the malthusian theory - brown university€¦ · the malthusian theory cross-country evidence=)...

The Malthusian TheoryCross-Country Evidence=)

Robustness

The Malthusian Theory

Department of EconomicsBrown University

December 17, 2012



Robustness

ProductionIndividualsThe Evolution of PopulationThe Evolution of Income Per CapitaTestable Implications

The Malthusian Epoch

Technological progress and land expansion

=) Temporary increase in the level of income per capita=) An increase in the size of the population

=) No e¤ect on the level of income per capita in the long run

Output per capita �uctuates around a subsistence level

Technologically advanced or land rich economies

=) Higher population density=) Similar level of income per-capita in the long-run



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Central Elements

Positive e¤ect of income on population

y " =) L "

Fixed factor of production - Land

L " =) MPL # =) y #



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The Basic Structure of the Malthusian Model

Overlapping-generations economy

t = 0; 1; 2; 3:::

One homogeneous good

2 factors of production:

LaborLand



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Production

The output produced in period t

Yt = (AX )�L1��t � 2 (0; 1)

Lt � labor employed in period tX � landA � technological levelAX � e¤ective resources

Output per worker produced at time t

yt =YtLt=

�AXLt

��



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Factor Supply

Land is �xed over time

Surface of planet earth

Labor evolves endogenously

Governed by the endogenous rate of population growthDetermined by households�optimal number of children



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Individuals

Live for 2 period

Childhood: (1st Period):

Passive economic agentsConsume �xed amount of their parental resources

Parenthood (2nd Period):

WorkAllocate income between consumption and children



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Preferences and Budget Constraint

Preferences of individual t(adult at time t)

ut = (nt) (ct)1� 2 (0; 1)

nt � number of children of individual tct � consumption of individual t

Budget constraint:�nt + ct � yt

� � cost of raising a child



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Optimization

Optimal expenditure on consumption and children

ct = (1� )yt

�nt = yt

Optimal number of children (note yt = (AX=Lt)�)

nt =

�yt =

�

�AXLt

��



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Population Dynamics

The evolution of the size of the working population

Lt+1 = ntLt

where

nt =

�

�AXLt

��Population dynamics:

Lt+1 =

�

�AXLt

��Lt =

�(AX )�L1��t � �(Lt ;A)



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Population Dynamics

1+tL

045

)(AL

tt LL =+1

);(1 ALL tt φ=+

tL



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The Steady-State Level of Population

The evolution of the size of the working population

Lt+1 =

�(AX )�L1��t

Steady-State: Lt+1 = Lt = �L

�L =

�(AX )��L1��

The steady-state level of the size of the working population

�L = (

�)1=�(AX ) � �L(A)



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Population Dynamics

1+tL

045

)(AL

tt LL =+1

);(1 ALL tt φ=+

tL



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Adjustment of Population to Advancements in Technology

1+tL

045

)( lAL

tt LL =+1

);(1l

tt ALL φ=+

tL

);(1h

tt ALL φ=+

)( hAL



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The Evolution of Income per Worker

The time path of income per worker

yt+1 =�AXLt+1

��=

�AXntLt

��=ytn�t

wherent =

�yt

income dynamics

yt+1 =��

��y1��t � (yt)



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1+ty

045

y

tt yy =+1

)(1 tt yy ψ=+

ty



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The Steady-State Level of Income per Worker

The time path of income per worker

yt+1 =��

��y1��t

Steady-State yt+1 = yt = �y

�y =��

��y1��

The steady-state level of income per worker

�y =��

�



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1+ty

045

y

tt yy =+1

)(1 tt yy ψ=+

ty



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The E¤ect of Technological Advancement on income per Worker

1+ty

045

y

tt yy =+1

)(1 tt yy ψ=+

tyy~



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The E¤ect of Technological Advancement on the Time Path of Population andIncome per Worker



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The E¤ect of Advancement in Technology or Land Productivity

Increases the short-run and the steady-state level of theworking population

@Lt@A

> 0 and@�L@A

> 0

Increases the level of income per capita in the short-run butdoes not a¤ect the steady-state levels of income per worker

@yt@A

> 0 and@�y@A

= 0



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Testable Implications

Variations in technology and land quality across countries willbe re�ected primarily in variation in population density:

Technological superiority will result primarily in higher popula-tion density without any sizable e¤ect on income per-capita inthe long-run

Superior land quality will result primarily in higher populationdensity without any sizable e¤ect on income per-capita in thelong-run



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Identi�cation StrategyEmpirical ModelFindings

Empirical Hurdles

Endogeneity of:

population and technology

Technology " =) Population "Population " =) Technology "



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Identi�cation Strategy



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Exploit exogenous sources of cross-country variation intechnological level

Resolving: reverse causality

Variation in the onset of the Neolithic Revolution (NR) acrossthe globe - a proxy for variation in the technological level

Resolving: omitted variable bias (i.e., 3rd factor (e.g., HC))a¤ected population & NR

Variation in prehistoric domesticable species of plants andanimals � IV for the timing of the NR



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Years Elapsed since the Onset of the Neolithic Revolution across the Globe



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The Neolithic Revolution as a proxy for Technological Advancement

OLS OLS OLS OLS OLS OLS

(1) (2) (3) (4) (5) (6)Dependent Variable:

Log Communications Log Industrial Log TransportationTechnology in: Technology in: Technology in:

1000 CE 1 CE 1000 CE 1 CE 1000 CE 1 CE

Log Years since Neolithic 0.368*** 0.283*** 0.074*** 0.068*** 0.380*** 0.367***Transition (0.028) (0.030) (0.014) (0.015) (0.029) (0.031)

Observations 143 143 143 143 143 143R2 0.48 0.26 0.17 0.12 0.52 0.51

Notes: Robust standard errors in parentheses; *** p<0.01, ** p<0.05, * p<0.1



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Robustness of Identi�cation Strategy

Robustness to the inclusion of direct measures of technology

Exploit variation in a direct measure of the technology levelVariation in prehistoric biogeographic endowments � IV for thisdirect measure of technology

Robustness to the exclusion of unobserved time-invariant country�xed e¤ects

First-di¤erence estimation strategy (with a lagged explanatoryvariable)The e¤ect of changes in the level of technology in1000 BCE-1 CE on population density and income per capitain 1-1000CE



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Empirical Model I

lnPi ;t = �0;t + �1;t lnTi ;t + �2;t lnXi + �03;t�i + �

04;tDi + �i ;t

ln yi ;t = �0;t + �1;t lnTi ;t + �2;t lnXi + �03;t�i + �

04;tDi + "i ;t

Pi;t � population density of country i in year t

yi;t � income per capita of country i in year t

Ti � years elapsed since the onset of agriculture in country i

Xi � measure of land productivity for country i

�i � vector of geographical controls for country i

Di� vector of continental �xed e¤ect in country i



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Determinants of Population Density in 1500 CE

(1) (2) (3) (4) (5) (6)OLS OLS OLS OLS OLS IV

Dependent Variable: Log population density in 1500 CELog years since Neolithic 0.833*** 1.025)*** 1.087*** 1.389*** 2.077***

(0.298) (0.223 (0.184) (0.224) (0.391)

Log land productivity 0.587*** 0.641*** 0.576*** 0.573*** 0.571***(0.071) (0.059) (0.052) (0.095) (0.082)

Log absolute latitude -0.425*** -0.353*** -0.314*** -0.278** -0.248**(0.124) (0.104) (0.103) (0.131) (0.117)

Distance to nearest -0.392*** 0.220 0.250coast or river (0.142) (0.346) (0.333)

% land within 100 km 0.899*** 1.185*** 1.350***of coast or river (0.282) (0.377) (0.380)

Continental dummies Yes Yes Yes Yes Yes YesObservations 147 147 147 147 96 96R2 0.40 0.60 0.66 0.73 0.73 0.70First-stage F-statistic 14.65Overident. p-value 0.44




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Timing of Neolithic and Population Density in 1500 CE

Conditional on land productivity, geographical factors, and continental �xed e¤ects



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Land Productivity and Population Density in 1500 CE

Conditional on transition timing, geographical factors, and continental �xed e¤ects



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Dependent Variable: Log population density in 1000 CELog years since Neolithic 1.232*** 1.435*** 1.480*** 1.803*** 2.933***

(0.293) (0.243) (0.205) (0.251) (0.504)


Log absolute latitude -0.377** -0.283** -0.229** -0.147 -0.095(0.148) (0.116) (0.111) (0.127) (0.116)

Distance to nearest -0.528*** 0.147 0.225coast or river (0.153) (0.338) (0.354)

% land within 100 km 0.716** 1.050** 1.358***of coast or river (0.323) (0.421) (0.465)





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Dependent Variable: Log population density in 1 CELog years since Neolithic 1.560*** 1.903*** 1.930*** 2.561*** 3.459***

(0.326) (0.312) (0.272) (0.369) (0.437)


Log absolute latitude -0.080 -0.030 0.057 0.116 0.113(0.161) (0.120) (0.101) (0.121) (0.113)

Distance to nearest -0.685*** -0.418 -0.320coast or river (0.155) (0.273) (0.306)

% land within 100 km 0.857** 1.108*** 1.360***of coast or river (0.351) (0.412) (0.488)





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E¤ects on Income per Capita versus Population Density

OLS OLS OLS OLS OLS OLS(1) (2) (3) (4) (5) (6)Log Income Per Capita in Log Population Density in

1500 CE 1000 CE 1 CE 1500 CE 1000 CE 1 CE

Log years since Neolithic 0.159 0.073 0.109 1.337�� 0.832�� 1.006��

(0.136) (0.045) (0.072) (0.594) (0.363) (0.483)

Log land productivity 0.041 -0.021 -0.001 0.584�� 0.364�� 0.681��

(0.025) (0.025) (0.027) (0.159) (0.110) (0.255)

Log absolute latitude -0.041 0.060 -0.175 0.050 -2.140�� -2.163��

(0.073) (0.147) (0.175) (0.463) (0.801) (0.979)

Distance to nearest 0.215 -0.111 0.043 -0.429 -0.237 0.118coast or river (0.198) (0.138) (0.159) (1.237) (0.751) (0.883)

% land within 100 km of 0.124 -0.150 0.042 1.855�� 1.326�� 0.228coast or river (0.145) (0.121) (0.127) (0.820) (0.615) (0.919)

Continental dummies Yes Yes Yes Yes Yes YesObservations 31 26 29 31 26 29R2 0.66 0.68 0.33 0.88 0.95 0.89




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Transition Timing and Population Density in 1500 CE




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Transition Timing and Income Per Capita in 1500 CE




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Land Productivity and Population Density in 1500 CE




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Land Productivity and Income Per Capita in 1500 CE




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Data QualityDirect Measure of TechnologyTechnological Di¤usionUnobserved Heterogeneity

Robustness to Income per Capita Data Quality Concerns

OLS OLS OLS OLS OLS OLSWeighted Weigthed Weighted Weigthed Weighted Weigthed(1) (2) (3) (4) (5) (6)

Weighted According to:Income Data Frequency Total Population Size

Dependent Variable: Log Income Per Capita in:1500 CE 1000 CE 1 CE 1500 CE 1000 CE 1 CE

Log years since Neolithic 0.173 0.122* 0.189 0.278 0.143* 0.289(0.162) (0.063) (0.121) (0.171) (0.068) (0.175)

Log land productivity 0.039 -0.045* 0.008 -0.005 -0.062* -0.011(0.023) (0.022) (0.031) (0.026) (0.030) (0.027)

Log absolute latitude -0.042 0.205* -0.442 -0.089 0.298*** 0.080(0.080) (0.108) (0.362) (0.052) (0.031) (0.089)

Distance to nearest 0.219 -0.370** 0.139 0.332** -0.592*** -0.180coast or river (0.202) (0.148) (0.298) (0.148) (0.108) (0.189)

% land within 100 km of 0.153 -0.228 0.159 0.329 -0.477*** 0.003coast or river (0.169) (0.137) (0.257) (0.227) (0.122) (0.277)





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Robustness to Direct Measures of Technological Sophistication

OLS OLS OLS OLS OLS OLS(1) (2) (3) (4) (5) (6)

Dependent Variable:Log Population Log Income Per Log PopulationDensity in: Capita in: Density in:

1000 CE 1 CE 1000 CE 1 CE 1000 CE 1 CE

Log Technology Index in 4.315*** 4.216*** 0.064 0.678 12.762*** 7.461**Relevant Period (0.850) (0.745) (0.230) (0.432) (0.918) (3.181)

Log land productivity 0.449*** 0.379*** -0.016 0.004 0.429** 0.725**(0.056) (0.082) (0.030) (0.033) (0.182) (0.303)

Log absolute latitude -0.283** -0.051 0.036 -0.198 -1.919*** -2.350***(0.120) (0.127) (0.161) (0.176) (0.576) (0.784)

Distance to nearest -0.638*** -0.782*** -0.092 0.114 0.609 0.886coast or river (0.188) (0.198) (0.144) (0.164) (0.469) (0.904)

% land within 100 km of 0.385 0.237 -0.156 0.092 1.265** 0.788coast or river (0.313) (0.329) (0.139) (0.136) (0.555) (0.934)





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The Causal E¤ect of Technological Sophistication on Population Density

OLS OLS IV OLS OLS IV(1) (2) (3) (4) (5) (6)

Dependent Variable: Population Density in:1000CE 1CE

Log Technology Index in 4.315*** 4.198*** 14.530*** 4.216*** 3.947*** 10.798***Relevant Period (0.850) (1.164) (4.437) (0.745) (0.983) (2.857)

Log land productivity 0.449*** 0.498*** 0.572*** 0.379*** 0.350** 0.464**(0.056) (0.139) (0.148) (0.082) (0.172) (0.182)

Log absolute latitude -0.283** -0.185 -0.209 -0.051 0.083 -0.052(0.120) (0.151) (0.209) (0.127) (0.170) (0.214)

Distance to nearest -0.638*** -0.363 -1.155* -0.782*** -0.625 -0.616coast or river (0.188) (0.426) (0.640) (0.198) (0.434) (0.834)

% land within 100 km of 0.385 0.442 0.153 0.237 0.146 -0.172coast or river (0.313) (0.422) (0.606) (0.329) (0.424) (0.642)


First-stage F-statistic 12.52 12.00Overid. p-value 0.941 0.160




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Robustness to Technology Di¤usion and Geographic Features

(1) (2) (3) (4) (5) (6)Log Population Log Income Per Log PopulationDensity in 1500 Capita in 1500 Density in 1500

Log Technology Index in 0.828*** 0.877*** 0.117 0.103 1.498** 1.478**Relevant Period (0.208) (0.214) (0.221) (0.214) (0.546) (0.556)

Log land productivity 0.559*** 0.545*** 0.036 0.047 0.596*** 0.691***(0.048) (0.063) (0.032) (0.037) (0.123) (0.122)

Log Distance to Frontier -0.186*** -0.191*** -0.005 -0.001 -0.130* -0.108*(0.035) (0.036) (0.011) (0.013) (0.066) (0.055)

Small Island Dummy 0.067 0.086 -0.118 -0.046 1.962** 2.720***(0.582) (0.626) (0.216) (0.198) (0.709) (0.699)

Landlocked Dummy 0.131 0.119 0.056 0.024 1.490*** 1.269***(0.209) (0.203) (0.084) (0.101) (0.293) (0.282)

% Land in Temperate -0.196 -0.192 -1.624*Climate Zones (0.513) (0.180) (0.917)




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Robustness to Unobserved Heterogeneity across Countries

lnPi ;t = 0+�1 lnAi ;t�1+ 1 lnXi++ 02�i+ 3Di+�

pi ;t

ln yi ;t = 0+�1 lnAi ;t�1+ 1 lnXi+ 02�i+

03Di+�

yi ;t

Pi ;t � population density in country i in year t

yi ;t � income per capita in country i in year t

Ai ;t�1 � technological level in country i in year t � 1�pi ;t � disturbance term for population density in country i in period t

�yi ;t � disturbance term for income per capita in country i in period t



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Unobserved Heterogeneity across Countries

�pi ;t = �pi + �0t+�pi ;t

�yi ;t = �yi + �0t + �yi ;t

�pi � unobserved time-invariant country �xed e¤ect on population density in

country i

�pi ;t � random disturbance in population density in country i in period t�0 [�0] � global time �xed-e¤ect on population density [income per capita]

�yi � unobserved time-invariant country �xed e¤ect on income per capita in

country i

�yi ;t � random disturbance in income per capita in country i in period t



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Control for Unobserved Heterogeneity across Country: Population Density

Changes in Population density in country i from time t � 1 to time t:

� lnPi ;t � lnPi ;t � lnPi ;t�1

= �0 + �1� lnAi ;t�1 + �i ;t

�i ;t � �pi ;t��pi ;t�1 � random disturbance in the change in population

density in country i from time t to time t + 1



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Control for Unobserved Heterogeneity across Country: Population Density

Changes in income per capita in country i from time t � 1 to time t:

� ln yi ;t � ln yi ;t � ln yi ;t�1

= �0 + �1� lnAi ;t�1 + i ;t

i ;t � �yi ;t��yi ;t�1 � random disturbance in the change in income per

capita in country i



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Robustness to First Di¤erences and Migration Theory

OLS OLS OLS(1) (2) (3)

Dependent Variable Di¤erences in:Log Population Density Log Income Per Capita

1 CE - 1000 CE 1 CE - 1000 CE

Di¤. in Log Technology Index 1.747*** 3.133* 0.073between 1000 BCE and 1 CE (0.429) (1.550) (0.265)

Constant 0.451*** -0.026 -0.040(0.053) (0.204) (0.064)

Observations 126 26 26R2 0.17 0.34 0.00




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Robustness to Migration Theory

Migration Theory: variations in technology and land qualityacross countries will induce migration from the low to thehigh productivity country:

Technological superiority will result primarily in higher popula-tion density

Technological superiority will not be re�ected in higher incomeper capita

Advancements in technology will result in higher income percapita in all countries (i.e., �0 > 0):

Findings: �0 = 0.


the malthusian theory - brown university€¦ · the malthusian theory cross-country evidence=)...

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