Selection, Agriculture and Cross-Country Productivity Differences David Lagakos
Michael E. Waugh
Arizona State University
New York University
July 10, 2012
Cross-Country Productivity Differences Largest in Agriculture
Cross-Country Labor Productivity Differences Sector
Ratio of 90th-10th Percentile
Agriculture
45
Aggregate
22
Non-Agriculture
4
Source: Caselli (2005)
Cross-Country Productivity Differences Largest in Agriculture
◮
Ten times as much variation in agriculture than non-agriculture
◮
Poor countries have most of workforce in agriculture; rich virtually none
◮
This “accounts” for much of aggregate productivity differences (Caselli, 2005; Restuccia, Yang, Zhu, 2009)
Why are Productivity Differences so Much Larger in Agriculture?
◮
Sector differences in capital per worker? - capital data by sector is limited - best existing data: only somewhat
Why are Productivity Differences so Much Larger in Agriculture?
◮
Sector differences in capital per worker? - capital data by sector is limited - best existing data: only somewhat
◮
Barriers that keep farm productivity low? - Barriers that keep intermediates low (Restuccia, Yang, Zhu 2009) - Misallocation of farm inputs (Adamopoulos & Restuccia, 2011)
Why are Productivity Differences so Much Larger in Agriculture?
◮
Sector differences in capital per worker? - capital data by sector is limited - best existing data: only somewhat
◮
Barriers that keep farm productivity low? - Barriers that keep intermediates low (Restuccia, Yang, Zhu 2009) - Misallocation of farm inputs (Adamopoulos & Restuccia, 2011)
◮
Challenges to the “agriculture barriers” theories - Barriers in non-agriculture too! (Hsieh & Klenow, 2009) - Theories require big exogenous barriers to leaving agriculture
This Paper: Selection of Heterogenous Workers by Sector
◮
Ingredients - Countries differ in “economy-wide efficiency,” A - Subsistence requirements in preferences - Workers heterogenous in productivity in each sector (Roy, 1951)
This Paper: Selection of Heterogenous Workers by Sector
◮
Ingredients - Countries differ in “economy-wide efficiency,” A - Subsistence requirements in preferences - Workers heterogenous in productivity in each sector (Roy, 1951)
◮
Result: Differences in A lead to larger productivity differences in agriculture than non-agriculture
This Paper: Selection of Heterogenous Workers by Sector
◮
Ingredients - Countries differ in “economy-wide efficiency,” A - Subsistence requirements in preferences - Workers heterogenous in productivity in each sector (Roy, 1951)
◮
Result: Differences in A lead to larger productivity differences in agriculture than non-agriculture - In low-A countries, most workers in agriculture sector - Many agriculture workers unproductive at agriculture work - Opposite in high-A economies
This Paper: Quantitative Results
◮
Quantitative model: agriculture Y /N differences twice as large in agriculture as non-agriculture
◮
Explains roughly 20% of agriculture Y /N variation relative to non-agriculture
◮
Model consistent with large wage gap in agriculture even without barriers
Outline of Talk
◮
Formalize theory in general equilibrium Roy model
◮
Quantitative analysis + tests of model
◮
Concrete example: role of women in agriculture
◮
Extension with land & capital
Model
Households
◮
Preferences U i = log(cai − ¯ a) + ν log(cni )
◮
Budget constraint pa cai + cni ≤ y i
◮
Endowment of “individual productivity”: {zai , zni } {zai , zni } drawn from distribution G (za , zn )
Production ◮
Economy-wide efficiency: A
◮
Production functions Ya = ALa
◮
Effective labor input Z La ≡
zai dGi
and
and
Yn = ALn
Ln ≡
i ∈Ωa
◮
Z
zni dGi
i ∈Ωn
Number of workers Na ≡
Z
dGi i ∈Ωa
and
Nn ≡
Z
dGi i ∈Ωn
Sector Choice and Labor Income
◮
Household i’s labor earnings y i ≡ max{pa Azai , wni = Azni }
◮
Optimality: work in non-agriculture if and only if zni ≥ pa zai
Equilibrium
An equilibrium is: Relative food price, pa , and allocations such that ◮
Households optimize • Pick sector with highest wage offer • Pick optimal cai and cni
◮
Markets clear
Relative Price of Food Higher in Poor Countries
Proposition 1 Consider two economies, rich and poor, with efficiency terms AR and AP such that AR > AP . In equilibrium, the relative price of agriculture is higher in the poor economy: paP > paR .
Relative Price of Food Higher in Poor Countries
Proposition 1 Consider two economies, rich and poor, with efficiency terms AR and AP such that AR > AP . In equilibrium, the relative price of agriculture is higher in the poor economy: paP > paR .
Intuition ◮
Poor country demands relatively more food because of subsistence needs
◮
To induce workers to enter agriculture, need a higher pa
Individual Productivity Distribution and Sector Productivity
Proposition 2 Consider two economies with efficiency terms AR and AP such that AR > AP . Let the individual productivity distribution be such that E (za |za /zn > x) and E (zn |zn /za > x) are increasing in x. Then equilibrium sector labor productivities are such that AR YaR /NaR > P P P A Ya /Na
and
YnR /NnR AR < P. P P A Yn /Nn
Individual Productivity Distribution and Sector Productivity
Proposition 2 Consider two economies with efficiency terms AR and AP such that AR > AP . Let the individual productivity distribution be such that E (za |za /zn > x) and E (zn |zn /za > x) are increasing in x. Then equilibrium sector labor productivities are such that AR YaR /NaR > P P P A Ya /Na
and
YnR /NnR AR < P. P P A Yn /Nn
Intuition ◮
If comparative advantage aligns with absolute advantage...
◮
...then productivity differences are larger in agriculture than non-agriculture
Illustrative Example: Independent Frechet Distributions
◮
Let za and zn be drawn independently from −θ
G (za ) = e −za
◮
and
−θ
G (za ) = e −zn
Lower θ means higher dispersion in productivity across individuals
Illustrative Example: Independent Frechet Distributions
◮
Equilibrium share of workers in agriculture n o πa = Prob Azni ≤ pa Azai =
1 pa−θ + 1
Illustrative Example: Independent Frechet Distributions
◮
Equilibrium sector employment and relative price of food log (πa /πn ) = θ log(pa )
◮
Lower elasticity of πa /πn when individual productivity dispersion higher
Illustrative Example: Independent Frechet Distributions
◮
Equilibrium average productivity in agriculture −1
E (za |za /zn > 1/pa ) = γ πa θ
◮
... and non-agriculture −1
E (zn |zn /za > pa ) = γπn θ
Illustrative Model: Independent Frechet Distributions
In two economies with efficiency AR and AP , such that AR > AP : YaR /NaR = YaP /NaP
πaP πaR
θ1
AR AP
AR > P A
and
YnR /NnR = YnP /NnP
πnP πnR
θ1
AR AP
<
AR . AP
Illustrative Model: Independent Frechet Distributions
In two economies with efficiency AR and AP , such that AR > AP : YaR /NaR = YaP /NaP ◮
πaP πaR
θ1
AR AP
AR > P A
and
YnR /NnR = YnP /NnP
Ballpark calibration: θ = 5, πaP = 0.78, πaR = 0.03
πnP πnR
θ1
AR AP
<
AR . AP
Illustrative Model: Independent Frechet Distributions
In two economies with efficiency AR and AP , such that AR > AP : YaR /NaR = YaP /NaP
πaP πaR
θ1
AR AP
AR > P A
and
YnR /NnR = YnP /NnP
◮
Ballpark calibration: θ = 5, πaP = 0.78, πaR = 0.03
◮
Sector productivity differences: YaR /NaR =2· YaP /NaP
AR AP
and
πnP πnR
YnR /NnR = 0.75 · YnP /NnP
θ1
AR AP
AR AP
<
AR . AP
Quantitative Analysis
Parameterization of Individual Productivity Joint distribution of individual productivities G (za , zn ) = C [F (za ), H(zn )],
where
and
−θa
F (za ) = e −za
C [u, v ] =
and
−θn
H(zn ) = e −zn
,
(e −ρu − 1)(e −ρv − 1) −1 log 1 + . ρ e −ρ − 1
◮
F (za ) and H(zn ) are cdfs for Fr´echet distributions.
◮
The function C [F (za ), H(zn )] is a Frank copula.
Parameterization of Individual Productivity Joint distribution of individual productivities G (za , zn ) = C [F (za ), H(zn )],
where
and
−θa
F (za ) = e −za
C [u, v ] =
and
−θn
H(zn ) = e −zn
,
(e −ρu − 1)(e −ρv − 1) −1 log 1 + . ρ e −ρ − 1
Why these assumptions? ◮
Non-parametric identification is difficult (Heckman and Honore, 1990)
◮
Fr´echet is an extreme value distribution
◮
They generate wage distributions similar to data.
Parameterization of Individual Productivity Joint distribution of individual productivities G (za , zn ) = C [F (za ), H(zn )],
where
and
−θa
F (za ) = e −za
C [u, v ] =
and
−θn
H(zn ) = e −zn
,
(e −ρu − 1)(e −ρv − 1) −1 log 1 + . ρ e −ρ − 1
Free parameters are. . . ◮
θa , θn control dispersion in individual productivity
◮
ρ controls dependence in individual productivity draws • ρ=0
⇒ independence.
• ρ>0
⇒ positive dependence.
Calibration Overview
◮
Jointly calibrate the five parameters: θa , θn , ρ, a¯, ν
◮
Target five moments from U.S. data 1. 2. 3. 4. 5.
◮
Variance of non-transitory component of wages in agriculture Variance of non-transitory component of wages in non-agriculture Ratio of average wages in agriculture to average wages in non-agriculture Long-run expenditure share of food Employment share of agriculture sector
Next few slides: more detail, some intuition about identification
Calibration of θa , θn : Intuition
◮
How θ works • Low θ ⇒ high variance in ability • High θ ⇒ low variance in ability
◮
Variance in ability maps into variance in wages.
◮
Thus variability in wages are informative moments. • Key issue: We observe the variance conditional on working in that sector. • θ controls the unconditional variance.
Calibration of θa , θn : Intuition
◮
Use data from 1996-2010 U.S. CPS • Use the (limited) panel structure
◮
Targets: non-transitory component of income by sector
◮
Basic idea: subtract component of variance linked to yearly fluctuations, not productivity
◮
Calibrated values • θn = 2.7 • θa = 5.3
Calibration of ρ: Intuition
◮
Increasing ρ ⇒ increases relative average wages
◮
Intuition:
wa wn
in the model.
- Higher is ρ, closer to world of “one good type, one bad type” - “Good types” more likely to have comparative advantage in non-agriculture, since variance of draws higher in non-agriculture - Average wages higher in non-agriculture
Wages with Low ρ
3.5
3
Log Mean Wage of Workers in Non−Ag
Work in Ag
2.5
Work in Non−Ag
2
Log Mean Wage of Workers in Ag
Log Wa
1.5
1
0.5
0
−0.5
−1
−1.5 −1.5
−1
−0.5
0
0.5
1
1.5
Log W
n
2
2.5
3
3.5
Wages with High ρ
3.5
3
Log Mean Wage of Workers in Non−Ag
Work in Ag
2.5
Work in Non−Ag
2
Log Wa
1.5
Log Mean Wage of Workers in Ag
1
0.5
0
−0.5
−1
−1.5 −1.5
−1
−0.5
0
0.5
1
1.5
Log W
n
2
2.5
3
3.5
Calibration of ρ: Intuition
◮
Intuitively: pick ρ that matches
◮
Calibration result:
wa wn
= 0.70, as in U.S. data
• ρ = 3.5 • Implies a linear correlation of 0.44
Parameterization of Preferences
◮
¯a, subsistence consumption need.
◮
ν, related to long run expenditure share on agriculture goods.
◮
Informed by two moments: 1. Long-run expenditure share of food 2. Employment share of agriculture sector
◮
Calibrated values ¯a = 2.4, ν = 276
Agriculture and Non-Agriculture Y /N Differences: 90th-10th Ratio Experiment 1: lower A to get factor of 22 difference in aggregate GDP per worker (as in 90th-10th ratio in data)
Agriculture and Non-Agriculture Y /N Differences: 90th-10th Ratio Experiment 1: lower A to get factor of 22 difference in aggregate GDP per worker (as in 90th-10th ratio in data) 90-10 Productivity Differences, Data and Benchmark Model Agriculture
Aggregate
Non-Agriculture
Ag/Non-Ag Ratio
Data
45
22
4
10.7
Model
29
22
13
2.2
Without Selection
19
19
19
1.0
Agriculture and Non-Agriculture Y /N Differences: 90th-10th Ratio Experiment 1: lower A to get factor of 22 difference in aggregate GDP per worker (as in 90th-10th ratio in data) 90-10 Productivity Differences, Data and Benchmark Model Agriculture
Aggregate
Non-Agriculture
Ag/Non-Ag Ratio
Data
45
22
4
10.7
Model
29
22
13
2.2
Without Selection
19
19
19
1.0
Note: Shutting down our mechanism ⇒ Ya /Na = Yn /Nn = Y /N.
Agriculture and Non-Agriculture Y /N Differences: 90th-10th Ratio
Expected Individual Productivity Relative to Population Mean Country
Agriculture
Non-Agriculture
90th Percentile
1.55
1.01
10th Percentile
1.00
1.42
Ratio
1.55
0.71
Support for Model’s Predictions
Cross-Country Data ◮
Shares of employment in agriculture.
◮
Relative agriculture prices
◮
Wage gaps in agriculture
Support for Model’s Predictions
Cross-Country Data ◮
Shares of employment in agriculture.
◮
Relative agriculture prices
◮
Wage gaps in agriculture
Direct Evidence ◮
Height and cognitive ability scores
◮
Role of women in agriculture across countries
Share of Employment in Agriculture
100
Share of Employment in Agriculture Data
90
BDI
BTN BFA RWA NER
NPL
Model GIN
80 ERI
70
KHM LBR
60
GNB MWI MOZ ETH MLI TZAGMB UGA LAO KEN MDG COM SEN AGO TCD CAF ZMB VNM SLE TGO
50
COG
NGA PRK MNG
20 10 0 1/128
1/64
CIV LSO
ZAR
30
1/32
ZWE IND CMR
THA
MRT BGD YEM
40
GNQ CHN
HTI
SDN GHA BEN
SYC PNG
TJK
IDN ALB PAK TUR BOL LKAGTM
BWA
PHL FJI NAM ANT OMN PRY TKM SWZ GAB EGY BLZ PER SLV IRN DZA ECU TUN DMA VCT CPV POLMEX JAM PAN COL CRI SUR GEO NIC GUY KAZ MYS CHLGRC BRA DOM CUB UKR ROM URY ARM BLR PRT LVA LTU MKD EST HUN MUS JOR RUS IRL ZAF CZEARG SVK TTO NZL KOR ISL SAU CYP VEN HRV ESP BGR LBY FINAUS ITA AUT NOR ARE CHE BIH BRB BHS JPN DNK NLD LBN FRA SWE ISR DEU CAN USA BEL MLT SVN BHR GBR SGP MAR
HND SYR AZE UZB KGZ MDA SRB
1/16 1/8 1/4 PPP GDP Per Worker Data, U.S. = 1
1/2
1
LUX
2
Relative Price of Agricultural Goods
4 COM NGA
Model
CAF TCD GMB SLE
ZAR
Pa / Pn Data, U.S. = 1
GNB
MWI NER KHM
2 LBR
TJK
TZA MDG TGO
ETH
GHA BEN SDN SEN MLI MRT LAO BFA MOZ KEN
CIV
LSO VNM RWA NPLCOG YEMBGD MNG UGA IRQ BTN ZMB
GIN PAK CMR
IRN ARM LKA
GAB
EG2 EG1
SWZ SGP KOR PHL BOLIDN TUN BWA MAR THA MYS GNQ MUS PER BRN MKD CPV ECU COL NAM JPNHKG TUR ROM BGR HRV BLR ISL MAC UKR LBN FJI JOR PRY VEN NOR ZAF MDV MLT CYPCAN SAU RU2 RU1 LTU NZL OMN CHL AUS SVK ARG POL GBR URY ITA IRL HUN GRC LVA ESTCZE SVN BHRISR
IND CHN SYR AZE GEO BIH ALB
MDA
BRA
KAZ MEX
PRT
1
FIN QAT AUT SWEFRA BEL KWT DNK DEU ESPCHE USA NLD
1/128
1/64
1/32
1/16 1/8 1/4 PPP GDP Per Worker Data, U.S. = 1
1/2
1
LUX
2
Average Wage in Agriculture Relative to Non-Agriculture
1
ALB BIH
SWE MKD
MNG GHA
0.8
POL HRV
SYC
TON BGR PER CZE DOM SVK LVA LTU TUR EST HUN
SCG
CHE NLD
Wa / Wn Data
ARM
0.6 MDAMDA KOR
PHL LKA UZB KGZ UKR GTM SLV
NPL MDG RWA MWI
PRY EGY
CHN
KEN TJK
GEO AZE
USA
MLT SGP CYP
ROM
0.4
BMU
SVN
MUS
BLR CRI VEN PAN
RUS BRA COL MEX KAZ NAM BWA THA
JPN GBR ISR BHR
QAT
NIC
0.2 ZWE
Model 0 1/64
1/32
1/16
1/8 1/4 1/2 PPP GDP Per Worker Data, U.S. = 1
1
2
Evidence Using Proxies for Individual Productivity ◮
Proxy for agriculture productivity: height
◮
Proxy for non-agriculture productivity: cognitive ability scores
Evidence Using Proxies for Individual Productivity ◮
Proxy for agriculture productivity: height
◮
Proxy for non-agriculture productivity: cognitive ability scores
◮
Correlation between height and cognitive ability: Data: 0.10 to 0.30 (Case & Paxson, 2005 + references therein) Model: 0.44
Evidence Using Proxies for Individual Productivity ◮
Proxy for agriculture productivity: height
◮
Proxy for non-agriculture productivity: cognitive ability scores
◮
Correlation between height and cognitive ability: Data: 0.10 to 0.30 (Case & Paxson, 2005 + references therein) Model: 0.44
◮
Agriculture workers in U.S. selected on height Average agriculture worker: 172.4 cm Average worker: 170.0 cm
Evidence Using Proxies for Individual Productivity ◮
Proxy for agriculture productivity: height
◮
Proxy for non-agriculture productivity: cognitive ability scores
◮
Correlation between height and cognitive ability: Data: 0.10 to 0.30 (Case & Paxson, 2005 + references therein) Model: 0.44
◮
Agriculture workers in U.S. selected on height Average agriculture worker: 172.4 cm Average worker: 170.0 cm
◮
Non-ag workers in developing countries selected on cognitive ability Miguel and Hamory, 2009: Kenya tracking survey De Weerdt et al, 2010: Tanzania tracking survey
Role of Women in Agriculture
◮
Women have an absolute disadvantage at agriculture work - Men are stronger; strength valued in agriculture (Pitt, Rosenzweig, Hassan, 2012) - Men do vast majority of plowing in practice (Foster & Rosenzweig, 1996)
◮
Women are more prevalent in agriculture in developing countries
Role of Women in Agriculture
Share of Agriculture Workers that are Women
80 Best Fit Line 70
LSO MOZ PRT
60 50 40 30 20 10
SLE
JOR
SYR GRC
SWZ TJK TKM
AZE DZA PLW MNG
COG TUR
MWI BWA
TCDPNG TZA AGO MDG GMB KHM COM LAO CAF VNM BGD KEN UGA GIN ZAR STP CHN CMR SEN DJI ZMB THA ETH GNB LBR SLB GHA ERI ALB GNQ BOL TGO IDN BEN SDN MLI CIVLKA NER MRT
CAN IRQ GABVUT AUT MAR NAM SVNITA KOR ROM UZB IRN CHE AUS TON JPN MNE CPV SRB EGY NOR NGA DEU ESP POL GEO FIN NLD SWE NZL FRA TUN LUX DMA BGR LBN MDA KGZPER WSM BEL HRV ZAF UKR DOM EST PAK KIR JAM LVA RUS KAZSUR ATG USA CZE LTU MUSBRA COL GBR DNK SVK PHL HUN ECU MYS GRD FJI BLR HND TTO ARM ISL ARG IRL VEN SAU
CHL URY MEX CRI GUY NIC PAN
BRNARE 0 SGP 0
10
20
SLV PRY
RWA BDI
ZWE
IND
BFA NPL
BTN AFG HTI
GTM OMN
BLZ
30
40 50 60 70 Share of Employment in Agriculture
80
90
100
Extension to Capital & Land
◮
Draws za and zn are now span-of-control parameters
◮
Land is fixed factor in agriculture; capital mobile - Lower A leads to even lower Ya /Na - Selection channel virtually unchanged
◮
Selection + land & capital: four times as much productivity variation in agriculture as non-agriculture
Conclusion
◮
Selection accounts for roughly 20% of why agriculture productivity differences larger than non-agriculture across countries
◮
Consistent with large wage gap in agriculture, even without barriers
◮
Implication: much of reason agriculture productivity differences so much larger may not be specific to agriculture
◮
Could be due to general factors (e.g. institutions) plus selection
Observed Structural Transformations: Women and Children Leave Faster
Evidence from Britain Composition of English Farm Workers
Men
1700
1800
1851
38.3
44.7
63.7
Women and Children
62.0
55.3
36.3
Total
100.0
100.0
100.0
Data Source: Allen (1994)
◮
Goldin and Sokoloff (1982; 1984) find a similar pattern in U.S.
Robustness to Correlation
Sensitivity of Sector Productivity differences to Correlation Parameter Correlation in individual productivity Ratio of average wage w ¯ a /w ¯n
0.00
0.20
0.30
0.35∗
0.40
0.50
0.99
∗
0.66
0.61
0.52
0.79
0.78
0.74
0.70
Ag. Productivity Difference
37
33
31
29∗
28
26
21
Non-Ag. Productivity Difference
10
11
13
13∗
14
15
18
Ag/ Non-Ag Ratio
3.8
3.0
2.5
2.2∗
1.9
1.7
1.2
Distribution of Hand Grip Strength by Sex
Source: Pitt, Rosenzweig, Hassan (2012)