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ISAW Papers 3 (2012)

Rome and the Economic Integration of Empire

Gilles Bransbourg *

http://doi.org/2333.1/280gb73f

Abstract:The modern economist Peter Temin has recently used econometrics to argue that the Roman grain market was an integrated and efficient market. This paper gathers additional data and applies further methods of modern economic analysis to reach a different conclusion. It shows that the overall Roman economy was not fully integrated, although the Mediterranean Sea did create some meaningful integration along a few privileged trade routes. Still, it is not possible to identify pure market forces that existed in isolation, since the political structures that maintained the Empire strongly influenced the movement of money and trade goods.

Subjects: Economic history--To 500.

Contents

“Much of the daily buying and selling of processed foods and other raw materials and of manufactured goods in all the cities of antiquity – I should even guess the largest quantity – was carried on without middlemen, through direct sale by individual craftsmen to individual consumers.”1

“This allowed a single market for wheat to emerge, whose existence we could verify from surviving prices.”2

Ancient Wheat Prices and Market Mechanisms

In several recent publications, Peter Temin has advocated the view that the Roman Mediterranean area was a single market, by studying the credit, labor and goods markets.3

In this paper, we will focus on the last of these. This is not to say that the other two topics are of no interest--far from it. But they require, especially for interest rates, specific numerical analysis that we hope to present in a future paper.

The grain market was undoubtedly the largest market by volume in the ancient Mediterranean world, although we cannot be certain it was always the first in value. A single ship engaged in the Indian trade was able to carry close to HS 10 million in value. This is equivalent to about 2.5 million modii of grain at the likely second-century A.D. Italian price and 4 million modii at Egyptian prices. This is about the volume of the entire annual Sicilian first tithe as reported by Cicero.4

The relatively low volumetric value of wheat may explain why we have little or no evidence about wealthy merchants specializing in the grain trade, although we have numerous examples linked with the luxury, oil, or wine trades.5 Numbers from hagiographic sources in the 6th and 7th centuries, for what they are worth, imply that the value of some precious cargos could exceed that of regular wheat loads by a factor of five to fifteen.6 Eventually, since the administration of the Roman and Constantinopolitan annonae owned a significant share of the grain that was transported by sea, it may well be that, although grain did represent the most important good transported in volume terms, it was not the most important traded good when accounted for in value.7

Nevertheless, the sheer importance of grain as the universal subsistence commodity of the Mediterranean area at this period led to some price recording. Although quite scattered and very often linked to crisis situations, these prices or indications of prices of grain in different contexts create a clear temptation for testing whether or not grain price behavior would fit within a global integrated market process. Grain offers the potential for price comparison since its quality and type had necessarily a much more limited impact on its median price than was the case for wine or oil, for instance.8

The “Temin Equations” of a Centralized Efficient Roman Market for Grain

In his 2006 article, extended in 2008 with the collaboration of David Kessler,9 Peter Temin uses various wheat “prices” essentially gathered by Geoffrey Rickman in his influential 1980 book The Corn Supply of Ancient Rome. From these a set of price differences between “Roman” prices and selected prices from outside Rome is built, and a linearity test between price differential and distance from Rome is run. The aim is to produce a linear relationship between price differentials and distances by means of the OLS (Ordinary Least Squares) methodology. This being achieved with a high degree of statistical confidence, the argument leads to the conclusion that the farther we are from Rome, the cheaper the grain becomes, since “the price would have been set in Rome where the excess supplies and the largest excess demand came together” and “wheat outside Rome would be valued by what it was worth in Rome,” the main component explaining the difference being transport costs.10 This would vindicate the view that Rome and to a lesser extent Italy would have been at the center of an integrated Mediterranean economy.

Free profit-driven traders, having to deal with Roman demand on the one hand and various supply areas on the other, while competing against each other, would have had to purchase wheat where it was the cheapest, transportation costs included. By doing so, they would have encouraged the comparatively cheaper areas to produce more and put pressure on the most expensive producers to reduce their own costs, effectively aligning distance-to-Rome-adjusted wheat prices all across the accessible wheat producing regions of the Mediterranean area. Implicitly, that commercial pressure would have affected wages and other prices altogether, the process of reaching the market equilibrium mainly involving emigration and agricultural shifts in the least competitive regions, while in the best positioned areas more marginal land would have been dedicated to wheat, increasing marginal costs over time. This is how the relationship between price differentials and distance to Rome would prove the existence of a single integrated free market operating at the scale of the entire Imperial area or, to use the author’s own words, “a single monetary market and a single wheat market across the whole Mediterranean.”11

An economy of trade centered on the city of Rome and, to a lesser extent, Italy would vindicate the “Tax and Trade” model advocated by Keith Hopkins and further developed by Hans-Ulrich von Freyberg. Rome would benefit from taxation intakes; the influx of liquidities would push local prices higher, making local goods too expensive. Producers from all over the Empire would exploit their comparative price advantage and outperform their Italian competitors.12

Temin and Kessler’s figures, showing a broadly negative linear relationship between distances from Rome and grain price differential, can be summarized as follows:

Table 1. Distance from Rome and grain prices according to Kessler and Temin13
Region Distance from Rome (km) Rome price (HS) Province price (HS) Distance from Rome "discount" (HS) Year
Sicily 427 4.00 2.00-3.00 -1.5 77 B.C.
Spain (Lusitania) 1363 3.00-4.00 1 -2.5 150 B.C.
Po Valley 1510 3.00-4.00 0.5 -3 150 B.C.
Asia Minor (Pisidian Antioch) 1724 5.00-6.00 2-2.25 -3.13 A.D. 80s
Egypt (Fayum) 1953 5.00-6.00 1.5 -4.00 20 B.C. – A.D. 56
Palestine 2298 5.00-6.00 2-2.50 -3.25 A.D. 15

This leads to the following chart between prices differentials and distances from Rome:14

Chart 1. Distances from Rome and price for grain

The rather neat linearity observable between price differentials and distance from Rome would imply the following relationship:

(Provincial price – Roman price) = β x (distance from Rome) + α + ε

where β is the multiplicative coefficient linking the distance from Rome to the price differential, α the constant, both factors minimizing the standard deviation between the linear regression results and the actual data, and ε the statistical residual of the equation, i.e.. what is left “unexplained” by the equation produced by the regression computation. The numerical results obtained by the authors eventually fit well with that linearity pattern:15

Regression factors β α R2
Value and statistical quality -0.001 (-3.9) -1.10 (-2.2) 79%

This would imply the dominance of market mechanisms, by which prices would be higher where demand is the highest and supply most constrained, whereas remote places far away from the center would enjoy a cheaper life. This is indeed a very seductive vision: Braudelian in the sense that Rome would emerge as the focal point of a wide web of merchant activity, as Bruges, Anvers, Venice, Genoa, Amsterdam, Paris, London, and New York were to become during pre-modern and modern times.16 Moreover, by introducing statistical treatment and a modern economic approach into the study of the ancient economy, Peter Temin opens the door to a completely renewed approach to ancient history, using numerical analysis, a field where most ancient historians have shown some degree of reluctance.

By doing so, David Kessler and Peter Temin clearly expose themselves to criticisms, of which they seem to be mostly conscious. This is how they address them:

In reality, most of these issues remain serious hurdles and need to be addressed with a less superficial scrutiny.

The Law of Small Numbers

Everybody is familiar with the Law of Large Numbers, which consists of performing the same experiment a large number of times in order to observe a close approximation of a probabilistic solution. By contrast, there is no such law for small numbers: small samples being less likely to be bulletproof, statisticians try to avoid situations where they have to rely on a dozen or fewer observations. A relatively recent paper went so far as to suggest as a rule of thumb that we should not study samples with fewer than twenty observations when faced with two variables, including the constant.24 Without entering into technical niceties, the main issue is that few available parameters do not allow the error term in the equation to sufficiently converge towards the true term, implying a significant loss of information.

Even when statistical quality may seem on the surface to be satisfactory, the results might differ from what a larger sample would produce. Because the equations run by Kessler and Temin contain between 5 and 6 parameters and 2 unknown coefficients, we are exactly in that situation.

The second issue that arises when conducting any analysis of that kind is the comparability of the “statistics.” If different measuring tools or concepts are used in gathering the numbers that are to be statistically studied, comparability distortions arise, and results are therefore affected.25

The dataset used by Kessler and Temin contains one obvious source of incomparability: most prices are observed in rural contexts, with the exception of Antioch in Pisidia and the estimations for Rome. The sales margin applied by the urban retailers should theoretically be deducted from these two prices to make them comparable. One argument against doing so is that the prefect in Antioch may well have addressed wholesalers’ prices rather than retail and that the Roman retailers’ margin will have been reflected in the constant factor of the equation. We will revert later to that topic.

Another major issue, particularly with limited samples, is what statisticians call the heteroscedasticity of the variables. This occurs when the measurement uncertainty of the observations differs from one to another.26 The typical way to handle this issue is to run weighted ordinary least squares, where the most uncertain inputs are inversely linked to their reliability by decreasing their impact on the final results.27

In the case of these ancient prices, we are clearly faced with such an issue, because of the heterogeneity of the observation process itself. For instance, at Antioch in Pisidia, the customary price is indicated in the Prefect’s edict itself.28 Egyptian prices are rather well documented as well through numerous surviving papyri, although this does not prevent issues from arising. For instance, the Egyptian price sample selected by Kessler and Temin relates to the years A.D. 45-46. However, there was a famine in 45-47 as a result of the excessive inundation of 45. Temin and Kessler are aware of this but decided to use this sole piece of Egyptian evidence. Interestingly, Dominic Rathbone returned in a more recent work to this topic and opted for a wider and later period of observation, A.D. 80 – 160, which yields a median price of 9 drachmas per artaba. This price, equivalent to HS 2 per modius,29 is 33% higher than the level used in their equation by Kessler and Temin and illustrates the high variance of the input data.

When we move from primary into secondary sources, the exercise becomes potentially even more unreliable. Although one may argue, with some justification, that Cicero (in the midst of a trial) and Polybius (because of his accuracy) are to be followed, it is quite clear that prices derived from literary sources are of a different nature from prices provided by primary materials recording real transactions.

The case of the Lusitanian price is illustrative: the relevant fragment of Polybius’s Histories has been transmitted through the later 2nd-century A.D. Alexandrian sophist Athenaeus. The price of barley is given as “1 drachma” and the price of wheat as “9 Alexandrine obols.”30 The word “Alexandrine” is a cause of concern, since it is highly unlikely that the Achaean Polybius would have used the Ptolemaic currency, whose use was restricted to Egypt, to translate a grain price in Cisalpine Gaul while addressing an aristocratic Greco-Roman audience.

Athenaeus might have turned Polybius’s 9 (Attic) obols into 9 “Alexandrine” (Ptolemaic) obols, knowing that the Egyptian currency was at that time locally translated at par against other Hellenistic coinage.31 In that case we have 1 medimnos = 1.5 drachma = 1.5 denarius = 6 sestertii. Then the modius is worth slightly over 1 sestertius, since 6 modii are a little over 1 medimnos. Alternatively, 9 Alexandrine (Ptolemaic) obols could be equated with 7.5 to 8 Attic obols after taking into account their lower silver content, and the modius would have been worth a figure close to HS 0.85 This is evidently the solution chosen by Rickman, since he writes “just less than 1 sesterce a modius.”32 As such, this is the figure that Kessler and Temin use.

However, if Athenaeus is paraphrasing Polybius and using the drachma and obol of the Roman Egypt that he and his audience knew, then 9 Alexandrian obols simply means HS 1.5 in the 2nd century A.D., i.e., 3/8 denarius for a medimnos, since at that time 1 Attic drachma = 1 denarius = 4 sestertii = 4 Alexandrian drachmas. In that case, Polybius would have originally written 2.25 (Attic) obols and Athenaeus would have translated this into something more customary to his Alexandrian readers, provided he was aware of the way these different monetary systems were translated into one another. If this is correct, the price of a modius of wheat in Lusitania in the 2nd century B.C. could have been as low as HS 0.25 instead of slightly below HS 1.

But the question is still not exhausted, for when Polybius was writing, the Romans modified their currency system and the denarius was revalued from 10 asses to 16 asses in c. 141 B.C.33 Since Polybius once approximates 1 obol with 2 asses,34 it is quite likely that he uses the pre-141 system where the sestertius was worth not 4 asses but 2.5 asses. As the sestertius remained a quarter of a denarius, this does not change the price translation computed by Rickman. Nevertheless, it is legitimate to question whether actual prices in copper currency did not rise by 60% during the years following the moment when the value of the denarius had been adjusted upward by 60% vs. the as. This would undermine the comparative character of the prices stated by Polybius just before the monetary reform.

It is possible that the Roman authorities adjusted their bimetallic monetary system to the actual market rate of exchange between their silver and copper currency at that time.35 The price computed by G. Rickman could thus be correct. Nevertheless, this example should remind us that ancient “numbers” are not always what they appear to be.

We must also face the issue of prices in the city of Rome. Available estimates offer quite a wide range, from HS 3 to 10 per modius. Rickman, whose work on Roman prices is Kessler and Temin’s nearly unique source, wrote: “the essence of our problem of course lies at Rome,” and “there is no evidence at all for ordinary prices of grain at Rome in the late Republic … The situation is no better for Augustus.”36

Indeed, we need to remember that we do not know any wheat price in Rome, and that all these “numbers” derive from scattered indications of State sponsored prices observed during unusual times between the 3rd and 1st centuries B.C., combined with the HS 2 subsidy offered by Tiberius as a reciprocity for capping prices, and the (low) price of HS 3 imposed by Nero in the aftermath of the great fire.37 Practically speaking, the prices in Rome could have averaged HS 4 or 8 at the beginning of the Principate without modern historians having any convincing way to reduce this level of uncertainty. The closest we can get is by following Richard Duncan-Jones and reducing the price range to HS 6-8.38 This is still a 30% margin of error and an exceptionally high degree of data instability.

Interestingly enough, the same can be said about the median wheat price in Palestine, which, according to Daniel Sperber, opposing here Heichelheim’s readings, would have been close to 1 denarius (HS 4) per modius. This is twice as high as in Egypt instead of being 50% higher.39

The sheer size of the uncertainties surrounding the explicative parameters then leads to even bigger dangers: data errors may be so large that different empirical findings could be supported with the same degree of likelihood.

Contemporary econometrics offer an interesting example of how a single error can significantly modify findings when data samples are small: Christina Romer, in an attempt to correlate wealth with durable goods consumption in the 20th century, was using about 30 pre-war data and a little bit under 45 post-war parameters reflecting the US stock index. The pre-war and post-war results showed significant unexplained differences. The cause of these was eventually found to be a single wrong observation within the post-war S&P 500 series.40

If one wrong parameter may have such an influence on a regression supported by about 40 data points, what might happen when the number of explicative parameters is reduced to 5 or 6?

Alternative relationships or absence of relationships?

To test the robustness of the model, I will use most of the parameters of Kessler and Temin, adjusting only those that seem the most clearly debatable. Notably, we will not change the Roman prices at this stage, since their level of uncertainty over the two centuries that are considered is just too wide to easily support any tighter and more relevant median estimate. It could even be argued that the average price does not matter very much, since we are aiming at a relationship between a price differential and a distance. Any shift in the Roman figure would simply translate into the constant factor of the equation, β.

What matters the most is actually whether the level of general prices in Rome did rise at all between the Late Republic and the Early Empire, since that assumption does have an influence on the actual correlation factor. Kessler and Temin assume a general rising trend that leads from HS 3.5 per modius during the 2nd century B.C. towards 5.5 in the 1st century A.D., finding some support in Rickman and Rathbone’s previous works.41 I will not challenge that assumption here, although some caution is to be advocated. To quote Rickman: “It is possible that by the end of the Republic and the early Empire, the price of grain in Rome had risen to a regular level of 5 or even 6 sesterces a modius.” As far as Egyptian prices are concerned, Rathbone argues for broad stability between the later first century A.D. and 160. Then his argument develops further, since “even the prices attested before A.D. 50 mostly fall within the later normal band, but they may represent a lower band of prices.”

Even that cautious assumption of a rise is potentially challengeable by the uncertainties surrounding the rate of exchange between the later Ptolemaic and early Imperial Egyptian drachma and the Imperial currency. The weight of silver in the Egyptian tetradrachm dramatically dropped from Ptolemy XII until Nero, from close to 12 grams before 50 B.C. to a 3.4 grams median weight under Tiberius and 3.1 grams under Claudius, before the Neronian reform brought it down to around 2.5 grams. The one to four rate of exchange between the denarius and the drachma is actually only attested from the later 1st century A.D. onward.42 Strictly speaking, it is thus difficult to prove that Egyptian prices converted in Roman units of value rose at all between the later Ptolemaic/early Imperial period and the 160s. We will come back to that topic.

For the sake of argument, let us nevertheless maintain the Roman price increase as assumed by Temin and Kessler. There remain three prices that they use outside Rome that need some obvious revision: those from Palestine, the Fayyum, and Antioch in Pisidia.

Equation instability with two prices’ adjustment

As previously seen, Palestine’s prices were most likely closer to HS 4 than 2-2.5 per modius. As far as Egypt is concerned, HS 1.5 seems significantly too low: a figure closer to 2 is preferable.43 This view is reinforced by the specificity of Egyptian sources: most of the time, they are part of estate accounts, whereas literary evidence and administrative injunctions originating from other provinces of the Empire normally deal with local consumption prices. A sales margin or at least some transportation costs must have frequently separated prices measured on estates and local consumption centers.44 Knowing actual transaction prices for wheat in Oxyrhynchus, Tebtunis or Karanis would suppress that source of heterogeneity. We have unfortunately no such evidence. Finally, in the case of Antioch, we must correct what is probably a typographical mistake in the Pisidian price used by Kessler and Temin. The prices provided by the Prefect’s edict are HS 2 and 2.25. The difference between a Roman price in a range of HS 5 to 6 and that in Pisidia should be HS 3.375 and not 3.13 (they meant 3.125).45

The relationship we obtain with these modified data displays a slope coefficient (β) that is -0.00044 instead of -0.001, which is not surprising since moving the Pisidian, the Egyptian and Palestine prices all closer to the Roman prices brings more horizontality to the sample of variables. This is not the worst thing yet; after all, no one would care about the slope as long as it was a statistically relevant number. What actually happens is that the R2, which expresses the proportion of the variance explained by the equation, dramatically falls from 79% to 10%, while the T-statistics are much too low to be statistically significant.46 That means we cannot reject the null hypothesis, i.e., the absence of any correlation at all. In simple words, distance and prices could be irrelevant to each other.

At this stage, this does not mean the relationship advocated by Kessler and Temin is necessarily wrong; rather, it is essentially unstable and highly dependent on how a handful of sources are interpreted. This is particularly true of the Judean price: multiplying it by a factor of two effectively destroys the relationship. In that respect we need to keep in mind that Sperber’s work postdates by several decades Heichelheim’s contribution to T. Frank’s ESAR and that his mastery of ancient Jewish sources goes far deeper. Since changing the Judean grain price is sufficient to potentially render the equation irrelevant, we are then exactly in the same situation we described for the post-war S&P 500, where alteration in one unique parameter could kill a numerical relationship.

It is then a true methodological weakness to write, “We assume that the prices we observe are drawn from a distribution of prices in the early Roman Empire.”47 The reality is that some of these prices are prices, some are testimonies, but some are uncertain reconstructions, and as such may be neither random nor normative.

Thus the equation supporting a market-oriented interpretation of the Roman economy could be the product of pure luck or, worse, careful data selection. The fact that challenging a single parameter leads to entirely different results, or, we should rather say, no result at all, simply means that the equation as formulated cannot be statistically upheld.

When Distance to Rome is not a Granted Parameter

Let us now focus on the other factor: distance to Rome. The authors, aware that land and river transportation are more expensive than sea transportation, ran their equation with and without the Po valley observation.48 The risk taken here was not big, since that variable nearly fits with the straight line, which means that its removal was unlikely to significantly alter the coefficients. What is more surprising is the way the Lusitania parameter was incorporated. The distance used by Kessler and Temin is exactly the mileage from Madrid to Rome, as can be found on an airline website. Since ancient Romans could not fly, and Madrid is not located in Portugal, it is more relevant to use sea distances instead. The shortest seaborne itinerary between the Douro River mouth and Civitavecchia accounts for 1334 nautical miles, that is 2470 km, and not 1363 km.49 Once that fact is introduced, the price differentials are visibly no longer aligned according to distance to Rome. The equation again becomes very weak to a point of near irrelevance, even by using the original prices as selected by Kessler and Temin.

Chart 2. Distances from Rome with Lusitania amended, and price for grain

Could landlocked areas trade?

Let’s examine another provenance of one of the sources used by Kessler and Temin: Antioch in Pisidia. This city is located in the Taurus range, at an altitude of 1200 m. (4000 ft.) and is separated from the sea by 200 kilometers of a hilly road, including a couple of steep climbs.50 Using a ratio of 1: 25 for relative sea: land transport costs,51 we would translate these 200 km into the equivalent of 5000 km, next to which the 1700 km or so of sea distance would be a minor factor.