The Ubiquity of Non-Neutrality

Francesco Caselli

SED 2017

1

Production Functions

Yct = Fct (X1ct ,X2ct , ...)

2

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

Factor Bias Term

Xct =[(A1ctX1ct )

ζ + (A2ctX2ct )ζ]1/ζ

MP1ctMP2ct

=

(A1ctA2ct

)ζ (X1ctX2ct

)ζ−1

6

Biased Technological Change

Corr

[(A1ctA2ct

)ζ

, t

]

7

Biased Technology Differences

Corr

[(A1ctA2ct

)ζ

,Yc

]

8

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

Overview (2)

Corr[ALc ,Yc

],Corr

[ALt , t

]> 0

Corr[AKc ,Yc

],Corr

[AKt , t

]< 0

10

Method

Xct =[(A1ctX1ct )

ζ + (A2ctX2ct )ζ]1/ζ

MP1ctMP2ct

=

(A1ctA2ct

)ζ (X1ctX2ct

)ζ−1

11

Method

Xct =[(A1ctX1ct )

ζ + (A2ctX2ct )ζ]1/ζ

P1ctP2ct

=

(A1ctA2ct

)ζ (X1ctX2ct

)ζ−1

12

Skilled and Unskilled Labor (across countries)

WSc

WUc=

(AScAUc

)ρ ( ScUc

)ρ−1

13

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

Reproducible Capital Bias Result

Corr((

AMcANc

)η

,Yc

)> 0 if

11− η

≤ 3

21

Up One Level

Yc =[(AKc Kc

)σ+(ALc Lc

)σ]1/σ

22

Up One Level

Yc =[(AKc Kc

)σ+(ALc Lc

)σ]1/σ

Wc =(ALc)σ(YcLc

)1−σ

Rc =(AKc

)σ(YcKc

)1−σ

23

Absolute Effi ciency

ALc =

(Wc LcYc

)1/σYcLc

AKc =

(Rc KcYc

)1/σYcKc

24

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

Absolute Effi ciency

ALc =

(Wc LcYc

)1/σYcLc

AKc =

(Rc KcYc

)1/σYcKc

26

Absolute Effi ciency

ALc = constant1 xYcLc

AKc = constant2 xYcKc

27

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

Capital Bias Result

Corr

((AKcALc

)σ

,Yc

)> 0 if

11− σ

< 1

30

Technology Choice

A1

A2

31

Technology Frontier

A1

A2

32

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

Capital Effi ciency Over Time

0.2

.4.6

.81

1970 1980 1990 2000 2010

FINITAUSAUKKORGERJPN

0.2

.4.6

.8

1980 1985 1990 1995 2000 2005

AUSAUTBELDNKESPFRANLDSWE

­.50

.51

1990 1995 2000 2005

CZEGRCHUNIRLLUXPOLPRTSVKSVN

37