Geography matters, but how much? Making economic geography a quantitative field

Geography matters, but how much?Making economic geography a quantitative eld

Dávid Krisztián Nagy

CREi and Barcelona GSE

October 14, 2016

Dávid Nagy (CREi and Barcelona GSE) Quantitative economic geography October 14, 2016 1 / 44

Geography matters

Why does geography a¤ect aggregate economic outcomes?

Some frictions are spatial by nature:I transport costsI mobility restrictionsI road congestionI di¤usion of technology across space

Some shocks are spatial by nature:I railroad constructionI political border changesI global warming rise in sea levels

The e¤ect of these shocks on aggregate output, welfare and growthis inuenced by spatial frictions, hence by geography.

Standing on the shoulders of giants

Krugman, P. (1991): Increasing Returns and Economic Geography.Journal of Political Economy, vol. 99(3), 483499.

Use formal modeling to explain facts such asI high concentration of economic activity across spaceI persistence of spatial patterns

F but also sudden changes caused by seemingly small shocks

Main mechanism: circular causation due to increasing returns,transport costs and labor mobility.

Krugman (1991): two locationsHigh transport costs

Krugman (1991): two locationsLow transport costs

What are the benets of Spains high speed rail network?

Quantitative models of international trade

Armington (Anderson, 1979)

Eaton and Kortum (2002)

Krugman (1980)

Melitz (2003)

Stay tractable, even with rich geography:I any number of countriesI any distribution of population, productivity and transport costs

Use them as a basis to develop quantitative geography models byadding

I mobility of labor (and frictions to mobility)I increasing returns (to Armington, EK)I congestionI dynamics

Krugman (1980)

Melitz (2003)

Krugman (1980)

Melitz (2003)

The Geography of DevelopmentKlaus Desmet, Dávid Krisztián Nagy and Esteban Rossi-Hansberg (JPE, forthcoming)

Where a person lives determines their productivity, income andwell-being.

But a persons location is neither a permanent characteristic nor afree choice.

I How do migratory restrictions shape the economy of the future?I How do they interact and a¤ect the spatial distribution of productivityand amenities?

We propose a theory of development that explicitly takes into accountI the geography of economic activityI the mobility restrictions and transport costs associated with it

A quantitative model of growth in space

Each location is unique in terms of itsI amenitiesI productivityI geography

Each location has rms thatI produce and trade subject to transport costsI innovate

Static part of the modelI Allen and Arkolakis (2014) and Eaton and Kortum (2002)I allow for migration restrictions

Dynamic part of the modelI Desmet and Rossi-Hansberg (2014)I land competition and technology di¤usion

Endowments and preferences

Economy occupies a two-dimensional surface S .I location is point r 2 SI S is partitioned into C countries

L agents, each supplying one unit of labor.

An agents period utility is

uit (r, r) = at (r)Z 1

0cωt (r)

ρ dω

εit (r)t

∏s=1

m (rs1, rs )1

I εit (r) is a location preference shock that is iid FréchetI m (rs1, rs ) is the cost of moving from rs1 to rsI amenities take the form

at (r) = a (r) Lt (r)λ

Agents earn income from work and local ownership of land.

Migration restrictions

Assumption: m (r , s) = m1 (r)m2 (s) and m (r , r) = 1.

Then an agents value function can be written as

Vr0, ε

1m1 (r0)

u1 (r1)m2 (r1)

εi1 (r1) + βEmaxr2

u2 (r2)m2 (r2)

εi2 (r2) + Vr2, ε

ut (r) = at (r)Z 1

0cωt (r)

ρ dω

I current location only inuences current utility and not future decision

Technology

Production per unit of land of a rm producing good ω 2 [0, 1]:

qωt (r) = φω

t (r)γ1 zω

t (r) Lωt (r)

φωt (r) is an innovation requiring νφω

t (r)ξ units of labor.

If γ1 < 1, there are decreasing returns to local innovation.

zωt (r) is the realization of a r.v. drawn from a Fréchet distribution

F (z , r) = eTt (r )zθ

where Tt (r) = τt (r) Lt (r)α and

τt (r) = φt1 (r)θγ1

ηt1 (r , s) τt1 (s) ds1γ2

τt1 (r)γ2

If γ2 < 1, we get global di¤usion of technology.

Productivity draws and competition

Firms face perfect local competition and innovate.I Productivity draws are i.i.d. across time and goods, but correlatedacross space (with perfect correlation as distance goes to zero).

I Firm prots are linear in land, so for any small interval there is acontinuum of rms that compete in prices.

I Firms bid for land up to point of making zero prots after coveringinvestment in technology.

Dynamic prot maximization simplies to sequence of static problems.I Next period all potential entrants have access to same technology(Desmet and Rossi-Hansberg, 2014).

Equilibrium

The spatial distribution of population at time t is given by

B1t (r ) Lt (r )λθ θ

γ1ξ [1µ]

iθi+Ω θ(1+θ)

ZSLt (s)

1λθ+ 1+θ1+2θ

γ1ξ [1µ]

iθiΩ θ2

1+2θ B2t (s) ς (r , s)θ ds

where B1t () ,B2t () , ς (, ) are exogenously given functions.I This is an integral equation for Lt ().

Does the equilibrium exist?

Is it unique?

How can we solve for it e¢ ciently?

Equilibrium

The spatial distribution of population at time t is given by

B1t (r ) Lt (r )λθ θ

γ1ξ [1µ]

iθi+Ω θ(1+θ)

ZSLt (s)

1λθ+ 1+θ1+2θ

γ1ξ [1µ]

iθiΩ θ2

1+2θ B2t (s) ς (r , s)θ ds

where B1t () ,B2t () , ς (, ) are exogenously given functions.I This is an integral equation for Lt ().

Does the equilibrium exist?

Is it unique?

How can we solve for it e¢ ciently?

The Handbook of Integral Equations

Equilibrium: Existence, uniqueness and solution algorithm

Lemma 3: An equilibrium exists and is unique if

γ1ξ λ+ 1 µ

I Moreover, a simple iterative procedure converges to the uniqueequilibrium.

Lemma 4: There exists a unique balanced growth path if

γ1ξ+

γ1[1 γ2] ξ

λ+ 1 µ

I This condition is stronger than the one in Lemma 3.

Calibration

1. Preferencesβ = 0.965 Discount factorρ = 0.75 Elasticity of substitution of 4 (Bernard et al., 2003)λ = 0.32 Relation between amenities and populationΩ = 0.5 Elasticity of migration ows to income (Monte et al., 2015)2. Technologyα = 0.06 Static elasticity of productivity to density (Carlino et al., 2007)θ = 6.5 Trade elasticity (EK, 2002; Simonovska and Waugh, 2014)µ = 0.8 Labor or non-land share in production

(Greenwood et al., 1997; Desmet and Rappaport, 2014)γ1 = 0.319 Relation between population distribution and growth3. Evolution of productivityγ2 = 0.993 Relation between population distribution and growthξ = 125 Desmet and Rossi-Hansberg (2015)ν = 0.15 Initial world growth rate of real GDP of 2%4. Trade Costs

Allen and Arkolakis (2014) and elasticity of trade owsto distance of 0.93 (Head and Mayer, 2014)

Benchmark calibration: Period 1

a. Population density b. Productivity:τt (r ) Lt (r )

α 1θ

c. Utility d. Real income per capita

Keeping migratory restrictions unchanged: Period 600

α 1θ

Free migration: Period 1

α 1θ

Free migration: Period 600

α 1θ

Large welfare gains from liberalizing migration

Mobility Discounted Real Income* Discounted Utility** Migration Flows***ϑ %∆ w.r.t. ϑ = 0 %∆ w.r.t. ϑ = 01a 0% 0% 0.30%0.75 31% 60% 21.2%0.5 69% 144% 43.2%0.25 102% 229% 60.2%0b 126% 306% 70.3%We use β = 0.965. a: Current Moving Costs. b: No Costs. *: Population-weightedaverage of cellsreal GDP. **: Population-weighted average of cellsutility levels.***: Share of world population moving to countries that grow between period 0

and 1 (immediately after the change in ϑ).

Evaluating the Economic Cost of Coastal FloodingDesmet, Kopp, Nagy, Oppenheimer and Rossi-Hansberg (2016)

We evaluate the economic cost of rising sea levels caused by globalwarming.

I based on Desmet, Nagy and Rossi-Hansberg (2016)I analysis is spatially detailed (1 1 cells), dynamic, and includesgeneral equilibrium linkages between locations

F trade, migration, agglomeration and congestion are all included

I economic data matched with realizations of local and dynamic sea-levelrise scenarios

I we study mean e¤ects, but also the degree of uncertainty in the costsof ooding

Existing literatureI accounting exercises based on current data (Dasgupta et al., 2007)I if they account for changing conditions (Nicholls, 2004)

F lack of detail: all regions in a country behave in the same wayF no linkages with areas that are not a¤ected directly

Average sea level rise for 40 random pathsMean severity scenario

Losses in real GDP per capitaMean severity scenario

Substantial loss in world welfareMean severity scenario

City Location and Economic DevelopmentNagy (2016)

Spatial frictions a¤ect aggregate economic growth through thelocations and sizes of cities as

I cities host rms that are the engines of innovation,I they provide dynamic externalities that foster growth.

Propose a quantitative model of endogenous growth andcity formation in space.

I any number of locationsI any distribution of trade costs, land and productivity

Use model to study determinants of city formation and growth in19th-century United States.

I e¤ect of railroad constructionI e¤ect of international trade

Consumption

Lt consumers, each endowed with one unit of labor and choosesI a location to live and workI a location to trade

A consumer living at location r and trading at location s obtainsper-period utility

Ut (r , s) =Z nt

0xNt (r , s, i)

ε1ε di

ν εε1xFt (r , s)

Consumers decide in which sector to work.I farmers produce at home, sell their good and shop at the trading placeI non-farm workers work for rms and shop at the trading place

F high enough commuting costs ) live, work and trade at the same place

Farm technology

Farmers at r use production function

xFt (r) = B (r) `Ft (r)

α ht (r)1α

Land available in exogenous supply Ht (r) > 0.I leads to dispersion of farm production across spaceI dispersion reinforced by population growth and territorial expansion

Shipping the good to trading place s subject to iceberg trade costςt (r , s) 1.

I leads to dispersion of consumers across space

Non-farm technologyEach non-farm variety is produced by a single rm, using labor andthe farm good:

xNt (s) =

"`Pt (s)

β1β +

hbAt (s) xFt (s)µi β1

# ββ1

I rising productivity bAt (s) induces structural change if β 6= 1Non-farm rms agglomerate and create cities due to

I increasing returns: xed per-period operation cost f > 0I shipping subject to iceberg trade costs τt (s, r) 1

Agglomeration reinforced by structural change.I calibrate β to match U.S. urbanization

Firm can increase its productivity by hiring workers to innovate:bAt (s) = At (s) `It (s)1µ

Evolution of non-farm technology

Fundamental productivity at s evolves according to

At+1 (s) = maxreδjrs jAt (r)

h`It (r)

1µ + gLNt (r)

iGrowth rate shifted by size-dependent dynamic externality g

LNt (r)

I choose gLNt (r)

γ if LNt (r) λ

0 if LNt (r) < λI motivated by evidence on di¤erent growth rates of cities vs towns,which suggests λ = 10, 000

I calibrate γ to di¤erence in city vs town growth rate

Technology di¤uses across space, with exponential decay eδjrs j.I perfect local di¤usion and free entry into non-farm sector (DRH, 2014)) rm solves a static problem as future gains to innovation are 0

Calibration

Parameter Target / Commentα = 0.71 Labor share in agriculture (Caselli and Coleman, 2001)ν = 0.75 Non-farm share in consumption (Lebergott, 1996)ε = 9 Trade elasticity (Donaldson and Hornbeck, 2015)δ = 0.005 Speed of technology di¤usion (Comin et al., 2013)B () FAO GAEZ data and 1860 Census of Agricultureφ = 0.44 Concentration of population, 1790A0 (k) Population of ve pre-existing cities k, 1790A0 (s) = 0.10 Non-farm employment share (s 6= k), 1790f = 4.4 Growth in real GDP per capita until 1860γ = 0.014 Di¤ between avg growth of cities vs towns until 1860µ = 0.9 Convergence in city size until 1860β = 0.29 Increase in urbanization until 1860

Expansion to the WestPopulation per square mile in 1790: model (top) vs data (bottom)

Railroads reordered population

Population per square mile in 1860, baseline simulation

Population per square mile in 1860, no railroads

Railroads had a large impact on cities and growth

The absence of railroadsI decreases the sizes of large cities, especially Boston (by 75% in 1860)and Philadelphia (by 25% in 1860),

I decreases real GDP in 1860 by 6.4%,I decreases the growth rate by 23%, from 1% to 0.77% per year.

Endogenous city development accounts for 40% of the e¤ect onreal GDP.

Other work

Bridges with Roc Armenter and Miklós KorenTransit Trade and Economic Geography with Roc Armenter andMiklós Koren

Geography matters, but how much? Making economic geography a quantitative field

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