|Dolia, an example of one type of pottery common in Roman times that |
completely disappeared from Western Europe after the fall of the empire.
"Ostia Antica Dolia" by AlMare - Own work. Licensed under CC BY-SA 3.0 via Wikimedia Commons.
Economic history blogger Pseudoerasmus published an interesting pair of posts earlier this month titled "Economic Growth in the Ancient Greece" and "Ian Morris' Calculations About the Ancient Greece Economy" in which he takes issue with the estimations historians Josiah Ober and Mogens Herman Hansen and archaeologist Ian Morris have developed to measure economic growth in classical Greece. I recommend reading the two post in their entirety. They are an interesting case study in the difficulty facing anyone who tries to apply economic theory to or gain cliometric insights from the ancient past.
The problem is one of data. We simply don't have it. There was no National Bureau of Economic Research, Economic and Statistics Administration, or Bureau of Labor Statistics, or Federal Reserve Division of Research and Statistics in the world of ancient Greece or Rome. While folks like Angus Maddison, Walter Scheidal, Dominic Ratheborne, Chris Wickham and a few others have tried to estimate or model the real wages, labor supply, and GDP per capita of the ancients, ancient economics remains an imperfect art. Wage data is particularly tricky--while useful for understanding economic change within specific classical societies, I cannot think of a wage estimate built on ancient data I would trust in a comparative study.
To try and get around this archaeologists, historians, and the occasional eccentric economist who turns his gaze to the far past will use proxies to gauge the extent of economic growth. Scholars will get quite creative with these proxies; they range from measuring the size of homes to the number and type of animal bones found in trash heaps. One of the most popular proxies are measures of health: things like disease incidence, average age of mortality, and height. There are good reasons for their popularity: they do not need to be fed into complex mathematical models to be used, the source of their data (skeletons) are relatively plentiful, they record the well being of average farmers as well as elites, and can easily be used to measure one society or time against another without the usual challenges that come with comparing quantitative data drawn from radically different social contexts.
I urge caution in using these 'biological standard of living' data points as a proxy for wealth. As I pointed out in a recent post on this question, it is not very difficult to find examples from both the modern and the ancient world where historical measurements of health and of wealth diverge from each other. The examples I discussed included data from the African American "great migration," China and England at the turn of the industrial revolution, the collapse of the Roman empire, and the Neolithic transition to agriculture. In all of these cases wealth did not move into tandem with health--in my mind compelling evidence that what we usually refer to as "'living standards" and wealth are not the same thing." 
I received some push back in the comments section of that post. The afore-mentioned Pseudoerasmus wrote:
The term "wealth" is used very loosely in this blogpost.
You need to keep in mind the difference between a society's production per capita and the incomes received by the median person. The former says nothing about how the incomes in the society are distributed, so there may be a lot of income per capita but the median person may be benefiting very little from it. Stature is a very good proxy for incomes received by ordinary people, especially before the 20th century.
There is a big debate on whether wages for the working classes rose during the first phase of the Industrial Revolution or no. Robert Allen for example is a very prominent "wage pessimist". If real wages fell in the period 1800-50 then there is no height paradox.
But this loose use of the word "wealth" most afflicts your statement about the Roman empire. It's plausible that the median Roman was better off in the 1st century than in the 6th, but who says the median inhabitant of the Roman empire was NOT better off in the 6th century than in the 5th?
Who says neolithic farmers were wealthier ? 
I will concede that in that earlier post I used the phrase "wealth" in a rather loose way. In less than 1,300 words I moved from industrial America to premodern agrarian empires to hunter gatherer bands. It is difficult to talk about any one variable that might describe all three economic systems without stretching its meaning a bit. What is really necessary in order to make useful comparisons between such different eras is a discussion of fundamentals: is there a meaningful conception of wealth that applies equally well to the paleolithic hunter gatherer and the information age office worker? What exactly is this thing we call "wealth"?
I cannot promise answers to these questions--I imagine it would take an entire book to answer them, and there are other topics much higher up on my priority list of things I plan to write books about. However, I do not think it is wasted effort to explore these questions a bit and see if we cannot approach proper answers to them. I must reserve a full exploration of that topic for a later post. Before I delve into it I would like to clarify why I think biometric data--especially average height--is often a poor proxy for wealth and why measurements of a population's biological standard of living should not be confused with a population's wealth. A good place to begin is with the Roman case study mentioned above. I was surprised to find it faulted as my weakest point, for I consider it the strongest and least controversial of the examples given.
Roman cliometrics are only slightly more solid than the uncertain attempts to piece together the size of the Greek economy discussed in Pseudoeramsus's posts. The most interesting data used in these studies involves wage estimates constructed from payrolls recorded on Egyptian papyri.  Unfortunately, there are no comparable records for the Western Empire and we must study the economics of that empire's fall by using what material proxies for wealth that might survive until some archaeologist digs it out of the earth or sea floor.
The most accessible introduction to this topic is Bryan Ward-Perkin's classic The Fall of Rome and the End of Civilization. As Ward-Perkin's title might suggest, the archaeological record shows that the collapse of the Western Empire can be seen in the collapse of an entire material culture--a "civilization." For awhile it was fashionable for historians to downplay this event, speaking not in terms of the empire's fall and Europe's descent into a "dark age" but of a "transition" or "evolution" of Europe into "late antiquity." Ward-Perkins will have none of this. He fights sophistry with data, providing one example after another of catastrophic collapse.
One of his first examples is pottery. Here is how the good professor describes the pottery found in archaeological sites from before the fall:
"In all but the remotest regions of the empire, Roman pottery of a high standard is common on the sites of humble villages and isolated farmsteads. For example, even on of a tiny farm stead in the hills behind the Roman city of Luna in Italy, which was occupied between the second century BC and the first century AD, produced the following range of pottery vessels: the huge storage jars (dolia) characteristic of the ancient world; coarse kitchenwares that were probably locally made (for the most part fast wheel turned, but including some vessels that were hand shaped), other kitchenwares imported from potteries along the West coast of Italy; amphorae from this same coastal area (with a few shards also from southern Italy and Africa) and finally, the fine glossy tablewares of Campania near Naples and of Arezzo in the Arno valley.... The list is not unimpressive for a peasant household." This contrasts with the pottery found in post-Roman sites:
"In the post-Roman West, almost all of the material sophistication disappeared. Specialized production and all but the most local distribution became rare, unless for luxury goods; and the impressive range and qualities of high quality functional goods, which had characterized the Roman period, vanished, or at the very least, were drastically reduced. The middle and lower markets, which under the Romans had absorbed huge quantities of basic, but good quality items, seem to have almost entirely disappeared.
Pottery again provides us with the fullest picture. In some regions like the whole of Britain and parts of coastal Span, all sophistication in the production and trading of pottery seems to have disappeared altogether: only vessels shaped without the use of the wheel were available, without any functional or aesthetic refinement.... In other areas, such as Northern Italy, some solid wheeled turned pots continued to be made and some soapstone vessels imported, but decorated tablewares entirely, or almost entirely disappeared and even among kitchenwares, and the range of vessels being manufactured was gradually reduced to only a few basic shapes. By the seventh century the standard vessel for Northern Italy was the olla (a simple bulbous cooking pot) whereas in Roman times this was only one vessel type in an impressive batterie de cuisine (jugs, plates, bowls, serving dishes, mixing and grinding bowls, casseroles, lids, amphorae, and others).
....It was not only the quality and diversity that declined; the overall quantities of pottery in circulation also fell dramatically. This fact is very difficult to demonstrate conclusively; but it will be familiar to anyone who has worked on a post-Roman site--mountains of Roman pottery are reduced to a few interesting but unassuming boxes of post Roman sherds. In both excavation and field survey while Roman pottery is so abundant that it can be a positive nuisance, post-Roman wares of any kind are almost invariably very scarce. " The same thing can be said for building materials and techniques:
In the Mediterranean region the decline in building techniques and quality was not quite so drastic [as in England]--what we witness here, as with the history of pottery production, is a drastic shrinkage rather than a complete disappearance. Domestic housing in post Roman Italy, whether in town or countryside, seems to have been almost exclusively of perishable materials. Houses, which in the Roman period had been primarily of stone and brick, disappeared, to be replaced by settlements constructed almost entirely of wood. Even the dwellings of the landed aristocracy became much more ephemeral, and far less comfortable: archaeologists, despite considerable effort, have so far failed to find any continuity into the late sixth century of the impressive rural and urban houses that had been a ubiquitous feature of the Roman period....
As with pottery, the change was most complete, and significant in the lower and middle markets. In the fifth and six centuries tiles, which as we have seen had been very widely available in Roman Italy, disappear from all but a few elite buildings. It may have been as much as a thousand years later, perhaps in the fourteenth or fifteenth centuries that roof tiles again became as readily available and as widely diffused in Italy as they had been in Roman times. In the meantime, the vast majority of the population made do with roofing material that were impermanent, inflammable, and insect infested. This change in roofing was not an isolated phenomenon, but symptomatic of a much wider decline in domestic building standards--early medieval flooring, for instance, in all but palaces and churches, seems to have been generally of simple beaten earth" And household goods:
"An object from the Sutton Hoo ship burial that attracts very little attention in its British Museum showcase speaks volumes; the pottery bottle. In the context of seventh century East Anglia, it was almost certainly a high status item, imported from abroad (since it was shaped on a wheel, at a time when all pottery in Britain was hand formed). But in any context of the Roman period, even a rural peasant context, it would be entirely unremarkable, or notable only for its porous fabric and course finish. The economy that sustained and supplied a massive middle and lower market for low-value functional goods had disappeared, leaving sophisticated production and exchange only for a tiny number of high-status objects." 
Ward-Perkins provides more examples, but this is sufficient for our purposes. The trend is clear: the quality and quantity of every-day material goods fell as the empire went into decline. Importantly, this was not just an elite affair. The decline was most dramatic in the households of the West European peasantry, not the West European nobility. The average European farmer in the 8th century lived in a worse house, bought far fewer of possessions from long distance trade, owned fewer possessions over all, and owned material goods of a lower quality than his 2nd century predecessor.
He was also more than three centimeters taller.
We thus have two proxies for wealth that moved in different directions at the same time. In terms of health the average European farmer was substantially better off than before; in terms of material possessions the same farmer was in a substantially worse position. How do we reconcile this? Which measure better accounts for this thing called "wealth"?
It is worth it to stop here and reflect on just what determines the changing heights of the populations used in "biological standard of living" measurements. The relationship between genes, diet, and the heritability of height is a fairly complex one. To simplify a bit, the heritability of height varies from 60-80% depending on the ethnicity of the population in question, and the remainder of variation in height reflects environmental effects, especially nutrition. When the average height of a population changes this is mostly a function of the changing nutritional quality of the food available to the population in question (though disease also plays a small part). 
The quality of the food a household has access to usually is directly related to the income of that household and the general prosperity of the society in which they live. However, this is not necessarily the case. There is no law of economics or nutrition that mandates this be so, and if we search through the historical data we can find instances where it clearly was not. One such example was described at length by Jo¨rg Baten and John E. Murray in their research on the heights of prison inmates in 19th century Bavaria. As they report:
One valuable characteristic of the Bavarian prisoner data sets is the capability of distinguishing among the effects of nativity in the several regions. These regions differed notably in the composition of their agricultural output. While some emphasized milk and dairy products in their production mix, others concentrated on potatoes and still others on bread grains. Surveys from the mid-century allowed us to assign each observation values that represented per capita agricultural production levels in their birth region: milk production as of 1840, potato production as of 1853, and bread grains also as of 1853 (no author, 1854–1859; see also Baten, 1999 for further explanation). To model potential nonlinearities and substitutabilities we used both linear and quadratic terms for the food-production variables.
Food production–adult height relationships were strongly nonlinear in the men’s case while mixed in the women’s case. For both men and women there was an optimal (in height terms) amount of milk production in their birth region; but for both men (353 liters) and women (371 liters) the optimum occurred at a standard deviation above average production levels. Availability of protein from dairy sources may thus have been a binding constraint in the growth process, even if subject to diminishing returns above a large production level. A similar pattern emerged for the effect of potato production on men’s heights. The optimal production level of potatoes was far above the average. The relationship between women’s heights and potato production was linear, positive, and significant, while bread grain production was unrelated to women’s heights. Overall, we find that food production in the prisoner’s birth region was generally positively related to final adult height, but in a complex and nonlinear relationship. The implication of these results is that the height of average lower-class Bavarians was strongly influenced by first the availability of milk and secondly the availability of potatoes in a given region.
There are several reasons why milk production might be so closely related to regional health differences. The first is simply that milk is perishable; in pre-industrial times raw milk could usually not be transported over 10 kilometers before spoilage, and soured milk could not be sold more than 40-50 kilometers before it too spoiled. Dairy produced locally had to be consumed locally. There was also, as Nikola Koepke points out, "an indirect advantage [to milk production] via equality: the transport problem lead to a very low shadow price of milk in remote milk producing areas. This induced a relatively egalitarian distribution of high-value proteins. Thus, even low income groups could consume a healthy diet. In contrast, in large cities, only high-income groups could afford a protein-rich diet which was based on meat there." 
Intrigued by these results, Baten later extended his study to other parts of Europe, looking at Prussian and French conscript records (as well as conscript records in Bavaria) to see if he could find a clearer relationship between milk production and height. The results were unequivocal: across all three countries "milk production per capita" was strongly correlated with average conscript height. This, combined with real wages, accounts for almost all of the variability in heights. 
Baten and Stegla found similar results in a long-range study of heights across the modern Near East during the 19th century. Here again we find that populations with most access to milk products--in this case Bedouin tribesmen--were far taller than their countrymen.  Perhaps the most interesting study along these lines, however, was Koepke and Baten's attempts to measure dairy production in the Roman and post Roman world. These are the same two researchers that originally reported the drop in average height as classical civilization expanded across Western Europe and then its three centimeter jump after the empire fell. What they found is that the prevalence of cow bones in trash heaps moved in parallel with the decline and jumps in human height. Archaeological sites from the zenith of the empire had few cattle remains, but plenty of bones from swine.  In other words, the changes in the average height of European farmers during the Roman and post Roman worlds can largely be explained as a function of the access these farmers had to the proteins found in dairy products.
As purchasing and feeding a cow requires a larger capital investment than purchasing and feeding a pig one could conclude that access to dairy is simply a measure of household wealth by another name. I do not think this fact alone tells the entire story. The prevalence of cattle over swine or pasturage over wheat cropland may just as well reflect a decision on the part of households to focus on the goods which would trade at the highest price on regional markets. Whether or not cultivating these goods created a side product that substantially improved the health of their children would be less important than the market price of wheat, leather, beef, pork, etc., and the cost of devoting farmland to their production. This also holds true for those peasant farmers too poor to raise larger amounts of livestock themselves or wage workers who did not raise livestock at all. Their access to protein rich dairy products were just as much a product of their location as of their wages or household wealth.
This is the problem with using "biological standard of living" as a straight proxy for wealth. There are simply too many intervening variables that complicate the picture. In the case of European data, the heights recorded over the centuries clearly reflected average household income--but they also reflected average household dairy consumption. Until economic historians begin controlling for dairy consumption in their models, measurements of biological standard of living that rely solely on height data must be used with caution.
 T. Greer, "Health ≠ Wealth," Scholar's Stage (22 March 2015).
 Pseudoerasmus, comment #2 (25 March 2015), on T. Greer, "Health ≠ Wealth," Scholar's Stage (22 March 2015).
 For an introduction to this line of study see Walter Scheidel, ‘Real wages in early economies: evidence for living standards from 1800 BCE to 1300 CE’, Journal of the Economic and Social History of the Orient 53 (2010), 425-462.
 Bryan Ward-Perkins, The Fall of Rome and the End of Civilization (Oxford: Oxford University Press, 2006), 92.
 ibid., 105-106.
 ibid., 107-108.
 ibid., 118.
 Jo¨rg Baten and John E. Murray, "Heights of Men and Women in 19th-Century Bavaria: Economic, Nutritional, and Disease Influences," Explorations in Economic History 37 (2000), 361.
 Nikola Koepke, "Regional Differences and Temporal Development of the Nutritional Status in Europe from the 8th century B.C. until the 18th century A.D.," PhD Diss., Universität Tübingen (2008), p. 100.
 Jo¨rg Baten, "Protein Supply and Nutritional Status in Nineteenth Century Bavaria, Prussia and France”, Economics and Human Biology 7, iss. 2 (2009), 165-180.
 Mojgan Stegla and Joerg Baten, "Tall and shrinking Muslims, short and growing Europeans: The long-run welfare development of the Middle East, 1850–1980," Explorations in Economic History 46, is 1 (2009), 132–148.
 Nikola Koepke & Joerg Baten, “Agricultural Specialization and Height in Ancient and Medieval Europe”, Explorations in Economic History 42, is. 2 (2008), pp. 127-146