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)