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Lecture2 FactorBiasinCross-countryTechnology Differencespersonal.lse.ac.uk/casellif/L2.pdf · BEL...
52
Lecture 2 Factor Bias in Cross-country Technology Differences Barcelona, June 17 1 / 52
Transcript of Lecture2 FactorBiasinCross-countryTechnology Differencespersonal.lse.ac.uk/casellif/L2.pdf · BEL...
Lecture 2Factor Bias in Cross-country Technology
Differences
Barcelona, June 17
1 / 52
Yesterday
Aggregate Production Function
Yc = Ac [Kσc + CLσc ]1/σ
Human Capital
Lc = h(Hc , Tc)
z−1∑j=1
eβj Lj,c
ρ
+ B
J∑j=z
eβj Lj,c
ρ1/ρ
Physical Capital
Kc = [(Nc)η + D (Mc)η]1/η
2 / 52
Today
Aggregate Production Function
Yc = Ac [Kσc + CcLσc ]1/σ
Human Capital
Lc = h(Hc , Tc)
z−1∑j=1
eβj Lj,c
ρ
+ Bc
J∑j=z
eβj Lj,c
ρ1/ρ
Physical Capital
Kc = [(Nc)η + Dc (Mc)η]1/η
3 / 52
Reasons to Expect Non-Neutrality
Appropriate technology
- Theory: Atkinson and Stiglitz (1969), Diwan and Rodrik(1991), Basu and Weil (1998), Acemoglu and Zilibotti (2001),Caselli and Coleman (2006)
- Evidence: Caselli and Coleman (2001), Caselli and Wilson(2004)
Induced innovation/directed change
- Hicks (1932), Kennedy (1964), Samuleson (1965, 1966),Acemoglu (1998, 2002), Jones (2005)
4 / 52
The Questions
Are there systematic non-neutralities in technology differencesacross countries?
If so, can they be seen as evidence of appropriate-technologychoice, i.e. can they be rationalized by factor endowments?
How does this fit with the "standard" view whereby poorcountries suffer from "barriers" to technology adoption?
5 / 52
Alternative representationWe have written aggregation functions of the form
Xc = Ω1c
[(X1c)ζ + Ω2c (X2c)ζ
]1/ζAlternative representation is
Xc =[(Z1cX1c)ζ + (Z2cX2c)ζ
]1/ζWith mapping
Ω1c = Z1c
Ω2c =
(Z2c
Z1c
)ζCan retrieve the Z s from the Ωs and viceversaWill be switching between two representations according toconvenience
6 / 52
Some terminology
Consider again
Xc =[(Z1cX1c)ζ + (Z2cX2c)ζ
]1/ζTime series:
Technical change factor-i augmenting if Zi increases over timeTechnical change factor-i biased if (Zi/Zj)
ζ increases over timeRationale
MPi
MPj∝(
Zi
Zj
)ζ (Xi
Xj
)ζ−1
Cross-section:
Technology differences factor-i augmenting if Zi higher inhigh-Xi countriesTechnology differences factor-i biased if (Zi/Zj)
ζ higher inhigh Xi/Xj countries
7 / 52
Quick aside
You might be more comfortable with
Xc =
[ω(Z1cX1c
)ζ+ (1− ω)
(Z2cX2c
)ζ]1/ζ
Think of the ωs as being there - I am just omitting them tokeep equations uncluttered(Will just remember they are there when let ζ → 0)The mapping is
Z1c = ω1/ζ Z1c , Z2c = (1− ω)1/ζ Z2c
Ω1c = ω1/ζ Z1c , Ω2c =1− ωω
(Z2c
Z1c
)ζ.
8 / 52
Plan of the lecture
Is there a bias towards workers with more schooling (relative toworkers with less schooling)?
Is there a bias towards reproducible capital (relative to naturalcapital)?
Is there a bias towards labour (relative to capital)?
9 / 52
Education Bias
Production Function
Yc = Fc(Kc ,CcLc)
Labour input
Lc = h(Hc , Tc)
z−1∑j=1
eβj Lj ,c
ρ
+ Bc
J∑j=z
eβj Lj ,c
ρ1/ρ
Want to know if/how Bc varies across countries
10 / 52
Backing out Bc
Yesterday we wrote
Wz,c
W1,c= Bc
(∑Jj=z eβj Lj ,c
)ρ−1
(∑z−1j=1 eβj Lj ,c
)ρ−1
We assumed Bc = B , retrieved it from skill premium andrelative supplies in USA, and 1/(1− ρ) = 1.5
For country-varying B , need estimates of country-specific skillpremia
Problem: cross-country data sets don’t report skill premia
11 / 52
Mincerian Returns v. Skill Premia
Cross-country datasets report bc from
logWi ,c = αc + bcsic + εic
estimated on country-specific microdata
Tempting to sayWz,c
W1,c= ebcn
Where n is year-of-schooling difference between benchmarkskilled type and benchmark unskilled type
Tempting, but wrong
12 / 52
Another slide from yesterday (almost)
Consider special case βj = βSjz−1∑j=1
eβSj Lj ,c
ρ
+ Bc
J∑j=z
eβSj Lj ,c
ρ1/ρ
Implies
log(Wj , j < z) = α + βSj
log(Wj , j ≥ z) = α + βSj
13 / 52
Mincerian Returns under imperfect substitutionLog Wage profile
0 2 4 6 8 10 12 141.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
years of schooling
log
wag
e
14 / 52
Mincerian Returns under imperfect substitutionEstimated Mincerian return
0 2 4 6 8 10 12 141.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
years of schooling
log
wag
e
15 / 52
Using Mincerian returns to back out skill premiaRecall
Wj (j < z) = W1eβj
Wj (j ≥ z) = Wzeβj
OLS Formula
b =
Pj Lj (Sj − µs)(log(Wj)− µlog(W ))P
j Lj (Sj − µs)2,
µs =X
j
LjSj
µlog(W ) =X
j
Lj log(Wj )
Plug from above and do some algebra
b =(log Wz − log W1)
Pj≥z Lj (Sj − µs) +
Pj Lj (Sj − µs)βjP
j Lj (Sj − µs)2
Solve for skill premium
(log Wz − log W1) =bP
j Lj (Sj − µs)2 −P
j Lj (Sj − µs)βjPj≥z Lj (Sj − µs)
16 / 52
Data on Mincerian returns
A collection of collections plus a new collection
70 countries in the 1990s
31 countries in the 2000s
17 / 52
Data on Mincerian returns (1990s)ZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERSGP
SGP
SGPBGR
BGR
BGRPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLNOR
NOR
NORDNK
DNK
DNKBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNPAK
PAK
PAKVEN
VEN
VENCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANJAM
JAM
JAMUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNTZA
TZA
TZANPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUBOL
BOL
BOLHND
HND
HNDDOR
DOR
DORVNM
VNM
VNM.05
.05
.05.1
.1
.1.15
.15
.15.2
.2
.2.25
.25
.25.3
.3
.3mincerian coeff.
min
ceria
n co
eff.
mincerian coeff.-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = -.008 (.004) [without Jamaica b = -.008 (.003)]
18 / 52
Data on Mincerian returns (2000s)ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN0
0
0.05
.05
.05.1
.1
.1.15
.15
.15mincerian coeff.
min
ceria
n co
eff.
mincerian coeff.-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = -.02 (.007)
19 / 52
Backed-Out Skill Premia (1995)ZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITAESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKCOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNTZA
TZA
TZANPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUVNM
VNM
VNM0
0
02
2
24
4
46
6
68
8
8log skill premium
log
skill
prem
ium
log skill premium-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = -.5 (.09) [without Tanzania b = -.27 (.06)]
20 / 52
Backed-Out Skill Premia (2005)ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN0
0
0.5
.5
.51
1
11.5
1.5
1.52
2
2log skill premium
log
skill
prem
ium
log skill premium-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = -.32 (0.09)
21 / 52
Reminder
Lc = h(Hc , Tc)
z−1∑j=1
eβj Lj ,c
ρ
+ Bc
J∑j=z
eβj Lj ,c
ρ1/ρ
Wz,c
W1,c= Bc
(∑Jj=z eβj Lj ,c
)ρ−1
(∑z−1j=1 eβj Lj ,c
)ρ−1
22 / 52
Education bias (1995)ZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITAESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKCOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNTZA
TZA
TZANPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUVNM
VNM
VNM-2
-2
-20
0
02
2
24
4
4log of Bc
log
of B
c
log of Bc-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = .16 (.09)
23 / 52
Education bias (1995) without TanzaniaZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITAESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKCOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNNPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUVNM
VNM
VNM-2
-2
-2-1
-1
-10
0
01
1
12
2
2log of Bc
log
of B
c
log of Bc-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = .4 (.06) [without Uganda b=.35 (.05)]
24 / 52
Education bias (2005)ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN0
0
0.5
.5
.51
1
11.5
1.5
1.5log of Bc
log
of B
c
log of Bc-4
-4
-4-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log relative supply of skills
log relative supply of skills
log relative supply of skills
b = .34 (.09)
25 / 52
Notation
LHc =J∑
j=z
eβSj Lj ,c
LLc =z−1∑j=1
eβSj Lj ,c
26 / 52
Understanding the result
Log(Wz/W1)
Model
Log(LH/LL)
Model’
Data
Where:
Model = log(Bc) + (ρ− 1) log„
LHc
LLc
«27 / 52
Interpreting the result
Use version
Lc = [(BLcLLc)ρ + (BHcLHc)ρ]1/ρ
want to explain why BHBL
increases with LHLL
Firms choose among “blueprints”
Each blueprint implies a certain combination of BL and BH
Firms choose the appropriate blueprint given factor prices
Skill-abundant countries adopt skill-biased technologies, andvice versa
28 / 52
Modelling strategy: technology frontiers
B
Aa
A
Ab
Ba
Bb
Efficiency of Unskilled Labor
Effic
ienc
y of
Ski
lled
Labo
r
A (B) is the technology frontier of country A (B). Aa and Ba (Ab and Bb) are
appropriate choices of technology for unskilled-labor (skilled labor) rich countries.29 / 52
The model
Competitive firms maximize profits subject to
Y = F[K , [(BLLL)ρ + (BHLH)ρ]
1ρ
](BH)ω + γ (BL)ω ≤ B
Choice variables: K ,LL,LH , and BL
WL, WH , and R determined in competitive factors’ markets
K ,LL,LH inelastically supplied
30 / 52
Equilibrium
If ω > ρ/(1− ρ) equilibrium is symmetric (all in the middle)
If ω < ρ/(1− ρ) equilibrium is asymmetric (all at the corners)
31 / 52
Properties of equilibrium
Firms’ choices
LH
LL=
(Wz
W1
) ω−ρωρ−(ω−ρ)
γρ
(ω−ρ)−ωρ
BH
BL=
(Wz
W1
) ρωρ−(ω−ρ)
γ1−ρ
(ω−ρ)−ωρ
Hence:
LHLL
decreasing in WzW1
if ρ > 0, BHBL
decreasing in WzW1
if ρ < 0, BHBL
increasing in WzW1
32 / 52
Properties of equilibrium (cont.)
General equilibrium(BH
BL
)ω−ρ= γ
(LH
LL
)ρHence:
if ρ > 0, BHBL
increasing in LHLL
, or skill bias
if ρ < 0, BHBL
decreasing in LHLL
33 / 52
Properties of equilibrium (cont.)
General equilibrium (cont.)
BH =
(B
1 + γρ/(ρ−ω)(LH/LL)ωρ/(ρ−ω)
)1/ω
BL =
(B/γ
1 + γρ/(ω−ρ)(LH/LL)ωρ/(ω−ρ)
)1/ω
With ρ > 0,
BH increasing in both B and LH/LL
BL increasing in B but decreasing in LH/LL
34 / 52
Using the empirical results to parametrize the frontier
We said (BH
BL
)ω−ρ= γ
(LH
LL
)ρOr
log(
BH
BL
)=
log γω − ρ
+ρ
ω − ρlog(
LH
LL
)
This is the OLS regeression we run before!
for both years we found ρω−ρ = 0.35, so ω ≈ 1.3
35 / 52
(not so small) aside: Bias and Income (1995)ZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITAESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKCOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNNPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUVNM
VNM
VNM-2
-2
-2-1
-1
-10
0
01
1
12
2
2log of Bc
log
of B
c
log of Bc6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = 0.33 (0.07)
36 / 52
Bias and income (2005)ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN0
0
0.5
.5
.51
1
11.5
1.5
1.5log of Bc
log
of B
c
log of Bc6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = -.03 (0.11))
37 / 52
How can it be?
Answer: small correlation between relative skill supply and incomein 2005 sample
All Data My Sample
1995 0.70 (N=142) 0.82 (N=58)2005 0.71 (N=142) 0.42 (N=31)
38 / 52
Natural v. Reproducible Capital
Yc = Fc
([(Nc)η + Dc (Mc)η]1/η , Lc
)Impose no arbitrage (ignore capital gains)
MPMcPMc
=MPNcPNc
Hence
Dc =PMc
PNc
(McNc
)1−η
39 / 52
Implications
Dc =PMc
PNc
(McNc
)1−η
Recall
Significant variation across countries in M/N
M/N higher in rich countries
Assume variation in quantities dominates variation in prices
Hence
Rich countries should have higher Dc
Consistent with theoretical model if η > 0
40 / 52
Capital v Labor
Work with alternative notation
Yc = [(AKcKc)σ + (ALcLc)
σ]1/σ
Marginal product pricing
Wc = (ALc)σ
„Yc
Lc
«1−σ
Rc = (AKc)σ
„Yc
Lc
«1−σ
So
ALc =
„WcLc
Yc
«1/σ Yc
Lc
AKc =
„RcKc
Yc
«1/σ Yc
Kc
and As can be retrieved if we know shares in income (and σ).
41 / 52
Stylized fact on income shares
Gollin: no systematic variation with income
Note: does not imply it’s the same for everyone!
42 / 52
Implication of Gollin “fact”
ALc =
(WcLc
Yc
)1/σ Yc
Lc
AKc =
(RcKc
Yc
)1/σ Yc
Kc
will inherit properties of YcLc
and YcKc
43 / 52
Labor productivity using Lc = eβHHc [LρLc + BcLρHc ]
1/ρ, 1995ZAF
ZAF
ZAFGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERPHL
PHL
PHLSLV
SLV
SLVITA
ITA
ITAESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKCOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEAUT
AUT
AUTIRL
IRL
IRLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDCHL
CHL
CHLURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCCZE
CZE
CZECHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FININD
IND
INDCHN
CHN
CHNCMR
CMR
CMRZWE
ZWE
ZWEGTM
GTM
GTMZMB
ZMB
ZMBPAN
PAN
PANUGA
UGA
UGANIC
NIC
NICCRI
CRI
CRIPRY
PRY
PRYSDN
SDN
SDNNPL
NPL
NPLKEN
KEN
KENECU
ECU
ECUVNM
VNM
VNM5
5
56
6
67
7
78
8
89
9
9log labor productivity (schooling only)
log
labo
r pro
duct
ivity
(sc
hool
ing
only
)
log labor productivity (schooling only)6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = 0.35 (0.10) [Tanzania excluded]
44 / 52
Labor productivity using Lc = eβHHc [LρLc + BcLρHc ]
1/ρ, 2005ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN5
5
56
6
67
7
78
8
89
9
9log labor productivity (schooling and health)
log
labo
r pro
duct
ivity
(sc
hool
ing
and
heal
th)
log labor productivity (schooling and health)6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = 0.89 (0.22)
45 / 52
Labor productivity using Lc = eβHHc+βT T [LρLc + BcLρHc ]
1/ρ
ZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPPOL
POL
POLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCHRV
HRV
HRVCZE
CZE
CZEBEL
BEL
BEL4
4
45
5
56
6
67
7
78
8
8log labor productivity (schooling, health, and tests)
log
labo
r pro
duct
ivity
(sc
hool
ing,
hea
lth, a
nd t
ests
)
log labor productivity (schooling, health, and tests)6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = 0.7 (0.29), year 2005
46 / 52
Capital productivity using reproducible capitalTTO
TTO
TTOZAF
ZAF
ZAFMAR
MAR
MARKWT
KWT
KWTIRN
IRN
IRNQAT
QAT
QATROM
ROM
ROMGHA
GHA
GHAKGZ
KGZ
KGZIDN
IDN
IDNPER
PER
PERSGP
SGP
SGPROU
ROU
ROUBGR
BGR
BGRPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAULUX
LUX
LUXITA
ITA
ITARUS
RUS
RUSLTU
LTU
LTUESP
ESP
ESPPOL
POL
POLNOR
NOR
NORDNK
DNK
DNKISL
ISL
ISLBRA
BRA
BRACOL
COL
COLSVK
SVK
SVKUSA
USA
USADEU
DEU
DEUTUN
TUN
TUNFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSVN
SVN
SVNSWE
SWE
SWEDZA
DZA
DZAAUT
AUT
AUTIRL
IRL
IRLNZL
NZL
NZLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDJOR
JOR
JORCHL
CHL
CHLHKG
HKG
HKGSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRTUR
TUR
TURTHA
THA
THAISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAMYS
MYS
MYSCZE
CZE
CZECHE
CHE
CHEMAC
MAC
MACGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FINKOR
KOR
KORUGA
UGA
UGAECU
ECU
ECUSLE
SLE
SLEBRN
BRN
BRNJAM
JAM
JAMGMB
GMB
GMBKAZ
KAZ
KAZBDI
BDI
BDIVNM
VNM
VNMLKA
LKA
LKACRI
CRI
CRILSO
LSO
LSORWA
RWA
RWAZMB
ZMB
ZMBARE
ARE
AREMNG
MNG
MNGIRQ
IRQ
IRQGUY
GUY
GUYMRT
MRT
MRTCOG
COG
COGCMR
CMR
CMRLBY
LBY
LBYTZA
TZA
TZAPAK
PAK
PAKPNG
PNG
PNGTWN
TWN
TWNCOD
COD
CODNER
NER
NERMWI
MWI
MWIYEM
YEM
YEMCIV
CIV
CIVSEN
SEN
SENDOR
DOR
DORSDN
SDN
SDNZWE
ZWE
ZWEMDV
MDV
MDVBOL
BOL
BOLMUS
MUS
MUSNAM
NAM
NAMBRB
BRB
BRBPRY
PRY
PRYHTI
HTI
HTINPL
NPL
NPLBEN
BEN
BENPAN
PAN
PANIND
IND
INDLBR
LBR
LBRGTM
GTM
GTMFJI
FJI
FJIGAB
GAB
GABHND
HND
HNDAFG
AFG
AFGKHM
KHM
KHMTGO
TGO
TGOSWZ
SWZ
SWZMLI
MLI
MLIMOZ
MOZ
MOZKEN
KEN
KENNIC
NIC
NICLAO
LAO
LAOBLZ
BLZ
BLZCHN
CHN
CHNTON
TON
TONCUB
CUB
CUBCAF
CAF
CAFBGD
BGD
BGDVEN
VEN
VEN-3
-3
-3-2
-2
-2-1
-1
-10
0
01
1
1log productivity of reproducible capital
log
prod
uctiv
ity o
f rep
rodu
cibl
e ca
pita
l
log productivity of reproducible capital6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = -.26 (0.04), year 2005
47 / 52
Capital productivity using total capitalTTO
TTO
TTOZAF
ZAF
ZAFMAR
MAR
MARIRN
IRN
IRNROM
ROM
ROMGHA
GHA
GHAIDN
IDN
IDNPER
PER
PERSGP
SGP
SGPROU
ROU
ROUBGR
BGR
BGRPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPNOR
NOR
NORDNK
DNK
DNKBRA
BRA
BRACOL
COL
COLUSA
USA
USADEU
DEU
DEUTUN
TUN
TUNFRA
FRA
FRAHUN
HUN
HUNARG
ARG
ARGSWE
SWE
SWEDZA
DZA
DZAAUT
AUT
AUTIRL
IRL
IRLNZL
NZL
NZLEGY
EGY
EGYMEX
MEX
MEXNLD
NLD
NLDJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYTUR
TUR
TURTHA
THA
THAISR
ISR
ISRPRT
PRT
PRTGRC
GRC
GRCLVA
LVA
LVAMYS
MYS
MYSCHE
CHE
CHEGBR
GBR
GBRBEL
BEL
BELEST
EST
ESTAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNFIN
FIN
FINKOR
KOR
KORECU
ECU
ECUJAM
JAM
JAMGMB
GMB
GMBBDI
BDI
BDILKA
LKA
LKACRI
CRI
CRILSO
LSO
LSORWA
RWA
RWAZMB
ZMB
ZMBGUY
GUY
GUYMRT
MRT
MRTCOG
COG
COGCMR
CMR
CMRPAK
PAK
PAKNER
NER
NERMWI
MWI
MWICIV
CIV
CIVSEN
SEN
SENDOR
DOR
DORZWE
ZWE
ZWEBOL
BOL
BOLMUS
MUS
MUSNAM
NAM
NAMBRB
BRB
BRBPRY
PRY
PRYHTI
HTI
HTINPL
NPL
NPLBEN
BEN
BENPAN
PAN
PANIND
IND
INDGTM
GTM
GTMFJI
FJI
FJIGAB
GAB
GABHND
HND
HNDTGO
TGO
TGOSWZ
SWZ
SWZMLI
MLI
MLIMOZ
MOZ
MOZKEN
KEN
KENNIC
NIC
NICBLZ
BLZ
BLZCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN-2
-2
-2-1.5
-1.5
-1.5-1
-1
-1-.5
-.5
-.50
0
0.5
.5
.5log productivity of total capital
log
prod
uctiv
ity o
f tot
al c
apita
l
log productivity of total capital6
6
68
8
810
10
1012
12
12log of income per worker
log of income per worker
log of income per worker
b = -.10 (0.05), year 2005
48 / 52
Labor productivity vs K/LZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPBRA
BRA
BRACOL
COL
COLHUN
HUN
HUNARG
ARG
ARGAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN5
5
56
6
67
7
78
8
89
9
9log labor productivity (schooling and health)
log
labo
r pro
duct
ivity
(sc
hool
ing
and
heal
th)
log labor productivity (schooling and health)5
5
56
6
67
7
78
8
89
9
910
10
10ratio tot. cap./labor (schooling and health)
ratio tot. cap./labor (schooling and health)
ratio tot. cap./labor (schooling and health)
b = .79 (0.05), year 2005
49 / 52
Capital productivity vs K/LZAF
ZAF
ZAFIDN
IDN
IDNBGR
BGR
BGRPHL
PHL
PHLITA
ITA
ITARUS
RUS
RUSESP
ESP
ESPBRA
BRA
BRACOL
COL
COLHUN
HUN
HUNARG
ARG
ARGAUT
AUT
AUTIRL
IRL
IRLMEX
MEX
MEXCHL
CHL
CHLTUR
TUR
TURTHA
THA
THAPRT
PRT
PRTGRC
GRC
GRCBEL
BEL
BELPAK
PAK
PAKBOL
BOL
BOLGTM
GTM
GTMCHN
CHN
CHNBGD
BGD
BGDVEN
VEN
VEN-2
-2
-2-1.5
-1.5
-1.5-1
-1
-1-.5
-.5
-.50
0
0.5
.5
.5log productivity of total capital
log
prod
uctiv
ity o
f tot
al c
apita
l
log productivity of total capital5
5
56
6
67
7
78
8
89
9
910
10
10ratio tot. cap./labor (schooling and health)
ratio tot. cap./labor (schooling and health)
ratio tot. cap./labor (schooling and health)
b = -.21 (0.05), year 2005
50 / 52
Summing up on AK and AL
Seems likely AL higher in rich countries
Seems possible AK higher in poor countries
Consistent with theoretical model?
Previous results also implies AL/AK increasing in K/L
Consistent with model if and only if σ < 0
51 / 52
Summary of lecture 2
Intimations of non-neutrality all over the place
Highly-educated labor relatively more efficient than lesseducated labor in countries with larger relative endowments ofhighly- educated laborReproducible capital relatively more efficient than naturalcapital in countries with larger relative endowments ofreproducible capitalAggregate labor relatively more efficient than aggregate capitalin countries with smaller relative endowments of labor
These findings are consistent with a simple model ofappropriate-technology choice if:
Highly educated and less educated are good substitutes (ρ > 0)Reproducible and natural capital are good substitutes (η > 0)Capital and labor are poor substitutes (σ < 0)
52 / 52
