CREI Lectures 2010 Differences in Technology Across Space and Time

CREI Lectures 2010 Differences in Technology Across Space and Time Francesco Caselli Barcelona, June 16-18 1 / 77

General Introduction 2 / 77

Adam Smith would be surprised 3 / 77

Adam Smith would be surprised Economists still asking the same fundamental question 240 years later 3 / 77

Adam Smith would be surprised Economists still asking the same fundamental question 240 years later Set of potential answers expanding rather than contracting 3 / 77

Adam Smith would be surprised Economists still asking the same fundamental question 240 years later Set of potential answers expanding rather than contracting Meanwhile, differences in the wealth of nations have increased by one order of magnitude (from 3 to 30) 3 / 77

So what s new? 4 / 77

So what s new? Data International Comparison Program, Penn World Tables, World Development 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 had the same factor endowments? i.e. is the production function (roughly) the same across countries? 6 / 77

Production-Function Questions (1) Would poor countries be as rich as rich countries if they had the same factor endowments? i.e. is the production function (roughly) the same across countries? Lecture 1 6 / 77

Production-Function Questions (2) If production functions differ across countries, how do they differ? And why? 7 / 77

Production-Function Questions (2) If production functions differ across countries, how do they differ? And why? Lecture 2 7 / 77

Production-Function Questions (3) Some factors of production are potentially mobile across countries Given each country s production function, are factors of production allocated efficiently by the world? If not, why not? 8 / 77

Production-Function Questions (3) Some factors of production are potentially mobile across countries Given each country s production function, are factors of production allocated efficiently by the world? If not, why not? Lecture 3 8 / 77

Technology Differences Differences in the (parameters of) the aggregate production function Hence, very broadly construed 9 / 77

Nature of the Lectures Rather than "... a high level summary..."... a series of updates and extensions New 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-country capital flows) Dan Wilson (capital heterogeneity) Superb RA on these lectures Jacopo Ponticelli 11 / 77

Lecture 1 Accounting for Cross-country Income Differences: Updates and Extensions Barcelona, June 16 12 / 77

Development Accounting Can differences in observed stocks of physical and human capital account for differences in incomes? Or: Is the magnitude of income differences roughly similar to the magnitude of differences that would be predicted by just looking at differences in observed stocks of capital? 13 / 77

The Production-Function Approach Per-capita income: Y c = F (K c, L c, efficiency c ) Hold efficiency constant: efficiency c = efficiency Compute: Compare with: V [log(f (K c, L c, efficiency))] V [log(y c )] 14 / 77

What is at stake If capital stocks can account for income differences, then the problem 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 of resources - a tougher nut to crack for both economists and policy makers 15 / 77

What is at stake (cont.) Under-accumulation hypothesis: working assumption of most economists and policy institutions until the 1990s. Still hugely influential today (e.g. all the emphasis on foreign aid) Causes of (recent) skepticism: Policy: persistent failure of policies predicated on it Theory: endogenous growth Data: Penn World Tables and development accounting 16 / 77

A short history of DA Denison (1967); Christensen, Cummings, and Jorgenson (1981). Nine rich countries. King and Levine (1994). PWT; only physical reproducible capital. Klenow and Rodriguez-Clare (1997); Hall and Jones (1999). PWT + Barro and Lee; Physical reproducible capital and schooling; Basic current conceptual framework. Others: extensions. 17 / 77

The (abandoned) econometric alternative Mankiw, Romer, and Weil (1992). In a OLS regression the accumulation hypothesis is hugely successful. Islam (1995); Caselli, Esquivel, and Lefort (1996). In a panel regression, it is not. 18 / 77

Income per worker: a first look 0.2 46.5 010 20 30 40 min 10th 50th 90th perc. max 50 46.5 10 30 20 40 0.2 0 min 10th perc. 50th perc. 90th perc. max source: PWT 6.3, year 2005 19 / 77

Income per worker: a first look 0.0 0.0 0.0 10.0 10.0 10.0 1 1 1 20.0 20.0 20.0 1980 1980 1980 1985 1985 1985 1990 1990 1990 1995 1995 1995 2000 2000 2000 2005 2005 2005 year year year 90th 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 inputs 5 Imperfect substitution between high/low education groups 6 Natural capital 7 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 Hence Y c = A c K α c 23 / 77

Technology differences: caveat Multiplicative technology terms allowed to vary; Elasticities held 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: K c,t+1 = I c,t + (1 δ)k c,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 COD BDI BDI BDI CHE CHE CHE SVN SVN SVN LKA LKA LKA SVK SVK SVK HKG HKG HKG THA THA THA KHM KHM KHM SGP SGP SGP VNM VNM VNM BHR BHR BHR MAR MAR MAR ARG ARG ARG EGY EGY EGY GMB GMB GMB MOZ MOZ MOZ IRL IRL IRL KEN KEN KEN ROU ROU ROU JAM JAM JAM IRN IRN IRN MUS MUS MUS HRV HRV HRV AFG AFG AFG ZMB ZMB ZMB USA USA USA JPN JPN JPN URY URY URY CRI CRI CRI MEX MEX MEX LVA LVA LVA ZAF ZAF ZAF UKR UKR UKR TON TON TON ALB ALB ALB ZWE ZWE ZWE PHL PHL PHL PRT PRT PRT ECU ECU ECU FRA FRA FRA SWE SWE SWE LBY LBY LBY PNG PNG PNG BRB BRB BRB CMR CMR CMR PAN PAN PAN ARM ARM ARM LSO LSO LSO BGD BGD BGD FIN FIN FIN SLV SLV SLV TZA TZA TZA NIC NIC NIC NPL NPL NPL MRT MRT MRT ARE ARE ARE PRY PRY PRY YEM YEM YEM BRN BRN BRN POL POL POL TTO TTO TTO VEN VEN VEN BGR BGR BGR PER PER PER DOR DOR DOR KOR KOR KOR EST EST EST BEL BEL BEL CYP CYP CYP NLD NLD NLD PAK PAK PAK GBR GBR GBR CAF CAF CAF DNK DNK DNK BOL BOL BOL SAU SAU SAU NZL NZL NZL IDN IDN IDN GAB GAB GAB TWN TWN TWN UGA UGA UGA CHN CHN CHN ISR ISR ISR RUS RUS RUS KAZ KAZ KAZ COL COL COL BLZ BLZ BLZ AUS AUS AUS TUR TUR TUR KWT KWT KWT MLI MLI MLI MYS MYS MYS SDN SDN SDN MWI MWI MWI MAC MAC MAC MLT MLT MLT GRC GRC GRC LTU LTU LTU IND IND IND GTM GTM GTM DEU DEU DEU ROM ROM ROM FJI FJI FJI ESP ESP ESP AUT AUT AUT CZE CZE CZE TUN TUN TUN CAN CAN CAN NAM NAM NAM HTI HTI HTI BEN BEN BEN NOR NOR NOR BRA BRA BRA MNG MNG MNG SLE SLE SLE KGZ KGZ KGZ LAO LAO LAO LUX LUX LUX BWA BWA BWA COG COG COG HUN HUN HUN CIV CIV CIV RWA RWA RWA JOR JOR JOR DZA DZA DZA IRQ IRQ IRQ CHL CHL CHL CUB CUB CUB SWZ SWZ SWZ NER NER NER ISL ISL ISL LBR LBR LBR HND HND HND MDV MDV MDV QAT QAT QAT SYR SYR SYR ITA ITA ITA TGO TGO TGO GUY GUY GUY SEN SEN SEN GHA GHA GHA 6 6 68 8 810 10 10 12 12 12 14 14 14 log capital per worker log capital per worker log capital per worker 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 142 countries appendix 26 / 77

Back to King and Levine Recall: Y c = A c K α c Calibration: since α assumed constant across countries, use US value of 0.33 27 / 77

Measuring success K accounts well for Y if is close to 1 V [log(kc α )] V [log(y c )] = V [αk c] V [y c ] 28 / 77

Measuring success K accounts well for Y if is close to 1 Alternative measure V [log(kc α )] V [log(y c )] = V [αk c] V [y c ] (K 90 /K 10 ) α Y 90 /Y 10 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 schooling increases earnings (and hence human capital) by about 10% If workers in country A have on average one year of schooling more than in country B, country A has 10% more human capital 30 / 77

Formalizing schooling capital Production function per worker still CD Y c = A c K α c L 1 α c But labour aggregate depends on schooling attainment L c = J e βss j L j,c j=1 where: L j,c is proportion of labour force in group j (in c) S j 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 education 2 Some primary 3 Primary completed 4 Some secondary 5 Secondary completed 6 Some college 7 College completed and more 32 / 77

Calibrating β s Given J Y c = A c Kc α e βss j L j,c and perfect labour markets, j=1 1 α log W j,c = α c + β s S j So β s is the Mincerian coefficient Note: perfect markets only needed in country supplying Mincerian coefficient 33 / 77

Two small differences with HJ 34 / 77

Two small differences with HJ Jensen inequality J e βss j L j,c v. P J e βs j=1 S j L j,c j=1 34 / 77

Two small differences with HJ Jensen inequality J e βss j L j,c v. P J e βs j=1 S j L j,c j=1 In HJ β varies with average schooling years 34 / 77

Two small differences with HJ Jensen inequality J e βss j L j,c v. P J e βs j=1 S j L j,c j=1 In HJ β varies with average schooling years Neither of these differences has any impact whatsoever 34 / 77

l vs y COD COD COD BDI BDI BDI CHE CHE CHE SVN SVN SVN LKA LKA LKA SVK SVK SVK HKG HKG HKG THA THA THA KHM KHM KHM SGP SGP SGP VNM VNM VNM BHR BHR BHR MAR MAR MAR ARG ARG ARG EGY EGY EGY GMB GMB GMB MOZ MOZ MOZ IRL IRL IRL KEN KEN KEN ROU ROU ROU JAM JAM JAM IRN IRN IRN MUS MUS MUS HRV HRV HRV AFG AFG AFG ZMB ZMB ZMB USA USA USA JPN JPN JPN URY URY URY CRI CRI CRI MEX MEX MEX LVA LVA LVA ZAF ZAF ZAF UKR UKR UKR TON TON TON ALB ALB ALB ZWE ZWE ZWE PHL PHL PHL PRT PRT PRT ECU ECU ECU FRA FRA FRA SWE SWE SWE LBY LBY LBY PNG PNG PNG BRB BRB BRB CMR CMR CMR PAN PAN PAN ARM ARM ARM LSO LSO LSO BGD BGD BGD FIN FIN FIN SLV SLV SLV TZA TZA TZA NIC NIC NIC NPL NPL NPL MRT MRT MRT ARE ARE ARE PRY PRY PRY YEM YEM YEM BRN BRN BRN POL POL POL TTO TTO TTO VEN VEN VEN BGR BGR BGR PER PER PER DOR DOR DOR KOR KOR KOR EST EST EST BEL BEL BEL CYP CYP CYP NLD NLD NLD PAK PAK PAK GBR GBR GBR CAF CAF CAF DNK DNK DNK BOL BOL BOL SAU SAU SAU NZL NZL NZL IDN IDN IDN GAB GAB GAB UGA UGA UGA CHN CHN CHN ISR ISR ISR RUS RUS RUS KAZ KAZ KAZ COL COL COL BLZ BLZ BLZ AUS AUS AUS TUR TUR TUR KWT KWT KWT MLI MLI MLI MYS MYS MYS SDN SDN SDN MWI MWI MWI MAC MAC MAC MLT MLT MLT GRC GRC GRC LTU LTU LTU IND IND IND GTM GTM GTM DEU DEU DEU ROM ROM ROM FJI FJI FJI ESP ESP ESP AUT AUT AUT CZE CZE CZE TUN TUN TUN CAN CAN CAN NAM NAM NAM HTI HTI HTI BEN BEN BEN NOR NOR NOR BRA BRA BRA MNG MNG MNG SLE SLE SLE KGZ KGZ KGZ LAO LAO LAO LUX LUX LUX BWA BWA BWA COG COG COG HUN HUN HUN CIV CIV CIV RWA RWA RWA JOR JOR JOR DZA DZA DZA IRQ IRQ IRQ CHL CHL CHL CUB CUB CUB SWZ SWZ SWZ NER NER NER ISL ISL ISL LBR LBR LBR HND HND HND MDV MDV MDV QAT QAT QAT SYR SYR SYR ITA ITA ITA TGO TGO TGO GUY GUY GUY SEN SEN SEN GHA GHA GHA 0 0 0.5.5.51 1 1.5 1.5 1.5 log of HJ schooling capital log of HJ schooling capital log of HJ schooling capital 6 6 68 8 810 10 10 12 12 12 log 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 0.20 Hall-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 on reaching 15 37 / 77

Implementing Health Capital In principle L c = J e β HH j +β ss j L j,c j=1 Where groups are now schooling-health groups, H j is the health indicator for group j, and β H maps health status in human capital In practice L c = e β H H c J e βss j L j,c j=1 38 / 77

Calibrating β H Time series evidence mapping survival rate into height Micro-evidence mapping height into wage Get β H 0.65 Translation: if Mincerian return is 0.10, 1 extra year of schooling is equivalent to the extra health capital associated with 15 percentage points of adult survival rate 39 / 77

Survival Rate vs y ZWE ZWE ZWE LSO LSO LSO SWZ SWZ SWZ ZMB ZMB ZMB BWA BWA BWA ZAF ZAF ZAF SLE SLE SLE UGA UGA UGA MOZ MOZ MOZ CAF CAF CAF MWI MWI MWI AFG AFG AFG KEN KEN KEN RWA RWA RWA CMR CMR CMR TZA TZA TZA BDI BDI BDI MLI MLI MLI COG COG COG COD COD COD NAM NAM NAM NER NER NER PNG PNG PNG CIV CIV CIV RUS RUS RUS GHA GHA GHA SEN SEN SEN GMB GMB GMB GAB GAB GAB SDN SDN SDN KHM KHM KHM MRT MRT MRT KAZ KAZ KAZ HTI HTI HTI UKR UKR UKR MNG MNG MNG YEM YEM YEM LBR LBR LBR THA THA THA TGO TGO TGO GUY GUY GUY IND IND IND LAO LAO LAO ROM ROM ROM BOL BOL BOL BGD BGD BGD LTU LTU LTU SLV SLV SLV NPL NPL NPL BEN BEN BEN LVA LVA LVA KGZ KGZ KGZ FJI FJI FJI TTO TTO TTO GTM GTM GTM EST EST EST BRA BRA BRA HUN HUN HUN JAM JAM JAM DOR DOR DOR NIC NIC NIC MUS MUS MUS PAK PAK PAK IDN IDN IDN BGR BGR BGR PRY PRY PRY COL COL COL TON TON TON HND HND HND MDV MDV MDV IRQ IRQ IRQ JOR JOR JOR ROU ROU ROU LKA LKA LKA POL POL POL EGY EGY EGY VEN VEN VEN PER PER PER PHL PHL PHL SVK SVK SVK IRN IRN IRN ECU ECU ECU MAR MAR MAR LBY LBY LBY MYS MYS MYS ARM ARM ARM CHN CHN CHN ARG ARG ARG SAU SAU SAU TUR TUR TUR QAT QAT QAT VNM VNM VNM DZA DZA DZA BLZ BLZ BLZ MEX MEX MEX CZE CZE CZE USA USA USA HRV HRV HRV SYR SYR SYR PAN PAN PAN URY URY URY TUN TUN TUN SVN SVN SVN FIN FIN FIN PRT PRT PRT CHL CHL CHL CUB CUB CUB BHR BHR BHR FRA FRA FRA BRB BRB BRB CRI CRI CRI DNK DNK DNK BEL BEL BEL KOR KOR KOR DEU DEU DEU AUT AUT AUT LUX LUX LUX BRN BRN BRN ALB ALB ALB GBR GBR GBR ESP ESP ESP ARE ARE ARE CAN CAN CAN NZL NZL NZL KWT KWT KWT IRL IRL IRL NLD NLD NLD NOR NOR NOR ISR ISR ISR GRC GRC GRC JPN JPN JPN SGP SGP SGP AUS AUS AUS SWE SWE SWE CHE CHE CHE ITA ITA ITA MAC MAC MAC MLT MLT MLT CYP CYP CYP ISL ISL ISL HKG HKG HKG.2.2.2.4.4.4.6.6.6.8.8.81 1 1survival rate of adult population 15-60 survival rate of adult population 15-60 survival rate of adult population 15-60 6 6 68 8 810 10 10 12 12 12 log 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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 41 / 77

Quality of Schooling/Parenting Hanushek and Woessman: big cross-country differences in standardized test scores, at given age Possible sign of differences in schooling quality (though micro evidence is weak) Also possible sign of differences in parental inputs (confirmed by micro evidence) 42 / 77

Test Scores in DA Use test scores as summary indicators of school quality/parental background L c = e β T T c e β H H c J e βss j L j,c j=1 β T is coefficient on test score in log-wage regression 43 / 77

Test Scores Data: The Details TIMSS math and science, PIRLS reading, PISA math and science, PISA reading Age: 8th grade Different dates and different sets of countries between 1995 and 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 β T : The Details Lazear (2003), National Education Longitudinal Survey: log(w i ) = α + β T T i + ε i, Where wages are observed in late 20s and school test is very similar to international ones Finds β T = 0.01 Given observed range in data, this is small 45 / 77

Test Scores vs y ZAF ZAF ZAF GHA GHA GHA KGZ KGZ KGZ PER PER PER QAT QAT QAT MAR MAR MAR KWT KWT KWT PHL PHL PHL BWA BWA BWA SLV SLV SLV ALB ALB ALB SAU SAU SAU BRA BRA BRA COL COL COL TUN TUN TUN ARG ARG ARG IDN IDN IDN DZA DZA DZA EGY EGY EGY MEX MEX MEX JOR JOR JOR CHL CHL CHL SYR SYR SYR URY URY URY BHR BHR BHR IRN IRN IRN TTO TTO TTO TUR TUR TUR THA THA THA ROU ROU ROU ISR ISR ISR CYP CYP CYP PRT PRT PRT BGR BGR BGR GRC GRC GRC MLT MLT MLT UKR UKR UKR HRV HRV HRV ARM ARM ARM LVA LVA LVA ROM ROM ROM ESP ESP ESP LUX LUX LUX NOR NOR NOR MYS MYS MYS ITA ITA ITA LTU LTU LTU POL POL POL ISL ISL ISL RUS RUS RUS SVK SVK SVK CZE CZE CZE DNK DNK DNK FRA FRA FRA CHE CHE CHE MAC MAC MAC USA USA USA DEU DEU DEU SVN SVN SVN GBR GBR GBR IRL IRL IRL BEL BEL BEL HUN HUN HUN EST EST EST AUT AUT AUT SWE SWE SWE NZL NZL NZL AUS AUS AUS CAN CAN CAN JPN JPN JPN NLD NLD NLD FIN FIN FIN KOR KOR KOR HKG HKG HKG SGP SGP SGP 30 30 30 40 40 40 50 50 50 60 60 60 test score test score test score 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker test scores year 1995-2007, output year 2005, 75 countries 46 / 77

β T TS vs y 1.1 1.2 1.3 1.4 test score human capital 68 810 12 log output per worker 1.4 ZAF GHA KGZ PER QAT MAR KWT PHL BWA SLV ALB SAU BRA COL TUN ARG IDN DZA EGY MEX JOR CHL SYR URY BHR IRN TTO TUR THA ROU ISR CYP PRT BGR GRC MLT UKR HRV ARM LVA ROM ESP LUX NOR MYS ITA LTU POL ISL RUS SVK CZE DNK FRA CHE MAC USA DEU SVN GBR IRL BEL HUN EST AUT SWE NZL AUS CAN JPN NLD FIN KOR HKG SGP SGP log test score human capital 1 1.1 1.2 1.3 GHA KOR HKG FIN JPN CAN NLD NZL ESTHUN SWE AUS AUT SVNDEU GBRBEL IRL RUS SVKCZE DNK CHE FRA MAC USA POL LTUMYS ISL ESP ITA NOR ROM ARM LVA HRV UKR BGR PRTMLT GRC CYPISR THAROU TUR TTO SYR URY IRN BHR JOR CHL EGY MEX IDN DZA COL TUN ARG BRA PHL ALB SLV BWA SAU KWT MAR QAT PER KGZ ZAF LUX 6 8 10 log output per worker 12 test scores year 1995-2007, output year 2005, 75 countries 47 / 77

(1 α)β T TS vs y.65.75.85.9 share-weighted log of test score human capital 68 810 12 log output per worker.9 ZAF GHA KGZ PER QAT MAR KWT PHL BWA SLV ALB SAU BRA COL TUN ARG IDN DZA EGY MEX JOR CHL SYR URY BHR IRN TTO TUR THA ROU ISR CYP PRT BGR GRC MLT UKR HRV ARM LVA ROM ESP LUX NOR MYS ITA LTU POL ISL RUS SVK CZE DNK FRA CHE MAC USA DEU SVN GBR IRL BEL HUN EST AUT SWE NZL AUS CAN JPN NLD FIN KOR HKG SGP share-weighted log of test score human capital.65.7.75.8.85 GHA SGP KOR HKG FIN JPN CAN NLD NZL ESTHUN SWE AUS AUT SVNDEU GBRBEL IRL RUS SVKCZE DNK CHE FRA MAC USA POL LTUMYS ISL ITA ESP NOR ROM ARM LVA HRV UKR BGR PRTMLT GRC CYPISR ROU THA TUR TTO SYR URY IRN BHR JOR CHL EGY MEX IDN DZA COL TUN ARG BRA PHL ALB SLV BWA SAU KWT MAR QAT PER KGZ ZAF LUX 6 8 10 log output per worker 12 test scores year 1995-2007, output year 2005, 75 countries 48 / 77

αk + (1 α)l vs y 4.5 6log Cobb-Douglas aggregate of K and HJ-W-Test L 68 810 12 output per worker log Cobb-Douglas aggregate of K and HJ-W-Test L 4 4.5 5 6 GHA NOR JPN AUS CHEIRL USA DEU ISL BEL KOR UKR NZL CAN NLD SWE FIN ITA ISR ESP FRA AUT HKG ESTCZE GRC DNKSGP GBR ROM CYP MLT SVKHUN SVN PRT MYS CHL MAC QAT POL TTOBHR ROU HRV MEX LVA LTU IRNARG SAU KWT DZABGRURY ALB TUR RUS THA JOR TUN PER PHL ARM SLV BWA COL BRA MAR EGY ZAF IDN KGZ SYR LUX ZAF GHA KGZ PER QAT MAR KWT PHL BWA SLV ALB SAU BRA COL TUN ARG IDN DZA EGY MEX JOR CHL SYR URY BHR IRN TTO TUR THA ROU ISR CYP PRT BGR GRC MLT UKR HRV ARM LVA ROM ESP LUX NOR MYS ITA LTU POL ISL RUS SVK CZE DNK FRA CHE MAC USA DEU SVN GBR IRL BEL HUN EST AUT SWE NZL AUS CAN JPN NLD FIN KOR HKG SGP 6 8 10 log output per worker 12 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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 Test sample 75 0.11 0.017 0.18 0.53 0.34 Test 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 changes in relative quantities of workers with different educational attainment Inconsistent with Hall-Jones schooling capital measure 51 / 77

Modelling Imperfect Substitution Replace With z 1 e β j L j,c j=1 J e βss j L j,c j=1 ρ ρ J + B e β j L j,c Where: z is lowest schooling group in high-education labour force (e.g. secondary school completed) j=z β 1 = β z = 1; other β j s are relative productivities 1/(1 ρ) is the elasticity of substitution 1/ρ 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: β j Functional form z 1 e β j L j,c j=1 ρ ρ J + B e β j L j,c j=z Suggests running two separate log-wage regressions log(w j, j < z) = α + β j log(w j, j z) = α + β j (Aside: Mincerian approach fundamentally inconsistent with imperfect substitution, more on this tomorrow) 1/ρ 54 / 77

Estimating the β j s Take CPS, 1991 Only white males Create 7 dummy variables, corresponding to 7 Barro-Lee schooling 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 0 Some Primary 0.32 Some College 0.14 Completed Primary 0.38 College and More 0.46 Some Secondary 0.56 56 / 77

Calibration with Imperfect Substitution: B From z 1 e β j L j,c j=1 j=z ρ ρ J + B e β j L j,c 1/ρ ( J ) ρ 1 ( J ) ρ 1 W z,c j=z eβ j L j,c e βz = B ( W 1,c z 1 ) ρ 1 e j=1 eβ j L β = B j=z eβ j L j,c ( 1 z 1 ) ρ 1 j,c j=1 eβ j L j,c Can retrieve B if for one country observe both relative wage and relative supply. US: Relative supply (from before) = 3 Relative wage (from a CPS log-wage regression) = 2.29 Then B = 4.76 57 / 77

l with imp. sub. vs y ZAF ZAF ZAF GHA GHA GHA KGZ KGZ KGZ PER PER PER QAT QAT QAT MAR MAR MAR KWT KWT KWT PHL PHL PHL BWA BWA BWA SLV SLV SLV ALB ALB ALB SAU SAU SAU BRA BRA BRA COL COL COL TUN TUN TUN ARG ARG ARG IDN IDN IDN DZA DZA DZA EGY EGY EGY MEX MEX MEX JOR JOR JOR CHL CHL CHL SYR SYR SYR URY URY URY BHR BHR BHR IRN IRN IRN TTO TTO TTO TUR TUR TUR THA THA THA ROU ROU ROU ISR ISR ISR CYP CYP CYP PRT PRT PRT BGR BGR BGR GRC GRC GRC MLT MLT MLT UKR UKR UKR HRV HRV HRV ARM ARM ARM LVA LVA LVA ROM ROM ROM ESP ESP ESP LUX LUX LUX NOR NOR NOR MYS MYS MYS ITA ITA ITA LTU LTU LTU POL POL POL ISL ISL ISL RUS RUS RUS SVK SVK SVK CZE CZE CZE DNK DNK DNK FRA FRA FRA CHE CHE CHE MAC MAC MAC USA USA USA DEU DEU DEU SVN SVN SVN GBR GBR GBR IRL IRL IRL BEL BEL BEL HUN HUN HUN EST EST EST AUT AUT AUT SWE SWE SWE NZL NZL NZL AUS AUS AUS CAN CAN CAN JPN JPN JPN NLD NLD NLD FIN FIN FIN KOR KOR KOR HKG HKG HKG SGP SGP SGP TGO TGO TGO JAM JAM JAM BEN BEN BEN ZWE ZWE ZWE FJI FJI FJI CMR CMR CMR KEN KEN KEN GTM GTM GTM BOL BOL BOL NAM NAM NAM BLZ BLZ BLZ SDN SDN SDN TZA TZA TZA MLI MLI MLI NIC NIC NIC LBR LBR LBR GAB GAB GAB SLE SLE SLE NPL NPL NPL MUS MUS MUS ECU ECU ECU NER NER NER HND HND HND CAF CAF CAF LKA LKA LKA SWZ SWZ SWZ RWA RWA RWA CRI CRI CRI KAZ KAZ KAZ CUB CUB CUB PAK PAK PAK HTI HTI HTI KHM KHM KHM GMB GMB GMB IRQ IRQ IRQ AFG AFG AFG LSO LSO LSO DOR DOR DOR PRY PRY PRY ARE ARE ARE MWI MWI MWI BDI BDI BDI VNM VNM VNM SEN SEN SEN COD COD COD BRB BRB BRB MNG MNG MNG BRN BRN BRN CIV CIV CIV MRT MRT MRT BGD BGD BGD MDV MDV MDV MOZ MOZ MOZ LAO LAO LAO TON TON TON GUY GUY GUY YEM YEM YEM PNG PNG PNG VEN VEN VEN IND IND IND COG COG COG LBY LBY LBY UGA UGA UGA CHN CHN CHN ZMB ZMB ZMB PAN PAN PAN 2.5 2.5 2.5 3 3 3.5 3.5 3.5 4 4 4.5 4.5 4.5 5 5 5log of schooling capital under imperfect substitution log of schooling capital under imperfect substitution log of schooling capital under imperfect substitution 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 142 countries 58 / 77

(1 α)l vs y ZAF ZAF ZAF GHA GHA GHA KGZ KGZ KGZ PER PER PER QAT QAT QAT MAR MAR MAR KWT KWT KWT PHL PHL PHL BWA BWA BWA SLV SLV SLV ALB ALB ALB SAU SAU SAU BRA BRA BRA COL COL COL TUN TUN TUN ARG ARG ARG IDN IDN IDN DZA DZA DZA EGY EGY EGY MEX MEX MEX JOR JOR JOR CHL CHL CHL SYR SYR SYR URY URY URY BHR BHR BHR IRN IRN IRN TTO TTO TTO TUR TUR TUR THA THA THA ROU ROU ROU ISR ISR ISR CYP CYP CYP PRT PRT PRT BGR BGR BGR GRC GRC GRC MLT MLT MLT UKR UKR UKR HRV HRV HRV ARM ARM ARM LVA LVA LVA ROM ROM ROM ESP ESP ESP LUX LUX LUX NOR NOR NOR MYS MYS MYS ITA ITA ITA LTU LTU LTU POL POL POL ISL ISL ISL RUS RUS RUS SVK SVK SVK CZE CZE CZE DNK DNK DNK FRA FRA FRA CHE CHE CHE MAC MAC MAC USA USA USA DEU DEU DEU SVN SVN SVN GBR GBR GBR IRL IRL IRL BEL BEL BEL HUN HUN HUN EST EST EST AUT AUT AUT SWE SWE SWE NZL NZL NZL AUS AUS AUS CAN CAN CAN JPN JPN JPN NLD NLD NLD FIN FIN FIN KOR KOR KOR HKG HKG HKG SGP SGP SGP TGO TGO TGO JAM JAM JAM BEN BEN BEN ZWE ZWE ZWE FJI FJI FJI CMR CMR CMR KEN KEN KEN GTM GTM GTM BOL BOL BOL NAM NAM NAM BLZ BLZ BLZ SDN SDN SDN TZA TZA TZA MLI MLI MLI NIC NIC NIC LBR LBR LBR GAB GAB GAB SLE SLE SLE NPL NPL NPL MUS MUS MUS ECU ECU ECU NER NER NER HND HND HND CAF CAF CAF LKA LKA LKA SWZ SWZ SWZ RWA RWA RWA CRI CRI CRI KAZ KAZ KAZ CUB CUB CUB PAK PAK PAK HTI HTI HTI KHM KHM KHM GMB GMB GMB IRQ IRQ IRQ AFG AFG AFG LSO LSO LSO DOR DOR DOR PRY PRY PRY ARE ARE ARE MWI MWI MWI BDI BDI BDI VNM VNM VNM SEN SEN SEN COD COD COD BRB BRB BRB MNG MNG MNG BRN BRN BRN CIV CIV CIV MRT MRT MRT BGD BGD BGD MDV MDV MDV MOZ MOZ MOZ LAO LAO LAO TON TON TON GUY GUY GUY YEM YEM YEM PNG PNG PNG VEN VEN VEN IND IND IND COG COG COG LBY LBY LBY UGA UGA UGA CHN CHN CHN ZMB ZMB ZMB PAN PAN PAN 1.5 1.5 1.5 2 2 2.5 2.5 2.5 3 3 3.5 3.5 3.5 share weighted log of schooling capital under imp. sub. share weighted log of schooling capital under imp. sub. share weighted log of schooling capital under imp. sub. 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 142 countries 59 / 77

log Cobb-Douglas aggregate of K and L under imp. sub. αk + (1 α)l vs y ZAF GHA KGZ PER QAT MAR KWT PHL BWA SLV ALB SAU BRA COL TUN ARG IDN DZA EGY MEX JOR CHL SYR URY BHR IRN TTO TUR THA ROU ISR CYP PRT BGR GRC MLT UKR HRV ARM LVA ROM ESP LUX NOR MYS ITA LTU POL ISL RUS SVK CZE DNK FRA CHE MAC USA DEU SVN GBR IRL BEL HUN EST AUT SWE NZL AUS CAN JPN NLD FIN KOR HKG SGP TGO JAM BEN ZWE FJI CMR KEN GTM BOL NAM BLZ SDN TZA MLI NIC LBR GAB SLE NPL MUS ECU NER HND CAF LKA SWZ RWA CRI KAZ CUB PAK HTI KHM GMB IRQ AFG LSO DOR PRY ARE MWI BDI VNM SEN COD BRB MNG BRN CIV MRT BGD MDV MOZ LAO TON GUY YEM PNG VEN IND COG LBY UGA CHN ZMB PAN 45 56 67 78 8log Cobb-Douglas aggregate of K and L under imp. sub. 68 810 12 output per worker 8 7 6 5 4 6 LBR year 2005, 142 countries COD BDITZA UKR JPN USA NOR KORDEU CHE AUS BEL IRL EST ISR SWE ROM CZE GRCISL FRA AUT NZL CAN NLD CYPESP FIN DNK ITA HKG SGP ARE HUN SVKCHL QAT BHR ROU JAM MYSSVN PERDZA IRN MEX PRTMLT LVA LTU BRB GBR MAC BRN FJI TON HRV PAN BGRCRI KAZ ARG LBY SAU JOR POL TTO KWT PHL ALB CHNARM ECU BWA COL TUR RUS BLZ MUS GUY IRQ THA URY BRA DORVEN MNG TUN SLV ZAF NIC BOL PRY NAM KGZ HND LKA MAR EGY GAB SWZ CUB MDV PAK IDN GTM BGD LSOVNM HTI ZWE PNG CMR GHA TGO BENNPL ZMB IND AFG LAO MRTSDN SYR CIV COG YEM KHM CAF GMB SEN MWI KEN MLI NER UGA SLE RWA MOZ 8 10 log output per worker LUX 12 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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 Test sample 75 0.11 0.017 0.18 0.53 0.34 Test correction 75 0.11 0.028 0.22 0.53 0.41 Imp. Sub. School. 141 0.26 0.150 0.72 1.30 0.55 61 / 77

With Health and Test Correction Adding health capital e β H H c z 1 e β j L j,c j=1 j=z ρ ρ J + B e β j L j,c Adding health capital and quality/parental capital e β T T t e β H H z 1 c e β j L j,c j=1 j=z ρ 1/ρ ρ J + B e β j L j,c 1/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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 Test sample 75 0.11 0.017 0.18 0.53 0.34 Test correction 75 0.11 0.028 0.22 0.53 0.41 Imp. 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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 Test sample 75 0.11 0.017 0.18 0.53 0.34 Test correction 75 0.11 0.028 0.22 0.53 0.41 Imp. 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 same 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 aggregate valued added They need to be accounted for Caselli and Feyrer: natural capital distributed more equally than reproducible capital Suggests this will dampen variability of total capital and reduce success 65 / 77

Data on Total Capital Constructed by a World Bank team, for year 2000 Natural capital: estimate value of rents (output) from a particular form of capital and then capitalize value using a fixed 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 7.0-0.13 Timber 1.7 2.6 0.8 0.9-0.34 Other forest 2.2 1.1 0.3-0.49 Cropland 11.4 1 5.1 3.2-0.73 Pasture 4.5 2.7 1.9-0.00 Protected areas 1.9 2.5 0.3 1.4 0.01 Urban land 13.1 4.6 13.5 16.5 0.70 Reproducible Capital 54.8 56.3 68.6 0.70 67 / 77

DA with Natural Capital First pass. In Y c = A c K α c L 1 α c Replace reproducible capital with total capital 68 / 77

Reproducible v Total Capital 14 68 810 12 ytotal (log) reproducible (log) 6 8 10 12 14 6 8 y 10 12 total (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 0.20 Hall-Jones 141 0.26 0.028 0.43 1.30 0.33 Weil 141 0.26 0.043 0.48 1.30 0.37 Test sample 75 0.11 0.017 0.18 0.53 0.34 Test correction 75 0.11 0.028 0.22 0.53 0.41 Imp. 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 same 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 Rep. Cap. (reduced sample) 100 0.23 0.170 0.75 1.10 0.70 Tot. Cap. 100 0.18 0.170 0.62 1.10 0.58 Rep. Cap. (reduced sample)* 56 0.11 0.071 0.32 0.53 0.61 Tot. 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 K c = (N c ) γ (M c ) 1 γ where N c is Nat. Cap. and M c 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] Ratio aggregation Linear 100 0.16 0.17 0.59 1.1 0.55 Cobb-Douglas 100 0.15 0.17 0.58 1.1 0.55 72 / 77

Next Level Up More general aggregate production function Y c = A c [K σ c + CL σ c ] 1/σ Still no consensus estimates of σ (Most estimates below 0 but range is huge and upper bound well above 0) Would it matter? Experiment with different σ s 73 / 77

Calibration Each σ implies a C. From Y c = A c [K σ c + CL σ c ] 1/σ W c = C Or ( ) 1 σ Yc L c W c L c Y c ( Yc L c ) 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(k σ + CL σ ) 1/σ ] V [log(y )] Ratio 0.5 100 0.58 1.1 0.55 1 100 0.59 1.1 0.55 1.5 100 0.58 1.1 0.55 75 / 77

Summary Only Rep. Cap. (K-L) 0.20 Schooling Cap. (H-K) + 0.13 Health Cap. (Weil) + 0.04 Test Correction + 0.07 Imp. Sub. Schooling + 0.23 Natural Capital - 0.06 Total 0.61 76 / 77

Conclusions Accumulation hypothesis comes out much better than in the past (though not a very demanding standard) Both functional forms and measurement issues important Results insensitive to substitutability between natural and reproducible 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? Y c = g π g Y g,c where: Y g,c is quantities π g is "international prices" summation taken over final expenditures back 78 / 77

Income per worker: the caveats (cont.) Key issue: whose prices? PWT: Geary-Khamis WDI: 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 0.1.2.3-6 -4-2 02 2PWT income distribution: WDI 0.1.2.3-6 -4-2 PWT 0 2 income distribution: WDI PWT 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 Program PWT (6.3): 1995 ICP Investment Variable: WDI: share of I in nominal GDP PWT: 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 of aggregate capital and aggregate labour only if all the goods are 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 K c,t = K(K 1 c,t,..., K k c,t,...) Hard, but not entirely impossible, to measure stocks of sub-types But we know nothing on function K. Direct calibration unfeasible with current knowledge. Growth-accounting approach may be feasible, but not pursued here back 85 / 77

Measuring Investment Growth-accounting approach: weight investment in sub-types by 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 COD BDI BDI BDI CHE CHE CHE SVN SVN SVN LKA LKA LKA SVK SVK SVK HKG HKG HKG THA THA THA KHM KHM KHM SGP SGP SGP VNM VNM VNM BHR BHR BHR MAR MAR MAR ARG ARG ARG EGY EGY EGY GMB GMB GMB MOZ MOZ MOZ IRL IRL IRL KEN KEN KEN ROU ROU ROU JAM JAM JAM IRN IRN IRN MUS MUS MUS HRV HRV HRV AFG AFG AFG ZMB ZMB ZMB USA USA USA JPN JPN JPN URY URY URY CRI CRI CRI MEX MEX MEX LVA LVA LVA ZAF ZAF ZAF UKR UKR UKR TON TON TON ALB ALB ALB ZWE ZWE ZWE PHL PHL PHL PRT PRT PRT ECU ECU ECU FRA FRA FRA SWE SWE SWE LBY LBY LBY PNG PNG PNG BRB BRB BRB CMR CMR CMR PAN PAN PAN ARM ARM ARM LSO LSO LSO BGD BGD BGD FIN FIN FIN SLV SLV SLV TZA TZA TZA NIC NIC NIC NPL NPL NPL MRT MRT MRT ARE ARE ARE PRY PRY PRY YEM YEM YEM BRN BRN BRN POL POL POL TTO TTO TTO VEN VEN VEN BGR BGR BGR PER PER PER DOR DOR DOR KOR KOR KOR EST EST EST BEL BEL BEL CYP CYP CYP NLD NLD NLD PAK PAK PAK GBR GBR GBR CAF CAF CAF DNK DNK DNK BOL BOL BOL SAU SAU SAU NZL NZL NZL IDN IDN IDN GAB GAB GAB TWN TWN TWN UGA UGA UGA CHN CHN CHN ISR ISR ISR RUS RUS RUS KAZ KAZ KAZ COL COL COL BLZ BLZ BLZ AUS AUS AUS TUR TUR TUR KWT KWT KWT MLI MLI MLI MYS MYS MYS SDN SDN SDN MWI MWI MWI MAC MAC MAC MLT MLT MLT GRC GRC GRC LTU LTU LTU IND IND IND GTM GTM GTM DEU DEU DEU ROM ROM ROM FJI FJI FJI ESP ESP ESP AUT AUT AUT CZE CZE CZE TUN TUN TUN CAN CAN CAN NAM NAM NAM HTI HTI HTI BEN BEN BEN NOR NOR NOR BRA BRA BRA MNG MNG MNG SLE SLE SLE KGZ KGZ KGZ LAO LAO LAO LUX LUX LUX BWA BWA BWA COG COG COG HUN HUN HUN CIV CIV CIV RWA RWA RWA JOR JOR JOR DZA DZA DZA IRQ IRQ IRQ CHL CHL CHL CUB CUB CUB SWZ SWZ SWZ NER NER NER ISL ISL ISL LBR LBR LBR HND HND HND MDV MDV MDV QAT QAT QAT SYR SYR SYR ITA ITA ITA TGO TGO TGO GUY GUY GUY SEN SEN SEN GHA GHA GHA 2 2 2.5 2.5 2.5 3 3 3.5 3.5 3.5 4 4 4.5 4.5 4.5 share-weighted log capital per worker share-weighted log capital per worker share-weighted log capital per worker 6 6 68 8 810 10 10 12 12 12 log 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 COD BDI BDI BDI CHE CHE CHE SVN SVN SVN LKA LKA LKA SVK SVK SVK HKG HKG HKG THA THA THA KHM KHM KHM SGP SGP SGP VNM VNM VNM BHR BHR BHR MAR MAR MAR ARG ARG ARG EGY EGY EGY GMB GMB GMB MOZ MOZ MOZ IRL IRL IRL KEN KEN KEN ROU ROU ROU JAM JAM JAM IRN IRN IRN MUS MUS MUS HRV HRV HRV AFG AFG AFG ZMB ZMB ZMB USA USA USA JPN JPN JPN URY URY URY CRI CRI CRI MEX MEX MEX LVA LVA LVA ZAF ZAF ZAF UKR UKR UKR TON TON TON ALB ALB ALB ZWE ZWE ZWE PHL PHL PHL PRT PRT PRT ECU ECU ECU FRA FRA FRA SWE SWE SWE LBY LBY LBY PNG PNG PNG BRB BRB BRB CMR CMR CMR PAN PAN PAN ARM ARM ARM LSO LSO LSO BGD BGD BGD FIN FIN FIN SLV SLV SLV TZA TZA TZA NIC NIC NIC NPL NPL NPL MRT MRT MRT ARE ARE ARE PRY PRY PRY YEM YEM YEM BRN BRN BRN POL POL POL TTO TTO TTO VEN VEN VEN BGR BGR BGR PER PER PER DOR DOR DOR KOR KOR KOR EST EST EST BEL BEL BEL CYP CYP CYP NLD NLD NLD PAK PAK PAK GBR GBR GBR CAF CAF CAF DNK DNK DNK BOL BOL BOL SAU SAU SAU NZL NZL NZL IDN IDN IDN GAB GAB GAB UGA UGA UGA CHN CHN CHN ISR ISR ISR RUS RUS RUS KAZ KAZ KAZ COL COL COL BLZ BLZ BLZ AUS AUS AUS TUR TUR TUR KWT KWT KWT MLI MLI MLI MYS MYS MYS SDN SDN SDN MWI MWI MWI MAC MAC MAC MLT MLT MLT GRC GRC GRC LTU LTU LTU IND IND IND GTM GTM GTM DEU DEU DEU ROM ROM ROM FJI FJI FJI ESP ESP ESP AUT AUT AUT CZE CZE CZE TUN TUN TUN CAN CAN CAN NAM NAM NAM HTI HTI HTI BEN BEN BEN NOR NOR NOR BRA BRA BRA MNG MNG MNG SLE SLE SLE KGZ KGZ KGZ LAO LAO LAO LUX LUX LUX BWA BWA BWA COG COG COG HUN HUN HUN CIV CIV CIV RWA RWA RWA JOR JOR JOR DZA DZA DZA IRQ IRQ IRQ CHL CHL CHL CUB CUB CUB SWZ SWZ SWZ NER NER NER ISL ISL ISL LBR LBR LBR HND HND HND MDV MDV MDV QAT QAT QAT SYR SYR SYR ITA ITA ITA TGO TGO TGO GUY GUY GUY SEN SEN SEN GHA GHA GHA.2.2.2.4.4.4.6.6.6.8.8.81 1 1share-weighted log of HJ schooling capital share-weighted log of HJ schooling capital share-weighted log of HJ schooling capital 6 6 68 8 810 10 10 12 12 12 log 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 COD BDI BDI BDI CHE CHE CHE SVN SVN SVN LKA LKA LKA SVK SVK SVK HKG HKG HKG THA THA THA KHM KHM KHM SGP SGP SGP VNM VNM VNM BHR BHR BHR MAR MAR MAR ARG ARG ARG EGY EGY EGY GMB GMB GMB MOZ MOZ MOZ IRL IRL IRL KEN KEN KEN ROU ROU ROU JAM JAM JAM IRN IRN IRN MUS MUS MUS HRV HRV HRV AFG AFG AFG ZMB ZMB ZMB USA USA USA JPN JPN JPN URY URY URY CRI CRI CRI MEX MEX MEX LVA LVA LVA ZAF ZAF ZAF UKR UKR UKR TON TON TON ALB ALB ALB ZWE ZWE ZWE PHL PHL PHL PRT PRT PRT ECU ECU ECU FRA FRA FRA SWE SWE SWE LBY LBY LBY PNG PNG PNG BRB BRB BRB CMR CMR CMR PAN PAN PAN ARM ARM ARM LSO LSO LSO BGD BGD BGD FIN FIN FIN SLV SLV SLV TZA TZA TZA NIC NIC NIC NPL NPL NPL MRT MRT MRT ARE ARE ARE PRY PRY PRY YEM YEM YEM BRN BRN BRN POL POL POL TTO TTO TTO VEN VEN VEN BGR BGR BGR PER PER PER DOR DOR DOR KOR KOR KOR EST EST EST BEL BEL BEL CYP CYP CYP NLD NLD NLD PAK PAK PAK GBR GBR GBR CAF CAF CAF DNK DNK DNK BOL BOL BOL SAU SAU SAU NZL NZL NZL IDN IDN IDN GAB GAB GAB UGA UGA UGA CHN CHN CHN ISR ISR ISR RUS RUS RUS KAZ KAZ KAZ COL COL COL BLZ BLZ BLZ AUS AUS AUS TUR TUR TUR KWT KWT KWT MLI MLI MLI MYS MYS MYS SDN SDN SDN MWI MWI MWI MAC MAC MAC MLT MLT MLT GRC GRC GRC LTU LTU LTU IND IND IND GTM GTM GTM DEU DEU DEU ROM ROM ROM FJI FJI FJI ESP ESP ESP AUT AUT AUT CZE CZE CZE TUN TUN TUN CAN CAN CAN NAM NAM NAM HTI HTI HTI BEN BEN BEN NOR NOR NOR BRA BRA BRA MNG MNG MNG SLE SLE SLE KGZ KGZ KGZ LAO LAO LAO LUX LUX LUX BWA BWA BWA COG COG COG HUN HUN HUN CIV CIV CIV RWA RWA RWA JOR JOR JOR DZA DZA DZA IRQ IRQ IRQ CHL CHL CHL CUB CUB CUB SWZ SWZ SWZ NER NER NER ISL ISL ISL LBR LBR LBR HND HND HND MDV MDV MDV QAT QAT QAT SYR SYR SYR ITA ITA ITA TGO TGO TGO GUY GUY GUY SEN SEN SEN GHA GHA GHA 2.5 2.5 2.5 3 3 3.5 3.5 3.5 4 4 4.5 4.5 4.5 5 5 5log of Cobb-Douglas aggregate of K and HJ L log of Cobb-Douglas aggregate of K and HJ L log of Cobb-Douglas aggregate of K and HJ L 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 142 countries back 90 / 77

β H SR vs y ZWE ZWE ZWE LSO LSO LSO SWZ SWZ SWZ ZMB ZMB ZMB BWA BWA BWA ZAF ZAF ZAF SLE SLE SLE UGA UGA UGA MOZ MOZ MOZ CAF CAF CAF MWI MWI MWI AFG AFG AFG KEN KEN KEN RWA RWA RWA CMR CMR CMR TZA TZA TZA BDI BDI BDI MLI MLI MLI COG COG COG COD COD COD NAM NAM NAM NER NER NER PNG PNG PNG CIV CIV CIV RUS RUS RUS GHA GHA GHA SEN SEN SEN GMB GMB GMB GAB GAB GAB SDN SDN SDN KHM KHM KHM MRT MRT MRT KAZ KAZ KAZ HTI HTI HTI UKR UKR UKR MNG MNG MNG YEM YEM YEM LBR LBR LBR THA THA THA TGO TGO TGO GUY GUY GUY IND IND IND LAO LAO LAO ROM ROM ROM BOL BOL BOL BGD BGD BGD LTU LTU LTU SLV SLV SLV NPL NPL NPL BEN BEN BEN LVA LVA LVA KGZ KGZ KGZ FJI FJI FJI TTO TTO TTO GTM GTM GTM EST EST EST BRA BRA BRA HUN HUN HUN JAM JAM JAM DOR DOR DOR NIC NIC NIC MUS MUS MUS PAK PAK PAK IDN IDN IDN BGR BGR BGR PRY PRY PRY COL COL COL TON TON TON HND HND HND MDV MDV MDV IRQ IRQ IRQ JOR JOR JOR ROU ROU ROU LKA LKA LKA POL POL POL EGY EGY EGY VEN VEN VEN PER PER PER PHL PHL PHL SVK SVK SVK IRN IRN IRN ECU ECU ECU MAR MAR MAR LBY LBY LBY MYS MYS MYS ARM ARM ARM CHN CHN CHN ARG ARG ARG SAU SAU SAU TUR TUR TUR QAT QAT QAT VNM VNM VNM DZA DZA DZA BLZ BLZ BLZ MEX MEX MEX CZE CZE CZE USA USA USA HRV HRV HRV SYR SYR SYR PAN PAN PAN URY URY URY TUN TUN TUN SVN SVN SVN FIN FIN FIN PRT PRT PRT CHL CHL CHL CUB CUB CUB BHR BHR BHR FRA FRA FRA BRB BRB BRB CRI CRI CRI DNK DNK DNK BEL BEL BEL KOR KOR KOR DEU DEU DEU AUT AUT AUT LUX LUX LUX BRN BRN BRN ALB ALB ALB GBR GBR GBR ESP ESP ESP ARE ARE ARE CAN CAN CAN NZL NZL NZL KWT KWT KWT IRL IRL IRL NLD NLD NLD NOR NOR NOR ISR ISR ISR GRC GRC GRC JPN JPN JPN SGP SGP SGP AUS AUS AUS SWE SWE SWE CHE CHE CHE ITA ITA ITA MAC MAC MAC MLT MLT MLT CYP CYP CYP ISL ISL ISL HKG HKG HKG 0 0 0.1.1.1.2.2.2.3.3.3.4.4.4 log health capital log health capital log health capital 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 141 countries back 91 / 77

(1 α)β H SR vs y ZWE ZWE ZWE LSO LSO LSO SWZ SWZ SWZ ZMB ZMB ZMB BWA BWA BWA ZAF ZAF ZAF SLE SLE SLE UGA UGA UGA MOZ MOZ MOZ CAF CAF CAF MWI MWI MWI AFG AFG AFG KEN KEN KEN RWA RWA RWA CMR CMR CMR TZA TZA TZA BDI BDI BDI MLI MLI MLI COG COG COG COD COD COD NAM NAM NAM NER NER NER PNG PNG PNG CIV CIV CIV RUS RUS RUS GHA GHA GHA SEN SEN SEN GMB GMB GMB GAB GAB GAB SDN SDN SDN KHM KHM KHM MRT MRT MRT KAZ KAZ KAZ HTI HTI HTI UKR UKR UKR MNG MNG MNG YEM YEM YEM LBR LBR LBR THA THA THA TGO TGO TGO GUY GUY GUY IND IND IND LAO LAO LAO ROM ROM ROM BOL BOL BOL BGD BGD BGD LTU LTU LTU SLV SLV SLV NPL NPL NPL BEN BEN BEN LVA LVA LVA KGZ KGZ KGZ FJI FJI FJI TTO TTO TTO GTM GTM GTM EST EST EST BRA BRA BRA HUN HUN HUN JAM JAM JAM DOR DOR DOR NIC NIC NIC MUS MUS MUS PAK PAK PAK IDN IDN IDN BGR BGR BGR PRY PRY PRY COL COL COL TON TON TON HND HND HND MDV MDV MDV IRQ IRQ IRQ JOR JOR JOR ROU ROU ROU LKA LKA LKA POL POL POL EGY EGY EGY VEN VEN VEN PER PER PER PHL PHL PHL SVK SVK SVK IRN IRN IRN ECU ECU ECU MAR MAR MAR LBY LBY LBY MYS MYS MYS ARM ARM ARM CHN CHN CHN ARG ARG ARG SAU SAU SAU TUR TUR TUR QAT QAT QAT VNM VNM VNM DZA DZA DZA BLZ BLZ BLZ MEX MEX MEX CZE CZE CZE USA USA USA HRV HRV HRV SYR SYR SYR PAN PAN PAN URY URY URY TUN TUN TUN SVN SVN SVN FIN FIN FIN PRT PRT PRT CHL CHL CHL CUB CUB CUB BHR BHR BHR FRA FRA FRA BRB BRB BRB CRI CRI CRI DNK DNK DNK BEL BEL BEL KOR KOR KOR DEU DEU DEU AUT AUT AUT LUX LUX LUX BRN BRN BRN ALB ALB ALB GBR GBR GBR ESP ESP ESP ARE ARE ARE CAN CAN CAN NZL NZL NZL KWT KWT KWT IRL IRL IRL NLD NLD NLD NOR NOR NOR ISR ISR ISR GRC GRC GRC JPN JPN JPN SGP SGP SGP AUS AUS AUS SWE SWE SWE CHE CHE CHE ITA ITA ITA MAC MAC MAC MLT MLT MLT CYP CYP CYP ISL ISL ISL HKG HKG HKG 0 0 0.1.1.1.2.2.2.3.3.3 share-weighted log health capital share-weighted log health capital share-weighted log health capital 6 6 68 8 810 10 10 12 12 12 log 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 ZWE LSO LSO LSO SWZ SWZ SWZ ZMB ZMB ZMB BWA BWA BWA ZAF ZAF ZAF SLE SLE SLE UGA UGA UGA MOZ MOZ MOZ CAF CAF CAF MWI MWI MWI AFG AFG AFG KEN KEN KEN RWA RWA RWA CMR CMR CMR TZA TZA TZA BDI BDI BDI MLI MLI MLI COG COG COG COD COD COD NAM NAM NAM NER NER NER PNG PNG PNG CIV CIV CIV RUS RUS RUS GHA GHA GHA SEN SEN SEN GMB GMB GMB GAB GAB GAB SDN SDN SDN KHM KHM KHM MRT MRT MRT KAZ KAZ KAZ HTI HTI HTI UKR UKR UKR MNG MNG MNG YEM YEM YEM LBR LBR LBR THA THA THA TGO TGO TGO GUY GUY GUY IND IND IND LAO LAO LAO ROM ROM ROM BOL BOL BOL BGD BGD BGD LTU LTU LTU SLV SLV SLV NPL NPL NPL BEN BEN BEN LVA LVA LVA KGZ KGZ KGZ FJI FJI FJI TTO TTO TTO GTM GTM GTM EST EST EST BRA BRA BRA HUN HUN HUN JAM JAM JAM DOR DOR DOR NIC NIC NIC MUS MUS MUS PAK PAK PAK IDN IDN IDN BGR BGR BGR PRY PRY PRY COL COL COL TON TON TON HND HND HND MDV MDV MDV IRQ IRQ IRQ JOR JOR JOR ROU ROU ROU LKA LKA LKA POL POL POL EGY EGY EGY VEN VEN VEN PER PER PER PHL PHL PHL SVK SVK SVK IRN IRN IRN ECU ECU ECU MAR MAR MAR LBY LBY LBY MYS MYS MYS ARM ARM ARM CHN CHN CHN ARG ARG ARG SAU SAU SAU TUR TUR TUR QAT QAT QAT VNM VNM VNM DZA DZA DZA BLZ BLZ BLZ MEX MEX MEX CZE CZE CZE USA USA USA HRV HRV HRV SYR SYR SYR PAN PAN PAN URY URY URY TUN TUN TUN SVN SVN SVN FIN FIN FIN PRT PRT PRT CHL CHL CHL CUB CUB CUB BHR BHR BHR FRA FRA FRA BRB BRB BRB CRI CRI CRI DNK DNK DNK BEL BEL BEL KOR KOR KOR DEU DEU DEU AUT AUT AUT LUX LUX LUX BRN BRN BRN ALB ALB ALB GBR GBR GBR ESP ESP ESP ARE ARE ARE CAN CAN CAN NZL NZL NZL KWT KWT KWT IRL IRL IRL NLD NLD NLD NOR NOR NOR ISR ISR ISR GRC GRC GRC JPN JPN JPN SGP SGP SGP AUS AUS AUS SWE SWE SWE CHE CHE CHE ITA ITA ITA MAC MAC MAC MLT MLT MLT CYP CYP CYP ISL ISL ISL HKG HKG HKG 2 2 23 3 34 4 45 5 56 6 6log Cobb-Douglas aggregate of K and HJ-W L log Cobb-Douglas aggregate of K and HJ-W L log Cobb-Douglas aggregate of K and HJ-W L 6 6 68 8 810 10 10 12 12 12 log output per worker log output per worker log output per worker year 2005, 141 countries back 93 / 77