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    Abstract
    Keywords
    JEL Classification Codes
    1. Growth at the Frontier
    1.1. Modern Economic Growth
    1.2. Growth Over the Very Long Run
    2. Sources of Frontier Growth
    2.1. Growth Accounting
    2.2. Physical Capital
    2.3. Factor Shares
    2.4. Human Capital
    2.5. Ideas
    2.6. Misallocation
    2.7. Explaining the Facts of Frontier Growth
    3. Frontier Growth: Beyond GDP
    3.1. Structural Change
    3.2. The Rise of Health
    3.3. Hours Worked and Leisure
    3.4. Fertility
    3.5. Top Inequality
    3.6. The Price of Natural Resources
    4. The Spread of Economic Growth
    4.1. The Long Run
    4.2. The Spread of Growth in Recent Decades
    4.3. The Distribution of Income by Person, Not by Country
    4.4. Beyond GDP
    4.5. Development Accounting
    4.6. Understanding TFP Differences
    4.7. Misallocation: A Theory of TFP
    4.8. Institutions and the Role of Government
    4.9. Taxes and Economic Growth
    4.10. TFPQ vs TFPR
    4.11. The Hsieh–Klenow Facts
    4.12. The Diffusion of Ideas
    4.13. Urbanization
    5. Conclusion
    Acknowledgments
    References

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Figures and tables

    GDP per person in the United States.
    Table 1
    Economic growth over the very long run.
    Table 2
    Table 3
    The ratio of physical capital to GDP.
    Investment in physical capital (private and public), United States.
    Relative price of investment, United States. Note: The chained price index for ...
    Capital and labor shares of factor payments, United States.
    Educational attainment, United States.
    The supply of college graduates and the college wage premium, 1963–2012. Note: ...
    Research and development spending, United States.
    Research employment share.
    Patents granted by the US Patent and Trademark Office.
    Employment in agriculture as a share of total employment.
    Health spending as a share of GDP.
    Life expectancy at birth and at age 65, United States.
    Average annual hours worked, select countries.
    Average weekly hours worked, United States.
    Fertility in the United States and France.
    Top income inequality in the United States and France.
    GDP per person, top 0.1% and bottom 99.9%. Note: This figure displays an ...
    The real price of industrial commodities.
    The great divergence. Note: The graph shows GDP per person for various ...
    The spread of economic growth since 1870.
    The spread of economic growth since 1980.
    GDP per person, 1960 and 2011.
    Convergence in the OECD.
    The lack of convergence worldwide.
    Divergence since 1960.
    Table 4
    The distribution of world income by population.
    Table 5
    Table 6
    Total factor productivity, 2010.
    The share of TFP in development accounting, 2010.
    Korea at night. Note: North Korea is the dark area in the center of the figure, ...
    The reversal of fortune. Note: Former European colonies that were proserous (at ...
    Taxes and growth in the United States.
    Tax revenues as a share of GDP. Note: Tax revenue is averaged for the available ...
    The distribution of TFPQ in 4-digit manufacturing industries. Note: This is the ...
    The distribution of TFPR in 4-digit manufacturing industries. Note: This is the ...
    Average employment over the life cycle. Note: The graph compares average ...
    Technology adoption is speeding up over time. Note: Adoption lags for each ...
    The number of “million cities.” Note: The histogram shows the number of cities ...

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Handbook of Macroeconomics

Volume 2 , 2016, Pages 3–69

Edited By John B. Taylor and Harald Uhlig
Cover image Cover image
Chapter 1 – The Facts of Economic Growth

    C.I. Jones

    Stanford GSB, Stanford, CA, United States
    NBER, Cambridge, MA, United States

    Available online 4 October 2016

  Show more   Show less

    https://doi.org/10.1016/bs.hesmac.2016.03.002 
    Get rights and content 

Abstract

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.
Keywords

    Economic growth ;
    Development ;
    Long-run growth ;
    Productivity

JEL Classification Codes

    E01 ;
    O10 ;
    04

    “[T]he errors which arise from the absence of facts are far more numerous and more durable than those which result from unsound reasoning respecting true data.”

    —Charles Babbage, quoted in ( Rosenberg, 1994 , p. 27).

    “[I]t is quite wrong to try founding a theory on observable magnitudes alone… It is the theory which decides what we can observe.”

    —Albert Einstein, quoted in ( Heisenberg, 1971 , p. 63).

Why are people in the United States, Germany, and Japan so much richer today than 100 or 1000 years ago? Why are people in France and the Netherlands today so much richer than people in Haiti and Kenya? Questions like these are at the heart of the study of economic growth.

Economics seeks to answer these questions by building quantitative models—models that can be compared with empirical data. That is, we’d like our models to tell us not only that one country will be richer than another, but by how much. Or to explain not only that we should be richer today than a century ago, but that the growth rate should be 2% per year rather than 10%. Growth economics has only partially achieved these goals, but a critical input into our analysis is knowing where the goalposts lie—that is, knowing the facts of economic growth.

The purpose of this paper is to lay out as many of these facts as possible. Kaldor (1961) was content with documenting a few key stylized facts that basic growth theory should hope to explain. Jones and Romer (2010) updated his list to reflect what we’ve learned over the last 50 years. The approach here is different. Rather than highlighting a handful of stylized facts, we draw on the last 30 years of the renaissance of growth economics to lay out what is known empirically about the subject. These facts are updated with the latest data and gathered together in a single place—potentially useful to newcomers to the field as well as to experts. The result, I hope, is a fascinating tour of the growth literature from the perspective of the basic data.

The paper is divided broadly into two parts. First, I present the facts related to the growth of the “frontier” over time: what are the growth patterns exhibited by the richest countries in the world? Second, I focus on the spread of economic growth throughout the world. To what extent are countries behind the frontier catching up, falling behind, or staying in place? And what characteristics do countries in these various groups share?
1. Growth at the Frontier

We begin by discussing economic growth at the “frontier.” By this I mean growth among the richest set of countries in any given time period. For much of the last century, the United States has served as a stand in for the frontier, and we will follow this tradition.
1.1. Modern Economic Growth

Fig. 1 shows one of the key stylized facts of frontier growth: For nearly 150 years, GDP per person in the US economy has grown at a remarkably steady average rate of around 2% per year. Starting at around $3,000 in 1870, per capita GDP rose to more than $50,000 by 2014, a nearly 17-fold increase.

GDP per person in the United States. GDP per person in the United States.
    Fig. 1. 

    GDP per person in the United States.

    Source: Data for 1929–2014 are from the U.S. Bureau of Economic Analysis, NIPA table 7.1. Data before 1929 are spliced from Maddison, A. 2008. Statistics on world population, GDP and per capita GDP, 1-2006 AD. Downloaded on December 4, 2008 from http://www.ggdc.net/maddison/ .
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Beyond the large, sustained growth in living standards, several other features of this graph stand out. One is the significant decline in income associated with the Great Depression. However, to me this decline stands out most for how anomalous it is. Many of the other recessions barely make an impression on the eye: over long periods of time, economic growth swamps economic fluctuations. Moreover, despite the singular severity of the Great Depression—GDP per person fell by nearly 20% in just 4 years—it is equally remarkable that the Great Depression was temporary . By 1939, the economy is already passing its previous peak and the macroeconomic story a decade later is once again one of sustained, almost relentless, economic growth.

The stability of US growth also merits some discussion. With the aid of the trend line in Fig. 1 , one can see that growth was slightly slower pre-1929 than post. Table 1 makes this point more precisely. Between 1870 and 1929, growth averaged 1.76%, vs 2.23% between 1929 and 2007 (using “peak to peak” dates to avoid business cycle problems). Alternatively, between 1900 and 1950, growth averaged 2.06% vs 2.16% since 1950. Before one is too quick to conclude that growth rates are increasing; however, notice that the period since 1950 shows a more mixed pattern, with rapid growth between 1950 and 1973, slower growth between 1973 and 1995, and then rapid growth during the late 1990s that gives way to slower growth more recently.

    Table 1.

    The stability of US Growth
    Period 	Growth Rate 	Period 	Growth Rate
    1870–2007 	2.03 	1973–1995 	1.82
    1870–1929 	1.76 	1995–2007 	2.13
    1929–2007 	2.23 		
    1900–1950 	2.06 	1995–2001 	2.55
    1950–2007 	2.16 	2001–2007 	1.72
    1950–1973 	2.50 		
    1973–2007 	1.93 		

    Note: Annualized growth rates for the data shown in Fig. 1 .

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The interesting “trees” that one sees in Table 1 serves to support the main point one gets from looking at the “forest” in Fig. 1 : steady, sustained exponential growth for the last 150 years is a key characteristic of the frontier. All modern theories of economic growth—for example, Solow, 1956 ; Lucas, 1988  ;   Romer, 1990 , and Aghion and Howitt (1992) —are designed with this fact in mind.

The sustained growth in Fig. 1 also naturally raises the question of whether such growth can and will continue for the next century. On the one hand, this fact more than any other helps justify the focus of many growth models on the balanced growth path, a situation in which all economic variables grow at constant exponential rates forever. And the logic of the balanced growth path suggests that the growth can continue indefinitely. On the other hand, as we will see, there are reasons from other facts and theories to question this logic.
1.2. Growth Over the Very Long Run

While the future of frontier growth is surely hard to know, the stability of frontier growth suggested by Fig. 1 is most certainly misleading as a guide to growth further back in history. Fig. 2 shows that sustained exponential growth in living standards is an incredibly recent phenomenon. For thousands and thousands of years, life was, in the evocative language of Thomas Hobbes, “nasty, brutish, and short.” Only in the last two centuries has this changed, but in this relatively brief time, the change has been dramatic. a

Economic growth over the very long run. Economic growth over the very long run.
    Fig. 2. 

    Economic growth over the very long run.

    Source: Data are from Maddison, A. 2008. Statistics on world population, GDP and per capita GDP, 1-2006 AD. Downloaded on December 4, 2008 from http://www.ggdc.net/maddison/ for the “West,” ie, Western Europe plus the United States. A similar pattern holds using the “world” numbers from Maddison.
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Between the year 1 C.E. and the year 1820, living standards in the “West” (measured with data from Western Europe and the United States) essentially doubled, from around $600 per person to around $1200 per person, as shown in Table 2 . Over the next 200 years; however, GDP per person rose by more than a factor of twenty, reaching $26,000.

    Table 2.

    The Acceleration of world growth
    Year 	GDP per person 	Growth rate 	Population (millions) 	Growth rate
    1 	 590 	 – 	 19 	–
    1000 	 420 	−0.03 	 21 	0.01
    1500 	 780 	0.12 	 50 	0.17
    1820 	 1240 	0.15 	125 	0.28
    1900 	 3350 	1.24 	280 	1.01
    2006 	26,200 	1.94 	627 	0.76

    Note: Growth rates are average annual growth rates in percent, and GDP per person is measured in real 1990 dollars.

    Source: Data are from Maddison, A. 2008. Statistics on world population, GDP and per capita GDP, 1-2006 AD. Downloaded on December 4, 2008 from http://www.ggdc.net/maddison/ for the “West,” ie, Western Europe plus the United States
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The era of modern economic growth is in fact even more special than this. Evidence suggests that living standards were comparatively stagnant for thousands and thousands of years before. For example, for much of prehistory, humans lived as simple hunters and gatherers, not far above subsistence. From this perspective—say for the last 200,000 years or more—the era of modern growth is spectacularly brief. It is the economic equivalent of Carl Sagan's famous “pale blue dot” image of the earth viewed from the outer edge of the solar system.

Table 2 reveals several other interesting facts. First and foremost, over the very long run, economic growth at the frontier has accelerated—that is, the rates of economic growth are themselves increasing over time. Romer (1986) emphasized this fact for living standards as part of his early motivation for endogenous growth models. Kremer (1993) highlighted the acceleration in population growth rates, dating as far back as a million years ago, and his evidence serves as a very useful reminder. Between 1 million B.C.E. and 10,000 B.C.E., the average population growth rate in Kremer's data was 0.00035% per year. Yet despite this tiny growth rate, world population increased by a factor of 32, from around 125,000 people to 4 million. As an interesting comparison, that's similar to the proportionate increase in the population in Western Europe and the United States during the past 2000 years, shown in Table 2 .

Various growth models have been developed to explain the transition from stagnant living standards for thousands of years to the modern era of economic growth. A key ingredient in nearly all of these models is Malthusian diminishing returns. In particular, there is assumed to be a fixed supply of land which is a necessary input in production. b Adding more people to the land reduces the marginal product of labor (holding technology constant) and therefore reduces living standards. Combined with some subsistence level of consumption below which people cannot survive, this ties the size of the population to the level of technology in the economy: a better technology can support a larger population.

Various models then combine the Malthusian channel with different mechanisms for generating growth. Lee, 1988  ;   Kremer, 1993 , and Jones (2001) emphasize the positive feedback loop between “people produce ideas” as in the Romer model of growth with the Malthusian “ideas produce people” channel. Provided the increasing returns associated with ideas is sufficiently strong to counter the Malthusian diminishing returns, this mechanism can give rise to dynamics like those shown in Fig. 2 . Lucas (2002) emphasizes the role of human capital accumulation, while Hansen and Prescott (2002) focus on a neoclassical model that features a structural transformation from agriculture to manufacturing. Oded Galor, with his coauthors, has been one of the most significant contributors, labeling this literature “unified growth theory.” See Galor and Weil (2000) and Galor (2005) .
2. Sources of Frontier Growth

The next collection of facts related to economic growth are best presented in the context of the famous growth accounting decomposition developed by Solow (1957) and others. This exercise studies the sources of growth in the economy through the lens of a single aggregate production function. It is well known that the conditions for an aggregate production function to exist in an environment with a rich underlying microstructure are very stringent. The point is not that anyone believes those conditions hold. Instead, one often wishes to look at the data “through the lens of” some growth model that is much simpler than the world that generates the observed data. A long list of famous papers supports the claim that this is a productive approach to gaining knowledge, Solow (1957) itself being an obvious example.

While not necessary, it is convenient to explain this accounting using a Cobb–Douglas specification. More specifically, suppose final output Y t is produced using stocks of physical capital K t and human capital H t :
equation ( 1 )
View the MathML source View the MathML source Y t = A t M t ︸ TFP K t α H t 1 − α
Turn   MathJax on
where α is between zero and one, A t denotes the economy's stock of knowledge, and M t is anything else that influences total factor productivity (the letter “M” is reminiscent of the “measure of our ignorance” label applied to the residual by Abramovitz (1956) and also is suggestive of “misallocation,” as will be discussed in more detail later). The next subsection provides a general overview of growth accounting for the United States based on this equation, and then the remainder of this section looks more closely at each individual term in Eq. ( 1 ).

2.1. Growth Accounting

It is traditional to perform the growth accounting exercise with a production function like ( 1 ). However, that approach creates some confusion in that some of the accumulation of physical capital is caused by growth in total factor productivity (eg, as in a standard Solow model). If one wishes to credit such growth to total factor productivity, it is helpful to do the accounting in a slightly different way. c In particular, divide both sides of the production function by View the MathML source View the MathML source Y t α and solve for Y t to get
equation ( 2 )
View the MathML source View the MathML source Y t = K t Y t α 1 − α H t Z t
Turn   MathJax on
where View the MathML source View the MathML source Z t ≡ ( A t M t ) 1 1 − α is total factor productivity measured in labor-augmenting units. Finally, dividing both sides by the aggregate amount of time worked, L t , gives
equation ( 3 )
View the MathML source View the MathML source Y t L t = K t Y t α 1 − α H t L t ⋅ Z t
Turn   MathJax on
In this form, growth in output per hour Y t / L t comes from growth in the capital-output ratio K t / Y t , growth in human capital per hour H t / L t , and growth in labor-augmenting TFP, Z t . This can be seen explicitly by taking logs and differencing Eq. ( 3 ). Also, notice that in a neoclassical growth model, the capital-output ratio is proportional to the investment rate in the long-run and does not depend on total factor productivity. Hence the contributions from productivity and capital deepening are separated in this version, in a way that they were not in Eq. ( 1 ).

The only term we have yet to comment on is H t / L t , the aggregate amount of human capital divided by total hours worked. In a simple model with one type of labor, one can think of H t = h t L t , where h t is human capital per worker which increases because of education. In a richer setting with different types of labor that are perfect substitutes when measured in efficiency units, H t / L t also captures composition effects. The Bureau of Labor Statistics, from which I’ve obtained the accounting numbers discussed next, therefore refers to this term as “labor composition.”

Table 3 contains the growth accounting decomposition for the United States since 1948, corresponding to Eq. ( 3 ). Several well-known facts emerge from this accounting. First, growth in output per hour at 2.5% is slightly faster than the growth in GDP per person that we saw earlier. One reason is that the BLS data measure growth for the private business sector, excluding the government sector (in which there is zero productivity growth more or less by assumption). Second, the capital-output ratio is relatively stable over this period, contributing almost nothing to growth. Third, labor composition (a rise in educational attainment, a shift from manufacturing to services, and the increased labor force participation of women) contributes 0.3 percentage points per year to growth. Finally, as documented by Abramovitz, Solow, and others, the “residual” of total factor productivity accounts for the bulk of growth, coming in at 2.0 percentage points, or 80% of growth since 1948.

    Table 3.

    Growth accounting for the United States
    		Contributions from
    Period 	Output per hour 	K / Y 	Labor composition 	Labor-Aug. TFP
    1948–2013 	2.5 	0.1 	0.3 	2.0
    1948–1973 	3.3 	−0.2 	0.3 	3.2
    1973–1990 	1.6 	0.5 	0.3 	0.8
    1990–1995 	1.6 	0.2 	0.7 	0.7
    1995–2000 	3.0 	0.3 	0.3 	2.3
    2000–2007 	2.7 	0.2 	0.3 	2.2
    2007–2013 	1.7 	0.1 	0.5 	1.1

    Note: Average annual growth rates (in percent) for output per hour and its components for the private business sector, following Eq. ( 3 ).

    Source: Authors calculations using Bureau of Labor Statistics, Multifactor Productivity Trends , August 21, 2014.
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The remainder of Table 3 shows the evolution of growth and its decomposition over various periods since 1948. We see the rapid growth and rapid TFP growth of the 1948–1973 period, followed by the well-known “productivity slowdown” from 1973 to 1995. The causes of this slowdown are much debated but not convincingly pinned down, as suggested by the fact that the entirety of the slowdown comes from the TFP residual rather than from physical or human capital; Griliches (1988) contains a discussion of the slowdown.

Remarkably, the period 1995–2007 sees a substantial recovery of growth, not quite to the rates seen in the 1950s and 1960s, but impressive nonetheless, coinciding with the dot-com boom and the rise in the importance of information technology. Byrne et al. (2013) provide a recent analysis of the importance of information technology to growth over this period and going forward. Lackluster growth in output per hour since 2007 is surely in large part attributable to the Great Recession, but the slowdown in TFP growth (which some such as Fernald, 2014 date back to 2003) is troubling. d
2.2. Physical Capital

The fact that the contribution of the capital-output ratio was modest in the growth accounting decomposition suggests that the capital-output ratio is relatively constant over time. This suggestion is confirmed in Fig. 3 . The broadest concept of physical capital (Total), including both public and private capital as well as both residential and nonresidential capital, has a ratio of 3 to real GDP. Focusing on nonresidential capital brings this ratio down to 2, and further restricting to private nonresidential capital leads a ratio of just over 1.

The ratio of physical capital to GDP. The ratio of physical capital to GDP.
    Fig. 3. 

    The ratio of physical capital to GDP.

    Source: Burea of Economic Analysis Fixed Assets tables 1.1 and 1.2. The numerator in each case is a different measure of the real stock of physical capital, while the denominator is real GDP.
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The capital stock is itself the cumulation of investment, adjusted for depreciation. Fig. 4 shows nominal spending on investment as a share of GDP back to 1929. The share is relatively stable for much of the period, with a notable decline during the last two decades.

Investment in physical capital (private and public), United States. Investment in physical capital (private and public), United States.
    Fig. 4. 

    Investment in physical capital (private and public), United States.

    Source: National Income and Product Accounts, U.S. Bureau of Economic Analysis, table 5.2.5. Intellectual property products and inventories are excluded. Government and private investment are combined. Structures includes both residential and nonresidential investment. Ratios of nominal investment to GDP are shown.
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In addition to cumulating investment, however, another step in going from the (nominal) investment rate series to the (real) capital-output ratio involves adjusting for relative prices. Fig. 5 shows the price of various categories of investment, relative to the GDP deflator. Two facts stand out: the relative price of equipment has fallen sharply since 1960 by more than a factor of 3 and the relative price of structures has risen since 1929 by a factor of 2 (for residential) or 3 (for nonresidential).

Relative price of investment, United States. Note: The chained price index for ... Relative price of investment, United States. Note: The chained price index for ...
    Fig. 5. 

    Relative price of investment, United States. Note : The chained price index for various categories of private investment is divided by the chained price index for GDP.

    Source: National Income and Product Accounts, U.S. Bureau of Economic Analysis table 1.1.4.
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A fascinating observation comes from comparing the trends in the relative prices shown in Fig. 5 to the investment shares in Fig. 4 : the nominal investment shares are relatively stable when compared to the huge trends in relative prices. For example, even though the relative price of equipment has fallen by more than a factor of 3 since 1960, the nominal share of GDP spent on equipment has remained steady.

The fall of equipment prices has featured prominently in parts of the growth literature; for example, see Greenwood et al. (1997) and Whelan (2003) . These papers make the point that one way to reconcile the facts is with a two-sector model in which technological progress in the equipment sector is substantially faster that technological progress in the rest of the economy—an assumption that rings true in light of Moore's Law and the tremendous decline in the price of a semiconductors. Combining this assumption with Cobb–Douglas production functions leads to a two-sector model that is broadly consistent with the facts we’ve laid out. A key assumption in this approach is that better computers are equivalent to having more of the old computers, so that technological change is, at least partially, capital (equipment) augmenting. The Cobb–Douglas assumption ensures that this nonlabor augmenting technological change can coexist with a balanced growth path and delivers a stable nominal investment rate. e
2.3. Factor Shares

One of the original Kaldor (1961) stylized facts of growth was the stability of the shares of GDP paid to capital and labor. Fig. 6 shows these shares using two different data sets, but the patterns are quite similar. First, between 1948 and 2000, the factor shares were indeed quite stable. Second, since 2000 or so, there has been a marked decline in the labor share and a corresponding rise in the capital share. According to the data from the Bureau of Labor Statistics, the capital share rose from an average value of 34.2% between 1948 and 2000 to a value of 38.7% by 2012. Or in terms of the complement, the labor share declined from an average value of 65.8% to 61.3%.

Capital and labor shares of factor payments, United States. Capital and labor shares of factor payments, United States.
    Fig. 6. 

    Capital and labor shares of factor payments, United States.

    Source: The series starting in 1975 are from Karabarbounis, L., Neiman, B. 2014. The global decline of the labor share. Q. J. Econ. 129 (1), 61–103. http://ideas.repec.org/a/oup/qjecon/v129y2014i1p61-103.html and measure the factor shares for the corporate sector, which the authors argue is helpful in eliminating issues related to self-employment. The series starting in 1948 is from the Bureau of Labor Statistics Multifactor Productivity Trends , August 21, 2014, for the private business sector. The factor shares add to 100%.
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It is hard to know what to make of the recent movements in factor shares. Is this a temporary phenomenon, perhaps amplified by the Great Recession? Or are some more deeper structural factors at work? Karabarbounis and Neiman (2014) document that the fact extends to many countries around the world and perhaps on average starts even before 2000. Other papers seek to explain the recent trend by studying depreciation, housing, and/or intellectual property and include Elsby et al ., 2013 ; Bridgman, 2014  ;   Koh et al ., 2015 , and Rognlie (2015) .

A closely-related fact is the pattern of factor shares exhibited across industries within an economy and across countries. Jones (2003) noted the presence of large trends, both positive and negative, in the 35 industry (2-digit) breakdown of data in the United States from Dale Jorgenson. Gollin (2002) suggests that factor shares are uncorrelated with GDP per person across a large number of countries.
2.4. Human Capital

The other major neoclassical input in production is human capital. Fig. 7 shows a time series for one of the key forms of human capital in the economy, education. More specifically, the graph shows educational attainment by birth cohort, starting with the cohort born in 1875.

Educational attainment, United States. Educational attainment, United States.
    Fig. 7. 

    Educational attainment, United States.

    Source: The blue ( dark gray in the print version) line shows educational attainment by birth cohort from Goldin, C., Katz, L.F. 2007. Long-run changes in the wage structure: narrowing, widening, polarizing. Brook. Pap. Econ. Act. 2, 135–165. The green ( gray in the print version) line shows average educational attainment for the labor force aged 25 and over from the Current Population Survey.
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Two facts emerge. First, for 75 years, educational attainment rose steadily, at a rate of slightly less than 1 year per decade. For example, the cohort born in 1880 got just over 7 years of education, while the cohort born in 1950 received 13 years of education on average. As shown in the second (green) line in the figure, this translated into steadily rising educational attainment in the adult labor force. Between 1940 and 1980, for example, educational attainment rose from 9 years to 12 years, or about 3/4 of a year per decade. With a Mincerian return to education of 7%, this corresponds to a contribution of about 0.5 percentage points per year to growth in output per worker.

The other fact that stands out prominently, however, is the leveling-off of educational attainment. For cohorts born after 1950, educational attainment rose more slowly than before, and for the latest cohorts, educational attainment has essentially flattened out. Over time, one expects this to translate into a slowdown in the increase of educational attainment for the labor force as a whole, and some of this can perhaps be seen in the last decade of the graph.

Fig. 8 shows another collection of stylized facts related to human capital made famous by Katz and Murphy (1992) . The blue line in the graph shows the fraction of hours worked in the US economy accounted for by college-educated workers. This fraction rose from less than 20% in 1963 to more than 50% by 2012. The figure also shows the college wage premium, that is the excess amount earned by college graduates over nongraduates after controlling for experience and gender. This wage premium averaged around 50% between 1963 and the early 1980s but then rose sharply through 2012 to peak at nearly 100%. Thus, even though the supply of college graduates was growing rapidly, the wage premium for college graduates was increasing sharply as well.

The supply of college graduates and the college wage premium, 1963–2012. Note: ... The supply of college graduates and the college wage premium, 1963–2012. Note: ...
    Fig. 8. 

    The supply of college graduates and the college wage premium, 1963–2012. Note: The supply of US college graduates, measured by their share of total hours worked, has risen from below 20% to more than 50% by 2012. The US college wage premium is calculated as the average excess amount earned by college graduates relative to nongraduates, controlling for experience and gender composition within each educational group.

    Source: Autor, D.H. 2014. Skills, education, and the rise of earnings inequality among the “other 99 percent”. Science 344 (6186), 843–851, fig. 3.
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Katz and Murphy (1992) provide an elegant way to understand the dynamics of the college wage premium. Letting “coll” and “hs” denote two kinds of labor (“college graduates” and “high school graduates”), the human capital aggregate that enters production is given by a CES specification:
equation ( 4 )
View the MathML source View the MathML source H = ( A c o l l L c o l l ) ρ + ( A h s L h s ) ρ 1 / ρ
Turn   MathJax on
An increase in the supply of college graduates lowers their marginal product, while an increase in the technology parameter A coll raises their marginal product. Katz and Murphy (1992) show that with an elasticity of substitution of around 1.4, a constant growth rate of A coll / A hs , which Katz and Murphy call “skill-biased technical change,” together with the observed movements in L coll / L hs can explain the time series for the college wage premium.

Human capital includes more than just education, of course. Workers continue to accumulate skills on the job. This human capital shows up as higher wages for workers, but separating this into a quantity of human capital and a price per unit of human capital requires work. One simple approach is to assume each year of work experience leads to a constant increase in human capital, and this approach is commonly pursued in growth accounting. Examples of richer efforts to measure human capital in a growth setting include Lucas, 2009 ; Erosa et al ., 2010  ;   Lucas and Moll, 2014 , and Manuelli and Seshadri (2014) .
2.5. Ideas

Our next set of facts relate to the economy's stock of knowledge or ideas, the A in the production function that we began with back in Eq. ( 1 ). It has long been recognized that the “idea production function” is hard to measure. Where do ideas come from? Part of the difficulty is that the answer is surely multidimensional. Ideas are themselves very heterogeneous, some clearly arise through intentional research, but others seem to arrive by chance out of seemingly nowhere. Confronted with these difficulties, Solow (1956) modeled technological change as purely exogenous, but this surely goes too far. The more people there are searching for new ideas, the more likely it is that discoveries will be made. This is true if the searching is intentional, as in research, but even if it is a byproduct of the production process itself as in models of learning by doing. The production of new ideas plays a fundamental role in the modern understanding of growth; see Romer, 1990  ;   Grossman and Helpman, 1991 , and Aghion and Howitt (1992) . f

With this in mind, Fig. 9 shows spending on research and development, as a share of GDP, for the United States. These data can now be obtained directly from the National Income and Product Accounts, thanks to the latest revisions by the Bureau of Economic Analysis. The broadest measure of investment in ideas recorded by the NIPA is investment in “intellectual property products.” This category includes traditional research and development, spending on computer software, and finally spending on “entertainment,” which itself includes movies, TV shows, books, and music.

Research and development spending, United States. Research and development spending, United States.
    Fig. 9. 

    Research and development spending, United States.

    Source: National Income and Product Accounts, U.S. Bureau of Economic Analysis via FRED database. “Software and entertainment” combines both private and public spending. “Entertainment” includes movies, TV shows, books, and music.
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Several facts stand out in Fig. 9 . First, total spending on investment in intellectual property products has risen from less than 1% of GDP in 1929 to nearly 5% of GDP in recent years. This overall increase reflects a large rise in private research and development and a large rise in software and entertainment investment, especially during the last 25 years. Finally, government spending on research and development has been shrinking as a share of GDP since peaking in the 1960s with the space program.

Fig. 10 provides an alternative perspective on R&D in two dimensions. First, it focuses on employment rather than dollars spent, and second it brings in an international perspective. The figure shows the number of researchers in the economy as a share of the population. g

Research employment share. Research employment share.
    Fig. 10. 

    Research employment share.

    Source: Data for 1981–2001 are from OECD Main Science and Technology Indicators, http://stats.oecd.org/Index.aspx?DataSetCode=MSTI_PUB . Data prior to 1981 for the United States are spliced from Jones, C.I. 2002. Sources of U.S. economic growth in a world of ideas. Am. Econ. Rev. 92 (1), 220–239, which uses the NSF's definition of “scientists and engineers engaged in R&D.”
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Each of the three measures in the figure tells the same story: the fraction of the population engaged in R&D has been rising in recent decades. This is true within the United States, within the OECD, and even if we incorporate China and Russia as well.

It is important to appreciate a significant limitation of the R&D data shown so far. In particular, these data only capture a small part of what an economist would call research. For example, around 70% of measured R&D occurs in the manufacturing industry. In 2012, only 18 million workers (out of US employment that exceeds 130 million) were employed by firms that conducted any official R&D. h According to their corporate filings, Walmart and Goldman-Sachs report doing zero R&D.

So far, we have considered the input side of the idea production function. We now turn to the output side. Unfortunately, the output of ideas is even harder to measure than the inputs. One of the more commonly-used measures is patents, and this measure is shown in Fig. 11 .

Patents granted by the US Patent and Trademark Office. Patents granted by the US Patent and Trademark Office.
    Fig. 11. 

    Patents granted by the US Patent and Trademark Office.

    Source: http://www.uspto.gov/web/offices/ac/ido/oeip/taf/h_counts.htm .
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On first glance, it appears that patents, like many other variables reviewed in this essay, have grown exponentially. Indeed, at least since 1980 one sees a very dramatic rise in the number of patents granted in the United States, both in total and to US inventors. The difference between these two lines—foreign patenting in the United States—is also interesting, and one testament to the global nature of ideas is that 56% of patents granted by the US patent office in 2013 were to foreigners.

A closer look at Fig. 11 , though, reveals something equally interesting: the number of patents granted to US inventors in 1915, 1950, and 1985 was approximately the same. Put another way, during the first 85 years of the 20th century, the number of patents granted to US residents appears to be stationary, in sharp contrast to the dramatic increase since 1985 or so. Part of the increase since the 1980s is due to changes in patent policy, including extending patent protection to software and business models and changes in the judicial appeals process for patent cases ( Jaffe and Lerner, 2006 ).

Griliches (1994) combined these two basic facts related to ideas (rapid growth in the inputs, stable production of patents) to generate a key implication: the productivity of research at producing patents fell sharply for most of the 20th century. Kortum (1997) developed a growth model designed to match these facts in which he emphasized that patents can be thought of as proportional improvements in productivity. If each patent raises GDP by a constant percent, then a constant flow of new patents can generate a constant rate of economic growth. The problem with this approach (or perhaps the problem with the patent data) is that it breaks down after 1980 or so. Since 1980, the number of patents has risen by more than a factor of four, while growth rates are more or less stable. The bottom line is that the idea production function remains something of a black box perhaps precisely because we do not have great measures of ideas or the inputs used to produce them. i
2.6. Misallocation

The organizing principle for this section of the paper is the production function given back in Eq. ( 1 ). In specifying that production function, I broke total factor productivity into two pieces: the stock of ideas, A , and everything else, which I labeled “M” either for the “measure of our ignorance” or for “misallocation.” It is this latter interpretation that I wish to take up now.

One of the great insights of the growth literature in the last 15 years is that misallocation at the micro level can show up as a reduction in total factor productivity at a more aggregated level. This insight appears in various places, including Banerjee and Duflo, 2005 ; Chari et al ., 2007  ;   Restuccia and Rogerson, 2008 and Hsieh and Klenow (2009) .

The essence of the insight is quite straightforward: when resources are allocated optimally, the economy will operate on its production possibilities frontier. When resources are misallocated, the economy will operate inside this frontier. But that is just another way of saying that TFP will be lower: a given quantity of inputs will produce less output.

As we explain in detail in the second part of this paper (in Section 4.7 ), there is a large literature on misallocation and development—this is our best candidate answer to the question of why are some countries so much richer than others. There is much less discussion of the extent to which misallocation is related to frontier growth, the subject at hand.

While it is clear conceptually that even the country or countries at the frontier of growth can suffer from misallocation and that changes in misallocation can contribute to growth, there has been little work quantifying this channel. Indeed, my own working hypothesis for many years was that this effect was likely small in the United States during the last 50 years. I now believe this is wrong.

Hsieh et al. (2013) highlight a striking fact that illustrates this point: in 1960, 94% of doctors and lawyers were white men; by 2008, this fraction was just 62%. Given that innate talent for these and other highly-skilled professions is unlikely to differ across groups, the occupational distribution in 1960 suggests that a large number of innately talented African Americans and white women were not working in the occupations dictated by comparative advantage. The paper quantifies the macroeconomic consequences of the remarkable convergence in the occupational distribution between 1960 and 2008 and finds that 15–20% of growth in aggregate output per worker is explained by the improved allocation of talent. In other words, declines in misallocation may explain a significant part of US economic growth during the last 50 years.

Examples to drive home these statistics are also striking. Sandra Day O’Connor—future Supreme Court Justice—graduated third in her class from Stanford Law School in 1952. But the only private sector job she could get upon graduation was as a legal secretary ( Biskupic, 2006 ). Closer to our own profession, David Blackwell, of contraction mapping fame, was the first African American inducted into the National Academy of Sciences and the first tenured at U.C. Berkeley. Yet despite getting his Ph.D. at age 22 and obtaining a postdoc at the Institute for Advanced Studies in 1941, he was not permitted to attend lectures at Princeton and was denied employment at U.C. Berkeley for racial reasons. He worked at Howard University until 1954, when he was finally hired as a full professor in the newly-created statistics department at Berkeley. j

Another potential source of misallocation is related to the economics of ideas. It has long been suggested that knowledge spillovers are quite significant, both within and across countries. To the extent that these spillovers are increasingly internalized or addressed by policy—or to the extent that the opposite is true—the changing misallocation of knowledge resources may be impacting economic growth. k

As one final example, Hsieh and Moretti (2014) suggest that spatial misallocation within the United States may be significant. Why is it that Sand Hill Road in Palo Alto has Manhattan rents without the skyscrapers? Hsieh and Moretti argue that land use policies prevent the efficient spatial matching of people to land and to each other. They estimate that places like Silicon Valley and New York City would be four to eight times more populous in the efficient allocation.

Quantifying these and other types of misallocation affecting frontier growth is a fruitful direction for future research.
2.7. Explaining the Facts of Frontier Growth

While this essay is primarily about the facts of economic growth, it is helpful to step back and comment briefly on how multiple facts have been incorporated into our models of growth.

The basic neoclassical growth framework of Solow (1956) and Ramsey (1928) / Cass (1965) / Koopmans (1965) has long served as a benchmark organizing framework for understanding the facts of growth. The nonrivalry of ideas, emphasized by Romer (1990) , helps us understand how sustained exponential growth occurs endogenously. I review this contribution and some of the extensive research it sparked in Jones (2005) . l

The decline in the relative price of equipment and the rise in the college wage premium are looked at together in Krusell et al. (2000) . That paper considers a setting in which equipment capital is complementary to skilled labor, so that the (technologically driven) decline in the price of equipment is the force of skill-biased technological change. That paper uses a general CES structure. One of the potential issues in that paper was that it could lead to movements in the labor share. But perhaps we are starting to see those in the data.

The presence of trends in educational attainment and research investment opens up interesting opportunities for future research. Why are educational attainment and the share of labor devoted to research rising over time? What are the implications of these trends for future growth? Restuccia and Vandenbroucke (2013) suggest that skill-biased technological change is itself responsible for driving the rise in educational attainment. Acemoglu (1998) examines the further interactions when the direction of technological change is itself endogenous. Jones (2002) considers the implication of the trends in education and research intensity for future growth, suggesting that these trends have substantially raised growth during the last 50 years above the economy's long-run growth rate.
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