Most ancient historians are comfortable with the idea that there were local markets in the late Roman Republic and the early Roman Empire. There are many documents attesting to purchases of local goods and services both in Rome and outlying areas. Any assertion that these local markets were tied together into a series of interdependent markets is more controversial, as noted in chapter 1. I use wheat prices in this chapter to test the proposition that many wheat markets across the Mediterranean were interconnected and interdependent.
The theory of comparative advantage described in chapter 1 implies that there were advantages to regional specialization in ancient Rome. The Romans put considerable effort into unifying the Mediterranean and clearing out pirates that impeded peaceful shipping. One purpose of that effort was to exploit the comparative advantage of different parts of the ancient world. As Erdkamp (2005, 207) noted, “Late Republican and early Imperial sources indicate that grain from almost the entire Mediterranean world arrived at Rome.” As noted in chapter 1, this interregional trade made everyone better off, although taxes on the provinces may have concentrated the benefits onto Rome itself. I argue for integrated wheat markets in this chapter and explore the implications for Roman incomes in chapter 11.
I show first that there was an enormous amount of wheat moving around the Mediterranean in the few centuries surrounding the beginning of this era. Most of this wheat was being sent, carried, and received by private merchants. So far, this is not terribly controversial, and more details of merchant activities will be described in chapter 5. I then extend the work of Hopkins (1980), Rathbone (1991), and Wilson (2008, 2009b) to show that many markets in distant places were linked by prices, that is, that prices around the Mediterranean were determined by those in Rome. This relationship is very unlikely to be the result of chance. It provides new evidence of a set of interconnected Mediterranean markets. I use two overlapping data sets of prices from Rickman (1980) and Rathbone (2011) to reveal the extensive Mediterranean market and some of its limitations.
This view conflicts with those expressed by Erdkamp (2005). He argued that “the corn market seems largely to have operated within restricted, sometimes isolated regions” (Erdkamp 2005, 204). Although there is much to be admired in his book, he appears confused on this point. He noted that wheat prices were higher in Rome than in other cities, but also that “the degree of connectivity should not be exaggerated, even along the Mediterranean coasts of the Roman Empire” (Erdkamp 2005, 194–95). These two statements are inconsistent; wheat prices were higher in Rome precisely because many wheat markets around the Roman Mediterranean were highly connected.
Ancient historians have been misled by facile comparisons with early modern Europe. Persson (1999, 100) noted that “not until the mid-nineteenth century when the modern information and transport systems have emerged do we find evidence of swifter adjustment to shocks.” Before then many European grain markets were subject to separate shocks and moved rather independently, as ancient historians claim did ancient grain markets. This comparison neglects the important geographic difference between the Roman Empire and early modern Europe. Trade within early modern Europe was over land, while the Mediterranean Sea was the center of the Roman Empire. It was far cheaper to ship goods by sea than over land before the advent of the railroad, and Rome had a far better chance of having an integrated grain market than early modern Europe.
Rome was a large city, probably the largest European city to exist before the Industrial Revolution. Its residents had to eat, and their diet was based on wheat, wine, oil, and dry legumes. Garnsey (1998, 240–42) argued that lentils, chickpeas, and broad beans were an important source of protein in the diet of common Roman people even if the bulk of their calories came from wheat. These products could not be grown in garden plots behind their houses; there was no room in a city. Some, particularly the legumes, might be grown near Rome, but there is abundant evidence that wheat was imported from Sicily, Spain, Egypt and North Africa. Oil also was imported from Africa and wine from Spain. There clearly was specialization of production around the Roman Mediterranean, and these agricultural products then were transported to Rome. How big was this transport of goods? It is even harder to find information on quantities than it is to find data on prices. The best we can hope to do is to make reasonable guesses about the magnitudes involved, focusing on grain since the evidence there is relatively most abundant. Given how large the city of Rome appears to have been, other food imports must have been large as well. That may be the only defensible statement, but I will try to be slightly more precise.
Hopkins (1978) suggested that the population of Rome was around 1 million. This estimate derives from Rex Gestae, stating that there were 250,000 free males over the age of ten in Rome around 1 CE. Hopkins expanded this estimate to 670,000 to 770,000 free people, with a preference for the higher figure. Adding an addition 70,000 soldiers and slaves brought the total to around 1 million. This remains the consensus estimate of Roman population, although it may be correct only to a single significant digit.
Brunt (1971) started from the number of free men receiving the annona, the free distribution of food in Rome, in 58 BCE, doubled the number to get the number of free men and women, and added 100,000 to 200,000 slaves. This provided a total of 600,000 to 840,000 people, and Brunt took the average, 750,000 as his estimate of the total population of Rome. Rickman (1980) started from the census of 5 BCE that reported 320,000 free adult males in Rome. He added 400,000 women and children and 200,000 slaves to bring the total close to Hopkins’s estimate. Garnsey (1998, 191 fn. 26) and Scheidel (2004) also adopted Hopkins’s estimate.
To go from the population to the consumption of wheat, we need an estimate of per capita wheat consumption. This measure appears less controversial than the size of the population, perhaps because it matters less to most historians. The range is between thirty modii per year as suggested by Garnsey (1998, 191) and forty modii per year as suggested by Rickman (1980, 10). This gives an annual consumption of wheat in Rome between 30 and 40 million modii a year.
Rathbone (2003b, 201) estimated that the average interprovincial ship of a medium size carried around ten thousand modii of wheat. He derived this estimate from “thin but nicely random” data and said that larger ships would have been used on the main large-scale routes such as the feeding of Rome. Using the average size of ships and the upper bound of Roman consumption to get a maximum number of trips, these estimates imply that it would have taken at least four thousand ship voyages to feed Rome every year. Since ships could make multiple trips in the roughly eight months a year when most trade took place, this implies that about 2,000 ships were needed to feed Rome. While we lack any good evidence on the total size of the Roman merchant fleet, this does not seem an unreasonable number.
The Romans ferried their grain from Ostia to Rome on barges that held about as much as an average sea-going ship. The trip, however, was much shorter, possibly taking only three days. It consequently would require a far smaller fleet of barges than of ships to bring wheat to Rome. River shipping may not have been much safer; almost three hundred barges were lost in a few days of 62 CE when two hundred sank in a storm at Ostia and one hundred more burned accidentally at Roman docks. Tacitus (Ann. 15) reported that there was no panic or even concern in Rome at this apparent disaster, and the supply of barges does not appear to have been a constraint on the transport of wheat to Rome.
Numerous large granaries in Ostia also provided a buffer for the market; grain could be stored if more grain arrived than was needed at Rome, and grain could be supplied from the granaries if ships did not arrive. Rickman (1971) described the granaries in detail. There were at least thirteen large granaries in Ostia, extending in size up to the huge and private Horrea di Hortensius, which covered 5,000 square meters. Rome clearly had developed the infrastructure needed to feed its large population.
Did the government operate all these facilities directly or were they the fruit of private initiative? The quick answer is that neither the republican government nor the early imperial governments were large enough to handle all this trade by themselves. Much of the process of feeding Rome had to be private. A more detailed answer involves considering government activities and comparing them with the total size of the wheat market.
The largest government activity was the annona. The government gave 60 modii per year to each male head of a household. The number of households receiving this largess is unclear, but it is generally thought to be between 200,000 and 250,000 during the reign of Augustus (Virlouvet 1995; Garnsey 1998, 236). That would make the total amount of wheat needed for the annona around 12 to 15 million modii. Taking the largest recipient population and the smallest total consumption, the annona used about half of the wheat imported into Rome. If the smaller recipient population and the larger total consumption are more accurate, the share falls to around one quarter. At least half of the wheat imported to Rome at the time of Augustus, and probably more, therefore was imported privately. Sirks (1991, 21) argued that the share of grain imported into Rome for the annona was even less, only around 15 percent, making the private share correspondingly larger.
The government transported the wheat for the annona privately. They let contracts to societates to provide wheat, and they offered inducements for private merchants to participate in this process. Claudius rewarded private merchants who used their own ships, carrying at least 10,000 modii, to import grain to Rome for five years in various ways. If the merchant was a citizen, he would be exempt from the lex Papia Poppaea, which penalized the childless. If the merchant was a woman, she could make a will without the intervention of a male tutor. And if the merchant was not a citizen, he would be granted citizenship. Hadrian extended these rewards by exempting any merchant devoting the greater part of his resources to the annona from compulsory services imposed by municipal authorities (Badian 1983; Garnsey 1988, 234; Sirks 1991, 63).
The limited size of the annona relative to the total food consumption and the government’s use of private merchants to get the supplies for the annona imply that the grand bulk of the grain brought to Rome came by the agency of private merchants. But although the government was not active in the provision of wheat during normal years, it did intervene in the wheat market when there was a shortage. The government supplemented the annona with attempts to avoid the hardships of price spikes when supplies ran short. In 74 BCE, the government sold grain cheaply to offset the loss of wheat in Sicilian floods. In 57 BCE Pompey negotiated extra purchases himself, sailing from province to province in search of wheat. In 24 BCE Augustus gave four hundred HS (HS standing for sestertii, the common Roman brass currency equal to one-fourth of silver denarii) apiece to 250,000 people, allowing them to purchase wheat that was temporarily expensive. In 19 CE Tiberius placed a price ceiling on grain and offered to compensate merchants two HS per modius, equal to about 6.5 kilograms, suggesting that the price before his intervention was at least two HS above the price he thought people could bear. In 64 CE Nero set another price ceiling for wheat, this time at three HS per modius (Garnsey 1988, 195–222; Rickman 1980, 150–54).
Government interventions like these are summarized in table 2.1. It is clear that the government intervened in the wheat market from time to time, particularly under Augustus. It also is clear, even from what must be a partial list, that these interventions were intermittent. Even if we assume that these interventions are only half of the actual actions, the others being unrecorded in our sources, the years in which there were interventions were still clearly a minority. In most years the market for wheat was allowed to work on its own.
Erdkamp (2005, 256–57) concluded after surveying this mixed system that “free trade in the Empire’s capital operated in the margins of a system that was characterized by public supply channels.” Nonetheless, he acknowledged that prices rose when grain was scarce, official interventions like those in table 2.1 were abnormal, and the price at which wheat was sold in Rome ordinarily was free of government intervention. The periodic interventions shown in table 2.1 may have even improved the market in other years by creating anticipations that restrictions of supply would not be tolerated. If so, these interventions may have facilitated the operation of the private market by discouraging hoarding and other noncompetitive actions. The question then is whether the resulting actions of Roman merchants created an integrated set of wheat markets in the Mediterranean? Despite the absence of good price series, it turns out that there are enough prices to provide an answer.
TABLE 2.1.
Selected government interventions in the grain market
If there had been a unified wheat market, the main market would have been in Rome, where the largest number of potential consumers lived and the Roman government was located. In other words, Rome was where the largest supplies and demands for wheat would have come together and where the price of wheat consequently would have been set. The price would have varied over time as supplies fluctuated due to harvests across the Roman world, storms affected the cost of transportation, and government actions altered the value of the currency. Normal variations in supplies and demands elsewhere in the empire would have affected the price, although most fluctuations would have been small relative to the total production and the consumption at Rome. Most places outside of Rome would have had an excess supply of wheat, and the price would have been set in Rome where the excess supplies and the largest excess demand came together. When local places were isolated, there could have been excess local demand as well as excess local supply, that is, local famines as well as local gluts.
Under these circumstances, wheat outside of Rome would be valued by what it was worth in Rome. Wheat at Palermo in Sicily, for example, normally would be worth less than wheat in Rome because it would have to be transported to Rome to be sold. The price of wheat in Sicily would be the price of wheat in Rome less the cost of getting wheat from Sicily to Rome. This would be true almost always, but there undoubtedly were circumstances when it was not. If storms prevented the shipment of grain to Rome, the Sicilian price might temporarily deviate from the level set by the price in Rome. If a harvest failure in Sicily created a local famine, the price of wheat in Sicily would rise above the level indicated by the Roman price until new wheat supplies could be brought in. In the absence of extreme events like these, a unified market would keep Sicilian prices near the Roman price less the transportation cost.
The market is an abstraction, as noted in chapter 1; it is misleading to say the market would determine Sicilian prices. More accurately, competition would determine Sicilian prices if there was a unified market. If the Sicilian price of wheat rose above the Roman level minus transportation costs, it would not make sense for merchants to buy wheat in Sicily to sell in Rome. The amount of wheat demanded in Sicily would fall, and the price consequently would fall as well. If the Sicilian price of wheat fell below the Roman level minus transportation costs, merchants would increase the amount of wheat they would buy in Sicily, for they could make an unusually high profit by taking it to Rome and selling it there. Merchants would bid against each other, raising the Sicilian price as described for general supplies and demands in chapter 1.
Wheat at Lusitania in Spain would be worth less than wheat at Palermo because it was further from Rome. The cost of transporting wheat from Spain to Rome was larger than the cost of bringing it from Sicily, and the price of wheat in Spain correspondingly would be lower. The reasoning is exactly like that for Sicily, only the transport cost is different. But while each price is compared to that in Rome, the price in Spain would be lower than the price in Sicily if there were a unified market. In fact, wheat around the Mediterranean would be worth less than the price at Rome, with the amount less depending on the distance from Rome. We do not know the transport cost in any detail, but we are reasonably sure that it rose with distance. If there was a unified wheat market, therefore, the price of wheat would have decreased as one moved farther and farther from Rome.
All this sounds very abstract. But if it is not an accurate picture of the Roman world, we need to think of the relevant alternative. If there were not a unified market, if there were only independent local markets, then there would not be any relationship between local and Roman prices. There would be prices in local markets that would be determined by local conditions. The prices might move together at some times, if storms across the Mediterranean caused simultaneous harvest failures everywhere or currency debasements caused prices to rise everywhere, but they would not in general be related one to another; any single identity of prices could be a coincidence. If we find several wheat prices in different places, we can test whether the pattern we find is due to coincidence or an underlying market process.
It is hardly necessary for all merchants to be trying to arbitrage prices to bring them into relation with each other. Most participants in most markets simply do today what they did yesterday. Markets work when there are a few arbitrageurs that act as described here; Pompey, as he sailed around to find scarce wheat, was arbitraging prices. There is no theory of how many participants need to arbitrage prices to get to the equilibriums described in chapter 1. With modern computer technology, a few people with a lot of band width can make money and coax even large markets into equilibrium. They also can go broke if they guess wrong where the equilibrium is, as Long Term Capital Management did spectacularly in 1998. In ancient Rome, a dozen or two merchants in each market might have been enough to bring local prices into a relation with Roman prices.
The question is not whether one or the other of these ideal types was observed, whether there was an efficient market or that there were no factors unifying separate local markets. It is rather whether the historical experience lies closer to one end of a continuum than the other. The interventions noted for Rome in table 2.1 were echoed by local actions elsewhere around the Mediterranean. There must have been at least occasional local grain shortages and even famines. The question then is whether the normal state of affairs was one of interconnected markets, so that prices in different places typically were related, or one of separated and independent markets. In the latter case, we should not observe any systematic relationship between the location and the price of grain.
I approach this test in two steps, the first of which uses a small set of wheat prices from varied locations from Rickman (1980). This familiar sample provides a way to examine monetary integration at least provisionally. When dealing with fragmentary data it is necessary to collect a sample that is not determined by the desired outcome. Rickman was writing about the Roman wheat market, and he collected his sample to show habitual prices in different places. The sample, albeit small, therefore looks like a random sample. It is, in Rathbone’s felicitous phrase, “thin but nicely random.” We cannot be completely sure that the prices Rickman selected or that survived to be collected are completely random, but they may be as close to random as we can get for Roman history. The second step is to check these results with a new data set in Rathbone (2011). These data were collected to exhibit the surviving prices from around the Mediterranean. They overlap Rickman’s sample, but the two authors made different choices in collecting data that allow us to delimit more precisely the extent of the Roman Mediterranean wheat market.
The Rickman sample consists of price pairs in outlying locations and in Rome at roughly the same time, accumulating six price pairs in almost two centuries ranging from the late republic to the early empire. This is not an overwhelming amount of evidence, but it is enough to test whether the patterns in the data are random or not. In each case the Roman price was subtracted from the price at the distant location to give a price differential. Wheat prices at Rome were subject to slow inflation according to Rickman (1980) and Duncan-Jones (1982). I characterize this period as having stable prices in chapter 4, with an allowance for slow and gradual price changes that can be documented here.
I describe the price observations in the order of their distance from Rome, calculated as straight-line distances on a map. This is only an approximation to the actual distance that wheat traveled, and this added randomness reduces the possibility of finding evidence of an integrated market. The closest price was from Sicily and came from Cicero’s Verrine Orations. One of his accusations was that Verres did not transact business at the market price, even though he acknowledged its level in a letter (Cicero, 2 Verr. 3. 189). This observation, like most of the others, reports the prevailing local price in round numbers. Since the observation is general rather than the record of any transaction, it is likely to be only approximate. This casual quality of the data also militates against finding any systematic relationship between prices. It introduces more noise into any relationship of the prices being paid because of the unknown difference between the reported averages and actual prices.
The second price came from Polybius (34.8.7) in his discussion of conditions in Lusitania. As before, this is a general statement about the prevailing price. While it is good to have an average, the casual quality of the averaging process again adds noise into any comparison of prices in different places.
The third price comes from the Po Valley in Italy; it is another observation by Polybius (2.15.1). While this observation is closer to Rome than the first two prices, I made an exception to the general rule of measuring distance. The Po Valley was linked to Rome more by rivers rather than sea, although the transport of a bulk commodity like wheat may well have gone by sea (Harris 1989b). I calculated the distance in two ways that fortunately give the same distance. Diocletian’s Price Edict fixed river transport prices at five times the level of sea transport, and I first took the cost of river transport from the Po Valley to have been five times as expensive as by sea. This evidence dates from over a century later than any of the other prices, but I assumed the ratio of sea and river transport costs remained constant over time as argued by Greene (1986, 40) and included the Po Valley in the price data by multiplying the distance from Rome by five. In addition, the distance by sea from the Po Valley to Rome is the same as the distance I calculated from the Diocletian Edict. The sea distance is not a straight line, and this observation therefore is slightly different from the others even if measured by sea. Despite the small sample, there is enough data to test whether this unusual attention to distance for this observation affects the statistical result.
The fourth price comes from an official intervention in the local market. An inscription records that the wheat price in Pisidian Antioch was high in a time of scarcity. The normal price was eight or nine asses (four asses equaled one sestertius) per modius; the acceptable limit price was one denarius per modius (AÉ1925, no. 126b). This inscription reveals several important aspects of the Mediterranean wheat market in addition to reporting the normal price. The need to damp down famine prices indicates that local markets were subject to local scarcities; they were not so well linked that wheat from elsewhere would be brought in instantly in response to a local shortage. The apparent success of such interventions, in this case limiting the price to double its normal range, indicates that many famines were not severe.
For Egypt, I preserve the spirit of Rickman’s data but improve on his data since Rathbone (1997) reworked the sale prices that Rickman took from Duncan-Jones. I averaged seven Egyptian prices from the “famine” of 45–47 CE to get a price for Egypt. Rathbone argued that these prices were unusual, but the previous discussion suggests that they may not be far from average. We cannot know how unusual these prices were, and any special conditions introduce noise into our data. The Egyptian prices also come from agricultural areas, not from a Mediterranean port. The purported famine would have raised the price, but using country prices would have depressed it compared to those at a port. These offsets introduce added uncertainty into the accuracy of this observation since there is no reason to expect them to be exact offsets. The average of Rathbone’s seven prices was seven drachmae per artaba. These prices in Egyptian currency and units were converted to HS per modius by following Duncan-Jones (1990, 372) and dividing by 4.5.
The final observation, from distant Palestine, is taken from Tenney Frank’s Economic Survey; it too is an average of a few actual transactions (Heichelheim 1933–40, 181–83).
All of these prices were compared with roughly contemporaneous prices at Rome. Rickman argued that the price of wheat at Rome was between three and four HS per modius in the late republic, rising to five to six HS in the early empire. Duncan-Jones confirmed the general price level; Rathbone confirmed the inflation, at least for Egypt where the data are more abundant. The order of observations turns out to be almost chronological even though the order of exposition was by distance. There are six prices in almost two centuries. This is not an overwhelming amount of evidence, but it is enough to test whether the patterns in the data are random or not. In each case the Roman price was subtracted from the price at the distant location to give a price differential. More prices come to light all the time, but this “thin but nicely random” sample provides a way to answer the question at least provisionally.
The prices and the differences between the prices at Rome and the local prices are listed in table 2.2. The differences are all negative, consistent with the story of an integrated market and with general observations that agricultural prices were lower outside Rome (Garnsey 1998, 241). Wheat prices clearly were lower outside of Rome than in Rome itself. The straight-line distances from each location to Rome also are in table 2.2. I test whether the differences between prices in these provincial locations and the price at Rome were proportional to their distance to Rome. The value of a statistical test is that one can say with some precision how unlikely it is that the observed result would be found if the data were generated by pure chance. I describe how the data are only approximate. Each approximation introduces an added element of randomness into the data, increasing the probability that any observed pattern is simply noise.
The price differentials are graphed against the distance to Rome in figure 2.1. The results are quite striking; prices were lower in places further from Rome, and the price differentials appear almost proportional to the distance from Rome. These prices come from all over the Mediterranean and from various times in the late republic and early empire. If there were not a unified grain market, there would be no reason to expect a pattern in these prices. Even if there was a unified market, our inability to find more prices or more accurate transportation costs might have obscured any true relationship among the prices. Yet figure 2.1 reveals a clear picture.
TABLE 2.2.
Distance and prices for grain
FIGURE 2.1. Plot of distance and Roman distance discount
It may appear as if the picture in figure 2.1 could only suggest such a story. It seems like a tiny bit of evidence on which to hang such a grand story of universal monetization and market integration. There is, however, a statistical technique that can be used to evaluate how likely it is that a picture like figure 2.1 could arise by chance. In other words, we can test the probability that the separate areas of the early Roman Empire were isolated and out of economic connection with Rome. Their prices would have been determined by local conditions, including perhaps the degree of monetization. There would have been no connection between the distance to Rome and the level of local prices.
This statistical technique is regression analysis. In this type of analysis we can evaluate the likelihood that there is a relation between the local price and the distance from Rome. We start by trying to draw a line that relates the price difference between the local price and the Roman price to the distance from Rome. We then adjust the line to make it the best description of the data in the sense that it minimizes the squared distance of the individual observations from the line. (We use the square of the distance to minimize the distance from points both above and below the line and to simplify the mathematics.) This process of regression analysis also is known as the method of “least squares,” and the resulting least-squares line is the regression line. It is shown in figure 2.2.
FIGURE 2.2. Relationship between distance and Roman distance discount
One of the values of regression analysis is that it generates tests of the hypotheses being tested. We can ask if an apparent relationship between the price discount and the distance from Rome is illusory, a result of observing only a few prices, rather than the result of a systematic process. In order to draw this line, we assumed that there was a relationship between the distance from Rome and the price discount. Regression analysis provides a test whether there is such an association in the data. This test tells us how unlikely it is for us to find a line like the one shown in figure 2.2 by chance. Assume that the prices we gathered from Rickman were randomly drawn from an underlying distribution of price observations. In another world, different prices could have survived from this same distribution. Taking account of the random quality of the observations we actually have, how unlikely is it for us to find the line in figure 2.2 by chance?
Regression analysis acknowledges that the slope of the line in figure 2.2 is not known with certainty. It is the best line that can be drawn with the data at hand, but it is subject to errors deriving from the incomplete sampling of the underlying distribution. In the jargon of regression analysis, the slope of the line has a standard error. If all the points in figures 2.1 and 2.2 lay in a straight line, then the slope of the regression line would be clear, and the standard error of the slope would be close to zero. If the points are spread out as they are in the figures here, then the line is not known as clearly, and there is a chance that the line has no slope at all, that is, that there is no relationship between the distance from Rome and the price difference.
The test is to compare the size of the slope, the coefficient in the regression, with the size of its standard error. If the coefficient is large relative to the standard error, then it is unlikely that the line was a random finding without support in the price data. On the other hand, if the coefficient is small relative to its standard error, then it is possible that even though the regression line has a slope, there is no underlying relationship between the price and distance. Statisticians call this ratio a t-statistic, and they have calculated tables that can translate t-statistics into probabilities that the line is observed by chance.
The tables take account of degrees of freedom, that is, the number of observations minus the number of coefficients. It takes two variables to define a line, its slope and its position (its height in the figures). With six observations and two variables, there are four degrees of freedom. Omitting the observation with river transport reduces the number of observations by one and the degrees of freedom to three. The t-statistic has to be larger with such few degrees of freedom than with more degrees of freedom to show that a given regression line is unlikely to be the result of chance.
One might think that the data—composed of only a few, badly observed values—are too poor for statistical analysis. Statistics are the best way of distinguishing signal from noise; they are particularly useful when there is a lot of noise in the system. They give us a precise sense of how unlikely it is that any putative pattern we think we observe would have been generated by random processes, that is, how unlikely it is that what looks like a pattern actually is noise. The value of statistics is that we can test a formal hypothesis, namely that wheat prices around the Mediterranean Sea were related in a simple way to those at Rome. We also can derive an explicit probability that this hypothesis is true, given the observations we have.
Errors in variables are a common problem in doing regressions. We often hypothesize a relationship between two variables—like the price in Rome and the price in Egypt—but cannot observe one or the other of them precisely. We then use a proxy such as the occasional price that happens to be mentioned in a surviving document. The errors introduced by such a procedure have been studied, and their effects are well known. The extra uncertainty introduced by using imperfect proxies reduces the explanatory power of regressions and tends to result in coefficients that are near zero; the addition of noise through imperfect observations makes the results look more like noise. The well-known scarcity of Roman prices therefore makes it very hard to find a pattern in them. When a pattern is found, however, it indicates both that there is a strong relationship between the prices and that the observations we have are reasonably representative.
TABLE 2.3.
Distance and distance discount regression results
|
N |
Constant |
Distance |
R2 |
Distance discount |
6 |
–1.150 |
–0.001 |
0.74 |
Distance discount (no Po Valley) |
5 |
–1.116 |
–0.001 |
0.75 |
Log distance discount |
6 |
0.125 |
0.002 |
0.81 |
Log distance discount (no Po Valley) |
5 |
0.116 |
0.002 |
0.83 |
Absolute values of t-statistics are below the coefficients.
Source: Table 2.2.
Statistical tests are needed to tell if the observed pattern could be the result of chance. The results of four separate regressions of the price differential on the distance from Rome are shown in table 2.3. Since the transportation from Bologna was by river rather than sea, I was not sure that the correction for the relative cost of transport was accurate and tried the regressions both with and without the Bologna data point. In addition, in the bottom two regressions the price differentials are expressed in logarithms to measure the proportional change in them. Since there are no logarithms of negative numbers, the signs in the bottom two regressions are changed. The dependent variable is the premium of the Roman price over the local price instead of the discount of the local price from the Roman price.
Several conclusions emerge from these results. The R2 shown in the final column measures the share of the variance of the price differentials that is explained by these simple regressions. Using the price differentials themselves, the regression explains three-quarters of the variation. Using logarithms of the differentials, the regressions explain even more. This result confirms the impression in table 2.2 and figure 2.1 that distance from Rome was a powerful explanatory factor in determining wheat prices around the Roman Mediterranean.
T-statistics are shown in parentheses beneath the coefficients in table 2.3, and they indicate whether the relationship between price differentials and distance was the result of chance. These statistics measure the probability that each coefficient is different from zero, taking account of the number of observations used to derive it as well as their variation. T-statistics above three indicate that there is less than one chance in twenty that the observed relationship between distance and price differentials was due to chance. In the more precise language normally used for regressions, the probability of observing the coefficients in the table if there were no relationship between the price of wheat and the distance from Rome is less than 5 percent in three out of four regressions and close to that probability in the fourth. The 5 percent value of the t-statistic for four degrees of freedom (six observations) is 2.8; for three degrees of freedom (five observations), 3.2. Higher t-statistics indicate lower probabilities that the observed relationship is the result of chance.
In other words, the regressions confirm with very high probability that there was a unified wheat market that extended from one end to the other of the Mediterranean Sea. Transport costs were roughly proportional to distance, and the effects of distance were larger than the idiosyncratic influences of particular markets and places.
The constant terms in these regressions were negative in the regressions for price discounts and positive in the regressions for the logarithms. They were not estimated as precisely as the relationship between distance and the price differentials, and they consequently could be the result of chance (as indicated by smaller t-statistics). Nonetheless, the constant terms are historically reasonable and indicate that not all costs were proportional to distance. There appear to have been other costs as well, albeit smaller and less well observed. These other costs were partly physical—the costs of transshipping wheat to and from seagoing ships—and partly administrative—port charges and taxes. Their presence does not detract from the effect of distance or the evidence in favor of a unified wheat market.
Finally, it does not make a difference whether Bologna is included or not. Removing this observation reduced our comparisons to five, but it did not affect the proportion of the variance explained or the evidence that the relationship of distance to price differentials was not random. The t-statistics take account of the reduction in the number of observations to calculate the probability that the observed correlation was due to chance. The logic behind this finding can be seen in figure 2.2. The observation for Bologna lies close to the regression line. Removing it therefore does not change the line.
These results can be extended with a new data set from Rathbone (2011), an expanded version of the data in Rathbone (2009). At first glance, this looks like a larger data set, with twenty-three observations and more power to test hypotheses. It turns out that the added data give us a way to clarify the previous results rather than to make a new start. We need first to consider how this sample was constructed. In Rathbones’s words, they are the extant prices “which are significant for market behavior.” In other words, they were not picked to prove a hypothesis, but rather to show what we know about Roman wheat markets. Again, thin but nicely random.
Eight of these observations are for prices at Rome. Rathbone recognized that the annona distorted the market at Rome, and he did not attempt to find a market price that prevailed in normal times. He presented high prices in severe shortages, although one of them is close to Rickman’s Rome price, and state-subsidized prices. He did not follow Rickman and try to estimate an average from these very diverse prices. Without a set of prices at Rome, I used the prices elsewhere instead of discounting them from the Roman price. I added a time variable to account for the slight inflation visible in Rickman’s data. The result is to lose eight observations and add a variable, decreasing the degrees of freedom by nine.
For other observations, I used the average where Rathbone provided ranges. I disregarded the few prices where Rathbone—ever cautious about data—added question marks to the prices or dates and a few prices from “extreme shortages.” I also discarded the observation for Judaea as being too imprecise and probably irrelevant. The timing was given only as the second century CE, which is after the Judaean revolt. It is likely that the turmoil after the destruction of the Judean temple caused trade to be disrupted. In fact, the Talmud prohibited wheat exports (Heichelheim 1938, 182). The date and effectiveness of this prohibition are not known, but it suggests that the kind of price arbitrage discussed earlier in setting up the regressions was not operative after the revolt. (I did not inquire into the timing of my Judaean observation in using the Rickman data, but removing the Judaean price does not affect the results in table 2.3, although it decreases the degrees of freedom.)
I ended up with eight observations. I used them all and also tried omitting the observations on the Po Valley since the distance measure is problematical as noted already and an Egyptian price from the third century after inflation had picked up. The results are shown in table 2.4, where it can be seen that these regressions reproduce the coefficients on distance in table 2.3. The coefficients are the same size and known with the same precision. The regressions as a whole, however, do not have the same explanatory power as those from Rickman’s data. Despite the overlap between the two data sets, there is more unexplained variation in this data set. In addition, when the two problematical observations are dropped, there are no more observations than in table 2.3. Since there is an additional variable, the degrees of freedom are like the second and fourth regressions in table 2.3 with only three degrees of freedom. As before, it is good that omitting these observations does not affect the results. The constant is larger than before because it includes an implied price at Rome in addition to any costs of taxes or transport to the city. The estimated inflation rate mysteriously is very large.
TABLE 2.4.
Distance and price regression results
Absolute values of t-statistics are below the coefficients.
Source: Rathbone (2011).
Several objections have been raised to this kind of test and its conclusion. The first objection is that prices were low outside Rome because coined money was scarce, not because transport to Rome was costly. This alternative cannot explain the prices in table 2.1. Coins may have been scarce in Lusitania at the time of Polybius, but coins were abundant in the eastern Mediterranean where the monetized Greek economy preceded the Roman one. Wheat prices there were lower than in Lusitania, as can be seen from the figures. Distance from Rome is a much better predictor of prices than coin scarcity.
A second objection is that the prices are unrepresentative because they are notional, biased because the observers had political motives, or unrepresentative due to price fluctuations. Such errors in the price observations may have been present, although Polybius was a very careful historian, not liable to falsify his evidence to make a rhetorical point. As noted already, such errors in recording the “true” prices introduce noise into the relationship between the price differential and distance from Rome. If there was a great deal of this distortion, any existing relationship might be obscured. Since the regressions show such a relation, it means that the relationship between distance and price was a strong one, visible even through the noise introduced by casual or distorted price observations.
More formally, we can think of the observed prices being determined by the true prevailing prices, which we observe with an error due to our approximation. Then the dependent variable we used in the regression is the true price differential plus an error. That error would add onto the error of the regression and result in a lower t-statistic and R2. Given that they both are large, the data show that this rough assumption is quite good, that the observed prices appear to represent prevailing prices in a reasonable fashion.
Another related objection is that prices fluctuated during the year and observations may have come from different seasons. Again, this source of noise strengthens the results because the seasonal price variation introduces another source of noise into the hypothesized relationship. I suspect that the casual nature of the price observations has helped here. Travelers were told of the prevailing price, not sometimes the high price that obtains just before the harvest comes in and sometimes the low price following the harvest. The result appears to be a consistent set of prices. Phrased differently, while the few prices that have survived for two millennia are quite random, it is perverse to insist that any observed pattern has to be spurious. There does not seem to be a reason to throw out evidence from the ancient world on the grounds that the pattern must be as random as the observations.
Yet another objection to the use of these prices is that the argument is circular: I assume the data are sound because they support the hypothesis, but the test of the hypothesis requires the data to be sound. On the contrary, I assume that the observed prices are drawn from a distribution of prices in the late republic and early Roman Empire. I do not assume they are accurate or come from a particular kind of investigation or a particular time of year (as in the previous paragraph). I only assume that they are prices collected before anyone thought of doing a regression test. Given that I am sampling from the population of wheat prices, the t-statistic tells us whether there is a relationship between price and distance. There is no more circularity here than in any statistical test of a hypothesis.
Another objection is that the samples are tiny, only six price pairs or eight prices. The small samples are unfortunate, but no barrier to the test of this hypothesis. As noted above, the standard errors and t-statistics are corrected for degrees of freedom. Having few observations makes it easier to reject hypotheses, but it does not affect the validity of the test. We would, of course, like to have many more prices, but there are no more to be found at this time. The new Rathbone sample has hardly more useable prices, and it confirms the main outlines of the test.
Some of Rathbone’s data come from periods of severe shortages, which also are noted in table 2.1. The few added observations do not give us more information on the frequency of these shortages, but they remind us that the Mediterranean wheat market was subject to events that increased the difficulty and cost of shipping wheat across the sea. The market worked in general, but there was not enough storage to smooth out the difficulties that arose from time to time.
Some objections are more emotional than rational. Erdkamp (2005, 256) talks of “the weaknesses of the grain market.” This is not an economic term; perhaps it refers to the occasional shortages. Seminar participants have said that if one data point of this small data set was moved, then the result would disappear. But choosing data points to make a result come out the way you want it makes the process circular; a statistical test only is possible when the data are chosen for reasons other than influencing the result of a test. And Bang (2008, 31) stated dramatically:
Peter Temin argued that Finley was quite simply wrong; the economy of the Roman Empire represented just such a conglomeration [“an enormous conglomeration of interdependent markets”]. This is an extraordinary claim. One might conceivably imagine that some markets had begun to be linked by middle-and long-distance trade. But to see the entire economy, spanning several continents, as organized by a set of interlinked markets is quite another matter. It is doubtful whether the mature eighteenth-century European economy, outside some restricted pockets, could be described in such terms.
The last sentence reveals a difficulty with references to early modern European economic history that is all too common among ancient historians. Bang reported staples of early modern trade practices—reports from agents, family networks, need for supercargoes, etc.—as if they precluded long-distance trade. He quoted the boilerplate at the end of a typical agent letter saying that prices vary over time as evidence that planning is impossible, and he decried the Roman failure to develop bills of exchange without understanding that the Roman universal currency area obviated the need for such bills. The best place to find a description of the relations between eighteenth-century international trade and the Industrial Revolution is Allen (2009b).
Bang also used an outmoded economic theory. He denied the presence of “Ricardian trade” by noting that complete specialization of Roman provinces did not take place (Bang 2008, 73–76). As shown in chapter 1, this is only a problem if Ricardo’s original formulation is used and no notice is taken of two centuries of elaboration of comparative advantage. As shown in figure 1.4 of chapter 1, Ricardo’s model still illuminates the principle of comparative advantage when we acknowledge there are two factors of production and the PPF is curved. The only difference is that the model used today allows for partial specialization if countries or regions are not too different.
This chapter presents evidence for the presence of a series of unified grain markets that stretched from one end of the Mediterranean to the other in the late republic and early empire. The extent of the Roman market has been debated exhaustively, but evidence to date has been restricted to local markets. The presence of localized market activity has ceased to be controversial, but the question of market integration is still alive. The evidence produced here demonstrates that there was something approaching a unified grain market in the Roman Mediterranean.
Government interventions in wheat markets summarized in table 2.1 make it clear that the market could not prevent shortages in Rome. The government intervened in the wheat market from time to time to lower prices and alleviate shortages, particularly under Augustus. It also is clear, even from what must be a partial list, that these interventions were intermittent. If these interventions are only half of the actual actions, the others being unrecorded in our sources, the years in which there were interventions were still clearly a minority. The market for wheat was allowed to work on its own in most years. In addition, if traders expected the government to interfere when famine loomed, they might have been discouraged from trying to corner the market in adversity. Government intervention therefore may have dampened speculation and made the underlying pattern of prices easier to see.
Of course, there also were local famines, and local areas were not always connected to the market in Rome. Rathbone recorded examples of isolated markets—with prices that do not fit this regression line—showing examples of prices not connected to the regular market. This test demonstrates that there were connections between far-flung Roman grain markets; only with more data will we be able to get a better idea of how often outlying markets were connected to the major consuming market in Rome.
This chapter illustrates the usefulness of regression analysis in ancient history; presenting existing information into a new format that offers the possibility of showing graphically the existence of a unified market, as in figure 2.1. It also provides a test of whether the observed pattern could have arisen by chance. Given the small number of observations, it always is possible that the pattern in figure 2.1 was simply a coincidence. Regression analysis allows us to quantify that possibility. The probability that the pattern in figure 2.1 was due to chance is about 5 percent, that is, one in twenty. This is a far more precise estimate of the probability that we are observing an actual relationship than has been available previously. Given the scarcity of data and the prevalence of shortages, it is clear that regressions can only help interpret existing data, not provide additional information to provide definitive answers to all questions, as will be seen again in chapter 4.
Finally, these regressions tested a very simple model of Roman trade, that there was a single wheat market across the whole Mediterranean. I tested this hypothesis with simple regressions with few degrees of freedom. Why should any ancient historian believe such a simple model and test? The purpose of a model is to provide an overall view of money and trade in Rome; it cannot explain every detail. Instead it provides an overview that helps our thinking. In this case, the regressions show that there were interconnected markets in the Mediterranean, but we also saw in the data that these markets did not work all the time or in all places. As expressed by Rathbone (2011):
Unsatisfactorily thin as the Roman wheat price data are, they seem to suggest a partially integrated market, determined primarily by regional productivity and demand on the one hand, and on the other by the ease or difficulty of transport. Basically the major coastal zones of the empire were linked into a hierarchical structure with the highest price band in Rome and Campania, where demand most exceeded production, a middle band in Sicily, the Greek cities and, to some extent, Judaea, and the lowest band in Egypt, which though not coastal was linked to the Mediterranean by the Nile, and where production most exceeded demand.
Rathbone sees a hierarchy where I see continuity, but we describe much the same conditions. He notes that the excess of demand over the supply of wheat was greatest in and around Rome, and he says other regions were “linked into a hierarchical structure.” This is the structure of an interconnected set of Mediterranean markets that extended—with occasional interruptions and the probable exception of turbulent Judaea—from Egypt to Lusitania in the late Roman Republic and early Roman Empire.
Bransbourg (2012) provides additional evidence of the Mediterranean wheat market in a recent paper. He criticized the data shown in figure 2.1 and analyzed in table 2.4. His new statistical analysis, however, confirmed the negative relation between local wheat prices and the distance from Rome. Using six observations from coastal areas, he found the distance from Rome explained almost all the local variation in wheat prices; adding another half-dozen observations from places away from the sea maintained the explanatory power of the distance from Rome but explained less of the local variation.
