The Economic Geography of Innovation
Peter H. Egger1,22

Nicole Püschel 1

1
ETH Zurich
CEPR, CESifo, WIFO

December 4, 2017

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Introduction

Introduction

Technology and productivity are key drivers of production potential, attractivenessfor mobile factors to locate, and for well-being.
Technological capabilities influenced by local innovations and innovations generated
elsewhere (spillovers).
Many countries have introduced R&D investment incentive policies.
What is the economic value and the spatial impact of innovations in general and ofsuch incentive schemes?

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Introduction

This Paper

In a first step
Formulate and calibrate a multi-region general equilibrium model of international
trade.
The model builds on Allen and Arkolakis ’14 and Desmet et al. ’171 and considers –beyond usual productivity shifters for the production of output – a productivity
shifter for workers employed in innovation.
In a second step
Structurally estimate this productivity shifter (and other model parameters) using
region-specific patent registrations and country-specific R&D- investment incentives.
In a third step
Conduct counterfactual experiments in order to quantify the steady-state effects ofinnovation and specific innovation incentives for the spatial distribution of economic
activity and well-being.

1

Henceforth: AA ’14 and DNRH ’17
Egger and Püschel (ETH Zurich)

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The Model

The Model

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The Model

Setup
Consider a world of S regions r on a two-dimensional surface, so r = 1, ..., S.
P
Region r has land density Gr > 0, and Gr is normalized by S1 Sr=1 Gr .
Each region r is unique in terms of: amenities, productivity, and geography.
In each location, firms produce product varieties ω, innovate, and trade subject toiceberg transport costs.
Firms have an incentive to innovate as it improves their productivity and allows
them to post a higher bid for land (land competition).
Innovation is less costly in locations with innovation incentive schemes.
Benefits from innovation last only for one period, then technology diffuses
completely.
The world economy is populated by L̄ agents, who are endowed with one unit oflabor each and are fully mobile across regions.
Static part of the model follows AA ’14 and Eaton and Kortum ’02 (EK ’02).
Dynamic part of the model follows Desmet and Rossi-Hansberg ’14.
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The Model

The Role of Innovation for Production (1)A firm’s production of variety ω per unit of land in intensive form is defined as
qrt (ω) = φrt (ω)γ1 zrt (ω) Lrt (ω)µ γ1 , µ ∈ (0, 1].

(1)

A firm’s productivity is determined by its decision to innovate, φrt (ω), and an
exogenous, good-specific productivity shifter, zrt (ω).
For each variety ω, zrt is the realization of a random variable Zrt that is drawn forma Fréchet distribution.
−θF (z, r ) = e −Trt z
Trt = τrt L̄αrt , α ≥ 0 and θ > 0
τit is evolving according to1θτrt = φγrt−1

1
S

1−γ2

Z
τst−1 ds
S

γ2
τrt−1
.

(2)

Note: If γ2 < 1 then the model implies global diffusion of technology.

Productivity draws are i.i.d across time and goods, but correlated across regions.
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The Model

The Role of Innovation for Production (2)All products are produced under perfect local competition.
Competition for land implies that firms bid until they break even.
Firms have an incentive to invest in innovation as it increases their productivity in(1) and eventually increases their bid for land.
Innovation is produced under Cobb-Douglas technology and constant returns to1/ξ, with hrt ≥ 1.
scale: φrt (ω) = ( ν1 Linnort (ω)hrt )Hence, to innovate, a firm has to employ additional units of labor
ξ −1
Linno
rt (ω) = νφrt (ω) hrt .

(3)where hrt is an innovation-worker-specific productivity shifter.

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The Model

The Role of Innovation for Production (3)Firms enjoy the benefit of their innovation for only one period, in the next period all
entrants to the market have the same access to technology.
This simplifies the dynamic profit maximization to a sequence of static problems:max
Lrt (ω),φrt (ω)

prt (ω) φrt (ω)γ1 zrt (ω) Lrt (ω)µ − wrt [Lrt (ω) + φrt (ω)ξ hrt−1 ] − brt

Prices of a good produced in r and sold in r are: prt (ω) = ort /zrt (ω).
An individual firm takes the input costs (ort ) as given.
Productivity draws affect prices without changing input costs.

Unit costs ort are defined as follows
γ

ort ∝ brt(1−µ)− ξ1γ− 1hrt ξ wrtγ(µ+ ξ1 ).

(4)

brt is the firm’s bid rent for land, which increases with the level of innovationξ(1 − µ)brt =− 1 wrt νφrt (ω)ξ hrt−1 .
γ1

(5)

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The Model

The Role of Innovation for Total Employment

Total employment in region r at period t is the sum of production workers, Lrt (ω),
and innovation workers, νφrt (ω)ξ hrt−1 , soγ1L̄rt (ω) = Lrt (ω) + νφrt (ω)ξ hrt−1 = Lrt (ω) 1 +.
(6)µξ
The last equality follows from the first-order-condition ratio between production
labor and innovation laborγ1γ1
νφrt (ω)ξ hrt−1 =
Lrt (ω) =L̄rt (ω).
(7)ξµµξ + γ1
Production labor is proportional to total employment in all regions r .

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The Model

Utility and Consumption (1)When choosing residence in region r, a representative worker in period t derives
utility from local amenities, art , and from consuming a set of differentiated productvarieties ω with CES preferences according to
σ
 1
 σ−1
Z
σ−1
urt = art Crt = art  crt (ω) σ dω with art = ār L̄−λ
rt

(8)

0

ār : time-invariant amenity attribute.
λ ≥ 0: congestion externalities parameter.
Crt : real consumption bundle.
σ ∈ (1, ∞): elasticity of substitution between varieties ω.

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The Model

Utility and Consumption (2)Agents earn income from work and from local ownership of land.
Rents are assumed to be uniformly distributed across agents.
Workers cannot write debt contracts with each other.
Perfect local competition implies that each worker consumes all her income.
Indirect utility:
urt = art yrt = art
Price index, Prt , is defined as Prt = Γ

wrt + brt /L̄rt
Prt
1

1−σ
+ 1 1−σθR

S Tkt [okt ζks ](9)
 1−θ dk − θAs in EK ’02 the share of consumption in region r of varieties produced in region s isdetermined by
Trt [ort ζrs ]−θπrst = R, ∀r , s ∈ S.
(10)
T [o ζ ]−θ dk
S kt kt ks
ζrs > 1: iceberg costs of transporting a product from r to s.
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Equilibrium

Equilibrium

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Equilibrium

Equilibrium in Each Period
Equilibrium in each period only depends on current profits, as each period is
self-contained and firms are not forward-looking.
1

Population density is determined by the location-specific utility derivedZ
urt 1/Ω
Gr L̄rt= R 1/Ω , with Gr Lrt dr = L̄
L̄
u dk
S
S kt

(11)

Ω: Fréchet parameter of a location-specific preference shock.
No other migration costs than ones captured by ār .
2

Wages through product-market clearing that requires total revenues in region r tobe equal to total expenditures on products of its customers:Z
wrt Gr L̄rt =πrst wst Gs L̄st ds ∀r , s ∈ S(12)SExistence and UniquenessAn equilibrium exists and is unique if congestion forces are not smaller than
agglomeration forces:αγ1+≤ λ + 1 − µ + Ω.
θ
ξ
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Equilibrium

Balanced Growth Path (BGP)

If a BGP exists then all locations grow at the same rate and the spatial distributionof employment is constant.
The investment decision will be constant but different across locations.
There exists a unique growth path if
α
γ1
+
+
θ
ξ

γ1
[1 − γ2 ]ξ
| {z }≤λ+1−µ+Ω

Dynamic agglomeration effect

In a BGP aggregate welfare and real consumption depend on population size, theproductivity shifter hrt and their distribution in space
Crt+1
urt+1
=
∝
urt
Crt

Z
(L̄s hs )θγ1[1−γ2 ]ξ

 1−γ2
θ

ds

(13)

S

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Calibration

Calibration of the Model

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Calibration

Calibration: Overview

1. Preferences
σ=4
Elasticity of substitution.
λ = 0.65
Relation between amenities and population.
Ω = 0.5
Elasticity of migration flows w.r.t. income.
2. Technology
α = 0.06
Elasticity of productivity w.r.t. population density.
θ = 6.5
Trade elasticity.
µ = 0.8
Labor share in production (non-land share).
γ1 = 0.1130
Elasticity of tomorrow’s productivity w.r.t. today’s innovation.
3. Evolution of productivity
γ2 = 0.9898
Elasticity of tomorrow’s productivity w.r.t. today’s productivity.
ξ = 125
Elasticity of innovation costs w.r.t. innovation.
ν = 0.15
Intercept parameter in innovation cost function.
4. Transport Costs
Based on AA ’14 and Fast Marching Algorithm.
4. Other Trade Costs
θ = 6.5
Elasticity of trade w.r.t. tariffs (tariffs from WDI).
κ = 0.078
Elasticity of trade w.r.t linguistic proximity (Melitz and Toubal, 2014).
Trade costs

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Estimation

Estimation

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Estimation

Amenity Parameter
Amenities are defined as: art = ār L̄−λrt
We estimate the region-specific amenity shock ār and the amenity parameter λ forthe baseline year 2005 as follows
log(ar ) = E (log(ār )) − λ log L̄r + εar(14)

ar : Amenity distribution (2005) is derived through an iterative process using thestructure of the model. AmenitiesL̄r : Gridded population data (2005) from SEDAC. AssignmentPL̄r is instrumented with a region-specific remoteness index, Rr = weightrarea S1ζrssFirst Stage
Dep. Var. log (L̄r )Second Stage
Dep. Var. log(ar )log (Rr )\log(L̄r )

cons#obs-0.581***(0.014)16.113***(0.060)
5633

cons
#obs

-0.650***(0.034)9.604***(0.473)5633

ār ≡ exp(E (log(ār )) + εar )18/52
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Estimation

Technology Parameters

The BGP implies (13). Taking logs and discretizing (13) giveslog(urt+1 ) − log(urt ) = log(yrt+1 ) − log(yrt )
=

γ /ν

X ∗
(1 − γ2 )γ1γ11 − γ2log(η) +log(Ψ) +log(SLn ) +log(
L̄rt )θξξθrΨ = γ 1+µξ , Ln = 1000, and L̄∗rt =
1

h

L̄rt
h
Ln r

i

θγ1
(1−γ2 )ξ(15).

yrt , L̄rt : Gridded GDP p/c and population data from G-Econ Project.
t: 1990(5)2005

Assignment

We do a grid search for the minimum sum of squared residuals.
We use the corresponding hr for each value of γ1 as the estimation of hr itself
depends on γ1 .
Optimal parameter values: γ1 = 0.1130, γ2 = 0.9898 (DNRH: γ1 = 0.319,
γ2 = 0.99246)

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Estimation

Estimation of hr
We estimate hrt using (7) and assume
φξrt = Patentsrtξ̃ =γ1L̄rt hrtξν[µ + γ1 /ξ](16)

Patentsrt : registered patents per unit of land in region r at year t (PATSTAT).
L̄rt : population density in region r at year t (SEDAC).

We parametrize hrt by country-specific binary tax instruments (Boesenberg andEgger, 2016), such that:
hrt = exp(Dct β + |latrt |Dct γ)(17)

Dct includes binary variables on R&D policy instruments: Dpatentboxct , Dgrantsct ,Dtaxcreditct , Dtaxholidayct , Dsuperdct , Ddeducct , Deatrrdct .

We estimate (16) as a cross section by negative binomial regression (year=2005)
Patentsr = exp(β0 +1
˜ + 1 log h + ε )log L̄
r
r
r
ξ˜
ξ˜

(18)

˜ = ξν[µ + γ /ξ]L̄ and ε is the error term.
where L̄
r
1
r
r
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Estimation

Data: 5633 PATSTAT regions in 213 countries, benchmark year: 2005.

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Estimation

PATSTAT Classification of Regions

Countries with a few patents do not have a regional classification.
Variable

Mean

Std.Dev.

Min.

Max.

N

Patents per norm. unit of land (avg. 2000-2010)
Total
One-region countries
One-region countries islands
One-region countries non-islands

1,201
988
4,233
1.511

8,058
9,044
18,549
3.475

0
0
0
0

375,281
113,542
113,54218.025

5,470
163
38
125

0.026
0.021
0.09
0

0.172
0.193
0.396
0

0
0
0
0

8.012
2.424
2.424
0

5,470
163
38
125

Patents per km2 (avg. 2000-2010)
Total
One-region countries
One-region countries islands
One-region countries non-islands

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Estimation

Summary Statistics

Variable

Mean

Std. Dev.

Min.

Max.

Patents per norm. unit of land
patentsr (inv) avg 2000-2010
patentsr (inv) 2005
patentsr (app) avg 2000-2010
patentsr (app) 2005

1,195
1,218
1,795
1,814

8,087
8,337
24,30324,2820000375,281
392,807
1,165,570
1,178,841

˜ )log(L̄
r

8.955

2.172

-1.58515.811

Dtaxcreditc
Dsuperdc
Dtaxholidayc
Dgrantsc
Dpatentboxc
Ddeducc
Deatrrdc

0.715
0.053
0.023
0.081
0.022
0.029
0.982

0.452
0.224
0.151
0.273
0.147
0.169
0.131

0
0
0
0
0
0
0

1
1
1
1
1
1
1

|latr |

40.2059.583

0.2

74.728

S= 5633
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Estimation

Estimation Results: Marginal Effects(1)
patentsr (inv)
avg 2000-2010(2)
patentsr (inv)
2005

(3)
patentsr (inv)
avg 2000-2010(4)
patentsr (inv)
2005

(5)
patentsr (app)avg 2000-2010(6)
patentsr (app)
2005

(7)
patentsr (app)avg 2000-2010(8)
patentsr (app)2005

1.260***(0.070)0.069(0.438)0.160(0.697)2.451**(1.024)
1.277***(0.430)-2.199**(1.059)0.102(0.324)1.775**(0.775)-9.498***(1.051)1.287***(0.038)0.223(0.426)-0.416(0.541)2.234***(0.732)
1.297***(0.396)-2.077***(0.769)0.272(0.266)2.004***(0.720)-10.023***(0.745)1.321***(0.062)0.146(0.501)
0.193(0.663)
1.394**(0.669)2.055(2.008)-1.813***(0.656)0.130(0.349)1.962**(0.784)-10.251***(0.935)1.315***(0.043)0.272(0.476)-1.609***(0.537)2.410***(0.489)2.307(2.100)-2.638***(0.502)
1.134**(0.471)2.093***(0.751)-10.375***(0.771)

1.098***(0.036)0.206(0.391)0.226(0.514)3.317***(0.542)
1.522***(0.375)-3.190***(0.565)
1.558*(0.908)-0.106(0.574)-6.243***(0.607)1.160***(0.058)0.427(0.372)-0.306(0.490)3.032***(0.395)
1.498***(0.361)-3.114***(0.400)0.178(0.290)-0.093(0.549)-6.955***(0.788)

1.153***(0.034)0.170(0.415)-1.301*(0.775)2.853***(0.560)2.576(2.187)-3.476***(0.604)
1.582*(0.933)0.093(0.581)-6.874***(0.589)1.186***(0.038)0.516(0.427)-1.298**(0.544)
3.108***(0.457)2.951(2.387)-3.668***(0.515)
1.007**(0.437)-0.108(0.571)-7.245***(0.601)# obs|latr |Dc

0.946***(0.188)5633
NO

1.509***(0.176)5633
NO

0.858***(0.177)5633
YES

1.438***(0.170)5633
YES

1.570***(0.170)5633
NO2.177***(0.323)5633
NO

1.463***(0.175)5633
YES

2.103***(0.331)
5633
YES

overall fit
tax instruments fit

0.64340.20910.77580.20900.64710.10570.57870.11710.47320.12590.63320.14170.39220.04310.31080.0310˜)log(L̄
r
Dtaxcreditc
Dsuperdc
Dtaxholidayc
Dgrantsc
Dpatentboxc
Ddeducc
Deatrrdc
cons

lnalpha

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Estimation

Kernel Density: Productivity Shifter hr

0.05

Density
.1

.15

.2

Kernel density estimate

0

20

40
hr

60

80

kernel = epanechnikov, bandwidth = 0.3455

Note: In the comparative statics we keep hr constant over all years.
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Estimation

Innovation and Patents in 2010: Data vs. Model (φξr = Patentsrξ̃ )1.1

Patentsr>0

1

Patents r

ξ̃/ξ

1.05

Negative binominal regression
ξ̃ξ
Dep Var: Patentsr
Patentsr > 0log(φr )0.156***(0.035)

cons

0.006*(0.003)
4642

.95

#obs

1.02

1.04

1.06

φr

1.08

1.1

1.12

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Counterfactual Analysis

Counterfactual Analysis

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Counterfactual Analysis

Counterfactual Experiments
We analyze key parameters (employment, welfare, productivity, innovation) in threedifferent scenarios:
1

No R&D tax incentives (hr = 1, ∀ r )2

No R&D tax holidays

3

No R&D grants
Tax Policy Instrument

Description

Countries (in 2005)

Tax credits

Tax credits on R&D investments

Austria, Canada, China, France, Ireland, Japan,
Mexico, Netherlands, Norway, Portugal, South Korea,
Spain, Taiwan, US, Venezuela.

Tax holidays

Tax holidays for firms with R&D investments.

France, Malaysia, Singapore, Switzerland.

Grants

R&D investments can benefit from grants

Germany, Hungary, Ireland, Israel.

Patent boxes(Partial) exemption of returns on R&D investments.

France, Hungary.

Deductions

Any form of deductions on R&D investments.

Australia, Belgium, Ireland, Japan, South Korea.

Super deductions

Super deductions of more than 100%for R&D investments.

Australia, China, Czech Republic, Hungary, India,
Malaysia, Malta, Puerto Rico, Singapore, UK.

EATRR&D

Effective average tax rate is lower on returns on
R&D investments than on other investments.

114 of 213 countries in the data.

France incl. Guadeloupe, French Guiana, Martinique, Reunion; Netherlands incl. Bonaire; US incl. American Samoa, US Minor Outlying Islands;
Australia incl. Cocos Islands; UK incl. Falkland Islands, Gibraltar, Montserrat, Pitcarn, St. Helena.
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Counterfactual Analysis

No tax incentives

Baseline

No tax holidays

0

0

.05

.05

Density.1 .15

Density.1 .15.2.2

Baseline.25.25

Kernel Densities of hr in Different Scenarios

20

.4

0

40
hr

60

0

20

40
hr

60

80

No grants

0.1

Density.2.3

Baseline

80

0

20

40
hr

60

80

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Counterfactual Analysis

1. The Evolution of R&D Incentives and Inequality Across Regions

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Counterfactual Analysis

Evolution of World Inequality: Population Distribution & Welfare

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Counterfactual Analysis

Evolution of World Inequality: Productivity & Innovation

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Counterfactual Analysis

Decomposition of Theil Index: Within Subgroup Welfare Inequality

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Counterfactual Analysis

Discussion: Inequality Analysis
Overall the different tax instruments have only little impact on considered inequality
aspects.
While the distribution of world population/utility/innovation is no more (un)equal if
R&D grants or R&D tax holidays were abandoned, world
population/utility/innovation would be more equally distributed if no tax
instruments at all were in place.
On the other hand, the different tax instruments have a more distinct impact on the
distribution of world productivity. Both, R&D grants and R&D tax holidays,
decrease the level of inequality in world productivity.
The decomposition of the Theil index allows for within-country comparisons, i.e.,comparison between regions of the same country.
The results suggest that countries experience an increase in welfare inequality
between regions, if a tax instrument was abolished that they had in place (France:
R&D tax holidays and Ireland/Germany: R&D grants)
There are spillover effects from abolishing R&D tax incentives in neighboring
economies: Germany’s welfare inequality would be lowest if R&D tax holidays wereabandoned abroad.
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Counterfactual Analysis

2. R&D Tax Holidays, R&D Grants and Welfare Levels at T=300

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Counterfactual Analysis

Welfare Change: Baseline vs. No R&D Tax Holidays in T=300

.2
-.2
-.4

-.4

-.2

Log(urLog( ur

No TH

No TH

) - Log(ur0) - Log(ur0Baseline

Baseline

)

)

.2

.4

Regions w/o Tax Holidays.4

Regions w Tax Holidays

5

10

Log(ār)15

Area of symbol proportional to region's observed population density in 2005

20

5

10

Log(ār)15

20

Area of symbol proportional to region's observed population density in 2005

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Counterfactual Analysis

Log( ur-.2

No TH) - Log(ur0Baseline).2.4

Welfare Change: Baseline vs. No R&D Tax Holidays, by Country with R&D
Tax Holidays (T=300)-.4FranceMalaysia
Singapore
Switzerland
6

8

Log(ār)1012Size symbol proportional to region's observed population density in 2005

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Counterfactual Analysis

Discussion: R&D Tax Holidays

Among those regions with R&D tax holidays, the majority experiences a drop in
welfare from abandoning that instrument.
There are regions which experience a welfare gain from abandoning R&D tax
holidays.
The country-specific analysis suggests that those regions are part of smaller
economies, e.g., Singapore or Malaysia.
There is only little correlation between amenities and the magnitude of the welfarechange.

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Counterfactual Analysis

Welfare Change: Baseline vs. No R&D Grants in T=300-.05)
Baseline) - Log(ur-.1

No GrantsLog(ur
-.15
-.2
-.25

-.25

-.2

Log(ur-.15

No Grants) - Log(ur-.1Baseline

)

-.05

0

Regions w/o Grants

0

Regions w Grants

5

10

Log(ār)15

Area of symbol proportional to region's observed population density in 2005

20

5

10

Log(ār)15

20

Area of symbol proportional to region's observed population density in 2005

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Counterfactual Analysis

Log(ur-.2

No Grants

Baseline) - Log(ur
)
-.15
-.1

-.05

Welfare Change: Baseline vs. No R&D Grants, by Country with R&D
Grants (T=300)-.25

Germany
Hungary
IrelandIsrael789Log(ār)10

11Size of symbol proportional to region's observed population density in 2005

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Counterfactual Analysis

Discussion: Grants

In all regions, independent of whether a R&D grants policy was in place, welfare
declines when abandoning R&D grants.
As for tax holidays, the welfare loss is heterogeneous in regions where the policy
instrument prevails.
The differences are well explained by a country effect – however, no indication thatthe size of the economy plays a role.

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Counterfactual Analysis

3. Welfare Change and Remoteness : R&D Tax Holidays, R&D Grants at
T=300

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Counterfactual Analysis.4.4Welfare Change and RemotenessRegions w/o TH

Regions w/o Grants

-.2
-.4

-.4

-.2

Log(urLog( ur

No TH

No Grants) - Log(ur0) - Log(ur0Baseline)

Baseline).2

Regions w Grants.2

Regions w TH

-5

0

5
Log(Rr)10

Size symbol proportional to region's observed population density in 2005

15

-5

0

5
Log(Rr)10

15Size symbol proportional to region's observed population density in 2005

The welfare change of the treated regions correlates with the remoteness of thoseregions (Corr. Tax holidays: 0.17, Corr. Grants: 0.12)
Egger and Püschel (ETH Zurich)

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Conclusions

Conclusions

Innovation incentives are important policy instruments to attract mobile factors andenhance regional well-being.
Results suggest that innovation incentives have only little impact on reducing
welfare inequalities.
However, there is evidence of spillover effects – Germany’s welfare inequality would
be comparatively lowest if R&D tax holidays were abandoned in the neighborhood(such policy exists in France and Switzerland, among others)
Heterogeneous effects for different tax polices: R&D grants have a positive welfare
effect on all regions, whereas R&D tax holidays only benefit those regions where thepolicy is in place.
The welfare change due to innovation incentives seems only weakly correlated withthe economic attractiveness of a region (amenities), while remoteness is important.

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Conclusions

Thank you!

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Appendix

Amenity Distribution
We substitute the indirect utility (9) into the first equilibrium condition (11) andsolve for art as followshR
(1/Ωθ) iΩ
R
1/Ω

Ω
(a
w
)
B
dj
dk
jt
kt
kt
S
S
Gr L̄rtart =(19)
(1/θ)RL̄
wrt S Bkt dkθγ /ξ −θζ(·)s−θ
B(·)t = τ(·)t L̄ρ(·)t w(·)th(·)t1ρ = α − ((1 − µ − γ1 /ξ)θ)Data
L̄rt : Observed population density in 2005 (SEDAC).
wrt : Observed wages per capita in 2005 (G-Econ Project).
τrt : Initial efficiency distribution obtained through iterative process using the model
structure and data on observed wages and population densities in 2005.
Back
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Appendix

Assignment Strategy
Some data that we use for estimation and simulation are on the 1◦ × 1◦ -cell level:
trade costs, wages per capita, GDP per capita.
Strategy to assign data to the regional level:12

M : 1 assignment: simple average of all cells falling in region r .
1 : M assignment: nearest cell within country border.

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Appendix

Assignment Strategy: Wages
1 : M assignment: wage levels are identical for regions that are assigned to the same1◦ cell.
We use night-light and population information (both 2005) to weight wages
accordingly.
Assumption:light p/c in region r
wage p/c in region r=
avg(light p/c ∀ regions of same cell)avg(wage p/c ∀ regions of same cell)Night light data is censored (0 ≤ light ≤ 63). We deal with the sum of all lightpixels in a given region. Hence, we only know the lower bound.
We run a tobit regression to predict the true night light values per region, sumlightr :(0
if sumlightr∗ ≤ 0sumlightr =.
∗sumlightrt if sumlightr∗ > 0
We specify the latent variable sumlightr∗ in a linear fashion as a function of theparameters of interest through.
log(sumlightr∗ ) = α1 log(wager ) + α2 log(popr ) + α3 log(arear ) + Vr ι + εlightr
Note: We also included quadratic terms of all explanatory variables in Vr .

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Appendix

Trade Costs (1)Contrary to DNRH ’17, we allow for intra-regional trade.
Transport costs within a region are obtained by two strategies
If many cells fall within a region: Simple average of transport costs.
If many regions get assigned to the same cell: We learn the exchange rate between fast
marching transport costs ζsk and the great circle distance (distsk in degrees).

log(ζsk ) = α0 + α1 log(distsk ) + εζsklog(distsk )
const
R2
#obs

0< distsk ≤ 3
1.021***(0.003)3.610***(0.002)
0.284
419,5803< distsk ≤ 20
0.832***(0.000)3.886***(0.001)
0.285
13,228,282(20)

20< distsk ≤ max(distsk )0.219***(0.000)5.979***(0.000)0.091
276,969,394

Back

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Appendix

Back

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Appendix

Trade Costs (2)Tariffs: We inflate the transport cost matrix by applied weighted tariffs for
manufactured products according to WTO rules (WDI).
Linguistic proximity (LP): We inflate the transport cost matrix by an indicator thatmeasures LP (Melitz and Toubal, 2014).
Impact on the results:
Fast Marching

Fast Marching
Tariffs & LP
1. Total country-to-country imports to total sales
t=1
0.03120.0286t=300
0.07620.0643
2. Total intra-regional trade to total sales
t=1
0.6596
0.6620t=300
0.73030.7413
3. Correlation btw. estimated and observed population density
levels 2010
0.99930.9993logs 2010
0.99960.9996levels diff 2010-2005
0.55510.5551logs diff 2010-2005
0.44460.4445Back

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Appendix.4.4

Welfare vs. Productivity Change: R&D Tax Holidays and R&D Grants, byGroups of Regions (T=300)

Regions w/o Grants & TH

Regions w/o Grants & TH
Regions w Grants

No TH

Log( zr
-.2
-.4

-.4

-.2

Log( urNo TH) - Log(zr0) - Log(ur0Baseline

Baseline)).2

Regions w TH

Regions w Grants.2

Regions w TH

-.25

-.2
Log(ur-.15
No Grants

-.1

-.05
Baseline) - Log(ur)

Size of symbol proportional to region's observed population density in 2005

0

-.25

-.2

-.15

-.1

No Grants

Log(zr-.05
Baseline) - Log(zr0)

Size of symbol proportional to region's observed population density in 2005

1/θ
Note: Productivity in the model is defined as zrt = (τrt L̄α
rt )Egger and Püschel (ETH Zurich)

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