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Estimating World GDP, One Million B.C. - Present

Department of Economics, U.C. Berkeley

delong@econ.berkeley.edu

I construct estimates of world GDP over the very long run by combining estimates of total human populations with estimates of levels of real GDP per capita.

Population

I take my estimates of human population from Kremer (1993), but it would not matter if I had chosen some other authority. All long-run estimates of human population that I have found are quite close together (with the exception of estimates of population around 5000 BC, where Blaxter (1986) (cited in Cohen (1995)) estimates a population some eight times that of other authorities). Note that this does not mean that the estimates are correct--just that they are the same.

Kremer (1993) sees human populations as growing at an increasing proportional rate from perhaps 125,000 in one million B.C. to 6 billion today. Population reached approximately 4 million by 10000 BC, 50 million by 1000 BC, and 170 million by the year 1. Population then reached 265 million by the year 1000, 425 million by 1500, and 720 million by 1750 before exploding to 1.2 billion by 1850, 1.8 billion by 1900, 2.5 billion by 1950, and 6 billion today. Up until 1950 Kremer calculates that the rate of growth of human populations was roughly proportional to their total level.

GDP per Capita

Angus Maddison (1995) has constructed estimates of real GDP per capita for the world from 1820 to 1992. His estimates are best thought of as Laspeyres purchasing power parity estimates in 1990 international dollars. That is, they:

• Compare income levels across countries not using current exchange rates, but instead trying to change one currency into another at rates that keep purchasing power constant ("purchasing power parity").
• Value goods in relative terms using the prices found in a country in the middle of the world distribution of income ("international").
• Calculate a value for 1990 GDP per capita in the United States equal to U.S. current-dollar GDP per capita in 1990 ("1990 dollars").
• Do not take explicit account of the benefits of the introduction of new goods and new types of goods, but instead calculate GDP per capita in the past by valuing the commodities produced in the past at recent prices--and not making any correction for the restricted range of choice enforced by limited production possibilities ("Laspeyres").

All of these save the last is reasonabl--is in fact a way of proceeding vastly preferable to the alternatives. I will return to the last of these later. But first I want to extend Maddison's estimates backward before 1820.

If you plot the rates of world population growth against Maddison's estimates of world GDP per capita, you find a very high and significant correlation between the two from the early nineteenth century until roughly World War II. After World War II the demographic transition has begun to take hold in large parts of the world, but before World War II the higher is world GDP per capita, the faster is population growth--with a 1 percentage point per year increase in population growth associated with an increase in average world GDP per capita of \$1,165 (with a t-statistic of 7.4 and an adjusted-R2 of 0.84).

If you are enough of a Malthusian to believe that this tight relationship before World War II is not coincidence but instead reflects a near-linear dependence of the rate of human population growth on the margin between actual production and bio-cultural subsistence, then you can use the fitted relationship between population growth and Maddison-concept GDP per capita to backcast estimates of world GDP per capita before 1820.

An alternative (preferred by Maddison) is to assume that GDP per capita was constant in Asia and Africa from 1500-1820, grew at 0.1 percent per year from 1500-1820 in Latin America and Eastern Europe, and grew at 0.2 percent per year from 1500-1820 in Western Europe (an estimate that Maddison attributes to Simon Kuznets (1973)); this alternative could then be backcast further by assuming that pre-1500 GDP per capita was constant at near-Malthusian bio-cultural subsistence.

I prefer the first alternative (and have used it). But I also report estimates using the second.

New Goods

A large proportion of our high standard of living today derives not just from our ability to more cheaply and productively manufacture the commodities of 1800, but from our ability to manufacture whole new types of commodities, some of which do a better job of meeting needs that we knew we had back in 1800, and some of which meet needs that were unimagined back in 1800.

How much has this change--the fact that we make not just the same goods, but new goods and new types of goods--enhanced our material prosperity? Nordhaus (1997) provides perhaps the most eloquent and sophisticated argument that standard measures--like those of Maddison--that do not take explicit account of these factors grossly understate the rate of economic growth over the past two centuries.

I know that I at least would be extremely unhappy if I were handed my current income, told that I could spend it on goods at current prices, but that I was prohibited from buying anything that was not made before 1800. Yet Maddison's procedures would implicitly take such a reduction in the range of goods I could purchase as having no effect on my real income or real material standard of living.

But by how much has our power to make new things--not just the same things more efficiently--amplified our material prosperity?

In at least some models of growth in which the set of goods that can be produced expands, the correct measure of real output is proportional to the product of purchasing power (income divided by the average price of a good) and the number of goods that can be produced. As best as I can determine, about three-quarters of world expenditure today is spent on commodities that simply did not exist back in 1800. So I (somewhat arbitrarily) use this to assign an additional fourfold multiplication to output per capita since 1800 in addition to the increases in output per capita calculated by Maddison.

But since this--large--extra adjustment is not to everyone's taste, I also report the "ex-Nordhaus" series without the "new kinds of goods" adjustment.

Conclusion

The outcome of this set of calculations is thus seven series: Kremer's (1993) estimates of population; three estimates of GDP per capita (my preferred estimate, the constant-before-1500 estimate, and the ex-Nordhaus estimate); and three estimates of total world real GDP (capita (my preferred estimate, the constant-before-1500 estimate, and the ex-Nordhaus estimate).

They are reported in the table below:

Average World GDP per Capita

(1990 International Dollars)

 Year Preferred Ex-Nordhaus Constant Pre-1500 GDP per Capita -1000000 92 340 115 -300000 92 341 115 -25000 92 343 115 -10000 93 344 115 -8000 96 357 115 -5000 103 381 115 -4000 109 406 115 -3000 113 420 115 -2000 112 415 115 -1600 121 449 115 -1000 127 471 115 -800 143 530 115 -500 137 509 115 -400 130 483 115 -200 113 420 115 1 109 404 115 14 102 380 115 200 98 362 115 350 94 350 115 400 97 360 115 500 102 379 115 600 104 387 115 700 112 414 115 800 116 430 115 900 131 486 115 1000 133 494 115 1100 124 459 115 1200 104 386 115 1250 99 367 115 1300 89 331 115 1340 109 406 115 1400 128 476 115 1500 138 512 115 1600 141 524 140 1650 150 556 155 1700 164 607 172 1750 178 662 190 1800 195 722 210 1850 300 788 300 1875 429 948 429 1900 679 1263 679 1920 956 1550 956 1925 1108 1735 1108 1930 1134 1716 1134 1940 1356 1915 1356 1950 1622 2138 1622 1955 1968 2505 1968 1960 2270 2792 2270 1965 2736 3251 2736 1970 3282 3768 3282 1975 3714 4119 3714 1980 4231 4533 4231 1985 4634 4797 4634 1990 5204 5204 5204 1995 5840 5641 5840 2000 6539 6103 6539

Total World Real GDP

(Billions of 1990 International Dollars)

 Year Preferred Ex-Nordhaus Constant Pre-1500 GDP per Capita -1000000 0.01 0.04 0.01 -300000 0.09 0.34 0.11 -25000 0.31 1.15 0.38 -10000 0.37 1.38 0.46 -8000 0.43 1.61 0.52 -5000 0.51 1.91 0.57 -4000 0.77 2.84 0.80 -3000 1.59 5.89 1.60 -2000 3.02 11.20 3.09 -1600 4.36 16.16 4.12 -1000 6.35 23.55 5.73 -800 9.72 36.05 7.79 -500 13.72 50.90 11.46 -400 16.02 59.44 14.09 -200 17.00 63.05 17.19 1 18.50 68.65 19.48 14 17.50 64.91 19.59 200 18.54 68.80 21.77 350 17.93 66.53 21.77 400 18.44 68.40 21.77 500 19.92 73.90 22.34 600 20.86 77.39 22.92 700 23.44 86.97 24.06 800 25.53 94.70 25.21 900 31.68 117.52 27.73 1000 35.31 131.00 30.36 1100 39.60 146.91 36.67 1200 37.44 138.90 41.25 1250 35.58 132.01 41.25 1300 32.09 119.06 41.25 1340 40.50 150.27 42.39 1400 44.92 166.64 40.10 1500 58.67 217.64 48.70 1600 77.01 285.70 76.41 1650 81.74 303.24 84.53 1700 99.80 370.26 104.67 1750 128.51 476.75 136.67 1800 175.24 650.11 189.00 1850 359.90 945.60 359.90 1875 568.08 1256.10 568.08 1900 1102.96 2052.38 1102.96 1920 1733.67 2810.15 1733.67 1925 2102.88 3293.03 2102.88 1930 2253.81 3409.69 2253.81 1940 3001.36 4237.90 3001.36 1950 4081.81 5379.21 4081.81 1955 5430.44 6913.80 5430.44 1960 6855.25 8431.84 6855.25 1965 9126.98 10845.34 9126.98 1970 12137.94 13934.06 12137.94 1975 15149.42 16801.40 15149.42 1980 18818.46 20162.78 18818.46 1985 22481.11 23270.25 22481.11 1990 27539.57 27539.57 27539.57 1995 33644.33 32503.40 33644.33 2000 41016.69 38281.97 41016.69

Total World Population

(Millions)

Year   Human Population (Kremer Series; millions)

-1000000 0.125

-300000 1

-25000 3.34

-10000 4

-8000 4.5

-5000 5

-4000 7

-3000 14

-2000 27

-1600 36

-1000 50

-800 68

-500 100

-400 123

-200 150

1 170

14 171

200 190

350 190

400 190

500 195

600 200

700 210

800 220

900 242

1000 265

1100 320

1200 360

1250 360

1300 360

1340 370

1400 350

1500 425

1600 545

1650 545

1700 610

1750 720

1800 900

1850 1200

1875 1325

1900 1625

1920 1813

1925 1898

1930 1987

1940 2213

1950 2516

1955 2760

1960 3020

1965 3336

1970 3698

1975 4079

1980 4448

1985 4851

1990 5292

1995 5761

2000 6272

References

Michael Kremer (1993), "Population Growth and Technical Change, One Million B.C. to 1990,"Quarterly Journal of Economics 108:3 (August), pp. 681-716.

Joel Cohen (1996), How Many People Can the Earth Support? (New York: W.W. Norton: 0393314952).

Angus Maddison (1995), Monitoring the World Economy, 1820-1992 (Paris: OECD: xxxx).

William Nordhaus (1997), "Do Real Wage and Output Series Capture Reality? The History of Lighting Suggests Not," in Timothy Bresnahan and Robert Gordon, eds., The Economics of New Goods (Chicago: University of Chicago Press: 0226074153).

Professor of Economics J. Bradford DeLong, 601 Evans Hall, #3880
University of California at Berkeley
Berkeley, CA 94720-3880
(510) 643-4027 phone (510) 642-6615 fax
delong@econ.berkeley.edu