research paper on endogenous growth model

An Overview of Endogenous Growth Models: Theory and Critique

International Journal of Physical and Social Sciences, Volume 5, Issue 3, March 2015

17 Pages Posted: 3 Nov 2015

Chukwuemeka Onyebuchi Onyimadu

Durham University - Department of Economics and Finance; National Institute for Legislative and Democratic Studies; Michael Okpara University of Agriculture

Date Written: November 3, 2015

The inability of neoclassical growth model in explaining long run economic growth is due to the existence of diminishing returns in capital. Therefore endogenous growth theory that models long run economic growth through technological transfers is necessitated. By reason of the obvious complex nature of modeling, the paper focuses on the intuition that the Endogenous Growth Model endeavors to capture. Thus, the paper provides to the reader, a non-technical overview and critique of the endogenous growth model, key literature in the study of the mechanism of the model as well as providing important references. The intended audiences are policy makers and analysts, students and optimistically anyone without a great deal of economic training.

Keywords: Economic Growth, Innovations, Endogenous Growth, Technological progress

JEL Classification: 031, 040

Suggested Citation: Suggested Citation

Chukwuemeka Onyebuchi Onyimadu (Contact Author)

Durham university - department of economics and finance ( email ).

Durham, DH1 3HY United Kingdom

National Institute for Legislative and Democratic Studies ( email )

18 Danube Street Maitama Abuja Nigeria 234 (Fax)

Michael Okpara University of Agriculture ( email )

Michael Okpara University of Agriculture, Umudike Umuahia Nigeria +234 (0) 908 004 3941 (Phone)

HOME PAGE: http://mouau.edu.ng/

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Economic Growth eJournal

• DOI: 10.2139/ssrn.2685545
• Corpus ID: 147619544

An Overview of Endogenous Growth Models: Theory and Critique

• C. Onyimadu
• Published 3 November 2015
• Econometric Modeling: Macroeconomics eJournal

12 Citations

A new theory of economic growth: why countries’ per capita income converge or diverge, investment in human capital to promote knowledge-based economy: data analysis in the gcc, productivity factors and the growth of the manufacturing sector among the east african community members states: testing the adequacy of the endogenous growth hypothesis, impact of capital market performance on economic growth in developing nations: a qualitative approach, economics of natural disasters and technological innovations in africa: an empirical evidence, the impact of foreign direct investment on economic growth in zambia, impact of foreign direct investment and inflation on economic growth of five randomly selected countries in africa, impact of remittance on economic growth of least developed countries in sub saharan africa.

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On convergence in endogenous growth models.

Discussion Paper 110 | Published March 1, 1996

In this paper we analyze the rate of convergence to a balanced path in a class of endogenous growth models with physical and human capital. We show that such rate depends locally on the technological parameters of the model, but does not depend on those parameters related to preferences. This result stands in sharp contrast with that of the one-sector neoclassical growth model, where both preferences and technologies determine the speed of convergence to a steady-state growth path.

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Long-Run Tax Incidence in a Human Capital-based Endogenous Growth Model with Labor-Market Frictions

In a second-best optimal growth setup with only factor taxes, it is in general optimal to fully replace capital by labor income taxation in the long run. We revisit this important issue by developing a human capital-based endogenous growth model with frictional labor search, allowing each firm to create multiple vacancies and each worker to determine market participation. We find that the conventional efficient bargaining condition is necessary but not sufficient for achieving constrained social optimality. We then conduct tax incidence exercises in balanced growth by calibrating to the U.S. economy with a pre-existing 20% flat tax on capital and labor income. Our quantitative results suggest that, due to a dominant channel via the interactions between vacancy creation and market participation, it is optimal to switch only partially from capital to labor taxation in a benchmark economy where human capital formation depends on both physical and human capital stocks. This main finding is robust even along the transition with time-varying factor tax rates. Moreover, our quantitative analysis under alternative setups suggest that while endogenous human capital and labor market frictions are essential for obtaining a positive optimal capital tax, endogenous leisure, nonlinear human capital accumulation and endogenous growth are not crucial.

We are grateful for valuable comments and suggestions from Marcus Berliant, Aubhik Khan, Kevin Lansing, Zheng Liu, Rody Manuelli, Milton Marquis, B. Ravikumar and John Williams, as well as participants at the Econometric Society Meeting, the Midwest Macroeconomic Conference, the Society for Advanced Economic Theory Conference, and the Society for Economic Dynamics Conference. Financial support from Academia Sinica, the National Science Council Grant (NSC 98-2911-H-001-001), the Program for Globalization Studies Grant (NTU 99R018), the Public Economics Research Center, and the Weidenbaum Center on the Economy, Government, and Public Policy is gratefully acknowledged. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

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The A.I. Dilemma: Growth versus Existential Risk April 2024, Version 2.0, conditionally accepted at AER Insights Paper | slides | GSB Insights | video Advances in artificial intelligence (A.I.) are a double-edged sword. On the one hand, they may increase economic growth as A.I. augments our ability to innovate. On the other hand, many experts worry that these advances entail existential risk: creating a superintelligence misaligned with human values could lead to catastrophic outcomes, even possibly human extinction. This paper considers the optimal use of A.I. technology in the presence of these opportunities and risks. Under what conditions should we continue the rapid progress of A.I. and under what conditions should we stop? History of Revisions: April 2024: Version 2.0. Model 2 is explicitly utilitarian in lifetime utility. Near-zero social discounting drops the social discount rate while holding the private discount rate constant. October 2023: Version 1.0. Population and Welfare: Measuring Growth when Lives are Worth Living (with Mohamad Adhami, Mark Bils, and Pete Klenow), August 2024, Version 2.0 Paper | Slides | Online Appendix Economic growth is typically measured in per capita terms. A long tradition in philosophy, however, suggests that social welfare may depend on the number of people as well. To illustrate how much this matters quantitatively, we decompose social welfare growth --- measured in consumption-equivalent (CE) units --- into contributions from rising population and rising per capita consumption. Because of diminishing marginal utility from consumption, population growth is scaled up by a value-of-life factor that empirically averages nearly 3 across countries since 1960. Population increases are therefore a major contributor to growth if one takes a total rather than per capita view. CE welfare growth around the world averages more than 6\% per year since 1960 as opposed to 2\% per year for consumption growth. Countries such as Mexico and South Africa rise sharply in the growth rankings, whereas China, Germany, and Japan plummet. These results are robust to incorporating richer individual preferences and endogenous fertility using time-use data from the U.S., Mexico, the Netherlands, Japan, South Africa, and South Korea. History of Revisions: August 2024: Version 2.0. Updated to new title. Old was "Population and Welfare: The Greatest Good for the Greatest Number." Improvements to framing and writing throughout the paper. February 2024: Version 1.05. Corrected small error in Section 4.2 on heterogeneity. December 2023: Version 1.0 Race and Economic Well-Being in the United States (with Brouillette and Klenow), November 2021, Version 1.0 Paper | Slides | SIEPR Writeup We construct a measure of consumption-equivalent welfare for Black and White Americans. Our statistic incorporates life expectancy, consumption, leisure, and inequality, with mortality rates playing a key role quantitatively. According to our estimates, welfare for Black Americans was 43\% of that for White Americans in 1984 and rose to 60\% by 2019. Going back further in time (albeit with more limited data), the gap was even larger, with Black welfare equal to just 28\% of White welfare in 1940. On the one hand, there has been remarkable progress for Black Americans: the level of their consumption-equivalent welfare increased by a factor of 28 between 1940 and 2019, when aggregate consumption per person rose a more modest 5-fold. On the other hand, despite this remarkable progress, the welfare gap in 2019 remains disconcertingly large. Mortality from COVID-19 has temporarily reversed a decade of progress, lowering Black welfare by 17% while reducing White welfare by 10%. The Past and Future of Economic Growth: A Semi-Endogenous Perspective Annual Review of Economics , Volume 14, August 2022, pp. 125-152 Paper | Slides | Video (Atkinson Lecture) The nonrivalry of ideas gives rise to increasing returns, a fact celebrated in Paul Romer's recent Nobel Prize. An implication is that the long-run rate of economic growth is the product of the degree of increasing returns and the growth rate of research effort; this is the essence of semi-endogenous growth theory. This paper interprets past and future growth from a semi-endogenous perspective. For 50+ years, U.S. growth has substantially exceeded its long-run rate because of rising educational attainment, declining misallocation, and rising (global) research intensity, implying that frontier growth could slow markedly in the future. Other forces push in the opposite direction. First is the prospect of ``finding new Einsteins'': how many talented researchers have we missed historically because of the underdevelopment of China and India and because of barriers that discouraged women inventors? Second is the longer-term prospect that artificial intelligence could augment or even replace people as researchers. Throughout, the paper highlights many opportunities for further research. Recipes and Economic Growth: A Combinatorial March Down an Exponential Tail Journal of Political Economy , Volume 131, August 2023, pp. 1994-2031. Paper | Slides | Replication Files | Short Video New ideas are often combinations of existing ideas, a point emphasized by Romer (1993) and Weitzman (1998). But this insight is largely absent from state-of-the-art models. Separately, Kortum (1997) created a new framework for modeling growth, one where ideas are draws from a probability distribution, and argued that the Pareto distribution plays an essential role. What happened to the Romer-Weitzman observation that combinations matter, and do we really need to make such a strong distributional assumption to get growth? This paper shows that combinatorial increases in the number of draws from standard thin-tailed distributions leads to exponential economic growth. More broadly, the paper provides a theorem linking the behavior of the max extreme value to the number of draws and the shape of the upper tail for probability distributions. History of Revisions: July 2022: Version 3.0 -- more intuition, more empirical evidence, and a discussion of future research opportunities. July 2021: Version 2.0 -- cleaned up technical details in proofs and expanded empirical evidence on patents and publication counts. January 2021: Version 1.0 The End of Economic Growth? Unintended Consequences of a Declining Population American Economic Review , November 2022, Vol. 112 (11), pp. 3489-3527 (lead article) Paper | Slides | Video | TheEconomist | Replication Files In many models, economic growth is driven by people discovering new ideas. These models typically assume either a constant or growing population. However, in high income countries today, fertility is already below its replacement rate: women are having fewer than two children on average. It is a distinct possibility that global population will decline rather than stabilize in the long run. In standard models, this has profound implications: rather than continued exponential growth, living standards stagnate for a population that vanishes. Moreover, even the optimal allocation can get trapped in this outcome if there are delays in implementing optimal policy. "I always loved growth theory as an economic kind of science fiction, in the best sense." -- Ben Golub History of Revisions: August 2022: Version 3.0 -- minor editorial changes. March 2022: Version 2.0 -- generalized Barro-Becker preferences, Results 4 and 5, phase diagram, simpler transition dynamics September 2020: Version 1.2 -- small revisions after NBER Growth meeting. First submission. January 2020: Version 1.0 Paul Romer: Ideas, Nonrivalry, and Endogenous Growth Scandinavian Journal of Economics July 2019, Vol. 121 (3), pp. 859-883. Paper (PDF) In 2018, Paul Romer and William Nordhaus shared the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. Romer was recognized "for integrating technological innovations into long-run macroeconomic analysis." This essay reviews his prize-winning contributions. Romer, together with others, rejuvenated the field of economic growth. He developed the theory of endogenous technological change, in which the search for new ideas by profit-maximizing entrepreneurs and researchers is at the heart of economic growth. And, underlying this theory, he pinpointed that the nonrivalry of ideas is ultimately responsible for the rise in living standards over time. History of Revisions: February 2019: First public version. Taxing Top Incomes in a World of Ideas Journal of Political Economy , September 2022, Vol. 130 (9), pp. 2227-2274 (lead article) Paper | Slides | Replication Files | GSBInsights Writeup 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 (though people can earn high incomes in other ways as well), 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 force affecting 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. History of Revisions: September 2021 (Verison 4.0): Calibration now explicitly tied to evidence in Akcigit et al (2021) on the elasticity of entrepreneurs to top tax rates. December 2020 (Version 3.0): Improved calibration -- now calibrating to the uncompensated elasticity, as the model in Section 4 suggests. Many other smaller changes. July 2019 (Version 2.0): Develops better intuition for the results. First-best effort. Substantial rewriting throughout to improve the presentation. March 2019 (Version 1.0): Incorporates "managers" from the start to make a tighter connection to the existing literature. September 2018 (Version 0.4): First public version. Nonrivalry and the Economics of Data (with Chris Tonetti) American Economic Review , September 2020, Vol. 110 (9), pp. 2819-2858. Paper (PDF) | Slides | Online appendix Research summary: Stanford GSB Insights | WSJ | VoxEU Data is nonrival: a person's location history, medical records, and driving data can be used by any number of firms simultaneously. 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 data being used broadly 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 balance their concerns for privacy against the economic gains that come from selling data to all interested parties. History of Revisions: August 2019 (Version 1.0): First main version, includes a simple model to start and robustness checks in the numerical section. July 2018 (Version 0.5): First public version. Artificial Intelligence and Economic Growth (with Philippe Aghion and Ben Jones) in Agrawal, Gans, and Goldfarb, The Economics of Artificial Intelligence: An Agenda University of Chicago Press, 2019. Paper (PDF) | Slides | Great presentation by Matt Clancy. 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. February 1, 2023: Thanks to Phil Trammell for finding in error in our proof of Example 3 on page 256-257 and providing a correct derivation . Are Ideas Getting Harder to Find? (with Nick Bloom, John Van Reenen, and Michael Webb) American Economic Review , April 2020, Vol. 110 (4), pp. 1104-1144 Paper (PDF) | Slides | Online Appendix | Replication Files | Vox summary 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: July 2019 (Version 4.0): Various edits for length and clarity. February 2019 (Version 3.0): Added results using firm-level data from the U.S. Census of Manufactures. Added a detailed literature review section. Various edits and other revisions to improve exposition and clarity. 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. Paper (PDF) | Figures (.eps) | Replication Files | Slides 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) Winner of the 2021 Robert E. Lucas Jr. Prize from the JPE. 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. Paper (PDF) | Data Spreadsheet " 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 Paper (PDF) | Slides | Data Spreadsheet | Replication files 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 Econometrica , September 2019, Vol. 87 (5), pp. 1439-1474 (lead article) (with Hsieh, Hurst, and Klenow) Paper (PDF) | Slides (old) | Online Appendix | EstimateTauZ | Replication Instructions | Replication Files | NYT | GSBInsights | MicroeconomicInsights | Video (10min) | Slides (10 mins) (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 the innate talent for these professions is unlikely to have changed differently across groups, the change in the occupational distribution since 1960 suggests that a substantial pool of innately talented women and black men in 1960 were not pursuing their comparative advantage. We examine the effect on aggregate productivity of the convergence in the occupational distribution between 1960 and 2010 through the prism of a Roy model. Across our various specifications, between 20\% and 40\% of growth in aggregate market output per person can be explained by the improved allocation of talent. History of Revisions: April 2019 (Version 7.0): Shortened for publication; results unchanged. March 2019 (Version 6.0): Major revision. Adds preference heterogeneity as well as talent heterogeneity. 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: April 2019: There is a typo in the published version (on page 2439). The value for ubar that we calibrate in the programs is actually 5.2325, not 5.00. This is noted in the PDF above. 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. Download the paper in Acrobat PDF format. 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. Download the paper . Slides . 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. Download the paper | Supplementary Materials (e.g. proofs) | Slides 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) Forum for Health Economics & Policy , 2006, Forum: Biomedical Research and the Economy: Article 4 . Download the paper in Acrobat PDF format. 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. Download the paper in Acrobat PDF format. 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. Download the paper in Acrobat PDF format. Slides . Click here for the matlab programs used in this paper. 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. Download the paper in 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. Why Have Health Expenditures as a Share of GDP Risen So Much? May 5, 2004 -- Version 3.0 Download the paper in Acrobat PDF format. 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. Download the paper in Acrobat PDF format. 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. Download the paper in Acrobat PDF format. 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. Download the paper in Acrobat PDF format. 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). Paper | Click here for the data set. 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 was circulated under the title " The Productivity of Nations " (NBER Working Paper No. 5812, November 1996). 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. Download the paper in Acrobat PDF format. 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). Download the PDF 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. View as PDF . 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). 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. Measuring the Social Return to R&D Quarterly Journal of Economics , November 1998, Vol. 113, pp. 1119-1135 (with John Williams). Download the paper in Acrobat PDF format. 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). Download the paper in Acrobat PDF format. 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). Download the working paper version in Acrobat PDF format or as a postscript (.ps) file. 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). Download the working paper version in Acrobat PDF format. 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 Download the working paper version in Acrobat PDF format. 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). Download the working paper version in Acrobat PDF format. Comment on Klenow-Rodriguez, "The Neoclassical Growth Revival: Has it Gone too Far?" NBER Macroeconomics Annual 1997 (MIT Press). Download the paper in Acrobat PDF format. 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.   Back to Home Page

A modified scenario bundling method for shortest path network interdiction under endogenous uncertainty

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• Published: 23 September 2024

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• Somayeh Sadeghi   ORCID: orcid.org/0000-0001-6353-9634 1 &
• Abbas Seifi   ORCID: orcid.org/0000-0003-2549-2200 1  

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We consider a shortest-path network interdiction problem under endogenous uncertainty on successful detection. Endogenous uncertainty arises from the fact that the interdictor may decide to enforce surveillance on some critical arcs, which would affect the prior probability of success on those arcs. The evader decision is formulated as a two-stage stochastic programming problem. In a “here and now situation”, he has to choose the shortest path in the network before realizing detection scenarios. Then, in the second stage, the evader tries to minimize the expected cost of being detected over all possible scenarios. We consider binary scenarios to represent whether or not the evader is detected on each path and apply a linearization method to deal with the non-linearity in the decision-dependent probability measure. A decomposition method is used to solve the proposed model for a case study of a worldwide drug trafficking network. The case study is concerned with finding the most critical arcs for interdicting drug trafficking. Numerical results show that a tiny increase in the probability of opium seizures leads to a significant change in the expected cost when the critical arcs are interdicted. Due to the exponential number of scenarios, the model could not be solved in a reasonable time. Common scenario reduction methods are designed for exogenous uncertainty. We apply an improved bundling method to reduce the number of scenarios in case of endogenous uncertainty. Computational results show that our method reduces the model size and solution time tremendously without significantly affecting the objective value.

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Source : UNODC Report

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Altner, D. S., & Uhan, N. A. (2009). The maximum flow network interdiction problem : valid inequalities, integrality gaps, and approximability. Operations Research, 38 (1), 1–12.

Google Scholar  

Anzoom, R., Nagi, R., & Vogiatzis, C. (2021). A review of research in illicit supply-chain networks and new directions to thwart them. IISE Transaction, 54 (2), 134–158. https://doi.org/10.1080/24725854.2021.1939466

Article   Google Scholar  

Assimakopoulos, N. (1987). A network interdiction model for hospital infection control. Computers in Biology and Medicine, 17 (6), 413–422.

Azizi, E., & Seifi, A. (2023). Shortest path network interdiction with incomplete information: A robust optimization approach. Annals of Operations Research . https://doi.org/10.1007/s10479-023-05350-1

Bakker, C., Webster, J. B., Nowak, K. E., Chatterjee, S., Perkins, C. J., & Brigantic, R. (2020). Multi-game modeling for counter-smuggling. Reliability Engineering and System Safety, 200 , 106958. https://doi.org/10.1016/j.ress.2020.106958

Bayrak, H., & Bailey, M. D. (2008). Shortest path network interdiction with asymmetric information. Networks, 52 (3), 133–140. https://doi.org/10.1002/net.20236

Bounitsis, G. L., Papageorgiou, L. G., & Charitopoulos, V. M. (2022). Data-driven scenario generation for two-stage stochastic programming. Chemical Engineering Research and Design, 187 , 206–224. https://doi.org/10.1016/j.cherd.2022.08.014

Choueiry, B.Y., & Davis, A. M. (2002). Dynamic bundling: Less effort for more solutions. In Lecture notes in computer science (including subseries lecture notes in artificial intelligence and lecture notes in bioinformatics ) (pp. 64–82). Springer. https://doi.org/10.1007/3-540-45622-8_6

Church, R. L., Scaparra, M. P., & Middleton, R. S. (2004). Identifying critical infrastructure: The median and covering facility interdiction problems. Annals of the Association of American Geographers, 94 (3), 491–502. https://doi.org/10.1111/j.1467-8306.2004.00410.x

Corley, H. W., & Sha, D. Y. (1982). most vital links and nodes in weighted networks. Operations Research Letters, I (4), 2–5.

Cormican, K. J., Morton, D. P., & Wood, R. K. (1998). Stochastic network interdiction. Operations Research, 46 (2), 184–197. https://doi.org/10.1287/opre.46.2.184

Delgadillo, A., Arroyo, J. M., & Alguacil, N. (2010). Analysis of electric grid interdiction with line switching. Power Systems, IEEE Transactions on, 25 (2), 633–641. https://doi.org/10.1109/TPWRS.2009.2032232

Fulkerson, D. R., & Harding, G. C. (1977). Maximizing the minimum source-sink path subject to a budget constraint. Mathematical Programming, 13 (1), 116–118. https://doi.org/10.1007/BF01584329

Granata, D., Steeger, G., & Rebennack, S. (2013). Network interdiction via a critical disruption path: Branch-and-price algorithms. Computers and Operations Research, 40 (11), 2689–2702. https://doi.org/10.1016/j.cor.2013.04.016

Haus, U.-U., Michini, C., & Laumanns, M. (2017). Scenario aggregation using binary decision diagrams for stochastic programs with endogenous uncertainty. http://arxiv.org/abs/1701.04055

Israeli, E., & Wood, R. K. (2002). Shortest-path network interdiction. Networks, 40 (2), 97–111. https://doi.org/10.1002/net.10039

Janjarassuk, U., & Linderoth, J. (2008). Reformulation and sampling to solve a stochastic network interdiction problem. Networks, 52 (3), 120–132. https://doi.org/10.1002/net.20237

Keutchayan, J., Ortmann, J., & Rei, W. (2021). Problem-driven scenario clustering in stochastic optimization. http://arxiv.org/abs/2106.11717

Laumanns, M., Prestwich, S., & Kawas, B. (2014). Distribution shaping and scenario bundling for stochastic programs with endogenous uncertainty ∗. In EURO-INFORMS Joint international meeting 2013 in rome and the international conference on operations research (OR 2014) in Aachen (pp. 1–24).

Liberatore, F., Scaparra, M. P., & Daskin, M. S. (2011). Analysis of facility protection strategies against an uncertain number of attacks: The stochastic R-interdiction median problem with fortification. Computers and Operation Research, 38 (1), 357–366. https://doi.org/10.1016/j.cor.2010.06.002

Lim, C., & Smith, J. C. (2007). Algorithms for discrete and continuous multicommodity flow network interdiction problems. IIE Transactions, 39 (1), 15–26. https://doi.org/10.1080/07408170600729192

Malaviya, A., Rainwater, C., & Sharkey, T. (2012). Multi-period network interdiction problems with applications to city-level drug enforcement. IIE Transactions, 44 , 368–380. https://doi.org/10.1080/0740817X.2011.602659

Malik, K., Mittal, A. K., & Gupta, S. K. (1989). The k-most vital arcs in the shortest path problem. Operations Research Letters, 8 (4), 223–227. https://doi.org/10.1016/0167-6377(89)90065-5

Morton, D. P., Pan, F., & Saeger, K. J. (2007). Models for nuclear smuggling interdiction. IIE Transactions, 39 (1), 3–14. https://doi.org/10.1080/07408170500488956

Najafi, M., Zolfagharinia, H., & Asadi, F. (2023). Angels against demons: Fight against smuggling in an illicit supply chain with uncertain outcomes and unknown structure. Computers and Industrial Engineering, 176 , 109007. https://doi.org/10.1016/j.cie.2023.109007

Nehme, M. V. (2009). Two-person games for stochastic network interdiction: Models, methods, and complexities . The University of Texas at Austin.

Nguyen, D. H., & Smith, J. C. (2021). Network interdiction with asymmetric cost uncertainty. European Journal of Operational Research . https://doi.org/10.1016/j.ejor.2021.04.055

Pan, F., & Schild, A. (2016). Interdiction problems on planar graphs. Discrete Applied Mathematics, 1979 (198), 215–231. https://doi.org/10.1007/978-3-642-40328-6_23

Rad, M. A., & Kakhki, H. T. (2013). Maximum dynamic network flow interdiction problem: New formulation and solution procedures. Computers and Industrial Engineering, 65 , 531–536.

Ramirez-Marquez, J. E., & Rocco, C. M. S. (2009). Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery. Reliability Engineering and System Safety, 94 (5), 913–921. https://doi.org/10.1016/j.ress.2008.10.006

Römisch, W. (2009). Scenario reduction techniques in stochastic programming. In O. Watanabe & T. Zeugmann (Eds.), Stochastic algorithms: Foundations and applications (pp. 1–14). Springer.

Rujeerapaiboon, N., Schindler, K., Kuhn, D., & Wiesemann, W. (2022). Scenario reduction revisited: Fundamental limits and guarantees. Mathematical Programming, 191 (1), 207–242. https://doi.org/10.1007/s10107-018-1269-1

Sadeghi, S., & Seifi, A. (2019). Stochastic maximum flow network interdiction with endogenous uncertainty. International Journal of Supply and Operations Management, 6 (3), 200–212. https://doi.org/10.22034/2019.3.2

Sadeghi, S., Seifi, A., & Azizi, E. (2017). Trilevel shortest path network interdiction with partial fortification. Computers and Industrial Engineering, 106 , 400–411. https://doi.org/10.1016/j.cie.2017.02.006

Salmeron, J., Wood, K., & Baldick, R. (2004). Analysis of electric grid security under terrorist threat. Power Systems, IEEE Transactions on, 19 (2), 905–912. https://doi.org/10.1109/TPWRS.2004.825888

Salmeron, J., Wood, K., & Baldick, R. (2009). Worst-case interdiction analysis of large-scale electric power grids. Power Systems, IEEE Transactions on, 24 (1), 96–104. https://doi.org/10.1109/TPWRS.2008.2004825

Sánchez-Pérez, M., Marín-Carrillo, M. B., Illescas-Manzano, M. D., & Souilim, Z. (2023). Understanding the illegal drug supply chain structure: A value chain analysis of the supply of hashish to Europe. Humanities and Social Sciences Communications, 10 (1), 276. https://doi.org/10.1057/s41599-023-01770-3

Smith, J. C., & Song, Y. (2019). A survey of network interdiction models and algorithms. European Journal of Operational Research . https://doi.org/10.1016/j.ejor.2019.06.024

Snyder, L. V., Scaparra, M. P., Daskin, M. S., & Church, R. L. (2006). Planning for disruptions in supply chain networks. In Tutorials in operations research (pp. 234–257).

Soleimani-Alyar, M., Ghaffari-Hadigheh, A., & Sadeghi, F. (2016). Controlling floods by optimization methods. Water Resources Management, 30 (12), 4053–4062. https://doi.org/10.1007/s11269-016-1272-3

Song, Y., & Shen, S. (2016). Risk-averse shortest path interdiction. INFORMS Journal on Computing, 28 (3), 527–539. https://doi.org/10.1287/ijoc.2016.0699

UN Office on Drugs and Crime (UNODC) (2009). Addiction, crime and insurgency. The transnational threat of Afghan opium. https://www.refworld.org/reference/countryrep/unodc/2009/en/70399

von Stackelberg, H. (1952). The theory of the market economy . William Hodge. http://books.google.com/books?id=o3ceAAAAIAAJ

Wei, X., Zhu, C., Xiao, K., Yin, Q., & Zha, Y. (2018). Shortest path network interdiction with goal threshold. IEEE Access . https://doi.org/10.1109/ACCESS.2018.2838570

Wollmer, R. (1964). Removing arcs from a network. Transportation Research Part b: Methodological, 12 , 934–940.

Wood, R. K. (1993). Deterministic network interdiction. Mathematical and Computer Modelling, 17 (2), 1–18. https://doi.org/10.1016/0895-7177(93)90236-R

Xiang, Y., & Wei, H. (2020). Joint optimizing network interdiction and emergency facility location in terrorist attacks. Computers and Industrial Engineering, 144 , 106480. https://doi.org/10.1016/j.cie.2020.106480

Zhang, J., Zhuang, J., & Behlendorf, B. (2018a). Stochastic shortest path network interdiction with a case study of Arizona—Mexico border. Reliability Engineering and System Safety, 179 (2017), 62–73.

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Sadeghi, S., Seifi, A. A modified scenario bundling method for shortest path network interdiction under endogenous uncertainty. Ann Oper Res (2024). https://doi.org/10.1007/s10479-024-06157-4

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