sciences # and Economic Spatial Models ## <img src="figs/bse_primary_logo.png" style="width: 35%" /><br><br>Bruno Conte ## 25-26/Feb/2026 --- # Geospatial Data and Spatial Models: Schedule 1. ~~Introduction to (spatial) data and programming in `R`~~ **[08/Jan/2026]** 2. ~~Week 2-4: Vector spatial data~~ **[14 - 29/Jan/2026]** 3. ~~Week 5-7: Raster spatial data + (basic) interactive tools~~ **[05 - 19/Feb/2026]** 4. Week 8-10: Spatial models and applications with data **[25/Feb - 12 Mar/2026]** - Week 8: Introduction to economic spatial models - Week 9: Linking models to (spatial) data - Week 10: Models, data, and counterfactual simulations<br> <br> 5. <span style="color: rgb(177,148,40)">Take-home exam</span> **[27/Mar/2026]** --- # Essential Reading 1. Fujita, M., P. Krugman, and A. Venables (1999) The Spatial Economy: Cities, Regions and International Trade, MIT Press, Chapters 4, 5 and 14 2. Allen, Treb and Costas Arkolakis (2014) "Trade and the Topography of the Spatial Economy," *Quarterly Journal of Economics*, 129(3), 1085-1140 3. Redding, S.J. and Rossi-Hansberg, E., 2017. Quantitative spatial economics. *Annual Review of Economics*, 9, pp.21-58. 4. Donaldson, D., 2022. Blending Theory and Data: A Space Odyssey. *Journal of Economic Perspectives*, 36(3), pp.185-210. --- # Food for thought Lecture notes on spatial economics (<g>inspiration for this lecture</g>): - Steve Redding's lectures on Spatial Economics - Esteban Rossi-Hansberg lectures on International Trade - Treb Allen's notes on Trade and Geography - Costas Arkolakis' class material on the Economics of Space - Dávid Nagy: "*Geography matters, but how much? Making economic geography a quantitative field*" --- # Motivation - Until the early 1990s, economic geography was (relatively) out of mainstream economic's radar - Nevertheless, production, trade and income are <g>differently distributed</g> across the space 1. <r>Agglomeration in cities</r> `\(\sim\)` 50 per cent of world's population, expected to sharply increase 2. Geographical <g>sectoral specialization</g> (e.g. soybean production in Brazil, Silicon Valley in the US, manufacturing in China, ...) - Since mid-1990's, an ever-growing number of (quantitative) studies established the field of spatial economics --- # Motivation - What is <r>spatial economics</r>? - Distribution of economic activity across the geography - First-order geography - Physical aspects: forests, coasts, montains, natural endowments, etc. - Second-order geography - Spatial aspects of economic mechanisms (spatial interaction of agents) - Spatial economics: <g>focus on second-order</g> geography - How the relationship between of agents across the space determine their (spatial) actions and (distributional and aggregate) welfare --- # Motivation - How do second-order geography affect economic choices and outcomes? - Several <g>frictions are spatial</g> by nature: - Transport costs - Mobility barriers - Traffic congestion - Pollution spillovers - Several <r>shocks are also spatial</r>: - Construction of transportation infrastructure - Political borders changes (e.g. European Union) - Climate change - Shocks affect economic agents' choices based on (spatial) frictions --- # This Class <r>**Introduce spatial economics**</r> and the spatial propagation of shocks 1. Introduction: a canonical <g>spatial model</g> (Redding, 2016) 2. Three recent applications: - Caliendo et al. (2018): spatial diffusion of productivity shocks - Donaldson (2018): welfare impacts of transportation infrastructure Common aspect: <g>theory + empirics</g> = <y>quantification + counterfactuals</y> --- class: center, middle # Introduction and the # Canonical Model --- # Introduction - Marshal (1890): first observations on specific aspects about the geographical location of economic activity - <g>Agglomeration in cities</g> and the role of agglomeration externalities - Factor (or labor) pooling, reduced trade costs, knowledge spillovers - Main pillars of urban economics (Henderson, Glaeser, among others) - Idea of agglomeration forces shaping <r>spatial economic activity</r> applies also across countries: - Fujita, Krugman, Helpman, Venables established the (new) economic geography as a field (the shoulder of giants) --- # Introduction Starting from the 2000's, there was a <g>revolution in the field</g> following theoretical, technological, and empirical advances - Theoretical: introduction of Ricardian forces into rich, yet <g>tractable models</g> (Eaton and Kortum, 2002) - Arbitrary number of asymetric locations (i.e., distributions of endowmnents, population, transportation costs,etc.) - Technological and empirical: advances in CPU power, <r>data availability</r> and technology (e.g. data sciences) - Feasibility to solve increasingly more complex mathmatical problems (models) - Immense availability of data at fine geographical resolution (within countries) - Main exponents: Ahlfeldt, Arkolakis, Donaldson, Rossi-Hansberg, Redding --- # A Spatial GE Model: Environment In what follows, I introduce the basics of the spatial model of Redding (2016) - `\(N\)` locations `\(n,i,s \in S = \{1,...,N\}\)` that are (potentially) asymetric with respect to - Land supply `\(H_n\)` - Productivity `\(A_n\)` - Amenties `\(B_n\)` - Geographical location (relative) - The economy is endowed with an initial `\(\mathcal{L} = \sum_{n \in S} L_n\)` population and produces a continuum of `\(j\)` varieties of a representative good - Static framework: `\(\mathcal{L}\)` workers "fall from the sky" and make them economic choices (e.g. production, consumption, location, trade) --- # A Spatial GE Model: Preferences Agents have <g>heterogeneous preferences</g>; worker `\(\omega\)` living in `\(n\)` enjoys $$ U_n(\omega) = b_n(\omega) C_n(\omega)^\alpha H_n(\omega)^{1-\alpha} \text{, where}\\ C_n = \left( \int c_n(j)^\rho dj \right)^{1/\rho} $$ is the consumption basket of the infinite `\(j\)` varieties in the economy `\((\rho \equiv \text{CES})\)`. `\(H_n(\omega)\)` is the per capita consumption of land (housing), and $$ b_n(v) \sim G_n = e^{-B_n v^\epsilon} $$ captures the <r>idiosyncratic location preferences</r> of workers in the economy. --- # A Spatial GE Model: Technology Firms face perfect competition and produce varieties `\(j\)` with a linear production function of labor $$ q_n(j) = z_n(j) L_n(j) \text{, where} \\ z_n(j) \sim F_n(z) = e^{-A_n z^{-\theta}} $$ is a productivity shifter that captures <g>firm heterogeneity</g> within `\(n\)`. Thus, `\(j\)` variety, if produced in `\(i\)` and traded with (consumed at) `\(n\)`, will be priced as `$$p_{ni}(j) = w_i d_{ni} / z_i(j) \text{, where}$$` `\(w_i \equiv\)` factor prices and `\(d_{ni} \equiv\)` <r>trade frictions</r> between the trade pairs --- # A Spatial GE Model: Implications **Nominal and real income.** Homogeneous consumption preferences imply that consumption equals real income; i.e. $$ C_n(\omega)^\alpha H_n(\omega)^{1-\alpha} = v_n / \mathcal{P}_n \text{, where} $$ `\(v_n = (w_n L_n + r_n H_n)/L_n \equiv\)` nominal income per capita and `\(\mathcal{P}_n \equiv\)` is the <g>price index</g>: an aggregate of land prices good prices: `$$\mathcal{P}_n = P_n^\alpha \times r_n^{1-\alpha} \text{, where}$$` `$$P_n = \left(\int p_{n}(j)^{1-\sigma}\right)^{\frac{1}{1-\sigma}}, \quad \sigma = \frac{1}{1-\rho}$$` is the <r>good's price index</r> --- # A Spatial GE Model: Implications **Location Choice.** Indirect utility becomes `$$U_n(\omega) = b_n(\omega) \times (v_n / \mathcal{P}_n);$$` worker `\(\omega\)` observe real incomes across space and choose `\(n\)` that maximizes utility. By the properties of `\(b_n(\omega)\)`, <g>location choice probabilities</g> are: `$$\lambda_n = \frac{L_n}{\mathcal{L}} = \frac{B_n (v_n / \mathcal{P}_n)^\epsilon}{\sum_i B_i (v_i / \mathcal{P}_i)^\epsilon} \iff L_n = \lambda_n \mathcal{L}$$` --- # A Spatial GE Model: Implications **Export Shares and Trade.** The export probabilities of goods from `\(i\)` to `\(n\)` is `$$\pi_{ni} = \frac{A_i \left( w_i d_{ni} \right)^{-\theta}}{\sum_{s \in S} A_s \left(w_s d_{ns} \right)^{-\theta}} = \gamma A_i \left( w_i d_{ni} \right)^{-\theta} P_n^\theta \text{, where}$$` `$$P_n = \gamma \left[ \sum_{i \in S} A_i (w_i d_{ni})^{-\theta} \right]^{-1/\theta}$$` is the goods' price index - equivalent to price index above - and `\(\gamma\)` is a constant. Note that the <g>price index depends on prices in all locations</g> (thus, real incomes)! --- # A Spatial GE Model: Equilibrium Given a <g>geography</g> `\(\{ A_n, B_n, H_n, d_{ni} \}_{n,i \in S}\)` and <r>structural parameters</r> `\(\{ \alpha , \rho , \theta , \epsilon\}\)`, a spatial equilibrium is `\(\{ w_n , L_n \}_{n \in S}\)` such that 1. Markets clear (trade balance): `\(X_i = \sum_{n \in S} \pi_{ni} v_n L_n\)` `\(\forall i\)` 2. Optimal location choice: `\(L_n = \lambda_n \mathcal{L}\)` Ultimately, it is a system of `\(N \times 2\)` equations and unknowns that can be solved for with an iterative algorithm (see Allen and Arkolakis, 2014) --- # A Spatial GE Model: Quantification When connecting these models with real-world data, one needs to quantify both 1. Structural parameters `\(\{ \alpha , \rho , \theta , \epsilon\}\)`; i.e. elasticities that discipline the <g>sensitivity of agents' choices</g> to the characteritics of (or shocks to) the geography - Similar estimation from other fields (e.g. exogenous variation for identification) - Model's fundamentals `\(\{ A_n, B_n, H_n, d_{ni} \}_{n,i \in S}\)`; i.e. <r>geographical distribution of primitives</r> with which economic forces interact - Particular method that requires models to be exactly identified (i.e. find the distribution of fundamentals such that the model identically fits data) The following three papers illustrate distinct quantification pieces/methods of the canonical model and applications of the quantified model --- class: center, middle # Three Application of # Spatial Models --- # Application 1: Trade linkages and spatial propagation of shocks (Caliendo et al., 2018) - How do economic <g>shocks propagate</g> through trade networks? - Relevant question for current (globalized) economy; recent salient events - China (import competition) shock, Suez Canal, Covid, Russia-Ukraine,... - However, shocks need not be negative - Silicon Valley, California; discovery of natural resources (Brazil, 2010s; fracking gas, US), ... - <u>Question:</u> how do US <r>interregional</r> and <y>intersectoral</y> trade linkages propagate shocks throughout its economy? - Importance: uneven distribution of (sectoral) economic activity (growth) in early 21st century --- .center[ Figure: Uneven distribution of economic activity (growth) in the US <img src="figs/zz_caliendo_1.png" style="width: 80%" /> ] --- .center[ Figure: Uneven distribution of economic activity (growth) in the US <img src="figs/zz_caliendo_2.png" style="width: 80%" /> ] --- # Application 1: Trade linkages and spatial propagation of shocks (Caliendo et al., 2018) - <r>Differences</r> with respect to the canonical model: - Multisector economy, intersector (input-output) linkages in production, multifactor production (labor, land, intermediates) - Trade imbalances (states can run into deficits) - Add tradables as well as non-tradable goods - Much richer environment! - Wide set of potential <g>counterfactuals</g> (positive and negative shocks) - However, large set of fundamentals and parameters to quantify --- # Application 1: Trade linkages and spatial propagation of shocks (Caliendo et al., 2018) - <r>Innovations</r> for quantification and/or counterfactuals: <g>hat algebra</g> `\((\hat{x} = x' / x)\)` - Instead of quantifying all needed "ingredients", solve the model in <y>differences</y> - Many time invarying parameters (like geographical) will not be needed - Application: <g>TFP impacts</g> of productivity shocks in the economy `$$\Delta \text{TFP}_n = \log \hat{\text{TFP}}_n = \log \hat{A}_n - \log \hat{P}_n^{1/\theta} \text{; recall}$$` `$$P_n = \gamma \left[ \sum_{i \in S} A_i (w_i d_{ni})^{-\theta} \right]^{-1/\theta} \text{(in levels).}$$` - Thus, a shock in `\(i\)` <u>propagates to</u> `\(n\)` through `\(d_{ni}\)` (the trade link)! --- .center[ Figure: Uneven impacts of productivity boom in California <img src="figs/zz_caliendo_3.png" style="width: 80%" /> ] --- .center[ Figure: Uneven impacts of Hurricane Katrina <img src="figs/zz_caliendo_4.png" style="width: 80%" /> ] --- # Application 2: Welfare impacts of transportation infrastructure (Donaldson, 2018) - Well established <g>gains from trade integration</g> from international trade theory - What about intranational gains? - What about developing, rural economies? - The British rule in India (the Raj): unique setting to study welfare gains of large scale <r>intranational integration</r> (railroad expansion) - <u>Question:</u> how large, and what explains, the benefits of large-scale infrastructure investments in rural economies? --- .center[ <br> Figure: Evolution of railroad infrastructure in India during the British Rule <br> <img src="figs/zz_donaldson_1.png" style="width: 45%" /> <img src="figs/zz_donaldson_2.png" style="width: 45%" /> ] --- # Application 2: Welfare impacts of transportation infrastructure (Donaldson, 2018) <g>Differences</g> with respect to the canonical model: - Multisector economy - Land as factor of production (rural economy) - Dismiss labor as factor (and mobility) Immense <r>data collection</r> (especially for a developing country): - Evolution of railroads' network India for `\(\sim\)` century - Data on prices, trade, and rural (land) income <y>across space and time</y> --- # Application 2: Welfare impacts of transportation infrastructure (Donaldson, 2018) - <r>Innovation</r> for <g>quantification of trade frictions</g> `\(d_{ni} \propto \text{railroad distance})\)` - Use spatial-time variation in bilateral distances and prices for identification `$$p_{ni} \propto \left( w_i /A_i \right) d_{ni} \quad \rightarrow \quad \log p_{ni} - \log p_{ii} = \log d_{ni}$$` `$$\log p_{ni,t} = \underbrace{\beta_{i,t}}_{\log p_{nn,t}}+ \underbrace{\beta_{n,t} + \delta \times \log \text{dist}(n,i)_t + \varepsilon_{ni,t}}_{\log d_{ni,t}}$$` - Use the result to quantify the <r>role of transportation expansion on welfare</r> (rural) income gains in India with the spatial GE model --- # Other (very nice) applications of Spatial Models - Role of (within city) transportation expansion (trains and tube) - Heblich et al. (2020): expansion from mid-1800 in London - Interaction with residential and commuting decisions - Exogenous variation (IV) to identify commuting elasticity `\((\epsilon)\)` - Pellegrina and Sotelo (2021): spatial diffusion of knowledge (by migrants) - Albert and Monràs (2022): migration, remittances, and residential choices - Monte et al. (2018): labor demand shocks (opening of large firms) - Heblich et al. (2021): role of spatial diffusion of pollution on long term development in the UK --- class: center, middle # Final Remarks --- # Final Remarks - Spatial Economics: rich combination of theory and data - Theoretical tractability: use models as macro laboratories for what-if questions (counterfactuals) - Current frontier - Dynamics (link to dynamic, discrete choie models) - Market failures and externalities (e.g. moral hazard) - Nested choices (investment, technology, capital accumulation) Any <r>questions?</r> --- # References - Albert, Christoph and Joan Monras, "Immigration and spatial equilibrium: the role of expenditures in the country of origin," *American Economic Review*, 2022, 112 (11), 3763–3802. - Allen, Treb and Costas Arkolakis, "Trade and the Topography of the Spatial Economy," *The Quarterly Journal of Economics*, 2014, 129 (3), 1085–1140. - Caliendo, Lorenzo, Fernando Parro, Esteban Rossi-Hansberg, and Pierre-Daniel Sarte, "The impact of regional and sectoral productivity changes on the US economy," *The Review of economic studies*, 2018, 85 (4), 2042–2096. - Conte, Bruno, “Climate change and migration: the case of africa,” 2023. - Donaldson, Dave, "Railroads of the Raj: Estimating the impact of transportation infrastructure," *American Economic Review*, 2018, 108 (4-5), 899–934. --- # References - Eaton, Jonathan and Samuel Kortum, "Technology, geography, and trade," *Econometrica*, 2002, 70 (5), 1741–1779. - Heblich, Stephan, Alex Trew, and Yanos Zylberberg, "East-Side Story: Historical Pollution and Persistent Neighborhood Sorting," *Journal of Political Economy*, 2021, 129 (5), 1508–1552. - -, Stephen J Redding, and Daniel M Sturm, "The making of the modern metropolis: evidence from London," *The Quarterly Journal of Economics*, 2020, 135 (4), 2059–2133. - Marshall, Alfred, The Principles of Economics, McMaster University Archive for the History of Economic Thought, 1890. - Monte, Ferdinando, Stephen J Redding, and Esteban Rossi-Hansberg, "Commuting, migration, and local employment elasticities," *American Economic Review*, 2018, 108 (12), 3855–90. --- # References - Pellegrina, Heitor S and Sebastian Sotelo, "Migration, Specialization, and Trade: Evidence from Brazil’s March to the West," Technical Report, National Bureau of Economic Research 2021. - Redding, Stephen J, "Goods trade, factor mobility and welfare," *Journal of International Economics*, 2016, 101, 148–167.