Handbook of LABOR ECONOMICS vol 3c

INTRODUCTION

TO THE SERIES

The aim of the Handbooks in Economics series is to produce Handbooks for various
branches of economics, each of which is a definitive source, reference, and teaching
supplement for use by professional researchers and advanced graduate students. Each
Handbook provides self-contained surveys of the current state of a branch of economics in the form of chapters prepared by leading specialists on various aspects of this branch
of economics. These surveys summarize not only received results but also newer developments, from recent journal articles and discussion papers. Some original material is also
included, but the main goal is to provide comprehensive and accessible surveys. The
Handbooks are intended to provide not only useful reference volumes for professional
collections but also possible supplementary readings for advanced courses for graduate
students in economics.


CONTENTS OF THE HANDBOOK

VOLUME 1
PART1-SUPPLY

OF LABOR

Chapter 1

Labor Supply of Men: A Survey
JOHN PENCAVEL
Chapter 2

Female Labor Supply: A Survey
MARK R. KILLINGSWORTHand JAMES J. HECKMAN

Chapter 3

Models of Marital Status and Childbearing
MARK MONTGOMERYand JAMES TRUSSELL
Chapter 4

Home Production - A Survey
REUBEN GRONAU
Chapter 5

Retirement from the Labor Force
EDWARD P. LAZEAR
Chapter 6

Demand for Education
RICHARD B. FREEMAN
Chapter 7

Forestalling the Demise of Empirical Economics: The Role of Microdata in Labor
Economics Research
FRANK STAFFORD


viii

Contents of the Handbook

PART 2 - DEMAND FOR LABOR
Chapter 8

The Demand for Labor in the Long Run
DANIEL S. HAMERMESH

Chapter 9

Dynamic Models of Labour Demand
S. J. NICKELL

PART 3 - WAGE STRUCTURE
Chapter 10

Wage Determinants: A Survey and Reinterpretation of Human Capital Earnings Functions
ROBERT J. WILLIS

Chapter 11

The Determination of Life Cycle Earnings: A Survey
YORAM WEISS

Chapter 12

The Theory of Equalizing Differences
SHERWIN ROSEN

Chapter 13

The Economic Analysis of Labor Market Discrimination: A Survey
GLEN G. CAIN

VOLUME 2

PART 4 - LABOR MARKET EQUILIBRIUM AND FRICTION
Chapter 14

The Employment Relationship: Job Attachment, Work Effort, and the Nature of Contracts
DONALD O. PARSONS

Chapter 15

Job Search and Labor Market Analysis
DALE T. MORTENSEN

Chapter 16

The Natural Rate of Unemployment: Explanation and Policy
G. E. JOHNSON and P. R. G. LAYARD


Contents of the Handbook
Chapter 17

Cyclical Fluctuations in the Labor Market
DAVID M. LILIEN and ROBERT E. HALL

PART 5 - THE INSTITUTIONAL STRUCTURES OF THE LABOR MARKET
Chapter 18

The Analysis of Union Behavior
HENRY S. FARBER

Chapter 19

The Economics of Strikes
JOHN KENNAN

Chapter 20

Union Relative Wage Effects
H. GREGG LEWIS

Chapter 21

Segmented Labor Markets
PAUL TAUBMAN and MICHAEL L. WACHTER

Chapter 22

Public Sector Labor Markets
RONALD G. EHRENBERG and JOSHUA L. SCHWARZ

V O L U M E 3A
PART 6 - OVERVIEW ISSUES
Chapter 23

Empirical Strategies in Labor Economics
JOSHUA D. ANGRIST and ALAN B. KRUEGER

Chapter 24

New Developments in Econometric Methods for Labor Market Analysis
ROBERT A. MOFFITT

Chapter 25

Institutions and Laws in the Labor Market
FRANC1NE D. BLAU and LAWRENCE M. KAHN

ix


Contents of the Handbook
Chapter 26

Changes in the Wage Structure and Earnings Inequality
LAWRENCE F. KATZ and DAVID H. AUTOR

PART 7 - THE SUPPLY SIDE
Chapter 27

Labor Supply: a Review of Alternative Approaches
RICHARD BLUNDELL and THOMAS MACURDY

Chapter 28

The Economic Analysis of Immigration
GEORGE J. BORJAS

Chapter 29

Intergenerational Mobility in the Labor Market
GARY SOLON

Chapter 30

The Causal Effect of Education on Earnings
DAVID CARD

Chapter 31

The Economics and Econometrics of Active Labor Market Programs
JAMES J. HECKMAN, ROBERT J, LALONDE and JEFFREY A. SMITH

V O L U M E 3B
PART 8 - THE DEMAND SIDE
Chapter 32

Minimum Wages, Employment, and the Distribution of Income
CHARLES BROWN

Chapter 33

Firm Size and Wages
WALTER Y. OI and TODD L, IDSON

Chapter 34

The Labor Market Implications of International Trade
GEORGE JOHNSON and FRANK STAFFORD


Contents of the Handbook

P A R T 9 - L O O K I N G W I T H I N FIRMS
Chapter 35
Individual Employment Contracts
JAMES M. MALCOMSON
Chapter 36
Careers in Organizations: Theory and Evidence
ROBERT GIBBONS and MICHAEL WALDMAN
Chapter 37
Mobility and Stability: the Dynamics of Job Change in Labor Markets
HENRY S. FARBER
Chapter 38
Executive Compensation
KEVIN J. MURPHY

P A R T 10 - I N T E R A C T I O N S B E T W E E N D E M A N D A N D S U P P L Y
Chapter 39
New Developments in Models of Search in the Labor Market
DALE T. MORTENSENand CHRISTOPHERA. PISSARIDES
Chapter 40
The Analysis of Labor Markets using Matched E m p l o y e r - E m p l o y e e Data
JOHN M. ABOWD and FRANCIS KRAMARZ
Chapter 41
Gross Job Flows
STEVEN J. DAVIS and JOHN HALTIWANGER

P A R T 11 - E M E R G E N T L A B O R M A R K E T S
Chapter 42
Labor Markets in the Transitional Central and East European Economies
JAN SVEJNAR

Chapter 43
Labor Markets in Developing Countries
JERE R. BEHRMAN

xi


xii

Contents of the Handbook

V O L U M E 3C
PART 12 - LABOR MARKETS AND THE MACROECONOMY
Chapter 44

Labor Markets and Economic Growth
ROBERT TOPEL

Chapter 45

Microeconomic Perspectives on Aggregate Labor Markets
GIUSEPPE BERTOLA

Chapter 46

Labor Market Institutions and Economic Performance
STEPHEN NICKELL and RICHARD LAYARD

Chapter 47

The Causes and Consequences of Longterm Unemployment in Europe
STEPHEN MACHIN and ALAN MANNING

PART 13 - POLICY ISSUES IN THE LABOR MARKET
Chapter 48

Race and Gender in the Labor Market
JOSEPH G. ALTONJI and REBECCA BLANK

Chapter 49

New Developments in the Economic Analysis of Retirement
ROBIN L. LUMSDAINE and OLIVIA S. MITCHELL

Chapter 50

Health, Health Insurance and the Labor Market
JANET CURRIE and BRIGITTE C. MADRIAN

Chapter 51

Economic Analysis of Transfer Programs Targeted on People with Disabilities
JOHN BOUND and RICHARD V. BURKHAUSER

Chapter 52

The Economics of Crime
RICHARD B. FREEMAN

Chapter 53

Recent Developments in Public Sector Labor Markets
ROBERT G, GREGORY and JEFF BORLAND


PREFACE TO THE HANDBOOK

Modem labor economics has continued to grow and develop since the first Volumes of this
Handbook were published. The subject matter of labor economics continues to have at its
core an attempt to systematically find empirical analyses that are consistent with a
systematic and parsimonious theoretical understanding of the diverse phenomenon that
make up the labor market. As before, many of these analyses are provocative and controversial because they are so directly relevant to both public policy and private decision
making. In many ways the modern development in the field of labor economics continues
to set the standards for the best work in applied economics.
But there has been change since the first two volumes of this Handbook were published.
First and foremost, what was once a subject heavily dominated by American and, to a
lesser extent British, writers is now also a growth field throughout the rest of the world.
The European Association of Labour Economists, formed well before its American rival,
has become the largest and most active organization of its kind. These volumes of the
Handbook have a notable representation of authors - and topics of importance - from
throughout the world. It seems likely that the explosive growth in the development and
study of modem labor economics throughout the world will be a major development that
will continue throughout the next decade.
Second, whereas the earlier volumes contained careful descriptions of the conceptual
apparatus for analysis of a topic, these new volumes contain a wealth of detailed empirical
analyses. The chapters in the new volumes tend to be correspondingly longer, with far
more detail in the empirical analysis than was possible in the earlier volumes. In some
cases, the topics covered could not have even been entertained for consideration a decade
ago.
The authors of the chapters in these volumes have been very responsive in the face of

some strict deadlines, and we are grateful to them for their good humor. We are also deeply
indebted to Barbara Radvany and Joyce Howell for their gracious assistance in helping to
manage the massive task of coordinating authors and the delivery of manuscripts. We
appreciate the efforts of everyone involved in the creation of these volumes, and we hope
that their readers will too.
Orley Ashenfelter and David Card


Chapter 44

L A B O R M A R K E T S A N D ECONOMIC G R O W T H
ROBERT TOPEL*
University of Chicago
Contents
1 Introduction
2 Labor markets and economic growth
2.1 Background
2.2 Growth theory and human capital
2.3 Transitional dynamics
2.4 Human capital and aggregate inequality
2.5 Empirical implications of neoclassical growth theory
2.6 lternative models of human capital and growth
2.7 Summary: human capital, education, and growth

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3 Empirical evidence

2954

4

3.1 Background
3.2 Growth accounting
3.3 Limitations of growth accounting
3.4 Measuring the social returns to human capital
3.5 Empirical results
3.6 New evidence from old data
3.7 Smnmary: what do we know about human capital and growth?
G r o w t h , i n v e s t m e n t , a n d relative w a g e s
4.1 Background
4.2 Wage inequality and development: evidence

5 Concluding remarks
References

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* Thanks to Kevin Murphy, Canice Prendergast, and Pete Klenow for helpful discussions; the usual disclaimer
applies. Support from the Lynde and Harry Bradley Foundation and the Sarah Scaife Foundation as administered
by the George J. Stigler Center for the Economy and the State is gratefully acknowledged.
Handbook of Labor Economics, Volume 3, Edited by O. AshenJ~lter and D. Card
© 1999 Elsevier Science B.V. All rights' reserved.
2943


2944

R. Topel

1. Introduction

This chapter is motivated by the recent resurgence of interest in the economics of growth.
Among macroeconomists, the shift of research effort is near total, eclipsing the businesscycle focus that had dominated the field for decades. Behind this is a recognition of the
enormous welfare implications of sustained economic growth, and a renewed desire to
understand the vast differences in living standards among countries, which dates back at
least to Smith. What some have called the "neoclassical revival" in growth economics has
come to dominate macroeconomic research.

Developments in this area should be of particular interest to labor economists because
much of the revival of growth economics builds on the theory of human capital. Because
human capital is, by definition, embodied skills and knowledge, and because advances in
technical knowledge drive economic growth, it follows that human capital accumulation
and economic growth are intimately related. Indeed, many of the issues of modern growth
economics involve questions that are familiar to labor economists. How is human capital
produced and distributed? What are the private and social returns to human capital investment, and how do people respond to those returns? How do labor markets operate during
the development process? Most of the growth-related work on these topics is carried on by
macroeconomists; traditional labor economists are conspicuous by their absence, even in
empirical work. It should not be that way.
This chaptdr~ reviews recent developments in growth economics, with a particular focus
on labor market ~/nd human capital issues. My openly confessed motive is to interest labor
economists in problems of economic growth, and especially to motivate empirical
research. The chapter has three substantive sections, and it unfolds as follows.
Section 2 surveys models of endogenous economic growth based on the accumulation
of human capital, beginning with Uzawa (1965) and Lucas (1988). This survey of theory is


Ch. 44: Labor Markets and Economic Growth

2945

in no way exhaustive, or even a modestly complete review of the field, but it serves as a
template for understanding the major empirical issues in growth economics as they apply
to labor markets. I briefly cover the theory's predictions about transitional dynamics for
economies that are away from their long run growth paths, the role of human capital in
producing new human capital, and the relation between economic growth and inequality.
This section closes with a summary of empirical implications.
Section 3 turns to the data, reviewing both empirical methodologies and the state of
evidence. Of particular interest is the contribution of education - as a measurable component of human capital - to economic growth. While richer countries are generally more

educated, it is difficult to isolate the channel through which education affects aggregate
prosperity. Remarkably, existing empirical literature finds virtually no relationship
between changes in the education of a country's labor force and changes in output per
worker. Instead, the level of education in a country does seem to affect growth. I reevaluate this evidence, using panel data on output per worker and educational attainment
for 111 countries over a 30-year period. Unlike previous literature, I find social returns to
investments in education that are as large as, or perhaps larger than, the estimates of
private returns that are generally found in micro data on individual wages and earnings.
Using within-country changes in education and productivity, I find that a 1-year increase
in average years of schooling for a country's workforce raises output per worker by
between 5 and 15%. The level of schooling also affects growth in this analysis, so it
appears that the social returns to education are at least as large as the private returns.
Section 4 takes up the "operation" of labor markets during development. A famous
hypothesis of Kuznets (1955) posits that wage inequality first rises and then falls as
development progresses. I provide a simple model of this process that incorporates
many of the stylized "facts" about labor markets during periods of rapid economic
growth. In the model, export-driven demand for industrial output raises the demand for
skilled labor. In turn, investment in human capital responds to differences in wages
between skilled and unskilled labor. Wage inequality spurs investment in human capital
and more rapid economic growth, but increased relative abundance of skills serves to
reduce inequality. One of the open questions of this and related models is the impact of
investment in human capital on the relative price of skills. Factor price equalization
indicates that this effect should be negligible, but empirical evidence suggests that a rising
relative supply of skilled labor reduces its relative wage. In spite of trade theories, factor
prices in most countries appear to depend on factor ratios.
Section 5 summarizes and concludes.

2. Labor markets and economic growth
This section reviews basic models of economic growth, as a basis for thinking about data. I
make no attempt to be exhaustive, or even to cover models in all of their technical detail.
The goal is to set out the broad outlines of growth models in a way that will be useful to

2946

R. Topel

labor economists. For technical surveys of growth theory see Barro and Sala-i-Martin,
1995 or Aghion and Howitt (1998).

2.1. Background
The last 10 years have witnessed a resurgence of economic growth as a field of study by
macroeconomists. Behind this renewed interest is the enormous impact that changes in
growth can have on economic well being. For example, real per capita income in the
United States in 1950 was $8605, the highest in the world. By 1990, this figure stood at
$18,258 (still the highest), for an average annual growth rate of 1.9%. In contrast, 1950 per
capita income in Canada - the third richest country at the time - was $6112, which grew to
$17,070 by 1990; a growth rate of 2.6% per year. If the United States had achieved the
same rate of growth as did Canada, the effect of a 0.7% higher growth rate - cumulated
over 40 years - would have raised per capita income in the US in 1990 to $24,033, a gain
of $5775 per person. At 5% interest (which is probably high for this calculation), this
represents a hypothetical gain in discounted lifetime wealth of over $100,000 p e r person. 1
Are there changes in institutions or government policies that could deliver such gains? As
a more extreme example, are there changes in policies or institutions that would transform
a growth laggard, like India, into an Asian " m i r a c l e " , like South Korea? Even tile remote
prospect of gains like these has led some economists to call economic growth "the part of
macroeconomics that really matters".2
It is nearly tautological that the process of economic growth is driven by a society's
accumulation of knowledge and the ability, or skills, needed to apply it. W e expect to be
wealthier in the future because we will know how to do more things than at present.
Seemingly supportive evidence comes from Denison (1985), who estimated that changes

in schooling accounted for about 25% of growth in US per-capita income after 1929, and
Schultz (1960), who estimated that investment in schooling grew much more rapidly than
investment in physical capital after 1910. 3 Indeed, one view of the growth process is that
differences in per-capita incomes across countries reflect differences in the ability to apply
technologies that are, in a general sense, already broadly known (Lucas, 1988). Then the
I Perhaps it is infeasiblefor the richest country in the world (the US) to raise its growth rate by 0.7 points per
year, since the richest countries are presumably at the frontier of available technologies and productive knowledge. So consider a less developed country like the Philippines. Suppose Philippine income had grown at the
Canadian rate of 2.6% instead of its actual rate of 1.6%. By 1990, per capita incomein the Philippines would have
been $2507 instead of its actual value of $1519; a 65% difference.
2 Barro and"Sala-i-Martin, 1995. They conclude that if economists can have "even small effects on the long
term growth rathe, then we can contribute much more to improvements in standards of living than has been
provided by the entlte history o]' macroeconomicanalysis of countercyclicalpolicy and fine tuning”. This
is no doubt true.
3Estimates of the contribution of labor - including human capital - to economicgrowth are all over the map.
Dougherty (1991) puts labor's share of US growth at 41% for the 1960-1990 period, but the conformableestimate
for Germany is -8.1%. Christianson et al. (1980) estimate essentially zero contribution from human capital in
Germany for the years 1947-1973.


2947

Ch. 44." Labor Markets and Economic Growth

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Fig. 1. Capital per worker and output per worker. 118 countries, 1960 and 1985. Source: Summers and Heston
(1991).
wealth of a society is determined by its stock of human capital, and economic growth is the
process of human capital accumulation at the level of an economy. This means that growth
is supported by human capital investment decisions that are made in labor markets. As it
turns out, the role of the labor market in modern growth theory is not much deeper than
that.
2.2. Growth theory and human capital

One of the key "facts" about economic growth is that most countries have experienced
sustained growth over long periods of time (Kaldor, 1963). For example, the annual rate of
growth in per-capita income in the US has averaged about 1.75% since the beginning of
the 20th century. Similarly, the capital-output ratio is remarkably stable across countries,
both rich and poor (see Fig. 1). To accommodate these facts, modern growth models
introduce some additional form of non-physical capital that offsets diminishing returns
to physical capital: In Solow's (1956) original contribution, an exogenous rate of laboraugmenting technical change offsets the effects of diminishing returns to capital. For
example, with a constant returns Cobb-Douglas aggregate production function and zero
labor force growth, output is
Y(t) = (K(t))~(A(t)L) I- ~,

(1)

where A denotes the state of labor augmenting technical progress, which grows at rate
a = dlog(A(t))/dt. Eq. (1) implies that output per worker is


2948

R. Topel

Y(t)/L = A(t)[K(t)/A(t)L] ~.

(2)

Assuming a constant saving rate, s, under perfect competition the per-worker rates of
output, capital, and consumption grow at the steady-state rate a. a Since capital and output
grow at a c o m m o n rate, the capital-output ratio is constant in the steady state. This
correspondence with the data is the motive for specifying technical change as laboraugmenting.
This model of growth has the unsatisfying feature that technical change is both exogenous (non-behavioral) and ill-defined, literally an unobserved residual that "explains"

growth after the contributions of other, observable, factors are taken into account. This
fact led Schultz (1961) and other development economists to reinterpret the residual in
terms of human capital, on the argument that technical progress is hard to distinguish from
advancement of knowledge. 5 The idea was formalized by in a modern growth model by
Uzawa (1965) and later Lucas (1988), who interpret A(t) as the average stock o f human
capital, or skills, embodied in workers, so H = AL. 6 In Lucas' influential formulation of
the problem, output and the law of motion for the accumulation of human capital are
Y(t) = K(t)~(uH(t)) 1-~,

(3)

H = BH(1-

(4)

u) - ~H,

where 1 - u is the portion of time devoted to production of new human capital, similar to
Ben-Porath's (1967) model of human capital accumulation for an individual. 7 Then (2)
postulates that average productivity depends on the ratio of the stocks of physical and
human capital used in production K/uH. In the L u c a s - U z a w a framework, workers
embody productive skills that are accumulated through endogenous, wealth maximizing
investment decisions - schooling, training, and learning-by-doing - that sacrifice present
consumption in order to raise future productivity and income. In the steady-state equilibrium of the model, the e c o n o m y ' s stocks of physical capital and human capital grow at
the same endogenous rate, which sustains economic growth in the long run. Human capital
investment decisions involve no distortions, and there are no externalities, so human
capital accumulates at the socially efficient rate. Economic growth is efficient, and there
is no role for government interventions in the process.
The conclusion that competitive growth is efficient is an artifact of the technology (3), in
which human capital produces no externalities, as well as the assumption that privately

4 It is straightlorward to endogenize the savings rate by modeling intertemporal optimization by consumers.
For present purposes, this only makes the analysis more complicated, without adding new insights.
5 Little (198~)contains ffbdef intellectual history of the connection between the technical progress and hmnan
capital in growth th~eoryand growth accounting.
6 See also Jones and Manuelli (1990), Rebelo (1991), and Stokey (1988). Others model human capital accumulation as learning by doing (Romer, 1986; Stokey, 1988; Young, 1991) or as knowledge accumulation through
R&D (Romer, 1990; Grossman and Helpman, 1991; Aghion and Howitt, 1992).
7The constant returns assumption in (4) is key. If investment is subject to diminishing returns then human
capital cannot grow indefinitely at a constant rate, so sustained growth is impossible.


Ch. 44: Labor Markets" and Economic Growth

2949

financed investments in human capital maximize individual wealth. Yet education is
almost always publicly financed to some (usually large) degree, and governments often
subsidize post-schooling training and apprenticeship programs as well. (German apprenticeship programs are the latest popular example, alleged to improve German economic
performance compared to the US). This positive role for government can be rationalized
when individual decisions to acquire human capital create external benefits for others. 8 For
example, it is plausible that an individual's human capital is more productive when other
members of society are more skilled. Lucas (1988) analyzes an extension of (3) in which
the output of each firm depends on the human capital of its workers, say h, as well as the
average value of human capital per worker in the economy, say ha With this technology,
decentralized decisionmaking yields too little investment in human capital, as individual
decisions to invest do not take into account the effect on others' productivity. Steady state
output is too low relative to the social optimum, and growth is too slow. 9
While models like Lucas' show that human capital accumulation can sustain growth,
they do not go far in detailing the role of the labor market and individuals' investment
decisions in this process. Second-generation models have enriched the basic approach,
adding refinements such as finite individual horizons, overlapping generations, transference of human capital across generations, and various externalities in the production and

utilization of human capital. Yet for labor economists and others interested in applied
work, the message of growth theory does not go far beyond a statement that "human
capital is important". The theory provides no guidance about why Singapore has grown
faster than, say, India, except perhaps the accounting answer that people in Singapore have
accumulated more skills (and other factors that go with them). It does, however, provide
some foundation for empirical studies of differences in growth rates across countries, and a
number of empirical implications that can be confronted with data (see Section 2.5). Even
so, the only tested implications have to do with transitional dynamics for economies that
may be off of their equilibrium growth paths (see below) and the issue of whether
measures of human capital - like education - raise productivity at all. On the latter
point, the connection of human capital to growth has proven surprisingly resistant to
empirical confirmation, which to some economists (e.g., Klenow and Rodriguez-Clare,
1997) calls the entire enterprise into question. At the least, there is substantial debate over
the channel through which human capital may affect growth. I take up this issue in Section
3.
2.3. Transitional dynamics

The human capital interpretation of (2) yields interesting transitional dynamics for econoLiquidity constraints will also do the trick, though I do not analyzethem in any detail. These may be relevant,
for the usual reason that human capital provides no collateral against which to finance investments.
9 Romer (1986) studies a similar model, in which aggregate capital enters each finn's production function,
because of spillover effects in R&D. As in the model with human capital externalities, competitive growth is
inefficient.


2950

R. Topel

mies that are away fi'om the steady state ratio of physical to human capital for one reason
or another. For example, consider an economy that "loses" capital in a war, leaving the

stock of human capital intact. The stock of physical capital is too low relative to the stock
of human capital. Then the path back to the steady state involves higher growth and more
rapid investment in physical capital. This is consistent with the actual performances of
Germany and Japan in the decades following World War II. Symmetrical dynamics are
implied for a country that finds itself with "too little" human capital per worker, say
because of past policy mistakes. The returns to human capital investment are high - due to
diminishing returns - and so output grows faster than in the steady state. These are
examples of what has come to be called "conditional convergence": an economy invests
more and grows faster when its current ratio of physical to human capital is different than
its steady state value. Note that this effect is different than the idea that countries with
greater stocks of human capital have an advantage in growing because human capital is an
aid to innovation. Conditional convergence follows solely from neoclassical properties of
production, together with optimal investment going forward.
One of the puzzles of economic growth is that some countries suddenly rise from
underdevelopment, accumulating human (and physical) capital along a path of rapid
output growth, while other countries seem to trapped in a low growth state. Becket,
Murphy, and Tamura (BMT) (Becker et al., 1990) and Azariadis and Drazen (1990)
model this as a problem of multiple growth equilibria, where the needed non-convexity
comes from the technology for producing human capital. Both of these papers argue that
human capital begets the production of more human capital: education and other sectors
that produce human capital are intensive users of skilled (e.g., educated) labor. Within a
country, this means that rates of return on investment in human capital may initially rise
instead of fall as the stock of human capital increases, because the large stock makes it
cheaper to produce more. Comparing countries, this means that differences in initial
conditions can lead to different long run growth paths. The result is multiple steady states,
one with low output, little human capital investment, and (in BMT) high fertility; the other
with higher returns, greater investment, skills, and growth, and lower fertility. BMT argue
that the circumstances that push an economy from one steady state to another may be
largely a matter of "history and luck," and "accidents and good fortune," while Azariadis
and Drazen see a role for government policy in getting the ball rolling. In their model of

overlapping generations with a threshold externality in the production of human capital, a
one-time intervention will do the trick.
Luck and accidents aside, this type of model can help us to understand a key feature of
human capital investment in the development process. In the Asian miracles like Taiwan
(Lu, 1993)and Korea (Kim and Topel, 1995) and in some Latin American economies
(Robbins, 1996), successive cohorts of the young acquire human capital in larger and
larger numbers. Yet empirical evidence discussed below suggests that increased stocks of
educated labor cause the returns to human capital to fall. With constant costs of educating
the young, declining returns should reduce investment. But a technology in which the
existing stock of human capital raises the productivity of current investment can generate


Ch. 44: Labor Markets and Economic Growth

2951

declining costs of adding to the stock. Then investment can rise in spite of declining
returns to human capital.

2.4. Human capital and aggregate inequality

Beginning with Kuznets (1955, 1973), a long tradition in development economics is
concerned with the effects of growth on wage and income inequality. Human capital
models of endogenous growth typically abstract from this issue by treating H as a homogeneous aggregate, so that the distribution of H among workers has no bearing on the
growth rate of output. Yet human capital investment affects inequality in at least two ways.
First, it affects the distribution of the stock of human capital, which could either increase or
decrease inequality depending on where in the distribution of skills the new investments
occur. For example, at the initial stages of economic development human capital investment in the form of education may be concentrated among a privileged elite. This would
tend to raise inequality. Later investment may be concentrated on the least skilled, especially with diminishing returns to investment at the individual level, so inequality may
eventually fall. This pattern is consistent with the "Kuznets Curve" hypothesis that

inequality first rises and then falls as development proceeds.
Glomm and Ravikumar (1992) and Benabou (1996) analyze different structures for
school finance, and how differential access to human capital among individuals can affect
inequality and growth. In Glomm and Ravikumar (1992) a spillover externality in public
school finance makes individual human capital accumulation more productive when the
average human capital of the population is higher. This effective "subsidy" of the less
skilled causes inequality of human capital to die out over time. In contrast, privately
financed schooling tends to make inequality persist. Benabou (1996) analyzes the effects
on growth of schooling when students of heterogeneous abilities can either be segregated
or mixed together. In the short run, segregation may increase growth because talented
people are complements in producing new human capital. In the long run, however,
segregation leaves intact the overall heterogeneity of skills in the economy, which is a
drag on productivity growth. This perpetuates inequality in the long run, and can reduce
growth. This has implications for school finance. If schools are financed locally, in
communities that are sorted on talent or resources, then expenditures on education will
tend to perpetuate inequality and, perhaps, reduce long run growth. Greater funding equity
say through centralized taxation to finance schools and reduced segregation on talent leads to lower lotag run inequality and higher growth. In this model, centralized financing
and a national curriculum - along the lines of some European countries - may provide a
long run advantage relative to a decentralized system. J0
The second effect of human capital accumulation on inequality occurs because human
capital investment affects factor proportions, which should impact relative wages. As
-

~0For example, Swedish schools are centrallyfinanced, and fundingequity is strictly adhered to. Curriculumis
uniform across schools.


2952

R. Topel

human capital accumulates, the aggregate share of skilled labor rises so that the relative
price of skills may fall. As Learner (1995) argues, this force is mitigated by StolperSamuelson effects of unimpeded trade. If output prices are fixed on international markets,
and if sectoral production functions exhibit constant returns, then factor price equalization
implies that relative wages of different skill groups are independent of their factor shares
within a particular country. (The technical conditions for this are discussed in greater
detail in Section 4). With constant returns, an increase in the labor force share of skilled
(educated) workers can be accommodated by shifting labor fi'om low-skill to high-skill
sectors, leaving factor proportions in each sector (and thus relative wages) unchanged.
Empirical evidence from a number of countries appears to reject this prediction, however.
increases in the aggregate share of educated labor do not simply increase the size of skillintensive sectors. Within-sector shares of educated labor rise as well (Murphy and Welch,
1991; Topel, 1994; Kim and Topel, 1995, Robbins, 1996), which indicates that the relative
"price" of skilled labor will fall as it becomes more abundant. Empirical evidence on this
issue is taken up in Section 4, below.

2.5. Empirical implications of neoclassical growth theory
Models that base sustained growth on human capital accumulation have a number of
important, and testable, empirical implications. Most obvious is that accumulation of
human capital increases economic growth. As discussed below (Section 3), this central
prediction has proven surprisingly resistant to empirical confirmation, at least in the form
that the theory implies. Secondary and more subtle predictions are: (i) rising returns to skill
should spur investment and, therefore, growth; (ii) the private and social returns to human
capital may differ when spillover effects are important; and (iii) economies that are
initially below their steady state values of physical or human capital will experience faster
growth. Complementarity between the existing stock of human capital and new investment implies that: (iv) investment in human capital may rise, even while the returns are
declining; (v) countries with little initial human capital may be "trapped" in a low growth,
low income state; and (vi) the distribution of human capital can affect investment, and
hence growth. Some of these predictions are taken up in Sections 3 and 4.

2.6. Alternative models of human capital and growth

In the models outlined above, human capital drives growth because it is an input to the
production of goods and services, as in (3). Then growth in human capital per worker is
equivalent to growth in output per worker; human capital simply earns its private marginal
product. NelSon and Phelps (1966) offer an alternative view. In their analysis, growth is
driven by the stock of human capital because skilled workers are more likely to innovate
new technologies and - for countries that are not at the technological frontier - more able
to adopt existing technologies. In this analysis, a greater level of human capital at time t
raises subsequent growth by producing technical change. A number of microeconomic
studies of the role of education in production, beginning with Welch (1966), find empirical


Ch. 44: Labor Markets and Economic Growth

2953

evidence for the idea that educated workers are more likely to adopt new productive
technologies. For example, in a study of Indian farmers, Foster and Rosenzweig (1996)
find that more educated farmers are the first to adopt new seed technologies.
At the aggregate level the most obvious empirical implication of this view is that
changes in the rate of output can depend on the level of human capital, rather than simply
on the change in human capital as implied by standard growth models. This prediction is
consistent with empirical results of Barro and Sala-i-Martin (1995) and Benhabib and
Spiegel (1994), who estimate models of economic growth on a cross-section of countries.
They find little evidence that growth of human capital is associated with growth of output,
but a higher level of education per worker (measured by average years of schooling in the
population) is associated with a higher rate of economic growth. In Barro and Sala-iMartin's analysis, average years of secondary education have a stronger effect than years
of primary education, which may also reflect greater ability to innovate and adopt technologies among more skilled workers. Benhabib and Spiegel find that the level of education has a stronger effect on growth for relatively low income countries, which may
indicate a role for education in "catching up" to technological leaders. The next section
provides a more detailed discussion of these and other empirical results.

2.7. Summary: human capital, education, and growth

The recent revival of growth theory is built on the idea that human capital is central to
growth. Yet there is little consensus on what is the channel of causality leading from
human capital investment to economic growth. Following Lucas (1988), neoclassical
models treat human capital as a produced input to a standard technology, so that growth
of human capital and growth of output are nearly synonymous. An alternative theory, with
support in some recent empirical work, is that the level of human capital affects growth
through greater innovation and adoption of technologies. As pointed out by Aghion and
Howitt (1998), the theories have starkly different implications for the effects of human
capital investment on long run growth. Narrowly interpreted, neoclassical models imply
that current investment leads to a one-time surge in output as new human capital is applied
in production. In contrast, models like that of Nelson and Phelps (1966) imply that current
investment - by raising the level of human capital - has a permanent effect on technical
change and hence growth.
It is plausible that both theories of the role of human capital are true. Growth of human
capital may increase output and set the stage for subsequent growth. Yet even then, the
differences between the theories is more semantic than real. Neoclassical theorists define
human capital broadly, so that accumulation of human capital encompasses the accumulation of knowledge and the ability to apply it in productive ways. When we think of new
ways to do things, human capital has increased, t~
HIn this sense, I think that Aghionand Howitt (1998) greatly exaggeratethe differencebetween neoclassical
and "Shumpertarian" models of human capital and growth.


2954

R. Topel

If this is so, then why do some empirical studies - like Barro and Sala-i-Martin (1995)
and Benhabib and Spiegel (1994) - find that the level of human capital, as measured by

average years of schooling, raises growth? An answer is that human capital is an input to
its own production, a fact that is central to many growth models, and that schooling is only
one form of human capital. Other forms of human capital accumulation - like on the j o b
training, acquisition of knowledge outside of formal schooling, and learning-by-doing are unmeasured. Empirically, this means that the level of schooling will be correlated with
growth because countries with more education invest more in other forms of human
capital. A related point is that countries with more schooling m a y have lower costs of
investing in other forms of human capital, so schooling is simply a proxy for unobserved
heterogeneity in the costs of investment. 12

3. Empirical evidence
3.1. Background
As I noted above, the role of labor markets in modern endogenous growth theory does not
go much beyond the idea that human capital should be important to sustained economic
growth. The empirical questions are (i) How important is it?; and (ii) What are the
channels through which human capital affects growth ? Does growth of broadly-defined
human capital "account" for what we would otherwise call productivity growth, as
suggested by Lucas (1988) and others? If so, would government policies that encourage
human capital investment improve welfare, especially among less developed countries
that might be able to "catch up" with more advanced countries, which are closer to the
technological frontier? Are some policies and institutions, such as income redistribution
and centralized wage setting, a hindrance or boon to human capital investment and
growth? These are key empirical issues for which we have few good answers.
There are two main strands of empirical research on economic growth. Both attempt to
measure the effect of input differences, or accumulation, on productivity and per-capita
incomes. Growth accounting divides output growth among changes in measurable input
quantities - physical and human capital - and a residual called "total factor productivity"
(TFP). The art in this approach lies in measuring inputs, which is especially difficult when
the input in question is an abstract stock like " h u m a n capital". The other main body o f
research is more regression-oriented, estimating cross-sectional and panel models of the
determinants of countries' incomes. Our main interest in this literature will stem from

what can b~e learned about the empirical relationship between education and economic
growth.
J~In earnings data for individuals, age-earnings data for more educated workers are steeper for more educated
workers. The starldard explanation is that education reduces the costs of subsequent, on-the-job investment in
human capital. Heterogeneity of talent has the same implication: those with more education have lower costs of
investing, so we expect them to invest more in other forms of human capital.


Ch. 44: Labor Markets and Economic Growth

2955

This section also provides some new evidence on the effects of schooling on economic
growth. I find that returns to schooling estimated from aggregate data on country growth
rates are generally as large, or larger than, the returns estimated by labor economists from
micro data on individuals' wages and earnings.

3.2. Growth accounting
Following Solow (1957), suppose that aggregate output is produced using physical capital
(K) and human capital (H) via F(K,AH), where A denotes the state of labor augmenting
technical progress. Assuming constant returns to scale and competitive factor markets, the
rate of change of output for country i at date t is given by
Yit = OLiJ£it -[- ( l -- OLit)hit -]-/0it,

(5)

where 3>,/~, h and p refer to the proportional rates of change of output, physical capital,
human capital, and TFP, respectively, and c~ is capital' s share of national income. With the
exception of p, all quantities in (5) are measurable, at least to some degree, which leaves
TFP as the part of output growth that remains unexplained after taking account of the

growth rates of physical and human capital. Hence the estimate of TFP is commonly called
the Solow residual.
Original applications of (5), such as Solow (1957) and Denison (1962, 1967) treated raw
labor as the human capital input, and did not account for changes in the quality of capital,
so that a large portion of growth was attributed to TFP. Later work by Jorgensen and
Griliches (1967), Chfistiansen et al. (1980) and Jorgensen et al. (1987) showed that a
substantial portion of the Solow residual could be accounted for by changes in input
quality. For our purposes, the quality of the human capital input has increased in most
countries because of improvements in health and in the quantity and quality of schooling
among working age populations. This means that subcategories of the labor force (years of
schooling and experience, gender, and so on) should be weighted by their marginal
products (wages) in forming a human capital aggregate. J3 Then accumulation of human
capital means that H grows faster than the labor force, which accounts for some of
productivity growth.
The most recent applications of this method are in three influential papers by Young
(1992, 1994, 1995). He studies the growth experience of the four "Asian tigers:" South
Korea, Hong Kong, Taiwan, and Singapore. As shown in Table 1, between 1966 and 1990
output per worker in these economies grew at average annual rates of between 4 and 5%,
far above the 1.4% rate achieved by the US over this period. Before Young's work, many

13The production function is y = F(K, EnIHi), where ni is the number of workers in group i and Hi is average
human capital of those in the group. Equating marginal products to wages for each group, we get H}H/ = w~lwj,
so Hi = (wi/wj)ttj. For example, an increase in the number of high school graduates relative to elementary school
graduates, holding population fixed, will raise the measured stock of human capital in proportion to the college/
high-school wage ratio.


2956

R. Topel

Table 1
Growth accounting results for selected countries ~
Country and
years

Average
value of
capital's
share, c~

Growth
rate of
GDP

Growth
rate of
GDP
per
capita

Growth
rate of
GDP
per
worker,
gi,

Amount
due to

capital,

0.007
(0.05)
0.030
(0.61)
0.034
(0.81)
0.020
10.41)

United States
1960-1990 (a)
South Korea
1966-1990 (b)
Singapore
1966-1990 (b)
Taiwan
1966-1990 (b)

0.41

0.031

0.020

0.014

0.32

0.103

0.087

0.049

0.53

0.085

0.072

0.042

0.29

0.091

0.072

0.048

Hong Kong
1966-1990 (b)
Japan
1960-1990 (a)
Germany
1960-1990 (a)
United
Kingdom

1960 1990 (a)
Canada
1960-1990 (a)
Mexico
1940-1980 (c)
Chile
1940-1980 (c)

0.37

0.073

0.055

0.047

0.29

0.068

0.059

0.052

0.37

0.032

0.028

0.025

0.42

0.025

0.022

0.020

0.40

0.041

0.028

0.019

0.69

0.063

0.033

0.034

0.52

0.038

0.018

0.017

(xitkit
11)

Amount
due to
human
capital,
(1 - oLit)hil
(2)
0.003
(0.21)
0.007
(0.14)
0.006
10.14)
0.002

Amount
due to
TFP, air

(3)
0.004
(0.29)
0.012
(0.24)

0.002
(0.05)
0.018
(0.37)

0.020
(0.43)
0.032
10.61)
0.016
(0.64)
0.011
(0.55)

(0.04)
0.004
(0.09)
0.001
(0.02)
-0.007
(-0.28)
0.004
(-0.2)

0.022
(0.47)
0.019
(0.37)
0.016
(0.64)

0.013
(0.65)

0.013
(0.68)
0.006
10.18)
0.002
(0.12)

0.002
(0.11)
0.006
10.18)
0.000
(0.00)

0.004
(0.21)
0.022
(0.65)
0.015
(0.88)

Notes: (1) Capital's share times growth rate of quality adjusted capital per worker; (2) labor's share times
growth rate of human capital per worker; (3) Solow residual. Figures in parentheses are shares of output growth.

observers attributed this remarkable growth r e c o r d to technical i m p r o v e m e n t s , driven
perhaps by g o v e r n m e n t "industrial p o l i c i e s " that e n c o u r a g e d the growth o f certain industries and technologies. B y carefully m e a s u r i n g the quantities o f physical and h u m a n
capital in these countries,_ Y o u n g concludes that their rapid growth is due to input accum u l a t i o n (and utilization, in the case o f labor), w h i l e T F P growth was not unusually h i g h

by w o r l d standards. In fact, for Singapore, Y o u n g finds that T F P growth contributed
essentially nothing to i n c o m e growth over this period. All of the growth in output can
be a c c o u n t e d for by changes in the quantity and quality of capital, sharply i n c r e a s e d labor
force participation, and increased years o f schooling o f workers. The implication is that the


Ch. 44: LaborMarkets and Economic Growth

2957

remarkable growth record of these economies is unlikely to be sustainable, since input
utilization cannot increase indefinitely. 14
The growth accounting literature suggests an important role for the labor market in
economic growth. Consider Young's results for Korea. Beginning in 1966, growth in labor
input (including quality) "contributed" a breathtaking 4.4% per year, for a 25-year period,
to growth in aggregate output. As shown in Table 1, almost all of this effect was due to
increased labor utilization rather than to any increase in measured human capital per
worker. Over this period, the Korean non-agricultural labor force grew at an annual rate
of 5.4% per year (!), while population grew at only 1.6%. The difference reflects increased
labor force participation and a wholesale migration out of agriculture. A growth accounting measure of human capital per Korean worker grew at an annual average rate of
0.007/(1 - 0.32) = 1% per year, faster than for any country in the table save Singapore.
This increase was driven by a massive investment in public education that reduced the
share of workers with a primary education from over 60% in 1970 to less than 30% by
1990 (Kim and Topel, 1995). Yet rising human capital per worker was swamped by the
concomitant rise in the capital/labor ratio, which "accounted" for 61% of the increase in
Korean labor productivity. By this method, human capital growth accounted for only 14%
of the growth in output per worker. Indeed, for the countries in Table 1, human capital
never accounts for the major portion of economic growth. Does this mean that human
capital is not so important after all?

3.3. Limitations of growth accounting
The obvious answer is "no". Growth accounting is mainly descriptive, treating human and
physical capital in virtually identical ways. It has nothing to say about how or why factor
accumulation took place, or whether human capital accumulation is essential for growth.
Three limitations of this approach seem particularly relevant.
The first point has to do with what it means to measure a factor' s contribution to growth.
Consider again the estimate that human capital contributed 0.7 percentage points per year
to Korea' s productivity growth. This figure is simply an average of marginal contributions
of labor, along the actual path of physical and human capital accumulation. It does not say
that output per worker would have grown at 0.7% had capital remained fixed. Even so, it
may vastly understate the importance of human capital to the growth process. Suppose for
the sake of argument that a Lucas-Uzawa style model is an appropriate description. Their
theory is that human capital is the whole story. In the steady state, the proportional rate of
growth of physical capital is equal to the proportional rate of growth of human capital,
given by ci = B(1 - u*) - 6 (see Eq. (4)). The ratio of physical to human capital is
constant in the steady state, so that output per capita also grows at rate d. Growth is driven
~4In Table 1, the differences between the growth rates of GDP and GDP per worker are largest for the four
"Asian Tigers". Much of GDP growth in these economieswas accomplishedby increased labor force participation.


2958

R. Topel

by human capital accumulation, but a growth accounting exercise attributes the product of
capital's share and a to capital.
More generally, the quantity and type of physical capital investments that actually
occurred may depend on the quality of human capital that is available to work with it.
Without large investments in human capital, particularly in education, Korea may not have
adopted the existing technologies that fueled its growth. In this sense, investments in

human capital, such as education, may be essential to the growth process. Then growth
accounting is uninformative about the importance of human capital accumulation.
A second limitation is that changes in human capital are poorly measured. A virtue of
studying developing nations is that changes in the amount of human capital employed in
production may be well measured by changes in observable quantities like the number of
workers and their years of schooling and experience. Think of the typical Korean worker
who, let's say, now enters the labor market with a secondary instead of a primary education. The things he learned in those additional years are "common knowledge," like
arithmetic and grammar, well inside the frontier of ideas. In this case, the change in the
quantity of human capital per worker may be well approximated by increased years of
schooling. Now think of workers in a developed economy, like the US, where average
years of schooling has changed by less. The additional knowledge that workers bring to the
labor market largely consists of new knowledge, like how to use a computer. Their human
capital is greater, but no observable measure picks this up. Conceptually, the contribution
of human capital is the same in both economies, but in Korea the increase in human capital
is more accurately measured by observables. In the US, where observable quantities did
not change by much, more of the contribution of human capital is attributed to "total factor
productivity".
More broadly, any measure of human capital for growth accounting is based on changes
in observable quantities - such as education or experience - and the relative prices that
those observables command. If school quality improves at all levels, or if post-schooling
investment in human capital becomes more widespread or productive, growth accounting
measures are unlikely to capture the change.
The third limitation of growth accounting is that it is silent about how the labor market
actually operates during economic growth. In rapidly growing Asian (and other) economies, we know that industrial expansion was fueled by migration of workers from agriculture. We also know that public investments in education sharply raised average
schooling levels. What market forces supported this? A market-driven scenario is that
the relative price of skilled labor, needed for industrial production, was initially quite high
because skilled labor was scarce. Expansion of public education increased opportunities to
invest in skill~ and wage inequality provided the incentive for young workers to do so. As
successive cohorts of yofing workers acquired more schooling, and migrated to industrial
employment, the relative price of skilled labor fell, which further fueled growth. This

description of events gives a prominent role to a smoothly operating labor market, with
market-determined wages, and fairly elastic responses of investment in education, in
supporting growth. Indeed, in this scenario, educational opportunities start the ball rolling.