Lecture Notes: Introduction to Economic History: Understanding the Ancient Economy ¶

1: The Biggest-Picture Perspective ¶

1.1: The Old and Middle Stone Ages ¶

70,000 years ago, back in the old stone age, there were perhaps 100,000 of us—100,000 east African plains apes who looked like us, moved like us, acted like us, talked like us, and from whom the overwhelming proportion of all of our heredity is derived. Yes, we have small admixtures (5%?) from other groups and subspecies and may be even species, but overwhelmingly we are those proto-hundred-thousand's children, and we are all all of their children: it is overwhelmingly likely that each of those who still has living descendants today has a place—has an astronomical number of places—on our http://ancestry.com family tree.

Back then we were very smart herd animals. We gathered, we hunted (some), we protected ourselves, we made stone and wood tools, we understood our environment, we manipulated our environment, we communicated with each other, we cooperated and we fought, we talked, and we did the things that humans. Our standard of living? If we had to slot it into emerging-markets standards of living in the world today, we might call it 3.25 dollars a day. Poverty, but not what the United Nations calls extreme poverty: natural resources were not scarce, our knowledge of our east African environment was profound, and we probably had to spend a little more than one-third of our waking hours collecting 2000 calories plus essential nutrients each day, plus enough shelter and fire and clothing that we were not unduly wet or cold. We were buff: life was strenuous. We were shortlived: a life expectancy at birth of perhaps 25-30, for hauling around a family in our then-seminomadic lifestyle was dangerous: life was strenuous.

1.2: An Index of Human Technological and Organizational Capabilities ¶

There are things that are objective and can be measured: five bushels of properly-threshed barley kernels, or three gallons of water. There are things that are subjective that can nevertheless be accurately measured in an objective form: the feeling of heat, for example: this northern California hot tub here in the fog feels hot, and, indeed, is at a temperature of 105F: its molecules have thermal kinetic energy above that of absolute zero by 565/180 times the difference in thermal kinetic energy between water on the edge of boiling and water on the edge of freezing. There are things that are subjective that cannot be measured: anger, rage, and sorrow. Economists start with objetively measured prices and quantities of goods and services exchanged in markets, and then go on to construct quantitative measures of subjective things like willingnesses-to-pay and willingnesses-to-substitute and values and so forth. Mid-twentieth century British economist John Maynard Keynes warned us against carrying this too far:

Approximate statistical comparisons depending on some broad element of judgment rather than of strict calculation… may possess significance and validity within certain limits. But the proper place for such things... lies within the field of historical and statistical description, and their purpose should be to satisfy historical or social curiosity... of a similar character to the statement that Queen Victoria was a better queen but not a happier woman than Queen Elizabeth—a proposition not without meaning and not without interest, but unsuitable as material for the differential calculus. Our precision will be a mock precision if we try to use such partly vague and non-quantitative concepts as the basis of a quantitative analysis...

Neverthless we do carry it far. For example, we have our estimates of how many people there were—100-thousand 70-thousand years ago, 3-million ten-thousand years ago—and we have our estimates of what their standard of living was on average—3.25 dollars per day. We can then make the truly heroic assumptions that underpin a more-or-less standard Solow-Malthus growth model like the one found here: https://nbviewer.jupyter.org/github/braddelong/LS2019/blob/master/2019-09-06-210a-ancient-intro.ipynb. We can then construct a quantitative index $H$ of the value of the useful ideas about how to cooperate and manipulate the environment in order to provide one another with what we need, find convenient, and simply want. Set that index $H_{-68000}$—the index of the level of human technological and organizational knowledge 70-thousand years ago, in 68-thousand BC by the common calendar—to 1.

Flash-forward 60,000 years, to 10,000 years ago, on the very eve of the invention/discovery of agriculture and of animal domestication. Things were much the same, save that there were then not one-hundred thousand of us in East Africa but rather perhaps two-and-a-half million of us, well, pretty much everywhere. Our living standards were much the same as they had been. We had better tools, but they were of stone and wood, plus fur and fiber, and not yet metal: it was still the Middle Stone Age. Our knowledge of our environment—or rather environments—was more profound, and so was our power to manipulate them. But in each environment we lived in we found ourselves in rough ecological balance. As of 8000 BC the index $H_{-8000}$ stands at 5.

1.3: The Neolithic Revolution, and After ¶

Then, at the end of the gatherer-hunter age, comes the upward leap (or was it an upward leap) of the neolithic—new stone¸—revolution: 2000 years after 8000 BC we are (poor) agriculturalists and (unsophisticated) herders of barely domesticated animals, with a human population of perhaps 7 million, but a lower living standard of perhaps 2.50 dollars a day, with an index $H_{-6000} = 6.5$.

Why a near-tripling of population? Because living was easier when you were sedentary or semi-sedentary: you no longer had to carry babies substantial distances, and you could accumulate more useful stuff than you could personally carry. Plus even early agriculture and herding were very productive relative to what had come before. Since life was easier, more babies survived to grow up and themselves reproduce?

Why a fall in the standard of living? Because population grew until humanity was once again in ecological balance, with population expanded to the environment's carrying capacity given technology and organization. But what keeps population from growing further? The fact that life has become harder again. But it became harder in a different way: agriculturalists are shorter—figure about three inches, 7.5 centimeters—malnourished, prone to endemic diseases, and vulnerable to plagues relative to gatherer-hunters. Biologically, it would seem much better to be a typical person in the gatherer-hunter than in the neolithic age: your life expectancy is no less, your daily life presents you with more interesting and less boring cognitive problems, and you are much more buff and swole.

Jared Diamond believes—or at least whoever wrote the title of his article believes—that the invention of agriculture was, as the title says, a bad mistaker: humans would be better-off had we remained gatherer-hunters.

Then comes further development of agriculture, craftwork, organization, literacy, civilization: by year 1 the index $H_{1} = 31$. By year 1500 we have $H_{1500} = 53$. By 1500 we have 500 million humans compared to the 7 million of 6000 BC. But typical standards of living seem much the same: still 2.5 dollars a day. This is a Malthusian Equilibrium: vast improvements in technological and organizational capabilities, from 6.5 to 53; but all of that improvement going to support a 70-fold increase in human population; and with only 1/70 the potential natural resources at their disposal, the typical peasant or craftsman in 1500 was able to use that technology to eak out roughly the same standard of living as their predecessors 7.5 millennia before.

There is definitely a spurious precision here. And even if we could gain universal assent as to technological capability in, say, ceramics and each of the other aspects of human productivity and creativity, squashing multi-dimensional objects down into a single one-dimensional index simply cannot be done. All we can say is that if there were an economy simple enough for such an index to be accurate, and if its levels of productivity corresponded to those we assign to the real history, then its index of human technological and organizational capabilities would be our H. Nevertheless, I find such a framework very useful as a metaphor in organizing my thoughts.

Queen Victoria does not appear to have been a much better queen than Queen Elizabeth. But, from all historical accounts, Gloriana appears to have been perhaps four times as happy as happy a woman as the Widow of Windsor.

And the statements that $H_{-8000} = 5$, $H_1 = 31$, and $H_{1500} = 53$ do carry meaning: look at pottery in 8000 BC, in year 1, and in 1500:

Technology in Ceramics, -8000 to 1500: Jomon, Roman, Ming ¶

(How certain are we of all this? For what we think we know—and how we think we know it—dive deeper into the Malthusian Economy: https://delong.typepad.com/teaching_economics/the-malthusian-economy.html.)

1.4: After the Ancient Economy: Speedup and Explosion ¶

Then comes a speedup: from 1500 to 1770 to 1870—over, first, the Commercial Revolution and, second, the Industrial Revolution eras—our quantitative index H grows from 53 to 79 to 125. This time there was some increase in typical standards of living: figure a world in 1870 with 3.5 dollars a day per person, albeit much more unevently distributed. But, still, the overwhelming bulk of improvements in human technology and organization went to supporting a larger population: the 500 million of 1500 had grown to 1.3 billion by 1800, as better living standards lowered death rates worldwide. (And you can dive deeper into the Commercial Revolution <> and the Industrial Revolution <>.)

Then came the explosion: from 1870 to today, in our era of Modern Economic Growth, our H has risen from 125 to 2720. Our population has risen from 1.3 to 7.6 billion. And our resources from 3.5 to 32 dollars a day. (And you can dive deeper into Modern Economic Growth: <>.)

1.5: Rates of Growth ¶

Over the Paleolithic Era of stone and the Mesolithic Era of stone plus some pottery and textiles from 70 to 10 thousand years ago, the rate at which the stock of useful ideas about technology and organization was growing was 0.0027% per year—and, with standards of living stagnant at an average of 3.5 dollars a day or so, the rate of growth of human populations was twice that: 0.0054% per year, or 0.135% per generation: a typical generation would see, an average, 1000 people turn into 1001 and a bit more. What if growth over the generations had been much faster? Then, given the—very slow, 0.0027% per year—rate of growth in useful ideas H, the population finds itself without sufficient resources too sustain itself and drops. What if growth over the generations had been much slower? The population would find itself better-nourished, with children's immune systems less compromised and women ovulating more regularly, and population growth would have accelerated. Malthusian equilibrium thus kept population growing along with useful ideas, and the rate of growth of useful ideas was very slow.

The rate of growth of ideas jumped up, to 0.011% per year, during the 8000-6000 BC Neolithic Revolution: herding and agriculture were really good ideas. And progress continued at 0.013% per year from 6000-3000 BC. Agriculture, craftwork, organization, literacy, and more advance civilization: from 3000-1000 BC and 1000 BC-1 we see H rise at first 0.03% per year, and then 0.06% per year, with a year-1 human population of 170 million, at least half of which was collected in three great empires—Roman, Parthian, and Han—enforcing imperial peace and spanning Eurasia.

Then from 1 to 1500 it looks like a definite not pause but slowdown in the progress of civilization and human knowledge: an ideas growth rate back to the 0.03% per year of 3000-1000 BC.

And, last, comes the breakout:

• a growth rate of useful ideas of 0.15% per year during the 1500-1770 Commercial Revolution.
• a growth rate of useful ideas of 0.44% per year during the 1770-1870 Industrial Revolution.
• a growth rate of useful ideas of 2.06% per year during the post-1870 Modern Economic Growth era.
• a population explosion, and then a slowdown toward zero population growth as prosperity brings female education, female education brings greater female autonomy, and literate women with rights to own property find that there are other ways to gain and maintain social power than to try as hard as possible to become the mohter of many sons and daughters.

From this perspective, there are two big questions in post-Neolithic Revolution global economic history:

1. Why was there and what determined the pace of the triple accelerations in growth to 0.15% and then 0.44% and now 2.06% per year?
2. Why was there and what determined the—much, much, much slower—pace of growth of 0.03% per year (with a 1000 BC-1 temporary jump up) from the invention of writing to 1500?

Right now we are studying the ancient economy. The first of these questions is thus well outside our field of vision. But keep it in the back of your mind.

2: The Solow-Malthus Model ¶

2.1: The Basic Solow Setup ¶

Here, as always, we do what economists do: ruthlessly simplify. People control resources, and use this resources in ways that respond to incentives, and so the societal system moves forward. Economists write down very simple equations describing this: behavioral relationships (how people act), equilibrium conditions (what people's interactions entail), and identities (adding-up conditions. From those they derive how the societal system should have behaved or be behaving. It goes wrong. So economists then go back and complicate the model, and see what the complication entails. They then iterate, until they believe that they have gotten close enough to say that the final-stage model is a good-enough one.

In economic growth, the basic setup model is the Solow Growth Model. It has total society income (and production) $Y$ as a function of the capital stock $K$, the labor force $L$, the efficiency of labor $E$, and a decreasing-returns parameter $\alpha$:

(2.1) $Y = K^{\alpha}(EL)^{1-\alpha}$ :: income and output

(2.2) $\ln(Y) = \alpha\ln(K) + (1-\alpha)\left(\ln(E)+\ln(L)\right)$ :: log form

Growth rates of the capital stock, the labor force, the efficiency of labor, and of production as functions of the savings-investment rate $s$, the population and labor force growth rate $n$, the efficiency-of-labor growth rate $g$, and the depreciation rate $\delta$:

(2.3) $\frac{dK/dt}{K} = \frac{d\ln(K)}{dt} = g_k = \frac{sY}{K} - \delta$ :: the proportional rate of growth of the capital stock

(2.4) $\frac{dL/dt}{L} = \frac{d\ln(L)}{dt} = n$ :: the proportional rate of growth of the labor force and population

(2.5) $\frac{dE/dt}{E} = \frac{d\ln(E)}{dt} = g$ :: the proportional rate of growth of the efficiency of labor

(2.6) $\frac{d\ln(Y)}{dt} = g_{n+y} = \alpha g_k + (1-\alpha)n + (1-\alpha)g$ :: the proportional rate of growth of total production

And define the capital-output ratio:

(2.7) $\kappa = \frac{K}{Y}$

(2.8) $\ln(\kappa) = \ln(K) - \ln(Y)$

(2.9) $\frac{d\ln(\kappa)}{dt} = g_\kappa = g_k - g_y$ :: proportional growth rate of the capital-output ratio

2.2 Determining the Equilibrium Capital-Output Ratio $\kappa^*$ ¶

Look for a situation in which $g_\kappa = 0$: in which the capital stock $K$ and production $Y$ are growing at the same rate so that the capital-output ratio $g_\kappa$ is constant.

Starting from (2.9) and substituting:

(2.10) $g_\kappa = g_k - \left( \alpha g_k + (1-\alpha)n + (1-\alpha)g \right)$

(2.11) $g_\kappa = (1-\alpha)\left( \frac{sY}{K} - \delta - n - g \right)$

(2.12) $\kappa^* = \frac{K}{Y} = \frac{s}{n + g + \delta}$ whenever $g_\kappa = 0$

We define $\kappa^*$ as the steady-state growth equilibrium capital-output ratio:

2.3: Determining Steady-State Growth-Path Production per Worker ¶

From (2.2) derive:

(2.13) $\ln(Y) = \alpha\left(\ln(\kappa) + \ln(Y) \right) + (1-\alpha)\left(\ln(E)+\ln(L)\right)$

(2.14) $\ln \left( \frac{Y}{L} \right) = \left( \frac{\alpha}{1-\alpha} \right)\ln(\kappa) + \ln(E)$

These $\alpha/(1-\alpha)$ terms are getting annoying:

(2.15) $\theta = \frac{\alpha}{1-\alpha}$

And so we define steady-state growth-path production-per-worker as:

(2.16) $\ln \left( \frac{Y}{L} \right)^* = \theta \ln(\kappa^*) =+ \ln(E)$

(2.17) $\frac{d}{dt} \left(\frac{Y}{L}\right)^* = g$

Along the steady-state growth path, production per worker $Y/L$, capital per worker $K/L$, and the efficiency of labor $E$ both grow at the proportional rate $g$; the population and labor force $L$ grows at the proportional rate $n$; total production $Y$ and the capital stock $K$ grow at the proportional rate $n + g$; and the capital-output ratio $\kappa = K/Y$ is constant.

An economy well-modeled by this Solow Growth Model heads for a balanced-growth equilibrium path on which there is a constant balanced-growth capital-output ratio $\kappa^* = s/(n+g+\delta)$, a constant growth rate $g$ of income (and production) and the capital stock per worker, a constant growth rate $n$ of the labor force, and a constant growth rate $n + g$ of total societal income (and production) and of the total capital stock.

But this is not the ancient economy. In the ancient economy $g = 0$, or is very close. The model is unsatisfactory in that it does not provide an explanation for why $g$ is near zero. Hence we complicate the model by introducing Malthusian elements.

2.4: Malthus: Population, Resource Scarcity, and the Efficiency of Labor ¶

Now let's make efficiency of labor growth a function of the rate $h$ at which economically useful ideas are generated, but also of the rate of population and labor force growth $n$ because a higher population makes resources per capita scarce, as determined by an effect-of-resource scarcity parameter $\gamma$:

(2.18) $\frac{dE/dt}{E} = \frac{d\ln(E)}{dt} = g = h - \frac{n}{\gamma}$

Thus:

(2.19) $\frac{d}{dt} \left(\frac{Y}{L}\right)^* = 0$ whenever $h - \frac{n}{\gamma} = 0$

(2.20) $n^{*mal} = \gamma h$

is the population growth rate at which $\frac{d}{dt} \left(\frac{Y}{L}\right)^* = 0$

When population is growing at the rate $n^{*mal}$, the efficiency of labor—and thus the steady-state growth-path level of production per worker $Y/L$—is constant.

2.5: Determinants of Population and Labor Force Growth ¶

Now let's make the rate of growth of the population and labor force depend on the level of prosperity $y = Y/L$; on the "subsistence" standard of living for necessities $y^{sub}$; and also on the fraction $1/\phi$ of production that is devoted to necessities, not conveniences and luxuries, and thus enters into reproductive and survival fitness:

(2.21) $\frac{dL/dt}{L} = \frac{d\ln(L)}{dt} = n = \beta \left( \frac{y}{\phi y^{sub}}-1 \right)$

Then for population to be growing at its Malthusian rate:

(2.22) $\gamma h = \beta \left(\frac{1}{\phi}\right) \left( \frac{y}{y^{sub}}- \phi \right)$

(2.23) $y^{*mal} = \phi y^{sub} \left( 1 + \frac{ n^{*mal}}{\beta}\right) = \phi y^{sub} \left( 1 + \frac{ \gamma h}{\beta}\right)$

2.6: The Full Equilibrium ¶

We can determine the log level $E$ of the efficiency of labor:

(2.24) $\ln(E) = \ln(H) - \frac{\ln(L)}{\gamma}$

Then since:

(2.25) $y^{*mal} = \left( \frac{s}{\gamma h +\delta} \right)^\theta E$

(2.26) $\ln(\phi) + \ln\left( y^{sub} \right) + \ln\left(1 + \frac{\gamma h}{\beta} \right) = \theta \ln(s) - \theta \ln(\gamma h +\delta) + \ln(E)$

The population and labor force in the full Malthusian equilibrium will be:

(2.27) $\ln(L_t^{*mal}) = \gamma \left[ \ln(H_t) - \ln( y^{sub}) \right] + \gamma \theta \left( \ln(s) - \ln(\delta) \right) - \gamma \ln(\phi) + \left( - \gamma \theta \ln(1 + \gamma h/\delta) -\gamma ln\left(1 + \frac{\gamma h}{\beta} \right) \right)$

Or:

(2.28) $L_t^{*mal} = \left[ \left( \frac{H_t}{y^{sub}} \right) \left( \frac{s}{\delta} \right)^\theta \left( \frac{1}{\phi} \right) \left[ \frac{1}{(1+\gamma h/\delta)^\theta} \frac{1}{(1+\gamma h/\beta)} \right] \right]^\gamma$

2.7: Interpretation and Analysis ¶

Thus to analyze the pre-industrial Malthusian economy, at least in its equilibrium configuration:

• Start with the rate $h$ at which new economically-useful ideas are being generated and with the responsiveness $\beta$ of population growth to increased prosperity.

• From those derive the Malthusian rate of population growth: $n^{*mal} = \gamma h$

• Then the Malthusian standard of living is: $y^{*mal} = \phi y^{sub} \left( 1 + \frac{ \gamma h}{\beta}\right)$

Thus at any date t, the Malthusian-equilibrium population is:

1. the current level $H_t$ of the valuable ideas stock divided by the (sociologically determined, by, for example western European delayed female marriage patterns, or lineage-family control of reproduction by clan heads) Malthusian-subsistence income level $y^{sub}$ consistent with a stable population on average, times

2. the ratio between the savings-investment rate $s$ and the depreciation rate $\delta$, raised to the parameter $\theta$ which governs how much an increase in the capital-output ratio raises income—with a higher $\theta$ the rule of law, imperial peace, and a culture of thrift and invetment matter more, and can generate "efflorescences"—times

3. one over the conveniences-and-luxuries parameter $\phi$—it drives a wedge between prosperity and subsistence as spending is diverted categories that do not affect reproduction, such as middle-class luxuries, upper-class luxuries, but also the "luxury" of having an upper class, and the additional conveniences of living in cities and having trade networks that can spread plagues—times

4. two nuisance terms near zero, which depend on how much the level of population must fall below the true subsistence level at which population growth averages zero to generate the (small) average population growth rate that produces growing resource scarcity that offsets the (small) rate of growth of useful ideas. all this

5. raised to the power $\gamma$ that describes how much more important ideas are than resources in generating human income and production.

(1) is the level of the stock of useful ideas relative to the requirements for subsistence. (2) depends on how the rule of law and the rewards to thrift and entrepeneurship drive savings and investment, and thus the divisio of labor. (3) depends on how society diverts itself from nutrition and related activities that aim at boosting reproductive fitness and, instead, devotes itself to conveniences and luxuries—including the "luxury" of having an upper class, and all the conveniences of urban life. (4) are constant, and are small. And (5) governs how productive potential is translated into resource scarcity-generating population under Malthusian conditions.

And recall the full Malthusian equilibrium standard of living:

(2.23) $y^{*mal} = \phi y^{sub} \left( 1 + \frac{ \gamma h}{\beta}\right)$

The level of income is:

1. The luxuries-and-conveniences parameter $\phi$, times
2. The level of subsistence $y^{sub}$, times
3. The (small and constant) nuisance parameter $1 + \gamma h/\beta$ needed to generate average population growth $n^{*mal} = \gamma h$.

Production per worker and thus prosperity are thus primarily determined by (a) true subsistence, (b) the wedge between prosperity and reproductive fitness produced by spending on conveniences and luxuries that do not impact reproductive success, plus a minor contribution by (c) the wedge above subsistence needed to generate population growth consonant with the advance of knowledge and population pressure's generation of resource scarcity.

With this model, we can investigate broader questions about the Malthusian Economy—or at least about the Malthusian model, with respect to its equilibrium:

• How much does the system compromise productivity, both static and dynamic, to generate inequality?
• How would one rise in this world—or avoid losing status relative to your ancestors?
• How does the system react to shocks?:
• like a sudden major plague—like the Antonine plague of 165, the St. Cyprian plague of 249, or the Justinian plague of 542—that suddenly and discontinuously pushes population down sharply...
• like the rise of a civilization that carries with it norms of property and law and commerce, and thus a rise in the savings-investment rate $s$...
• like the rise of an empire that both creates an imperial peace, and thus a rise in the savings-investment rate $s$, and that also creates a rise in the taste for luxuries $\phi$ (and possibly reduces biological subsistence $y^{sub}$...
• like the fall of an empire that destroys imperial peace, and thus a fall in the savings-investment rate $s$, and in the taste for luxuries $\phi$ (and possibly reduces biological subsistence $y^{sub}$ as looting barbarians stock the land...
• a shift in the rate of ideas growth...
• a shift in sociology that alters subsistence...

The fall of an empire, for example, would see a sharp decline in the savings-investment share $s$, as the imperial peace collapsed, a fall in the "luxuries" parameter $\phi$, as the taste for urbanization and the ability to maintain gross inequality declined, and possibly a rise in $y^{sub}$, if barbarian invasions and wars significantly raised mortality from violent death.

This model provides an adequate framework—or I at least, think it is an adequate framework—for thinking about the post-Neolithic Revolution pre-Industrial Revolution economy.

2.8: Model Simulation Experiments ¶

And, with respect to its dynamics, in Python:

delong_classes.malthusian



at:

we can examine how the simulated model behaves dynamically.

Digression on Malthusian Convergence will be maintained at: https://github.com/braddelong/long-form-drafts/blob/master/malthusian_convergence.ipynb¶

In [1]:
# DEFINING CLASS MALTHUSIAN
#
# kept in delong_classes
#
# in general use:
#    import delong_classes
#
#    m = delong_classes.malthusian
#
#    .__init__ :: initialize
#    .update :: calculate the next year's values
#    .gen_seq :: return time series of selected variable

import matplotlib.pyplot as plt
%matplotlib inline

import numpy as np

class malthusian:

"""
Implements the Malthusian Model with:

1. population growth
n =  β*(y/(ϕ ysub)-1)

2. growth of efficiency-of-labor
g = h-n/γ
"""
def __init__(self,
L = 1,               # initial labor force
E = 1/3,             # initial efficiency of labor
K = 3.0,             # initial capital stock

# determinants of n (population growth):
β = 0.025,           # responsiveness of population growth to increased prosperity.
ϕ = 1,               # luxuries parameter
ysub = 1,            # subsistence level

# determinants of g(efficiency-of-labor growth):
h = 0,               # rate at which useful ideas are generated
γ = 2.0,             # effect-of-resource scarcity parameter

s = 0.15,            # savings-investment rate
α = 0.5,             # orientation-of-growth-toward-capital parameter
δ = 0.05,            # deprecation rate on capital parameter
):
self.L, self.E, self.K, self.h, self.γ, self.s, self.α, self.δ = L, E, K, h, γ, s, α, δ
self.β, self.ϕ, self.ysub = β, ϕ, ysub

# production (or output)
self.Y = self.K**self.α*(self.E*self.L)**(1-self.α)
self.y = self.Y/self.L

# capital-output ratio
self.κ = self.K/self.Y

# population growth
self.n = self.β*((self.y/(self.ϕ*self.ysub)) - 1)

# growth rate of efficiency-of-labor
self.g = self.h-self.n/self.γ

# store initial data
self.initdata = vars(self).copy()

def update(self):
# unpack parameters
K, s, Y, δ, L, n, E, g, α =self.K, self.s, self.Y, self.δ, self.L, self.n, self.E, self.g, self.α
β, ϕ, ysub, h, γ = self.β, self.ϕ, self.ysub, self.h, self.γ

#update variables
K = s*Y + (1-δ)*K
L = L*np.exp(n)
E = E*np.exp(g)
Y = K**α*(E*L)**(1-α)
y = Y/L
κ = K/Y
n = β*(y/(ϕ*ysub)-1)
g = h-n/γ

#store variables
self.K, self.s, self.Y, self.δ, self.L, self.n, self.E, self.g, self.α = K, s, Y, δ, L, n, E, g, α
self.κ, self.y = κ, y

def gen_seq(self, t, var = 'κ', init = True, log = False):
"Generate and return time series of selected variable. Variable is κ by default."

path = []

# initialize data
if init == True:
for para in self.initdata:
setattr(self, para, self.initdata[para])

for i in range(t):
path.append(vars(self)[var])
self.update()

if log == False:
return path
else:
return np.log(np.asarray(path))

"Calculate variable values in the steady state"
#unpack parameters
s, γ, h, δ, ϕ, ysub, β, α= self.s, self.γ, self.h, self.δ, self.ϕ, self.ysub, self.β, self.α

self.mal_κ = s/(γ*h+δ)
# malthusian rate of population growth
self.mal_n = γ*h
# malthusian standard of living
self.mal_y = ϕ*(ysub+γ*h/β)
self.mal_E = self.mal_y*((γ*h+δ)/s)**(α/(1-α))

if display == True:
return(f'Malthusian rate of population growth n: {self.mal_n: .2f}')
return(f'Malthusian standard of living y: {self.mal_y:.2f}')
else:
return(self.mal_κ,self.mal_n,self.mal_y,self.mal_E)


3: Using the Framework ¶

3.1: Slow Growth of Technology ¶

3.1.1: The Solow-Malthus Framework ¶

The Solow-Malthus model predicts that a pre-Commercial Revolution economy will have a slowly growing population and labor force at a rate:

(3.1) $n^{*mal} = \gamma h$

where $h$ is the proportional growth rate of the stock of useful human ideas and $\gamma$ is the relative importance of technology and organization vis-a-vis resources in production.

The Solow-Malthus model predicts that a pre-Commercial Revolution economy, on its Malthusian steady-state growth path, will have a living standard close to "subsistence" $y^{sub}$ multiplied by a factor $\phi$ determined by the diversion of resources into "luxuries" that do not boost reproduction and survival: civilization, urbanization, and those luxuries-for-some that are inequality:

(3.2) $y^{*mal} = \phi y^{sub} \left( 1 + \frac{ \gamma h}{\beta}\right)$

plus a small nuisance term $\gamma h/\beta$ proportional to the Malthusian trend population growth rate.

The Solow-Malthus model predicts that a pre-Commercial Revolution economy, on its Malthusian steady-state growth path, will have a population level determined by the balance between the stock of useful human ideas $H$ and the requirements of a stable-population standard of living at sociological "subsistence" $y^{sub}$

(3.3) $\ln(L_t^{*mal}) = \gamma \left[ \ln(H_t) - \ln( y^{sub}) \right] + \gamma \theta \left( \ln(s) - \ln(\delta) \right) - \gamma \ln(\phi) + \left( - \gamma \theta \ln(1 + \gamma h/\delta) -\gamma ln\left(1 + \frac{\gamma h}{\beta} \right) \right)$

with population being boosted by things—an imperial peace or a culture of thrift—that boost savings and investment, with population being reduced by a desire for "luxuries"—comforts, upper-class consumption, and urbanization—and by two small nuisance terms depending on depreciation and what the Malthusian trend is in population growth.

This then gives us a framework within which we can discuss the slow growth of humanity's capabilities, "efflorescences" and dark ages—the rise and fall of empires and civilizations—and other topics.

3.1.2: Competing Theories ¶

Recall the relevant entries in our big-picture summary table: from the coming of literacy around 3000 BC up to 1500, the average proportional rate of growth of the stock of human ideas useful for technology and organization grew at an average rate of 0.039% per year—and that is 1% per 25-year generation:

The Big Picture: Summary Table ¶

Source: https://www.icloud.com/numbers/0jaPx8AjooD2TDbNM4Og3Z2ow¶

That is, admittedly, better than the 0.4% per 25-year generation that came in the illiterate post-Mesolithic economy, and better than the 0.07% per 25-year generation that came in the pre-agricultural gatherer-hunter age. But we today get proportional growth in the useful-ideas stock 50 times as fast: what they got in a generation in the ancient economy, we get in six months in today's world.

3.1.2.1: The Two-Heads Theory 3.1.2.2: Culture Theory 3.1.2.3: Incentives Theory 3.1.2.4: Unlucky Theory

One explanation is the two-heads-are-better-than-one explanation of thinkers like Jared Diamond: Guns, Germs, and Steel: The Fates of Human Societies https://delong.typepad.com/diamond.pdf and Michael Kremer: Population Growth and Technological Change: One Million B.C. to 1990 https://delong.typepad.com/kremer-million.pdf. We have 50 times as many people alive today as were alive then, and we can and do communicate and broadcast ideas much faster and wider. With 50 times the brains thinking up useful ideas, and with a considerable amount of "standing on the shoulders of giants" in the idea-generation process, is it any surprise that technological and organizational progress today is 50 times as fast?

Yet we do not appear to see economic growth pressures building up at an increasing pace in the post-literacy pre-commercial revolution years from 3000 BC to 1500. We see the proportional rate of growth of the worldwide useful-ideas stock bounce around at about 0.9% per 25-year generation for 4.5 millennia, with one excursion up to 1.5% per generation during the 1000 BC-1 "classical" age. It is only after 1500 and the coming of the Commercial Revolution era that, globally, two heads seem genuinely better than one over time, and the average pace of idea-stock growth accelerates to nearly 4% per generation, and then to 16% per generation, and now to 67% per generation.

In addition to "two-heads-are-better-than-one" theories, there are "culture" theories and "incentive" theories—and they shade into one another. And there are also "humanity-was-just-unlucky" theories: that there were a number of times when we might have broken through to sustained commercial growth and then non-human power sources, automatic machinery, and true metallurgy—and thus attained an earlier and an alternative Industrial Revolution.

Moses Finley wrote: Moses Finley: Technical Progress and Economic Innovation in the Ancient World https://delong.typepad.com/finley-technical.pdf: "It is a commonplace that the Greeks and Romans together added little to the world's store of technical knowledge and equipment. The Neolithic and Bronze Ages between them invented or discovered, and then developed, the essential processes of agriculture, metallurgy, pottery, and textile-making. With these the Greeks and Romans built a high civilization, full of power and intellect and beauty, but they transmitted to their successors few new inventions. The gear and the screw, the rotary mill and the water-mill, the direct screw- press, glass-blowing and concrete, hollow bronze-casting, the dioptra for surveying, the torsion catapult, the water-clock and water organ, automata (mechanical toys) driven by water and wind and steam-this short list is fairly exhaustive, and it adds up to not very much for a great civilization over fifteen hundred years...

...Paradoxically, there was both more and less technical progress in the ancient world than the standard picture reveals. There was more, provided we avoid the mistake of hunting solely for great radical inventions and we also look at developments within the limits of the traditional techniques. There was less—far less—if we avoid the reverse mistake and look not merely for the appearance of an invention, but also for the extent of its employment.... Painted pottery is the best instance, one which takes on special significance from the fact that it is the only ancient industry whose history we can write (or will some day be able to write). The potter's wheel is a very ancient invention, and the Aegean world of the Bronze Age already knew all about the properties of clays, how to fashion a variety of pleasing shapes, how to colour and fire and produce a sheen. The heights to which the Greeks then carried this art is evident in museums all over the world. Yet these advances were all accomplished without any technical innovation, by greater mastery of the already known processes and materials, and, above all, by greater artistry.

Then, in the course of the fourth century B.C., the taste for fine painted pottery disappeared, almost abruptly, and at once there was a sharp decline in quality. But people continued to need pots, and rich Greeks and Romans continued to demand better pots with some sort of decoration. Moulded decorations replaced painting and therefore a new technique was introduced in the industry, the only one in its history throughout classical antiquity. That is to say, the long-familiar technique of casting in a mould was adapted from metal to clay in order to produce commodities in the new style. Experts seem to be agreed that neither the speed nor the cost of production was significantly changed as a result. A new fashion was met by the transfer of an old technique. Fourth-century Greeks were not Neanderthal men and we need not hail this particular step as a brilliant accomplishment...

It is not clear to me that Moses Finley's distinction between "technical innovation" and "greater mastery... and... greater artistry" can be maintained:

Technology in Ceramics, -8000 to 1500: Jomon, Roman, Ming ¶

In [57]:
# THE TWO-HEADS THEORY

import numpy as np
import pandas as pd

pop = [0, np.sqrt(15*7), np.sqrt(15*50), np.sqrt(50*170)]

growth = [0, 0.25, 0.6, 1.22]

year = [-10000, -4500, -2000, -500]

data = {'year': year,
'pop': pop,
'growth': growth}

import matplotlib.pyplot as plt
%matplotlib inline

twoheadsdata.plot(x = "pop", y = "growth", kind = "scatter")
plt.show()

# at a population of 75 million, we have an annual
# population growth rate of 0.1% per year.
# that gives us a differential equation, with
# population measured in millions, of:
#
#     (1/x)(dx(t)/dt) = (1.333e-05)x(t)
#
#     x(t) = 100000/(100000c1 + 1.333t)
#
# (see: https://www.wolframalpha.com/input/?i=%281%2Fx%29%28dx%2Fdt%29+%3D+%281.333e-05%29x)

forecast = [170]

for t in range(435):
forecast = forecast + [forecast[t]*(1+(1.333e-05)*forecast[t])]

df_forecast =pd.DataFrame(forecast)
df_forecast.plot()
plt.show()


3.2.1.1: The Incentives Theory:

3.2.1.1: Cultural Theory:

3.1.3: An Industrial Revolution in the Classical Age? ¶

Historically, we see the pace of proportional growth in the stock of ideas pick up around 3000 BC (with a 2.5 amplification), with the coming of literacy, pick up temporarily (with a further doubling—for a millennium—around 1000 BC, with the coming of the iron age, and then pick up much more (with a quadrupling) and for good (so far) around 1500 AD, with the coming of the commercial revolution era, and then the subsequent further industrial-revolution tripling and modern economic growth quadrupling. Could these have happened earlier?

The Big Picture: Summary Table ¶

Source: https://www.icloud.com/numbers/0jaPx8AjooD2TDbNM4Og3Z2ow¶

Mark Koyama... Gunpowder Empire

Mark Koyama (2017): Could Rome Have Had an Industrial Revolution? https://medium.com/@MarkKoyama/could-rome-have-had-an-industrial-revolution-4126717370a2: "Consider some prominent views about what caused the British Industrial Revolution. At the risk of grossly simplifying matters we can put them into three bins: First... that market expansion is sufficient for sustained economic growth.... They will be inclined to favorably quote Adam Smith from his lectures on jurisprudence that 'Little else is requisite to carry a state to the highest degree of opulence from the lowest barbarism, but peace, easy taxes, and a tolerable administration of justice'.... Second... that colonial empires or natural resources like coal were crucial for modern economic growth.... Third... that ultimately only innovation can explain the transition to modern economic growth. This is the position of the majority of economic historians.... The idea that simple economics could explain why innovators developed labor-saving machinery like the spinning jenny in 18th century England (but not in France or India) is advanced by Bob Allen.... Two prominent alternative versions of 3b are associated with Deirdre McCloskey and Joel Mokyr... both would agree that the inventive and enterprising spirit that characterized 18th century England cannot be explained in terms of simple incentives. They instead argue that it required recognition of 'Bourgeois Dignity' or a 'Culture of Growth'...

3.2: Imperial Rise and Fall ¶

3.2.1: "Efflorescences" ¶

based on the Solow-Malthus model: https://github.com/braddelong/LS2019/blob/master/2019-10-14-Ancient_Economies.ipynb

Jack Goldstone (2002): Efflorescences and Economic Growth in World History: Rethinking the "Rise of the West" and the Industrial Revolution https://delong.typepad.com/efflorescences_and_economic_growth_in_world_histor.pdf: "Jan de Vries (2001) has attacked the notion of disparate 'premodern' and 'modern' growth patterns to argue that extensive, Smithian, and Schumpeterian growth coexisted 'in both the pre-industrial past and the modern present', although their proportions have varied over space and time...

...I wish to argue that this attack has not gone far enough.... It was been widely recognized that well before the Industrial and French revolutions, European societies and economies departed from the ideal-typical view of "feudal" economically and technologically stagnant agrarian societies dominated by a predatory elite that wasted all surpluses. Rather... from at least the twelfth century onward... a trans-European set of urban networks that combined management of urban and rural market-oriented craft production... with a flourishing intra-European and extra-European global trade; and from at least the sixteenth century national rulers brought their unruly agrarian elites to heel bybuilding bureaucratized central ("absolutist") governments that provided a rule of law and framework for the protection and accumulation of private property and capital... many of the characterisics of 'modern' growth, or of 'modern' political and social structures, in gestation....

Every one of the above trends observed in Europe and labeled as proof of 'early modern' character—technical improvements in agriculture and production providing rising total output and per capital productivity (including aggressive transformation of the natural landscape); vast urban-based regional and global trade networks supporting wealthy merchant classes; and increasingly centralized and bureaucratized political regimes thatcreated ordered territories and subordinated elites—are also widely evident outside of Europe prior to the eighteenth century... often earlier and in a higher state of development....

Let me propose... 'efflorescence," intended as the opposite of 'crisis'. Where a crisis is a relatively sharp, unexpected downturn in significant demographic and economic indices, often accompanied by political turmoil and cultural conflicts, an 'efflorescence' is a relatively sharp, often unexpected upturn... usually accompanied by political expansion and institution building and cultural synthesis and consoliidation.. involv[ing] both Smithian and Schumpeterian growth... often seen by contemporaries or successors as 'golden ages'... often set[ting] new patterns for thought, political organization, and economic life that last for many generations.... Throughout history, all societies have experienced periods of efflorescence, as well as extensive growth, stagnation, and crises—but that these processes are all distinct from Kuznetzian 'modern' economic growth founded on the continual and conscious application of scientific and technological progress to economic activity...

Biomedical health: $y^{sub}$, as pushed up/down by increasing/decreasing risks/strenuousness of life...

Prosperity: ${\phi}y^{sub}$

• $\phi$: middle-class comfort commodities, an upper class, urbanization and its disease burden/division of labor costs/benefits, barbarian invasions (turn $\phi$ negative, but also push up $y^{sub}$)...

• Efflorescence cannot be due to a rise in $h$... too slow...

• Some efflorescences from a discontinuous jump in $H$, perhaps...

• Efflorescence a rise in $s$ and a rise in $\phi$...

"industrious" vs. "industrial" revolutions:

• extensive/intensive
• Smithian
• Schumpeterian

3.2.2: The Rise of the Classical East-Central Mediterranean ¶

Ian Morris: Economic Growth in Ancient Greece https://delong.typepad.com/morris-greece.pdf: "The first complex societies emerged in Mesopotamia (what is now southern Iraq), Egypt, the Indus Valley (in what is now Pakistan), and China around 3500 BC. Their rulers claimed special relationships with the gods, and organized at least some sectors of the economy through redistribution. Palace- or temple- bureaucracies oversaw certain kinds of production, bringing goods in and redistributing them as rations to different kinds of workers...

...Similar palaces... appearing on Crete around 2000 BC, and in Greece by 1600. The palatial elites shared a sophisticated international culture, linked by letters, gift exchange, and dynastic marriages. Finds of Greek artifacts in eastern Sicily, southern Italy, and Sardinia from 1400 on suggest that the system was still expanding at this point.

Around 1200, though, most of the great palaces... were set on fire.... Migrations and earthquakes were involved. Egypt and southern Iraq escaped the destructions, but... suffered demographic decline and a weakening of state authority. Egypt fared best, and Greece worst. In Greece, palaces disappeared after 1200, and with them writing and many advanced artistic skills.... Greece was depopulated, with simple societies living at a low technological level. This changed rapidly in the eighth century, as all across the Mediterranean, trade revived, and competition between communities stimulated the formation of small city-states. Learning from the Phoenecians, thousands of Greeks colonized the coasts of Sicily and southern Italy. Greeks invented a new style of writing around 775-750 BC, and used it to record Homer's epic poetry. Monumental architecture revived, and representational art. The Greek city-states developed peculiar forms of male civic e based on the idea that all locally born free men were more or less city-states, this developed by 500 into democratic institutions, in which all male citizens... voted equally on all major decisions. Elsewhere more limited groups of men (usually defined by wealth) made the key decisions, but were answerable to the larger community.

Sparta, Athens, and Syracuse emerged as the most powerful city states early in the sixth century. In 480 Sparta and Athens led an alliance that repulsed from the Persian Empire, and in the same year Syracuse defeateda Carthaginian invasion of Sicily.... Athens and Syracuse then went on, in very different ways, to build up powerful states in the fifth century. Both populations of 40,000-50,000. This period also saw a dramatic cultural flourescence.... By the 430s it looked as if Athens might convert the Aegean into a unified state... so in 431 Sparta went to war.... This Peloponnesian War... ended when Sparta secured Persian funding, built a great navy, and starved Athens inot submission. Sparta then took over Athens's empire, but failed to hold it together, while in Sicily Syracuse, after repulsing an Athenian attack in 415-13, was badly battered by Carthage after 409....

Macedonian kings adopted Greek military and organizational skills... [and] by 338 he had humbled the main Greek powers.... Alexander... in 331 killed the Persian king. He spent the next eight years subduing the empire. By the time Alexander died in 323, the old city-state... were losing their relevance. Hundreds of thousands of Greeks... settled in the newly conquered Middle East, particularly in Egypt, coastal Syria, and what is now Turkey. The greatest Greek city, Alexandria in Egypt, grew to 500,000 people, dwarfing anything in the old Greek world, and several cities in Iraq reached 100,000 in the third century. Alexander's generals fought over his empire for a quarter-century... dividing it into three major kingdoms in Egypt, the Near East, and Macedon....

From 200 onward, Rome systematically destroyed these Hellenistic kingdoms in the greatest outpourings of military energy in premodern history. Two centuries of war devastated the Greek world, which experienced demographic collapse. Recovery came only in the fourth century AD.... As the western part of the Roman Empire disintegrated before Germanic invaders in the fifth century, the part flourished. But in the late sixth century its expansion slowed, and crippling plagues hit the Greek east. In the early seventh century Islamic Arabs... swe[pt]... away Greek control of Egypt, Israel, Lebanon, and Syria. Constantinople itself twice came close to falling, although in fact it resisted Islam until the Turks took it in 1453.

The

We could write down our four possible rought description cases in math, using "c" rather than "t" for our time index because there is no real point to working in units of less than a century, and to remind us that that is what we are doing:

$\frac{dP_{c}}{dc} = γ{P_{c}}^{2}$

$\frac{dP_{c}}{dc} = γ{P_{c}}^{(3/2)}$

$\frac{dP_{c}}{dc} = P_{c}\left(γ{\ln{P_{c}}}\right)$

$\frac{dP_{c}}{dc} = γP_{c}$

And then use http://wolframalpha.com to get us analytic solutions:

$\frac{dP_{c}}{dc} = γ{P_{c}}^{2} → P_{c} = \frac{1}{A - γc}$

$\frac{dP_{c}}{dc} = γ{P_{c}}^{(3/2)} → P_{c} = \frac{4}{{(A + γc)}^2}$

$\frac{dP_{c}}{dc} = P_{c}\left(γ{\ln{P_{c}}}\right) → P_{c} = li^{^{(-1)}}\left(A + γc\right)$

$\frac{dP_{c}}{dc} = γP_{c} → P_{c} = Ae^{(γc)}$

(Yes, I had forgotten that the "log integral" function $li( )$ existed, let alone that its inverse $li^{^{(-1)}}()$ was a thing.)

Lecture Notes: Introduction to Economic History: The Ancient Economy ¶

Catch Our Breath—Further Notes:¶

[email protected]

38524 Athy Court Fremont, CA 94536

Meet again on July 8 (carrel; keycard?; wifi account)?

The Roman peace...- Investments and the division of labor Ivar the Boneless Luxury Romeo and Juliet

Inequality

Liberty and Incorporation of others into the polity

Anthology intelligence

Gift exchange, trust, fictive kinship, and consensus

Personification Altruistic punishment Vulnerability to the grift Thugs with spears Thugs with calendars Thugs with spreadsheets

Moses Finley: Technical Progress and Economic Innovation in the Ancient World https://delong.typepad.com/finley-technical.pdf

There is admittedly a danger, in pursuing this line of argument, of falling into the trap of assuming that certain values are always and necessarily paramount. The idea that efficiency, increased productivity, economic rationalism and growth are good per se is very recent in human thinking (although it seems to take hold in a most remarkable way once it gets an effective start). We might consider the Pont du Gard a fantastically expensive way of bringing fresh water to a not very important provincial town in southern Gaul; the Romans in Gaul ranked fresh water and the demonstration of power higher on the value-scale than costs. That was a rational view, too, though not economic rationalism...

Granted that, the ancient world still presents us with a big question, one that is forced on us by at least two facts. The first is that the ancient world was very unambiguous about wealth. Wealth was a good thing, a necessary condition for the good life, and that was all there was to it. There was no nonsense about wealth as a trust, no subconscious guilt feelings, no death-bed restitutions of usury. The other fact, which I have already mentioned, is that, intellectually (or scientifically) speaking, there was a basis for more technical advance-in production-than was actually made. Why did productivity then not advance markedly, if the interest, the knowledge, and the necessary intellectual energy would seem to have been present? The question cannot be dismissed simply by pointing to alternative values, not, at least, when one of those was a very powerful desire for wealth and for large-scale consumption...

At the end of the first section of the Politics (I 258b 33ff.), [Aristotle] wrote as follows (in Barker's translation):

A general account has now been given of the various forms of acquisition: to consider them minutely, and in detail, might be useful for practical purposes; but to dwell long upon them would be in poor taste.... There are books on these subjects by several writers.... Anyone who is interested should study these subjects with the aid of these writings...

Aristotle was the greatest polymath of antiquity, a tireless researcher, and the founder of any number of new disciplines in science and philosophy. His curiosity was unbounded, but 'good taste', a moral category, interposed to put beyond the pale knowledge in its practical applications except when the application was ethical or political...

Vitruvius... ten books.... In the whole work I can find only one passage which considers the achievement of greater economy of effort or greater productivity. Vitruvius recommends (5.1O.1), that in public baths the hot-water room for men be placed next to the one for women, so that they can be fed from a single heat source. It will be conceded that this is not a very impressive instance. By contrast, the description of the water-mill for corn-grinding is astonishingly brief, just one short paragraph (1O.5.2), and it is absolutely bare of comment, so much so that only the reader who is so minded will appreciate the implications for effort and productivity. Vitruvius gives no hint in that direction. All in all, it is correct to say that for Vitruvius the sole aim of technical advance (apart from aesthetic considerations) is the achievement of operations which are otherwise impossible, or possible only by excessive effort.... Scattered in the prefaces there are several stories drawn from the history of inventions. Invariably the circumstance, and therefore the explanation, is either accidental (as in the discovery of the marble quarries at Ephesus when two fighting rams chipped a bit of the hillside) or frivolous (as in Archimedes' discovery of the principle of specific gravity in response to a request for a way in which to unmask a dishonest silversmith). Neither for the past nor for the present nor for the future did Vitruvius conceive of technology as something which could be advanced by sustained, systematic effort. His outlook was altogether utilitarian. Quite the reverse of Aristotle, he discussed only practical matters and referred the reader who wished to bother with 'things which are not for use but for the purposes of our delight' (Ctesibius's automata) to the available literature (1O.7.5). Yet on the matter which concerns us, Vitruvius and Aristotle were of one mind. In essence so were all the other writers on such subjects, and it is this unanimity which justifies the argument from silence.... Attitudes are the key to the blockage...

Impossible as it is to lump the whole of ancient society into one generalization, it would not be far wrong to say that from the Homeric world to Justinian great wealth was landed wealth, that new wealth came from war and politics (including such by-products as tax-farming), not from enterprise, and that whatever was available for investment found its way into the land as quickly as it could. There was never a time, so far as I know, when the large landholders of antiquity did not prosper as a class. Agrarian crisis was chronic among the little men, but even in the worst days of the third century, or the fifth, the magnates drew large rents and profits from their estates. In most periods they were absentee urban-dwellers, who left the management and operation of their estates either to tenants or to slaves and slave bailiffs. In either case their psychology was that of the rentier, and hence neither their material circumstances nor their attitudes were favourable to innovation. They were not so stupid or so hide-bound that they could not abandon grain production for olive and vine cultivation or pasture when circumstances pressed them, or that they could not (sometimes) tell a better landed invest- ment from a poorer one. But essentially their energies went into spending their wealth, not making it, and they spent it on politics and the good life...

In the fifth century B.C. Athens supplied much of the fine pottery for the whole Greek world and for the Etruscans, and the total production at any one time was the work of about I25 painters working with a still smaller number of shapers and assistants.... In the following century this trade died because demand disappeared, but the Athenian economy was not visibly affected, nor was its prosperity.... A few craftsmen were displaced, quality dropped sharply-that is all. The first century of the Roman Empire offers another kind of example. The fine pottery of this period was the terra sigillata, rather simple, well-made red ware, with moulded decorations if any. It is often called Arretine ware because at the beginning of the period the north Italian town of Arezzo monopolized production. But not for long: the Augustan peace and the consequent expansion of population and urbanization in the western provinces saw the diffusion of the manufacture of terra sigillata to various centres in Gaul and along the Rhine. Arezzo was knocked out of the market and quality declined. Out of this and one or two similar developments, in the manufacture of terra cotta lamps, for example, Rostovtzeff and others following him have constructed a great theory about economic decentralization, the ruin of the bourgeoisie, the end of emergent capitalism, and the seeds of the decline of the Roman Empire. I mean no offence, but this theory is an anachronistic burlesque.... All that had happened was that a few minor trades over-reached the market, some hundreds of craftsmen in the western Empire in a few cities were displaced by some hundreds in a few other cities, and nothing else.... It reveals, first, that the minimum technology and small amounts of capital required, the wide diffusion of craft skills, and the excessive costs of transport by land, all combined to promote diffusion of manufacture when population spread away from the Mediterranean coasts; and second, that production for the domestic market and inelasticity of demand were as predominant as Xenophon believed. On the larger issue David Hume saw the picture exactly, when he wrote: 'I do not remember a passage in any ancient author, where the growth of a city is ascribed to the establishment of a manu- facture. The commerce, which is said to flourish, is chiefly the exchange of those commodities, for which different soils and climates were suited'...

Servile and other forms of dependent labour were very profitable. Such changes as occurred in the Roman Empire in the position of the wealthy were political, not economic, and therefore they had no significant incentive to alter the productive arrangements. In the end, it was the military and political breakdown of the Empire which drove the western aristocracy back onto their estates and to the beginnings of a manorial system. The interests of the state were another matter; from the second century on, the emperors were faced with continuing difficulties and crises in supplies and revenues. They had good reason to think of more production. That, instead, they thought of more regimentation, of a bigger bite out of the old pie, seems to me explicable largely in terms of attitudes, of thought-processes...

The pejorative judgments of ancient writers about labour, and specifically about the labour of the artisan, and of anyone who worksfor another, are too continuous, numerous, and unanimous, too wrapped up in discussions of every aspect of ancient life, to be dismissed as empty rhetoric.... Tocqueville['s]... notebooks... are filled with the theme that 'slavery is even more prejudicial to the masters than to the slaves', because, as a leading Louisville merchant said to him, 'it deprives us of the energy and spirit of enterprise that characterizes the States that have no slaves'. Greek and Roman slavery functioned in a different context, to be sure, both internally and externally, and comparisons must be made with caution and reserve. But this particular one seems to me to be valid and necessary...

Karl Polanyi: Aristotle Discovers the Economy https://delong.typepad.com/aristotlediscovers.pdf:

In the philosophy of Aristotle the three prizes of fortune were: honor and prestige; security of life and limb; wealth. The first stands for privilege and homage, rank and precedence; the second ensures safety from open and secret enemies, treason and rebellion, the revolt of the slave, the overbearing of the strong, and even protection from the arm of the law; the third, wealth, is the bliss of proprietorship, mainly of heirloom or famed treasure. True, utilitarian goods, food and materials, accrue as a rule to the possessor of honor and security, but the glory outshines the goods. Poverty, on the other hand, goes with an inferior status; it involves working for one’s living, often at the bid- ding of others. The les^s restricted the bidding, the more abject the condition. Not so much manual labor—as the farmer’s ever respected position shows—but dependence upon another man’s personal whim and command causes the serving man to be despised. Again, the bare economic fact of a lower income is screened from view...

We must refer back to the texts.... Some of his key terms, notably kapeJike, metadosis and chrematistike, were misinterpreted in translation. Sometimes the error becomes subtle. Kapelike was rendered as the art of retail trade instead of the art of "commercial trade,” chrematistike as the art of money-making instead of that of supply, i.e., the procuring of the necessaries of life in kind. In another instance, the distortion is manifest: metadosis was taken to be exchange or barter, while patently meaning its opposite, namely, "giving one's share"....

Kapelike, grammatically denotes the art of the kapelos. The meaning of kapelos as used by Herodotus in the middle of the fifth century, is broadly established as some kind of retailer, especially of food.... The invention of coined money was linked by Herodotus with the fact that the Lydians had turned kapeloi. Herodotus also recounts that Darius was nicknamed kapelos. Indeed, under him military stores may have begun the practice of retailing food. Eventually kapelos became synonymous with “trickster, fraud, cheat”.... Kapelike... was not in use; the dictionary mentions only one instance (apart from Aristotle).... Aristotle was using kapelike with an ironical overtone. Commercial trade was of course, not huckstering; nor was it retail trading; and whatever it was, it deserved to be called some form or variant of emporia which was the regular name for seafaring trade, together with any other form of large-scale or wholesale trade. When Aristotle referred specifically to the various kinds of maritime trade, he fell back on emporia, in the usual sense. Why, then, did he not do so in the main theoretical analysis of the subject but use instead a newfangled word of pejorative connotation? Aristotle enjoyed inventing words, and his humor, if any, was Shavian. The figure of the kapelos was an unfailing hit of the comic stage.... Commercial trade was no mystery. When all is said, it was but huckstering written large....

Chrematistike was deliberately employed by Aristotle in the literal sense of providing for the necessaries of life, instead of its usual meaning of “money-making.” Laistner rendered it correctly as “the art of supply,” and Ernest Barker in his commentary recalled the original sense of chremata, which, he warned, was not money, but the necessaries themselves....

The signal error in rendering metadosis as "exchange" in the three crucial passages of the Politics and the Ethics cut deeper.... In an archaic society of common feasts, raiding parties, and other acts of mutual help and practical reciprocity the term metadosis possessed a specific operational connotation—it signified "giving a share" especially to the common pool of food, whether a religious festivity, a ceremonial meal, or other public venture was in question.... Yet we are faced with the astonishing fact that in the translation of these passages in which Aristotle insisted on the derivation of exchange from metadosis... they rendered metadosis by "exchange," and thus turned Aristotle's statement into an empty truism.... his derivation of exchange from "giving one's share"... provided a logical link between his theory of the economy in general and the practical questions at issue. Commercial trade, we recall, he regarded as an unnatural form of trade; natural trade was gainless since it merely maintained self-sufficiency.... Thus the derivation of exchange from contributing one's share to the common pool of food was the linchpin that held together a theory of the economy based on the postulate of self-sufEciency of the community and the distinction between natural and unnatural trade...

Will Baumol: Entrepreneurship: Productive, Unproductive, and Destructive https://delong.typepad.com/files/baumol-entrepreneurship.pdf:

The avenues open to those Romans who sought power, prestige, and wealth are instructive. First, it may be noted that they had no reserva- tions about the desirability of wealth or about its pursuit (e.g., Finley 1985, pp. 53-57). As long as it did not involve participation in industry or commerce, there was nothing degrading about the wealth acquisition process. Persons of honorable status had three primary and acceptable sources of income: landholding (not infrequently as absentee landlords), "usury," and what may be described as "political payments"...

The allocation of entrepreneurship between productive and unproductive activities, though by no means the only pertinent influence, can have a profound effect on the innovativeness of the economy and the degree of dissemination of its technological discoveries. It is hard to believe that a system of payoffs that moves entrepreneurship in unproductive directions is not a substantial impediment to industrial innovation and growth in productivity.... One can only note what appears to be a remarkable correlation between the degree to which an economy rewarded productive entrepreneurship and the vigor shown in that economy's innovation record. Historians tell us of several industrial "near revolutions"... that are highly suggestive.... Two... never went anywhere, while two of them were rather successful in their fashion....

My earlier discussion cited ancient Rome and its empire as a case in which the rules did not favor productive entrepreneurship. Let us compare this with the evidence on the vigor of innovative activity in that society. The museum at Alexandria was the center of technological innovation in the Roman empire. By the first century B.C., that city knew of virtually every form of machine gearing that is used today, including a working steam engine. But these seem to have been used only to make what amounted to elaborate toys. The steam engine was used only to open and close the doors of a temple....

The spate of inventions that occurred in ancient China (before it was conquered by the barbarian Yuan dynasty in 1280)... paper, (perhaps) the compass, waterwheels, sophisticated water clocks, and, of course, gunpowder.... In China too, as we have seen, the rules did not favor productive entrepreneurship. Balazs (1964, p. 53) concludes that

what was chiefly lacking... was not mechanical skill or scientific a titude, nor a sufficient accumulation of wealth, but scope for individual enterprise. There was no individual freedom and no security for private enterprise, no legal foundation for rights other than those of the state, no alternative investment other than landed property, no guarantee against being penalized by arbitrary exactions from officials or against intervention by the state. But perhaps the supreme inhibiting factor was the overwhelming prestige of the state bureaucracy, which maimed from the start any attempt of the bourgeoisie to be different, to become aware of themselves as a class and fight for an autonomous position in society. Free enterprise, ready and proud to take risks, is therefore quite exceptional and abnormal in Chinese economic history....

By the beginning of the fourteenth century, according to Gimpel (1976), 68 mills were in operation on less than one mile of the banks of the Seine in Paris, and these were supplemented by floating mills anchored to the Grand Pont. The activity in metallurgy was also considerable-sufficient to denude much of Europe of its forests and to produce a rise in the price of wood that forced recourse to coal (Nef [1934].... The industrial revolution of the twelfth and thirteenth centuries was a surprisingly robust affair, and it is surely plausible that improved rewards to industrial activity had something to do with its vigor. The end of all this period of buoyant activity in the fourteenth century... has a variety of explanations, many of them having no connection with entrepreneurship. For one thing... average temperatures dropped.... The plague returned.... The church clamped down on new ideas and other manifestations of freedom. Roger Bacon himself was put under constraint. The period during which new ways of thinking brought rewards and status was apparently ended.... The first half of the devastating Hundred Years' War... the associated renewal of rewards to military enterprise....

I'm never sure whether I should begin my economic history survey courses with Aristotle or not.

As Moses Finley powerfully argues, Aristotle does not care about the economy. The fragments in his Ethics and Politics that economists like Joseph Schumpeter point to are, mostly, concerned with other things than economic analysis. Karl Polanyi thought that Aristotle's naivete was the result of the fact that a mercantile, market, commercial economy was something very new. He was surely wrong: it was not something new, but rather something that Aristotle as a Hellenic aristocrat would have been embarrassed to be caught thinking seriously about.

Aristotle's perspective is so different from ours that it provides a useful mental shock when you consider that Aristotle of Stagira was not an idiot. For two thousand years people—pagan Hellenes, Christian Europeans, and Islamic Arabs, Egyptians, Mesopotamians,and Iranians—called Aristotle of Stagira "the philosopher", as if there could be only one. Think of the way seventeenth, eighteenth, and nineteenth century Britons regarded Newton (or the way we regard Einstein). So we need to take Aristotle seriously.

Think about how a very good mind, thinking very hard, in pre-industrial-revolution economic circumstances, could wind up thinking the thoughts on the economy that Aristotle does:

Aristotle of Stagira was not an idiot. For two thousand years people called him "the philosopher”—as if there was only one.

Aristotle on the Necessity of Slavery:

• "Let us first speak of master and slave, looking to the needs of practical life.... [Some] affirm that the rule of a master over slaves is contrary to nature.... Property is a part of the household... no man can live well, or indeed live at all, unless he be provided with necessaries.... [T]he workers must have their own proper instruments... of various sorts; some are living, others lifeless; in the rudder, the pilot of a ship has a lifeless, in the look-out man, a living instrument.... [I]f every instrument could accomplish its own work, obeying or anticipating the will of others, like the statues of Daedalus, or the tripods of Hephaestus... the shuttle would weave and the plectrum touch the lyre without a hand to guide them, chief workmen would not want servants, nor masters slaves.... But is there any one thus intended by nature to be a slave, and for whom such a condition is expedient and right?... There is no difficulty in answering this question... that some should rule and others be ruled is a thing not only necessary, but expedient; from the hour of their birth, some are marked out for subjection, others for rule..."

Aristotle on Acquisition:

• “A general account has now been given of the various forms of acquisition: to consider them minutely, and in detail, might be useful for practical purposes; but to dwell long upon them would be in poor taste.... There are books on these subjects by several writers…”
• The “natural art of acquisition” has “a boundary fixed, just as there is in the other arts; for the instruments of any art are never unlimited...”
• “There are two sorts of wealth-getting... one is a part of household management, the other is retail trade: the former necessary and honorable, while that which consists in exchange is justly censured; for it is unnatural, and a mode by which men gain from one another…”

Aristotle on Economics:

• Shepherds are '...the laziest [of men]... lead an idle life... get their subsistence without trouble from tame animals...’?
• Aristotle's story of Thales of Miletos and his corner of the olive-press-rental market on Khios: Aristotle is saying “we could get rich (or richer) with little effort, but that is not an important or proper thing to do…”
• Note: Aristotle's "limit" is probably the full-time year-round labor of at least fifty people, at today's OECD wage levels some 3,000,000 dollars a year: in one sense very, very few of us will ever come near to Aristotle's point of satiation; in another sense every single one of us has already gone far beyond Aristotle's limit...

Aristotle on Slavery:

• If every instrument could accomplish its own work, obeying or anticipating the will of others, like the statues of Daedalus, or the catering serving carts of Hephaestus... the shuttle would weave and the plectrum touch the lyre without a hand to guide them, chief workmen would not want servants, nor masters slaves...
• But is there any one thus intended by nature to be a slave, and for whom such a condition is expedient and right?... There is no difficulty in answering this question... that some should rule and others be ruled is a thing not only necessary, but expedient; from the hour of their birth, some are marked out for subjection, others for rule...

Ancient Ain't Primitive, Is It?:

• Could we teach:
• Themistokles or Augustus much about politics?
• Homer much about writing poetry?
• Gaius Julius Caesar of Leonidas much about generalship?
• Michelangelo di Lodovico Buonarroti Simon much about painting ceilings?
• Johann Sebastian Bach much about music?
• Yet technological progress and economics seem to be different—areas where we have a serious edge. Why?

What Does Finley Have to Say?:

• Assertions about responsiveness to fashion and imperatives of craftsmanship…
• Lots of incremental improvements
• Little wide dissemination
• “Intellectually (or scientifically) speaking, there was a basis for more technological advance—in production—than was actually made…”
• “Archimedes' practical inventions, I hasten to add, were military and were made only under the extraordinary and irresistible stimulus of the siege of his native Syracuse by the Romans.”
• “It is this unanimity which justifies the argument from silence…”
• “Why did neither the Ptolemies nor the Sicilian tyrants nor the Roman emperors systematically (or even spasmodically) turn their engineers to the search for higher productivity, at least in those sectors of the economy which produced the royal revenues? Whatever the answer, it was not lack of capital (or lack of authority). Funds, manpower and technical skills were made available (and wasted) in vast and ever increasing amounts for roads, public buildings, water supply, drainage and other amenities, but not for production. Of course, the effort to increase productivity might have proved unsuccessful - but it was never even attempted…”
• “It is unnecessary to examine the economic history of the later Roman Empire in detail to make the point, with which no one disagrees, that neither technique nor productivity nor economic rationalism made an advance in those final centuries of antiquity. It is, necessary, however, to ask once more why, when circumstances seemed to demand progress on those lines, the only solutions to the problems of labour and production were bureaucratic pressures, greater tax exploitation, and a general debasement of the status (and perhaps the standards) of the free elements in the productive population. The answers, I suggest, are those I pointed to earlier. Servile and other forms of dependent labour were very profitable. Such changes as occurred in the Roman Empire in the position of the wealthy were political, not economic, and therefore they had no significant incentive to alter the productive arrangements. In the end, it was the military and political breakdown of the Empire which drove the western aristocracy back onto their estates and to the beginnings of a manorial system…”
• Finley says “culture”. But there are other possibilities:
• 7 billion heads are better than 5 million…
• Standing on the shoulders of giants…
• Incentives to innovate rather than plunder (William Gates vs. William Marshall)…
• Note to Self: Re: Aristotle and Polanyi: Karl Polanyi thought Aristotle's economic naivete was because the commercial economy was new. He was surely wrong: it was rather something that Aristotle as a Hellenic aristocrat would have been embarrassed to be caught thinking seriously about...

Aristotle: Politics https://delong.typepad.com/aristotle-politics-selections.pdf: Book I Excerpts:

Keynote: Aristotle and Finley https://www.icloud.com/keynote/0ZlslVp11hMCkX7-KbOniyOiA

Note to Self: Polanyi: Aristotle Discovers the Economy: Hoisted from the Archives: A whole bunch of this article is simply wrong: the claims that "in the fourth century... Greeks initiated the gainful business practices that in much later days developed into the dynamo of market comnpetition" are false. This means that Polanyi is wrong when he says that Aristotle is examining a new phenomenon when he looks at the economy. Aristotle is examining an old phenomenon from the point of view of an Athenian aristocrat. But there is much of value in Polanyi's exposition of what Aristotle says:

• Trade is "natural" when it serves the survival of the community by maintaining its self-sufficiency...
• The operation of giving a share... from one's surplus.
• The rate... follows from the requirement of philia, i.e., that the goodwill among the members persist.... The just price, then, derives from the demands of philia... [and] conform[s] to the standing of the participants in the community, thereby strenghening the goodwill on which community rests.... In such exchange no gain is involved, goods have their known prices, fixed beforehand. If exceptionally gainful retailing there must be for the sake of a convenient distribution of goods in the marketplace, let it be done by noncitizens...
• Commercial trade..... How should the phenomenon be classified?... Aristotle... call[s]... commercial trade kapelike... hucksterism writ large...

Reading List for an Ungiven Course: The "Classical" Mediterranean Economy Fall of rome Google Search

It looks to me as though I should admit (to myself at least) that I am unlikely to ever teach my course the "classical" Mediterranean economy. Thus it is time for me to move it to the Assignment Desk--things that I really wish other people work on.

Here is the skeleton of the reading list: things that I think must be on it.

They all, of course, require ancillary follow-on pieces developing, applying, and critiquing each of the principal authors' arguments. In addition, many of them are sufficiently difficult and demanding that they require a preparatory warm-up reading or two as well. All of those are absent:

Jared Diamond (1987): THE INVENTION OF AGRICULTURE: THE WORST MISTAKE IN THE HISTORY OF THE HUMAN RACE http://delong.typepad.com/sdj/2005/09/the_malthusian_.html

Rick Steckel (2008): BIOLOGICAL MEASURES OF THE STANDARD OF LIVING http://www.aeaweb.org/articles.php?doi=10.1257/jep.22.1.129

Moses Finley (1954): THE WORLD OF ODYSSEUS http://delong.typepad.com/finleyodysseus.pdf http://amzn.to/2rQxFhI

Moses Finley (1965): TECHNICAL INNOVATION AND ECONOMIC PROGRESS IN THE ANCIENT WORLD http://www.jstor.org/stable/2591872

William Baumol (1990): ENTREPRENEURSHIP: PRODUCTIVE, UNPRODUCTIVE, AND DESTRUCTIVE http://delong.typepad.com/baumol-1990-entrepreneurship.pdf

Aldo Schiavone (2002): THE END OF THE PAST http://amzn.to/2rzcJfI

Moses Finley (1973): THE ANCIENT ECONOMY http://delong.typepad.com/files/finleythe-ancient-economy.pdf http://amzn.to/2ryMiqj

Peter Temin (2013): THE ROMAN MARKET ECONOMY http://delong.typepad.com/temin2013.pdf http://amzn.to/2rz7E6Y

Paul Seabright (2010): THE COMPANY OF STRANGERS: A NATURAL HISTORY OF ECONOMIC LIFE http://amzn.to/2tp56K6

H.N. Turteltaub (2001): OVER THE WINE-DARK SEA http://amzn.to/2rzelGs

James Davidson (1998) COURTESANS AND FISHCAKES: THE CONSUMING PASSIONS OF CLASSICAL ATHENS http://amzn.to/2sSzn6F

Aristotle (350 BC): THE NECESSITY OF SLAVERY http://delong.typepad.com/egregious_moderation/2009/04/aristotle-on-the-necessity-of-slavery.html

Karl Polanyi (1957): ARISTOTLE DISCOVERS THE ECONOMY http://delong.typepad.com/polanyi-aristotle.pdf

Karl Polanyi (1957): THE ECONOMY AS INSTITUTED PROCESS http://delong.typepad.com/polanyiinstituted-process.pdf

Bryan Ward-Perkins (2006): THE FALL OF ROME AND THE END OF CIVILIZATION http://amzn.to/2to4Wma

Erich Auerbach (1953): MIMESIS: THE REPRESENTATION OF REALITY IN WESTERN LITERATURE http://amzn.to/2sSpHZH, chs. 1-6

Perry Anderson (1974) PASSAGES FROM ANTIQUITY TO FEUDALISM http://amzn.to/2sLyyMD

Michael Kremer: Population Growth and Technological Change: One Million B.C. to 1990 https://delong.typepad.com/kremer-million.pdf

What Do Our Readings Have to Say? ¶

Slow Growth of Technology ¶

Moses Finley: Technical Progress and Economic Innovation in the Ancient World https://delong.typepad.com/finley-technical.pdf

Karl Polanyi: Aristotle Discovers the Economy https://delong.typepad.com/aristotlediscovers.pdf

Will Baumol: Entrepreneurship: Productive, Unproductive, and Destructive https://delong.typepad.com/files/baumol-entrepreneurship.pdf

"Substantivist" Perspectives ¶

Moses Finley: The World of Odysseus https://delong.typepad.com/worldofodysseusexcerpts2.pdf: Excerpts: Wealth and Labor; Household, Kin, and Community

Moses Finley: The Ancient Economy https://delong.typepad.com/files/finleyancientexcerpts.pdf: Excerpts: Landlords and Peasants; Town and Country

"Marketist" Perspectives ¶

Peter Temin: The Roman Market Economy https://delong.typepad.com/files/temin2013exerpts.pdf: Excerpts: The Grain Trade; The Labor Market; Financial Intermediation; Economic Growth

Agrarian Immiserization ¶

Jared Diamond: The Invention of Agriculture: The Worst Mistake In the History of the Human Race http://delong.typepad.com/sdj/2005/09/the_malthusian_.html

John A. Hall: Powers and Liberties

Empires ¶

Willem M. Jongman*, Jan P.A.M. Jacobs, and Geertje M. Klein Goldewijk: Health and Wealth in the Roman Empire https://delong.typepad.com/rome.pdf

Willem Jongman: Gibbon Was Right: The Decline and Fall of the Roman Empire https://delong.typepad.com/jongman-gibbon-was-right.pdf

Moses Finley: The World of Odysseus https://delong.typepad.com/finleyodysseus.pdf: entire

Moses Finley: The Ancient Economy https://delong.typepad.com/files/finleythe-ancient-economy.pdf: entire

Alasdair Macintyre: Musings on the utility function of an ancient Greek: https://delong.typepad.com/files/utilityfunctionofagreek.pdf

Alasdair Macintyre: After Virtue https://delong.typepad.com/files/aftervirtue.pdf: entire

Peter Temin: The Roman Market Economy https://delong.typepad.com/files/temin2013percapitagdp.pdf: Per Capita GDP in the Early Roman Empire

Peter Temin: The Roman Market Economy https://delong.typepad.com/temin2013.pdf: entire

Modeling a Pre-Industrial Economy:

IMF: World Economic Outlook (April 2019): Gross Domestic Product: https://www.imf.org/external/datamapper/datasets/WEO/1

Longest-Run Global Economic Growth (2019) https://www.icloud.com/numbers/0jaPx8AjooD2TDbNM4Og3Z2ow

In [10]:
import statsmodels.api as sm
import statsmodels.formula.api as smf

reg1 = sm.OLS(endog=Growth, exog=Pop, missing='drop')

print(reg1.fit().summary())

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-10-a6d4b30e569c> in <module>
18 data = pd.DataFrame(Pop, Growth)
19
---> 20 data.plot(kind='scatter')
21 plt.show()
22

/anaconda3/lib/python3.6/site-packages/pandas/plotting/_core.py in __call__(self, x, y, kind, ax, subplots, sharex, sharey, layout, figsize, use_index, title, grid, legend, style, logx, logy, loglog, xticks, yticks, xlim, ylim, rot, fontsize, colormap, table, yerr, xerr, secondary_y, sort_columns, **kwds)
2940                           fontsize=fontsize, colormap=colormap, table=table,
2941                           yerr=yerr, xerr=xerr, secondary_y=secondary_y,
-> 2942                           sort_columns=sort_columns, **kwds)
2943     __call__.__doc__ = plot_frame.__doc__
2944

/anaconda3/lib/python3.6/site-packages/pandas/plotting/_core.py in plot_frame(data, x, y, kind, ax, subplots, sharex, sharey, layout, figsize, use_index, title, grid, legend, style, logx, logy, loglog, xticks, yticks, xlim, ylim, rot, fontsize, colormap, table, yerr, xerr, secondary_y, sort_columns, **kwds)
1971                  yerr=yerr, xerr=xerr,
1972                  secondary_y=secondary_y, sort_columns=sort_columns,
-> 1973                  **kwds)
1974
1975

/anaconda3/lib/python3.6/site-packages/pandas/plotting/_core.py in _plot(data, x, y, subplots, ax, kind, **kwds)
1738         if isinstance(data, ABCDataFrame):
1739             plot_obj = klass(data, x=x, y=y, subplots=subplots, ax=ax,
-> 1740                              kind=kind, **kwds)
1741         else:
1742             raise ValueError("plot kind %r can only be used for data frames"

/anaconda3/lib/python3.6/site-packages/pandas/plotting/_core.py in __init__(self, data, x, y, s, c, **kwargs)
858             # the handling of this argument later
859             s = 20
--> 860         super(ScatterPlot, self).__init__(data, x, y, s=s, **kwargs)
861         if is_integer(c) and not self.data.columns.holds_integer():
862             c = self.data.columns[c]

/anaconda3/lib/python3.6/site-packages/pandas/plotting/_core.py in __init__(self, data, x, y, **kwargs)
796         MPLPlot.__init__(self, data, **kwargs)
797         if x is None or y is None:
--> 798             raise ValueError(self._kind + ' requires an x and y column')
799         if is_integer(x) and not self.data.columns.holds_integer():
800             x = self.data.columns[x]

ValueError: scatter requires an x and y column