2-Development-Accounting-Lecture02.pdffjkdfhjsd

macro of development

1. ECON33001 Macroeconomics of Development
Lecture 2: Development Accounting
´Akos Valentinyi
University of Manchester
Autumn 2024
Macroeconomics of Development L1: Introduction; Data and Facts

2. Living Standards and Productivity

3. Living Standards and Productivity
•Income per capita is the most commonly used indicator of living standards.•In the national accounts Income=GDP•Much of the variation in GDP per capita is accounted for by GDP per
worker.
⇒Living standards are closely linked to production.
⇒This allows one to focus on properties of production.
Macroeconomics of Development L1: Introduction; Data and Facts

4. Living Standards and Productivity
continued...Aruba
AngolaAlbania
United Arab Emirates
ArgentinaArmenia
AustraliaAustria
Azerbaijan
Burundi
Belgium
BeninBurkina FasoBangladesh
Bulgaria
BahrainBahamasBosnia and HerzegovinaBelarus
Belize
Bermuda
BoliviaBrazilBarbados
Brunei Darussalam
BhutanBotswana
Central African Republic
CanadaSwitzerland
ChileChina
Côte d'IvoireCameroon
D.R. of the Congo
Congo
Colombia
ComorosCabo VerdeCosta RicaCuraçao
Cayman IslandsCyprusCzech RepublicGermany
Djibouti
Denmark
Dominican RepublicAlgeriaEcuador
Egypt
SpainEstonia
Ethiopia
Finland
Fiji
France
Gabon
United Kingdom
GeorgiaGhanaGuineaGambia
Equatorial GuineaGreeceGrenadaGuatemalaGuyana
Hong Kong
Honduras
Croatia
Haiti
HungaryIndonesiaIndia
Ireland
IranIraq
IcelandIsraelItaly
JamaicaJordan
JapanKazakhstan
KenyaKyrgyzstanCambodia
Republic of KoreaKuwait
Lao People's DRLebanon
Liberia
Saint LuciaSri Lanka
Lesotho
Lithuania
Luxembourg
Latvia
Macao
MoroccoRepublic of Moldova
Madagascar
MaldivesMexicoNorth Macedonia
Mali
Malta
Myanmar
MontenegroMongolia
Mozambique
Mauritania
MontserratMauritius
Malawi
MalaysiaNamibia
Niger
NigeriaNicaragua
NetherlandsNorway
Nepal
New ZealandOman
Pakistan
PanamaPeruPhilippines
PolandPortugalParaguayState of Palestine
Qatar
RomaniaRussian Federation
Rwanda
Saudi Arabia
SudanSenegal
Singapore
Sierra Leone
El SalvadorSerbia
Sao Tome and Principe
SurinameSlovakiaSloveniaSweden
Eswatini
Seychelles
Syrian Arab Republic
ChadTogo
Thailand
Tajikistan
TurkmenistanTrinidad and Tobago
TunisiaTurkeyTaiwan
TanzaniaUganda
UkraineUruguay
United States
UzbekistanSt. Vincent and the GrenadinesVenezuela
British Virgin Islands
Viet NamYemen
South Africa
Zambia
Zimbabwe
211/21/41/81/161/321/641/128
GDP per Capita at PPP $, USA=1
211/21/41/81/161/321/64
GDP per Worker at PPP $, USA=1Source: Penn World Tables 10.01
GDP per Worker and GDP per Capita in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

5. Proximate versus Fundamental Causes Differences in Living
Standards
•Proximate causes
◦Are some countries invest less in physical and human capital?
◦Are some countries fail to adopt new technologies and to organise production
efficiency?
•Fundamental causes◦Institutions (humanly-devised rules shaping incentives)
◦Geography (exogenous differences of environment)◦Culture (differences in beliefs, attitudes and preferences)
•Proximate causes help to identify fundamental causes
◦Development accounting can identify fundamental causes via identifying
proximate causes.
Macroeconomics of Development L1: Introduction; Data and Facts

6. Development Accounting

7. Development Accounting
Production
GDP per worker=F(Production Factors,Efficiency).
Development accounting
•uses cross-country data on output and inputs at one point in time,
•to assess the relative contribution of differences◦in factor quantities, and
◦in the efficiency with which those factors are used
to the cross-country differences in GDP per worker.
Macroeconomics of Development L1: Introduction; Data and Facts

8. Development Accounting
Usefulness...
Development Policy Design
•If differences in factors account primarily for differences in income per
capita,
⇒the goal of development policy is to engineer higher rates factor
accumulation.
•If differences in efficiency account primarily for differences in income per
capita,
⇒the goal of development policy is to engineer higher efficiency.
Efficiency
•Efficiency plays a very large role.•Experience suggests that this additional question is the hardest to crack.
Macroeconomics of Development L1: Introduction; Data and Facts

9. Development Accounting
Proximate causes: First lookArubaAngolaAlbaniaUnited Arab EmiratesArgentinaArmeniaAustraliaAustriaAzerbaijanBurundi
BelgiumBeninBurkina FasoBangladeshBulgariaBahrainBahamasBosnia and HerzegovinaBelarusBelizeBermudaBoliviaBrazilBarbadosBrunei DarussalamBhutanBotswanaCentral African RepublicCanadaSwitzerlandChileChinaCôte d'IvoireCameroonD.R. of the Congo
Congo
ColombiaComorosCabo VerdeCosta RicaCuraçaoCayman IslandsCyprusCzech RepublicGermanyDjiboutiDenmarkDominican RepublicAlgeriaEcuador
Egypt
SpainEstoniaEthiopiaFinlandFijiFranceGabonUnited KingdomGeorgiaGhanaGuineaGambiaEquatorial GuineaGreeceGrenadaGuatemalaGuyanaHong KongHondurasCroatiaHaitiHungaryIndonesiaIndiaIrelandIranIraqIcelandIsraelItalyJamaicaJordanJapanKazakhstanKenyaKyrgyzstanCambodiaRepublic of KoreaKuwaitLao People's DRLebanonLiberiaSaint LuciaSri LankaLesothoLithuaniaLuxembourgLatviaMacaoMorocco
Republic of MoldovaMadagascar
MaldivesMexicoNorth MacedoniaMaliMaltaMyanmarMontenegroMongoliaMozambiqueMauritaniaMontserratMauritiusMalawiMalaysiaNamibiaNigerNigeriaNicaraguaNetherlandsNorwayNepalNew ZealandOman
Pakistan
PanamaPeruPhilippinesPolandPortugalParaguayState of PalestineQatarRomaniaRussian FederationRwandaSaudi Arabia
SudanSenegalSingapore
Sierra Leone
El SalvadorSerbiaSao Tome and PrincipeSurinameSlovakiaSloveniaSwedenEswatiniSeychelles
Syrian Arab Republic
ChadTogoThailandTajikistanTurkmenistanTrinidad and TobagoTunisiaTurkeyTaiwanTanzaniaUgandaUkraineUruguayUnited StatesUzbekistanSt. Vincent and the GrenadinesVenezuelaBritish Virgin IslandsViet NamYemenSouth AfricaZambia
Zimbabwe
0.0750.1500.3000.600
Investment rate at PPP $
211/21/41/81/161/321/641/128
GDP per Worker at PPP $, USA=1Source: Penn World Tables 10.01GDP per Worker and Investment Rate at PPP in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

10. Development Accounting
Proximate causes: First look, continued...AlbaniaUnited Arab EmiratesArgentinaArmeniaAustralia
Austria
Burundi
Belgium
BeninBangladesh
BulgariaBahrainBelizeBoliviaBrazilBarbadosBrunei DarussalamBotswana
Central African Republic
CanadaSwitzerlandChileChinaCote dIvoireCameroonDemocratic Republic of the CongoCongoColombiaCosta RicaCyprusCzech RepublicGermanyDenmark
Dominican Rep.
AlgeriaEcuadorEgyptSpainEstoniaFinlandFijiFranceGabonUnited Kingdom
Ghana
GambiaGreeceGuatemalaGuyanaHong KongHondurasCroatiaHaitiHungaryIndonesiaIndiaIrelandIranIraqIcelandIsraelItalyJamaicaJordanJapanKazakhstanKenyaKyrgyzstanCambodiaRepublic of KoreaKuwaitLao People's Democratic RepublicLiberiaSri LankaLesothoLithuania
Luxembourg
LatviaMacao
Morocco
MaldivesMexicoMali
MaltaMyanmarMongoliaMozambiqueMauritaniaMauritius
Malawi
MalaysiaNamibia
NigerNicaragua
Netherlands
Norway
Nepal
New ZealandPakistan
Panama
PeruPhilippinesPolandPortugalParaguayQatarRomaniaRussian Federation
Rwanda
Saudi Arabia
SudanSenegal
Singapore
Sierra LeoneEl SalvadorSlovakiaSloveniaSweden
Swaziland
Syrian Arab RepublicTogoThailandTajikistan
Trinidad and Tobago
TunisiaTurkeyTaiwan
TanzaniaUgandaUkraineUruguayUSAVenezuelaViet NamYemenSouth AfricaZambiaZimbabwe
211/21/41/81/161/321/64
GDP per Worker, USA=1, in 2015
234567891011121314
Average years of schooling 2015Source: Penn World Tables 10.01. Barro-Lee Database 2021.GDP per Worker and Years of Schooling in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

11. Development Accounting
Proximate causes: First look, continued...Angola
AlbaniaUnited Arab EmiratesArgentinaArmeniaAustraliaAustriaAzerbaijan
Burundi
Belgium
Burkina FasoBulgariaBahrainBosnia and HerzegovinaBelarusBermudaBoliviaBrazil
Brunei Darussalam
BotswanaCanadaSwitzerlandChileChinaCôte d'IvoireD.R. of the CongoColombiaCabo VerdeCosta RicaCyprusCzech RepublicGermanyDenmarkAlgeriaEcuadorEgyptSpainEstonia
Ethiopia
FinlandFranceGabonUnited KingdomGeorgiaGhanaGambiaGreece
Guatemala
Hong KongHondurasCroatiaHungaryIndonesiaIndiaIrelandIranIraqIcelandIsraelItalyJamaicaJordanJapanKazakhstanKenyaKyrgyzstanCambodiaRepublic of KoreaKuwaitLao People's DRSri LankaLesothoLithuaniaLuxembourgLatviaMacaoMoroccoRepublic of MoldovaMadagascar
MexicoNorth MacedoniaMaliMaltaMyanmarMontenegroMongoliaMozambiqueMauritiusMalaysiaNamibiaNigeriaNicaraguaNetherlandsNorway
NepalNew ZealandOmanPakistanPanamaPeruPhilippinesPolandPortugalParaguayState of PalestineQatarRomaniaRussian FederationRwanda
Saudi ArabiaSudanSenegal
SingaporeEl SalvadorSerbiaSlovakiaSlovenia
Sweden
EswatiniSeychellesChadTogoThailandTajikistan
Trinidad and Tobago
TunisiaTurkeyTanzaniaUgandaUkraineUruguay
United States
UzbekistanSt. Vincent and the GrenadinesVenezuelaViet NamSouth AfricaZambia
211/21/41/81/161/321/64
Real GDP per Worker at PPP $, USA=1
0.00030.00060.00120.00240.00480.00960.01920.0384
R&D expenditure as fraction of GDP at current domestic pricesSource: Penn World Tables 10.01Real GDP per capita at PPP and R&D expenditure in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

12. Development Accounting
Principles of measurement, continued...
Key steps in development accounting
1. F,2.3.We cannot measure efficiency directly: back out efficiency as residual
Efficiency
•Solow residual or TFP•Our measure of ignorance•one potentially promising research strategy is to try to “chip away” at this
residual by improving on steps (1) and (2),
Macroeconomics of Development L1: Introduction; Data and Facts

13. Development Accounting Framework

14. Development Accounting Framework
Functional form: Cobb–Douglas
Y=AK
α
(Lh)
1−α
(1)
•Y: output (GDP)•K: capital stock•L: labour input (number of workers)•h: human capital of the average worker•A: efficiency or total factor productivity; the measure of our ignorance•α: factor share; a parameter; same across–countries•the variables,Y,K,L,h,Aare country specific.•Could we estimate?
log(Y) =α
|{z}
βk
log(K) + (1−α)
|{z}
βl
log(Lh) + log(A)
|{z}
ε
•Inputs are likely top be correlated withlog(A)⇒biased estimation.
Macroeconomics of Development L1: Introduction; Data and Facts

15. Development Accounting Framework
continued...Aruba
Angola
Albania
United Arab Emirates
ArgentinaArmenia
AustraliaAustria
Azerbaijan
Belgium
BeninBurkina Faso
Bangladesh
Bulgaria
BahrainBahamasBosnia and HerzegovinaBelarusBelize
Bermuda
Bolivia
BrazilBarbados
Brunei Darussalam
BhutanBotswana
Central African Republic
CanadaSwitzerlandChileChina
Côte d'IvoireCameroon
D.R. of the Congo
CongoColombiaComorosCabo VerdeCosta Rica
Cayman IslandsCyprusCzech RepublicGermany
Djibouti
Denmark
Dominican RepublicAlgeriaEcuadorEgypt
SpainEstonia
Ethiopia
Finland
Fiji
FranceGabonUnited Kingdom
GeorgiaGhana
GuineaGambiaGuinea-Bissau
Equatorial GuineaGreece
GrenadaGuatemala
Hong Kong
Honduras
Croatia
Haiti
HungaryIndonesiaIndia
IrelandIranIraq
IcelandIsraelItaly
JamaicaJordanJapan
Kazakhstan
KenyaKyrgyzstanCambodia
Republic of KoreaKuwait
Lao People's DR
Lebanon
Liberia
Saint LuciaSri LankaLesotho
LithuaniaLuxembourgLatviaMacao
MoroccoRepublic of Moldova
Madagascar
MaldivesMexicoNorth Macedonia
Mali
Malta
Myanmar
MontenegroMongolia
Mozambique
MauritaniaMauritius
Malawi
MalaysiaNamibia
Niger
NigeriaNicaragua
NetherlandsNorway
Nepal
New ZealandOman
Pakistan
PanamaPeruPhilippines
Poland
Portugal
ParaguayState of Palestine
Qatar
RomaniaRussian Federation
Rwanda
Saudi Arabia
SudanSenegal
Singapore
Sierra Leone
El Salvador
SerbiaSao Tome and Principe
SurinameSlovakiaSloveniaSweden
EswatiniSeychelles
Syrian Arab Republic
ChadTogo
ThailandTajikistanTurkmenistanTrinidad and TobagoTunisia
TurkeyTaiwan
TanzaniaUganda
UkraineUruguayUnited States
Uzbekistan
St. Vincent and the GrenadinesVenezuelaBritish Virgin Islands
Viet Nam
YemenSouth Africa
Zambia
Zimbabwe
211/21/41/81/161/321/641/128
Capital Per Worker, USA=1
211/21/41/81/161/321/64
GDP per worker, USA=1Source: Penn World Tables 10.01, own calculations.
Capital and GDP per Worker in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

16. Development Accounting Framework
continued...
Kis correlated withAon the data•Economic theory can imply that
K
Y
is uncorrelated withA
•To see, consider the Solow model
Kt+1=It+ (1−δ)KtIt=sYtYt=AK
α
t(Lh)
1−α
◦δ∈(0,1)is the rate of depreciation
◦We assume thatA,Landhare constant over time
Macroeconomics of Development L1: Introduction; Data and Facts

17. Development Accounting Framework
continued...
Solow–model in steady state
•Kt+1=Kt
Kt=sYt+ (1−δ)Kt⇒δKt=sYt⇒
Kt
Yt
=
s
δ
theK/Yis independent of TFP in steady state
•K/Yis likely to vary across countries because the savings rate does and
depreciation may as well
Macroeconomics of Development L1: Introduction; Data and Facts

18. Development Accounting Framework
continued...ArubaAngolaAlbaniaUnited Arab EmiratesArgentinaArmeniaAustraliaAustriaAzerbaijan
BelgiumBeninBurkina FasoBangladeshBulgariaBahrainBahamasBosnia and HerzegovinaBelarusBelizeBermudaBoliviaBrazilBarbadosBrunei DarussalamBhutanBotswana
Central African Republic
CanadaSwitzerlandChileChinaCôte d'IvoireCameroon
D.R. of the Congo
CongoColombiaComorosCabo VerdeCosta RicaCayman IslandsCyprusCzech RepublicGermanyDjiboutiDenmarkDominican RepublicAlgeriaEcuadorEgypt
SpainEstoniaEthiopiaFinlandFijiFranceGabonUnited KingdomGeorgiaGhanaGuineaGambiaGuinea-BissauEquatorial GuineaGreeceGrenadaGuatemalaHong KongHondurasCroatiaHaitiHungaryIndonesiaIndiaIrelandIranIraqIcelandIsraelItalyJamaicaJordanJapanKazakhstanKenyaKyrgyzstanCambodiaRepublic of KoreaKuwaitLao People's DRLebanonLiberiaSaint LuciaSri LankaLesothoLithuaniaLuxembourgLatviaMacaoMoroccoRepublic of MoldovaMadagascarMaldivesMexicoNorth MacedoniaMaliMaltaMyanmarMontenegroMongoliaMozambiqueMauritaniaMauritius
Malawi
MalaysiaNamibiaNigerNigeriaNicaraguaNetherlandsNorwayNepalNew ZealandOmanPakistanPanamaPeruPhilippinesPolandPortugalParaguayState of PalestineQatarRomaniaRussian FederationRwandaSaudi ArabiaSudanSenegalSingaporeSierra LeoneEl SalvadorSerbiaSao Tome and PrincipeSurinameSlovakiaSloveniaSwedenEswatiniSeychellesSyrian Arab RepublicChadTogoThailandTajikistanTurkmenistanTrinidad and TobagoTunisiaTurkeyTaiwanTanzaniaUgandaUkraineUruguayUnited StatesUzbekistanSt. Vincent and the GrenadinesVenezuelaBritish Virgin IslandsViet Nam
YemenSouth AfricaZambiaZimbabwe
4211/21/41/8
Capital-Output Ratio, USA=1
211/21/41/81/161/321/64
GDP per worker, USA=1Source: Penn World Tables 10.01, own calculations.Capital-Output Ratio and GDP per Worker in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

19. Development Accounting Framework
continued...
Production function in terms ofK/Yinstead ofK
Y=AK
α
(Lh)
1−α
divide both sides byY
α
⇒Y
1−α
=A
`
K
Y
´
α
(Lh)
1−α
⇒ Y=A
1
1−α
`
K
Y
´α
1−α
(Lh)⇒
Y
L
=A
1
1−α
`
K
Y
´α
1−α
h=ZYKh=ZYKYH=ZYKHwhere
Z≡A
1
1−α YK≡
`
K
Y
´α
1−α
YH≡h Y KH≡YKYH
Macroeconomics of Development L1: Introduction; Data and Facts

20. Development Accounting Framework
continued...
Development Accounting
•How much of the variation in GDP per worker is accounted for variation in
◦capital-output ratios,YK
◦human capital,YH
◦TFP, the residual,Z.
•There are more than one way to answer this question quantitatively
Macroeconomics of Development L1: Introduction; Data and Facts

21. Development Accounting Framework
continued...
Calculating contributions to GDP per worker differences
•Chose a reference country. Typically the USA.•Take the log of the production function
Y
L
=A
1
1−α
`
K
Y
´α
1−α
h=ZYKYH⇒log(Y/L) = logZ+ logYK+ logYH
Macroeconomics of Development L1: Introduction; Data and Facts

22. Development Accounting Framework
continued...
Calculating contributions to GDP per worker differences•Take the difference between countryiand the USA of the log of the
production functionlog(Y/L) = logZ+ logYK+ logYH
implyinglog(Y/L)i−log(Y/L)USA= (logZi−logZUSA)+ (logYK,i−logYK,USA)+ (logYH,i−logYH,USA).Divide bylog(Y/L)i−log(Y/L)USAto get the contribution of each
component
1=
logZi−logZUSA
log(Y/L)i−log(Y/L)USA
+
logYK,i−logYK,USA
log(Y/L)i−log(Y/L)USA
+
logYH,i−logYH,USA
log(Y/L)i−log(Y/L)USAMacroeconomics of Development L1: Introduction; Data and Facts

23. Development Accounting Framework
continued...
Variance decomposition of cross country GDP per worker•Iflog(Y/L) = logZ+ logYKH,
then the variance oflog(Y/L)is
var[log(Y/L)] =var[logZ] +var[logYKH] +2cov[logZ,logYKH]
•Measure of success
Success=
var(log (yKH))
var
Γ
log(Y/L)
∆
Alternatively, assign covariance equally
Success=
var(log (yKH)) +cov(log(Z),log (yKH))
var
Γ
log(Y/L)
∆
Macroeconomics of Development L1: Introduction; Data and Facts

24. Development Accounting: Data

25. Development Accounting: Data
Output per worker,Y/L
Penn World Tables (PWT) – Key Data Source
•To compare living standards:
◦GDP at international prices (PPP adjusted quantities)
◦population data
•To compare productivity,Y/L
◦GDP at international prices (PPP adjusted quantities)
◦employment data
◦hours data worked for a smaller set of countries (53 in 2015)
Macroeconomics of Development L1: Introduction; Data and Facts

26. Development Accounting: Data
Capital-Output ratio,K/Y
Current PWT considers investment in
•machinery and electronic equipments•transportation equipments•structures (buildings)•intellectual property products (IPP) (patents, softwares etc.)
Macroeconomics of Development L1: Introduction; Data and Facts

27. Development Accounting: Data
Capital-Output ratio,K/Y, continued...
From investment,Xtto capital stock,Kt•Perpetual inventory method•Stock of capital evolves
Kt=Xt−1+ (1−δ)Kt−1⇒Kt=Xt−1+ (1−δ)(Xt−2+ (1−δ)Kt−2)=Xt−1+ (1−δ)Xt−2+ (1−δ)
2
Kt−2⇒Kt=Xt−1+ (1−δ)Xt−2+ (1−δ)
2
(Xt−3+ (1−δ)Kt−3)=Xt−1+ (1−δ)Xt−2+ (1−δ)
2
Xt−3+ (1−δ)
3
Kt−3⇒Kt=Xt−1+ (1−δ)Xt−2+. . .+ (1−δ)
t−1
X0+ (1−δ)
t
K0⇒Kt=
t−1
X
s=0
(1−δ)
s
Xt−s−1+ (1−δ)
t
K0
whereδ∈(0,1)is the depreciation rate.
Macroeconomics of Development L1: Introduction; Data and Facts

28. Development Accounting: Data
Capital-Output ratio,K/Y, continued...
From investment to capital stock
•We observe investment but to use the perpetual inventory method, we also
needK0
•K0is not observable
◦In the steady state (balanced growth path) of the Solow model if TFP is
growing at rateγ
K0=
X0
γ+δ
•If we have long enough time series the term(1−δ)
t
K0will be small
because(1−δ)
t
will be small, but for most poor countries the time series is
not long enough.
•There are substantial measurement issues here.
Macroeconomics of Development L1: Introduction; Data and Facts

29. Development Accounting: Data
Capital share,α
Capital share as income share
•What is the empirical equivalent ofα?
◦The marginal product of capital
MPK=
∂Y
∂K
=αAK
α−1
(hL)
1−α
◦The marginal product of capital equals to rental rate of capital,runder
perfect competition
◦Payments to the owners of capital
rK=MPK·K
=αAK
α−1
(hL)
1−α
K=αAK
α
(hL)
1−α
=αY
•αis the share of capital income in GDP•Until recently it has been stable, but we return to this issue•We setα=1/3 for now as suggested by the time-series evidence.Macroeconomics of Development L1: Introduction; Data and Facts

30. Development Accounting: Data
Human capital,h
Human capital
•What is human capital?
◦How we measure it?◦Average years of schooling? Or something else?•Economic concept of human capital
◦Human capital is the stock of skills embodied in workers which affects their
productivity, hence their wages on the labour market.
◦The effect of education and training can be measured on wages
Macroeconomics of Development L1: Introduction; Data and Facts

31. Development Accounting: Data
Human capital,h...Mincer regression
Mincer regression
•How much an additional year of education/training affects wages?•It is similar to the empirical micro literature (Mincer regressions)
log(wi) =κ+µSj+βXj+εj (2)
where
◦κ: intercept.
◦Sj: years of schooling of workeri;
◦µ: the increase in wages for an additional years of schooling.◦X: set of additional controls such as experience, location, gender, age, etc;◦β: the marginal effect of the controls.◦εi: error term.
•Results based on similar regression was first time published by Jacob
Mincer in 1974.
Macroeconomics of Development L1: Introduction; Data and Facts

32. Development Accounting: Data
Linking human capital,h, to Mincerian regression
Human capital production function
•We have to make assumption about human capital production function
◦How years of schooling affects human capital?
◦Assume that
∂log(hj)
∂Sj
=µ
then human capital production function could be
hj= exp(µSj),
thus,f(S)is linear.
Macroeconomics of Development L1: Introduction; Data and Facts

33. Development Accounting: Data
Linking human capital,h, to Mincerian regression
Human capital production function
•Piece–wise linear returns to education instead of linear as above
f(Sj) =





0.134·Sj ifSj≤4
0.134·4+0.101·(Sj−4)if 4<Sj≤80.134·4+0.101·4+0.068·(Sj−8)if 8<Sj.
(3)
•The numbers for returns to schooling are based on a large scale
cross-country study applying to Mincerian regressions to country specific
micro data
•The returns to schooling numbers are averages across these country
regressions
Macroeconomics of Development L1: Introduction; Data and Facts

34. Development Accounting
Results continued...BelgiumSwedenNetherlandsFranceHong KongAustraliaDenmark
Taiwan
GermanyCanadaSpainFinlandIcelandJapanIsraelTurkeyMaltaCyprusRepublic of KoreaNew ZealandGreeceCzech RepublicSlovakiaPoland
Slovenia
Trinidad and TobagoPortugalLithuaniaEstoniaHungaryPanamaCroatiaLatviaChileMaldivesGabonRussian FederationRomaniaMalaysiaKazakhstanEgyptIranAlgeriaIraqArgentinaMauritiusMexicoJordanUruguaySerbiaSouth AfricaBulgariaBotswanaCosta RicaNamibiaAlbaniaFijiDominican RepublicEswatiniTunisiaBrazilSri LankaColombiaArmeniaThailandBarbadosUkraineParaguayMongoliaEcuadorMoroccoChinaIndonesiaPeruRepublic of MoldovaSyrian Arab RepublicJamaicaGuatemalaPhilippinesMauritaniaEl SalvadorSudanBelizeNigeriaPakistanBoliviaCôte d'IvoireAngolaIndiaYemenLao People's DRHondurasNicaraguaGhanaCongoVenezuelaMyanmarZambiaKyrgyzstanTajikistanLesothoViet NamBangladeshBeninCameroonSenegalGambiaKenyaCambodiaZimbabweUgandaTanzaniaMaliSierra LeoneNepalBurkina FasoRwandaTogoHaitiMozambiqueEthiopiaD.R. of the CongoLiberiaMadagascarNigerMalawiCentral African RepublicBurundi0.00.20.40.60.81.01.21.41.6
Share of TFP
11/21/41/81/161/321/64
GDP per worker, USA=1Source: Penn World Tables 10.01, own calculations.Contribution of TFP to Difference in GDP per Worker in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

35. Development Accounting
Results continued...-0.10.00.10.20.30.40.50.60.70.80.9
1960197019801990200020102020
TFPCapital-output ratioHuman capital
Source: Penn World Tables 10.01, own calculations.Median Contributions to GDP per workers
Macroeconomics of Development L1: Introduction; Data and Facts

36. Variance Decomposition

37. Development Accounting
Variance Decomposition
Factor-only component of output-per-worker
•Factor-only component of output-per-workery:
YKH≡
`
K
Y
´α
1−α
h
•Output per worker
Y
L
=ZYKH Z≡A
1
1−α
•Variance decomposition in logs
var
Θ
log(Y/L)
Λ
=var
Θ
log(Z)
Λ
+var[log (YKH)] +2cov[log(Z),log (YKH)]
Macroeconomics of Development L1: Introduction; Data and Facts

38. Development Accounting
Variance Decomposition, continued...
Measure of success
var
Γ
log(Y/L)
∆
=var
Γ
log(Z)
∆
+var(log (YKH)) +2cov(log(Z),log (YKH))
Success=
var
Γ
log
Γ
y
KH
∆∆
var
Γ
log(y)
∆
•Variance of output-per-worker: 0.65•Variance of factors-per-worker KH: 0.18
Success=0.27
Macroeconomics of Development L1: Introduction; Data and Facts

39. A Fundamental Cause
What makes TFP so much different across countriesAngolaAlbaniaUnited Arab EmiratesArgentinaArmeniaAustraliaAustriaBelgiumBeninBurkina FasoBangladeshBulgariaBahrainBelizeBoliviaBrazilBarbadosBrunei DarussalamBotswanaCentral African Republic
CanadaSwitzerlandChileChinaCôte d'IvoireCameroonCongoColombiaCosta RicaCyprusCzech RepublicGermanyDenmarkDominican RepublicAlgeriaEcuadorEgyptSpainEstoniaEthiopiaFinlandFijiFranceGabonUnited KingdomGhanaGambiaGreeceGuatemalaHong KongHondurasCroatiaHaitiHungaryIndonesiaIndiaIranIraqIcelandIsraelItalyJamaicaJordanJapanKazakhstanKenyaKyrgyzstanCambodiaRepublic of KoreaKuwaitLao People's DRLiberiaSri LankaLesothoLithuaniaLuxembourgLatviaMacaoMoroccoRepublic of MoldovaMadagascarMaldivesMexicoMaliMaltaMyanmarMongoliaMozambiqueMauritaniaMauritiusMalawiMalaysiaNamibiaNigerNigeriaNicaraguaNetherlandsNorwayNepalNew ZealandPakistanPanamaPeruPhilippinesPolandPortugalParaguayQatarRussian FederationRwandaSaudi ArabiaSudanSenegalSingaporeSierra LeoneEl SalvadorSerbiaSlovakiaSloveniaSwedenEswatiniSyrian Arab RepublicTogoThailandTajikistanTrinidad and TobagoTunisiaTurkeyTaiwanTanzaniaUgandaUkraineUruguayUnited StatesViet NamYemenSouth AfricaZambiaZimbabwe
211/21/41/81/161/321/64
TFP, USA=1
-2.5-2.0-1.5-1.0-0.50.00.51.01.52.02.5
Rule of law indexSource: Penn World Tables 10.01, World Governance Indicators 2022.TFP and the Rule of Law in 2015
Macroeconomics of Development L1: Introduction; Data and Facts

40. Summary
•Differences in TFP are the most important contributor to differences in
GDP per worker
•Broad institutional environment strongly influences TFP•Measurement of production factors faces problems•Technology specification matters
Macroeconomics of Development L1: Introduction; Data and Facts