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HUMAN CAPITAL

BY

SHEKHAR ATYAR

M.A., UNIVERSITY OF TORONTO, 1997 B.A., OXFORD UNIVERSITY, 1994

B.A.(HONS.), ST STEPHEN’S COLLEGE (UNIVERSITY OF DELHI), 1992

A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

IN THE DEPARTMENT OF ECONOMICS AT

BROWN UNIVERSITY, PROVIDENCE, RHODE ISLAND

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unauthorized copying under Title 17, United States Code

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Department of Economics as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date 3 AY c©x2/⁄2.z David N Weil, Director Recommended to the Graduate School Date se] DJ Ns — Oded Galor, Reader na 0° (or _ ý/Z=—=zÊ^

Anthony Lancaster, Reader

Approved by the Graduate School

pate //27//0/ bs 7

Peter J Estrup

Dean of the Graduate School and Research

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Shekhar Aiyar

Department of Economics Date of Birth: May, 5, 1971 Brown University Place of Birth: New Delhi, India Providence, RI 02912

Ph: (401) 421-5938

e-mail: s.aiyar@yahoo.com

EDUCATION

Brown University, Providence, Rhode Island, USA

e Ph.D Program in Economics (Degree Expected May 2001)

e Areas of specialization: Macroeconomics, Economic Growth, Econometrics e Recipient of Teaching Fellowship and Ehrlich Fellowship

University of Toronto, Toronto, Canada

e MA in Economics (July 1997)

e Recipient of Simcoe Special Fellowship and International Fellowship St Edmund Hall, Oxford University, Oxford, UK

e BA in Philosophy and Economics (PPE) (May 1994)

e Recipient of Inlaks Scholarship and St Edmund Hall Open Exhibition e Received First Class Degree

St Stephen’s College, University of Delhi, Delhi, India

« B.A (Honors) in Economics (July 1992)

e Received First Division Degree

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Essays on Total Factor Productivity and Human Capital ACADEMIC PUBLICATIONS AND MANUSCRIPTS

e “A Contribution to the Empirics of Total Factor Productivity”, with James Feyrer, Manu- script, Brown University, September 2000

e “Convergence Across the Indian States: A Panel Study”, in Callen, T et al, eds., India at the Crossroads: Sustaining Growth and Reducing Poverty, IMF, Washington, D.C., February 2001 e “Total Factor Productivity Revisited: A Dual Approach to Levels-Accounting”, with Carl- Johan Dalgaard, Manuscript, Brown University, December 2000

e “Econometric Analysis of Dynamic Models: A Growth Theory Example”, with Tony Lan- caster, in Bunzel, H et al, eds., Panel Data and Structural Labour Market Models, North Holland,

Elsevier, 2000

e “The Human Capital Constraint: Of Increasing Returns, Education Choice, and Co-

ordination Failure”, Manuscript, Brown University, August 2000 (Presented at the NEUDC Con- ference, Cornell University, October 2000)

e “Why Does Technology Sometimes Regress? A Model of Knowledge-Diffusion and Popula- tion Density”, with Carl-Johan Dalgaard, Manuscript, Brown University, April 2001

OTHER PUBLICATIONS

e “Who’s Afraid of Population Growth ?”, Op-Ed opinion piece, Times of India, September

2000

e “The Silent Revolution”, Op-Ed opinion piece, Times of India, August 2000 © Continental Drift, Volurne of Collected Poems, Writer’s Workshop, Calcutta, 1997

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e Instructor, Department of Economics, Brown University, 1999-2001 e Consultant, Oxus Investments and Research, New Delhi, Summer 2000 e Intern, International Monetary Fund, Washington, D.C., Summer 1999 © Referee: Journal of Economic Growth, European Economic Review, 1999- # Economics Don, Trinity College, University of Toronto, 1996-97

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A Ph.D thesis is both a labour of love and a miracle of compression First comes the labour of love; the endless stream of lectures, articles, internet-searches, conversa- tions and seminar presentations; the beer-soaked late-night dialogues reconciling venerable frameworks with what one fondly hopes are fresh insights Then comes the miracle of compression; the stripping away of the inessential, the concentration of four years of rela- tively free-ranging thought into a handful of short chapters that are expected to bear some linear relation to one another Often the latter exercise obliterates all traces of the former The complex influence of all the people without whom one’s dissertation would not have been started, sustained or completed is quite obscured behind the inscrutable theorems and cursory literature reviews Luckily prefaces were invented to redress the balance - to remember, to recount, and above all, to give thanks

I was extremely fortunate in my choice of advisors David Weil walked me through the maze of graduate economics with Socratic forbearance and an unerring ability to tell the escape route from the blind alley Oded Galor taught a course in growth theory so superb that it made my choice of specialization easy Tony Lancaster gave me the confidence to embark on independent research by co-authoring a paper with me in my second year, and by reminding me that Time’s Winged Charriot Hurries Near

Several professors at Brown University commented on the papers that I wrote Peter Howitt encouraged me greatly by always being available to discuss ideas old and new I received much guidance from John Driscoll, Pravin Krishna and Andrew Foster My second summer in graduate school was spent at the IMF, where Chris Towe and Patricia Reynolds, with unusual kindness, put me to work on an independent project connected with

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who taught me the practical value of triple-checking one’s data-set for inconsistencies before even thinking of running regressions

From my friends and colleagues in the department I learned more than any book has ever taught me Brown University enjoys considerable economies of scale in the large number of aspiring growth theorists that it produces; of these economies I was a grate- ful beneficiary Areendam Chanda, Kyung-Mook Lim, Len Erickson, Seiro Ito, Azam Chaudhry, Phil Garner and several others conspired to make lunch in the Blue Room a source of intellectual inspiration Jim Feyrer and Carl-Johan Dalgaard went a step further and wrote considerable bits of my dissertation for me

My thanks must also wing their way to my families, who have supported me through thick and thin, wherever in the world I have found myself and however limitless my time in school has seemed to grow Papa, Mum, Naiyya, Shahnaz, Gang: to you I owe far more than this Ph.D

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1 A Contribution to the Empirics of Total Factor Productivity 1.1 1.2 1.3 1.4 1.5 1.6 lntroductlion - Q Q Q HQ Q ee ee ee Literature RevileW_ - Q Q HQ HH HH 2020202002005 1.21 2 GrowtbEmpHics -.Ặ QẶ Q TQ HQ HS HH RE} TT

1.2.2 Technological Spillovers and Human Capital - Calculating Total Factor Productivity . -2-2-.

1.3.1 2 Methodology and Data .Ặ.-Ặ Ặ QQ SH HS HS

1.3.2 Variance Decomposition .-0 2.022 002 ee eae

The Model 2 2 0 22.202 0.0202 02220 ee eee ee ee ene

16.1 Base Results . -.- 0-2-0 pee eee ee eee

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1.7.1 FullSample - -2 .-.-.0 2-0+2+0-0 24 1.72 Mining Correction - - - 2.22202 ee eee eee 26

1.7.3 Human Capital Specifcation - QQẶ SH ST 27

1.7.4 Disaggregated Human Capital—” 28

18 Conclusion Ặ HQ Q HH SH HH ee ee ee 29

1.9 Appendix A:Data on the Share of Mining .- -. - 33 1.10 Appendix B: GMM Estimation . - -2 -.-2 - 36

1.11 References 2-2-2 ee ee ee ee ee es 38

The Human Capital Constraint: Of Increasing Returns, Education Choice

and Coordination Failure 42

2.1 Introduction - ee ee ee 42

2.1.1 Three Hypotheses anda Puzzle . -. 42

2.1.2 Outline and Literature Review .-.-0206- 43 2.2 The Two-Sector Model - -.-2. 5 2 .0 48

2.2.1 Production - 2 ee ee ee ee ee 48

2.2.2 Individuals and Education Choice .-.-2. .- 50

2.2.3 Equilibrium .- -2.2.22-2. 0 .-2-04 52

2.2.4 Minimum Scale and Co-ordination Falure - 55

2.3 The Three Sector Model .-.- 2 2-2 2 eee ee eee eee eee 57

2.3.1 Production 2.1 eee ee ee ee ee 57

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2.3.4 Equilibrium With Three Sectors . - 60

2.3.5 Discussion 2 2.2 eee ee ee ee ee eee 62

2.3.6 Equilibrium With Two Sectors - - 63

2.3.7 Co-ordination and Subsidies - - 64

2.4 Conclusion 2.22.22 2 eee ee ee Và 69

2.5 References Ặ Ặ Q 2.2.02 2 ee ee ee eee ee ee eee 72

Total Factor Productivity Revisited: A Dual Approach to Levels Ac-

counting 75

3-1 Introduction - -Ặ Q Q Q Q Q HQ HQ SH ky 75

3.2 “Theory - - - Q HQ HQ HH HH HH HH KH HH kia 79

°ˆ “6 ng ẼE ee eee eee eee 81

3.4 Results: Primal vs Dual Q QẶ Q Q HQ HS SẺ KT 84

3.5 Income Shares and The Cobb-Douglas Hypothesis 87 3.6 Total vs Multi-Factor Productivity .-20.2.02282222- 91

3.7 Concluding Remarks .2.2 0.202022 eee eee eee 95

3.8 References 2 eee ee ee ee ee 105

The Econometric Analysis of Dynamic Panel Models: A Growth Theory

Example 109

4.1 Introduction 2 2 2.2.2.2 0 022.002 eee eee 109 4.2 Model and Data .2 2 2.2 2.2 .-.-0 006- 111

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Results - QC QO QO ĐO HO Q Q Q Q nu NV ew ee 117

Concluding Remarks Ặ.ẶQẶ Q Q Q Q SẺ SẺ 120

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11 The Evolution of TEP for a Selection ofCountries 10

1.2 Variance Decomposition of Log Incomes by Year - - - 12

1.3 Regression Results- non-OECD countries 19

1.4 Variance Decomposition of Steady State Productivity 24

1.5 Results forthe FullSample .20 2.222-6+224 25 1.6 Results With and Without Adjusting for Natural Resource-Extraction 26

1.7 Results With an alternative human capital specification .- 27

1.8 Results With Disaggregated Schooling .- -.-2-+.25.- 28

3.1 Primal Vs Dual TP Ặ.Ặ QẶ Q HQ HQ HH HS Ta 97

ở.2 TEP Vs.MEP ẶOẶ TQ HQ eee eee ee ee 98

3.3 Factor Shares and Factor Returns .-2.-0-2-0-e-200- 99

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1.1 1.2 1.3 3.1 3.2 3.3 3.4 3.5 4.1 4.2 4.3 4.4 4.5 4.6

The Effect of Shocks to Human Capital on Productivity Growth Rates 31 The Effect of Shocks to Human Capital on Productivity Levels 32 The Effect of Shocks to Human Capital on Output 33

Primal Vs Dual TEP - Q Q ee ee ee ee eee 101 Calibrated Vs Cobb-Douglas (Primal) .- 102 National Accounts Vs Cobb-Douglas (Primal) 103

National Accounts Vs Cobb-Douglas (Dual) 104

Primal TFP Vs MFP .-. - eee eee eee ee ee eee 105

Rho Posterior Distribution - 2 2 2-222 2. -2 2-2 - 122 Lambda Posterior Distribution - - -2. 2-2-. . 123 Beta One Posterior Distribution .-.- - - 2 -22 - 124 Beta Two Posterior Distribution .-. 2.2 eee ee ee eee 125 Sum of the Regressor Coefficients - - -2 -0820202020 eee 126

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A Contribution to the Empirics of Total Factor Productivity With James Feyrer

1.1 Introduction

Over the last decade the literature has seen a lively debate as to whether it is differences in factor accumulation or in total factor productivity (TFP) that are mainly responsible for the observed variation in per capita incomes across countries This paper argues that the dichotomy is spurious, resting on a conflation of the proximate determinants of income variation with the ultimate determinants of the same

Two important recent contributions to the debate are Klenow and Rodriguez-Clare

(1997) and Hall and Jones (1999) They utilize microeconomic evidence on the private

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varia-This paper takes a different view about the linkages between factor accumulation and productivity We suggest that the key to understanding productivity growth in most countries is through technology spillovers from the handful of countries that perform R&D These spillovers are contingent on a domestic stock of human capital sufficient to take advantage of products and techniques developed elsewhere The spillovers are dynamic, so that increases in human capital intensity today will have an impact on productivity in all subsequent periods, not just the current one

Our model is based on three assumptions about spillovers First, for most countries the technological frontier is expanding exogenously Second, the ability of a country to take advantage of technological spillovers is a function of its stock of human capital In the long run, countries with more educated work forces will be closer to the technological frontier Third, movement to the balanced growth path of productivity is not immediate To use the language of the traditional empirical growth literature, our model is one of conditional convergence in productivity, where the long run level of productivity is determined by the

level of human capital

We find that human capital has a significant and positive effect on the long run pro- ductivity level.2 This effect is not immediate; convergence toward the long run level is at a rate of about 3% per year Increases in human capital stocks will therefore significantly

'In theory, panel growth studies should be capable of identifying these externalities if they exist In work by Knight, Loyaza and Villanueva (1993), Islam (1995) and Caselli, Esquivel and Lefort (1996), the coefficients on physical and human capital correspond to the social returns to factor accumulation These coefficients they find are typically lower than the private returns utilized in the accounting work In fact, these studies fail to find a positive and significant coefficient on human capital at all This seems to indicate that simple externalities are not a problem for the accounting framework

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This result has significant consequences for the factor accumulation versus productivity debate While the proximate cause of differences between countries appears to be produc- tivity, we find that the ultimate cause of productivity differences may be different levels of human capital In fact, we find that human capital levels can account for the vast majority of the long run differences in productivity levels

1.2 Literature Review

1.2.1 Growth Empirics

Mankiw, Romer and Weil (1992)(MRW) purported to show that the Solow model, when augmented to include human capital as a factor of production, did a reasonable job of explaining the variations in per capita real income that are observed across a large and heterogeneous sample of countries They found that factor accumulation could account for a majority of differences in income per capita under the assumption that all countries shared a common level of productivity

However, their crucial assumption that all countries enjoy identical levels of productiv- ity has been challenged by a series of panel studies such as Knight, Loyaza and Villanueva

(1993), Islam (1995) and Caselli, Esquivel and Lefort (1996)(CEL) This body of work

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These panel results suggest that an analysis of why countries differ so much in their technologies and of how differences in technology between countries have evolved is es- sential Unfortunately, panel studies of the kind carried out by Islam and CEL cannot, by their nature, show the evolution of differences in technology, since only a single fixed effect is recovered for each country Although they allow for differences in productivity across nations, they are forced to assume that each country’s relative productivity remains entirely unchanged over the sample period

With the increased focus on productivity, several recent papers have concentrated on calculating TFP for a large sample of countries at a single point in time.? TFP is calculated as a (Solow) residual from real income per capita, after accounting for the contribution of various factors of production Klenow and Rodriguez-Clare (1997) calculate TFP for a sample of countries after accounting for the contributions made by labor, physical capital and human capital They then decompose the variance of per capita income into that attributable to differences in factors of production and that attributable to differences in TFP Using a number of formulations they conclude that, in general, differences in TFP

play a greater role.*

3TFP is more or less synonymous with technology broadly defined, since both are a measure of the efficiency with which a country combines its factors of production to obtain goods and services The terms are used interchangeably in this paper

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This paper argues that differences in TFP indeed play a central role in the growth process, and that it is therefore both interesting and important to analyze how differences in TFP between countries have evolved over time There are several theoretical models in the literature concerning technological growth Grossman and Helman (1991) and Aghion and Howitt (1992) describe economies in which purposive research and development is the engine that drives technical progress

However, empirical evidence suggests that most research and development is concen-

trated in a handful of rich countries, so that these models are of limited relevance in describing the evolution of TFP in the vast majority of nations It seems more promis- ing to consider models that emphasize the ability of “follower” countries to imitate the innovations carried out in “leader” countries Various factors may be thought to influence the efficacy with which such imitation may be carried out, such as the degree to which a country is open to dealings with the rest of the world (because an open country is able to take advantage of imports from countries that do perform R&D, and also to foreign direct investment from firms at the world technological frontier), and the social, legal and geo- graphical features peculiar to that country Another crucial factor in determining the ease of imitation, which this paper concentrates on, is the stock of human capital per worker in a given country

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technologies comes from Foster and Rosenzweig (1995), Wozniak (1984) and Bartel (1987)

More recently several empirical papers, such as Benhabib and Speigel (1994), have argued that the relationship between human capital and income growth is best viewed in the context of the positive effect that human capital has on TFP, rather than its direct effect as an accumulable factor in the production function

Bils and Klenow (2000) argue that microeconomic evidence on returns to schooling

is inconsistent with the large and positive coefficients on human capital found in growth regressions by Barro (1991); this, too, suggests that human capital impacts income through

the separate channel of TFP Borensztein et al (1998) regress GDP growth rates on both foreign direct investment (FDI) and a term that interacts FDI with human capital They

find that while the coefficient on FDI by itself is negative, the coefficient on the interactive term is positive and significant, suggesting that human capital is essential to the process of technological diffusion through FDI

Our paper aims to contribute to the empirics of TFP by calculating Solow residuals for a large panel of countries over a thirty year period, and then examining the evolution of these residuals Particular attention will be paid to the issue of whether TFP is converging, and whether human capital stocks affect the steady state TFP level toward which each country is converging Our working hypothesis is that the rate of growth of a country’s TFP is a positive function of the gap between its actual TFP level at a point in time, and its potential (or steady-state) TFP level

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frontier, and a country specific fixed effect From this hypothesis we derive an empirical specification that consists of a fixed-effects dynamic panel regression, which we proceed to estimate using our panel of TFP figures To preview our results, we find that countries converge to their individual steady states at about 3% per year Human capital stocks have a positive and significant effect on each country’s steady state TFP level We further find that a large share of the variation in steady state TFP across countries is attributable to variation in human capital stocks

The next section of our paper describes the methodology we use to obtain our panel of TFP figures, the sources that we use in our calculations, and some of the patterns in the data that become evident Section 3 lays out the theoretical framework from which our empirical specification is derived Section 4 describes and briefly reviews the econometric techniques that we employ Section 5 contains our main empirical results Section 6 presents some additional results The subsequent section concludes

1.3 Calculating Total Factor Productivity

1.3.1 Methodology and Data

Our methodology for calculating TFP follows recent work by Klenow and Rodriguez-Clare

(1997)(KRC) and Hall and Jones (1999) (HJ) We assume that the aggregate production

function takes a simple Cobb-Douglas form and then calculate TFP as a Solow residual

¥i = KP(AiHi)** (1.1)

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Hị = etfŒ)T, (1.2)

where the size of the labor force is multiplied by the average efficiency units embodied in the workers that comprise the labor force E; denotes the average years of schooling attained by a worker in country 7, and the derivative y’(E) is the return to education estimated in a Mincerian wage regression (0) = 0, so that a person with no education

owns only the single efficiency unit comprised of her raw labor, while a person with E years

of education owns e“‘#) efficiency units of labor.®

Defining y = Y/L and h = H/L we can rewrite the production function in terms of

output per worker as:

—_2

yi = A; Ca hị (1.3)

This formulation enables us to calculate A; as a residual once we have data on income per worker, human capital per worker, the capital-output ratio of the economy, and the share of physical capital in output

Our data on GDP per worker are from the Penn World Tables 5.6, and our series for capital per worker is taken from Easterly and Levine (2000).§ Before calculating TFP, we make an adjustment to correct for the use of natural resources: we subtract from GDP the share of it that is attributable to Mining and Quarrying in national income accounts, using

*Following HJ, u(E) is assumed to be piecewise linear, with a coefficient of 13.4 for the first 4 years of schooling, 10.1 for the second four years of schooling, and 6.8 for schooling beyond the 8th year The coefficient on the first four years is taken from to the return to an additional year of schooling in sub-Saharan Africa The coefficient on the second four years is the average return to an additional year of schooling worldwide The coefficient on schooling above eight years is taken from the average return to an additional year in the OECD All three coefficients are from Psacharopoulos (1994)

®both data sets are available from the World Bank website

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ensure that it reflects value added after accounting for factors of production, rather than

simply resource-wealth Not making the adjustment leads to implausibly high values of TFP for countries that are rich in oil or minerals, as noted previously by HJ In addition, mining income is very volatile over time If left uncorrected, swings in natural resource prices would induce large movements in the measured TFP of countries with significant mining output

In order to carry out our adjustment we needed data on the share of mining in all our sample countries in 1960, 1965, and so on up to 1990 Unfortunately the UN data has some gaps; and we have to extrapolate values for the mining shares of some countries in some years Our extrapolation procedures are discussed in Appendix A.”

Finally, we assume that a = 1/3, as is standard in the literature We are then able to obtain TFP figures for a complete five-year panel from 1960 to 1990, for a sample of 86 countries Table 1.1 below shows TFP for some representative countries for the years 1960, 1975 and 1990 To facilitate comparison, all figures are normalized by the 1960 TFP level of the USA

The average rate of growth of TFP over the whole period for the full sample is 0.9% a year However, average productivity actually seems to be lower in 1990 than in 1975

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Table 1.1: The Evolution of TFP for a Selection of Countries Country Ae Ae Ags n Romania | 0.04 (86) | 0.12 (86)] 0.15 (82) Kenya 0.13 (82) | 0.21 (80) | 0.19 (79) India 026 (71) | 0.22 (79) | 0.30 (67) Hong Kong 0.28 (66) | 0.68 (41) |1.24 (7) Japan 0.31 (62) | 0.58 (50) | 0.79 (34) Singapore 0.40 (50) | 0.90 (22)] 1.33 (3) Brazil 0.52 (37) | 0.98 (18); 0.78 (35) Columbia 0.45 (45) | 0.67 (43) | 0.69 (42) Germany 0.61 (32) | 0.87 (26); 1.13 (13) Canada 0.79 (15) | 1.07 (13) | 1.17 (11) U.K 0.81 (13) | 0.91 (21) ] 1.18 (10) U.S.A 1.00 (6) {1.10 (10){ 1.19 (9) World Average | 0.51 0.69 0.67 OECD Average | 0.68 0.93 1.06 Rank in Parenthesis

(although TFP rises between 1975 and 1980, falling only thereafter) This pattern, however, is not true for rich countries; for the OECD countries in our sample average productivity grew steadily in every five year period except between 1975 and 1980, when it fell by a little under 1% In the USA productivity fell during both periods in the 1970s, but rose in all other periods (note that the 1970s correspond to the well-known “productivity slowdown” as measured using far more disaggregated data in the labor literature)

The lowest TFP in our sample belonged to Romania for most of our thirty year period,

although in general a group of sub-Saharan African countries brought up the rear West

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10 in 1990 On the other hand there was spectacular movement for some countries which started out in the middle The success of East Asia stands out Hong Kong moved up an incredible 59 places in the rankings, registering an average growth rate of TFP of almost 5% per year over the period, while Singapore moved up 47 places with a 4% per year growth rate.® At the other end of the spectrum, Guyana registered negative productivity growth at an average of 3.8% per year, while Nicaragua, Iran and Haiti registered negative

growth of over 2% per year

1.3.2 Variance Decomposition

As a final preliminary exercise, it is of interest to perform a decomposition (in logs) of the variance of GDP per capita into the variance of the factors of production on the one hand, and TFP on the other, in the manner of Klenow and Rodriguez-Clare Define

Ki,

X; = (—) eh; (Reh (1.4) A

Substituting into the production function and taking logs,

logy: = log A; + log X; (1.5)

var(logy;) _ cou(logy;,log A;) | cov(logy:,log Xi) _ 1

uar(lOog) - uar(log¡) ar(log 1;) (1.6)

This “split” gives us an idea of how much of the static variation in income can be attributed to the variation in TFP, and how much laid at the door of factor variations Of course, this

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decomposition is equivalent to examining the OLS coefficients from separate regressions of log A; and log _X; respectively on logy; Thus, as KRC point out, the decomposition

amounts to asking how much higher our conditional expectation of A (or X) is, if we

observe a 1% higher y in a country relative to the mean of all countries Table 1.2 shows the results of this decomposition by year

Table 1.2: Variance Decomposition of Log Incomes by Year covflog(y), log(Z)|/var log(y) Year| Z=(#)"* Z=h|Z=X Z=A 1960 0.186 0.230 | 0.416 0.586 1965 0.190 0.227 | 0.417 0.583 1970 0.190 0.238 | 0.427 0.573 1975 0.206 0.246 | 0.452 0.548 1980 0.190 0.255 | 0.445 0.555 1985 0.184 0.249 | 0.432 0.568 1990 0.170 0.238 | 0.408 0.592

It is apparent that the decomposition has remained rather stable over the years, ranging

from a 41% - 59% split between factors of production in 1990 and TFP to a 45% - 55% split

in 1975 at the extremes Our premise that differences in TFP are at least as important as differences in factors of production in explaining the static variation in income finds overwhelming support in every year of our sample Accordingly, the next section develops our hypotheses about the evolution of TFP and derives the empirical specification that we

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1.4 The Model

We start with a working hypothesis in the spirit of Nelson and Phelps (1996), which captures the idea that the rate of change of TFP in a country is positively related to the size of the gap between its actual TFP at a point in time, and its potential TFP at the same moment in time

A *

F(t) = Mlog A" (#) — log A(z) (1.7)

In the above formulation, A*(t) represents the country’s steady-state level of TFP at

time t, and we hypothesize that it is determined in the following way:

A*(t) = Fh*T(t) (1.8)

where F’ is an index of fixed factors specific to the country, and T(t) represents the TFP level at the world technological frontier

It is apparent that in our formulation ¢ represents the elasticity of the potential TFP level of a country with respect to its stock of human capital per worker, while À is the coefficient of conditional convergence (i.e an economy closes half the gap between its current and potential level of TFP in log2/X years)

Noting that A/A is the time derivative of log A, multiplying equation (4) through by

et and rearranging terms allows us to obtain:

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Finally, performing the integration in (1.10), multiplying through by e~**? and rear- ranging terms yields:

t2

log A(tz2) = e~>" log A(t1) + (1 — e—*7) logh + (1 — e7>") log F + e772 / e* log T(t)dt

t 1

(1.11) where T = (t2 —t,) Equation (1.11) falls neatly into the class of dynamic panel models

with a fixed effect and a time trend To see this, define: ait = log A(é2)

@iz—1 = log A(ti) tit-1 = logh fi=(1—e™") log F p=¢(-e) p= ecXx» t2 nh = ee | e* log T(t)dt (1.12) tt

Then, with the addition of a disturbance term, we can write (1-11) as:

Qi2 = fit Pp Qir-1 + Briz-1 + MH + Ut (1.13)

where f; is a country specific fixed effect, 7; is a time trend that is common to all countries, and u;,; is the random error term It is apparent that A and ¢ are easily recovered from the coefficients p and @ respectively We use equation (1.13) for estimation

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data For example, the recent growth literature emphasizes that factor productivity may be driven by the import of products from countries that perform R&D in their own right

Coe and Helpman (1995) test this hypothesis for a small sample of OECD countries for

which data are available on the R&D stocks of each country and on the share of each country’s products in the total imports of every other country.2 Were this data available for our panel, we could have added an index of the R&D stocks of trading partners weighted by import shares to our determinants of potential productivity A similar exercise could have been undertaken with respect to FDI as a share of GDP, or with respect to an index of the R&D stocks of international investors weighted by FDI shares, but, again, the non- comprehensive nature of available data prevents us from doing so It may be argued that these other channels of technological diffusion are subsumed in our country-specific fixed effect, but of course this holds true only to the extent that FDI and imports as a proportion of GDP and the composition of a country’s trade and investment partners stay unchanged over the thirty year period that we examine

Our model is one of technology adoption and the movement of the technological frontier is assumed to be exogenously determined The model may not be appropriate for countries that produce new technologies For this reason, our main results in section 1.6 focus on the 64 non-OECD countries in our sample Results from the full sample do not contradict our main results and are reported in section 1.7

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1.5 Estimation Procedure

In the previous section we derived a regression specification of the form?

địt = f¡ +0 đt—1 Ð ỔZct—¡ ĐT Dưa, t=1 N, t=2 T (1.14)

We estimate (1.14) using an application of the generalized method of moments esti- mator (GMM) for dynamic panels suggested by Arellano and Bond (1991) and familiar to

the empirical growth literature through Caselli, Esquivel and Lefort (1996)(CEL) GMM

estimation is appropriate in this context because it is capable of addressing two econo-

metric problems with the estimation of (1.14) It produces consistent estimates in the

presence of a lagged dependent variable and it allows for varying degrees of endogeneity in the explanatory variables

In order to estimate (1.14) we must perform two transformations First, to eliminate

the time varying component all variables are measured as deviations from their period

specific means, 7:2 = Ti — we zi,t/N Second, the first difference is taken to remove the

country- specific effects

Git — Gie—1 = p(ỗ¡t—+1 — G22) + B(Zie—1 — #Zi¿—a) + (Uae — Uit-1) (1.15) @=1 N, t=3 T

This equation cannot be estimated by OLS because G;4_1 is correlated with Ø;¿_1 FOr

this reason, the lagged dependent variable term must be instrumented Lagged values of

the dependent variable are valid instruments under the assumption that E(@; tz) = 0

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for all s < £— 1 This assumption requires that there is no serial correlation in the error

terms, i.e E(ti2%i,2-1) = 0.14 Our estimation procedure will utilize all valid y instruments

for each time period

There is also the potential problem of endogeneity, arising from the fact that Z;,-1 may be correlated with u; 4-1 Because our explanatory variable, the log of human capital, is a stock variable, we will assume that Z;; is predetermined at time t such that E(Zi,5 Ui) = 0 for all s < t Both this assumption as well as the assumption concerning the absence of correlation in the error terms are tested later

The moment restrictions exploited by our GMM estimation procedure are:

E@i,s tz) =0, s<t—1

E(Zis uit) =0, s<t (1.16)

These are the assumptions embodied in our preferred GMM estimator, which we label GMMa, and which we will argue is the most appropriate for the investigation at hand All lags of a which are valid instruments are employed, as are all orthogonal lags of the x observations

Our second estimator is labeled GMMb, and it too utilizes all valid lags of a It differs from GMMa in that the differenced z values are instrumented on themselves, without using any additional lags as instruments This estimator also requires the predeterminacy of x We employ this estimator because there are some Monte Carlo simulations that indicate that while additional z instruments always increase the efficiency of the GMM procedure,

“ Although for notational simplicity we are indexing time in unit increments, recall that our base time- interval is 5 years In annual terms, we assume that there is no fifth order serial correlation in the error

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they may increase bias in short panels

Our third instrumentation scheme, labeled GMMc, is identical to the first, except that

the most recent z observation is dropped from the instrument set This is equivalent to relaxing the predeterminacy assumption on z by one period, so that E(Ziz t2) # 0 is allowed This estimation is performed primarily as a test of the stronger predeterminacy

assumption

All our estimates are accompanied by the Sargan test statistic to check the validity of our overidentifying restrictions, and the m2 test statistic described in Arellano and

Bond (1991) The latter statistic checks for second-order serial correlation in the errors

of the equation in first-differences, which must be absent if our assumption of no serial correlation in the model in levels is correct Under the null hypothesis that there is no serial correlation, m2 is distributed as a standard normal statistic Note that if our tests reject serial correlation in general, they also reject it for the special case in which such correlation is generated by business-cycle effects

Our estimation procedures are discussed in greater detail in Appendix B

1.6 Results

1.6.1 Base Results

The results for the non-OECD sample are reported in Table 1.3 below The reduced form coefficients p and G are significant at the 1% level for all three regressions The coefficient on lagged productivity, our estimator for convergence, is significantly different from unity at the 1% level for the more efficient estimators, GMMa and GMMc

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Table 1.3: Regression Results — non-OECD countries GMMa GMMb GMMc p 0.854 0.841 0.819 (s.e) (0.053) (0.133) (0.060) 8 0.646 0.596 0.736 (s.e) (0.106) (0.271) (0.283) implied A 0.032 0.035 0.040 (s.e.) (0.013) (0.032) (0.015) implied @ 4.414 3.752 4.071 (s.e.) (1.942) (4.302) (1.958) Sargan Stat 33.13 19.01 29.39 DOF 33 14 28 (p-value) (0.46) (0.16) (0.39) m2 0.848 0.859 0.850 (p-value) (0.20) (0.20) (0.20) N 64 64 64 T 5 5 5

All figures in parentheses are standard errors, unless otherwise specified

we cannot reject the hypothesis that our identification assumptions are valid Similarly, the values of the m2 statistic support our assumption that the errors in the levels model are not serially correlated

The second regression, GMMb, was performed because simulations by Kiviet (1995)

and Judson and Owen (1996) suggest that the smaller instrument set often results in

lower bias for p (at the cost of lower efficiency) In this case, the p estimates for GMMa and GMMb are nearly identical, and therefore we prefer the GMMa results on efficiency grounds

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embod-ied in GMMa are valid Because all three estimators provide nearly identical estimates,

the rest of our analysis will focus on the more efficient GMMa results

Using the reduced form coefficients, we can recover the structural parameters of our model Asymptotic standard errors are calculated using the delta method The convergence coefficient, A, and the elasticity of human capital, ¢ are significant at the 1% level and 2% level respectively

We draw two primary conclusions from our results First, the significance of A indicates

that there is conditional convergence in productivity, confirming the catch-up hypotheses of

Gerschenkron (1962) and others Conditional on the level of human capital, countries with

lower productivity will tend to see higher productivity growth The speed of convergence is about 3% per year, which corresponds to a half-life of just under 24 years for deviations from the steady state

Second, the level of human capital in a country exerts a strong influence on the dynamic path of TFP, by positively affecting the steady state level of productivity.12 Our results support the Nelson-Phelps hypothesis that the level of human capital has a positive effect on a country’s ability to take advantage of technological spillovers Countries with higher levels of human capital converge to higher levels of productivity

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1.6.2 Dynamic and Static Effects of Human Capital

Our results imply that there is a useful distinction to be made between human capital’s static effect and its dynamic effect Our production function assumes that human capital directly impacts output in its role as an accumulable factor of production An increase in human capital has an immediate level effect on income, whose magnitude is measured by the private Mincerian returns to education This is the static effect

An increase in human capital also increases the steady state level of productivity; our estimate for ¢ suggests that a one percent increase in a country’s human capital leads to an increase in potential productivity of almost four and a half percent Following an increase in human capital, productivity growth will be more rapid as productivity converges to the new steady state, implying correspondingly faster growth in output This is the dynamic effect

Figures 1.1, 1.2 and 1.3 illustrate the process All three figures are generated under the parameters estimated in GMMa The hypothetical country shown is initially in its steady state growth path of 2% per year (due to the exogeneously shifting world technology frontier) We examine the effect on the growth rate of A, log A and logy of an increase in human capital at time zero

Figure 1.1 shows the response of the growth rate of A to a 30% increase in human capital, a 10% increase, and no increase.!® In the absence of change, A grows at 2% per year When there is a positive shock to human capital, the growth rate jumps up; the

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greater the shock, the higher the jump Then it asymptotes back to 2% per year

Figures 1.2 and 1.3 show the effect of shocks to human capital on log A and logy At time zero there is a discrete jump in log y; this corresponds to the static effect that human capital has on output as a component of the production function In subsequent periods the growth rate of y (the slope of logy) is raised above its steady state level of 0.02; the greater the increase in human capital, the higher the growth rates in subsequent periods These growth rates asymptote back to the steady state rate eventually, but the higher rates of growth persist for a considerable period

The importance of transitional dynamics may be gauged by a cursory look at Figure 1.3 The static effect of a 30% shock to human capital is captured by the discrete vertical jump in log y at time zero To see the magnitude of the dynamic effect, trace a line parallel to the no-shock line from ¢ = 0 to t = 100 and examine the vertical distance between this line and the 30% shock-line It is evident that over such a long period the dynamic effect of the increase in human capital is over three times as large as its static effect In fact the two effects are about equal in as short a span as 10 years Models that simply treat human capital as an accumulable factor in the production function while neglecting its dynamic role as a technology-enabler are therefore missing the most crucial link between education and output

1.6.3 Fixed Effects, Steady State Productivity and Human Capital

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by human capital, and how much by the fixed factors in our formulation Here we will show that our analysis is capable of offering some indicative answers

Our fixed effects are recovered as follows: z 1 em S\ (aie — Paie—1 — B2ie—-1 — 7) T (1.17) t=1 Further, from equation (1.8), taking account of our panel notation, it is apparent that we may write:

log Aj, = log F; + dloghiz-1+Tt (1.18)

Letting a bar above variables denote deviations from the mean over countries at each point in time, it follows that:

log A;, = log F; + dlog hy 4-1 (1.19)

From equation (1.19) it is possible to obtain a full set of estimates for the steady state TFP of each country in each five year period (in deviations from country means) except for the earliest one.14 This set of estimates can then be analyzed to determine what proportion of the variance in log A; can be attributed to each of the two components

Table 1.4 contains the results of a variance decomposition, following the method de- scribed in Section 1.3.2 The two columns describe the proportion of the variance of log A; which can be attributed to the fixed effects and human capital, respectively The majority of the variance can be attributed to the human capital term The decomposition is rela-

tively stable over time, with human capital accounting for between 87% and 96% of the

variation in log A; 15

4The fact the steady state TFP levels depend on lagged human capital implies that these levels may

be recovered only for those periods for which we have lagged values of human capital available; this means that we cannot recover steady state levels for 1960

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