METHODS OF EXTRAPOLATION

INTRODUCTION

With large ancient coinages, so much is missing that a simple die-count is usually not enough to show how many dies were there originally. Thus in the Crepusius die-set with explicit numbering, the die-series remains seriously incomplete, despite the very large samples that have been collected. And with the larger coin-populations of the Principate, even a three-quarter sample of dies is usually far out of reach. The need to extrapolate is widely recognised, but there is much less agreement about how to do this.

Existing methods of extrapolation cannot be discussed individually here. But most are too simple to be capable of modelling the frequencies of Roman coin-types or dies. These frequency-patterns are usually highly skewed, although their skewness varies. Modelling them requires the use of two parameters, which reflect the degree of dispersal as well as the ratio of dies to coins. But most methods applied to coin-evidence rely on the second parameter alone.

The present discussion uses general statistical theory in preference to any of the formulae specially devised for coin-evidence. Roman numismatic data are in fact highly amenable to modelling by a well-known statistical distribution, and modelling by this distribution is considerably more efficient than by most other techniques. The distribution happens to be laborious to calculate, and it is applied here by means of computer programs.

EXTRAPOLATION: METHOD A

The present study deliberately began with the Reka Devnia silver hoard of more than 80,000 coins.

CHRONOLOGY

INTRODUCTION

In the last chapter, it was argued from correlations by reign with civilian handouts in Rome that most coin-hoards in this period originated from the parallel handouts to the provincial armies. If correct, that identification must mean that particular handouts generated particular groups of hoards. The first part of this chapter explores this association chronologically.

Looked at in detail, most known handouts at Rome seem to have a potential echo in the hoards found in the empire at large. But hoard-dates and the dates of handouts are often slightly out of alignment. Taken by itself, that could call the present interpretation into question. But granted the strong correlations by reign between hoards and handouts at Rome, what it suggests is that in many cases the latest coin available for handouts in the provinces may have been several years old, because of slow circulation. The amount of timelag appears to vary, thus blurring arguments from detailed chronology which could otherwise contribute to the main diagnosis. The detailed implications of that diagnosis must still be examined. But it should be understood that the associations suggested below cannot be firm identifications in the absence of more specific evidence.

Army donatives of the Principate and civilian handouts in Rome figure as joint events in the sources. Certain special occasions tended to trigger handouts. They included the accession of a new Emperor, the naming or coming of age of an heir, and the holding of a triumph.

BARTER AND NON-MONETISED EXCHANGE

Limited monetisation can take two obvious forms. One is pre-monetary exchange based on barter. The other is monetary deprivation, where the market-place expects money, but too little coin is available. Both phenomena seem to exist in the Roman world. Barter may be a survival from a premonetary era, or an indication of metal shortage, or a sign that although there was enough coin, the State was not concerned to distribute it efficiently. What seems clear in the Roman world is that where money was available, it was used. The wear-rate of low-denomination coin was quite high, even if by modern standards valuable coin wore out slowly and circulated slowly. The ready market for counterfeit coin vividly suggests that more money was needed than was actually circulating. Barter can be difficult to detect, and there is a strong likelihood that it was widespread in many less urbanised areas.

Some documents from a much earlier society give interesting insights into types of exchange characteristic of the pre-modern world. In the Babylonian Code of Hammurabi, which is further from the time of Augustus than Augustus is from today, payment in grain was specified for hiring oxen or farm-labourers. But silver was specified for paying surgeons, brickmakers and tailors. This showed a demarcation between a countryside which used exchange in kind, and non-rural occupations which used money or proto-money.

The aim of this chapter is to look at the broad lines of coin-output, and then to show how coin disappeared from circulation through wastage and re-minting. Separate discussions are devoted to denarii, aurei and Egyptian tetradrachms.

CHANGES IN THE AMOUNT OF DENARIUS COIN IN CIRCULATION

It is possible to assess the amount of coin in circulation as a proportion of the coin produced. This involves a simple test based on the output-index for denarii in chapter 8 (Table 8.7). Comparisons between the output-index and the contents of individual hoards normally imply that in a given hoard one reign is better represented than the others. Almost all hoards show contrasting gradients, which are produced by progressive wastage of earlier coin, and by slow input of recent coin from the centre. The peak is the reign where the two gradients meet.

The peak can be identified by dividing the coin for each major reign by the index figure for that reign. The peak is the reign with most coin per index-point, and this reign is taken as being represented at full strength. The number of coins in all major reigns, divided by the number of coins per index-point in the peak reign, then gives the representation quotient for the hoard as a whole.

As an illustration, in the Londonthorpe hoard of 420 denarii (AD 153/4), the peak reign proves to be Hadrian, after dividing the various reign-totals by the index figures in Table 8.7.

Although it is so remote in time, the Roman Empire has left a gigantic amount of coin. The amount from relatively modern discoveries must run into millions, even without allowing for finds in earlier centuries which were mostly melted down. Survival on this scale has its own interest, and seems to have a specific explanation, which is discussed in Part II. This book seeks to use coin evidence to study Roman minting policy, monetary organisation, and the monetary economy. For these purposes, co-ordinated analysis of a large amount of data has clear advantages over piecemeal study. Coin hoards of the Principate provide a rich source material whose potentialities as historical evidence are only slowly being exploited, partly because so many hoards remain unpublished. But the material available is now increasing rapidly, thanks partly to discoveries by metal detector, and has grown substantially while this book has been in preparation.

As a preliminary, the early chapters consider the Empire's finances and financial structure. And an initial economic chapter discusses the role of currency, the availability of coin, and monetary inflation. In the main part of the book, the evidence mainly comes from physical survivals of coin. The period examined ends at AD 235, close to the point at which written sources sharply diminish. The invaluable survey by J.-P. Callu takes up from AD 238. Some evidence from the Late Empire is also used, particularly in the discussion of taxation in chapter 4.

DIE PRODUCTIVITY

This chapter considers the implications of the die-estimates for the volume of coin minted. For Rome coin of Hadrian, the die-estimates in chapter 10 show a projected population of about 40,000 dies for silver and for gold, alternative levels of about 1,032 and 530 dies. But no Roman evidence directly shows how many coins a given number of dies produced. Other figures for pre-industrial die-productivity nevertheless suggest broad orders of magnitude. In practice, the relatively stable ratio between gold and silver in large Roman coin samples narrows the range of possibilities.

In an important study of the Amphictionic coinage struck at Delphi in the late fourth century BC, Kinns combined die-study with analysis of the inscription recording the amount minted. He concluded that output was between 11,053 and 27,563 coins per reverse die. These coins were silver staters, larger than Roman denarii. Modern experiments in striking large-diameter coins based on ancient Greek coinage suggested quantities in the range 10,000 to 16,000 for hot striking (Roman mints used hot striking). Moving to the Middle Ages, detailed thirteenth-century evidence about mint-operations from England and France agrees in suggesting a production target per reverse die of between 16,500 and 17,000 coins (Appendix 9). This normally referred to cold striking of silver coins with low relief, using steel or iron dies. Experiments carried out in the nineteenth century with three dies forged by hand produced totals per die of 18,927, 22,432 and 69,399 coins.

THE CASE OF EGYPT

INTRODUCTION

Egypt provides our one practical example of how Rome taxed her provinces. The source is stray documentary survivals, which are cumulatively impressive, although they are concentrated in particular districts. The tax-system is apparently thorough and minute, with farm land surveyed and taxed almost to the last square foot. The tax assessments take into account irrigation status and to a lesser extent poor harvests. But tax-yield declines substantially over the long term, suggesting that the land was being taxed too heavily or over-exploited.

Hyginus shows tax-rates of one-seventh and one-fifth in different provinces, and rates as low as one-tenth are also known. But only Egypt provides enough evidence to show in detail how provincial taxation worked under the Empire. The position here was complicated by Egypt's unique dependence on the Nile flood. Nevertheless, Egypt remains the one province where extensive tax-details have survived, and since it was one of the most important provinces, the government's handling of this resource should provide some index of its financial policies as a whole.

THE AVERAGE TAX-RATE FOR GRAIN LAND

A primary aim of this discussion is to assess the scale of tax-revenue and how this changed. But that means some investigation of how taxes worked and how they were applied. Whether land was public or private made an enormous difference to how much tax it paid.

INTRODUCTION

Roman hoards have usually been seen as cross-sections of coin in ordinary private ownership, either drawn from current circulation (‘circulation’ hoards) or accumulated over an extended period (‘savings’ hoards). Although this dual classification remains widespread, its validity has been questioned, and it does not seem to fit the hundreds of precious-metal hoards from the Principate. Analysis of this evidence instead suggests a specialised and artificial origin.

The present survey uses a very large sample of substantial precious-metal hoards between 31 BC and AD 235. They come from an enormous area, which stretches from Hadrian's Wall to Upper Egypt, and from Portugal to eastern Syria (Table 5.2). Roman hoards survive from an even bigger area, but hoards from beyond the frontier have been considered separately. Any find of more than one or two coins can be called a hoard. But for most serious purposes, a sampling minimum is necessary, and the threshold of 100 denarii adopted here should eliminate some cases of incomplete survival.

SIZE-CLUSTERS

Conclusions about hoard-size cannot always be pressed very far, because recovery may be incomplete, and some reported totals may be inexact. Nevertheless, any large-scale sample is worth examining for signs of patterning. This reveals a number of size-clusters.

At the bottom of the scale, five gold hoards have a face value below HS1400. Four have the identical value of HS500.

INTRODUCTION

When chance winds drove a Roman tax-collector from the Red Sea to Ceylon, the island's king was said to be much impressed by the consistent weight of the silver coins that he brought with him. But an observer meeting it in the twentieth century would be more likely to notice the diversity of Roman coinage, not merely its varied coin-types, but also the inconsistent weights, differing standards, and irregular shape. Some of this diversity obviously reflected mass production in a traditional society with pre-industrial technology. But there are other features of the Empire which throw light on Roman minting policy and the monetary role of coin.

The Empire of the Principate was not fully monetised, and the state collected much of its revenue in kind. Big private estates, like small peasant farms, were said to aim at self-sufficiency and to avoid the market place where they could. But at the centre, there is little sign that the government could do without money, except when it distributed some of its grain revenue to a privileged elite. Money was of the utmost importance for the state's biggest spending commitment, maintaining a large army. Budgetary problems showed themselves in the form of shortage of money. A state which functioned in this way was almost bound to turn some of its regular revenue in kind into cash through the market-place.

But in its fiscal operations, the Roman government seems to have done without credit.