Growth: Exponential, Convergent, Logistic: How much of this will my students this semester know? How much of this will I have to remind them? And how much of this will I have to teach them for the first time?
Growth: Exponential, Convergent, Logistic: How much of this will my students this semester know? How much of this will I have to remind them? And how much of this will I have to teach them for the first time?
If we are to talk about "equitable growth", we should have firm notions of both what is "equitable" and of "economic growth". Let us leave the first to the side for now. What do we know or can we infer about the shape of economic growth to serve as the background against which our policy and discussions can proceed?
Start with the idea that an economy can grow along either of two dimensions: it can either increase in its number of people (holding material living standards constant), or it can increase its average material living standards (holding the number of people constant). Call the first kind of growth "extensive" and the second "intensive". And in order to track these two dimensions of growth we need estimates of two things: human populations, and levels of material well-being--levels of average real annual incomes per capita.
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) 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 roughly the same.
Kremer (1993), following McEvedy and Jones (1978), 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 perhaps 4 million toward the end of the mesolithic hunter-gatherer age 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 7.2 billion today.
Consensus forecasts are that the world will complete its demographic transition and attain zero population growth around 2050, with a maximum global population then of some 9.2 billion.
http://www.gapminder.org, relying on the U.N. International Comparison Project, Angus Maddison (1995), and a number of other sources, has constructed estimates of real annual incomes per capita for the world from 1800 to 2012. I am more comfortable thinking about labor productivity than about income per capita, and if you are willing to accept the rule of thumb that about half the population are adults engaged in net economic production that contributes to measured national income (or would contribute to national income if it were measured properly), the second measure is simply double the first. And I feel confident enough to update the 2012 numbers to 2015, so that they will be more current rather than more stale for the rest of this current decade. These estimates:
Assign a value for 2005 real annual income per capita in the United States equal to what U.S. current-dollar income per capita was in 2005, and use that as a yardstick. Thus the estimates are in "2005 dollars": "2005" for the year, and "dollars" for the country whose currency is used.
Assign values for 2005 annual incomes per capita in other countries based not on purely on the U.S. dollar value of incomes in that country in 2005, but correcting for systematic differences in price levels across countries. In all countries the prices of internationally-traded manufactured goods are pretty much the same, but the wages of unskilled labor and the prices of goods and services produced using substantial proportions of unskilled labor are much lower. This is a purchasing-power-parity adjustment, or a "PPP-adjustment".
Calculate real annual incomes moving forward and backward in time from 2005 not by calculating the change in the number of dollars received but adjusting that for inflation--for changes in the amount of goods and services that a given quantity of money commands. This is an "inflation adjustment". The estimates it creates are called "real" or "inflation-adjusted", as opposed to "nominal" estimates.
Value goods in relative terms using the relative prices found not in the U.S. but instead in a country in the middle of the world distribution of income. This produces "international dollar" as opposed to "U.S. dollar" estimates.
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 in the past.
All of these save the last (5) are very reasonable ways of proceeding--are, in fact, in my view vastly preferable to the alternatives. Let us return to the last of these later. Adding up these estimates produces numbers for:
With graphical snapshots showing the divergence of average annual real incomes in different countries from the global average:
In the 2012 graph, on the far right we have the oil sheikdom of Qatar and the money-laundering havens of Macau and Luxembourg, all with annual income per capita levels above $70,000. Then come Singapore, Norway, Brunei, Greenland, Hong Kong, Kuwait, and the United States, all with levels between $40,000 and $50,000. Germany at $34,000, Japan and Britain at $31,000, France at $29,000, Russia at $15,000, Mexico at $12,000, South Africa and Brazil at $10,000, China at $8,000, and by the time we get to India, Pakistan, and Vietnam at $3,000 we have covered nearly all of the world outside of Sub-Saharan Africa. Below $3,000 we get the bulk of Sub-Saharan Africa between Nigeria at $2,500 and the Democratic Republic of the Congo at $400, with Yemen, Bangladesh, Afghanistan, and Haiti also in that range.
In the 1800 graph, on the far right we have Britain—the first industrial nation—at $2,700, followed by the Netherlands at $2,400, the United States at $1,900, Germany at $1,700, and Belgium, Switzerland, and the Czech Republic at $1,600. China, Russia, and Mexico are at $1,000. India is at $600. And the Democratic Republic of the Congo (and a few others in Sub-Saharan Africa) is down at $400.
The first thing to note is the extraordinary rise in averages: from $1,500 in 1800 to $22,200 in 2012—a nearly fifteen-fold rise in material prosperity.
The second thing to note is the extraordinary rise in range: from a range of six to one in 1800 to a range of two hundred to one in 2012—a more than thirty-fold rise in how much relative difference choosing parents of the right (or the wrong) nationality can make. There are major issues involved in a world of such extraordinary inequality of choosing one number as an index of economic growth and prosperity. When we do so, recognize that this number is much more an indicator of humanity's societal productive power at the current data. Because of its extraordinary maldistribution, taking the average as some kind of indicator of human material well-being as opposed to productive potential is extremely hazardous.
But we would like to extend our temporal vision: what can we say about global-scale economic growth in the future? And how does the economic growth we have seen in the past two centuries compare with what went on before?
First let us extend these http://gapminder.org estimates forward into the future via growth forecasts to 2050. We are fairly confident in our 9.2 billion population estimate for 2050--a lot would have to change and change relatively quickly as far as demography is concerned to get a 2050 population much below 9 billion or above 9.5 billion.
The question of what the global average real annual income per capita will be in 2050 is much more up for grabs. The U.S. value for labor productivity in 2015 is $90,000 per year. That is a reasonable guide to the average level of labor productivity that our modern technology could enable if it were properly-distributed around the globe.
One line of reasoning would be to note that modern information and communications technologies should allow modern technologies to diffuse across the globe quickly, and that a generation should be more than enough time. It would note that for more than a century labor productivity in the U.S. has been growing at an average pace of 2.0%/year. Do we then project forward today's $90,000/year number for the U.S to 2050 at this growth rate, reach a number of $181,000/year, and forecast that this technologically-feasible level of labor productivity will be reached over the entire globe?
A second line of reasoning would note that, historically, human productivity has been constrained by three things: the need for strong backs to perform large-scale gross manipulations of matter, the need for nimble fingers to perform large-scale fine manipulations of matter, and the need for human brains to make these matter manipulations useful. The rise of the nineteenth-century First Industrial Revolution first-wave machines--of steam, coal, iron, and machinery--removed the first constraint. The flowering in the early twentieth century of the Second Industrial Revolution second-wave machines--those of petroleum, internal combustion, machinery, chemicals, continuous process, and the assembly line--removed the second constraint. And now the coming of modern information processing and communications technologies is, finally, allowing for the control of gross-manipulation and fine-manipulation machines by something cheaper than a human brain. The human brain is a hitherto-unequalled cybernetic control mechanism: after all, it fits inside a shoebox, and draws only 50 watts of power. But the replacement of human brains as cybernetic control mechanisms by third-wave machines promises a previously-unimaginable upward leap in the pace of economic growth, so this line of argument. Is a level of $181,000/year for 2050 labor productivity too pessimistic?
Yet another line of argument is that what we demand is, overwhelmingly, food, shelter, clothing, and medical care; but that the major innovations to make those commodities cheaper already happened in the century-long enormous wave of the Second Industrial Revolution; and further technological progress in better satisfying those core human needs will be slow and difficult. There will be sectors of enormous technological progress, this line of argument goes, but those sectors will take up only a small portion of what we spend and hence have only a small impact on our overall well-being: yes, we will have godlike powers to read any book or watch any drama we wish instantly, but how much will that really matter? This line of argument foresees a fall in the rate of technological progress in the U.S. to 0.5%/year or so: not $181,000 in 2050, but $107,000.
Yet a fourth line of argument notes that global income inequality has, except for the years since 1975, been rising steadily since 1800. It is certainly the ace that modern technologies of information, communication, migration, and goods transportation should make it much easier to transfer technology across the globe, but it has not happened. Moreover, this line of argument notes, the reduction in the variance of the global income distribution since 1975 has been entirely the result of successful accelerations of economic growth in two and only two of the 200 countries in the world: China and India. Because these countries have such huge shares of the world population, their convergence toward North Atlantic standards has had an enormous impact on global statistics. But, this line of argument concludes, it would be rash to think that the world in 2050 will be, in relative terms, any less unequal than the world today. Even at the 2%/year growth rate seen in the United States for the past century and more, that would only give us a year-2050 level of global average real annual income per worker of $44,000.
A fifth line of argument could combine (3) and (4): a slowdown in productivity growth in the North Atlantic, and no further relative convergence toward North Atlantic levels across the rest of the globe. That would give us a year-2050 level of $26,000/year per worker.
And a sixth line of argument would note that the twentieth century brought us three violent totalitarian régimes and the admission of three world rulers--Hitler, Stalin, and Mao--to the 30 million club, that club consisting of those rulers whose policies led directly and immediately to the premature deaths of more than 30 million people. And they barely had chemical, and did not have biological or nuclear weapons at their disposal. Our, or other people's, rulers might get medieval, or get 1984, or both on us.
As we construct our picture of global economic growth, let us be relatively optimistic. Let us eschew (5) and (6) and settle on (4): forecast a year-2050 world average level of labor productivity of 44,400/year $2005. (And let us recognize that the more optimistic scenarios of (3), (1), and most optimistic of all (2) are out there in our possible future.)
The Distant Past
Suppose we want to peer backward into the economic past before 1800. Suppose we want to look as far back as the beginnings of agrarian civilizations, around 5000 BC.
Malthus: The first thing we note is that the economies in the long-ago past were very different from our economy of today. For 95% of the time since the invention of agriculture, economies have been Malthusian. Back in the agrarian age, improvements in productivity and technology showed up in the long run not as increases in average standards of living but as increases in population levels at a roughly constant standard of living. The second thing we note is that in the long-long ago the pace of invention and innovation can most optimistically be described as glacial: two hundred years or so to achieve the pace of relative change in technology that we see in twelve months. And the third thing we note is that, from the first two, arithmetic tells you that in the long-long ago the overwhelming majority of those who are or become well-off have either held on to what their parents bequeathed them or proven successful in zero-sum (marrying the right heir or heiress) or negative-sum redistributional struggles—rather than having found or placed themselves at a key chokepoint of positive-sum productive processes.
This means that, even though we lack reliable quantitative data on what economies were like before 1800, we can get remarkably close by simply spinning numbers out of thin air according to the logic of a slowly-growing technologically-stagnant Malthusian economy.
For example, we can make sound and solid global inferences from very low pre-1500 population growth rates. We know that a preindustrial not-very literate population with ample access to food and resources can and will roughly double every generation: that is the pace of European settler expansion in the Americas, after all. And we know that from 5000 BC to 1345 the average rate of global population growth was 0.07%/year—not the 2.5%/year of normal human biology with ample food and other resources. The inescapable conclusion is that resources were scarce: just barely more than necessary to keep human populations from declining given the socio-cultural institutions then prevailing. We are thus confident that during the long agrarian age—from 5000 BC up until the Black Death, say—global average material standards of living tracked “subsistence”, whatever that “subsistence” might be.
We can check this inference by consulting the long-run biomedical studies of Rick Steckel (1995), “Stature and the Standard of Living,” Journal of Economic Literature 33:4 (December), pp. 1903-40, and many others. We can use Steckel’s estimates of the relationship between height and income found in a cross-section of people alive today and evidence from past burials to infer what real incomes were in the past. The conclusion is inescapable: people in the preindustrial past were short—very short—with adult males averaging some 63 inches compared to 69 inches either in the pre-agricultural Mesolithic or today. Therefore people in the pre-industrial past were poor—very poor. If they weren’t very poor, they would have fed their children more and better and their children would have grown taller. And they were malnourished compared to us or to their pre-agricultural predecessors: defects in their teeth enamel, iron-deficient, skeletal markers of severe cases of infectious disease, and crippled backs.
Pre-industrial dire poverty lasted late. Even as of 1750 people in Britain, Sweden, and Norway were four full inches shorter than people are today—consistent with an average caloric intake of only some 2000 calories per person per day, many of whom were or were attempting to be engaged in heavy physical labor. And societies in the preindustrial past were stunningly unequal: the upper classes were high and mighty indeed, upper class children growing between four and six inches taller than their working-class peers. Moreover, there are no consistent trends in heights between the invention of agriculture and the coming of the industrial age. Up until the eve of the industrial revolution itself, the dominant human experience since the invention of agriculture had been one of poverty so severe as to produce substantial malnutrition and stunted growth.
It is this experience that makes Jared Diamond conclude that the invention of agriculture was the worst mistake ever made by the human race.
Quantifying Malthus: If we look at the http://gapminder.org data we have for 1960, if we look at the scatter of population growth and life expectancy, and if we draw a line through the scatter of those countries that had not in 1960 gone through the demographic transition, we would conclude (a) that zero population growth for a pre-demographic transition economy goes with a life expectancy of 15, but (b) that there are no such economies in 1960—not even close.
If we look at the guesstimates we have for 1800, if we accept http://gapminder.org definitions of real income per capita in 2005 PPP-adjusted international dollars, and if we draw a line through the scatter of life expectancy and estimates of real GDP per capita, we conclude that an economy would have a life expectancy of 15 if it had a level of income per capita of $160 2005 PPP-adjusted international dollars per year—and, once again, that there are no economies anywhere near that level of penury in 1800.
And if we wanted to erect a structure on top of these extremely shaky foundations, we would then say that the long-run demographic data suggests to us that material standards of living in the world during the long agrarian age from 5000 BC to the Black Death were—roughly—30% of the world’s standard of living in 1800: $160/year in 2005 PPP-adjusted international dollars in income per capita, or, with about half the population in the effective adult labor force, some $320/year in average labor productivity.
Now two corrections are needed. First, as Lemin Wu has pointed out convincingly, humans do not just produce necessaries and conveniences. They also produce luxuries, defined as commodities that we enjoy but that do not help us scramble out of the muck and have more children who will survive to adulthood. If the fraction of spending that is spending on luxuries is higher, a society will have a higher standard of living with the same generation-to-generation population growth rate. We know that luxuries tend to be invented and developed over time. Does spending on them increase? How much of spending is spending on luxuries? I do not know. And your guess is as good as mine.
Second, there is the matter of “public health”: The same level of necessaries and conveniences that could fuel a given amount of demographic expansion could fuel more or less depending on whether the health environment is better or worse. And note that “health environment” here has to be broadly construed: the classical Greek practice of large-scale female infanticide via exposure is part of the health environment. (It certainly isn’t a luxury.) How has the “health environment” changed over time? How much does it matter? I do not know. And your guess is as good as mine.
We thus find that we have to make a number of guesses in order to construct our picture of world economic growth since 5000 BC:
We have to guess at what the level of "subsistence" labor productivity was in 1800: at what level of output per worker would women have been so malnourished that their fat levels fell so low that they did not ovulate regularly, would children have been so vitamin-deprived that their immune systems were compromised and they would fall victim in larger numbers to disease, and would general poverty have robbed society of the stored grain needed to tide the population over a minor famine without severe loss, all given global institutions as they stood in 1800? My guess is: 320/year $2005. But your guess will be different.
We have to guess at how much worse “public health” was back in 1300 than in 1800. By how much would extra mortality and non-fertility raise the level of material prosperity corresponding to “subsistence” and effective zero population growth? (Note that this increase in material prosperity consistent with zpg--whether due to war and chevauchee, plague, lack of sewers, more virulent diseases, large-scale infanticide, enforced celibacy, or whatever--is not an increase in human utility. My guess is: 80/year $2005. But your guess will be different.
We have to guess at how much less availability of “luxuries” in 1300 than in 1800 lowered the level of material prosperity (and the level of human utility!) corresponding to “subsistence”. My guess is: $0. But your guess will be different.
We have to guess at the annual pre-1300 trend in “public health”--as things got even worse in the more distant past, this raises the level of material production (although not of human utility!) consistent with the extremely slow generation-to-generation population growth that we see. My guess at the effect of this trend in raising “subsistence” as we go further back in time is: 0.01%/year. But your guess will be different.
We have to guess at the annual pre-1300 trend in the introduction of new “luxuries”, which has the countervailing effect of raising the growth rate of “subsistence” over time. My guess is: 0.01%/year. But your guess will be different.
A guess as to what the global level of material prosperity was in 1500, on the eve of the Colombian Exchange, in the moment well before we are willing to even try to make quantitative estimates as crude as those of http://gapminder.org for 1800, but well after the negative population and positive income shock of the Black Death diverts the global economy from its high-Malthusian trap trajectory. I really do guess--and this really is a complete guess: $550. But yours will be different.
Remember: we also need our estimate of growth in global average labor productivity from 2015-2050. Mine is the relatively optimistic: 2%/year. But yours will be different.
And then there is a wild card: an extra factor to deal with the tremendous expansion since 1800 in the types of commodities we can even imagine producing. My guess is: 4. But yours will be different.
New Goods: This last wild card needs considerable additional explanation. 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.
Consider the question of what the 1500/year $2005 global average labor productivity in 1800 from http://gapminder.org is supposed to mean. The number is one-quarter of the present-day prosperity of India, and about equal to the average material prosperity of the poorer half of the countries of today’s Africa. But when we say “someone has an income of $1500 in today’s dollars” we think of what $1500 could buy today. And that is wrong. Looking at the things around me right now, $1500 in 1800 could be used to buy cups, water, paper, seats, foodstuffs, glass, textiles (seats and clothes), buttons (clothes), leather (shoes and wallets), keys, books, and orange juice. It could not be used to buy plastic tray-tables, styrofoam insulating cups, sealed aluminum cans of diet coke, other plastics, ice in summer (unless you were very lucky), headphones, LCD screens, iPhones, iPads, Macbook Airs, or the services of a stretched late-model Boeing 737 with just barely the range to carry me from SFO to EWR in 5 hours and 15 minutes (with a healthy tail wind) in no greater discomfort than the London-to-Bath stagecoaches of 1800. How much would I think $1500 would be worth today if I was also told: “Oh, you have to spend this only on marginal additions to your consumption out of commodities that existed in 1800”? Would it be worth $750? $375? When we calculate the rate of growth in global output per worker since 1800, should we take the gap minder.org growth rate of 1.25%/year and boost it up to the1.9%/year needed to get in two additional doublings in material standard of living because of all the new luxuries that are rapidly becoming conveniences and necessities in our minds that we did not have the slightest clue how to produce back then?
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 underlie much of http://gapminder.org—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. 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.
Thus my (8) guess of 4: an additional fourfold multiplication to real labor productivity since 1800 in addition to what is in http://gapminder.org. But your guess will differ. Angus Maddison's certainly did--this number of 4 made him very unhappy indeed.
So consider both sets of numbers: those that do and those that do not make this crude adjustment for new goods and new types of goods...
Choosing numbers for these eight guesstimates--these eight fudge factors--gives me my best-guess bird's-eye picture of economic growth on a global scale, at least as far as global averages are concerned, from 5000 BC to 2050.
This is what I think it looks like. But you can and will have a very different view.
So go and download a copy of:
Then fill in your own guesstimates in the eight yellow boxes. Choose for yourself the eight numbers we need in order to build a longest-run picture off of http://gapminder.org. And argue for your choices in comments, if you wish...
Over at the Washington Center for Equitable Growth: When I look at Thomas Piketty's big book, I see one thing that he failed to do that I think he really should have done. A large part of the book is about the contrast between "r", the rate of return on wealth, and "g" the growth rate of the economy. However, there are four different r's. And in his book he failed to distinguish between them.
The four different r's are:
The real interest rate at which metropolitan governments can borrow: call this r1.
The real interest rate that is the actual average return on wealthin the society and economy: call this r2.
The real interest rate that is the average risky net rate of accumulation--what capital receives, minus the risk of confiscation or destruction or taxation, plus appreciation in valuation multiples, minus what is spent in order to keep the world in the appropriate social position: call this r3.
A measure of the extent to which capital and wealth serve as an effective claim on income independent of how much capital there is--a standardized measure of what the society and economy's return on wealth would be at some standardized ratio of wealth to annual income: say, 4: call this ρ.
These four r's are very different animals. READ MOAR
Over at the Washington Center for Equitable Growth: A Few Finger Exercises with the Saez and Zucman Wealth-Concentration Estimates...: From Emmanuel Saez and Gabriel Zucman (March 2014): The Distribution of US Wealth, Capital Income and Returns since 1913:
From today's perspective, the $800K per capita in today's purchasing that the circa-1949 average member of the "merely rich"--those between the 99%ile and the 99.9%ile--had looks extraordinarily small. Why, a 3% rate of spending relative to assets would leave them with only $24K per capita to spend! Barely enough to give you the median standard of living in 2014! (OK, OK: a much bigger house and a much more comfortable commute than the median today--but no electronic toys and air travel a very exceptional treat.) Even the truly rich of 1949--the upper 15,000--would find that a 3% rate of spending relative to assets would give them only the upper-middle class standard of living today or, well, me: the kind of style of life at which one stays at the Crowne Plaza or the Holiday Inn Express because more fancy seems not worth it given other demands on one's cash.
Looking at it the other way, our truly rich today--the top 0.01%, the top 30,000--have a standard of living that, if one trusts the real income figures, was only matched by the top 0.0003%--the top 400 in 1949...
Feel free to click on, play with, and edit the spreadsheet if you want to--but do play nice, please... READ MOAR
"I now know it is a rising, not a setting, sun" --Benjamin Franklin, 1787