## Research Papers by Charles I. Jones

### Taxing Top Incomes in a World of Ideas

September 2018 -- Version 0.5 (Preliminary)

Paper (PDF)

This paper considers the taxation of top incomes when the following conditions apply: (i) new ideas drive economic growth, (ii) the reward for creating a successful innovation is a top income, and (iii) innovation cannot be perfectly targeted by a separate research subsidy --- think about the business methods of Walmart, the creation of Uber, or the idea'' of Amazon.com. These conditions lead to a new term in the Saez (2001) formula for the optimal top tax rate: by slowing the creation of the new ideas that drive aggregate GDP, top income taxation reduces everyone's income, not just the income at the top. When the creation of ideas is the ultimate source of economic growth, this force sharply constrains both revenue-maximizing and welfare-maximizing top tax rates. For example, for extreme parameter values, maximizing the welfare of the middle class requires a {\it negative} top tax rate: the higher income that results from the subsidy to innovation more than makes up for the lost redistribution. More generally, the calibrated model suggests that incorporating ideas and economic growth cuts the optimal top marginal tax rate substantially relative to the basic Saez calculation.

History of Revisions:

• September 2018 (Version 0.4): First public version.

### Nonrivalry and the Economics of Data

(with Chris Tonetti)
July 2018 -- Version 0.6

Paper (PDF) | Slides
Research summary: Stanford GSB Insights

Data is nonrival: a person's location history, medical records, and driving data can be used by any number of firms simultaneously without being depleted. Nonrivalry leads to increasing returns and implies an important role for market structure and property rights. Who should own data? What restrictions should apply to the use of data? We show that in equilibrium, firms may not adequately respect the privacy of consumers. But nonrivalry leads to other consequences that are less obvious. Because of nonrivalry, there may be large social gains to sharing data across firms, even in the presence of privacy considerations. Fearing creative destruction, firms may choose to hoard data they own, leading to the inefficient use of nonrival data. Instead, giving the data property rights to consumers can generate allocations that are close to optimal. Consumers appropriately balance their concerns for privacy against the economic gains that come from selling data to all interested parties.

History of Revisions:

• July 2018 (Version 0.5): First public version.

### Artificial Intelligence and Economic Growth

(with Philippe Aghion and Ben Jones)
October 2017 -- Version 1.0

Paper (PDF) | Slides

This paper examines the potential impact of artificial intelligence (A.I.) on economic growth. We model A.I. as the latest form of automation, a broader process dating back more than 200 years. Electricity, internal combustion engines, and semiconductors facilitated automation in the last century, but A.I. now seems poised to automate many tasks once thought to be out of reach, from driving cars to making medical recommendations and beyond. How will this affect economic growth and the division of income between labor and capital? What about the potential emergence of singularities'' and superintelligence," concepts that animate many discussions in the machine intelligence community? How will the linkages between A.I. and growth be mediated by firm-level considerations, including organization and market structure? The goal throughout is to refine a set of critical questions about A.I. and economic growth and to contribute to shaping an agenda for the field. One theme that emerges is based on Baumol's cost disease'' insight: growth may be constrained not by what we are good at but rather by what is essential and yet hard to improve.

History of Revisions:

• February 2017 (Version 1.0): First main version.

### Are Ideas Getting Harder to Find?

(with Nick Bloom, John Van Reenen, and Michael Webb)
March 2018 -- Version 2.0

In many growth models, economic growth arises from people creating ideas, and the long-run growth rate is the product of two terms: the effective number of researchers and their research productivity. We present a wide range of evidence from various industries, products, and firms showing that research effort is rising substantially while research productivity is declining sharply. A good example is Moore's Law. The number of researchers required today to achieve the famous doubling every two years of the density of computer chips is more than 18 times larger than the number required in the early 1970s. Across a broad range of case studies at various levels of (dis)aggregation, we find that ideas --- and in particular the exponential growth they imply --- are getting harder and harder to find. Exponential growth results from the large increases in research effort that offset its declining productivity.

History of Revisions:

• March 2018 (Version 2.0): Added semiconductor TFP growth to Table 1 as an alternative output measure. Added agricultural TFP growth to Section 5. Added subsection 8.2 on "selection and measurement" as well as a paragraph on this at the end of the introduction. Various edits and additional citations to improve the exposition.
• August 2017 (Version 1.0): First main version. Includes data appendix and replication files (see above).
• February 2017 (Version 0.7): Preliminary and incomplete.

### The Facts of Economic Growth

Handbook of Macroeconomics, 2016, Vol. 2A, pp. 3-69.

Why are people in the richest countries of the world so much richer today than 100 years ago? And why are some countries so much richer than others? Questions such as these define the field of economic growth. This paper documents the facts that underlie these questions. How much richer are we today than 100 years ago, and how large are the income gaps between countries? The purpose of the paper is to provide an encyclopedia of the fundamental facts of economic growth upon which our theories are built, gathering them together in one place and updating them with the latest available data.

### A Schumpeterian Model of Top Income Inequality

(with Jihee Kim)
Journal of Political Economy, October 2018, Volume 126 (5), pp. 1785-1826 (lead article)

Paper (PDF) | JPE | Slides | Replication Files

Top income inequality rose sharply in the United States over the last 40 years but increased only slightly in economies like France and Japan. Why? This paper explores a model in which heterogeneous entrepreneurs, broadly interpreted, exert effort to generate exponential growth in their incomes. On its own, this force leads to rising inequality. Creative destruction by outside innovators restrains this expansion and induces top incomes to obey a Pareto distribution. The development of the world wide web and a reduction in top tax rates are examples of changes that raise the growth rate of entrepreneurial incomes and therefore increase Pareto inequality. In contrast, policies that stimulate creative destruction reduce top inequality. Examples include research subsidies or a decline in the extent to which incumbent firms can block new innovation. Differences in these considerations across countries and over time may explain the varied patterns of top income inequality that we see in the data.

History of Revisions:

• February 2017 (Version 3.0): (i) Section 7 now contains an analysis of transition dynamics, showing that transitions are relatively slow and "level effects" in GDP can be important, leading to a positive correlation between growth and inequality over, e.g. a 20 year period. (ii) Incorporates Guvenen, Karahan, Ozkan, and Song's (2016) rich data on wages and salaries since 1981. (iii) Highlights entrepreneurial income from the IRS public use panel, 1979-1990.
• July 2015 (Version 2.0): Updated to include the Luttmer (2011) and Gabaix, Lasry, Lions, and Moll (2015) insight of heterogeneous mean growth rates. Empirical work focuses on upper tail of the growth rates for top earners and combines IRS and Guvenen et al Social Security data while we wait for more comparable data, hopefully in the near future.
• October 2014 (Version 1.0): First major version.

### Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality

Journal of Economic Perspectives, Winter 2015, Volume 29 (1), pp. 29-46.

"Simple Models of Top Income and Wealth Inequality" -- Contains the model details.

Since the early 2000s, research by Thomas Piketty, Emmanuel Saez, and their coathors has revolutionized our understanding of income and wealth inequality. In this paper, I highlight some of the key empirical facts from this research and comment on how they relate to macroeconomics and to economic theory more generally. One of the key links between data and theory is the Pareto distribution. The paper describes simple mechanisms that give rise to Pareto distributions for income and wealth and considers the economic forces that influence top inequality over time and across countries. For example, it is in this context that the role of the famous $r-g$ expression is best understood.

### The Future of U.S. Economic Growth

(with John Fernald)
American Economic Review Papers and Proceedings 104(5): 44-49, May 2014

What do modern growth theory and empirical evidence suggest about the future of U.S. economic growth? Rising educational attainment and research intensity reveal that up to 75% of growth during the last 50 years may have been due to transition dynamics. Moreover, because of the nonrivalry of ideas, long-run future growth in income per person is arguably tied to population growth, which seems to be slowing around the world. Both of these channels suggest substantially slower U.S. economic growth at some point in the future. Counterbalancing these concerns, at least for awhile, is the rise of China, India, and other emerging economies, which likely implies rapid growth in world researchers for at least the next several decades. Finally, and more speculatively, the shape of the idea production function introduces a fundamental uncertainty into the future of growth. For example, the possibility that artificial intelligence will allow machines to replace workers to some extent could lead to higher growth in the future.

Notes:

• There is a typo in footnote 2: A should be equal to (beta/g*R)^gamma.

### The Allocation of Talent and U.S. Economic Growth

April 2018 -- Version 5.0 (with Hsieh, Hurst, and Klenow)

Paper (PDF) | Slides (old) | Online Appendix | Replication Instructions | Replication Files | NYT
(More info on the latex style file used to format this paper.)

In 1960, 94 percent of doctors and lawyers were white men. By 2010, 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. We examine the effect on aggregate productivity of the remarkable convergence in the occupational distribution between 1960 and 2010 through the prism of a Roy model. About one-quarter of growth in aggregate output per person over this period can be explained by the improved allocation of talent.

History of Revisions:

• April 2018 (Version 5.0): Major revision. Preserves life cycle setup but allows people to make decisions only when they are young, which simplifies everything (especially the estimation) considerably.
• August 2016 (Version 4.0): Major revision. Model and empirics now consider a life cycle where the human capital barrier is essentially a "cohort effect" and the labor market barrier is a "time effect" common to all cohorts in a given year.
• February 2013 (Version 3.0): Updated to include correlation of talent across occupations for each person and various robustness checks.
• December 2012 (Version 2.0): Cleaned up for NBER working paper and first journal submission.
• October 2012 (Version 1.0): Finally a complete draft!
• February 2012 (Version 0.8): Preliminary and incomplete.

### Misallocation, Economic Growth, and Input-Output Economics

in D. Acemoglu, M. Arellano, and E. Dekel, Advances in Economics and Econometrics, Tenth World Congress, Volume II, Cambridge University Press, 2013

Published PDF | Working Paper (color figures) | Slides
(More info on the latex style file used to format this paper.)

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 2011 (Version 2.0): Added references, minor changes.
• January 2011 (Version 1.0): Added the proofs to the paper and made various minor changes.
• July 2010 (Version 0.5): Updated and reshaped for the Econometric Society presenatation. Previous title was "Input-Output Multipliers, General Purpose Technologies, and Economic Development."
• September 2007 (Version 0.26): Very preliminary and incomplete. If you only read papers once, do not read this version.

### Beyond GDP? Welfare across Countries and Time

February 10, 2016 -- Version 5.0 (with Pete Klenow)
American Economic Review, September 2016, Vol. 106 (9), pp. 2426-2457.

Paper (PDF) | Slides (Full seminar version) | BeyondGDP500.xls | Data Appendix
Replication Instructions | Matlab Replication Files | Stata Replication Files
Research summaries: WSJ | AEA Research Highlight | Microeconomic Insights
(More info on the latex style file used to format this paper.)

We propose a summary statistic for the economic well-being of people in a country. Our measure incorporates consumption, leisure, mortality, and inequality, first for a narrow set of countries using detailed micro data, and then more broadly using multi-country data sets. While welfare is highly correlated with per capita GDP, deviations are often large. Western Europe looks considerably closer to the U.S., emerging Asia has not caught up as much, and many developing countries are further behind. Each component we introduce plays a significant role in accounting for these differences, with mortality being most important.

History of Revisions:

• February 2016 (Version 5.0): Minor revisions.
• April 2015 (Version 4.0): Main analysis is based on micro data (household surveys) for 13 countries. Results for 152 countries are available at the end of the paper. Uses PWT 8.0.
• February 2011 (Version 3.0): Various data improvements (hours measure for more countries from The Conference Board, better cleaning of Gini coefficient data from the WIID). The May 2011 NBER WP version is here.
• September 2010 (Version 2.0): First main version of the paper, circulated as NBER working paper.

### The New Kaldor Facts: Ideas, Institutions, Population, and Human Capital

June 17, 2009 -- Version 2.0 (with Paul Romer)
American Economic Journal: Macroeconomics, January 2010, Vol. 2 (1), pp. 224-245.

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?''

### Life and Growth

Journal of Political Economy, April 2016, Vol. 124 (2), pp. 539-578.

Data: Replication Files | NSF-AllYears-IndustrialRND.xls | 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:

• April 5, 2013 (Version 3.0): Formalizes the "Russian roulette" model, makes population growth exogenous, numerical solution of transition dynamics, patent evidence.
• May 21, 2011 (Version 2.0): Completely revamped. Title changed to "Life and Growth" instead of "The Costs of Economic Growth" to better reflect the present emphasis. New model and new evidence.
• September 25, 2009 (Version 1.0): Added a simple version of the model to the beginning that is quite useful (the "Russian roulette" model of growth). Added additional empirical evidence. Tightened proofs.
• June 10, 2008 (Version 0.4): Preliminary and incomplete. If you only read papers once, do not read this version.

### Intermediate Goods and Weak Links in the Theory of Economic Development

American Economic Journal: Macroeconomics April 2011, Vol. 3 (2), pp. 1-28.

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:

• September 21, 2010 (Version 6.0): Shortened the paper and cleaned up the numerical exercises; now focuses on the Hsieh-Klenow numbers.
• September 9, 2009 (Version 4.0): Substantial editing and rewriting.
• January 23, 2009 (Version 3.0): Revised Table 4 to use the latest Hsieh-Klenow (2009) evidence. Improved exposition.
• September 2008 (Version 2.5): Added a range of empirical evidence, re-inserted a simple model at the start, and improved exposition.
• February 2008 (Version 2.0): Improved exposition and fixed typos.
• December 2007 (Version 1.9): Major revisions. (1) Model now puts substitution and complementarity on equal footing: final goods are highly substitutable in consumption (or utility), whereas intermediate goods are complementary in production. This leads to a "superstar effect" in addition to the weak link effect: other things equal, aggregate TFP depends also on something like the maximum sectoral TFP because of substitution in consumption. Entire paper is reworked in this improved framework. (2) Model has explicit tax wedges and studies a competitive equilibrium with these micro-level distortions. The intermediate goods multiplier (and superstar and weak link effects) now operates on these micro-distortions in generating aggregate TFP differences across countries.
• April 2007 (Version 1.5): Significant revisions: (1) Changed title to emphasize intermediate goods. (2) Use a log-normal distribution of productivity instead of the Weibull -- more familiar and simpler formulas (thanks for this suggestion to Roland Benabou and Guido Lorenzoni). (3) Emphasize that the model itself has a way of generating the needed 2-fold difference in $Q$: the misallocation of resources represented by the symmetric allocation reduces TFP directly. (4) Cut the section on endogenizing physical and human capital to shorten the paper; the material on the Mincerian approach to schooling is now in a short note available here. (The May 18 version 1.51 fixes a few small typos.)
• March 2007 (Version 1.2): Added references, fixed typos. This version, like earlier versions, was titled "The Weak Link Theory of Economic Development."
• January 2007 (Version 1.1): Clarified several issues, cut the discussion of the gamma function. Second-best rather than optimal allocation.
• October 2006 (Version 1.0): Reorganized parts of paper so the ideas come through more clearly. Put complementarity and linkages through intermediate goods on an equal footing. Cumulative effect of reforms.
• June 2006: A more elegant mathematical treatment of complementarity than before. Importance of linkages across sectors, and the role of 1/(1-sigma).
• April 2006: This version was titled "Knowledge and the Theory of Economic Development." Emphasizes complementarity to replace increasing returns.
• November 2005: These ideas first appeared in a preliminary working paper called "The Value of Information in Growth and Development," as the second half of that paper. The first half of that paper is something I may still come back to.

### Insurance and Incentives for Medical Innovation

March 29, 2006 (with Alan Garber and Paul Romer)

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.

### A New Proof of Uzawa's Steady-State Growth Theorem

March 29, 2007 -- Version 5.01 (with Dean Scrimgeour)
Review of Economics and Statistics, February 2008, Vol. 90 (1), pp. 180-182.

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:

• Version 5.01 (March 2007): Added the reference to Wan (1971), who had an early version of Schlicht's proof. Thanks to Lutz Arnold.
• Version 5.0 (October 2006): Substantial revisions -- replaced our original, slightly tedious proof with the one provided by Schlicht (2006).
• Version 3.01 (November 16, 2005): This was the final working paper version that included our original proof and intuition (which partially movtivated Schlicht's proof). That version was titled "The Steady-State Growth Theorem: Understanding Uzawa (1961)". It is available by clicking on the title.

### The Value of Life and the Rise in Health Spending

(with Robert E. Hall)
Quarterly Journal of Economics, February 2007, Vol. 122 (1), pp. 39-72.

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:

• Version 5.0 (April 2006): Minor revisions to prepare for publication.
• Version 4.0 (February 2006): Substantial revisions to the quantitative section of the paper. The analysis illustrates the key parameter values that determine the time path of optimal health spending. Better explanation of identification.

### The Shape of Production Functions and the Direction of Technical Change

Quarterly Journal of Economics, May 2005, Vol. 120 (2), pp. 517-549.

Paper | (slides).
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.

### Growth, Capital Shares, and a New Perspective on Production Functions

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.

### Growth and Ideas

in P. Aghion and S. Durlauf (eds.) Handbook of Economic Growth (Elsevier, 2005) Volume 1B, pp. 1063-1111.

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.

### Why Have Health Expenditures as a Share of GDP Risen So Much?

May 5, 2004 -- Version 3.0

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.

### Was an Industrial Revolution Inevitable? Economic Growth Over the Very Long Run

Advances in Macroeconomics (2001) Volume 1, Number 2, Article 1.

Download the paper in Acrobat PDF format or as a postscript (.ps) file.

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.

### Sources of U.S. Economic Growth in a World of Ideas

American Economic Review, March 2002, Vol. 92 (1), pp. 220-239.

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."

### Growth: With or Without Scale Effects?

American Economic Review Papers and Proceedings, May 1999, Vol. 89, pp.139-144.

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.

### Population and Ideas: A Theory of Endogenous 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.

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.

### R&D-Based Models of Economic Growth

Journal of Political Economy, August 1995, Vol. 103, pp. 759-784.

View the paper in PDF format.

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.

### Time Series Tests of Endogenous Growth Models

Quarterly Journal of Economics, May 1995, Vol. 110, pp. 495-525.

View the paper in PDF file.

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.

### Why Do Some Countries Produce So Much More Output per Worker than Others?

Quarterly Journal of Economics, February 1999, Vol. 114, pp. 83-116 (with Robert E. Hall).

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."

### On the Evolution of the World Income Distribution

Journal of Economic Perspectives, Summer 1997, Vol. 11, pp. 19-36.

View the paper in PDF format.

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.

### Convergence Revisited

Journal of Economic Growth, July 1997, Vol. 2, pp. 131-153.

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.

### Levels of Economic Activity across Countries

American Economic Review Papers and Proceedings, May 1997, Vol. 87, pp.173-177 (with Robert E. Hall).

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.

### Economic Growth and the Relative Price of Capital

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.

### Too Much of a Good Thing? The Economics of Investment in R&D

Journal of Economic Growth, March 2000, Vol. 5, No. 1, pp. 65-85 (with John Williams).

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).

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.

### Comparing Apples to Oranges: Reply

December 7, 2000 (with Andrew Bernard).

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.

### Comparing Apples to Oranges: Productivity Convergence and Measurement Across Industries and Countries

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.

### Technology and Convergence

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.

### Productivity and Convergence across U.S. States and Industries

Empirical Economics, March 1996, Vol. 21, pp. 113-135 (with Andrew Bernard).

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.

### A Note on the Closed-Form Solution of the Solow Model

Stanford mimeo, January 2000

This brief note presents the closed-form solution of the Solow (1956) model when the production function is Cobb-Douglas.

### Comment on Rodriguez-Rodrik, "Trade Policy and Economic Growth: A Skeptic's Guide to the Cross-National Evidence"

NBER Macroeconomics Annual 2000 (MIT Press).

### Comment on Klenow-Rodriguez, "The Neoclassical Growth Revival: Has it Gone too Far?"

NBER Macroeconomics Annual 1997 (MIT Press).

### Human Capital, Ideas, and Economic Growth

in Edmund S. Phelps (ed.) conference volume, forthcoming.

Download the paper in Acrobat PDF format or as a postscript (.ps) file.

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.