creilectures2010 …personal.lse.ac.uk/casellif//l1.pdfincomeperworker: afirstlook 0.2 0.2 1.0 1.0...
TRANSCRIPT
CREI Lectures 2010Differences in Technology Across Space and Time
Francesco Caselli
Barcelona, June 16 - 18
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General Introduction
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Adam Smith would be surprised
Economists still asking the same fundamental question 240years later
Set of potential answers expanding rather than contracting
Meanwhile, differences in the wealth of nations have increasedby one order of magnitude (from 3 to 30)
3 / 77
Adam Smith would be surprised
Economists still asking the same fundamental question 240years later
Set of potential answers expanding rather than contracting
Meanwhile, differences in the wealth of nations have increasedby one order of magnitude (from 3 to 30)
3 / 77
Adam Smith would be surprised
Economists still asking the same fundamental question 240years later
Set of potential answers expanding rather than contracting
Meanwhile, differences in the wealth of nations have increasedby one order of magnitude (from 3 to 30)
3 / 77
Adam Smith would be surprised
Economists still asking the same fundamental question 240years later
Set of potential answers expanding rather than contracting
Meanwhile, differences in the wealth of nations have increasedby one order of magnitude (from 3 to 30)
3 / 77
So what’s new?
Data
International Comparison Program, Penn World Tables, WorldDevelopment Indicators, Education (quantity and quality) ...
4 / 77
So what’s new?
Data
International Comparison Program, Penn World Tables, WorldDevelopment Indicators, Education (quantity and quality) ...
4 / 77
The Production-Function Approach
Tracing quantities produced to quantities of inputs
Not a new tool, but newly useful in light of the data explosion
5 / 77
Production-Function Questions (1)
Would poor countries be as rich as rich countries if they hadthe same factor endowments?
i.e. is the production function (roughly) the same acrosscountries?
Lecture 1
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Production-Function Questions (1)
Would poor countries be as rich as rich countries if they hadthe same factor endowments?
i.e. is the production function (roughly) the same acrosscountries?
Lecture 1
6 / 77
Production-Function Questions (2)
If production functions differ across countries, how do theydiffer?
And why?
Lecture 2
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Production-Function Questions (2)
If production functions differ across countries, how do theydiffer?
And why?
Lecture 2
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Production-Function Questions (3)
Some factors of production are potentially mobile acrosscountries
Given each country’s production function, are factors ofproduction allocated efficiently by the world?
If not, why not?
Lecture 3
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Production-Function Questions (3)
Some factors of production are potentially mobile acrosscountries
Given each country’s production function, are factors ofproduction allocated efficiently by the world?
If not, why not?
Lecture 3
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Technology Differences
Differences in the (parameters of) the aggregate productionfunction
Hence, very broadly construed
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Nature of the Lectures
Rather than "... a high level summary ..."
... a series of updates and extensionsNew data (e.g. PWT 6.3 instead of 6.1)New dates (e.g. 2005 rather than 1995)New calculations
Partial default: no US wage inequality material
10 / 77
Acknowledgements
Co-authors
John Coleman (CES DA; non-neutral technology differences)
Jim Feyrer (importance of natural capital; cross-countrycapital flows)
Dan Wilson (capital heterogeneity)
Superb RA on these lectures
Jacopo Ponticelli
11 / 77
Lecture 1Accounting for Cross-country Income Differences:
Updates and Extensions
Barcelona, June 16
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Development Accounting
Can differences in observed stocks of physical and human capitalaccount for differences in incomes?
Or: Is the magnitude of income differences roughly similar to themagnitude of differences that would be predicted by just looking atdifferences in observed stocks of capital?
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The Production-Function Approach
Per-capita income:
Yc = F (Kc , Lc , efficiencyc)
Hold efficiency constant:
efficiencyc = efficiency
Compute:V [log(F (Kc , Lc , efficiency))]
Compare with:V [log(Yc)]
14 / 77
What is at stake
If capital stocks can account for income differences, then theproblem of development is a problem of accumulation(and/or of the workings of international capital markets)
If not the problem of development is one of inefficient use ofresources - a tougher nut to crack for both economists and policymakers
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What is at stake (cont.)
Under-accumulation hypothesis: working assumption of mosteconomists and policy institutions until the 1990s. Still hugelyinfluential today (e.g. all the emphasis on foreign aid)
Causes of (recent) skepticism:Policy: persistent failure of policies predicated on itTheory: endogenous growthData: Penn World Tables and development accounting
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A short history of DA
Denison (1967); Christensen, Cummings, and Jorgenson(1981). Nine rich countries.
King and Levine (1994). PWT; only physical reproduciblecapital.
Klenow and Rodriguez-Clare (1997); Hall and Jones (1999).PWT + Barro and Lee; Physical reproducible capital andschooling; Basic current conceptual framework.
Others: extensions.
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The (abandoned) econometric alternative
Mankiw, Romer, and Weil (1992).In a OLS regression the accumulation hypothesis is hugelysuccessful.
Islam (1995); Caselli, Esquivel, and Lefort (1996).In a panel regression, it is not.
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Income per worker: a first look0.2
0.2
0.21.0
1.0
1.05.2
5.2
5.219.2
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19.246.5
46.5
46.50
0
010
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50min
min
min10th perc.
10th perc.
10th perc.50th perc.
50th perc.
50th perc.90th perc.
90th perc.
90th perc.max
max
max
source: PWT 6.3, year 2005
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Income per worker: a first look
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18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.718.7
18.7
18.719.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.919.9
19.919.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.219.2
19.2
19.25.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.5
5.5
5.55.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.9
5.9
5.95.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.3
5.3
5.35.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
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5.0
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5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
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5.0
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5.0
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5.0
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5.0
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5.0
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5.0
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5.05.0
5.0
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5.0
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5.0
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5.0
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5.0
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5.0
5.05.0
5.0
5.05.0
5.0
5.05.0
5.0
5.05.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.4
5.4
5.45.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.25.2
5.2
5.21.0
1.0
1.01.0
1.0
1.01.0
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1.01.0
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1.01.0
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1.01.0
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1.0
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1.0
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1.0
1.01.0
1.0
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1.0
1.01.0
1.0
1.01.0
1.0
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1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.01.0
1.0
1.00.0
0.0
0.05.0
5.0
5.010.0
10.0
10.015.0
15.0
15.020.0
20.0
20.01980
1980
19801985
1985
19851990
1990
19901995
1995
19952000
2000
20002005
2005
2005year
year
year90th perc.
90th perc.
90th perc.50th perc.
50th perc.
50th perc.10th perc.
10th perc.
10th perc.
source: PWT 6.3
appendix
20 / 77
Let’s get started
1 Only reproducible capital (King-Levine)2 Schooling capital (Hall-Jones)3 Health capital (Weil)4 Quantity of schooling/parental inputs5 Imperfect substitution between high/low education groups6 Natural capital7 CES aggregation of physical and human capital
21 / 77
Notation
Y, K, L : GDP, Physical Capital, Human Capital, per worker
y, k, l : logs of above
22 / 77
King and Levine (1994)
Cobb-Douglas production function
Capital is physical reproducible capital
Labour is only raw labour
HenceYc = AcKα
c
23 / 77
Technology differences: caveat
Multiplicative technology terms allowed to vary; Elasticitiesheld constant
This is entirely arbitrary and not w.l.g.
Furthermore in this case:
Constant α clearly rejected by data
(Though Corr(α,Y)=0 not rejected)
24 / 77
Measuring Physical Reproducible Capital
Perpetual inventory calculation:
Kc,t+1 = Ic,t + (1− δ)Kc,t
Where:I is PWT real investment series
δ is 0.06 (results not sensitive to this)
Initial stock is I(g+δ) (res. not sensitive)
25 / 77
k vs y
COD
COD
CODBDI
BDI
BDICHE
CHE
CHESVN
SVN
SVNLKA
LKA
LKASVK
SVK
SVKHKG
HKG
HKGTHA
THA
THAKHM
KHM
KHMSGP
SGP
SGPVNM
VNM
VNMBHR
BHR
BHRMAR
MAR
MARARG
ARG
ARGEGY
EGY
EGYGMB
GMB
GMBMOZ
MOZ
MOZIRL
IRL
IRLKEN
KEN
KENROU
ROU
ROUJAM
JAM
JAMIRN
IRN
IRNMUS
MUS
MUSHRV
HRV
HRVAFG
AFG
AFGZMB
ZMB
ZMBUSA
USA
USAJPN
JPN
JPNURY
URY
URYCRI
CRI
CRIMEX
MEX
MEXLVA
LVA
LVAZAF
ZAF
ZAFUKR
UKR
UKRTON
TON
TONALB
ALB
ALBZWE
ZWE
ZWEPHL
PHL
PHLPRT
PRT
PRTECU
ECU
ECUFRA
FRA
FRASWE
SWE
SWELBY
LBY
LBYPNG
PNG
PNGBRB
BRB
BRBCMR
CMR
CMRPAN
PAN
PANARM
ARM
ARMLSO
LSO
LSOBGD
BGD
BGDFIN
FIN
FINSLV
SLV
SLVTZA
TZA
TZANIC
NIC
NICNPL
NPL
NPLMRT
MRT
MRTARE
ARE
AREPRY
PRY
PRYYEM
YEM
YEMBRN
BRN
BRNPOL
POL
POLTTO
TTO
TTOVEN
VEN
VENBGR
BGR
BGRPER
PER
PERDOR
DOR
DORKOR
KOR
KOREST
EST
ESTBEL
BEL
BELCYP
CYP
CYPNLD
NLD
NLDPAK
PAK
PAKGBR
GBR
GBRCAF
CAF
CAFDNK
DNK
DNKBOL
BOL
BOLSAU
SAU
SAUNZL
NZL
NZLIDN
IDN
IDNGAB
GAB
GABTWN
TWN
TWNUGA
UGA
UGACHN
CHN
CHNISR
ISR
ISRRUS
RUS
RUSKAZ
KAZ
KAZCOL
COL
COLBLZ
BLZ
BLZAUS
AUS
AUSTUR
TUR
TURKWT
KWT
KWTMLI
MLI
MLIMYS
MYS
MYSSDN
SDN
SDNMWI
MWI
MWIMAC
MAC
MACMLT
MLT
MLTGRC
GRC
GRCLTU
LTU
LTUIND
IND
INDGTM
GTM
GTMDEU
DEU
DEUROM
ROM
ROMFJI
FJI
FJIESP
ESP
ESPAUT
AUT
AUTCZE
CZE
CZETUN
TUN
TUNCAN
CAN
CANNAM
NAM
NAMHTI
HTI
HTIBEN
BEN
BENNOR
NOR
NORBRA
BRA
BRAMNG
MNG
MNGSLE
SLE
SLEKGZ
KGZ
KGZLAO
LAO
LAOLUX
LUX
LUXBWA
BWA
BWACOG
COG
COGHUN
HUN
HUNCIV
CIV
CIVRWA
RWA
RWAJOR
JOR
JORDZA
DZA
DZAIRQ
IRQ
IRQCHL
CHL
CHLCUB
CUB
CUBSWZ
SWZ
SWZNER
NER
NERISL
ISL
ISLLBR
LBR
LBRHND
HND
HNDMDV
MDV
MDVQAT
QAT
QATSYR
SYR
SYRITA
ITA
ITATGO
TGO
TGOGUY
GUY
GUYSEN
SEN
SENGHA
GHA
GHA6
6
68
8
810
10
1012
12
1214
14
14log capital per worker
log
capi
tal p
er w
orke
r
log capital per worker6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
appendix
26 / 77
Back to King and Levine
Recall:Yc = AcKα
c
Calibration: since α assumed constant across countries,use US value of 0.33
27 / 77
Measuring success
K accounts well for Y if
V [log(Kαc )]
V [log(Yc)]=
V [αkc ]
V [yc ]
is close to 1
Alternative measure(K90/K10)
α
Y90/Y10
gives broadly similar results (not reported)
28 / 77
Measuring success
K accounts well for Y if
V [log(Kαc )]
V [log(Yc)]=
V [αkc ]
V [yc ]
is close to 1
Alternative measure(K90/K10)
α
Y90/Y10
gives broadly similar results (not reported)
28 / 77
Measured success
Experiment N V [αk] V [y ] Ratio
King-Levine 142 0.26 1.30 0.20
29 / 77
Hall and Jones
Add schooling capital
Specifically
Log-wage regressions suggest one extra year of schoolingincreases earnings (and hence human capital) by about 10%
If workers in country A have on average one year of schoolingmore than in country B, country A has 10% more humancapital
30 / 77
Formalizing schooling capital
Production function per worker still CD
Yc = AcKαc L
1−αc
But labour aggregate depends on schooling attainment
Lc =J∑
j=1
eβsSjLj ,c
where:
Lj ,c is proportion of labour force in group j (in c)
Sj is years of schooling of group j
31 / 77
Implementing schooling capital
Barro and Lee dataset (2010 version)
For each country, proportion of labour force with:1 No education2 Some primary3 Primary completed4 Some secondary5 Secondary completed6 Some college7 College completed and more
32 / 77
Calibrating βs
Given
Yc = AcKαc
J∑j=1
eβsSjLj ,c
1−α
and perfect labour markets,
logWj ,c = αc + βsSj
So βs is the Mincerian coefficientNote: perfect markets only needed in country supplyingMincerian coefficient
33 / 77
Two small differences with HJ
Jensen inequality
J∑j=1
eβsSjLj ,c v. eβsPJ
j=1 SjLj,c
In HJ β varies with average schooling years
Neither of these differences has any impact whatsoever
34 / 77
Two small differences with HJ
Jensen inequality
J∑j=1
eβsSjLj ,c v. eβsPJ
j=1 SjLj,c
In HJ β varies with average schooling years
Neither of these differences has any impact whatsoever
34 / 77
Two small differences with HJ
Jensen inequality
J∑j=1
eβsSjLj ,c v. eβsPJ
j=1 SjLj,c
In HJ β varies with average schooling years
Neither of these differences has any impact whatsoever
34 / 77
Two small differences with HJ
Jensen inequality
J∑j=1
eβsSjLj ,c v. eβsPJ
j=1 SjLj,c
In HJ β varies with average schooling years
Neither of these differences has any impact whatsoever
34 / 77
l vs y
COD
COD
CODBDI
BDI
BDICHE
CHE
CHESVN
SVN
SVNLKA
LKA
LKASVK
SVK
SVKHKG
HKG
HKGTHA
THA
THAKHM
KHM
KHMSGP
SGP
SGPVNM
VNM
VNMBHR
BHR
BHRMAR
MAR
MARARG
ARG
ARGEGY
EGY
EGYGMB
GMB
GMBMOZ
MOZ
MOZIRL
IRL
IRLKEN
KEN
KENROU
ROU
ROUJAM
JAM
JAMIRN
IRN
IRNMUS
MUS
MUSHRV
HRV
HRVAFG
AFG
AFGZMB
ZMB
ZMBUSA
USA
USAJPN
JPN
JPNURY
URY
URYCRI
CRI
CRIMEX
MEX
MEXLVA
LVA
LVAZAF
ZAF
ZAFUKR
UKR
UKRTON
TON
TONALB
ALB
ALBZWE
ZWE
ZWEPHL
PHL
PHLPRT
PRT
PRTECU
ECU
ECUFRA
FRA
FRASWE
SWE
SWELBY
LBY
LBYPNG
PNG
PNGBRB
BRB
BRBCMR
CMR
CMRPAN
PAN
PANARM
ARM
ARMLSO
LSO
LSOBGD
BGD
BGDFIN
FIN
FINSLV
SLV
SLVTZA
TZA
TZANIC
NIC
NICNPL
NPL
NPLMRT
MRT
MRTARE
ARE
AREPRY
PRY
PRYYEM
YEM
YEMBRN
BRN
BRNPOL
POL
POLTTO
TTO
TTOVEN
VEN
VENBGR
BGR
BGRPER
PER
PERDOR
DOR
DORKOR
KOR
KOREST
EST
ESTBEL
BEL
BELCYP
CYP
CYPNLD
NLD
NLDPAK
PAK
PAKGBR
GBR
GBRCAF
CAF
CAFDNK
DNK
DNKBOL
BOL
BOLSAU
SAU
SAUNZL
NZL
NZLIDN
IDN
IDNGAB
GAB
GABUGA
UGA
UGACHN
CHN
CHNISR
ISR
ISRRUS
RUS
RUSKAZ
KAZ
KAZCOL
COL
COLBLZ
BLZ
BLZAUS
AUS
AUSTUR
TUR
TURKWT
KWT
KWTMLI
MLI
MLIMYS
MYS
MYSSDN
SDN
SDNMWI
MWI
MWIMAC
MAC
MACMLT
MLT
MLTGRC
GRC
GRCLTU
LTU
LTUIND
IND
INDGTM
GTM
GTMDEU
DEU
DEUROM
ROM
ROMFJI
FJI
FJIESP
ESP
ESPAUT
AUT
AUTCZE
CZE
CZETUN
TUN
TUNCAN
CAN
CANNAM
NAM
NAMHTI
HTI
HTIBEN
BEN
BENNOR
NOR
NORBRA
BRA
BRAMNG
MNG
MNGSLE
SLE
SLEKGZ
KGZ
KGZLAO
LAO
LAOLUX
LUX
LUXBWA
BWA
BWACOG
COG
COGHUN
HUN
HUNCIV
CIV
CIVRWA
RWA
RWAJOR
JOR
JORDZA
DZA
DZAIRQ
IRQ
IRQCHL
CHL
CHLCUB
CUB
CUBSWZ
SWZ
SWZNER
NER
NERISL
ISL
ISLLBR
LBR
LBRHND
HND
HNDMDV
MDV
MDVQAT
QAT
QATSYR
SYR
SYRITA
ITA
ITATGO
TGO
TGOGUY
GUY
GUYSEN
SEN
SENGHA
GHA
GHA0
0
0.5
.5
.51
1
11.5
1.5
1.5log of HJ schooling capital
log
of H
J sc
hool
ing
capi
tal
log of HJ schooling capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
appendix
35 / 77
The numbers
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33
36 / 77
Weil
Add health capital
Adult survival rate as an indicator of health status
Adult survival rate: probability of reaching 60 conditional onreaching 15
37 / 77
Implementing Health Capital
In principle
Lc =J∑
j=1
eβHHj+βsSjLj ,c
Where groups are now schooling-health groups, Hj is thehealth indicator for group j , and βH maps health status inhuman capitalIn practice
Lc = eβH H̄c
J∑j=1
eβsSjLj ,c
38 / 77
Calibrating βH
Time series evidence mapping survival rate into height
Micro-evidence mapping height into wage
Get βH ≈ 0.65
Translation: if Mincerian return is 0.10, 1 extra year ofschooling is equivalent to the extra health capital associatedwith 15 percentage points of adult survival rate
39 / 77
Survival Rate vs y
ZWE
ZWE
ZWELSO
LSO
LSOSWZ
SWZ
SWZZMB
ZMB
ZMBBWA
BWA
BWAZAF
ZAF
ZAFSLE
SLE
SLEUGA
UGA
UGAMOZ
MOZ
MOZCAF
CAF
CAFMWI
MWI
MWIAFG
AFG
AFGKEN
KEN
KENRWA
RWA
RWACMR
CMR
CMRTZA
TZA
TZABDI
BDI
BDIMLI
MLI
MLICOG
COG
COGCOD
COD
CODNAM
NAM
NAMNER
NER
NERPNG
PNG
PNGCIV
CIV
CIVRUS
RUS
RUSGHA
GHA
GHASEN
SEN
SENGMB
GMB
GMBGAB
GAB
GABSDN
SDN
SDNKHM
KHM
KHMMRT
MRT
MRTKAZ
KAZ
KAZHTI
HTI
HTIUKR
UKR
UKRMNG
MNG
MNGYEM
YEM
YEMLBR
LBR
LBRTHA
THA
THATGO
TGO
TGOGUY
GUY
GUYIND
IND
INDLAO
LAO
LAOROM
ROM
ROMBOL
BOL
BOLBGD
BGD
BGDLTU
LTU
LTUSLV
SLV
SLVNPL
NPL
NPLBEN
BEN
BENLVA
LVA
LVAKGZ
KGZ
KGZFJI
FJI
FJITTO
TTO
TTOGTM
GTM
GTMEST
EST
ESTBRA
BRA
BRAHUN
HUN
HUNJAM
JAM
JAMDOR
DOR
DORNIC
NIC
NICMUS
MUS
MUSPAK
PAK
PAKIDN
IDN
IDNBGR
BGR
BGRPRY
PRY
PRYCOL
COL
COLTON
TON
TONHND
HND
HNDMDV
MDV
MDVIRQ
IRQ
IRQJOR
JOR
JORROU
ROU
ROULKA
LKA
LKAPOL
POL
POLEGY
EGY
EGYVEN
VEN
VENPER
PER
PERPHL
PHL
PHLSVK
SVK
SVKIRN
IRN
IRNECU
ECU
ECUMAR
MAR
MARLBY
LBY
LBYMYS
MYS
MYSARM
ARM
ARMCHN
CHN
CHNARG
ARG
ARGSAU
SAU
SAUTUR
TUR
TURQAT
QAT
QATVNM
VNM
VNMDZA
DZA
DZABLZ
BLZ
BLZMEX
MEX
MEXCZE
CZE
CZEUSA
USA
USAHRV
HRV
HRVSYR
SYR
SYRPAN
PAN
PANURY
URY
URYTUN
TUN
TUNSVN
SVN
SVNFIN
FIN
FINPRT
PRT
PRTCHL
CHL
CHLCUB
CUB
CUBBHR
BHR
BHRFRA
FRA
FRABRB
BRB
BRBCRI
CRI
CRIDNK
DNK
DNKBEL
BEL
BELKOR
KOR
KORDEU
DEU
DEUAUT
AUT
AUTLUX
LUX
LUXBRN
BRN
BRNALB
ALB
ALBGBR
GBR
GBRESP
ESP
ESPARE
ARE
ARECAN
CAN
CANNZL
NZL
NZLKWT
KWT
KWTIRL
IRL
IRLNLD
NLD
NLDNOR
NOR
NORISR
ISR
ISRGRC
GRC
GRCJPN
JPN
JPNSGP
SGP
SGPAUS
AUS
AUSSWE
SWE
SWECHE
CHE
CHEITA
ITA
ITAMAC
MAC
MACMLT
MLT
MLTCYP
CYP
CYPISL
ISL
ISLHKG
HKG
HKG.2
.2
.2.4
.4
.4.6
.6
.6.8
.8
.81
1
1survival rate of adult population 15-60
surv
ival
rate
of a
dult
popu
latio
n 15
-60
survival rate of adult population 15-606
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 141 countries
appendix
40 / 77
Contribution of Health to success
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37
41 / 77
Quality of Schooling/Parenting
Hanushek and Woessman: big cross-country differences instandardized test scores, at given age
Possible sign of differences in schooling quality (though microevidence is weak)
Also possible sign of differences in parental inputs (confirmedby micro evidence)
42 / 77
Test Scores in DA
Use test scores as summary indicators of schoolquality/parental background
Lc = eβT T̄c eβH H̄c
J∑j=1
eβsSjLj ,c
βT is coefficient on test score in log-wage regression
43 / 77
Test Scores Data: The Details
TIMSS math and science, PIRLS reading, PISA math andscience, PISA reading
Age: 8th grade
Different dates and different sets of countries between 1995and 2007
High correlation across different tests for same country
Scale each to 1-100, and average over all available tests(resulting in 75 data points)
44 / 77
Calibrating βT : The Details
Lazear (2003), National Education Longitudinal Survey:
log(Wi ) = α+ βTTi + εi ,
Where wages are observed in late 20s and school test is verysimilar to international ones
Finds βT = 0.01
Given observed range in data, this is small
45 / 77
Test Scores vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGP30
30
3040
40
4050
50
5060
60
60test score
test
sco
re
test score6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
test scores year 1995-2007, output year 2005, 75 countries
46 / 77
βT TS vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGP1
1
11.1
1.1
1.11.2
1.2
1.21.3
1.3
1.31.4
1.4
1.4log test score human capital
log
test
sco
re h
uman
cap
ital
log test score human capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
test scores year 1995-2007, output year 2005, 75 countries
47 / 77
(1− α)βT TS vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGP.65
.65
.65.7
.7
.7.75
.75
.75.8
.8
.8.85
.85
.85.9
.9
.9share-weighted log of test score human capital
shar
e-w
eigh
ted
log
of t
est
scor
e hu
man
cap
ital
share-weighted log of test score human capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
test scores year 1995-2007, output year 2005, 75 countries
48 / 77
αk + (1− α)l vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGP4
4
44.5
4.5
4.55
5
55.5
5.5
5.56
6
6log Cobb-Douglas aggregate of K and HJ-W-Test L
log
Cobb
-Dou
glas
agg
rega
te o
f K a
nd H
J-W
-Tes
t L
log Cobb-Douglas aggregate of K and HJ-W-Test L6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
test scores year 1995-2007, output year 2005, 75 countries
49 / 77
Contribution of Test Scores to Success
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37Test sample 75 0.11 0.017 0.18 0.53 0.34Test correction 75 0.11 0.028 0.22 0.53 0.41
50 / 77
Imperfect Substitution in Schooling
Overwhelming evidence that relative wages respond to changesin relative quantities of workers with different educationalattainment
Inconsistent with Hall-Jones schooling capital measure
51 / 77
Modelling Imperfect Substitution
ReplaceJ∑
j=1
eβsSjLj ,c
With z−1∑j=1
eβjLj ,c
ρ
+ B
J∑j=z
eβjLj ,c
ρ1/ρ
Where:z is lowest schooling group in high-education labour force (e.g.secondary school completed)
β1 = βz = 1; other βjs are relative productivities
1/(1− ρ) is the elasticity of substitution
52 / 77
Calibration with Imperfect Substitution: z , ρ
Many estimates of EOS clustered around 1.4, 1.5
Ciccone and Peri
US census data, IV
z is high-school completed
1/(1− ρ) = 1.5
Set z and ρ accordingly
53 / 77
Calibration with Imperfect Substitution: βj
Functional formz−1∑j=1
eβjLj ,c
ρ
+ B
J∑j=z
eβjLj ,c
ρ1/ρ
Suggests running two separate log-wage regressions
log(Wj , j < z) = α+ βj
log(Wj , j ≥ z) = α+ βj
(Aside: Mincerian approach fundamentally inconsistent withimperfect substitution, more on this tomorrow)
54 / 77
Estimating the βjs
Take CPS, 1991
Only white males
Create 7 dummy variables, corresponding to 7 Barro-Leeschooling groups
Regression 1: bottom four groups
Regression 2: top three groups
Control for full set of age dummies
55 / 77
Relative Productivities of Attainment Groups
Low Education High Education
No Schooling 0 Secondary Complete 0Some Primary 0.32 Some College 0.14Completed Primary 0.38 College and More 0.46Some Secondary 0.56
56 / 77
Calibration with Imperfect Substitution: B
From z−1∑j=1
eβjLj ,c
ρ
+ B
J∑j=z
eβjLj ,c
ρ1/ρ
Wz,c
W1,c= B
(∑Jj=z e
βjLj ,c
)ρ−1
(∑z−1j=1 eβjLj ,c
)ρ−1eβz
eβ1= B
(∑Jj=z e
βjLj ,c
)ρ−1
(∑z−1j=1 eβjLj ,c
)ρ−1
Can retrieve B if for one country observe both relative wageand relative supply. US:
Relative supply (from before) = 3Relative wage (from a CPS log-wage regression) = 2.29
Then B = 4.76
57 / 77
l with imp. sub. vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGPTGO
TGO
TGOJAM
JAM
JAMBEN
BEN
BENZWE
ZWE
ZWEFJI
FJI
FJICMR
CMR
CMRKEN
KEN
KENGTM
GTM
GTMBOL
BOL
BOLNAM
NAM
NAMBLZ
BLZ
BLZSDN
SDN
SDNTZA
TZA
TZAMLI
MLI
MLINIC
NIC
NICLBR
LBR
LBRGAB
GAB
GABSLE
SLE
SLENPL
NPL
NPLMUS
MUS
MUSECU
ECU
ECUNER
NER
NERHND
HND
HNDCAF
CAF
CAFLKA
LKA
LKASWZ
SWZ
SWZRWA
RWA
RWACRI
CRI
CRIKAZ
KAZ
KAZCUB
CUB
CUBPAK
PAK
PAKHTI
HTI
HTIKHM
KHM
KHMGMB
GMB
GMBIRQ
IRQ
IRQAFG
AFG
AFGLSO
LSO
LSODOR
DOR
DORPRY
PRY
PRYARE
ARE
AREMWI
MWI
MWIBDI
BDI
BDIVNM
VNM
VNMSEN
SEN
SENCOD
COD
CODBRB
BRB
BRBMNG
MNG
MNGBRN
BRN
BRNCIV
CIV
CIVMRT
MRT
MRTBGD
BGD
BGDMDV
MDV
MDVMOZ
MOZ
MOZLAO
LAO
LAOTON
TON
TONGUY
GUY
GUYYEM
YEM
YEMPNG
PNG
PNGVEN
VEN
VENIND
IND
INDCOG
COG
COGLBY
LBY
LBYUGA
UGA
UGACHN
CHN
CHNZMB
ZMB
ZMBPAN
PAN
PAN2.5
2.5
2.53
3
33.5
3.5
3.54
4
44.5
4.5
4.55
5
5log of schooling capital under imperfect substitution
log
of s
choo
ling
capi
tal u
nder
impe
rfec
t su
bstit
utio
n
log of schooling capital under imperfect substitution6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
58 / 77
(1− α)l vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGPTGO
TGO
TGOJAM
JAM
JAMBEN
BEN
BENZWE
ZWE
ZWEFJI
FJI
FJICMR
CMR
CMRKEN
KEN
KENGTM
GTM
GTMBOL
BOL
BOLNAM
NAM
NAMBLZ
BLZ
BLZSDN
SDN
SDNTZA
TZA
TZAMLI
MLI
MLINIC
NIC
NICLBR
LBR
LBRGAB
GAB
GABSLE
SLE
SLENPL
NPL
NPLMUS
MUS
MUSECU
ECU
ECUNER
NER
NERHND
HND
HNDCAF
CAF
CAFLKA
LKA
LKASWZ
SWZ
SWZRWA
RWA
RWACRI
CRI
CRIKAZ
KAZ
KAZCUB
CUB
CUBPAK
PAK
PAKHTI
HTI
HTIKHM
KHM
KHMGMB
GMB
GMBIRQ
IRQ
IRQAFG
AFG
AFGLSO
LSO
LSODOR
DOR
DORPRY
PRY
PRYARE
ARE
AREMWI
MWI
MWIBDI
BDI
BDIVNM
VNM
VNMSEN
SEN
SENCOD
COD
CODBRB
BRB
BRBMNG
MNG
MNGBRN
BRN
BRNCIV
CIV
CIVMRT
MRT
MRTBGD
BGD
BGDMDV
MDV
MDVMOZ
MOZ
MOZLAO
LAO
LAOTON
TON
TONGUY
GUY
GUYYEM
YEM
YEMPNG
PNG
PNGVEN
VEN
VENIND
IND
INDCOG
COG
COGLBY
LBY
LBYUGA
UGA
UGACHN
CHN
CHNZMB
ZMB
ZMBPAN
PAN
PAN1.5
1.5
1.52
2
22.5
2.5
2.53
3
33.5
3.5
3.5share weighted log of schooling capital under imp. sub.
shar
e w
eigh
ted
log
of s
choo
ling
capi
tal u
nder
imp.
sub
.share weighted log of schooling capital under imp. sub.6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
59 / 77
αk + (1− α)l vs y
ZAF
ZAF
ZAFGHA
GHA
GHAKGZ
KGZ
KGZPER
PER
PERQAT
QAT
QATMAR
MAR
MARKWT
KWT
KWTPHL
PHL
PHLBWA
BWA
BWASLV
SLV
SLVALB
ALB
ALBSAU
SAU
SAUBRA
BRA
BRACOL
COL
COLTUN
TUN
TUNARG
ARG
ARGIDN
IDN
IDNDZA
DZA
DZAEGY
EGY
EGYMEX
MEX
MEXJOR
JOR
JORCHL
CHL
CHLSYR
SYR
SYRURY
URY
URYBHR
BHR
BHRIRN
IRN
IRNTTO
TTO
TTOTUR
TUR
TURTHA
THA
THAROU
ROU
ROUISR
ISR
ISRCYP
CYP
CYPPRT
PRT
PRTBGR
BGR
BGRGRC
GRC
GRCMLT
MLT
MLTUKR
UKR
UKRHRV
HRV
HRVARM
ARM
ARMLVA
LVA
LVAROM
ROM
ROMESP
ESP
ESPLUX
LUX
LUXNOR
NOR
NORMYS
MYS
MYSITA
ITA
ITALTU
LTU
LTUPOL
POL
POLISL
ISL
ISLRUS
RUS
RUSSVK
SVK
SVKCZE
CZE
CZEDNK
DNK
DNKFRA
FRA
FRACHE
CHE
CHEMAC
MAC
MACUSA
USA
USADEU
DEU
DEUSVN
SVN
SVNGBR
GBR
GBRIRL
IRL
IRLBEL
BEL
BELHUN
HUN
HUNEST
EST
ESTAUT
AUT
AUTSWE
SWE
SWENZL
NZL
NZLAUS
AUS
AUSCAN
CAN
CANJPN
JPN
JPNNLD
NLD
NLDFIN
FIN
FINKOR
KOR
KORHKG
HKG
HKGSGP
SGP
SGPTGO
TGO
TGOJAM
JAM
JAMBEN
BEN
BENZWE
ZWE
ZWEFJI
FJI
FJICMR
CMR
CMRKEN
KEN
KENGTM
GTM
GTMBOL
BOL
BOLNAM
NAM
NAMBLZ
BLZ
BLZSDN
SDN
SDNTZA
TZA
TZAMLI
MLI
MLINIC
NIC
NICLBR
LBR
LBRGAB
GAB
GABSLE
SLE
SLENPL
NPL
NPLMUS
MUS
MUSECU
ECU
ECUNER
NER
NERHND
HND
HNDCAF
CAF
CAFLKA
LKA
LKASWZ
SWZ
SWZRWA
RWA
RWACRI
CRI
CRIKAZ
KAZ
KAZCUB
CUB
CUBPAK
PAK
PAKHTI
HTI
HTIKHM
KHM
KHMGMB
GMB
GMBIRQ
IRQ
IRQAFG
AFG
AFGLSO
LSO
LSODOR
DOR
DORPRY
PRY
PRYARE
ARE
AREMWI
MWI
MWIBDI
BDI
BDIVNM
VNM
VNMSEN
SEN
SENCOD
COD
CODBRB
BRB
BRBMNG
MNG
MNGBRN
BRN
BRNCIV
CIV
CIVMRT
MRT
MRTBGD
BGD
BGDMDV
MDV
MDVMOZ
MOZ
MOZLAO
LAO
LAOTON
TON
TONGUY
GUY
GUYYEM
YEM
YEMPNG
PNG
PNGVEN
VEN
VENIND
IND
INDCOG
COG
COGLBY
LBY
LBYUGA
UGA
UGACHN
CHN
CHNZMB
ZMB
ZMBPAN
PAN
PAN4
4
45
5
56
6
67
7
78
8
8log Cobb-Douglas aggregate of K and L under imp. sub.
log
Cobb
-Dou
glas
agg
rega
te o
f K a
nd L
und
er im
p. s
ub.log Cobb-Douglas aggregate of K and L under imp. sub.6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
60 / 77
Implications of Imperfect Substitutability
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37Test sample 75 0.11 0.017 0.18 0.53 0.34Test correction 75 0.11 0.028 0.22 0.53 0.41Imp. Sub. School. 141 0.26 0.150 0.72 1.30 0.55
61 / 77
With Health and Test Correction
Adding health capital
eβH H̄c
z−1∑j=1
eβjLj ,c
ρ
+ B
J∑j=z
eβjLj ,c
ρ1/ρ
Adding health capital and quality/parental capital
eβT T̄teβH H̄c
z−1∑j=1
eβjLj ,c
ρ
+ B
J∑j=z
eβjLj ,c
ρ1/ρ
62 / 77
Implications of Imp. Sub. (cont.)
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37Test sample 75 0.11 0.017 0.18 0.53 0.34Test correction 75 0.11 0.028 0.22 0.53 0.41Imp. Sub. School. 141 0.26 0.150 0.72 1.30 0.55+ health capital 141 0.26 0.180 0.79 1.30 0.61
63 / 77
Implications of Imp. Sub. (cont.)
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37Test sample 75 0.11 0.017 0.18 0.53 0.34Test correction 75 0.11 0.028 0.22 0.53 0.41Imp. Sub. School. 141 0.26 0.150 0.72 1.30 0.55+ health capital 141 0.26 0.180 0.79 1.30 0.61same in test sample 75 0.11 0.045 0.23 0.53 0.44+ test correction 75 0.11 0.061 0.28 0.53 0.52
64 / 77
Natural Capital
Land, trees, mineral deposits, etc. are inputs into aggregatevalued added
They need to be accounted for
Caselli and Feyrer: natural capital distributed more equallythan reproducible capital
Suggests this will dampen variability of total capital andreduce success
65 / 77
Data on Total Capital
Constructed by a World Bank team, for year 2000
Natural capital: estimate value of rents (output) from aparticular form of capital and then capitalize value using afixed discount rate
Reproducible capital: perpetual inventory method
Urban land: 24% percent of the value of reproducible capital
66 / 77
Natural Capital
Table: Proportion of Different Types of Wealth in Total Wealth in 2000
Variable Mean St. dev Median Weighted Corr w/mean log(GDP)
Subsoil resources 10.5 16.4 1.5 7.0 -0.13Timber 1.7 2.6 0.8 0.9 -0.34Other forest 2.2 5.4 1.1 0.3 -0.49Cropland 11.4 15.2 5.1 3.2 -0.73Pasture 4.5 5.4 2.7 1.9 -0.00Protected areas 1.9 2.5 0.3 1.4 0.01Urban land 13.1 4.6 13.5 16.5 0.70Reproducible Capital 54.8 19.2 56.3 68.6 0.70
67 / 77
DA with Natural Capital
First pass. InYc = AcKα
c L1−αc
Replace reproducible capital with total capital
68 / 77
Reproducible v Total Capital
6
6
68
8
810
10
1012
12
1214
14
146
6
68
8
810
10
1012
12
12y
y
ytotal (log)
total (log)
total (log)reproducible (log)
reproducible (log)
reproducible (log)
69 / 77
Effects of Natural Capital
Experiment N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratio
King-Levine 142 0.26 1.31 0.20Hall-Jones 141 0.26 0.028 0.43 1.30 0.33Weil 141 0.26 0.043 0.48 1.30 0.37Test sample 75 0.11 0.017 0.18 0.53 0.34Test correction 75 0.11 0.028 0.22 0.53 0.41Imp. Sub. School. 141 0.26 0.150 0.72 1.30 0.55+ health capital 141 0.26 0.180 0.79 1.30 0.61same in test sample 75 0.11 0.045 0.23 0.53 0.44+ test correction 75 0.11 0.061 0.28 0.53 0.52Rep. Cap. (reduced sample) 100 0.23 0.170 0.75 1.10 0.70Tot. Cap. 100 0.18 0.170 0.62 1.10 0.58Rep. Cap. (reduced sample)* 56 0.11 0.071 0.32 0.53 0.61Tot. Cap., test correction 56 0.11 0.071 0.32 0.53 0.60
*: Tot. Cap. test
70 / 77
Natural and Reproducible Capital: Imperfect Substitutes
Previous exercise assumes perfect substitutes
Patterns of substitutability unknown
Would it matter?
Experiment with
Kc = (Nc)γ (Mc)
1−γ
where Nc is Nat. Cap. and Mc is Rep. Cap.
Calibrate γ by average share of natural capital in total capital(= 0.52)
71 / 77
Sensitivity to Capital Aggregation
Nat. and Rep. Cap. N V [αk] V [(1− α)l ] V [αk + (1− α)l ] V [y ] Ratioaggregation
Linear 100 0.16 0.17 0.59 1.1 0.55Cobb-Douglas 100 0.15 0.17 0.58 1.1 0.55
72 / 77
Next Level Up
More general aggregate production function
Yc = Ac [Kσc + CLσc ]1/σ
Still no consensus estimates of σ
(Most estimates below 0 but range is huge and upper boundwell above 0)
Would it matter? Experiment with different σ’s
73 / 77
Calibration
Each σ implies a C . From
Yc = Ac [Kσc + CLσc ]1/σ
Wc = C(Yc
Lc
)1−σ
Or
WcLc
Yc
(Yc
Lc
)σ= C
Use US Data, get a C for every σ
74 / 77
Sensitivity to K, L, EOS
EOS K and L N V [log(Kσ + CLσ)1/σ] V [log(Y )] Ratio
0.5 100 0.58 1.1 0.551 100 0.59 1.1 0.551.5 100 0.58 1.1 0.55
75 / 77
Summary
Only Rep. Cap. (K-L) 0.20Schooling Cap. (H-K) + 0.13Health Cap. (Weil) + 0.04Test Correction + 0.07Imp. Sub. Schooling + 0.23Natural Capital - 0.06
Total 0.61
76 / 77
Conclusions
Accumulation hypothesis comes out much better than in thepast (though not a very demanding standard)
Both functional forms and measurement issues important
Results insensitive to substitutability between natural andreproducible capital as well as between capital and labor
Not clear where the next lowest-hanging fruit is
77 / 77
Income per worker: the caveats
What is being measured?
Yc =∑g
πgYg ,c
where:Yg ,c is quantitiesπg is "international prices"
summation taken over final expenditures
back
78 / 77
Income per worker: the caveats (cont.)
Key issue: whose prices?
PWT: Geary-KhamisWDI: Mixture of CPD and EKS
Infinite other possibilities
Key message:No such thing as a "PPP Income"A purely statistical, not an economic, construct
back
79 / 77
...and it does make a difference
0
0
0.1
.1
.1.2
.2
.2.3
.3
.3-6
-6
-6-4
-4
-4-2
-2
-20
0
02
2
2PWT
PWT
PWTincome distribution:
income distribution:
income distribution:PWT
PWT
PWTWDI
WDI
WDI
sources: PWT 6.3, WDI(2009), year 2005
back
80 / 77
PWT-WDI comparison cont. (2005, N=142)
PWT 6.3 WDI (2009)
Log-Variance 1.3 1.7
90-10 ratio 19 30
Correlation 0.97
back
81 / 77
Trade-Off
Quality of price data:
WDI (2009): 2005 International Comparison ProgramPWT (6.3): 1995 ICP
Investment Variable:
WDI: share of I in nominal GDPPWT: share of I in real GDP
Use PWT 6.3 and wait for PWT 7 for book
back
82 / 77
Aggregate production function: the caveats
In a multi-good economy aggregate GDP is a CES function ofaggregate capital and aggregate labour only if all the goodsare produced with identical CES technologies
i.e. only if it is effectively a one-good economy
i.e. at best we are working with approximations here
back
83 / 77
K caveats
Huge cross-country heterogeneity in reproducible capital stocks
source: Caselli and Wilson (2004)
back
84 / 77
Implications of heterogeneity
Capital aggregation
Kc,t = K (K 1c,t , ...,K
kc,t , ...)
Hard, but not entirely impossible, to measure stocks ofsub-typesBut we know nothing on function K. Direct calibrationunfeasible with current knowledge.Growth-accounting approach may be feasible, but not pursuedhere
back
85 / 77
Measuring Investment
Growth-accounting approach: weight investment in sub-typesby their share in total capital income
National-account (and PWT) approach: weight by (PPP)price
Results same only if different types are perfect substitutes(function K linear)
back
86 / 77
αk vs y
COD
COD
CODBDI
BDI
BDICHE
CHE
CHESVN
SVN
SVNLKA
LKA
LKASVK
SVK
SVKHKG
HKG
HKGTHA
THA
THAKHM
KHM
KHMSGP
SGP
SGPVNM
VNM
VNMBHR
BHR
BHRMAR
MAR
MARARG
ARG
ARGEGY
EGY
EGYGMB
GMB
GMBMOZ
MOZ
MOZIRL
IRL
IRLKEN
KEN
KENROU
ROU
ROUJAM
JAM
JAMIRN
IRN
IRNMUS
MUS
MUSHRV
HRV
HRVAFG
AFG
AFGZMB
ZMB
ZMBUSA
USA
USAJPN
JPN
JPNURY
URY
URYCRI
CRI
CRIMEX
MEX
MEXLVA
LVA
LVAZAF
ZAF
ZAFUKR
UKR
UKRTON
TON
TONALB
ALB
ALBZWE
ZWE
ZWEPHL
PHL
PHLPRT
PRT
PRTECU
ECU
ECUFRA
FRA
FRASWE
SWE
SWELBY
LBY
LBYPNG
PNG
PNGBRB
BRB
BRBCMR
CMR
CMRPAN
PAN
PANARM
ARM
ARMLSO
LSO
LSOBGD
BGD
BGDFIN
FIN
FINSLV
SLV
SLVTZA
TZA
TZANIC
NIC
NICNPL
NPL
NPLMRT
MRT
MRTARE
ARE
AREPRY
PRY
PRYYEM
YEM
YEMBRN
BRN
BRNPOL
POL
POLTTO
TTO
TTOVEN
VEN
VENBGR
BGR
BGRPER
PER
PERDOR
DOR
DORKOR
KOR
KOREST
EST
ESTBEL
BEL
BELCYP
CYP
CYPNLD
NLD
NLDPAK
PAK
PAKGBR
GBR
GBRCAF
CAF
CAFDNK
DNK
DNKBOL
BOL
BOLSAU
SAU
SAUNZL
NZL
NZLIDN
IDN
IDNGAB
GAB
GABTWN
TWN
TWNUGA
UGA
UGACHN
CHN
CHNISR
ISR
ISRRUS
RUS
RUSKAZ
KAZ
KAZCOL
COL
COLBLZ
BLZ
BLZAUS
AUS
AUSTUR
TUR
TURKWT
KWT
KWTMLI
MLI
MLIMYS
MYS
MYSSDN
SDN
SDNMWI
MWI
MWIMAC
MAC
MACMLT
MLT
MLTGRC
GRC
GRCLTU
LTU
LTUIND
IND
INDGTM
GTM
GTMDEU
DEU
DEUROM
ROM
ROMFJI
FJI
FJIESP
ESP
ESPAUT
AUT
AUTCZE
CZE
CZETUN
TUN
TUNCAN
CAN
CANNAM
NAM
NAMHTI
HTI
HTIBEN
BEN
BENNOR
NOR
NORBRA
BRA
BRAMNG
MNG
MNGSLE
SLE
SLEKGZ
KGZ
KGZLAO
LAO
LAOLUX
LUX
LUXBWA
BWA
BWACOG
COG
COGHUN
HUN
HUNCIV
CIV
CIVRWA
RWA
RWAJOR
JOR
JORDZA
DZA
DZAIRQ
IRQ
IRQCHL
CHL
CHLCUB
CUB
CUBSWZ
SWZ
SWZNER
NER
NERISL
ISL
ISLLBR
LBR
LBRHND
HND
HNDMDV
MDV
MDVQAT
QAT
QATSYR
SYR
SYRITA
ITA
ITATGO
TGO
TGOGUY
GUY
GUYSEN
SEN
SENGHA
GHA
GHA2
2
22.5
2.5
2.53
3
33.5
3.5
3.54
4
44.5
4.5
4.5share-weighted log capital per worker
shar
e-w
eigh
ted
log
capi
tal p
er w
orke
r
share-weighted log capital per worker6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
87 / 77
Sources of bias in Var [k]
Government investment - downward (Pritchett)
Natural capital - upward (see below)
(Aggregation issues - ambiguous)
88 / 77
(1- α)l vs y
COD
COD
CODBDI
BDI
BDICHE
CHE
CHESVN
SVN
SVNLKA
LKA
LKASVK
SVK
SVKHKG
HKG
HKGTHA
THA
THAKHM
KHM
KHMSGP
SGP
SGPVNM
VNM
VNMBHR
BHR
BHRMAR
MAR
MARARG
ARG
ARGEGY
EGY
EGYGMB
GMB
GMBMOZ
MOZ
MOZIRL
IRL
IRLKEN
KEN
KENROU
ROU
ROUJAM
JAM
JAMIRN
IRN
IRNMUS
MUS
MUSHRV
HRV
HRVAFG
AFG
AFGZMB
ZMB
ZMBUSA
USA
USAJPN
JPN
JPNURY
URY
URYCRI
CRI
CRIMEX
MEX
MEXLVA
LVA
LVAZAF
ZAF
ZAFUKR
UKR
UKRTON
TON
TONALB
ALB
ALBZWE
ZWE
ZWEPHL
PHL
PHLPRT
PRT
PRTECU
ECU
ECUFRA
FRA
FRASWE
SWE
SWELBY
LBY
LBYPNG
PNG
PNGBRB
BRB
BRBCMR
CMR
CMRPAN
PAN
PANARM
ARM
ARMLSO
LSO
LSOBGD
BGD
BGDFIN
FIN
FINSLV
SLV
SLVTZA
TZA
TZANIC
NIC
NICNPL
NPL
NPLMRT
MRT
MRTARE
ARE
AREPRY
PRY
PRYYEM
YEM
YEMBRN
BRN
BRNPOL
POL
POLTTO
TTO
TTOVEN
VEN
VENBGR
BGR
BGRPER
PER
PERDOR
DOR
DORKOR
KOR
KOREST
EST
ESTBEL
BEL
BELCYP
CYP
CYPNLD
NLD
NLDPAK
PAK
PAKGBR
GBR
GBRCAF
CAF
CAFDNK
DNK
DNKBOL
BOL
BOLSAU
SAU
SAUNZL
NZL
NZLIDN
IDN
IDNGAB
GAB
GABUGA
UGA
UGACHN
CHN
CHNISR
ISR
ISRRUS
RUS
RUSKAZ
KAZ
KAZCOL
COL
COLBLZ
BLZ
BLZAUS
AUS
AUSTUR
TUR
TURKWT
KWT
KWTMLI
MLI
MLIMYS
MYS
MYSSDN
SDN
SDNMWI
MWI
MWIMAC
MAC
MACMLT
MLT
MLTGRC
GRC
GRCLTU
LTU
LTUIND
IND
INDGTM
GTM
GTMDEU
DEU
DEUROM
ROM
ROMFJI
FJI
FJIESP
ESP
ESPAUT
AUT
AUTCZE
CZE
CZETUN
TUN
TUNCAN
CAN
CANNAM
NAM
NAMHTI
HTI
HTIBEN
BEN
BENNOR
NOR
NORBRA
BRA
BRAMNG
MNG
MNGSLE
SLE
SLEKGZ
KGZ
KGZLAO
LAO
LAOLUX
LUX
LUXBWA
BWA
BWACOG
COG
COGHUN
HUN
HUNCIV
CIV
CIVRWA
RWA
RWAJOR
JOR
JORDZA
DZA
DZAIRQ
IRQ
IRQCHL
CHL
CHLCUB
CUB
CUBSWZ
SWZ
SWZNER
NER
NERISL
ISL
ISLLBR
LBR
LBRHND
HND
HNDMDV
MDV
MDVQAT
QAT
QATSYR
SYR
SYRITA
ITA
ITATGO
TGO
TGOGUY
GUY
GUYSEN
SEN
SENGHA
GHA
GHA.2
.2
.2.4
.4
.4.6
.6
.6.8
.8
.81
1
1share-weighted log of HJ schooling capital
shar
e-w
eigh
ted
log
of H
J sc
hool
ing
capi
tal
share-weighted log of HJ schooling capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
back
89 / 77
αk + (1- α)l vs y
COD
COD
CODBDI
BDI
BDICHE
CHE
CHESVN
SVN
SVNLKA
LKA
LKASVK
SVK
SVKHKG
HKG
HKGTHA
THA
THAKHM
KHM
KHMSGP
SGP
SGPVNM
VNM
VNMBHR
BHR
BHRMAR
MAR
MARARG
ARG
ARGEGY
EGY
EGYGMB
GMB
GMBMOZ
MOZ
MOZIRL
IRL
IRLKEN
KEN
KENROU
ROU
ROUJAM
JAM
JAMIRN
IRN
IRNMUS
MUS
MUSHRV
HRV
HRVAFG
AFG
AFGZMB
ZMB
ZMBUSA
USA
USAJPN
JPN
JPNURY
URY
URYCRI
CRI
CRIMEX
MEX
MEXLVA
LVA
LVAZAF
ZAF
ZAFUKR
UKR
UKRTON
TON
TONALB
ALB
ALBZWE
ZWE
ZWEPHL
PHL
PHLPRT
PRT
PRTECU
ECU
ECUFRA
FRA
FRASWE
SWE
SWELBY
LBY
LBYPNG
PNG
PNGBRB
BRB
BRBCMR
CMR
CMRPAN
PAN
PANARM
ARM
ARMLSO
LSO
LSOBGD
BGD
BGDFIN
FIN
FINSLV
SLV
SLVTZA
TZA
TZANIC
NIC
NICNPL
NPL
NPLMRT
MRT
MRTARE
ARE
AREPRY
PRY
PRYYEM
YEM
YEMBRN
BRN
BRNPOL
POL
POLTTO
TTO
TTOVEN
VEN
VENBGR
BGR
BGRPER
PER
PERDOR
DOR
DORKOR
KOR
KOREST
EST
ESTBEL
BEL
BELCYP
CYP
CYPNLD
NLD
NLDPAK
PAK
PAKGBR
GBR
GBRCAF
CAF
CAFDNK
DNK
DNKBOL
BOL
BOLSAU
SAU
SAUNZL
NZL
NZLIDN
IDN
IDNGAB
GAB
GABUGA
UGA
UGACHN
CHN
CHNISR
ISR
ISRRUS
RUS
RUSKAZ
KAZ
KAZCOL
COL
COLBLZ
BLZ
BLZAUS
AUS
AUSTUR
TUR
TURKWT
KWT
KWTMLI
MLI
MLIMYS
MYS
MYSSDN
SDN
SDNMWI
MWI
MWIMAC
MAC
MACMLT
MLT
MLTGRC
GRC
GRCLTU
LTU
LTUIND
IND
INDGTM
GTM
GTMDEU
DEU
DEUROM
ROM
ROMFJI
FJI
FJIESP
ESP
ESPAUT
AUT
AUTCZE
CZE
CZETUN
TUN
TUNCAN
CAN
CANNAM
NAM
NAMHTI
HTI
HTIBEN
BEN
BENNOR
NOR
NORBRA
BRA
BRAMNG
MNG
MNGSLE
SLE
SLEKGZ
KGZ
KGZLAO
LAO
LAOLUX
LUX
LUXBWA
BWA
BWACOG
COG
COGHUN
HUN
HUNCIV
CIV
CIVRWA
RWA
RWAJOR
JOR
JORDZA
DZA
DZAIRQ
IRQ
IRQCHL
CHL
CHLCUB
CUB
CUBSWZ
SWZ
SWZNER
NER
NERISL
ISL
ISLLBR
LBR
LBRHND
HND
HNDMDV
MDV
MDVQAT
QAT
QATSYR
SYR
SYRITA
ITA
ITATGO
TGO
TGOGUY
GUY
GUYSEN
SEN
SENGHA
GHA
GHA2.5
2.5
2.53
3
33.5
3.5
3.54
4
44.5
4.5
4.55
5
5log of Cobb-Douglas aggregate of K and HJ L
log
of C
obb-
Doug
las
aggr
egat
e of
K a
nd H
J L
log of Cobb-Douglas aggregate of K and HJ L6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 142 countries
back
90 / 77
βH SR vs y
ZWE
ZWE
ZWELSO
LSO
LSOSWZ
SWZ
SWZZMB
ZMB
ZMBBWA
BWA
BWAZAF
ZAF
ZAFSLE
SLE
SLEUGA
UGA
UGAMOZ
MOZ
MOZCAF
CAF
CAFMWI
MWI
MWIAFG
AFG
AFGKEN
KEN
KENRWA
RWA
RWACMR
CMR
CMRTZA
TZA
TZABDI
BDI
BDIMLI
MLI
MLICOG
COG
COGCOD
COD
CODNAM
NAM
NAMNER
NER
NERPNG
PNG
PNGCIV
CIV
CIVRUS
RUS
RUSGHA
GHA
GHASEN
SEN
SENGMB
GMB
GMBGAB
GAB
GABSDN
SDN
SDNKHM
KHM
KHMMRT
MRT
MRTKAZ
KAZ
KAZHTI
HTI
HTIUKR
UKR
UKRMNG
MNG
MNGYEM
YEM
YEMLBR
LBR
LBRTHA
THA
THATGO
TGO
TGOGUY
GUY
GUYIND
IND
INDLAO
LAO
LAOROM
ROM
ROMBOL
BOL
BOLBGD
BGD
BGDLTU
LTU
LTUSLV
SLV
SLVNPL
NPL
NPLBEN
BEN
BENLVA
LVA
LVAKGZ
KGZ
KGZFJI
FJI
FJITTO
TTO
TTOGTM
GTM
GTMEST
EST
ESTBRA
BRA
BRAHUN
HUN
HUNJAM
JAM
JAMDOR
DOR
DORNIC
NIC
NICMUS
MUS
MUSPAK
PAK
PAKIDN
IDN
IDNBGR
BGR
BGRPRY
PRY
PRYCOL
COL
COLTON
TON
TONHND
HND
HNDMDV
MDV
MDVIRQ
IRQ
IRQJOR
JOR
JORROU
ROU
ROULKA
LKA
LKAPOL
POL
POLEGY
EGY
EGYVEN
VEN
VENPER
PER
PERPHL
PHL
PHLSVK
SVK
SVKIRN
IRN
IRNECU
ECU
ECUMAR
MAR
MARLBY
LBY
LBYMYS
MYS
MYSARM
ARM
ARMCHN
CHN
CHNARG
ARG
ARGSAU
SAU
SAUTUR
TUR
TURQAT
QAT
QATVNM
VNM
VNMDZA
DZA
DZABLZ
BLZ
BLZMEX
MEX
MEXCZE
CZE
CZEUSA
USA
USAHRV
HRV
HRVSYR
SYR
SYRPAN
PAN
PANURY
URY
URYTUN
TUN
TUNSVN
SVN
SVNFIN
FIN
FINPRT
PRT
PRTCHL
CHL
CHLCUB
CUB
CUBBHR
BHR
BHRFRA
FRA
FRABRB
BRB
BRBCRI
CRI
CRIDNK
DNK
DNKBEL
BEL
BELKOR
KOR
KORDEU
DEU
DEUAUT
AUT
AUTLUX
LUX
LUXBRN
BRN
BRNALB
ALB
ALBGBR
GBR
GBRESP
ESP
ESPARE
ARE
ARECAN
CAN
CANNZL
NZL
NZLKWT
KWT
KWTIRL
IRL
IRLNLD
NLD
NLDNOR
NOR
NORISR
ISR
ISRGRC
GRC
GRCJPN
JPN
JPNSGP
SGP
SGPAUS
AUS
AUSSWE
SWE
SWECHE
CHE
CHEITA
ITA
ITAMAC
MAC
MACMLT
MLT
MLTCYP
CYP
CYPISL
ISL
ISLHKG
HKG
HKG0
0
0.1
.1
.1.2
.2
.2.3
.3
.3.4
.4
.4log health capital
log
heal
th c
apita
l
log health capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 141 countries
back
91 / 77
(1− α)βH SR vs y
ZWE
ZWE
ZWELSO
LSO
LSOSWZ
SWZ
SWZZMB
ZMB
ZMBBWA
BWA
BWAZAF
ZAF
ZAFSLE
SLE
SLEUGA
UGA
UGAMOZ
MOZ
MOZCAF
CAF
CAFMWI
MWI
MWIAFG
AFG
AFGKEN
KEN
KENRWA
RWA
RWACMR
CMR
CMRTZA
TZA
TZABDI
BDI
BDIMLI
MLI
MLICOG
COG
COGCOD
COD
CODNAM
NAM
NAMNER
NER
NERPNG
PNG
PNGCIV
CIV
CIVRUS
RUS
RUSGHA
GHA
GHASEN
SEN
SENGMB
GMB
GMBGAB
GAB
GABSDN
SDN
SDNKHM
KHM
KHMMRT
MRT
MRTKAZ
KAZ
KAZHTI
HTI
HTIUKR
UKR
UKRMNG
MNG
MNGYEM
YEM
YEMLBR
LBR
LBRTHA
THA
THATGO
TGO
TGOGUY
GUY
GUYIND
IND
INDLAO
LAO
LAOROM
ROM
ROMBOL
BOL
BOLBGD
BGD
BGDLTU
LTU
LTUSLV
SLV
SLVNPL
NPL
NPLBEN
BEN
BENLVA
LVA
LVAKGZ
KGZ
KGZFJI
FJI
FJITTO
TTO
TTOGTM
GTM
GTMEST
EST
ESTBRA
BRA
BRAHUN
HUN
HUNJAM
JAM
JAMDOR
DOR
DORNIC
NIC
NICMUS
MUS
MUSPAK
PAK
PAKIDN
IDN
IDNBGR
BGR
BGRPRY
PRY
PRYCOL
COL
COLTON
TON
TONHND
HND
HNDMDV
MDV
MDVIRQ
IRQ
IRQJOR
JOR
JORROU
ROU
ROULKA
LKA
LKAPOL
POL
POLEGY
EGY
EGYVEN
VEN
VENPER
PER
PERPHL
PHL
PHLSVK
SVK
SVKIRN
IRN
IRNECU
ECU
ECUMAR
MAR
MARLBY
LBY
LBYMYS
MYS
MYSARM
ARM
ARMCHN
CHN
CHNARG
ARG
ARGSAU
SAU
SAUTUR
TUR
TURQAT
QAT
QATVNM
VNM
VNMDZA
DZA
DZABLZ
BLZ
BLZMEX
MEX
MEXCZE
CZE
CZEUSA
USA
USAHRV
HRV
HRVSYR
SYR
SYRPAN
PAN
PANURY
URY
URYTUN
TUN
TUNSVN
SVN
SVNFIN
FIN
FINPRT
PRT
PRTCHL
CHL
CHLCUB
CUB
CUBBHR
BHR
BHRFRA
FRA
FRABRB
BRB
BRBCRI
CRI
CRIDNK
DNK
DNKBEL
BEL
BELKOR
KOR
KORDEU
DEU
DEUAUT
AUT
AUTLUX
LUX
LUXBRN
BRN
BRNALB
ALB
ALBGBR
GBR
GBRESP
ESP
ESPARE
ARE
ARECAN
CAN
CANNZL
NZL
NZLKWT
KWT
KWTIRL
IRL
IRLNLD
NLD
NLDNOR
NOR
NORISR
ISR
ISRGRC
GRC
GRCJPN
JPN
JPNSGP
SGP
SGPAUS
AUS
AUSSWE
SWE
SWECHE
CHE
CHEITA
ITA
ITAMAC
MAC
MACMLT
MLT
MLTCYP
CYP
CYPISL
ISL
ISLHKG
HKG
HKG0
0
0.1
.1
.1.2
.2
.2.3
.3
.3share-weighted log health capital
shar
e-w
eigh
ted
log
heal
th c
apita
l
share-weighted log health capital6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 141 countries back
92 / 77
αk + (1− α)l vs y
ZWE
ZWE
ZWELSO
LSO
LSOSWZ
SWZ
SWZZMB
ZMB
ZMBBWA
BWA
BWAZAF
ZAF
ZAFSLE
SLE
SLEUGA
UGA
UGAMOZ
MOZ
MOZCAF
CAF
CAFMWI
MWI
MWIAFG
AFG
AFGKEN
KEN
KENRWA
RWA
RWACMR
CMR
CMRTZA
TZA
TZABDI
BDI
BDIMLI
MLI
MLICOG
COG
COGCOD
COD
CODNAM
NAM
NAMNER
NER
NERPNG
PNG
PNGCIV
CIV
CIVRUS
RUS
RUSGHA
GHA
GHASEN
SEN
SENGMB
GMB
GMBGAB
GAB
GABSDN
SDN
SDNKHM
KHM
KHMMRT
MRT
MRTKAZ
KAZ
KAZHTI
HTI
HTIUKR
UKR
UKRMNG
MNG
MNGYEM
YEM
YEMLBR
LBR
LBRTHA
THA
THATGO
TGO
TGOGUY
GUY
GUYIND
IND
INDLAO
LAO
LAOROM
ROM
ROMBOL
BOL
BOLBGD
BGD
BGDLTU
LTU
LTUSLV
SLV
SLVNPL
NPL
NPLBEN
BEN
BENLVA
LVA
LVAKGZ
KGZ
KGZFJI
FJI
FJITTO
TTO
TTOGTM
GTM
GTMEST
EST
ESTBRA
BRA
BRAHUN
HUN
HUNJAM
JAM
JAMDOR
DOR
DORNIC
NIC
NICMUS
MUS
MUSPAK
PAK
PAKIDN
IDN
IDNBGR
BGR
BGRPRY
PRY
PRYCOL
COL
COLTON
TON
TONHND
HND
HNDMDV
MDV
MDVIRQ
IRQ
IRQJOR
JOR
JORROU
ROU
ROULKA
LKA
LKAPOL
POL
POLEGY
EGY
EGYVEN
VEN
VENPER
PER
PERPHL
PHL
PHLSVK
SVK
SVKIRN
IRN
IRNECU
ECU
ECUMAR
MAR
MARLBY
LBY
LBYMYS
MYS
MYSARM
ARM
ARMCHN
CHN
CHNARG
ARG
ARGSAU
SAU
SAUTUR
TUR
TURQAT
QAT
QATVNM
VNM
VNMDZA
DZA
DZABLZ
BLZ
BLZMEX
MEX
MEXCZE
CZE
CZEUSA
USA
USAHRV
HRV
HRVSYR
SYR
SYRPAN
PAN
PANURY
URY
URYTUN
TUN
TUNSVN
SVN
SVNFIN
FIN
FINPRT
PRT
PRTCHL
CHL
CHLCUB
CUB
CUBBHR
BHR
BHRFRA
FRA
FRABRB
BRB
BRBCRI
CRI
CRIDNK
DNK
DNKBEL
BEL
BELKOR
KOR
KORDEU
DEU
DEUAUT
AUT
AUTLUX
LUX
LUXBRN
BRN
BRNALB
ALB
ALBGBR
GBR
GBRESP
ESP
ESPARE
ARE
ARECAN
CAN
CANNZL
NZL
NZLKWT
KWT
KWTIRL
IRL
IRLNLD
NLD
NLDNOR
NOR
NORISR
ISR
ISRGRC
GRC
GRCJPN
JPN
JPNSGP
SGP
SGPAUS
AUS
AUSSWE
SWE
SWECHE
CHE
CHEITA
ITA
ITAMAC
MAC
MACMLT
MLT
MLTCYP
CYP
CYPISL
ISL
ISLHKG
HKG
HKG2
2
23
3
34
4
45
5
56
6
6log Cobb-Douglas aggregate of K and HJ-W L
log
Cobb
-Dou
glas
agg
rega
te o
f K a
nd H
J-W
L
log Cobb-Douglas aggregate of K and HJ-W L6
6
68
8
810
10
1012
12
12log output per worker
log output per worker
log output per worker
year 2005, 141 countries
back
93 / 77