Notes on Mark Koyama on Rome on Medium...

Hadrian s Tomb

Mark Koyama: Could Rome Have Had an Industrial Revolution?/span>

The Malthusian Epoch and Its End

The agrarian age Malthusian epoch in human economic-demographic history had three principal driving characteristics:

  1. Technological and organizational advance was slow and stable relative to movements in population.

  2. Standards of living wer near "subsistence", in that increases in living standards produced increases in population growth, and decreases in living standards declines.

  3. Resources were important, inasmuch as average productivity declined with increasing population, adjusting for the state of technology and organization.

In the Malthusian epoch living standards were near "subsistence": just enough above the level the would have produced zero population growth to generate slow population growth at the rate warranted by the slow advance of technology and organization. When population growth was faster than that warranted rate, living standards tended to decline and population growth thus to slow. When population growth was faster than that warranted rate, living standards would then rise and population growth would then accelerate.

In history, humanity broke out of the Malthusian epoch. The pace of technological and organizational advance became rapid enough that sustaining the then-warranted rate of population growth required living standards that were high enough above "subsistence" that other factors became dominant. People became rich enough and literate enough to take an extra degree of control of their own fertility. Malthus’s preventative and positive checks ceased to rule. Population growth fell below the rate that would have kept the world poor in barefoot. And modern economic growth began.

In history, we speak of the commercial, industrial, and second industrial revolutions over 1500-1930 that carried first northwest Europe and now the rest of the world from Malthusian poverty to today’s epoch of modern economic growth. But was the door through which we exited agrarian age Malthusian poverty the only possible door? Was the economic-demographic-political-cultural history as it really happened in northwest Europe the only key?

The most obvious way, to me at least, to start thinking about this question is the Diamond-Kremer-Romer assertion: Two heads are better than one. It is not just in software that “with enough eyes, all bugs are shallow“. Thanks to language, humans are an anthology intelligence: what useful thoughts one of us has, all can quickly copy and learn. Thanks to writing, the human anthology intelligence binds time: our shared collective brain is composed not just of the living but of many of the the dead as well; in large part what they knew we know too; and so we do not have to painfully relearn it via our own experience.

More brains: faster technological and organizational progress. How much faster? There are a great number of possibilities.

Quantifying "Two Heads Are Better than One"

Let us take four cases as possible rough descriptions of the agrarian age from 5000 BCE to 1500 CE. Note that all of these apply only during the agrarian age Malthusian epoch. They are irrelevant and do not apply during the previous pre-agriculture, pre-herding, pre-writing gatherer-hunter age. They are irrelevant and do not apply during the subsequent commercial age, when it did or whenever it would have started. They are:

  1. Two heads are better than one, and twice as good as one: the rate of technological and organizational progress might be proportional to the global population.

  2. While two heads are better than one, each of us has only a limited amount of time to listen; The rate of technological and organizational progress might be proportional to the square root of the global population.

  3. While two heads are better than one, we really are far from being a true anthology intelligence: each doubling of the population only does as much to advance inmeaning that the rate of technological and organizational progress might be proportional to the logarithm of the global population.

  4. Two heads are not better than one after all: technological and organizational progress does not fall from the air, but rather drops from the air at a near-constant rate.

We know that there were about 5 million people on the earth in 5000 BCE, when the agrarian age more or less began. We know that there were about 50 million people on earth in 1000 BCE. What do those two benchmarks imply about when there would be enough people on the earth thinking and communicating enough about better ways to perform tasks and organize societies to break us out of Malthusian poverty?

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:


And then use to get us analytic solutions:


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

But unless you know or remember and have much more intuition than I do for this math, it is simpler to BF&MI—Brute Force & Massive Ignorance—It:

# take a century to be our time period
# take our starting point to be 5000 BCE :

year = range(-5000, 2000, 100)

# initialize our four cases with an initial global 
# population in 5000 BCE of 5 million:

pop_con = [5]
pop_log = [5]
pop_sqr = [5]
pop_lin = [5]

# by trial-and-error determine the γ values that 
# get us to 50 million population by 1000 BCE:

gamma_con = 0.0593
gamma_log = 0.0231
gamma_sqr = 0.0159
gamma_lin = 0.00475

# calculate human populations up through 2000 
# assuming a "Malthusian" regime

for i in range(0,70):
    pop_con = pop_con + [pop_con[i] * (1 + gamma_con)]
    pop_log = pop_log + [pop_log[i] * (1 + gamma_log * np.log(pop_log[i]))]
    pop_sqr = pop_sqr + [pop_sqr[i] * (1 + gamma_sqr * (pop_sqr[i]**(0.5)))]
    pop_lin = pop_lin + [pop_lin[i] * (1 + gamma_lin * pop_lin[i])]

# shove the results into a pandas dataframe:

pop_df = pd.concat([pd.Series(dict(zip(year, pop_con)), index = year),
                    pd.Series(dict(zip(year, pop_log)), index = year),
                    pd.Series(dict(zip(year, pop_sqr)), index = year),
                    pd.Series(dict(zip(year, pop_lin)), index = year)], 
pop_df.columns = ['pop_con', 'pop_log', 'pop_sqr', 'pop_lin']

# and plot:


Out 298

The "two heads are twice as good as one" case clearly exits the Malthusian regime before the year 1. Let's take a look at what happens:


Out 287

By 700 BCE the "two heads are better than one" case is already seeing global human population growing at more than 50 percent per century. By 300 BCE the population of the globe is 3 billion. The economy is clearly no longer well-described by the Malthusian framework, and so that model equation blows up. The conclusion is that if two heads really were twice as good as one as far as technological and organizational progress are concerned, then a world with 5 million people in 5000 BCE and 50 million in 1000 BCE would have escaped from agrarian age Malthusian poverty into something else technologically and organizationally advanced well before the year one.

So let's drop that case and look at the other 3:

pop_df = pop_df.drop(['pop_lin'], axis=1)

# and plot:


Out 295

The "Two Heads Are Root-2 Better than One" case tuned to hit 5 million population in 5000 BCE and 50 million in 1000 BCE overshot actual global population in the year 1. (There is, remember, no year zero, no matter what the graph and arithmetic may say.) We think there were 170 million people then. The Root-2 case had 198. The "Two Heads Are Log-2 Better than One" case similarly tuned undershot global population in the year 1: it had only 129 million people. And the constant growth case way undershot—90 million people, only half of the actual population then. The first millennium BCE was a good thousand years for humanity: it really does look like there was then something to "Two Heads Are Better than One".

Take a look at the numbers:


Out 297

Both the "Root-2" and the "Log" cases would have predicted a further growth acceleration in the first millennium CE. By 600 CE the actual human population was, we think, some 200 billion. The "Root-2" case expected nearly a billion, the commercial revolution well-launched, and the Malthusian population equation ceasing to be adequate. The "Log" case, having undershot in the year 1, overshot by year 600. It expected a doubling of human population in the 600 years between Jesus and Muhammed, rather than the much smaller increase from about 170 to 200 million that we actually saw.

The "Two Heads Are Better than One" approach thus focuses our attention on what was, for it, a profound anomaly. The world in 600 CE—whether in China, the Roman Empire or ex-Empire, or in between—fell far short of what its Whig progressive narrative would have expected to have been created by then.

Decline and Fall

There was indeed a great anomaly here. We find, in Mark Koyama's excellent medium post: Drawing on Kyle Harper and William Jongman, he quotes first Kyle on Rome in the second century CE, the age of the Antonine dynasty:

Peace, law, and transportation infrastructure fostered the capillary penetration of markets everywhere. The clearing of piracy from the Mediterranean in the late Republic may have been the single most critical precondition for the burst of commercial expansion that the Romans witnessed; risk of harm has often been the costliest impediment to seaborne exchange. The umbrella of Roman law further reduced transaction costs. The dependable enforcement of property rights and a shared currency regime encouraged entrepreneurs and merchants.... Roman banks and networks of commercial credit offered levels of financial intermediation not attained again until the most progressive corners of the seventeenth-eighteenth century global economy. Credit is the lubricant of commerce, and in the Roman empire the gears of trade whirred... (Harper, 2017, p 37)

And then William:

Crucial performance indicators show dramatic aggregate and per capita increases in production and consumption from the 3rd century BCE, or sometimes a bit later, until the Roman economy reached a spectacular peak during the 1st century BCE and the 1st century CE, lasting until perhaps the middle of the 2nd century CE... (Jongman, 2015, 81)

But this was something that we knew, and that the Renaissance and post-Renaissance saw clearly. We have all read our Gibbon, have we not?:

If a man were called to fix the period in the history of the world, during which the condition of the human race was most happy and prosperous, he would, without hesitation, name that which elapsed from the death of Domitian to the accession of Commodus. The vast extent of the Roman empire was governed by absolute power, under the guidance of virtue and wisdom. The armies were restrained by the firm but gentle hand of four successive emperors, whose characters and authority commanded involuntary respect. The forms of the civil administration were carefully preserved by Nerva, Trajan, Hadrian, and the Antonines, who delighted in the image of liberty, and were pleased with considering themselves as the accountable ministers of the laws. Such princes deserved the honor of restoring the republic, had the Romans of their days been capable of enjoying a rational freedom. The labors of these monarchs were overpaid by the immense reward that inseparably waited on their success; by the honest pride of virtue, and by the exquisite delight of beholding the general happiness of which they were the authors...

And Aldo Schiavone's The End of the Past makes great use of the Roman Oration of Publius Aelius Aristides Theodorus in 155 CE

Whatever the seasons make grow and whatever countries and rivers and lakes and arts of Hellenes and non-Hellenes produce are brought from every land and sea, so that if one would look at all these things, he must needs behold them either by visiting the entire civilized world or by coming to this city. For whatever is grown and made among each people cannot fail to be here at all times and in abundance. And here the merchant vessels come carrying these many products from all region in every season and even at every equinox, so that the city appears a kind of common emporium of the world. Cargoes from India and, if you will, even from Arabia the Blest one can see in such numbers as to surmise that in those lands the trees will have been stripped bare and that the inhabitants of these lands, if they need anything, must come here and beg for a share of their own. Again one can see Babylonian garments and ornaments from the barbarian country beyond arriving in greater quantity and with more ease than if shippers from Naxos or from Cythnos, bearing something from those islands, had but to enter the port of Athens. Your farms are Egypt, Sicily and the civilized part of Africa.... And whatever one does not see here neither did nor does exist....

When were there so many cities both inland and on the coast, or when have they been so beautifully equipped with everything? Did ever a man of those who lived then travel across country as we do, counting the cities by days and by days on the same day through two or three cities as if passing through sections of merely one?... It might very well be said that while the others have been kings, as it were, of open country and strongholds. you alone are rulers of civilized communities.... As on holiday the whole civilized world lays down the arms which were its ancient burden and has turned to adornment and all glad thoughts with power to realize them.... All localities are full of gymnasia, fountains, monumental approaches, temples, workshops, schools, and one can say that the civilized world, which had been sick from the beginning, as it were, has been brought by the right knowledge to a state of health. Gifts never cease from you to the cities, and it is not possible to determine who the major beneficiaries have been, because kindness is the same to all.... You have measured and recorded the land of the entire civilized world; you have spanned the rivers with all kinds of bridges and hewn highways through the mountains and filled the barren stretches with posting stations; you have accustomed all areas to a settled and orderly way of life.... Though the citizens of Athens began the civilized life of today, this life in its turn has been firmly established by you, who came later but who, men say, are better....

The gods, beholding, seem to lend a friendly hand to your empire in its achievement and to confirm to you its possession—Zeus, because you tend for him nobly his noble creation, the civilized world; Hera, who is honored because of marriage rites properly performed; Athena and Hephaestus because of the esteem in which the crafts are held; Dionysius and Demeter, because their crops are not outraged; Poseidon because the sea has been cleansed for him of naval battles and has received merchant vessels instead of triremes. The chorus of Apollo, Artemis and the Muses never ceases to behold its servants in the theaters; for Hermes there are both international games and embassies. And when did Aphrodite ever have a better chance to plant the seed and enhance the beauty of the offspring, or when did the cities ever have a greater share in her blessings? It is now that the gracious favors of Asclepius and the Egyptian gods have been most generously bestowed upon mankind...

Schiavone further quotes from F.W. Walbank in 1946:

What we must ask is: Why within a hundred years did this vigorous and complicated structure [the principate of the Antoninesl cease to operate as a going concern? Why has there been not a straight upward line from the time of Hadrian to the twentieth century, but instead the familiar sequence of decay, middle ages, renaissance, and modern world?...

and seeks:

an important priority. An explanation for why Roman society failed to rise any further once it had reached the peak of its development, why there was no transformative impulse of the kind that Pirenne identified in Europe after the year 1000," must be a prerequisite for ensuing collapse of Rome and its particular characteristics.... [What were] the structures and events that prevented the formation of stronger evolutionary ties and rendered the end of the ancient world an epochal period in... history?... It would be superficial and simplistic to interpret the entire history of Byzantium in the sixth to fifteenth centuries as simply the extreme protraction of a long period of stagnation, but it is undeniable that the continuity East brought stability to features and characteristics that were entirely different from those that the crisis imposed on the west. Thus, when Rostovtzeff and Walbank raised their question ("Why has there been not a straight upward line of progress from the time o fHadrian to the twentieth century?" in Walbank's words; and "Why had modern civilization to be built up laboriously as something new... instead of being a direct continuation of it?" as Rostovtzeff put it), neither was inventing an improbable historical situation.... They were performing a kind of conceptual experiment that brought them right to the heart of the history of Rome and the history of Europe.... The emphasis is on something that can be present only in modern consciousness: its failure to develop, the potential transformations that went unrealized, just when the first signs of this evolution appeared most clear...

And So We Finally Get to Mark Koyama...


First, there those who tend to think that market expansion is sufficient for sustained economic growth.... Second, there are those who argue that colonial empires or natural resources like coal were crucial for modern economic growth.... Third, there are those who argue that ultimately only innovation can explain the transition to modern economic growth... divided between those who seek to explain the increase in innovation in purely economic terms... and those who... that the answer has to be sought... in something... broadly defined as culture....

Adherents of... the view that trade, commerce, and market development were a sufficient condition for modern economic growth should find the Roman Industrial Revolution counterfactual highly appealing.... Similarly... the Roman empire was a coherent, capitalist, “world system”... colonies... periphery... based around the Mediterranean economy rather than the Atlantic world, but there seems little intrinsic reason why it should have been less successful than the early modern world system in generating economic growth....

The demand for slaves soared after 200 BCE, and... their ready supply encouraged landlords to practice commercial agriculture on a vast scale. Such an economy was ill-suited for modern economic growth....

The arguments of McCloskey and Mokyr suggest greater skepticism towards the counterfactual we have outlined. Mokyr argues that made 18th century Britain distinctive was a “culture of growth”... the importance of a competitive Republic of Science.... Similarly, I am not aware of evidence of the kind of rhetorical change in attitudes towards commerce in the Rome world that McCloskey documents in the 17th century Dutch Republic or 18th century England—no new-found respect for traders and merchants, over and above soldiers and adventurers, and no evidence of lessening distain for commerce or business. If these cultural attitudes were the binding constraint in late medieval and early modern Europe, then they were equally binding in antiquity. I’ve speculated... on the ways in which slavery and other Roman institutions reinforced a cultural ethos that was hostile to trade-based economic betterment.... But I would be eager to read counter evidence....

All of this suggests that a better understanding of why sustained or modern economic growth did not occur during earlier “efflorescences” can help us better understand which factors were important in the explaining the transition that did take place after 1800.



MOAR Housekeeping


IPython.OutputArea.prototype._should_scroll = function(lines) {
return false;}

# keep output cells from shifting to autoscroll...

# set up the environment by reading in libraries: 
# os... graphics... data manipulation... time... math...
# statistics...

import sys
import os
from urllib.request import urlretrieve

import matplotlib as mpl
import matplotlib.pyplot as plt
%matplotlib inline
import PIL as pil
import plotly'delong',
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.graph_objs import Scatter
from IPython.display import Image

import pandas as pd
from pandas import DataFrame, Series
import pandas_datareader
from datetime import datetime

import scipy as sp
import numpy as np
import math
import random

import statsmodels
import statsmodels.api as sm
import statsmodels.formula.api as smf

# graphics setup: seaborn-whitegrid and figure size...'seaborn-whitegrid')

figure_size = plt.rcParams["figure.figsize"]
figure_size[0] = 10
figure_size[1] = 7
plt.rcParams["figure.figsize"] = figure_size

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