Fluent Essays

(1) what methods Chad Jones uses in predicting how the World Income Distribution will evolve in the future, what he finds and your critique of his method and findings; (2) what methods Lant Pritchett uses in predicting how the World Income Distribution will evolve in the future, what he finds and your critique of his method and findings; Then, by the end of Sunday: (3) provide concrete and constructive feedback on a fellow discussion group member's original post. American Economic Association Divergence, Big Time Author(s): Lant Pritchett Source: The Journal of Economic Perspectives, Vol. 11, No. 3 (Summer, 1997), pp. 3-17 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2138181 Accessed: 10/09/2010 12:32 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. 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For more information about JSTOR, please contact [email protected] American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The Journal of Economic Perspectives. http://www.jstor.org http://www.jstor.org/action/showPublisher?publisherCode=aea http://www.jstor.org/stable/2138181?origin=JSTOR-pdf http://www.jstor.org/page/info/about/policies/terms.jsp http://www.jstor.org/action/showPublisher?publisherCode=aea Journal of Economic Perspectives-Volume 11, Number 3-Summer 1997-Pages 3-17 Divergence, Big Time Lant Pritchett ivergence in relative productivity levels and living standards is the domi- nant feature of modern economic history. In the last century, incomes in the "less developed" (or euphemistically, the "developing") countries have fallen far behind those in the "developed" countries, both proportionately and absolutely. I estimate that from 1870 to 1990 the ratio of per capita incomes between the richest and the poorest countries increased by roughly a factor of five and that the difference in income between the richest country and all others has increased by an order of magnitude.' This divergence is the result of the very dif- ferent patterns in the long-run economic performance of two sets of countries. One set of countries-call them the "developed" or the "advanced capi- talist" (Maddison, 1995) or the "high income OECD" (World Bank, 1995) -is easily, if awkwardly, identified as European countries and their offshoots plus Japan. Since 1870, the long-run growth rates of these countries have been rapid (by previous historical standards), their growth rates have been remarkably sim- ilar, and the poorer members of the group grew sufficiently faster to produce considerable convergence in absolute income levels. The other set of countries, called the "developing" or "less developed" or "nonindustrialized," can be easily, if still awkwardly, defined only as "the other set of countries," as they have nothing else in common. The growth rates of this set of countries have been, on average, slower than the richer countries, producing divergence in ' To put it another way, the standard deviation of (natural log) GDP per capita across all countries has increased between 60 percent and 100 percent since 1870, in spite of the convergence amongst the richest. * Lant Pritchett is Senior Economist, World Bank, Washington, D.C. 4 Journal of Economic Perspectives relative incomes. But amongst this set of countries there have been strikingly different patterns of growth: both across countries, with some converging rapidly on the leaders while others stagnate; and over time, with a mixed record of takeoffs, stalls and nose dives. The next section of this paper documents the pattern of income growth and convergence within the set of developed economies. This discussion is greatly aided by the existence of data, whose lack makes the discussion in the next section of the growth rates for the developing countries tricky, but as I argue, not impossible. Finally, I offer some implications for historical growth rates in developing countries and some thoughts on the process of convergence. Convergence in Growth Rates of Developed Countries Some aspects of modern historical growth apply principally, if not exclusively, to the "advanced capitalist" countries. By "modern," I mean the period since 1870. To be honest, the date is chosen primarily because there are nearly complete na- tional income accounts data for all of the now-developed economies since 1870. Maddison (1983, 1991, 1995) has assembled estimates from various national and academic sources and has pieced them together into time series that are compa- rable across countries. An argument can be made that 1870 marks a plausible date for a modern economic period in any case, as it is near an important transition in several countries: for example, the end of the U.S. Civil War in 1865; the Franco- Prussian War in 1870-71, immediately followed by the unification of Germany; and Japan's Meiji Restoration in 1868. Perhaps not coincidentally, Rostow (1990) dates the beginning of the "drive to technological maturity" of the United States, France and Germany to around that date, although he argues that this stage began earlier in Great Britain.2 Table 1 displays the historical data for 17 presently high-income industrialized countries, which Maddison (1995) defines as the "advanced capitalist" countries. The first column of Table 1 shows the per capita level of income for each country in 1870, expressed in 1985 dollars. The last three columns of Table 1 show the average per annum growth rate of real per capita income in these countries over three time periods: 1870-1960, 1960-1980 and 1980-1994. These dates are not meant to date any explicit shifts in growth rates, but they do capture the fact that there was a golden period of growth that began some time after World War II and ended sometime before the 1980s. Three facts jump out from Table 1. First, there is strong convergence in per capita incomes within this set of countries. For example, the poorest six countries in 1870 had five of the six fastest national growth rates for the time period 1870- 2 For an alternative view, Maddison (1991) argues the period 1820-1870 was similar economically to the 1870-1913 period. Lant Pritchett 5 Table 1 Average Per Annum Growth Rates of GDP Per Capita in the Presently High- Income Industrialized Countries, 1870-1989 Per annum growth rates Level in 1870 Country (1985 P$) 1870-1960 1960-80 1980-94 Average 1757 1.54 3.19 1.51 Std dev. of growth rates .33 1.1 .51 Australia 3192 .90 2.43 1.22 Great Britain 2740 1.08 2.02 1.31 New Zealand 2615 1.24 1.39 1.28 Belgium 2216 1.05 3.70 1.52 Netherlands 2216 1.25 2.90 1.29 USA 2063 1.70 2.48 1.52 Switzerland 1823 1.94 2.07 .84 Denmark 1618 1.66 2.77 1.99 Germany 1606 1.66 3.03 1.56 Austria 1574 1.40 3.81 1.58 France 1560 1.56 3.53 1.31 Sweden 1397 1.85 2.74 .81 Canada 1360 1.85 3.32 .86 Italy 1231 1.54 4.16 1.62 Norway 1094 1.81 3.78 2.08 Finland 929 1.91 3.77 1.09 Japan 622 1.86 6.28 2.87 Source: Maddison, 1995. Notes: Data is adjusted from 1990 to 1985 P$ by the U.S. GDP deflator, by a method described later in this article. Per annum growth rates are calculated using endpoints. 1960; conversely, the richest five countries in 1870 recorded the five slowest growth rates from 1870 to 1960.3 As is well known, this convergence has not happened at a uniform rate. There is as much convergence in the 34 years between 1960 and 1994 as in the 90 years from 1870 to 1960. Even within this earlier period, there are periods of stronger convergence pre-1914 and weaker convergence from 1914 to 1950. Second, even though the poorer countries grew faster than the richer countries did, the narrow range of the growth rates over the 1870-1960 period is striking. The United States, the richest country in 1960, had grown at 1.7 percent per annum since 1870, while the overall average was 1.54. Only one country, Australia, grew either a half a percentage point higher or lower than the average, and the standard deviation of the growth rates was only .33. Evans (1994) formally tests the hypothesis 'The typical measure of income dispersion, the standard deviation of (natural log) incomes, fell from .41 in 1870 to .27 in 1960 to only .11 in 1994. 6 Journal of Economic Perspectives that growth rates among 13 European and offshoot countries (not Japan) were equal, and he is unable to reject it at standard levels of statistical significance. Third, while the long run hides substantial variations, at least since 1870 there has been no obvious acceleration of overall growth rates over time. As CharlesJones (1995) has pointed out, there is remarkable stability in the growth rates in the United States. For instance, if I predict per capita income in the United States in 1994 based only on a simple time trend regression of (natural log) GDP per capita estimated with data from 1870 to 1929, this prediction made for 65 years ahead is off by only 10 percent.4 Although this predictive accuracy is not true for every country, it is true that the average growth rate of these 17 countries in the most recent period between 1980 and 1994 is almost exactly the same as that of the 1870- 1960 period. However, this long-run stability does mask modest swings in the growth rates over time, as growth was considerably more rapid in the period between 1950 to 1980, especially outside the United States, than either in earlier periods or since 1980. These three facts are true of the sample of countries that Maddison defines as the "advanced capitalist" countries. However, the discussion of convergence and long-run growth has always been plagued by the fact that the sample of countries for which historical economic data exists (and has been assembled into convenient and comparable format) is severely nonrepresentative. Among a sample of now "advanced capitalist" countries something like convergence (or at least nondiver- gence) is almost tautological, a point made early on by De Long (1988). Defining the set of countries as those that are the richest now almost guarantees the finding of historical convergence, as either countries are rich now and were rich historically, in which case they all have had roughly the same growth rate (like nearly all of Europe) or countries are rich now and were poor historically (likejapan) and hence grew faster and show convergence. However, examples of divergence, like countries that grew much more slowly and went from relative riches to poverty (like Argen- tina) or countries that were poor and grew so slowly as to become relatively poorer (like India), are not included in the samples of "now developed" countries that tend to find convergence. Calculating a Lower Bound For Per Capita GDP This selectivity problem raises a difficult issue in trying to estimate the possible magnitude of convergence or divergence of the incomes since 1870. There is no 'Jones (1995) uses this basic fact of the constancy of growth to good effect in creating a compelling argument that the steadiness of U.S. growth implies that endogenous growth models that make growth a function of nonstationary variables, such as the level of R&D spending or the level of education of the labor force, are likely incorrect as they imply an accelerating growth rate (unless several variablesworking in opposite directions just happen to offset each other). These issues are also discussed in his paper in this issue. Divergence, Big Time 7 historical data for many of the less developed economies, and what data does exist has enormous problems with comparability and reliability. One alternative to searching for historical data is simply to place a reasonable lower bound on what GDP per capita could have been in 1870 in any country. Using this lower bound and estimates of recent incomes, one can draw reliable conclusions about the his- torical growth rates and divergence in cross-national distribution of income levels. There is little doubt life was nasty, brutish and short in many countries in 1870. But even deprivation has its limit, and some per capita incomes must imply stan- dards of living that are unsustainably and implausibly low. After making conservative use of a wide variety of different methods and approaches, I conclude that $250 (expressed in 1985 purchasing power equivalents) is the lowest GDP per capita could have been in 1870. This figure can be defended on three grounds: first, no one has ever observed consistently lower living standards at any time or place in history; second, this level is well below extreme poverty lines actually set in impov- erished countries and is inconsistent with plausible levels of nutritional intake; and third, at a lower standard of living the population would be too unhealthy to expand. Before delving into these comparisons and calculations, it is important to stress that using the purchasing power adjustments for exchange rates has an especially important effect in poor countries. While tradable goods will have generally the same prices across countries because of arbitrage, nontradable goods are typically much cheaper in poorer countries because of their lower income levels. If one applies market exchange rates to convert incomes in these economies to U.S. dol- lars, one is typically far understating the "true" income level, because nontradable goods can be bought much more cheaply than market exchange rates will imply. There have been several large projects, especially the UN International Compari- sons Project and the Penn World Tables, that through the collection of data on the prices of comparable baskets of goods in all countries attempt to express different countries' GDP in terms of a currency that represents an equivalent purchasing power over a basket of goods. Since this adjustment is so large and of such quan- titative significance, I will denote figures that have been adjusted in this way by 1$. By my own rough estimates, a country with a per capita GDP level of $70 in U.S. dollars, measured in market exchange rates, will have a per capita GDP of J$250. The first criteria for a reasonable lower bound on GDP per capita is that it be a lower bound on measured GDP per capita, either of the poorest countries in the recent past or of any country in the distant past. The lowest five-year average level of per capita GDP reported for any country in the Penn World Tables (Mark 5) is J$275 for Ethiopia in 1961-65; the next lowest is J$278 for Uganda in 1978-1982. The countries with the lowest level of GDP per capita ever observed, even for a single year, are J$260 for Tanzania in 1961, J$299 for Burundi in 1965 and J$220 Uganda in 1981 (in the middle of a civil war). Maddison (1991) gives estimates of GDP per capita of some less developed countries as early as 1820: J$531 for India, J$523 for China and J$614 for Indonesia. His earliest estimates for Africa begin in 1913: J$508 for Egypt and J$648 for Ghana. Maddison also offers increasingly 8 Journal of Economic Perspectives speculative estimates for western European countries going back much further in time; for example, he estimates that per capita GDPs in the Netherlands and the United Kingdom in 1700 were P$1515 and P$992, respectively, and ventures to guess that the average per capita GNP in western Europe was P$400 in 1400. Kuz- nets's (1971) guess of the trough of the average per capita GDP of European coun- tries in 900 is around P$400.' On this score, P$250 is a pretty safe bet. A complementary set of calculations to justify a lower bound are based on "subsistence" income. While "subsistence" as a concept is out of favor, and right- fully so for many purposes, it is sufficiently robust for the task at hand. There are three related calculations: poverty lines, average caloric intakes and the cost of subsistence. Ravallion, Datt and van de Walle (1991) argue that the lowest defen- sible poverty line based on achieving minimally adequate consumption expendi- tures is P$252 per person per year. If we assume that personal consumption expen- ditures are 75 percent of GDP (the average for countries with GDP per capita less than P$400) and that mean income is 1.3 times the median, then even to achieve median income at the lowest possible poverty line requires a per capita income of $437.6 As an alternative way of considering subsistence GDP per capita, begin with the finding that estimated average intake per person per day consistent with work- ing productively is between 2,000 to 2,400 calories.7 Now, consider two calculations. The first is that, based on a cross-sectional regression using data on incomes from the Penn World Tables and average caloric intake data from the FAO, the predicted caloric consumption at P$250 is around 1,600.8 The five lowest levels of 5 More specifically, Kuznets estimated that the level was about $160, if measured in 1985 U.S. dollars. However, remember from the earlier discussion that a conversion at market exchange rates-which is what Kuznets was using-is far less than an estimate based on purchasing power parity exchange rates. If we use a multiple of 2.5, which is a conservative estimate of the difference between the two, Kuznets's estimate in purchasing power equivalent terms would be equal to a per capita GDP of $400 in 1985 U.S. dollars, converted at the purchasing power equivalent rate. " High poverty rates, meaning that many people live below these poverty lines, are not inconsistent with thinking of these poverty lines as not far above our lower bound, because many individuals can be in poverty, but not very far below the line. For instance, in South Asia in 1990, where 33 percent of the population was living in "extreme absolute poverty," only about 10 percent of the population would be living at less than $172 (my estimates from extrapolations of cumulative distributions reported in Chen, Datt and Ravallion, 1993). 7The two figures are based on different assumptions about the weight of adult men and women, the mean temperature and the demographic structure. The low figure is about as low as one can go because it is based on a very young population, 39 percent under 15 (the young need fewer calories), a physically small population (men's average weight of only 110 pounds and women of 88), and a temperature of 250 C (FAO, 1957). The baseline figure, although based on demographic structure, usually works out to be closer to 2,400 (FA0, 1974). 8 The regression is a simple log-log of caloric intake and income in 1960 (the log-log is for simplicity even though this might not be the best predictor of the level). The regression is ln(average caloric intake) = 6.37 + .183*ln(GDP per capita), (59.3) (12.56). Lant Pritchett 9 caloric availability ever recorded in the FAO data for various countries- 1,610 calories/person during a famine in Somalia in 1975; 1,550 calories/person during a famine in Ethiopia in 1985; 1,443 calories/person in Chad in 1984; 1,586 calories/person in China in 1961 during the famines and disruption associated with the Cultural Revolution; and 1,584 calories/person in Mozambique in 1987-reveal that nearly all of the episodes of average daily caloric consumption below 1,600 are associated with nasty episodes of natural and/or man-made catastrophe. A second use of caloric requirements is to calculate the subsistence income as the cost of meeting caloric requirements. Bairoch (1993) reports the results of the physiolog- ical minimum food intake at $291 (at market exchange rates) in 1985 prices. These calculations based on subsistence intake of food again suggest J$250 is a safe lower bound. That life expectancy is lower and infant mortality higher in poorer countries is well documented, and this relation can also help establish a lower bound on income (Pritchett and Summers, 1996). According to demographers, an under-five infant mortality rate of less than 600 per 1000 is necessary for a stable population (Hill, 1995). Using a regression based on Maddison's (1991) historical per capita income estimates and infant mortality data from historical sources for 22 countries, I predict that infant mortality in 1870 for a country with income of J$250 would have been 765 per 10O.9 Although the rate of natural increase of population back in 1870 is subject to great uncertainty, it is typically estimated to be between .25 and 1 percent annually in that period, which is again inconsistent with income levels as low as J$250.1o Divergence, Big Time If you accept: a) the current estimates of relative incomes across nations; b) the estimates of the historical growth rates of the now-rich nations; and c) that even in the poorest economies incomes were not below J$250 at any point-then you cannot escape the conclusion that the last 150 years have seen divergence, big time. The logic is straightforward and is well illustrated by Figure 1. If there had been no divergence, then we could extrapolate backward from present income of the poorer countries to past income assuming they grew at least as fast as the United 'The regression is estimated with country fixed effects: ln(IMR) = -.59 ln(GDP per capita) _ .013*Trend _ .002*Trend*(l if >1960) (23.7) (32.4) (14.23) N = 1994 and t-statistics are in parenthesis. The prediction used the average country constant of 9.91. "' Livi-Basci (1992) reports estimates of population growth in Africa between 1850 and 1900 to be .87 percent, and .93 percent between 1900 and 1950, while growth for Asia is estimated to be .27 1850 to 1900, and .61 1900 to 1950. Clark (1977) estimates the population growth rates between 1850 and 1900 to be .43 percent in Africa and India and lower, .33 percent, in China. 10 Journal of Economic Perspectives Figure 1 Simulation of Divergence of Per Capita GDP, 1870-1985 (showing only selected countries) 1870 1960 1990 Richest / poorest 8.7 38.5 45.2 std. dev.: 0.64 0.88 1.06 o | l j~~~~~~~~~~~~~~P$18054 USA USA - - -Ethiopia < <5 ..... Chad 90 - -- MirlimumI ct 00 W P$20631 1 ~~~~~~~~~~~Actual l X _ l ~~~~~~~~Imputed ll = _ l *-- | l ~~~~~~~~~~Chad P$250 (assumed lower bound) I l t ,,,, I,,,,,,,,,~~~~~~~~~ ~~~~ I, , I, , I, ,1,,, I . 1850 1870 1890 1910 1930 1950 1970 1990 2010 States. However, this would imply that many poor countries must have had incomes below J$100 in 1870. Since this cannot be true, there must have been divergence. Or equivalently, per capita income in the United States, the world's richest indus- trial country, grew about four-fold from 1870 to 1960. Thus, any country whose income was not fourfold higher in 1960 than it was in 1870 grew more slowly than the United States. Since 42 of the 125 countries in the Penn World Tables with data for 1960 have levels of per capita incomes below $1,000 (that is, less than four times $250), there must have been substantial divergence between the top and bottom. The figure of J$250 is not meant to be precise or literal and the conclusion of massive divergence is robust to any plausible assumption about a lower bound. Consider some illustrative calculations of the divergence in per capita incomes in Table 2. I scale incomes back from 1960 such that the poorest country in 1960 just reaches the lower bound by 1870, the leader in 1960 (the United States) reaches its actual 1870 value, and all relative rankings between the poorest country and the United States are preserved." The first row shows the actual path of the U.S. econ- " The growth rate of the poorest country was imposed to reach F$250 at exactly 1870, and the rate of the United States was used for the growth at the top. Then each country's growth rate was assumed to be a weighted average of those two rates, where the weights depended on the scaled distance from the bottom country in the beginning period of the imputation, 1960. This technique "smushes" the distri- Divergence, Big Time 11 Table 2 Estimates of the Divergence of Per Capita Incomes Since 1870 1870 1960 1990 USA (F$) 2063 9895 18054 Poorest (F$) 250 257 399 (assumption) (Ethiopia) (Chad) Ratio of GDP per capita of richest to poorest country 8.7 38.5 45.2 Average of seventeen "advanced capitalist" countries 1757 6689 14845 from Maddison (1995) Average LDCs from PWT5.6 for 1960, 1990 (imputed for 740 1579 3296 1870) Average "advanced capitalist" to average of all other 2.4 4.2 4.5 countries Standard deviation of natural log of per capita incomes .51 .88 1.06 Standard deviation of per capita incomes F$459 F$2,112 F$3,988 Average absolute income deficit from the leader F$1286 F$7650 F$12,662 Notes: The estimates in the columns for 1870 are based on backcasting GDP per capita for each country using the methods described in the text assuming a minimum of P$250. If instead of that method, incomes in 1870 are backcast with truncation at P$250, the 1870 standard deviation is .64 (as reported in Figure 1). omy. The second row gives the level of the poorest economy in 1870, which is J$250 by assumption, and then the poorest economies in 1960 and 1990 taken from the Penn World Tables. By division, the third row then shows that the ratio of the top to the bottom income countries has increased from 8.7 in 1870 to 38 by 1960 and to 45 by 1990. If instead one takes the 17 richest countries (those shown in Table 1) and applies the same procedure, their average per capita income is shown in the fourth row. The average for all less developed economies appearing in the Penn World Tables for 1960 and 1990 is given in the fifth row; the figure for 1870 is calculated by the "backcasting" imputation process for historical incomes de- scribed above. By division, the sixth row shows that the ratio of income of the richest to all other countries has almost doubled from 2.4 in 1870 to 4.6 by 1990. bution back into the smaller range between the top and bottom while maintaining all cross country rankings. The formula for estimating the log of GDP per capita (GDPPC) in the ith country in 1870 was GDPPCi 870' = GDPPCi 96"* *(1/w,) where the scaling weight wi was wi = (1 - ai)*min(GDPPC'96()/F$250 + ai*GDPPCusA/GDPPCusA, and where ai is defined by ai = (GDPPC19N - min (S DPPC'9"))/(GDPPCL9? -min(CDPPC'96"()). 12 Journal of Economic Perspectives The magnitude of the change in the absolute gaps in per capita incomes between rich and poor is staggering. From 1870 to 1990, the average absolute gap in incomes of all countries from the leader had grown by an order of magnitude, from $1,286 to $12,662, as shown in the last row of Table 2.12 While the growth experience of all countries is equally interesting, some are more equally interesting than others. China and India account for more than a third of the world's population. For the conclusion of divergence presented here, however, a focus on India and China does not change the historical story. One can estimate their growth rates either by assuming that they were at $250 in 1870 and then calculating their growth rate in per capita GDP to reach the levels given by the Penn World Tables in 1960 (India, $766; China, $567), or by using Maddison's historical estimates, which are shown in Table 3, India's growth rate is a fifth and China's a third of the average for developed economies. Either way, India's and China's incomes diverged significantly relative to the leaders between 1870 and 1960. The idea that there is some lower bound to GDP per capita and that the lower bound has implications for long-run growth rates (and hence divergence) will not come as news either to economic historians or to recent thinkers in the area of economic growth (Lucas, 1996). Kuznets (1966, 1971) pointed out that since the now-industrialized countries have risen from very low levels of output to their pres- ently high levels, and that their previously very low levels of output were only con- sistent with a very slow rate of growth historically, growth rates obviously accelerated at some point. Moreover, one suspects that many of the estimates of income into the far distant past cited above rely on exactly this kind of counterfactual logic. Considering Alternate Sources of Historical Data Although there is not a great deal of historical evidence on GDP estimates in the very long-run for the less developed countries, what there is confirms the finding of massive divergence. Maddison (1995) reports time series data on GDP per capita incomes for 56 countries. These include his 17 "advanced capitalist" countries (presented in Table 1), five "southern" European countries, seven eastern Euro- pean countries and 28 countries typically classified as "less … Journal of Economic Perspectives—Volume 11, Number 3—Summer 1997—Pages 19–36 On the Evolution of the World Income Distribution Charles I. Jones H ow rich are the richest countries in the world relative to the poorest? Are poor countries catching up to the rich countries or falling further be- hind? How might the world income distribution look in the future? These questions have been the subject of much empirical and theoretical work over the last decade, beginning with Abramovitz (1986) and Baumol (1986), continuing with Barro (1991) and Mankiw, Romer and Weil (1992), and including most re- cently work by Quah (1993a, 1996). This paper provides one perspective on this literature by placing it explicitly in the context of what it has to say about the shape of the world income distribution. We begin in the first section by documenting several empirical facts concerning the distribution of GDP per worker across the countries of the world and how this distribution has changed since 1960.1 The main part of the paper attempts to characterize the future of the world income distribution using three different techniques. First, we use a standard growth model to project the current dynamics of the income distribution forward, assuming the policies in place in each country during the 1980s continue. One can interpret this exercise as forecasting the near-term income distribution. The results indicate that the near-term income distribution looks broadly like the current dis- tribution. However, there are some notable exceptions, primarily at the top of the income distribution, where a number of countries are predicted to continue to converge toward and even overtake the United States as the richest country in the world. Second, we exploit insights from the large literature on cross-country growth 1For a related review of the facts, see Parente and Prescott (1993) and Jones (forthcoming). • Charles I. Jones is Assistant Professor of Economics, Stanford University, Stanford, Cali- fornia. His e-mail address is [email protected] 20 Journal of Economic Perspectives regressions following Barro (1991) and Mankiw, Romer and Weil (1992). An im- portant finding of this literature is that one can interpret the variation in growth rates around the world as reflecting how far countries are from their "steady state" positions. Korea and Japan have grown rapidly because their steady state positions in the income distribution are much higher than their current positions. Venezuela has grown slowly because the reverse is true. We use this insight to provide a second way of predicting where countries are headed based on current policies. Finally, we step back and consider how the steady states toward which countries are headed are themselves changing. The evidence from the last 30 years suggests that growth miracles are occurring more frequently than growth disasters and that the relative frequency of miracles has increased. Projecting these dynamics forward indicates that the long-run world income distribution involves a substantial im- provement in the incomes of many countries. For example in 1960, 60 percent of countries had incomes less than 20 percent of incomes in the richest country. In the long run, the empirical results indicate that the fraction of "poor" countries will fall from 60 percent to only 27 percent. Facts Before examining several facts about the world income distribution, it is worth pausing for a moment to consider which definition of income to use. GDP per capita seems like a natural definition if one is interested in an important determi- nant of average welfare. However, in many developing countries, nonmarket pro- duction is quite important, leading GDP per capita to understate true income in these countries. A coarse correction for this problem is to focus on GDP per worker. Both the numerator and the denominator then correspond to the market sector. To the extent that wages are equalized at the margin between the market and nonmarket sectors, this is a natural measure of income, and it is the one employed in most of this paper. The world distribution of GDP per worker has changed substantially during the post-World War II period. Figure 1 plots the density of GDP per worker relative to the United States in 1960 and 1988 for 121 countries.2 Roughly speaking, the more countries there are at a particular level of income, the higher the density will be at that point in the figure. The 121-country sample, which includes all countries for which Summers and Heston (1991) report real GDP per worker in both years, will make up the "world" for the purposes of this paper. The most notable omissions are several Eastern European economies and several economies in the Middle East for which data are not reported in 1960. A number of features in this figure deserve comment. First, the distribution is 2 T h e data are from the Penn World Tables Mark 5.6 update of Summers and Heston (1991) and therefore are in principle corrected for differences in purchasing power across economies. The density estimates are computed using a Gaussian kernel with a bandwidth chosen as .9AN–1/5 where A is the standard deviation of the data and N is the number of observations. Charles I. Jones 21 Figure 1 World Income Distribution, 1960 and 1988 wide. In 1988, for example, the ratio of the income in the richest country (the United States) to the poorest country (Myanmar) was 35. Second, the 1960 distri- bution is single-peaked and looks roughly normal, although the tails are too thick. In contrast, the distribution in 1988 exhibits "twin-peaks," to use the appellation coined by Quah (1993a). This change reflects a shift in the mass of the distribution away from the middle and toward the ends. In particular, the "hump" in the 1960 distribution between about 5 and 30 percent of U.S. income has shifted upward into the 20 to 65 percent range. Finally, the world income distribution is wider in 1988 than it was in 1960, both at the top and at the bottom. What cannot be seen in the figure is the general growth in GDP per worker throughout the world. Though this paper is almost entirely about relative incomes, it is important to remember that in absolute terms, income growth is a prevalent feature around the world. For example, U.S. GDP per worker grew at an average annual rate of 1.4 percent from 1960 to 1988. In other words, if in Figure 1 we plotted actual instead of relative incomes, the 1988 distribution would be shifted noticeably to the right. Nevertheless, not all countries experienced positive growth. GDP per worker actually declined from 1960 to 1988 in 11 percent of the countries. Throughout this paper, we will consider incomes relative to U.S. income; that is, we will focus on the GDP per worker of the countries of the world divided by U.S. GDP per worker. The choice of the denominator is an important one, and U.S. income is chosen for several reasons. First, the United States had the highest GDP per worker in both 1960 and 1988, so the units of relative income are readily interpreted. Second, U.S. growth has been relatively steady over this 30-year period. Finally, it is natural to think of the U.S. economy as lying close to the technological frontier. Therefore, U.S. growth is probably a reasonable proxy for the growth rate of the technological frontier. These considerations indicate that the U.S. economy 22 Journal of Economic Perspectives is "well-behaved" and that normalizing by U.S. income will not distort our view of the income distribution. One drawback of Figure 1 is that individual countries cannot be identified. Figure 2 helps to address this concern by plotting GDP per worker relative to the United States in 1960 and in 1988 on a natural log scale.3 Changes in the world distribution of income are then illustrated by departures from the 45-degree line. Countries with GDP per worker greater than about 15 percent of U.S. income in 1960 typically experienced increases in relative income. These countries corre- spond to the shift in the mass of the income distribution toward the top in Figure 1. On the other hand, many countries with relative incomes of less than 10 or 15 percent in 1960 experienced a decrease in relative income over this period. They grew more slowly than did the United States and more slowly than did most of the countries above the 15 percent mark. These are the countries that make u p the peak at the lower end of the income distribution. One way of interpreting these general movements is that there has been some convergence or "catch-up" at the top of the income distribution and some divergence at the bottom. Figure 2 also allows us to identify the growth miracles and growth disasters of this 28-year period. Hong Kong (HKG), Singapore (SGP), Japan (JPN), Korea (KOR) and Taiwan (OAN) all stand out as growth miracles, having increased their relative incomes substantially. For example, Hong Kong, Singapore and Japan grew from about 20 percent of U.S. GDP per worker in 1960 to around 60 percent in 1988. Korea rose from 11 percent to 38 percent. Several less well known growth miracles are also noteworthy. Relative income in Botswana (BWA) increased from 5 percent to 20 percent, in Romania (ROM) from 3 percent to 12 percent, and in Lesotho (LSO) from 2 percent to 6 percent. A large number of the growth disasters—countries that experienced large de- clines in relative incomes—are located in sub-Saharan Africa. Chad (TCD), for example, fell from a relative income of 8 percent to 3 percent. However, growth disasters outside Africa are also impressive. For example, Venezuela (VEN) was the third richest economy in the world in 1960 with an income equal to 84 percent of U.S. income. By 1988, relative income had fallen to only 55 percent. The facts about the world income distribution so far have concerned the be- havior of incomes in terms of countries. While this is a common way to view the data, it can be misleading: for example, if we drew national borders differently— for example, so that each of the 50 U.S. states were a separate country—the shape of the densities in Figure 1 would look different. An alternative approach is to weight each country by its population. The unit of observation is then a person instead of a country.4 The most important fact to note in this regard is that roughly 40 percent of the world's population lives in China (23 percent in 1988) and India (17 percent in 1988). The experience of these two countries largely determines 3 A complete guide to the country codes used in this figure can be found on the World Wide Web at http://www.stanford.edu/~chadj/growth.html. 4 O f course, this exercise says nothing about changes in the income distribution within a particular country. On the Evolution of the World Income Distribution 23 Figure 2 Relative Y/L, 1960 vs. 1988 (log scale) what happens to the "typical" poor person in the world. In contrast, less than 10 percent of the world's population lives in the 39 countries that make up sub- Saharan Africa. Figure 3 plots the density of GDP per worker relative to the United States, weighted by population. In comparing this figure to Figure 1, one sees the over- whelming importance of India and China. While the distribution of countries has exhibited some divergence at the bottom, the same is not true for the distribution weighted by population. Both China and India have grown faster than the United States in the last three decades, leading to some catch-up at the bottom of the income distribution weighted by population. The catch-up in the top part of the income distribution also remains evident in Figure 3. The cumulative distribution of GDP per worker by population—that is, the area under the density—provides additional information that is helpful in inter- preting Figure 3. In terms of the cumulative distribution, 50 percent of the world's population lives in countries in which GDP per worker is about 10 percent of that in the United States. To be more exact, the income of the country containing the median person has improved from 8.1 percent of U.S. income in 1960 to 11.8 percent in 1988. Improvements for people higher up in the distribution have 24 Journal of Economic Perspectives Figure 3 Density of GDP Per Worker Weighted by Population been even more substantial. The 75th percentile of the population lived in a country with 22.5 percent of U.S. income in 1960, but 40.3 percent in 1988. The 90th percentile of the population lived in a country with 59.2 percent of U.S. income in 1960, and 79 percent in 1988. The Assumption of Similar Long-Term Growth Rates The remainder of this paper considers various techniques for making state- ments about the future shape of the world income distribution. First, however, there is an important issue to consider. The world income distribution will only settle down to a stable, nondegenerate distribution if all countries eventually grow at the same rate. Why? Well, suppose one thinks growth in Japan will permanently be higher than growth in the United States. In that case, the ratio of Japanese to U.S. income will diverge to infinity. If this is the way the world works, one might be more interested in the long-run distribution of growth rates than in incomes. However, I will argue here that in the long run, all countries are likely to share the same rate of growth. This assertion may seem counterintuitive. After all, growth rates of output per worker over long periods of time do differ substantially, and there may be an initial inclination to believe that the endogenous growth literature has pro- vided ample evidence against this hypothesis. Nevertheless, there are both con- ceptual and empirical reasons to think that most countries are likely to share the same rate of growth in the long run. The conceptual reason is most persua- Charles I. Jones 25 sive and has been presented in several recent papers (Eaton and Kortum, 1994; Parente and Prescott, 1994; Barro and Sala-i-Martin, 1995; Bernard and Jones, 1996). Following the recent endogenous growth literature, let us assume that the engine of growth is technological progress: output per worker grows in the long run because of the creation of ideas. Ideas diffuse across countries, perhaps not instantaneously, but eventually. Belgium does not grow only or even largely because of the ideas created by Belgians, but rather a substantial amount of growth in Belgian output per worker is due to ideas invented elsewhere in the world. In this framework, the fact that countries of the world eventually share ideas means that their incomes cannot get infinitely far apart. All countries even- tually grow at the average rate of growth of world knowledge, as shown in each of the papers cited above. Which brings us to the empirical reason. What do we make of the large em- pirical variation in growth rates? Japan, for example, grew at an average rate of 5.1 percent per year between 1960 and 1988 while the United States grew only at 1.4 percent. Or consider an even longer horizon using the GDP per capita data reported by Maddison (1995). Over the century and a quarter spanning 1870 to 1994, the United States grew at an average rate of 1.8 percent per year while the United Kingdom grew only at 1.3 percent. In fact, such differences—even over 125 years—are not inconsistent with the hypothesis that all countries share a common long-run growth rate. The resolution of this apparent inconsistency is transition dynamics. To the extent that countries are changing position within the world income distribution, their average growth rate can be faster or slower than the growth rate of world knowledge over any finite period. This point is illustrated clearly by a closer look at the U.S. and U.K. evidence for the last century. Figure 4 plots the log of GDP per capita in the United States and United Kingdom from 1870 to 1994 using the data from Maddison (1995). As men- tioned above, average growth in the United States has been a half a percen- tage point higher than in the United Kingdom over this 125-year period. How- ever, as the figure shows, nearly all of this difference is accounted for by the pre-1950 experience. Between 1870 and 1950, the U.S. economy grew at 1.7 percent while growth in the United Kingdom was a comparatively sluggish 0.9 percent. This growth performance occurred as the United States overtook the United Kingdom as the world's richest country around the turn of the century. Since 1950, however, average growth rates have been almost identical, with the United States growing at 1.95 percent and the United Kingdom growing at 1.98 percent. Forecasters who in 1950 expected the large growth differentials of the preceding 70 years to continue were clearly mistaken. Similarly, the fact that Japan has grown faster than the United States since 1950 says very little about whether or not these two economies will grow at the same rate in the long run. Rather, in a world where Japan and the United States have a common long-run growth rate, the experience of the last half-century is evidence that Japan is moving " u p " in the income distribution. 26 Journal of Economic Perspectives Figure 4 Income in the United States and United Kingdom (log scale) The Future of the Global Income Distribution Under the assumption that all countries grow at the same average rate in the long run, there are a number of ways to make statements about the eventual shape of the income distribution. The remainder of this paper employs three such tech- niques. First, we examine the predictions generated from a standard, well-known growth model due to Solow (1956). Second, we use a prediction based on transition dynamics. And finally, we employ a statistical technique that looks at the frequency of growth miracles and growth disasters. Projecting from Current Investment Levels The Solow (1956) growth model predicts that the level of output per worker in an economy in the long run is a function of the rate of investment in capital, the growth rate of the labor force, and the level of technology. 5 Statements about the future of the income distribution can be made if we can make statements about the future of investment rates, population growth rates, and (relative) technology levels. Notice that nothing really hinges on our following Solow in assuming ex- ogenously given and constant investment rates and population growth rates. Pro- vided these variables "settle down" in steady state to some constant value (which is nearly a definition of the steady state), what we really need empirically is to be 5 Mathematically, y(t) = (s/(n + g + δ ) ) α / 1 - α A ( t ) , where s is the investment rate, n is the population growth rate, δ is the constant rate at which capital depreciates, α is capital's share in production, and A(t) is the level of labor-augmenting technology, which is assumed to grow at the constant, exogenous rate g. On the Evolution of the World Income Distribution 27 able to predict where these variables are going to settle. The Solow model then tells us how to map these values into steady state incomes. Jones (1997) follows this line of reasoning in a more general model that in- corporates human capital as well as physical capital. A simple way of predicting where investment rates and population growth rates will settle is to assume that the rates that prevailed in the 1980s will persist. Of course, this simple method ignores the fact that investment rates, for example, may be affected by the transition dy- namics of the economy. Moreover, what this exercise cannot predict are underlying changes in policy, which are presumably very important in the actual evolution of the income distribution. Still, this is a useful benchmark to consider. Later sections will address these other concerns. Figure 5 plots steady state relative incomes based on this forecasting exercise against relative incomes in 1988 for 74 countries.6 Two features of Figure 5 stand out. First, broadly speaking, the 1988 distribution is quite similar to the distribution of steady states. Uganda (UGA) and Malawi (MWI) are not poor because of tran- sition dynamics. Rather, they are poor because investment rates are low and tech- nology levels are low. (Population growth rates are also high, but a little analysis illustrates that changes in population growth rates have relatively small effects in most neoclassical models.) Based on recent experience in the 1980s, there is no reason to expect these broad features driving the world income distribution to change in the near future. Second, this similarity is less pronounced at the top of the income distribution, where countries continue to "catch up" to the United States, than it is at the bottom. One notable exception is India (IND), which is predicted to grow from a relative income of 9 percent in 1988 to 13 percent based on policies in place in the 1980s. Similarly, Malaysia (MYS), Korea, Hong Kong and Singapore are all pre- dicted to continue to grow faster than the United States during a transition to higher relative incomes, as are a number of OECD economies like Spain (ESP), Italy (ITA) and France (FRA). In fact, according to this particular exercise, a number of countries such as Singapore, Spain, France and Italy are predicted to surpass the United States in GDP per worker. While the exact location of particular countries is somewhat sensitive to assumptions, this general feature that the United States is not expected to retain its lead in output per worker is robust. The expla- nation is simple. Ignoring differences in technology for the moment, differences in income are driven by differences in investment rates in physical and human capital. The United States is one of the leaders in human capital investment (though not by much), but its investment rate in physical capital is substantially lower than are investment rates in a number of other countries. A high U.S. tech- nology level helps, but it is insufficient to compensate for the lower U.S. investment 6Specifically, the exercise assumes a common capital share of 1/3 across countries. Educational attain- ment is assumed to augment labor, and a common rate of return to schooling of 10 percent is used. Investment rates, schooling enrollment rates and population growth rates from the 1980s and the level of (labor-augmenting) total factor productivity from 1988 are used in the computation. See Jones (1997) for more details. 28 Journal of Economic Perspectives Figure 5 Steady State Incomes, Based on Current Policies rate. It is largely these differences that are driving the differences in incomes at the top of the distribution.7 Transition Dynamics and Steady State Incomes A second way of estimating the shape of the steady state income distribution exploits recent work in the cross-country growth literature. According to this work, one of the most persuasive explanations for why some countries have grown faster than others over long periods of time is transition dynamics. The further a country is below its steady state position in the income distribution, the faster the country should grow. I will refer to this as the principle of transition dynamics. This principle can be found in the Solow and Ramsey growth models, as well as in models that emphasize the importance of technology transfer and the diffusion of ideas.8 7 Jones (1997) considers several scenarios to check the robustness of these findings, including models in which technology levels converge, a demographic transition leads to identical population growth rates around the world, human capital investment rates converge, and physical capital flows internationally to equalize returns. 8 O n l y the simplest growth models in which the dynamics are driven by foregoing consumption to invest output in physical capital, human capital, or research generally obey the principle as written (for ex- Charles I. Jones 29 According to this principle, the growth rate of the economy is proportional to the gap between the country's current position in the income distribution and its steady state position. In an unfortunate choice of terminology, the factor of pro- portionality is sometimes called the "speed of convergence." This phrase uses the word convergence in the mathematical sense of a sequence of numbers converging to some value. It describes the rate at which a country closes the gap between its current and steady state positions in the income distribution. This use is unfortu- nate because it seems to suggest that this equation has something to do with dif- ferent countries getting closer together in the income distribution, which is not the case (at least not directly). With this definition, the principle of transition dynamics can be stated as Growth rate of relative income = Speed of convergence × Percentage gap to own steady state. For example, suppose a country has a GDP per worker relative to the United States of 0.4 and a steady state value equal to 0.5. This represents a 20 percent gap. If the speed of convergence is 5 percent per year, then the country can expect its relative income to grow at 1 percent per year. Its actual GDP per worker will then grow at 1 percent plus the underlying growth rate of world technological progress (assum- ing the United States has reached its steady state).9 This relation has been exploited by the cross-country growth literature to ex- plain differences in growth rates. The numerous right-hand side variables included in such regressions, in addition to the initial GDP per worker variable, are an at- tempt to measure the gap between initial income and the steady state position of the country in the world income distribution. A key parameter estimated by these regressions is the speed of convergence. For example, a number of authors such as Mankiw, Romer and Weil (1992) and Barro and Sala-i-Martin (1992) have documented using econometric techniques the well-known "2 percent" speed of convergence. Other authors, however, have recently argued for faster rates of con- vergence.10 The standard Solow model implies a speed of convergence of about 6 percent for conventional parameter values. Alternatively, in a model that incorpo- rates the diffusion of technology across countries, the speed of convergence is re- lated to the rate of diffusion. In general, the authors in the cross-country growth literature have not exam- ined the shape of the steady state world income distribution implied by their re- gressions. However, the principle of transition dynamics suggests a simple, intuitive way to calculate the distribution of steady states. Instead of using the principle to ample, Mankiw, Romer and Weil, 1992). More sophisticated models require more than one state variable and cannot typically be reduced to so simple a formulation, although a similar relation often holds, either as an approximation or when applied to a slightly different variable such as total factor productivity. 9Mathematically, the principle of transition dynamics is dlog (t)/dt = λ(log * – log (t)) where is relative income, * denotes the steady state value of relative income, and λ is the "speed of convergence." 1 0 F o r example, see the work employing panel data of Islam (1995) and Caselli, Esquivel and Lefort (1996). 30 Journal of Economic Perspectives estimate speeds of convergence in a regression, we can simply impose alternative values. Then, data on growth rates from 1960 to 1988 and initial incomes in 1960 can be used to back out the implied steady states.11 To the extent that countries roughly obeyed a stable principle of transition dynamics over this 28-year period, we can calculate the targets toward which they were growing. Figure 6 reports the results of this exercise for several cases, corresponding to speeds of convergence of 2 percent, 4 percent and 6 percent. In general, the steady state distributions are determined as follows. Countries that have grown faster than the United States has over the 28-year period are predicted to continue to increase relative to the United States; countries that have grown more slowly are predicted to continue to fall. The extent to which the changes continue is determined by the speed of convergence. If this speed is slow, as in the first panel of Figure 6, then steady states must be far away in order to explain a given growth differential, im- plying large additional changes in the income distribution. On the other hand, if the speed is fast, say at 6 percent as in the last panel, then small deviations from the steady state can generate large growth differences; as a result, the current dis- tribution looks quite similar to the steady state distribution. Looking more carefully at the first panel of the figure, the steady state relative incomes for a number of countries seem implausibly large with a 2 percent speed of convergence. A number of East Asian countries are predicted to have incomes of more than 150 percent of U.S. income. The explanation for this prediction is that these countries have grown very rapidly for 30 years; with a very low speed of convergence, the only way to obtain such rapid growth rates is if the countries are extremely far from their steady states. In contrast, the steady states computed with a 4 percent or a 6 percent rate of convergence seem more reasonable.12 The Very Long-Run Income Distribution So far, we have considered the future of the income distribution under the assumption …