THE ECONOMETRICS OF HEADHUNTING AMONGST LATE BRONZE AGE CELTS

David Foster Wallace Department of Something-or-Other (With Apologies to the Entire Discipline of Cliometrics)

Abstract

This paper deploys a battery of semi-parametric and quasi-experimental techniques—difference-in-differences, instrumental variables constructed from the relative scarcity of bog-iron, and a frankly desperate application of Heckman selection correction—to the residual physical and mythological evidence of headhunting among the late Bronze Age populations conventionally (if problematically) labeled “Celtic.” The central claim is that the decision to detach, preserve, and display a human head can be modeled as a rational, if gruesomely path-dependent, response to a binding constraint on prestige capital in a zero-sum status economy whose primary medium of exchange was the severed cranial vault. Results suggest that the marginal head, once obtained, yielded positive but rapidly diminishing returns after the third or fourth specimen, a finding robust to a variety of robustness checks that the author himself finds only partially convincing.

1. Introduction

It is a truth universally acknowledged—by which I mean it is a truth that has been repeated so often in seminar rooms that it has acquired the force of a natural law—that the Celts of the European Bronze Age were into heads. Not in the modern, therapeutic, “getting into one’s own head” sense, but in the older, wetter, more emphatically pre-modern sense of removing other people’s heads from their bodies and then doing interesting things with the resulting objects. The archaeological record is dotted with skulls that have been carefully modified, suspended, or interred in positions of honor; the literary record (such as it is, filtered through later classical and medieval lenses) is full of warriors who collect heads the way certain contemporary collectors accumulate limited-edition sneakers. What has been missing is a formal econometric treatment of the practice. This paper supplies that treatment, or at least a recognizable parody of one.

The question is not whether headhunting occurred. It did. The question is whether the observed pattern of head acquisition, retention, and occasional disposal can be rationalized within a coherent model of constrained optimization. I argue that it can, provided one is willing to accept a utility function in which the arguments include (a) the prestige elasticity of a newly acquired head, (b) the depreciation rate of previously acquired heads under conditions of damp Atlantic climate, and (c) the opportunity cost of the time and risk required to obtain the next head when the alternative is simply staying home and minding one’s cattle.

A brief terminological note is in order. “Bronze Age Celts” is, strictly speaking, a chronological and ethnic solecism. The archaeological cultures of the European Bronze Age (circa 2300–800 BCE) predate the emergence of anything recognizably Celtic in the linguistic or classical ethnographic sense. Nevertheless, the term has become a convenient shorthand in certain popular and semi-scholarly discourses, and I adopt it here with the same cheerful disregard for precision that characterizes most discussions of “Celtic” anything. The reader who finds this objectionable is invited to perform a mental search-and-replace of “Celtic” with “Atlantic Late Bronze Age” every time the word appears; the econometrics will remain identical.

2. Theoretical Framework

Consider a representative warrior i in period t. His prestige stock P_{it} evolves according to:

P_{it} = (1 − δ)P_{i,t−1} + αH_{it} + ε_{it}

where H_{it} is the number of heads acquired in period t, δ is the depreciation rate of prestige (itself a function of climate, the rate at which rival warriors acquire heads, and the tendency of wooden head-poles to rot), α is the marginal prestige product of an additional head, and ε is a stochastic term that captures the random arrival of especially prestigious victims (e.g., a chieftain’s son, a poet of unusual skill, a visitor from the continent who still has all his teeth).

The warrior maximizes expected lifetime utility subject to a production function for heads that is increasing in personal combat skill, decreasing in the density of rival headhunters, and discontinuous at the point where the local supply of suitable victims is exhausted. The first-order condition is the usual equating of marginal benefit to marginal cost, except that the marginal cost now includes a non-negligible probability of becoming someone else’s H_{jt}.

This framework is, of course, anachronistic to a degree that would make an actual Bronze Age warrior either laugh or remove the author’s head. That is rather the point.

3. Data and Identification

The data are, to put it gently, thin. We have (1) a modest number of modified skulls from sites in Ireland, Britain, and the near Continent; (2) later literary traditions that may or may not preserve genuine memory of the practice; and (3) comparative ethnographic material from other headhunting societies that the author has read about in secondary sources while procrastinating. From these materials one can construct, with heroic assumptions, a panel of sorts in which the unit of observation is a roughly datable deposit of cranial remains and the outcome variable is some proxy for the intensity of head-related activity.

Identification is achieved primarily through a difference-in-differences design that exploits the staggered arrival of certain bronze-working techniques across regions, under the (contestable) assumption that improved metallurgy raised the opportunity cost of time spent hunting heads by making cattle-raiding and bronze-casting more profitable. An instrumental-variables strategy that uses the local availability of bog iron as an instrument for the intensity of bronze production is also attempted; the first-stage F-statistic is, in the author’s private estimation, “not great.”

4. Results

The preferred specification yields a positive and statistically significant coefficient on lagged head acquisition, consistent with the hypothesis that prestige is cumulative. The coefficient declines after the third head, suggesting diminishing returns—a finding that will surprise no one who has ever collected anything. The interaction between head acquisition and a proxy for local warrior density is negative, as theory predicts: when everyone is hunting heads, the marginal prestige of any given head falls.

Robustness checks that exclude Irish sites, re-date several British deposits, or replace the continuous head-count variable with a simple binary indicator for “any heads present” leave the qualitative conclusions unchanged, which is either reassuring or evidence that the results are driven by a small number of influential observations, depending on one’s priors.

5. Discussion and Conclusion

The econometrics of Bronze Age headhunting turn out to look remarkably like the econometrics of many other status competitions: initial returns are high, subsequent returns diminish, and the whole enterprise is constrained by the physical and social technology available to the participants. Whether this constitutes a genuine insight or merely the projection of modern analytic habits onto a past that had no need of them is a question the author is content to leave open. The heads themselves, of course, remain silent.

Notes

1. The phrase “zero-sum status economy” is used advisedly. Status is rarely strictly zero-sum, but the rhetoric of headhunting literature tends to treat it as such, and the econometrician is obliged to meet the data halfway.
2. Depreciation rates for prestige under Atlantic conditions are, needless to say, not directly observed. The author has experimented with rates calibrated to the known half-life of untreated wood in Irish bogs and finds the exercise both illuminating and slightly nauseating.
3. On the chronological solecism of “Bronze Age Celts,” see any competent handbook of European prehistory. The author has read several and remains unrepentant.
4. The instrumental-variables strategy is included largely for completeness. Readers who find the exclusion restriction implausible are in good company; the author is among them.
5. A longer version of this paper, complete with additional robustness tables and a digression on the possible role of hallucinogenic plants in the utility function, is available from the author upon request, or would be if the author had not already decided that the present version is quite long enough.

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