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Production Functions
Yct = Fct (X1ct ,X2ct , ...)
Fct (X1ct ,X2ct , ...) = Act G (X1ct ,X2ct , ...)
3
Production Functions
Yct = Fct (X1ct ,X2ct , ...)
Fct (X1ct ,X2ct , ...) = Act G (X1ct ,X2ct , ...)
Fct (X1ct ,X2ct , ...) = G (A1ctX1ct ,A2ctX2ct , ...)
4
Choice of Inputs and Functional Form
Yct =[(AKctKct )
σ + (ALctLct )σ]1/σ
Lct =[(AUctUct )
ρ + (ASctSct )ρ]1/ρ
Kct =[(ANctNct )
η + (AMctMct )η]1/η
5
Overview (1)
Skill bias
Corr[(AScAUc
)ρ
,Yc
],Corr
[(AStAUt
)ρ
, t]> 0
Reproducible-Capital Bias
Corr[(AMcANc
)η
,Yc
]> 0
Capital Bias
Corr
[(AKcALc
)σ
,Yc
],Corr
[(AKtALt
)σ
, t
]> 0
Experience Bias
9
Relative Skill Supply Across Countries
URY
TON
CUB
DEU
VNM
POLNIC
JPN
ESP
PAN
BLZ
CZE
PRT
BEN
JAM
PHL
NZL
MEX
PNG
TGO
GABMLT
TUN
BOL
SDN
MDV
TJK
GMB
AUS
BEL
MWI
PER
TUR LBY
DZA
LBR
CAN
LSO
PRY
SVK
SGP
LVA
CIV
FRA
COL
ARE
SLV
MYS
INDSEN
CMR
CHE
MACBRB
ITA
RWA
ISR
KAZ
IRL
ARM
ROM
IRN
NOR
DOM
KGZ
LAO
HKG
NPL
HNDNAM
IDN
SER
TTO
ECU
MNG
THASWZ
LTU
BWA
IRQ
CHN
ZMB
CRI
SWERUS
MRT
BHR
ZAF
KEN
COG
MAR
LKA
DNK
ALB
GHA
UGAKHM
TWN
BRA
ARGKWT
CAF
FINBGR
BDI
SVN
KOR
JOR
USA
HRV
UKR
GBR
ROU
PAK
GRCLUX
ZWE
MLI
TZA
MUS
ISL
YEM
HUN
NLD
GUY
EST
CHLCYP
EGY
HTI
BRN
SLE
MOZ
SAU
AUT
COD
BGDVEN
AFG
SYR
QAT
FJI
NER
GTM
.01
.02
.04
.08
.16
.32
.64
1
.01 .02 .04 .08 .16 .32 .64 1
1995
PNG
PAK
JAM
MLT
EST
BHR
ROU
KEN
PER
TWN
DZAAUT
BRN
IRL
BRBPOLPRT
GAB
RWA
URYVEN
UGA
PAN
CIV
TZA
NOR
NPL
DEU
LBY
TUN
USA
UKR
LBR TTOTON
HUN
FJICOL
GBR
TGO
LKA
AREHKG
THA
COG
NAMGHA
TJK SVK
IND
LVA GRC
ARM
SYR
LTU AUSNZL
NIC
RUS
KHM
HND
SEREGY
CMR
MOZ
SAU
LAO
ITA
KAZ
CUB
MRT
HTI
ZMB
MYS
CAF
BEN
FIN
BGD GUY
MEX
BLZ
KGZ
KWT
GMB
BDI
NLD
CRI
CHL
SLV
AFG
NER
MUS
IDN
SGP
COD
CHEPHL
SVN
CZE
CHN
LSO
TUR
ARG MAC
ISR
JPN
SWEKOR
ECU
DOM
DNKESPBGR
BEL
PRY
SDN
YEM
SWZ
CYP
IRNROM
HRV
GTM
CAN
QAT
MDV
FRA
MAR
BOL
MLI
BRAALB
IRQ
VNM
SLE
MNG
ZAF
MWI
BWA
ISL
SEN
LUX
JOR
ZWE
.01 .02 .04 .08 .16 .32 .64 1
2005re
lativ
e su
pply
of s
kills
(US=
1)
income per worker (US=1)
14
Skill Premium Across Countries
KHM
KORNPL NZLSWEUKREGY CYPZAFSDN ISRNORCHNVNM DNKBGR CZE AUSHRV NLDBLZECU BELSVK GRCZWE LBYCMR POLLVA KWTJPNPERBOLGMB ROU CRI ITATURSLV CANMEX FRAUSALUXESPFINAUTRUSGHA SVNHUNVEN IRLIDN ARGCOL CHEMYS DEUHND URYPHLKEN DOMMAR GBRTHA PRT
PRY HKGCHLNIC PANZMB SGPBRA
PAKINDLSO GTM
BWA
.25
.51
24
.01 .02 .04 .08 .16 .32 .64 1
1995
SDN
MARSENJAMDZADOMSLVCRI GRCNIC QATTJK SYRECUPRY PAN IRLUKREGY BELESPITASWEKWTNORGBRCZEJORHND SVKKHM SER AUTROM BGR DEULVAIRN SVNFRAHRVPRTRUSVNM FINMNGMLI LKA ROU POLKAZPER HUN USACOLPAK ARGBOL TUR ISRZAFMYSCHNBGD AUSIND VENMEXCHLURY
BEN PHLHTI
SGPIDNTGO BRACIV GTM
THABWANER
MLTTZA
.01 .02 .04 .08 .16 .32 .64 1
2005sk
ill pr
emiu
m (U
S=1)
income per worker (US=1)
15
Skill Bias Result
KHM
KOR
NPL
NZLSWEUKR
EGY
CYP
ZAF
SDN
ISRNOR
CHN
VNM
DNKBGR
CZE
AUS
HRV
NLD
BLZ
ECU
BEL
SVKGRC
ZWELBY
CMR
POL
LVAKWT
JPNPER
BOL
GMB
ROUCRI ITA
TURSLV
CAN
MEX
FRA
USA
LUXESPFIN
AUT
RUS
GHA
SVN
HUN
VEN
IRL
IDN
ARGCOL
CHE
MYS
DEU
HND
URY
PHL
KEN
DOMMAR GBRTHAPRTPRY
HKGCHL
NIC
PAN
ZMB
SGPBRA
PAK
INDLSO
GTM
BWA
.01
.05
.25
1.25
.01 .02 .04 .08 .16 .32 .64 1
1995
SDN
MAR
SEN
JAMDZA
DOMSLV
CRI
GRC
NIC
QATTJK
SYR
ECUPRY
PAN
IRL
UKR
EGY
BEL
ESPITA
SWE
KWT
NOR
GBR
CZE
JOR
HND
SVK
KHM
SER
AUTROM
BGR
DEU
LVAIRN
SVN
FRA
HRVPRT
RUS
VNM
FINMNG
MLI
LKA
ROU
POL
KAZPERHUN
USA
COL
PAK
ARG
BOL
TUR
ISR
ZAF
MYSCHN
BGD
AUS
IND
VEN
MEX
CHL
URYBEN
PHL
HTI
SGP
IDN
TGO
BRA
CIV GTM
THA
BWA
NER
MLT
TZA
.01 .02 .04 .08 .16 .32 .64 1
2005sk
ill bi
as (U
S=1)
income per worker (US=1)
16
Why the Data Want Bias
21
01
2
6 4 2 0log relative supply of skills
Fitted values
21
01
2
6 4 2 0log relative supply of skills
Counterfactual values
log
skill
prem
ium
Counterfactual =(ρ− 1) log( SU
)17
Natural and Reproducible Capital
Kct =[(ANctNct )
η + (AMctMct )η]1/η
MPMc
MPNc=
(AMcANc
)η (Mc
Nc
)η−1
18
Reproducible/Natural Capital Across Countries
CAF SDN TONUGA
CODBDI BEN GUYMOZMWINER BOLNPL GHASLE PNGMLIRWA PAKIND BLZKEN SWZMNGZMB NICCOG GTMFJISEN ECUHNDTGO SAUKWTBRNSYR VENZWE BGD CMR IRNLKA AREHTIMRTCIV CRICHN EGYCOL BHRMUSGMB NAM GABZAFIDN JAMSLVPANPHL CHLDOMBRA TTONZLDZATHABWAMEXURYMYSPER ARGMAR TUN CANJOR NORAUSLSO IRLHUN
FINCYPSWEUSAISLGRCDNKNLD
ESPPRTISRAUTFRAITAGBRCHEKOR LUX
DEUMLTBEL
JPN.0
1.0
4.1
6.6
42.
56
.01 .02 .04 .08 .16 .32 .64 1
1995
BDILBRCAF
CODTONRWAUGASLE GUYSDNBOLNER LAO KWTPNGCOG GTMNPL ECU SAUHNDCIV BLZBEN BRNKGZZWE MRTPAKCMRMWI GHA SYRKENVNM BHRVENMLI TTOSWZ GABRUSMOZ IRN AREEGYGMBTJK NICMNGZMB DZATGOBGD IND FJIBRAPHLIDNROM COLSEN CHLUKR ARGCRIURYPERTHA MYSSLVARMALBHTI NZLPANCHN ROUMUSNAMLKA NORDOMBGRTUNZAF
POL CANJORMAR TURJAM AUSLVAMEXLTUBWAHRV FIN
HUN SWESVK DNKUSAMDV NLDGRCCZEISRIRLMLTFRAESPISLITAAUTGBRPRTLSODEUCHEBELKOR
LUX
JPN
.01 .02 .04 .08 .16 .32 .64 1
2005re
lativ
e su
pply
of r
epro
duci
ble
capi
tal (
US=
1)
income per worker (US=1)
19
Relative Marginal Productivities Across Countries
BEN
MOZ
NER BOL
SLE
RWA
IND
KEN MNG
ECU
HND
SAUKWTVEN
CMR
IRN
LKA
MRT
CIVCRI
CHN
EGY
COL
BHR
NAMZAF
IDN
PAN
PHL
CHL
DOM
BRA
TTO
NZL
THA MEX
URY
MYS
PER
ARG
MARTUN
CAN
JOR
AUSLSO
IRL
HUNFIN
CYP
SWEUSA
ISL
GRC
DNK
NLDESP
PRT
ISR
AUT
FRA
ITA
GBRCHEDEU
MLT
HKG
02
46
8
.01 .02 .04 .08 .16 .32 .64 1
1995
NER
KWT
ECU
SAU
HND
CIV
KGZ
MRT
CMR
KEN
BHR
VENGAB
MOZ
IRN
EGY
TJK
MNG
IND
FJI
BRA
PHL
IDN
ROM
COL
SEN
CHLUKR
ARG
CRI
URYPER
THA
MYS
ARM
NZL
CHN
ROU
NAM
LKA
NOR
DOM
BGR
TUN
ZAF
POL
CAN
MAR
TUR
JAMAUS
LVA
MEX
LTU
BWA
HRV
FIN
HUN
SWESVK
DNK
USANLD
GRC
CZE
ISR
IRL
FRA
ESP
ISL
ITA
AUT
GBRPRT
LSO
DEUCHE
BEL
LUX
HKG
02
46
8
.01 .02 .04 .08 .16 .32 .64 1
2005re
lativ
e m
argi
nal p
rodu
ct o
f rep
rodu
cibl
e ca
pita
l (U
S=1)
income per worker (US=1)
20
Labor Share
CAF
BDI
BEN
MOZ
NERBOL
SLERWA
IND
KEN
SWZ
MNG
GTM
FJI
SEN
ECU
HND
TGO
SAU
KWT
VEN
ZWE
CMR
IRN
LKA
MRT
CIV
CRI
CHN
EGY
COL
BHR
MUS
NAM
GAB
ZAF
IDN
JAM
PANPHL CHLDOM
BRA
TTONZL
THA
BWA
MEX
URYMYS
PER
ARG
MAR
TUN
CAN
JOR
NORAUS
LSO
IRL
HUN
FIN
CYP
SWE USA
ISL
GRC
DNKNLDESP
PRT
ISR
AUTFRA
ITA
GBR
CHE
KORLUX
DEU
MLT
BEL
JPN
HKG
SGP
TJK
POL
KGZ
ROM
IRQ
QAT
KAZ
LTUPRY
SVK
EST
BRB
TWN
BGR
ARM
RUS
HRV
CZE
UKR
LVA
TUR
MAC
ROU
SVN
TZA
.2.4
.6.8
1
0 .5 1 1.5 2
1995
BDI
CAF
RWASLE
BOL
NER
KWT
GTM
ECU
SAU
HND
CIV
BEN
KGZZWEMRT
CMR
KEN
BHRVEN
TTO
SWZ
GAB
RUS
MOZ
IRN
EGY
TJK
MNG
TGO
INDFJIBRA
PHLIDN
ROM
COL
SENCHL
UKR
ARG
CRI
URY
PER
THA
MYS
ARM
NZL
PAN
CHN
ROU
MUS
NAM
LKA
NOR
DOM
BGRTUN
ZAFPOL
CAN
JOR
MAR
TUR
JAMAUS
LVA
MEX
LTU
BWA
HRVFINHUNSWE
SVK
DNK USANLD
GRCCZE ISR
IRL
MLT
FRAESP
ISL
ITA
AUTGBR
PRT
LSO DEU
CHE
BEL
KORLUX
JPNHKG
SGP
ESTPRY
MAC
QAT
KAZ
SVN
BRB
IRQ
TZATWN
CYP
.2.4
.6.8
1
0 .5 1 1.5
2005la
bor s
hare
in in
com
e
income per worker (US=1)
Figure:25
Effi ciency of Labor
KOR
KHM
NZLSWE
UKR
ZAF
CZE
VNM
CHN
HRV
CYP
EGY
NPL
DNK
BGR
NOR
ISR
SVKSDN
ZWE
BLZ
AUSECU
CMR
LVAROU
NLD
LBY
BEL
GMB
BOL
SLV
KEN
ITAKWT
GHA
PER
MEXGRC
TUR
IDN
FRAPOL
AUTCRI
VEN
RUS
JPN
ESP
LUX
HNDHUN
CANCOL
FIN
MYS
DEU
MAR
DOM
SVN
ARGURY
CHE
IRLTHA
IND
USA
ZMB
PRT
GBR
PHL
NIC
PRYHKG
LSO CHLPAN
BRA
SGP
PAK
GTM
BWA
110
100
.01 .02 .04 .08 .16 .32 .64 1
1995
JAM
TJK
SDN DZA
DOM
MAR
SEN
CRISLV
PRY
GRC
NIC
SYR
ECU
ESP
QAT
UKR
ITA
PAN
KWT
BELIRL
EGY
SWE
SVKHND
CZE
SER
JOR
AUTHRV
GBR
KHM
VNM
BGR
FRA
RUS
DEU
ROM
IRNMLI
LVA
PRT
NOR
SVN
LKA
TZA
MNG
IND
ROUPAK
FIN
ZAF
PERKAZ
COL
BGD
VEN
BOL
TUR
CHN
POL
MYS
BEN
HUN
MEXARGIDN
TGO
URY
CHL
NERCIV
ISR
USA
HTI
GTM
PHL
AUS
SGP
BRATHABWA MLT
.01 .02 .04 .08 .16 .32 .64 1
2005ef
ficie
ncy
of la
bor (
US=
1)
income per worker (US=1)
28
Effi ciency of Capital
CAF
SDNTON
UGA
COD
BDI
BEN
GUYMOZ
MWI
NERBOL
NPL
GHASLE
PNG
MLI
RWA
PAK
IND
BLZ
KEN SWZ
MNG
ZMB
NIC
COG
GTM
FJI
SEN
ECU
HND
TGO
SAUKWT
BRN
SYR
VEN
ZWE
BGD
CMR
IRN
LKA
ARE
HTI
MRT
CIV
CRI
CHN
EGY
COL
BHR
MUS
GMB
NAM
GAB
ZAF
IDNJAM
SLV
PAN
PHL
CHL
DOM
BRA
TTO
NZL
DZATHABWA
MEX
URY
MYSPER
ARG
MAR
TUN
CAN
JOR
NOR
AUSLSO
IRLHUN
FIN
CYPSWE
USA
ISL
GRC
DNK
NLD
ESP
PRT
ISR
AUT
FRAITA
GBR
CHE
KOR
LUXDEU
MLT
BEL
JPN
.51
2
.01 .02 .04 .08 .16 .32 .64 1
1995
BDI
LBR
CAF
COD
TONRWA
UGA
SLE
GUY
SDNBOL
NER
LAO
KWT
PNG
COG
GTM
NPL
ECU
SAU
HNDCIV
BLZBEN
BRN
KGZ
ZWE
MRT
PAK
CMRMWI
GHASYR
KEN
VNM
BHR
VEN
MLI
TTO
SWZ
GAB
RUS
MOZ
IRN
ARE
EGY
GMBTJK
NICMNGZMB
DZATGO
BGD
IND
FJIBRA
PHL
IDNROM
COLSEN
CHL
UKR
ARGCRI
URYPER
THA
MYS
SLV
ARM
ALB
HTI
NZL
PAN
CHN ROUMUSNAM
LKA
NOR
DOMBGRTUN
ZAFPOL
CAN
JOR
MAR
TUR
JAM
AUS
LVA
MEXLTU
BWA
HRV
FIN
HUN
SWE
SVK
DNK
USA
MDV
NLD
GRC
CZE
ISR
IRL
MLT
FRAESP
ISL
ITA
AUT
GBR
PRTLSODEU
CHE
BELKOR
LUXJPN
.01 .02 .04 .08 .16 .32 .64 1
2005ef
ficie
ncy
of c
apita
l (U
S=1)
income per worker (US=1)
29
Firm Problem
maxX1,X2,A1,A2
[(A1ctX1ct )
ζ + (A2ctX2ct )ζ]1/ζ− P1X1 − P2X2
s.t. A1,A2 within frontier
33
Implications of Model (1)
Technology biased towards abundant factor
Skill Bias√
Reproducible-capital bias√
Capital Bias√
34
Implications of Model (1)
Technology biased towards abundant factor
Skill Bias√
Reproducible-capital bias√
Capital Bias√
34
Implications of Model (1)
Technology biased towards abundant factor
Skill Bias√
Reproducible-capital bias√
Capital Bias√
34
Implications of Model (1)
Technology biased towards abundant factor
Skill Bias√
Reproducible-capital bias√
Capital Bias√
34
Implications of Model (2)
If EOS <1, effi ciency declines with relative abundance
Corr(AK , KL
)< 0√
Corr(AL, KL
)> 0√
35
Implications of Model (2)
If EOS <1, effi ciency declines with relative abundance
Corr(AK , KL
)< 0√
Corr(AL, KL
)> 0√
35
Implications of Model (2)
If EOS <1, effi ciency declines with relative abundance
Corr(AK , KL
)< 0√
Corr(AL, KL
)> 0√
35
Labor Effi ciency Over Time
1.5
1.5
0.5
1970 1980 1990 2000 2010
FINITAUSAUKKORGERJPN
.8.6
.4.2
0
1980 1985 1990 1995 2000 2005
AUSAUTBELDNKESPFRANLDSWE
.6.4
.20
.2
1990 1995 2000 2005
CZEGRCHUNIRLLUXPOLPRTSVKSVN
36
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