February 22, 2013 -- Version 3.0 (with Hsieh, Hurst, and Klenow)
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In 1960, 94 percent of doctors and lawyers were white men. By 2008, the fraction was just 62 percent. Similar changes in other highly-skilled occupations have occurred throughout the U.S. economy during the last fifty years. Given that innate talent for these professions is unlikely to differ across groups, the occupational distribution in 1960 suggests that a substantial pool of innately talented black men, black women, and white women were not pursuing their comparative advantage. This paper measures the macroeconomic consequences of the remarkable convergence in the occupational distribution between 1960 and 2008 through the prism of a Roy model. We find that 15 to 20 percent of growth in aggregate output per worker over this period may be explained by the improved allocation of talent.
History of Revisions:
February 24, 2011 -- Version 2.0
Prepared for the 10th World Congress of the
Econometric Society
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One of the most important developments in the growth literature of the
last decade is the enhanced appreciation of the role that the
misallocation of resources plays in helping us understand income
differences across countries. Misallocation at the micro level
typically reduces total factor productivity at the macro level.
Quantifying these effects is leading growth researchers in new
directions, two examples being the extensive use of firm-level data
and the exploration of input-output tables, and promises to yield new
insights on why some countries are so much richer than others.
History of Revisions:
February 16, 2011 -- Version 3.0 (with Pete Klenow)
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We propose a simple summary statistic for a nation's flow of welfare,
measured as a consumption equivalent, and compute its level and growth
rate for a broad set of countries. This welfare metric combines data
on consumption, leisure, inequality, and mortality. Although it is
highly correlated with per capita GDP, deviations are often
economically significant: Western Europe looks considerably closer to
U.S. living standards, emerging Asia has not caught up as much, and
many African and Latin American countries appear farther behind. Each
of the four components we introduce plays an important role in
accounting for these differences.
History of Revisions:
June 17, 2009 -- Version 2.0 (with Paul Romer)
American Economic Journal: Macroeconomics, January 2010, Vol. 2 (1), pp. 224-245.
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AEJMacro-20090057-Replication.zip contains the matlab programs for generating all the graphs in the paper. After unzipping the file, please see README.txt for more information. tfpdata2000.txt contains the TFP data for 2000 used in Figure 4.
In 1961, Nicholas Kaldor used his list of six ``stylized'' facts both to
summarize the patterns that economists had discovered in national income
accounts and to shape the growth models that they were developing to
explain them. Redoing this exercise today, nearly fifty years later,
shows how much progress we have made. In contrast to Kaldor's facts,
which revolved around a single state variable, physical capital, our six
updated facts force consideration of four far more interesting
variables: ideas, institutions, population, and human capital. Dynamic
models have uncovered subtle interactions between these variables and
generated important insights about such big questions as: Why has growth
accelerated? Why are there gains from trade?
Prepared for a session at the January 2009 annual meeting of
the American Economic Assocation on ``The secrets of growth: What
have we learned from research in the last 25 years?''
April 5, 2013 -- Version 3.0
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Data: NSF-AllYears-IndustrialRND.xls
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STAN-HealthRND.xls
Some technologies save lives --- new vaccines, new surgical techniques,
safer highways. Others threaten lives --- pollution, nuclear accidents,
global warming, the rapid global transmission of disease, and
bioengineered viruses. How is growth theory altered when technologies
involve life and death instead of just higher consumption? This paper
shows that taking life into account has first-order consequences. Under
standard preferences, the value of life may rise faster than
consumption, leading society to value safety over consumption growth. As
a result, the optimal rate of consumption growth may be substantially
lower than what is feasible, in some cases falling all the way to zero.
History of Revisions:
American Economic Journal: Macroeconomics April 2011, Vol. 3 (2), pp. 1-28.
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Per capita income in the richest countries of the world exceeds that in
the poorest countries by more than a factor of 50. What explains these
enormous differences? This paper returns to two old ideas in development
economics and proposes that linkages and complementarity are a key part
of the explanation. First, linkages between firms through intermediate
goods deliver a multiplier similar to the one associated with capital
accumulation in a neoclassical growth model. Because the intermediate
goods share of gross output is about 1/2, this multiplier is
substantial. Second, just as a chain is only as strong as its weakest
link, problems at any point in a production chain can reduce output
substantially if inputs enter production in a complementary fashion.
This paper builds a model to quantify these forces and shows that they
substantially amplify distortions to the allocation of resources,
bringing us closer to understanding large income differences across
countries.
History of Revisions:
March 29, 2006 (with Alan Garber and Paul Romer)
Forum for Health Economics & Policy, 2006, Forum: Biomedical Research and the Economy: Article 4.
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This paper studies the interactions between health insurance and the
incentives for innovation. Although we focus on pharmaceutical
innovation, our discussion applies to other industries producing novel
technologies for sale in markets with subsidized demand. Standard
results in the growth and productivity literatures suggest that firms
in many industries may possess inadequate incentives to innovate.
Standard results in the health literature suggest that health
insurance leads to the overutilization of health care. Our study of
innovation in the pharmaceutical industry emphasizes the interaction
of these incentives. Because of the large subsidies to demand from
health insurance, limits on the lifetime of patents and possibly
limits on monopoly pricing may be necessary to ensure that
pharmaceutical companies do not possess excess incentives for
innovation.
March 29, 2007 -- Version 5.01 (with Dean Scrimgeour)
Review of Economics and Statistics, February 2008, Vol. 90 (1), pp. 180-182.
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This note revisits the proof of the Steady-State Growth Theorem, first
given by Uzawa in 1961. We provide a clear statement of the theorem,
discuss intuition for why it holds, and present a new, elegant proof
due to Schlicht (2006).
History of Revisions:
(with Robert E. Hall)
Quarterly Journal of Economics, February 2007, Vol. 122 (1), pp. 39-72.
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Over the past half century, Americans spent a rising share of total
economic resources on health and enjoyed substantially longer lives as
a result. Debate on health policy often focuses on limiting the growth
of health spending. We investigate an issue central to this debate: Is
the growth of health spending a rational response to changing economic
conditions---notably the growth of income per person? We develop a
model based on standard economic assumptions and argue that this is
indeed the case. Standard preferences---of the kind used widely in
economics to study consumption, asset pricing, and labor
supply---imply that health spending is a superior good with an income
elasticity well above one. As people get richer and consumption rises,
the marginal utility of consumption falls rapidly. Spending on health
to extend life allows individuals to purchase additional periods of
utility. The marginal utility of life extension does not decline. As a
result, the optimal composition of total spending shifts toward
health, and the health share grows along with income. In projections
based on the quantitative analysis of our model, the optimal health
share of spending seems likely to exceed 30 percent by the middle of
the century.
History of Revisions:
Quarterly Journal of Economics, May 2005, Vol. 120 (2), pp. 517-549.
Download the paper in Acrobat PDF format. This paper largely replaces "Growth, Capital Shares, and a New Perspective on Production Functions," although the material on capital's share in that paper remains useful.
This paper views the standard production function in macroeconomics as a
reduced form and derives its properties from microfoundations. The
shape of this production function is governed by the distribution of
ideas. If that distribution is Pareto, then two results obtain: the
global production function is Cobb-Douglas, and technical change in the
long run is labor-augmenting. Kortum (1997) showed that Pareto
distributions are necessary if search-based idea models are to exhibit
steady-state growth. Here we show that this same assumption delivers
the additional results about the shape of the production function and
the direction of technical change.
June 12, 2003 -- Version 1.0
Download the paper in Acrobat PDF format. This paper has been replaced by "The Shape of Production Functions and the Direction of Technical Change" (see above). This paper may still be of interest because of its evidence on capital shares.
Standard growth theory implies that steady-state growth in the presence
of exponential declines in the prices of computers and other capital
equipment requires a Cobb-Douglas production function. Conventional
wisdom holds that capital shares are relatively constant, so that the
Cobb-Douglas approach might be a good way to model growth.
Unfortunately, this conventional wisdom is misguided. Capital shares
exhibit substantial trends and fluctuations in many countries and in
many industries. Taken together, these facts represent a puzzle for
growth theory. This paper resolves the puzzle by (a) presenting a
production function that exhibits a short-run elasticity of substitution
between capital and labor that is less than one and a long-run
elasticity that is equal to one, and (b) providing microfoundations for
why the production function might take the Cobb-Douglas form in the long
run.
in P. Aghion and S. Durlauf (eds.) Handbook of Economic Growth (Elsevier, 2005) Volume 1B, pp. 1063-1111.
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Acrobat PDF format.
Web
version with html links to many references (scroll down).
Ideas are different from nearly all other economic goods in that they
are nonrivalrous. This nonrivalry implies that production possibilities
are likely to be characterized by increasing returns to scale, an
insight that has profound implications for economic growth. The purpose
of this chapter is to explore these implications.
May 5, 2004 -- Version 3.0
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As is well-known, aggregate health expenditures as a share of GDP have
risen in the United States from about 5 percent in 1960 to nearly 15
percent in recent years. Why? This paper presents a model based on an
explanation that has received increased attention in the last decade:
technological progress. Medical advances allow diseases to be cured
today, at a cost, that could not be cured at any price in the past.
When this technological progress is combined with a Medicare-like
transfer program to pay the health expenses of the elderly, the model is
able to reproduce the basic facts of recent U.S. experience, including
the large increase in the health expenditure share, a rise in life
expectancy, and an increase in the size of health-related transfer
payments as a share of GDP.
Advances in Macroeconomics (2001) Volume 1, Number 2, Article 1.
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This paper studies a growth model that is able to match several key
facts of economic history. For thousands of years, the average standard
of living seems to have risen very little, despite increases in the
level of technology and large increases in the level of the population.
Then, after thousands of years of little change, the level of per capita
consumption increased dramatically in less than two centuries.
Quantitative analysis of the model highlights two factors central to
understanding this history. The first is a virtuous circle: more people
produce more ideas, which in turn makes additional population growth
possible. The second is an improvement in institutions that promote
innovation, such as property rights: the simulated economy indicates
that arguably the single most important factor in the transition to
modern growth has been the increase in the fraction of output paid to
compensate inventors for the fruits of their labor.
American Economic Review, March 2002, Vol. 92 (1), pp. 220-239.
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At least since 1950, the U.S. economy has benefited from increases in both educational attainment and research intensity. Such changes suggest, contrary to the conventional view, that the U.S. economy is far from its steady-state balanced growth path. This paper develops a model in which these facts are reconciled with the stability of average U.S. growth rates over the last century. In the model, long-run growth is driven by the worldwide discovery of new ideas, which in turn is tied to world population growth. Nevertheless, a constant growth path can temporarily be maintained at a rate greater than the long-run rate provided research intensity and educational attainment rise steadily over time. Growth accounting with this model reveals that 30 percent of U.S. growth between 1950 and 1993 is attributable to the rise in educational attainment, 50 percent is attributable to the rise in worldwide research intensity, and only about 10 to 20 percent is due to population growth in the idea-producing countries.
This is a substantially revised version of a previous paper, "The Upcoming Slowdown in U.S. Economic Growth."
American Economic Review Papers and Proceedings, May 1999, Vol. 89, pp.139-144.
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The property that ideas are nonrivalrous leads to a tight link between
idea-based growth models and increasing returns to scale. In
particular, changes in the size of an economy's population generally
affect either the long-run growth rate or the long-run level of income
in such models. This paper provides a partial review of the expanding
literature on idea-based models and scale effects. It presents simple
versions of various recent idea-based growth models and analyzes their
implications for the relationship between scale and growth.
in Aghion, Frydman, Stiglitz, and Woodford (eds.) Knowledge, Information, and Expectations in Modern Macroeconomics: In Honor of Edmund S. Phelps (Princeton University Press) 2003.
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All models of sustained growth are linear in some sense, and the
endogenous growth literature can be read as the search for the
appropriate linear differential equation. Linearity is a ``crucial''
assumption, in the sense used by Solow (1956), and it therefore seems
reasonable to ask that this assumption have an intuitive and compelling
justification. This paper proposes that such a justification can be
found if the linearity is located in an endogenous fertility equation.
It is a fact of nature that the law of motion for population is linear:
people reproduce in proportion to their number. By itself, this
linearity will not generate per capita growth, but it is nevertheless
the first key ingredient of such a model. The second key ingredient is
increasing returns to scale. A justification for increasing returns,
rather than linearity in the equation for technological progress, is the
fundamental insight of the idea-based growth literature according to
this view. Endogenous fertility together with increasing returns
generates endogenous growth.
Journal of Political Economy, August 1995, Vol. 103, pp. 759-784.
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This paper argues that the "scale effects" prediction of many recent
R&D-based models of growth is inconsistent with the times-series
evidence from industrialized economies. A modified version of the Romer
model that is consistent with this evidence is proposed, but the
extended model alters a key implication usually found in endogenous
growth theory. Although growth in the extended model is generated
endogenously through R&D, the long-run growth rate depends only on
parameters that are usually taken to be exogenous, including the rate of
population growth.
Quarterly Journal of Economics, May 1995, Vol. 110, pp. 495-525.
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According to endogenous growth theory, permanent changes in certain
policy variables have permanent effects on the rate of economic growth.
Empirically, however, U.S. growth rates exhibit no large persistent
changes. Therefore, the determinants of long-run growth highlighted by
a specific growth model must similarly exhibit no large persistent
changes, or the persisten movement in these variables must be
offsetting. Otherwise, the growth model is inconsistent with times
series evidence. This paper argues that many AK-style models and
R&D-based models of endogenous growth are rejected by this criterion.
The rejection of the R&D-based models is particularly strong.
Quarterly Journal of Economics, February 1999, Vol. 114, pp. 83-116 (with Robert E. Hall).
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Output per worker varies enormously across countries. Why? On an accounting basis, our analysis shows that differences in physical capital and educational attainment can only partially explain the variation in output per worker --- we find a large amount of variation in the level of the Solow residual across countries. At a deeper level, we document that the differences in capital accumulation, productivity, and therefore output per worker are driven by differences in institutions and government policies, which we call social infrastructure. We treat social infrastructure as endogenous, determined historically by location and other factors captured in part by language.
A previous version of this paper, with a different emphasis, was
circulated under the title "The Productivity of Nations" (NBER Working
Paper No. 5812). Version 3.0 of this paper also had a different title,
"Fundamental Determinants of Output per Worker across Countries."
Journal of Economic Perspectives, Summer 1997, Vol. 11, pp. 19-36.
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The post-World War II period has seen substantial changes in the
distribution of GDP per worker around the world. In the upper half of
the distribution, a number of countries have exhibited large increases
in income relative to the richest countries. In the bottom half, several
countries have seen incomes fall relative to the richest countries. The
net result of these changes is a movement in the shape of the world
income distribution from something that looks like a normal distribution
in 1960 to a bi-modal ``twin-peaks'' distribution in 1988. Projecting
these changes into the future suggests a number of interesting findings.
First, it seems likely that the U.S. will lose its position as
the country with the highest level of GDP per worker. Second, growth
miracles have been more common in recent decades than growth disasters.
If these dynamics continue, the future income distribution will involve
far more ``rich'' countries and far fewer ``poor'' countries than
currently observed.
Journal of Economic Growth, July 1997, Vol. 2, pp. 131-153.
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The recent literature on convergence has departed from the earlier
literature by focusing on the shape of the production function and the
rate at which an economy converges to its own steady state. This paper
uses advances from the recent literature to look back at the question
that originally motivated the convergence literature: what will the
steady state distribution of per capita income look like? Several
results are highlighted by the analysis. First, ignoring changes in
technology levels over time, the long-run distribution is likely to be
broadly similar to the 1990 distribution; the main exception is at the
top of the distribution, where a number of NICs and industrialized
countries continue to catch up to or even overtake the U.S. Second,
differences in total factor productivity levels across economies are
substantial---nearly the same magnitude as differences in per capita
incomes. Third, TFP convergence would result in substantial
changes in the income distribution. Finally, there is little reason to
expect that the U.S. will maintain its position as world leader in terms
of output per worker.
American Economic Review Papers and Proceedings, May 1997, Vol. 87, pp.173-177 (with Robert E. Hall).
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This paper was prepared for the American Economic Association meetings
in New Orleans, January 5, 1997, for a session organized by Andrew
Warner on "What have we learned from recent empirical growth research?"
The paper examines some of our recent work on levels of economic
activity (instead of growth rates) across countries, and discusses how
this work relates to empirical growth research.
Journal of Monetary Economics, December 1994, Vol. 34, pp. 359-382.
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This paper examines empirically the relationship between the relative
price of capital and the rate of economic growth. In the results,
machinery appears to be the most important component of capital: when
the relative price of machinery and the relative price of nonmachinery
are included in a Barro (1991) growth regression, a strong negative
relationship between growth and the machinery price emerges while the
nonmachinery price enters insignificantly. These results indicate that
the tax treatment of machinery is an important policy instrument with
respect to long-term growth and welfare.
Journal of Economic Growth, March 2000, Vol. 5, No. 1, pp. 65-85 (with John Williams).
Download the paper version in Acrobat PDF format.
Research and development (R&D) is a key determinant of long run
productivity and welfare. A central issue is whether a decentralized
economy undertakes too little or too much R&D. We develop an
endogenous growth model that incorporates parametrically four important
distortions to R&D: the surplus appropriability problem, knowledge
spillovers, creative destruction, and duplication externalities. We
show that our model is consistent with the available evidence on R&D,
growth, and markups. Calibrating the model to micro and macro data, we
find that the decentralized economy typically underinvests in R&D
relative to what is socially optimal. The only exceptions to this
conclusion occur when the duplication externality is strong and the
equilibrium real interest rate is simultaneously high. These results
are robust to reasonable variations in model parameters.
Quarterly Journal of Economics, November 1998, Vol. 113, pp. 1119-1135 (with John Williams).
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Is there too much or too little private research and development (R&D)?
A large empirical literature reports estimates of the rate of return to
R&D ranging from 30% to over 100%, supporting the notion that there
is too little private investment in research. However, this conclusion
is challenged by the new growth theory, which emphasizes a richer
description of the connection between R&D and productivity. In this
paper we bridge the gap between the theoretical and empirical
literatures. Using the framework of an R&D-based growth model, we
derive analytically the relationship between the social rate of return
to R&D and the coefficient estimates of the empirical literature.
Somewhat surprisingly, we show that these estimates represent a lower
bound on the true social rate of return. Furthermore, our analytic
framework provides a direct mapping from the rate of return to the
degree of underinvestment in research. Using a conservative estimate of
the rate of return to R&D of about 30%, optimal R&D investment is at
least four times larger than actual investment.
December 7, 2000 (with Andrew Bernard).
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This is a brief reply to an interesting comment by Anders Sorensen on
Bernard and Jones (1996) "Comparing Apples to Oranges: Productivity
Convergence and Measurement Across Industries and Countries"
(AER 1996). Sorensen's
comment, which is forthcoming in the AER, can be downloaded
here.
American Economic Review, December 1996, Vol. 86, pp. 1216-1238 (with Andrew Bernard).
View the paper in JStor or download the JStor Acrobat PDF file.
This paper examines the role of sectors in aggregate convergence
for 14 OECD countries from 1970-1987. The major finding is that
manufacturing shows little evidence of either labor productivity or
multifactor productivity convergence while other sectors, especially
services, are driving the aggregate convergence result. To determine
the robustness of the convergence results, the paper introduces a new
measure of multi-factor productivity which avoids many problems
inherent to traditional TFP measures when comparing productivity
levels. The lack of convergence in manufacturing is robust to the
method of calculating multi-factor productivity.
Economic Journal, July 1996, Vol. 106, pp. 1037-1044 (with Andrew Bernard).
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The empirical convergence literature envisions a world in which the
presence or lack of convergence is a function of capital accumulation.
This focus ignores a long tradition among economic historians and growth
theorists which emphasizes technology and the potential for technology
transfer. We suggest here that this neglect is an important oversight:
simple models which incorporate technology transfer provide a richer
framework for thinking about convergence. Empirically, differences in
technologies across countries and sectors appear to match differences in labor
productivity and to exhibit interesting changes over time.
Empirical Economics, March 1996, Vol. 21, pp. 113-135 (with Andrew Bernard).
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We examine the sources of aggregate labor productivity movements and
convergence in the U.S. states from 1963 to 1989. Productivity levels
vary widely across sectors and across states, as do sectoral output and
employment shares. The main finding is the diverse performance of
sectors regarding convergence. Using both cross-section and time series
methods, we find convergence in labor productivity for both
manufacturing and mining. However, we find that convergence does not
hold for all sectors over the period. Decomposing aggregate convergence
into industry productivity gains and changing sectoral shares of output,
we find the manufacturing sector to be responsible for the bulk of
cross-state convergence.
Stanford mimeo, January 2000
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This brief note presents the closed-form solution of the Solow (1956)
model when the production function is Cobb-Douglas.
NBER Macroeconomics Annual 2000 (MIT Press).
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NBER Macroeconomics Annual 1997 (MIT Press).
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in Edmund S. Phelps (ed.) conference volume, forthcoming.
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This paper presents a simple model of human capital, ideas, and economic growth that integrates contributions from several different strands of the growth literature. The model generates a regression specification that is very similar to that employed by Mankiw, Romer, and Weil (1992), but the economics underlying the specification is very different. In particular, the model emphasizes the importance of ideas and technology transfer in addition to capital accumulation. The model suggests that cross-country data on educational attainment is most appropriately interpreted from the macro standpoint as something like an investment rate rather than as a capital stock. Finally, this setup helps to resolve a puzzle recently highlighted by the empirical growth literature concerning human capital and economic growth by following Bils and Klenow (1996) in emphasizing a relationship between wages and educational attainment that is consistent with Mincerian wage regressions.
Prepared for VIII Villa Mondragone International Economic Seminar in
Rome on June 25-27, 1996.