Malthus and capital

Why did agricultural civilization remain mired in the Malthusian trap for over 5,000 years? And how was it possible to eventually escape from it? Recall the Malthusian isoclines and how various kinds of societies can be situated along them (click to enlarge all graphs):



Plagues move the economy “northwest” along the isoclines, as more marginal lands are abandoned leaving the fewer people to work and share the more productive lands. Births beyond replacement by contrast move the economy “southeast” towards higher population, the use of more marginal lands, and thus a lower standard of living. Here, for example, is a graph using actual statistics for English real farm labor wage income from 1260 to 1849. Even though England during this period was slowly escaping from the Malthusian trap -- note that each 80 years has advanced farther "northeast" than the previous 80 -- it still followed the basic Malthusian pattern of births and deaths. Observe how the real wage greatly increased after the Black Plague in the mid-14th century, then slowly declines thereafter:



Much less well appreciated than the effects of births and plagues with respect to the Malthusian isocline are creation and destruction of productive capital. Every act of plowing, sowing, weeding, and so on was a seasonal capital investment, and the resulting harvest (and thus the short-term isocline) depended on the qualities and quantities of these short-term investments, as well as on vagaries of pests, weather, etc. Longer-term capital investment could include conditioning, fertilizing, and draining soil, buying livestock, breeding crops and livestock, watering meadows, and so on. Long term progress towards the "northeast" depended on long-term accumulation of capital. It was exceedingly rare to maintain such progress over long periods of time, and the British capital accumulation over such a long period, leading to the breakout from the Malthusian trap, was unprecedented.

Good harvests caused progress that was temporary unless the food was stored and long-term capital investment was substituted for investment in next year’s harvest as well as other pursuits such as luxury and military buildup. Productive innovation, whether institutional or technological, also led to moving the isoclines “northeast”, as they made capital more secure or productive.



Poor harvests (from pests, poor weather, etc.) caused a setback that was temporary as long as it didn’t lead to the destruction of capital. If it resulted in starvation, the deaths boosted the economy up the isocline, so that the standard of living of the remaining population in subsequent years of better harvests was higher than with prior better harvests at higher populations.

Destruction of productive capital was for most of agricultural history as common as creation of capital. Causes included high rents and taxes that forced a choice between going hungry and consuming capital. War (quartering and foraging of troops, destruction of enemy crops and livestock, etc.) was a frequent cause of capital destruction. Some kinds of capital, e.g. livestock and the fertility of the soil, could be destroyed simply by being neglected.

Mancur Olson distinguished between societies of “roving bandits”, where nomadic rulers stole the surpluses of foragers or farmers wherever they went, and “stationary bandits”, who controlled a specific area and simply taxed that area. Rational stationary bandits taxed only to the Laffer maximum, because any further taxation actually reduced their revenues. Indeed, because over-taxation resulted in the destruction of capital, a secure rational stationary bandit reduced taxes below the short-term Laffer maximum to prevent lower tax revenues in future years. Roving bandits, on the other hand, stole nearly all, resulting in destruction of nearly all capital, because anything insecure that one roving bandit didsn't steal was stolen by another.

Stationary bandits did not always confine themselves to taxation that resulted in no destruction of capital. Uncertainty over future power could cause a leader to get greedy and tax at capital-destroying levels while they were still in power. Threats of assasination, coup, or conquest could move stationary bandits closer to roving bandits, since the bandits lost their future revenues if they lost power or territory: in such cases they rationally taxed far higher than the Laffer maximum, usually destroying much capital in the process.



As a result, we can characterize societies and locate their isoclines based on their mode of banditry. This often gets confused with the mobility of production, and the two usually coincided, but they could and often were distinct. Thus most pastoral societies, based on moving livestock from pasture to pasture, also featured roving banditry. And societies based on fixed arable agriculture were generally controlled by stationary bandits. But early modern Britain was a semi-pastoral society but with stationary bandits. And Dark Ages Europe featured roving bandits from pastoral societies frequently conquering arable societies, and being conquered in turn, resulting in a move to a lower-capital society with a mix of roving and stationary banditry.

The Problem of Edible Capital

Of all the ways in which capital can be destroyed, the hardest to avoid, in a hard year, was eating it. Eating your milk cow or your draft animal was like eating your seed corn: very unwise but very likely if your alternative was imminent starvation.

The temptation to eat your capital created vicious cycles of capital destruction. Capital destruction lowered labor productivity, which meant that people produced less calories per calories consumed. This moved the Malthusian isoclines “southwest”, which meant even more people starved during the next equally bad year. War and excessive taxation could trigger or extend the vicious cycle by killing livestock, poisoning farmland, etc.– and rendering future returns insecure, rendering further destruction of capital more probable. The vicious cycle of capital consumption during times of famine may be the main factor that kept ancient agricultural civilizations mired in the Malthusian trap.

Who owned the capital mattered. Edible capital was much more likely to survive (and in the short term the starving people less likely to) if the capital was owned by people who were not themselves starving. Thus, societies living under the feudal hierarchy of long-term tenancy, where livestock was often owned by the local lord rather than a peasant, many have maintained themselves farther above subsistence levels than societies where peasants completely controlled their own livestock.

Culture was filled with warnings against “eating your seed corn.” Thus, as one example of many, Aesop’s stories of “The Goose That Laid the Golden Egg.” It was also filled with warnings about the importance of saving up for bad times, e.g. “The Ant and the Grasshopper.”

Conversely, capital creation that increased labor productivity increased the calories produced per calories consumed, moving the Malthusian isocline up and right. With storage of food it also freed labor for further capital creation, which in future equally good years in turn freed further labor for ancillary or non-agricultural capital investment (transportation, manufacturing, financial services, etc.). However, for nearly all of agricultural history the vast majority of this surplus went to population growth, military expenditure, and luxury display rather than capital investment.

Thus, until the British breakout, agricultural societies remained in the Malthusian trap. Prior agricultural socieities lacked an institutional ratchet that could incentivize capital creation in good harvests, but prevent too much capital destruction in bad harvests. And they generally lacked low-cost protection from foreign wars, so that stationary bandits often started to act more like roving bandits when faced with threats of conquest. To escape the trap, capital creation must exceed capital destruction to such an extent that farm labor productivity grows faster than population. How Britain did this I hope to explore in future posts.

Elements, evolution, and the nitrogen crisis

The oxygen crisis in the history of life is well known. When photosynthesis arose, cyanobacteria and later plants started dumping large amounts of oxygen into earth’s atmosphere. At first this oxygen, dissolved in the oceans, combined with metals in the oceans and “rusted out.” Eventually, however, the free metals in the oceans were largely depleted and oxygen levels increased in the atmosphere. At first this proved very poisonous, but eventually life not only adapted but took advantage of the oxygen, with some organisms evolving new high-energy respiration pathways that reacted oxygen with carbohydrates from eaten plants. Respiration fueled the Cambrian explosion of sophisticated lifeforms which in turn led to us.

Much less well known, but of similar importance, was the much earlier nitrogen crisis. This was not an overabundance of nitrogen, but the depletion of nitrogen in the readily usable forms that early life had evolved to consume. One might think that life would evolve to reflect at least roughly the same distribution of elements as are available in its environment. Let’s see if this true relative to abundance in our planet’s present oceans:

Elemental abundance in bacteria vs. in seawater (ref):

This is misleading for the metals before the oxygen crisis (i.e. for most of the history of life), when they were far more abundant in the oceans than the present levels shown. But for elements that did not “rust out” of oxygenated seawater, such as oxygen, hydrogen, carbon, nitrogen, phosphorous, and potassium, the above graph is illuminating.

There is a great deal of correlation here to be sure, but there are also outliers, elements that life must concentrate by several orders of magnitude: particularly carbon, nitrogen, and phosphorous, and to a lesser extent potassium. A reasonable guess is that this reflects contingency: life originated in a certain unusual environment, an environment disproportionately rich in certain chemicals, and its core functions cannot evolve to be based on any other molecules. Every known living thing requires, in its core functions, nucleic acids (which make up RNA and DNA), amino acids (which make up proteins, including the crucial proteins that catalyze chemical reactions called enzymes), and the “energy currency” though which all metabolisms consume and produce energy, the adenosine phosphates. Let’s briefly scan some core biological molecules to see how elements are distributed in them:

Adenosine phosphates:


Nucleic acid:



Amino acids:



Lots of hydrogen and oxygen in these molecules, to be sure, but those are the elements in water. So short of a drought or desert, organisms generally have plenty of readily accessible hydrogen and oxygen. Carbon, nitrogen, phosphorous – those are the elements most used by the core molecules of life out of proportion to their existence in the environment.

Carbon, as carbon dioxide, is abundant in the atmosphere (and earlier in earth’s history was far more abundant still). Through the process of photosynthesis, the two double bonds in carbon dioxide can be readily cleaved in order to form other bonds with the carbon in biological molecules. Indeed, instead of storing energy directly as ATP, life can and does take advantage of the relative accessibility of carbon, hydrogen, and oxygen to store energy as carbohydrates and fats, and then through respiration convert them to ATP only when needed.

Nitrogen is also abundant in earth’s atmosphere, but in the form of dinitrogen – two nitrogens superglued together with an ultra-strong triple bond. To form nucleic acids, amino acids, and ATP, something must crack apart the nitrogen. Phosphorous, to the extent it is available in the natural environment, comes in the readily incorporated form of phosphates. The trouble is, phosphorous in any form is just plain uncommon. Nevertheless, all life still relies on it at the center of the genetic code (DNA, RNA) and every metabolism (ATP).

Generally speaking, the result of the chemical contingencies of known life – which for its core functions uses molecules rich in hard-to-obtain nitrogen and phosphorous -- is that in known natural environments ecosystems are either nitrogen-limited or phosphorous-limited. In other worse, the biomass of the ecosystem is usually limited by the amount of nitrogen or phosphorous available. Liebig’s principle states that in any given environment, there is generally one nutrient that limits the growth of an organism or ecosystem. In earth environments that nutrient is usually nitrogen (as ammonia or nitrate) or phosphorous (as phosphate).

The eukaryotes (basically, complicated multi-celled life including all plants, animals and fungi) seem to lack the ability to evolve metabolisms that go beyond a certain point. Instead it’s the simpler prokaryotes -- archae and bacteria -- that have a far wider range of energy chemistry: a dizzying variety of chemosynthetic and photosynthetic metabolisms and ecosystems.

For certain crucial chemicals, the eukaryotes rely on archae and bacteria in their ecosystem. Exhibit A is nitrogen fixation. Life doubtless originated in an environment rich in ammonia and/or nitrates, molecules with only single nitrogens and thus no need to split the superglued dinitrogen bond. But these early organisms would have soon depleted the levels of nitrates and ammonia in the local environment to very low levels. Call it the nitrogen crisis.

Dinitrogen, N2, is the most abundant molecule in our atmosphere. But few things are powerful or precise enough to crack dinitrogen. Lightning can do it, converting dinitrogen and dioxygen in the earth’s atmosphere into nitrates. Lightning thus can, albeit very slowly, put usable nitrates back into sea and soil where they have been depleted by life. Trouble is (a) the resulting equilibrium level is far below the concentrations of nitrogen in organisms, and far below levels for optimum growth, and (b) the process requires an atmosphere rich in oxygen, which the earth until less than a billion years ago did not possess. (Alternatively, lightning might have made significant nitrates from reacting carbon dioxide with nitrogen, a possibility explored here. However, early life probably evolved in water so hot that it destroyed these nitrates).

Prokaryotes came to the rescue – probably very early in the history of life, when local nitrates and ammonia had been exhausted – by evolving perhaps the most important enzyme in biology, nitrogenase, “the nitrogen-splitting anvil.” Nitrogenase’s metal-sulfur core makes it precise enough a catalyst to crack the triple bond of dinitrogen.

Nitrogenase:
The general reaction fixing dinitrogen to ammonia, whether with nitrogenase or artificially, is as follows:

N2 + 6 H + energy → 2 NH3

The dinitrogen is split and combined with hydrogen to form ammonia. Ammonia can then be readily used as an ingredient that ends up, via the sophisticated metabolism that exists in all life, as amino acids, nucleic acids, and adenosine phosphates. When nitrogenase fixes nitrogen it consumes a prodigious amount of energy in the form of ATP. In particular for each atom of nitrogen it consumes the energy of 8 phosphate bonds:

N2 + 8 H+ + 8 e− + 16 ATP → 2 NH3 + H2 + 16 ADP + 16 P

Nitrogenase is extremely similar all organisms known to contain it. It thus probably only ever evolved once. Given its crucial function of supplying a limiting nutrient, despite its high energy cost it proved to be so useful that it spread to many phyla of archae and bacteria. Either it evolved very early in the history of life (before the “LCA”, the Last Common Ancestor of all known life) or it spread through horizontal gene transmission:

Alternative origins and evolution of nitrogenase (click to enlarge) ( ref):

The archae and bacteria that contain nitrogenase, and can thus fix nitrogen, are called diazotrophs. One of the earliest diazotrophs may have been a critter that, like this one, lived in high pressure hot water in an undersea vent. In today’s ocean, the most common diazotroph is the phytoplankton Trichodesmium.

Colonies of Trichodesmium:
The biomass earth's oceans is probably limited by the population of such diazotrophs. Supplying the iron they use to make nitrogenase would increase the amount of nitrogen fixation and thus the biomass in the oceans. A larger ocean ecosystem would draw out more carbon dioxide from the atmosphere, and so is of great interest. This process in the ocean seems to have its limits, however: too much ocean biomass in a particular area can, when it decomposes, deplete oxygen from the ocean, suffocating animals. Oxygen replacement from the atmosphere appears to be too slow to prevent this effect when nitrogen concentrations are high enough, but nitrogen concentrations in almost all ocean areas are far lower than this and would remain lower even while drawing out substantial amounts of carbon dioxide. (Here is a nice Flash animation of the nitrogen cycle in the oceans).

On land, certain plants, especially legumes, are symbiotic with certain diazotrophs. The bugs grow in root nodules in which the legume supplies them large amounts of sugar to power the energy-greedy nitrogenase. In turn, the diazotrophs supply their legume hosts with fixed nitrogen allowing the legumes to generate more protein more quickly than other plants: but at the expense of more photosynthesis needed to feed the energy-hungry bugs.

Petrus Sabbatius comes to power

The Roman Empire was a military dictatorship. Its emperors came and went in a relentless spree of assassinations and civil wars (example) that lasted for nearly 1500 years. One and one-half millennia of violent government extended across history from the victories of Octavian (a.k.a. Caesar Augustus) over his rivals in decades before Christ to the fall of Constantinople to the Turks in 1453. Despite the violence, or perhaps because of it, Roman elites accumulated vast surpluses and left spectacular monuments unmatched until much later in European history.

By the opening of the 6th century the city of Rome itself was no longer a part of the Empire. Instead Italy was ruled by the Goths and the capital city of the remaining empire, “Romania”, was Constantinople. This city (in modern times called Istanbul) controlled the strategic straights linking the Black Sea and the Mediterranean.

No topics dominated the culture of Constantinople so much as (1) the horse races, and (2) the debate over the relative contributions of the divine and the human to the nature of Christ.

The debate over the nature of Christ divided Christians into numerous sects: Orthodox Catholics, Monophysites, Arians, Manicheans, Nestorians, and many others. The Orthodox Catholics believed that Christ was both God and man, Monophysites divine only, Arians human only, and there were a dizzying number of variations on and nuances to these dogmas. Theology was the hottest topic of debate and biggest motivation for political division and persecution in Constantinople. Constantinople was dominated by Orthodox Catholics and Monophysites, while the Arian heresy held by the Goths and Vandals that had taken over the Western part of the Empire was considered a heresy beyond the pale. Other positions, such as Manicheaism, were sometimes tolerated and sometimes not.

With the coming to power of Christianity the brutal gladiatorial fights had been suppressed and horse racing was now the dominant spectator sport. The Hippodrome in Constantinople was the main place of public gathering. Spectators shouted political opinions at the emperor, who in turn used the crowd to gauge public opinion. Indeed, for the normal citizen, this was the only form of political participation.

The racing teams and their colors – Red, White, Blue, Green – dated far back to the early Empire. By the 6th century, the two dominant teams were the Blues and the Greens. The political nature of the Hippodrome had converted their fans into political factions. The Blues tended to be government types, land owners, and Orthodox Catholics (or, during the frequent schisms with Rome, Chalcedonians). Greens tended to be merchants and Monophysites.

During the reign of Anastasius, in a village in Illyria (probably in modern Macedonia just north of modern Greece), where the natives still spoke a passable Latin, lived a young peasant bachelor. Instead of taking up farming he left the village and came to Constantinople to join the army. Dropping his humble family name and styling himself “Justin” – “just man” -- he fought in several wars and was promoted through the ranks of the palace guards. Eventually he was promoted to Count (head) of the Excubitors, one of the two palace guard groups.

Justin then adopted his nephew, one Petrus Sabbatius, and brought him to Constantinople. Sabbatius too dropped his humble name and, aspiring to the achievements of his uncle and benefactor, restyled himself “Justinian”.

Justin’s master, the emperor Anastatius, was a Green and Monophysite. Justin, and to an even greater degree his nephew, were Orthodox Catholics (or during the schism of the time Chalcedonians) who supported the Blue faction.

Anastasius failed to make formal provisions for the succession. His death in 518 threw Constantiople into confusion, as none his three nephews had strong support. The Manichean eunuch Amantius, Chamberlain to Anastasius, hoped to be a power behind the throne of his chosen puppet, an obscure character named Theocritus. The palace guards had traditionally dominated the succession in Rome, so Amantius needed the support of at least one of the two palace guard groups, the Excubitors and the Scholarians.

Justin, head of the Excubitors, secretly promised to support Theocritus and took money from Amantius to bribe the support of influential fence-sitters. But instead of carrying out this secret plot, Justin lobbied and bullied the Blues, their Senate allies (most Senators were Blue), and his own soldiers. Finally winning acclamation of most of the Blues in the Hippodrome, and fearful acquiescence of the Greens, Justin assumed the purple robes of emperor.

Roman imperial successions had always been highly irregular, but the ideal of authority that other political players would most accept is suggested by Justin’s letter, upon assuming power, to the Pope in Rome: “We have been elected to the Empire by the favor of the indivisible Trinity, by the choice of the highest ministers of the sacred Palace, and of the Senate, and finally by the election of the army.”

To cover his tracks, Justin had Amantius and Theocritus executed, under the pretext that Amantius (a heretic Manichean, but tolerated under Anastatius) had insulted the Orthodox Patriarch of Constantinople. He named his nephew Count of the Domestics. Justinian was a, or perhaps the, power behind the throne. Falling in love with a repentant prostitute, Theodora, he had Justin’s quaestor, Proclus, cleverly draft a law that allowed him to marry a former prostitute while still forbidding such a degrading marriage to other Senators.

Early in 527 AD, Justin fell sick and named Justinian Augustus (co-ruler) and successor. A few months later, Justin died and Justinian at age 45 became emperor.

The former Petrus Sabbatius was to lavish his adoptive name and the empire's treasure on cities new and old, grand buildings, and wars of reconquest. Most importantly for our purposes, Justinian would plaster his just-sounding name on a recompilation of Roman law that has profoundly shaped the West down to our own time.

Coming: Tribonian, John of Cappadocia, revolt, massacre, prostration, and the the birth of a bloody code.

References
Procopius, Anecdota (Secret History)
Procopius, History of the Wars
J.B. Bury, History of the Later Roman Empire
Gibbon, The Decline and Fall of the Roman Empire

Signals, gifts, and politics

(I recently rediscovered this old post of mine and thought it deserved re-posting).

Paraphrasing Robin Hanson from a recent podcast: "In gifts, it's common signals of quality that matter, not private signals of quality."

Robin Hanson has a great theory for why neoclassical economics so often fails to explain human relationships and institutions, especially personal relationships. Why, he asks for example, do guests bring wine to dinner at an acquaintance's home instead of paying cash, like they would at a restaurant? Traditional economics cannot explain such basic things.

Instead Robin posits, building on the work of previous economists and evolutionary psychologists, that signaling dominates most of our relationships and many of our institutions. In other words, much of our behavior is used to signal, or prove by our behavior, to our fellows our intelligence, empathy, status, and so on. In the hunter-gatherer environments in which our genes evolved, such relationships were far more impportant to our genetic success than any other aspects of our environment. Thus our behaviors are dominated by the signals that would have most advantageously (for our genes) developed our relationships in that environment.

The general theory is sound -- I've held a version of it for quite a long time -- but many of the conclusions he draws from this theory, such as the above quote about gifts, are quite questionable. The thoughtful gift, namely the gift that is targeted towards the recipient's unique preferences, is widely welcomed as the best kind of gift. "It's the thought that counts" may be a cliche and an exaggeration, but it nevertheless carries substantial truth. The thoughtful gift signals our intelligence, our empathy, and the fact that those skills are being used in favor of the gift recipient.

This (and a second theory described below) explains far better than Robin does why cash makes such a bad gift. A gift or exchange like bringing wine to dinner provides the opportunity to signal that one has remembered the dinner menu, and often also signals that one knows the hosts' wine preferences. Cash by sharp contrast is the most thoughtless gift. Cash is suitable only for contractual dealings with strangers; it is worse than useless for developing relationships.

Gift cards exhibit a modicum more empathy than cash (you have to know your pal likes Starbucks), but prior generations who put more effort into relationships considered gift certificates to be rather rude as a personal gift: they were only considered suitable as, for example, a substitute for a cash wage bonus. Today, like "friends" links on Facebook, gift cards signal a modicum of passing fancy which substitutes for the many closer relationships and more thoughtful gifts that most of our forebears enjoyed.

A second reason that cash makes such a poor gift is that it provides a very poor emotional and sensory experience. Most signals, as at least indirect products of evolution, are targeted at our emotions far more than they are targeted at the intellect. A good wine, for example, will be experienced far more fondly and thus remembered far longer than a dirty dollar bill. The most common signals also tend to signal emotional states or skills (e.g. empathy) far more than intellectual ones.

Per Friedrich Hayek, this emotional infrastructure breaks down when we are dealing with strangers -- in those cases contractual relationships and "filthy lucre" are far more efficient and effective ways of relating. But the cold natures of these transactions, i.e. the fact that these relationships are divorced from the emotional signals evolution has wired us to expect, explains much of the political resistance to markets with their "filthy lucre", "greed", etc. Merchants, property, contracts, and so on are crucial to our modern economy, but they send the wrong emotional signals to our hunter-gatherer brains.

Most politics, and in particular the pathologies of politics, are themselves about instinctive signaling -- for example signaling tribal loyalty on the right, or signaling altruistic natures on the left. Most political ideologies freely and fraudulently ignore the crucial distinction between friend and stranger: in the world of political signaling we are supposed to care as much about the vast anonymous "poor" as we do about our own children who we well know to be helpless, and we are supposed to be loyal to a vast country of hundreds of millions of strangers (including more than a few very strange strangers) as if they were all familiar kin. In both cases, these are largely fake signals that don't cost the fraudulent signaler very much: the right-winger does not actually have to be patriotic, and the left-winger does not actually have to be altruistic, and in both cases they usually are not. Few of the children of hawk Congressmen served in the Iraq War, and Barack Obama has given only a miniscule portion of his income to charity. But they are very good at making the politically correct noises that most humans emotionally expect to hear. Thus left-wingers can get great social mileage from calling right-wingers "greedy", meaning that right-wingers are failing to send enough altruistic signals, and right-wingers can get great social mileage from calling left-wingers "unpatriotic." People who, due to real altruism, care more about the actual consequences of political policies than about sending the proper social signals to their peers, usually end up being called both "greedy" and "unpatriotic" in the bargain.