A Cartel's response to cheating: an empirical investigation of the De Beers diamond empire.

1. Introduction

Cartel theory suggests that serious punishment in the form of price competition is the predicted response to cheating by a cartel member, but recent work on cartel operations suggests that some cartels might use a richer set of more measured responses to support their arrangements. Levenstein (1997) and Genesove and Mullin (2001) describe cartels that used limited retaliation, as well as communication, to maintain collusion. However, even these cartels reacted to massive public cheating with the retaliatory response predicted by traditional theory.

The record of the diamond cartel, headed by De Beers, suggests that in some circumstances a cartel might be flexible in its response to cheating even when that cheating is massive. In this paper, we study a particular episode of such cheating by one of the diamond cartel's principal members, namely, Russia. Our findings suggest that De Beers did not respond with aggressive price competition, but rather used a policy that combined accommodation and negotiation. Key to this result were the importance to De Beers of preventing diamond prices from falling and the firm's willingness and ability to absorb excess diamonds into inventory.

De Beers, as head of the diamond cartel, influences the entire diamond trade from mining to retail. The bulk of its direct involvement, however, aside from mining, is in the purchase and sale of just-mined diamonds, or "rough." The Central Selling Organization (CSO) (1) buys the rough from mines owned or controlled by De Beers, from cartel members, and also from independent producers. As a result, much of world production flows through the CSO to be sorted, valued, and ultimately resold. (2) On the other hand, the CSO's sales downstream are carefully monitored to keep prices from falling. Consequently, the CSO holds a fluctuating stockpile of diamonds, which rises when growth in production exceeds growth in final diamond demand.

De Beers supports this "supply management" strategy with legendary advertising campaigns that create and nurture final demand for diamonds while also reinforcing the image of diamonds as rare and valuable gems. It is important to keep prices from falling so as to perpetuate consumers' belief that diamonds remain as scarce as they were before the South African discoveries in the 19th century began a large expansion in their supply. (3) Promoting demand allows De Beers to maintain diamond prices, despite growth in diamond production, while keeping the size of the CSO inventory under control. Together, the supply management strategy and the cartel-funded advertising that encourages final demand have convinced cartel members of the value of cooperation: diamond prices are maintained and members have a sure flow of funds from sales of rough to the CSO (Johnson, Marriott, and von Saldern 1989).

The result of De Beers' strategy has been a long-lived cartel that continues to sell diamonds at prices far above the marginal cost of mining them (Ariovich 1985), despite sometimes rapid growth in world production. Nevertheless, cartel members have occasionally cheated, and De Beers has a reputation for aggressive action against anyone threatening the long-run stability of the diamond market. For instance, in the early 1980s, De Beers is alleged to have punished Zaire for attempting to leave the cartel by flooding the market with the low-quality industrial diamonds that were Zaire's principal product (Spar 1994). Similarly, De Beers greatly increased its sales of low-quality rough diamonds to Indian diamond cutters in 1996 when Argyle, an Australian company, left the cartel (Hart 2001). (4)

In both cases, De Beers was willing to drive down prices and take the short-term losses to punish defectors. However, because the grade of diamonds involved was low, price reductions at this level did not threaten the popular image of diamonds as a luxury item. In contrast, De Beers has always treated the controllers of the Siberian mines, first the government of the Soviet Union and more recently of Russia, with more caution. The Siberian finds of 1954 developed into some of the richest sources of diamonds in the world, producing roughly 20% of the world's gemstone-quality diamonds during the period of our analysis. As such, the output of these mines could have seriously disrupted the diamond markets, and, despite periodic difficulties, De Beers worked hard to negotiate contracts that would keep Soviet and Russian governments as members of the diamond cartel. (5)

Yet De Beers faced a serious challenge in the mid 1990s when Russia began leaking diamonds onto the market. The financial crisis in the Russian Federation apparently encouraged clandestine sales from the Russian diamond stockpile, which was of unknown, but reportedly large, size. These sales, most notably those from 1993 to 1996 (when, according to press reports, close to $1 billion in rough diamonds was leaked from Russia) threatened the pricing structure carefully developed by De Beers over the previous 100 years. (6)

De Beers' public stance, according to a statement by Gary Ralfe, the Managing Director of De Beers, was that the cartel tried to avoid purchasing leaked diamonds so as not to bankroll those doing the leaking (Gooding 1997). However, the CSO is popularly supposed to have increased its purchases of rough diamonds to absorb some of the extra diamonds and, thus, maintain diamond prices. Our goal in this paper is to identify and then separate long-run changes in CSO inventory and in the quantity of CSO diamond sales from short-run movements in these two variables that occurred in response to the Russian dumping. We find that the cointegration techniques that were developed to identify long-run common movements among major macroeconomic time series variables are well suited to our task.

If a set of time series variables can be shown to be cointegrated (i.e., they tend to move together over the long term), then current changes in the variables can be separated into those changes that bring variables back toward the long-run relationship, and short-run changes in response to other influences. We present evidence suggesting that a long-run relationship between diamond production, CSO inventory, and final diamond demand does exist, as would be suggested by the supply management strategy. We then use an error correction model to search for any evidence that the Russian leaks can be related to short-run changes in CSO decisions about inventory, the quantity of carats sold, or the diamond price and find that only inventory appears to have been affected by the leaks.

Although applying cointegration techniques to a microeconomic problem is uncommon, we believe it has some advantages in this case. We are principally interested in separating long-run from short-run movements in a single time series, namely, the CSO inventory. This approach allows us to do so without having to specify a model of De Beers' buying and selling decisions that incorporates their calculations about how different possible responses to cheating might affect their future relationship with Russia or with other cartel members or might threaten the popular image of diamonds in the eyes of consumers.

In the next section, we briefly review the steps involved in establishing cointegration among variables, of estimating the long-run, cointegrated relationship(s), and finally of estimating the associated short-run relationships, known as the error correction model. We then return to the diamond industry, describing the variables we expect to be cointegrated, and why. A section describing the data follows, and we then present our empirical analysis. We end with a short discussion of the results and some information about recent developments in this industry.

2. Methodology (7)

The first step in a cointegration study is to identify variables that are potentially cointegrated, that is, that move together over time. To be part of a cointegrated relationship, a variable must have the property of being nonstationary, in particular, the variable must be stochastically trended. Consider, for example, the variable [x.sub.t], where

[x.sub.t] = [alpha] [x.sub.t-1] + [[epsilon].sub.t]

and [[epsilon].sub.t] is white noise with zero mean. If [absolute value of [alpha]] < 1, then [x.sub.t] is mean-reverting and thus has no stochastic trend over time: the variable is said to be stationary, or I(0). But if [alpha] = 1, then the history of this variable strongly affects its current value, causing a stochastic trend. (8) The variable is thus nonstationary, and potentially could be cointegrated with other nonstationary variables. Nonstationary variables are said to be integrated of order n, or I(n), if differencing n times induces stationarity. In our example, a single difference operation creates [DELTA][x.sub.t] = [x.sub.t] - [x.sub.t-1] = [[epsilon].sub.t], which is stationary, so n = 1 and [x.sub.t] is I(1).

Once nonstationarity is established for each variable of interest, we check statistically for the existence of relationships among them, that is, for evidence that the variables move together over the long term. Such a relationship is called a cointegrated vector of the variables involved and is a special case: cointegration implies that there is a weighted average of the nonstationary variables that is itself stationary, that is, that has no stochastic trend. Suppose, for example, that in the long run [x.sub.1], and [y.sub.t] are related so that [y.sub.t] = b[x.sub.t] + [v.sub.t], where [v.sub.t] is stationary. Then the weighted average [y.sub.t] - b[x.sub.t] is stationary and the two variables are cointegrated.

Because the weighted average series is stationary, the relationship among the variables in a cointegrated vector remains stable over the long run, although at any particular time period variables might deviate from it. In economic terms, the idea is that a set of cointegrated variables can depart from a common trend in the short and intermediate run but, in the long run, will return to an equilibrium path. (9)

Statistical techniques only allow us to identify whether (and how many) such relationships exist within the data. We then use our knowledge of the industry and of economic theory to suggest restrictions that allow identification of the individual vectors. After testing for the acceptability of these restrictions, we can then find numerical estimates of the vectors, which show how different sets of variables move together in a long-run relationship.

Once any long-term relationships have been identified, we estimate an error correction model that consists of a particular specification of the changes in each of the cointegrated variables. (10) Suppose again that [x.sub.t] and [y.sub.t] are cointegrated, and let us concentrate on [x.sub.t]. Changes in [x.sub.t] are specified as

[DELTA][x.sub.t] = [alpha][DELTA][x.sub.t-1] + [beta][DELTA][y.sub.t-1] + [eta][z.sub.t] + [gamma]E[C.sub.t-1] + [u.sub.t],

where [z.sub.t] is not cointegrated with [x.sub.t] and [y.sub.t] but could be related to changes in [x.sub.t] and where E[C.sub.t] = [y.sub.t]--b[x.sub.t]. That is, current changes in the variable [x.sub.t] could be affected by lagged changes in itself (here just one lag) or lagged changes in [y.sub.t] (i.e., in the variable with which it is cointegrated). It is also possible to add I(0) variables, here [z.sub.t], to the right-hand side to test whether they are related to short-run changes in [x.sub.t]. Finally, E[C.sub.t-1] (the error correction term) controls for current changes in [x.sub.t] that represent adjustment back toward its long-run relationship with other variables and is calculated with the use of the cointegrated vector linking x to those other variables. In sum, the error correction model estimates how current changes in [x.sub.t] are the result of (i) recent changes in itself and in other variables with which it is cointegrated, (ii) changes in variables with which x is not cointegrated, and (iii) adjustments in response to deviations from long-run equilibrium.

3. The Diamond Cartel

We begin by thinking of the CSO as a dominant firm with a fringe of independent suppliers. In such a model, the dominant firm chooses its price and output to maximize profit, taking into account the supply response of the fringe. Dynamic versions of the model involve the dominant firm making price and output choices that trade off short-term profits against the incentives given to fringe firms to expand. The CSO's pricing decisions are restricted, however, by its strong interest in preventing reductions in diamond prices. Furthermore, even aside from the fringe, the firm does not perfectly control the supply of rough diamonds but instead represents a cartel of diamond-mining firms and nations. In this section, we describe how De Beers has responded to these challenges, and why, as a result, we expect to find cointegrating relationships among the CSO inventory, world diamond production, the quantity of diamonds the CSO sells, diamond prices, and growth in final diamond demand.

De Beers' control of the diamond market was originally based on its near monopoly of diamond mines in South Africa, but today the firm's wholly or jointly owned mines represent only about 40% of the total world supply. As its production share slipped, De Beers drew new suppliers into the cartel with contractual arrangements that allowed it continued sway over much of the world's supply of rough diamonds, about 60-65% during the period of our study (Picton 1996; Harvard Business School 1998). The contracts call for the producers to sell their rough diamonds to the CSO. Although actual contracts with partners are secret, it appears they guarantee a certain amount of sales at minimum prices and thus provide members with the valuable assurance of a steady stream of revenue (Johnson, Marriott, and von Saldern 1989). The contracts apparently do give the CSO some leeway to reduce purchases in particularly weak markets, relieving some of the pressure on the stockpile, but given that many cartel members count on the payments, it is generally presumed that the firm usually fully exercises its purchase rights (Lenzen 1970; Harvard Business School 1998). Diamonds that De Beers does not buy are inventoried by producers or, depending on their arrangement with De Beers, sold independently in the market.

In addition to its usual purchases from cartel members, the CSO also regularly purchases additional rough diamonds in the open market. The diamonds that appear in this market consist of the production of independent mines (e.g., mines in Brazil, Venezuela, Ghana, and Sierra Leone), cartel members' production that is sold outside the cartel by agreement, leaks by cartel members, and stolen diamonds. (11) CSO purchases are not public information, but industry experts suggest that the firm buys enough to increase its share of rough from 60% to 65% up to 75% of all rough diamonds mined. Some of those same experts emphasize that the CSO might buy more, enough so that it controls 80-85% of the rough market (see Johnson, Marriott, and von Saldern 1989). In sum, although De Beers is not the single dominant source of mined diamonds, it has maintained control over much of the world's supply because the CSO contracts and open market purchases ensure that much of the rough ends up flowing into the CSO inventory.

De Beers' other challenge has been to prevent retail diamond prices from falling as the supply of diamonds expanded. The firm's answer has been to finance enormously successful advertising campaigns, at roughly the level of $200 million per year (Hart 2001), despite the cartel not being involved in the retail diamond business (and despite the free ride for noncartel diamond sellers on this advertising). (12) De Beers' advertising has successfully fostered and maintained a link between marriages and the demand for diamonds with the diamond engagement ring, and more recently, De Beers has been successful in introducing new products, such as the eternity ring in the 1970s, the tennis bracelet in the 1980s, the diamond pendant in the 1990s, and currently the fight-hand ring. (13)

The CSO inventory forms a cushion between the inflow of rough diamonds and the outflow to about 200 diamond cutting and polishing firms, expanding and contracting to ensure stable diamond prices. Firms in other industries have allowed their inventories to rise, curtailing sales so as to maintain cartel prices in response to severe downturns, although those smoothing activities have tended to be relatively short lived and have not generally involved purchases of excess supplies by those firms (Scherer and Ross 1990). In the case of diamonds, we hypothesize that De Beers has maximized long-run profits, despite its incomplete control of supply, by allowing potentially large fluctuations in CSO inventories for longer periods. (14)

Although we do not model them explicitly, the firm's long-run inventory management decisions would depend on its expectations regarding its own and others' exploration and production activities, its ability to acquire or negotiate partial control of new supplies, the cost of open market purchases and of financing the inventory, and its expectations about the effectiveness of its own advertising to encourage demand. Thus, we expect to find a long-run equilibrium relationship linking the CSO inventory, world diamond production, and the final demand for diamonds that reflects this long-run profit maximization by De Beers. (15)

We also include the quantity of diamonds sold by the CSO and the diamond price set by the CSO among the variables we examine for cointegration. Certainly they should be related to each other, although the demand for diamonds is fairly inelastic (von Saldern 1992). However, world production should also be affected over time by the price and the quantity sold by the growth in demand. (Given the goal of price stability, we expect that in the long run, the quantity sold might be more strongly associated with demand growth than with price.) Furthermore, if these variables are cointegrated, we can then use an error correction model to check whether the Russian leaks appeared to affect them in the short run. (16)

The Russian Diamond Leaks

We use the error correction model to examine whether the Russian diamond leaks in the 1990s have short-run effects on the CSO inventory in particular, but also possibly on the quantity of diamonds sold, or the diamond price, depending on the cartel's reaction to those leaks. We expect to find that De Beers did not respond to these leaks aggressively, hut instead continued its supply management strategy, increasing its intake of diamonds to mop up "excess supply." As stated above, the firm itself claimed that it avoided purchasing leaked diamonds, which would have put downward pressure on diamond prices. However, in either case, the CSO might have altered the quantity of diamonds it was itself releasing onto the market, either downward to counteract the effects of leaked diamonds it had not purchased on the price, or alternatively upward, to punish the cheaters.

Because data on the leaks are unavailable, we assume that they were determined mostly by the condition of the Russian economy, and we use the Russian Government's budget deficit to proxy this condition. (17) The worse the economy or greater the budget deficit and need for hard currency, the more diamonds we expect to have been released. Use of the Russian budget deficit also allows for the possibility that leaks occurred at other times of fiscal pressure. (18)

4. Variables and Data Sources

We estimate our model with annual data from 1973 through 2001, the earliest and the latest years we could get information on all our variables. We expect to find a long-run relationship between the CSO inventory, diamond production, and diamond demand. The variable [I.sub.t] is the value of the CSO inventory in year t: we obtained inventory data, in current U.S. dollars, from various issues of the De Beers Annual Report and Annual Review, from Jones (1985) and from Harvard Business School (2000). The variable [PROD.sub.t] is world production of diamonds. We obtained estimates of the annual world production of gemstones (which include near- and cheap-gem qualities), measured in carats, from various issues of the U.S. Bureau of Mines, Mineral Commodity Summaries.

We use two variables to capture shifts in diamond demand: marriages and per capita income, both for the United States. Diamond sales in the United States represent from 30% to 40% of the world market in the period of our analysis (Ariovich 1985; Hart 2001), so we use two variables--MA[R.sub.t], the number of U.S. marriages in year t, and D[I.sub.t], the per capita disposable income in the United States in year t--as proxies for diamond demand. (19) Data on the number of U.S. marriages is from the Statistical Abstract of the United States (2002), published by the U.S. Department of Commerce, and data on the per capita disposable income for the United States was obtained from the U.S. Department of Commerce Survey of Current Business.

We are also interested in the possible long-run relationships between these variables and [Q.sub.t], the quantity of diamonds the CSO sells, and [P.sub.t], the price that it sets. Data on CSO sales of rough diamonds, in U.S. dollars, are from Harvard Business School (1998), Doshi (1998), various issues of the De Beers Annual Report and Annual Review, and the website of the South African firm E-Data (Pty.) Ltd., an Internet-based provider of financial information. (20) Data on rough diamond prices are not publicly available. However, von Saldem (1990) was able to observe them for one year and extrapolate to other years according to announced price increases. We constructed an index corresponding to the average per-carat price for gem and near-gem diamonds with the use of von Saldern's data for 1973 through 1989 and the announced percent changes in prices found in Bates (1996), Sielaff (1998), Costanza (1998, 1999), Indian Express Newspapers (Bombay) Ltd. (1999), Diamonds and Jewelry View (2000), Weldon (2000), Muller (2001), Rapaport (2001), and Goldstein (2002). (21)

We constructed the series on the Russian budget deficit, [RBD.sub.t], from a variety of sources because the official statistics reported by the Russian government seemed rather inconsistent. For the years 1976-1997, a back-up source was sought for most years of the study, and Russian publications (rather than general international sources such as the Financial Times or Wall Street Journal Europe) were primarily employed. (22) Data for the years 1973-1975 and for 1998-2001 are from Handbook Russia 2000 (Federal State Statistics Service 2000), the Center for Strategic and International Studies (2002), and The Statesman's Yearbook (various editions). Because Russia's reported dollar/ruble exchange rate was often unreliable or suspect, we decided to use the black market rates published by the Worm Currency Yearbook (Cowitt 1985, 1991; Cowitt, Edwards, and Boyce 1996) to convert to hundreds of billions of U.S. dollar equivalents.

The Consumer Price Index (1982-84 = 100) was used to deflate data on rough diamond prices, disposable income in the United States, the Russian budget deficit, and the dollar-denominated inventory held by the CSO. Table A1, column 1 in the Appendix lists the means and standard deviations of the variables used in the final estimations.

5. Empirical Analysis (23)

We first tested our variables to see whether they were nonstationary and thus possibly cointegrated. Both graphical analysis and the augmented Dickey-Fuller test suggested that inventory, production, disposable income, marriages, prices, and quantity sold are nonstationary. We tested the Russian budget deficit series and found the evidence for nonstationarity mixed. (Here, we assume that RBD is a stationary variable, but our qualitative conclusions are largely unaltered if we consider RBD as an I(1) variable that belongs in a cointegrating relationship with inventory.) We tested to see whether, as we assumed, marriages and disposable income are exogenous data series and failed to reject that hypothesis. All the other variables are plausibly linked, and we therefore treat them as endogenous.

Having identified inventory, production, disposable income, marriages, prices, and quantity sold as nonstationary, we then tested to see whether any were cointegrated. Unfortunately, collinearity among our variables forced us to drop marriages from the model, although our overall conclusions were unaltered. Evaluation of the data series suggested the existence of three cointegrated vectors.

Having established the existence of these vectors, it is necessary to impose restrictions on some of the variable coefficients to identify them. Each vector is identified by setting the coefficient of one of the variables to 1 (normalizing) and setting the coefficients of two other variables to 0. These choices of restrictions are guided by our hypotheses about the cartel and by basic economic theory; the likelihood ratio test of the restrictions suggests that the restrictions we imposed are valid.

We identified the first vector by normalizing the coefficient of inventory to 1 and setting the coefficients of price and quantity to 0. These restrictions allow us to focus attention on the key long-run relationship that we want to control for: that of any long-term smoothing behavior by the CSO. With the use of the Johansen maximum likelihood procedure, we estimate a long-ran equilibrium relationship among the remaining variables as

ln [I.sub.t] = 1.2586 ln [PROD.sub.t] - 3.1278 ln [DI.sub.t] +
               (0.3108)                 (1.6345)

38.330 [R.sup.2] = 0.54. (1)
(17.794)

(Standard errors are in parentheses, with [R.sup.2] computed as the squared correlation between the observed and fitted values of In It.) Given De Beers' supply management strategy, it is no surprise to find that the vector suggests a long-run direct relationship between inventory levels and world production, and a long-ran inverse relationship between inventory levels and our demand shift variable, disposable income. Over our sample period, a 1% increase in world production leads to a 1.26% increase in inventory and a 1% increase in disposable income leads to a reduction of 3.13% in inventory. (24)

We are also interested in controlling for any long-run behavior in quantity and prices, so that we can check for short-run fluctuations with the error correction model. Given that the CSO tends to keep diamond prices stable over time, we expect that shifts in demand might be more directly related to quantity sold rather than price. We therefore identify the second vector by normalizing the coefficient of quantity to 1, and setting the coefficients on price and world output to 0. The resulting vector is

ln [Q.sub.t] = -0.17289 ln [I.sub.t] + 1.7462 ln [DI.sub.t] + 19.717
                (0.0900)               (0.3187)               (3.0865)

[R.sup.2] = 0.72. (2)

We find that quantity sold is negatively and significantly related to inventory and positively and significantly related to disposable income: a 1% increase in the dollar inventory level implies a 0.17% decrease in quantity supplied, whereas a 1% increase in disposable income is associated with a 1.75% increase in quantity supplied. The first result implies that long-run inventory levels and sales are inversely related; the second seems reasonable given that diamonds might well be termed a luxury item with a demand particularly sensitive to income fluctuations.

For the third vector, we normalize price to 1 and set the coefficients of inventory and world production to 0. The coefficient on disposable income was statistically insignificant and thus was dropped from the relationship. We find that

ln [P.sub.t] = -0.1559 ln [Q.sub.t] + 0.3735 [R.sup.2] = 0.0006. (3)
                (0.1263)              (0.4360)

Over the long term, a 1% increase in quantity leads to a 0.16% decrease in price. But the size and statistical insignificance of the coefficient of ln [Q.sub.t] and the exceptionally low [R.sup.2] indicate that prices are insensitive to changes in quantity. (25) Again, this seems to match a model of long-run CSO behavior in which the firm responds to changes in demand variables by changing quantity sold more than price.

Having identified these long-run equilibrium relationships among these variables, we are able to estimate an error correction model that allows us to examine the effect of Russian leaks, as proxied by the Russian budget deficit, on changes in the CSO's inventory, prices, and the quantity sold. The full error correction model includes an equation for each endogenous cointegrated variable, with an error correction term included for each long-run relationship found in the data. Thus, we estimate four equations, each showing how current changes in a variable can be associated with current changes in other variables, whether cointegrated or not, as well as with adjustments back into long-run equilibrium relationships. The details are again found in the Appendix, and we include here only those terms that were statistically significant at the 10% level. (26) The estimated system is shown in Equations 4-7.

[DELTA] ln [I.sub.t] = 0.3099 [DELTA] ln [PROD.sub.t-1] + 1.1295 [ECP.sub.t-1] + 0.9914[RBD.sub.t] [R.sup.2] = 0.65 (4)

[DELTA] ln [Q.sub.t] = 0.8412 [DELTA] ln [P.sub.t-1] - 0.3508 [DELTA] ln [PROD.sub.t-1] - 0.6798[ECP.sub.t-1] - 0.8811[ECQ.sub.t-1] - 0.1872[ECI.sub.t-1] [R.sup.2] = 0.67 (5)

[DELTA] ln [P.sub.t] = -0.1371[ECI.sub.t-1] [R.sup.] = 0.37 (6)

[DELTA] ln [PROD.sub.t] = 1.3761 [DELTA] ln [P.sub.t-1] - 0.4555[ECQ.sub.t-1] + 0.2316[ECI.sub.t-1] [R.sup.2] = 0.42 (7)

where [DELTA] ln [P.sub.t] = ln [P.sub.t] - ln [P.sub.t-1], [DELTA] ln [Q.sub.t] = ln [Q.sub.t] - ln [Q.sub.t-1], [DELTA] ln [I.sub.t] = ln [I.sub.t] - ln [I.sub.t-1], [DELTA] ln [PROD.sub.t] = ln [PROD.sub.t] - ln [PROD.sub.t-2], [ECP.sub.t-1] + 0.1559 ln [Q.sub.t-1] - 0.3735, [ECQ.sub.t-1] = ln [Q.sub.t-1] + 0.1729 ln [I.sub.t- 1] - 1.7462 ln [DI.sub.t-1] - 19.7166, and [ECI.sub.t-1] = ln [I.sub.t-1] - 1.2586 ln [PROD.sub.t-1] + 3.1278 ln [DI.sub.t-1] + 38.3302.

Two findings are of principal interest concerning the short-run changes in these variables. The first is that the Russian budget deficit is positively related to short-run changes in the inventory: a $1 billion increase in RBD is associated with about a 1% increase in the CSO inventory, holding other influences constant. (Recall that [DELTA]ln [Y.sub.t] approximates the growth rate of [Y.sub.t].) We also ran simulations with RBD set to $20 billion, the largest deficit observed during the fiscal crisis of the 1990s, and all other variables set to their means. The simulations show that the value of ln(I) increases from 2.68 to 3.01 within a few years, implying a 39% increase in the CSO inventory, quick increases that we see in the inventory data. To the extent, then, that RBD is a good proxy for Russian diamond leaks, it appears that the CSO did respond by increasing purchases of diamonds and allowing its inventory to rise.

The second finding of interest is that the RBD variable is not significantly related to any of the other cointegrated variables: in particular, changes in neither quantity sold nor price appear associated with the RBD. This suggests that much of the cartel response to the leaks is represented by the changes in inventory; there is no evidence of any aggressive price or output response.

Other results for the short-run dynamics are mostly intuitive. First, short-run growth in disposable income has no apparent affect on price, sales, inventory, or production, suggesting that De Beers mostly ignores nonsustainable growth or declines in income in its price and output decisions. Second, an increase in price is associated with increases in future sales. Third, an increase in world production is associated with decreases in future sales but increases in inventory: a 1 percentage point increase in the rate of world production results in a 0.33% reduction in the growth of CSO sales and a 0.33% increase in the rate of inventory accumulation. This appears to be evidence of the same sort of smoothing behavior seen in the long-run relationships but carried out in response to short-run deviations. If world production of diamonds temporarily increases, De Beers appears to decrease its own sales (presumably to maintain gem prices) and to absorb some of that production into its inventories. Finally, an increase in price leads to future increases in world production.

The signs and magnitudes of the coefficients on the error correction terms are likewise mostly intuitive. If price is above its long-run sustainable path, then growth in sales will subsequently decline and inventories will increase. (27) Furthermore, downward pressure is exerted on future sales growth when current sales are above their long-run equilibrium path: the large magnitude of the coefficient on [ECQ.sub.t-1] in Equation 5 implies that deviations from the long-run equilibrium growth in sales are apt to be short lived. Both of these results seem compatible with cartel management of inventories, prices, and quantities aimed at maintaining price levels. Observe too that downward pressure is exerted on world production when CSO sales are above their long-run equilibrium path.

We also see that if inventory levels are above their long-run equilibrium path, then growth in prices moderates. The results show that unexpected inventory buildups are also associated with slower growth in sales, but with faster growth in world production, suggesting that world producers actually took advantage of De Beers' willingness to buy during periods of inventory excess. These effects are relatively small and hence somewhat economically insignificant, but they do lend additional support to our view of De Beers as a firm willing to incur large inventory accumulations to support prices. That is, inventory appears to serve as a buffer both in the long run, as the cointegration results show, and in the short run: only an organization like De Beers with immense financial capital could afford to adopt such a strategy over long periods of time.

6. Discussion

The principal goal of this paper was to investigate how the diamond cartel responded to massive Russian cheating in the mid 1990s. To do so, we first estimated a long-run relationship between inventory, world production, and final demand growth that allowed us to control for this aspect of cartel behavior when searching for short-run responses to the leaks through estimation of an error correction model. The error correction model that we then estimate substantiates the existence of the long-run equilibrium we hypothesized, and which we believe reflects long-run profit maximization by De Beers.

More to the point, the error correction model gives us our key finding, namely that the Russian budget deficit was associated with contemporary changes in the CSO inventory, but not with such changes in diamond prices or quantity sold. Together our results suggest that De Beers followed a long-run smoothing strategy and that the firm did not waiver from this strategy during the 1990s despite considerable anecdotal evidence that the Russian coffers were substantially depleted during this period and despite De Beers' reputation for aggressive responses to cheating.

Our findings conflict with the stated desire of De Beers to avoid buying rogue Russian diamonds for its inventory. News reports suggest that some of the rogue Russian diamonds were labeled as Zairian to legitimize their sale (Kaplan and Caryl 1998). Although this might have been a way for the CSO to save face, it is difficult to believe that they were deceived, given the volume of Russian leaks, given that Russian diamonds were generally of much higher quality than those from Zaire, and especially given that De Beers was arguing with Russia about leaks at the time. (28)

In sum, the Russian Federation seems to have succeeded in capturing some of the cartel profits through the willingness of the CSO to buy their leaked diamonds on the open market. De Beers apparently gambled that they could weather the storm and maintain order in the diamond markets, particularly protecting diamond prices. Although the diamond cartel seemed to survive Russian cheating, the cost was high: the CSO inventory rose to its highest levels ever and was put under additional stress when the Asian financial crisis of 1997 reduced final demand for diamonds. (29) Furthermore, other developments in the 1990s, including international outrage over blood diamonds fueling African civil wars and rich diamond discoveries in Canada, presented new challenges to the cartel's control of both demand and supply of the world's diamonds. Subsequent decisions by De Beers suggest that the firm no longer believed that its traditional role managing the diamond market was viable.

De Beers underwent a significant review of its long-term strategy and announced in July 2000 that it would abandon its supply management policy (Harvard Business School 2000; Weber 2001). Instead, De Beers has opted for a new strategy based on differentiating its diamonds with a microscopic brand (Bergenstock and Maskulka 2001) so as to become the "supplier of choice" (Guerrera et al. 2000). If successful, this differentiation strategy would strengthen the cartel and De Beers' place within it by cashing in on the strong name recognition of the De Beers brand, ending the flee ride that De Beers advertising had always given to diamonds not sold through the CSO, and allowing the CSO to charge a premium for the cartel's diamonds. The value of belonging to the cartel will increase, and the return to leaking diamonds will decrease, giving cartel members new incentive to remain cooperative. The CSO will no longer have to finance huge inventories to stabilize the prices of all diamonds.

In another break with its traditional strategy, De Beers has begun moving into retail sales of diamonds, announcing in 2000 a joint venture with LVMH Moet Hennessy-Louis Vuitton, a luxury goods marketer. Perhaps as a result, the firm pleaded guilty in July 2004 to a charge of fixing prices for industrial diamonds in the United States, a charge first made in 1994. The settlement, which involves a maximum fine of $10 million, has freed De Beers executives to travel and live in the United States, the most important retail diamond market.

It remains to be seen whether customers can be persuaded to pay more for a diamond with a De Beers' brand, but initial test market results appeared favorable, and De Beers might maintain enough leverage to ensure the cartel's survival. Yet, De Beers might not have to rely only on the success of the new strategy. Record sales in 1999 allowed the CSO to reduce its inventory by over 20% in a single year. In addition, shareholders recently approved an offer to take De Beers private (Jewelers' Circular Keystone 2001), which should reduce pressure for short-term gains and allow the firm, should it choose, to return to some version of the long-run supply management strategy to which it has clung so tenaciously for over a century. We simply must wait on events to see how completely the new strategy displaces the old in this period of change.

Appendix

The Johansen maximum likelihood procedure was employed to estimate the relationship among our variables: ln P, ln Q, ln DI, ln MAR, ln I, ln PROD, and RBD. Graphical analysis revealed a trend in all of the variables but RBD, the Russian budget deficit. As demonstrated in Figure A1, RBD has no apparent trend, but we used the augmented Dickey-Fuller test (without a trend term) to formally test whether RBD is stationary. At the 5% significance level, we do not reject the null hypothesis of nonstationarity, but this could be because of the low power of the Dickey-Fuller test. With a critical value of somewhere between -2.60 and -2.63 and a calculated value of -2.6181, the null hypothesis is on the cusp of being rejected at the 10% significance level. Too, the least squares regression of RBD on its lagged value (along with two lagged differences) suggests that RBD is stationary. The coefficient on the lagged value of RBD was a mere 0.64. For the other variables, we employed the augmented Dickey-Fuller (ADF) test with a trend term. The maximum lag length was set equal to 2 and the results are found in Table A1.

[FIGURE A1 OMITTED]

From Table A1, the null hypothesis of nonstationarity is not rejected at the 5% significance level. The Schwarz Bayesian criterion (SBC) indicates that ADF(1) is a more appropriate test than ADF(2). We thus conclude from Figure A1 and Table A1 that all of our time series, with the possible exception of RBD, are first difference stationary. Here, we will model RBD as a stationary endogenous variable, but we note that our qualitative conclusions about the Russian budget deficit remain the same regardless of our decision concerning RBD.

Marriages and disposable income are treated as exogenous I(1) variables, whereas the Russian budget deficit is classified as I(0). To test the exogeneity assumption, we determined whether a cointegrating relationship exists among ln DI and ln MAR. We also included RBD as an I(0) variable in the possible relationship and "allowed a maximum of two lags in the vector autoregression. If the I(1) variables are exogenous, then no cointegrating relationship should exist among them. For a vector with no trend or intercept, the likelihood ratio value based on the maximal eigenvalue statistic (trace statistic) was 3.77 (4.91) for the alternative of one cointegrating vector against the null of zero cointegrating vectors. The 95% critical value was 14.88 (17.86), and we conclude that there exists no cointegrating vector between the I(1) exogenous variables.

We then jointly identified the cointegrating vectors from a vector autoregression of order 2, treating ln P, ln Q, ln I, and ln PROD as fully endogenous and ln DI and ln MAR as exogenous. The likelihood ratio value based on the maximal eigenvalue (trace) statistic is 22.5032 (28.8509) for r = 3. The 95% critical value is 21.920 (30.46), and the 90% critical value is 19.67 (27.58). We conclude that there exist three cointegrating vectors. The SBC model selection criterion validates this conclusion. Unfortunately, collinear variables forced us to drop ln MAR from the cointegrating relationships. After dropping the variable we again found evidence of r = 3 cointegrating vectors by using the 90% critical value for the test statistics or by using the SBC model selection criterion. With the use of a general-to-specific modeling strategy and after imposing one overidentifying restriction, the final maximum likelihood estimates for a vector autoregression of order 2, VAR(2), are reported in Table A2.

From Table A2, we see that the three overidentifying restrictions appear valid on the basis of the chi-square statistic. The [R.sup.2] value is computed as the squared correlation between the observed and fitted values. Note that [R.sup.2] for the price equation is very low, implying a weak relationship between price and quantity. For clarity, the corresponding equilibrium conditions implied by the three vectors are shown in Equations A1-A3.

ln [I.sub.r] = 1.2586 ln [PROD.suv.t] - 3.1278 ln [DI.sub.t] + 38.330 (A1)

ln [Q.sub.t] = -0.1729 ln [I.sub.t] + 1.7462 ln [DI.sub.t] + 19.717 (A2)

ln [P.sub.t] = -0.1559 ln [Q.sub.t] + 0.3735. (A3)

The corresponding error correction models are found in Table A3, and diagnostics for the error correction models are given in Table A4. Diagnostics for the error correction equations corresponding to [DELTA] ln [I.sub.t], [DELTA]ln [Q.sub.t], and [DELTA] ln [P.sub.t] have high p values and thus do not indicate any specification problems. There is possibly a functional form or heteroskedasticity problem for the final error correction equation corresponding to [DELTA] ln PROD. This did not overly concern us because (i) with so many diagnostics, it is likely that a few of these will have low p values even when the model is acceptable, (ii) the variable involved, [DELTA] ln [PROD.sub.t], was not among those coefficients that were normalized in the cointegrating relationships from Table A2, and (iii) our conclusions concerning the Russian budget deficit appear to be robust across a number of specifications and not just those reported here.

Table A1. Augmented Dickey-Fuller Tests (a)

Variable                Test Statistic      SBC

ln P
  mean = -0.253        ADF(1) = -2.9111   19.1259
  Standard deviation   ADF(2) = -2.7514   17.5962
    (SD) = 0.157
ln Q
  mean = 3.47          ADF(1) = -2.6744    5.8790
  SD = 0.261           ADF(2) = -3.0548    5.3097
ln DI
  mean = -9.04         ADF(1) = -3.0129   69.3123
  SD = 0.138           ADF(2) = -3.1214   68.2668
ln MAR
  mean = 7.75          ADF(1) = -1.3925   64.8494
  SD = 0.040           ADF(2) = -1.6445   63.8632
ln I
  mean = 2.68          ADF(1) = -2.0533    7.5062
  SD = 0.610           ADF(2) = -2.2479    6.3545
ln PROD
  mean = 9.91          ADF(1) = -1.9374   -2.5841
  SD = 0.702           ADF(2) = -1.4610   -3.7717
RBD
  mean = 0.042         ADF(1) = -2.6181   41.2646
  SD = 0.067           ADF(2) = -1.9453   39.9527

(a) The ADF critical value is -3.5731 for each variable
except RBD, for which the critical value is -2.9665.
The SBC criterion indicates that ADF(1) is a more
appropriate test than ADF(2).

Table A2. Estimates of Restricted Cointegrating Relations (a)

Variable    Vector 1 (ln I)    Vector 2 (ln Q)    Vector 3 (ln P)

ln P               .                  .             1.000 (none)
ln Q               .             1.000 (none)     0.1559 (0.1263)
ln I          1.000 (none)     0.1729 (0.0900)           .
ln PROD     -1.2586 (0.3108)          .                  .
ln DI       3.1278 (1.6345)    -1.7462 (0.3187)          .
Intercept   38.330 (17.794)    -19.717 (3.0865)   -0.3735 (0.4360)
[R.sup.2]        0.5447             0.7216             0.0006

(a) Standard errors are in parentheses. Likelihood ratio test
of restrictions: chi-square(1) = 1.6712 (0.196).

Table A3. Error Correction Models from a VAR(2) (a)

                                    [DELTA] ln [I.sub.t]

Regressor                   Estimate          SE            p

[DELTA]ln  [P.sub.t-1]      -0.6232         0.4630        0.193
[DELTA]ln  [Q.sub.t-1]       0.1872         0.1890        0.333
[DELTA]ln  [I.sub.t-1]      -0.1652         0.2131        0.447
[DELTA]ln  [PROD.sub.t-1]    0.3099         0.1538        0.057
[DELTA]ln  [DI.sub.t-1]      1.6561         1.4798        0.276
[ECP.sub.t-1]                1.1295         0.3144        0.002
[ECQ.sub.t-1]               -0.2682         0.3088        0.395
[ECI.sub.t-1]                0.0314         0.0940        0.742
[RBD.sub.t]                  0.9914         0.5702        0.097
                                       [R.sup.2] = 0.65

                                  [DELTA] ln [Q.sub.t]

Regressor                   Estimate          SE            p

[DELTA] ln [P.sub.t-1]       0.8412         0.4330        0.066
[DELTA] ln [Q.sub.t-1]       0.0021         0.1768        0.991
[DELTA] ln [I.sub.t-1]       0.1009         0.1993        0.618
[DELTA] ln [PROD.sub.t-1]   -0.3508         0.1438        0.024
[DELTA] ln [DI.sub.t-1]      0.8782         1.3841        0.533
[ECP.sub.t-1]               -0.6798         0.2941        0.031
[ECQ.sub.t-1]               -0.8811         0.2888        0.006
[ECI.sub.t-1]               -0.1872         0.0879        0.045
[RBD.sub.t]                  0.6524         0.5333        0.235
                                       [R.sup.2] = 0.67

                                   [DELTA] ln [P.sub.t]

Regressor                   Estimate          SE            p

[DELTA] ln [P.sub.t-1]      -0.0160         0.3885        0.967
[DELTA] ln [Q.sub.t-1]       0.1449         0.1587        0.371
[DELTA] ln [I.sub.t-1]      -0.0024         0.1789        0.990
[DELTA] ln [PROD.sub.t-1]   -0.1121         0.1291        0.395
[DELTA] ln [DI.sub.t-1]      0.6281         1.2420        0.618
[ECP.sub.t-1]               -0.3925         0.2639        0.152
[ECQ.sub.t-1]                0.0588         0.2592        0.823
[ECI.sub.t-1]               -0.1371         0.0789        0.097
[RBD.sub.t]                  0.0284         0.4785        0.953
                                       [R.sup.2] = 0.37

                                 [DELTA] ln [PROD.sub.t]

Regressor                   Estimate          SE            p

[DELTA] ln [P.sub.t-1]       1.3761         0.7128        0.067
[DELTA] ln [Q.sub.t-1]       0.4815         0.2910        0.113
[DELTA] ln [I.sub.t-1]      -0.0464         0.3281        0.889
[DELTA] ln [PROD.sub.t-1]   -0.2906         0.2368        0.233
[DELTA] ln [DI.sub.t-1]     -3.1393         2.2784        0.183
[ECP.sub.t-1]               -0.4726         0.4840        0.340
[ECQ.sub.t-1]               -0.4555         0.4754        0.349
[ECI.sub.t-1]                0.2316         0.1447        0.124
[RBD.sub.t]                 -0.0316         0.8779        0.972
                                       [R.sup.2 = 0.42]

SE, standard error.

(a) [DELTA]ln [P.sub.t] = ln [P.sub.t] - ln [P.sub.t-1];
[DELTA]ln [Q.sub.t] = ln [Q.sub.t] - ln [Q.sub.t-1];
[DELTA]ln [I.sub.t] = ln [I.sub.t] - ln [I.sub.t-1];
[DELTA]ln [PROD.sub.t] = ln [PROD.sub.t] - ln
[PROD.sub.t-1]; [DELTA]ln [P.sub.t-1] = ln
[P.sub.t-1] - ln [P.sub.t-2]; [DELTA]ln [Q.sub.t]
= ln [Q.sub.t-1] - ln [Q.sub.t-2]; [DELTA]ln
[I.sub.t-1] = ln [I.sub.t-1] - ln [I.sub.t-2];
[DELTA]ln [PROD.sub.t-1] = ln [PROD.sub.t-1] - ln
[PROD.sub.t-2]; [DELTA]ln [DI.sub.t-1] = ln [DI.sub.t-1]
- ln [DI.sub.t-2]; [ECP.sub.t-1] = ln [P.sub.t-1]
+ 0.1559 ln [Q.sub.t-1] - 0.3735; [ECQ.sub.t-1] = ln
[Q.sub.t-1] + 0.1729 ln [I.sub.t-1] - 1.7462 ln
[DI.sub.t-1] - 19.7166; and [ECI.sub.t-1] = ln
[I.sub.t-1] - 1.2586 ln [PROD.sub.t-1] + 3.1278
ln [D.sub.t-1] + 38.3302.

Table A4. Diagnostics for the Error Correction Models

                        [DELTA]ln [I.sub.t]

Test Statistic       d.f.   Chi-Square     p

Serial correlation    1       1.468      0.226
Functional form       1       0.005      0.944
Normality             2       1.042      0.594
Heteroskedasticity    1       0.393      0.531

                        [DELTA]ln [Q.sub.t]

Test Statistic       d.f.   Chi-Square     p

Serial correlation    1       0.462      0.497
Functional form       1       0.081      0.776
Normality             2       2.578      0.276
Heteroskedasticity    1       0.042      0.838

                        [DELTA]ln [P.sub.t]

Test Statistic       d.f.   Chi-Square    p

Serial correlation    1       0.659     0.417
Functional form       1       0.290     0.591
Normality             2       3.440     0.179
Heteroskedasticity    1       2.194     0.139

                       [DELTA]ln [PROD.sub.t]

Test Statistic       d.f.    Chi-Square      p

Serial correlation    1        0.646       0.422
Functional form       1       10.80        0.001
Normality             2        0.535       0.765
Heteroskedasticity    1        9.900       0.002

We thank James Picton for very helpful background information on the diamond industry and James Dearden for his comments and suggestions. Deily received support from a grant from the College of Business and Economics at Lehigh University funded by William W. Crouse III. Taylor gratefully acknowledges partial financial support from the Arthur F. Searing Fund.

Received June 2004: accepted November 2005.

References

Ariovich, G. 1985. The economics of diamond price movements. Managerial and Decision Economics 6:234-40.

Bates, Rob. 1996. "De Beers Raises Prices 3%." National Jeweler. 15 July. Accessed 1 May 2006. Available http:// www.natinnaljeweler.com/.

Bergenstock, Donna J. 2005. De Beers and the Diamond Trading Company: Their economic, political, and behavioral impact on the global diamond industry. Lewiston, NY: The Edwin Mellen Press.

Bergenstock, Donna J., and James M. Maskulka. 2001. The De Beers diamond story: Are diamonds forever? Business Horizons 44:37-44.

Center for Strategic and International Studies. 2002. "Net Assessment of the Russian Economy: The Russian Economy in September 2002--Highlights.'" CSIS Prospectus 3(Spring). Accessed 14 January 2003. Originally accessed at http:// www.csis.org/mseura/msecon.htm; hard copy available from authors.

Costanza, Frank. 1998. "De Beers Profits Fall; CSO Scales Back Allocations." National Jeweler. 16 March. Accessed 1 May 2006. Available at http://www.nationaljeweter.com/.

Costanza, Frank. 1999. "'U.S. Rough Diamond Prices on the Rise." National Jeweler. 28 September. Accessed 1 May 2006. Available http://www.nationaljeweler.com/.

Cowitt, Philip P., editor. 1985. World Currency Yearbook, 1984. Brooklyn, NY: International Currency Analysis, Inc.

Cowitt, Philip P., editor. 1991. World Currency Yearbook. 1988-1989. 1991. Brooklyn, NY: International Currency Analysis, Inc.

Cowitt, Philip P., Carolyn A. Edwards, and Elliot R. Boyce, editors. 1996. World Currency Yearbook, 1990-1993, 27th edition. Brooklyn, NY: Currency Data & Intelligence, Inc.

De Beers Annual Report. Various issues. De Beers Corporate Communications Department.

De Beers Annual Review. Various issues. Accessed 1 May 2006. Available at http://www.debeersgroup.com/debeersweh.

Defterios, John. 1996. "Diamond Talks to Begin in Russia." CNNfn, the Financial Network. 15 January. Available http:// cnnfn.cnn.com/archive/news/9601/15/diamonds/.

Diamonds and Jewelry View. 2000. "The Supply Choices of the Supplier of Choice." December. Originally accessed online at http://www.diamondsview.com/ed; hard copy available from authors.

Diebold, Francis X. 2004. The Nobel Memorial Prize for Robert F. Engle. Scandinavian Journal of Economics 106:165-85.

Doshi, Shreyas. 1998. Forum: Manufacturing--The Manufacturer's Tale--India. In The 3rd Annual Financial Times Diamonds Conference. Financial Times Conference in Antwerp, Belgium, 28 October. London: The Financial Times Limited, p. 6.

The Economist. 1998. De Beers is it. 349(19 December-1 January), pp. 89-90.

Engle, Robert F., and Clive W. J. Granger. 1987. Cointegration and error correction: Representation, estimation and testing. Econometrica 55:251-76.

Farrelly, Paul. 1996. The bear necessities; A traditional Kremlin fix seems to have saved the diamond market. The Independent (London), 3 March, p. B4.

Federal State Statistics Service. 2000. Handbook Russia. Moscow: State Committee of the Russian Federation on Statistics (Goskomstat). Accessed 1 May 2006. Available http://www.gks.ru/eng/bd.asp.

Genesove, David, and Wallace P. Mullin. 2001. Rules, communication, and collusion: Narrative evidence from the Sugar Institute case. American Economic Review 91:379-98.

Goldstein, Marc. 2002. "A Christmas Surprise." Diamonds.Net. 31 January. Accessed 1 May 2006. Available http:// www.diamonds.net/news/.

Gooding, Kenneth. 1997. New setting for old partners: Russia has little choice but to sign a deal with the leaders of the world's diamond cartel. Financial Times, London Edition 1, 11 February, p. 21.

Granger, Clive W. J. 1981. Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16:121-30.

Granger, Clive W. J. 1991. Developments in the study of cointegrated economic variables. In Long-Run Economic Relationships: Readings in Cointegration, edited by Robert F. Engle and Clive W. J. Granger. New York: Oxford University Press, pp. 65-80.

Guerrera, Francesco, Michael Holman, Andrew Parker, Sathnam Sanghera, and Nicholas Shaxton. 2000. De Beers: All that glitters is not sold. Financial Times, (London), 11 July, Special Report, p. 16.

Hart, Mathew. 2001. Diamond: The Histol), of a Cold-Blooded Love Affair. New York: The Penguin Group. Harvard Business School. 1998. De Beers Consolidated Mines Ltd. (A). Harvard Business School Case 9-391-076, revised 30 March.

Harvard Business School. 2000. Forever: De Beers and U.S. antitrust law. Harvard Business School Case 9-700-082, revised 20 April.

Indian Express Newspapers (Bombay) Ltd. 1999. "De Beers Rewrites Diamond Prices, Roughs Waver." 11 October. Accessed 2 January 2003. Orignally accessed at http://www.financialexpress.com/fe/daily/; hard copy available from authors.

Jewelers' Circular Keystone. 2001. "Shareholders OK De Beers Buyout." 18 May. Accessed 1 May 2006. Available http:// www.jckmagazine.com/.

Johnson, Charles J., Martyn Marriott, and Michael yon Saldern. 1989. World diamond industry: 1970-2000. Natural Resources Forum May:90-106.

Jones, Jim. 1985. De Beers paying price to keep hold on market. Houston Chronicle, 3 June, Business, p. 2.

Kaplan, David E., and Christian Caryl. 1998. "The Looting of Russia: An FBI agent and an honest Moscow cop stop the plundering of the national treasury." U.S. News Online, 3 August. Available http://www.usnew.com/usnews/issue/ 980803/3gold.htm/.

Kenney, Roy W., and Benjamin Klein. 1983. The economics of block booking. Journal of Law and Economics 26:497-540.

Lenzen, Godehard. 1970. The History, of Diamond Production and the Diamond Trade, translated by F. Bradley. New York: Praeger Publishers.

Levenstein, Margaret C. 1997. Price wars and the stability of collusion: A study of the pre-World War I bromine industry. Journal of Industrial Economics 45:117-37.

Muller, Emma. 2001. Dealers fear falling diamond prices. The Financial Times, London, edition 2, 15 June, p. 34.

Picton, James. 1996. Africa's position in world diamond production--Now and in the future. In Diamonds--New Horizons in Mines and Markets. Financial Times Conference in London, 7 October. London: FF Conferences, pp. 1-15.

Rapaport, Martin. 2001. "Weekly Market Comments 11/16/01." Diamonds.Net, I1 November. Accessed 9 November 2005. Available http://www.diamonds.net/news/.

Scherer, F. M., and David Ross. 1990. Industrial market structure and economic performance, 3rd edition. Boston, MA: Houghton Mifflin Company.

Sielaff, Whitney. 1998. "Major Players Say Diamond Market Will Remain Stable." National Jeweler.com, 17 November. Accessed 2 January 2003. Available http://www.nationaljeweler.com/.

Spar, Debora L. 1994. The cooperative edge." The internal politics of international cartels. Ithaca, NY: Cornell University Press.

The Statesman's Yearbook. 1975-76, 1980-81, 1985-86, 2003. Editions 112, 117, 122, edited by John Paxton; edition 139, edited by Barry Turner. New York: Palgrave Macmillan.

United States Department of Commerce. Various issues. Survey of current business. Washington, DC: Department of Commerce.

United States Department of Commerce. Bureau of the Census. 2002. Statistical abstract of the United States. Washington, DC: Department of Commerce, Bureau of the Census.

United States Department of the Interior. Various issues. Mineral commodity summaries. Through 1996: Washington, DC: Department of the Interior, Bureau of Mines. After 1996: Reston, VA: Department of the Interior, U.S. Geological Survey.

von Saldern, Michael. 1990. Price forecast for rough diamonds: A nonlinear optimization model of dominant firm behavior. Ph.D. dissertation, Colorado School of Mines, Golden, CO.

von Saldern, Michael. 1992. Forecasting rough diamond prices. Resources Policy March: 45-58.

Weber, Lauren. 2001. The diamond game, shedding its mystery. The New York Times, 8 April, section 3, p. 1.

Weldon, Robert. 2000. "De Beers To Raise Rough Prices." Professional Jeweler, 31 May. Accessed 4 November 2005. Available http://www.professionaljeweler.com/archives/news/2000.

(1) The CSO is wholly owned by De Beers. It has recently been renamed the Diamond Trading Company.

(2) Diamonds are graded on color, clarity, carats, and cut (shape). Although the CSO buys rough diamonds of all types, the gem- and near-gem-quality stones that are our principal interest represent more than 80% of the value of rough diamonds sold. These diamonds are used mostly to make jewelry.

(3) In fact, nominal prices have rarely fallen. De Beers has repeatedly reiterated its dedication to maintaining stable and rising diamond prices; see Sielaff (1998) for a recent example.

(4) Although we focus on cartel members, De Beers has displayed equally ruthless behavior toward downstream actors that it perceived as threatening the diamond market. For example, see Johnson, Marriott, and von Salderu (1989) and Spar (1994) for descriptions of the firm's response to downstream speculation in the early 1980s.

(5) See Spar (1994) for a discussion of this history.

(6) The Russian leaks were significant; average annual CSO sales of rough diamonds over 1993-1996 were $4.5 billion.

(7) We briefly review here the basics of cointegration techniques. Readers familiar with these techniques should skip to section 3. Readers looking for more information might start with Granger (1991) or Diebold (2004).

(8) Such a trend makes the use of common statistical approaches inappropriate because the series [x.sub.t], although smooth, rarely returns to an earlier value. A stationary variable, on the other hand, tends to fluctuate around a fixed mean value.

(9) "Equilibrium path" in this usage means that there are forces bringing the variables back into the long-term relationship. Those forces might be market based, but might also be the result of government actions or, in our case, the result of cartel actions.

(10) Granger (1981) and Engle and Granger (1987) show that a cointegrated set of variables must necessarily have an error correction representation and vice versa.

(11) Theft appears to be endemic at all stages of the supply chain (Hart 2001). Some of these sales represent "war" or "blood" diamonds, so called because of their use to finance violent insurgencies in African nations.

(12) Although not the focus of our interest, another, more immediate tool for maintaining prices has been the CSO's practice of no-negotiation sales to a select few diamond buyers (the famous "sights") by which they carefully manage the outflow of different grades of diamonds (see Kenney and Klein [1983] and Hart [2001] for descriptions). However, Kenney and Klein (1983) also argue that, aside from controlling prices, the CSO's sorting, valuing, and sales practices significantly reduce transaction costs and that these savings are an important element explaining the longevity of the CSO and its practices.

(13) We do not think of consumers as forward-looking agents whose full information about changes in diamond supplies and the CSO inventory causes them to adjust their valuation of diamonds. Rather, they are rational in their acceptance of diamond values given the information they have.

(14) Scherer and Ross (1990, p. 272) point out that storable goods are more likely to be kept in inventories until demand conditions warrant sale if fixed costs are high and the good's price is much greater than its marginal cost, conditions that obtain in the diamond industry.

(15) In theory, the interest rate should also play a role in determining the level of the inventory. Our empirical evidence, however, indicates that the real rate of interest has finite memory and thus would not belong in a cointegrated relationship. Neither does it appear that the interest rate belongs as an I(0) variable in the error correction representation. Thus, in the interest of parsimony, we decided to exclude the interest rate from our empirical analysis.

(16) However, we do not expect to find that CSO prices fell much, if at all, in response to the leaks. Bergenstock (2005) estimated a model with the cartel as a dominant firm and found no relationship between prices and Russian leaks.

(17) A variety of news stories draw links between the Russian budget deficit and sales of Russian diamonds, as well as precious metals (see, e.g., Farrelly 1996).

(18) See Spar (1994) for a description of the relationship between De Beers and the Soviet Union and for some evidence that at least one other episode of leaked diamonds in 1984 might have been prompted by Soviet fiscal necessity.

(19) We tried including Japanese marriages and Japanese per capita income as well because Japan is also a major diamond market. However, the variables did not add much additional information about the overall demand for diamonds, so in the interests of parsimony, we dropped them from the analysis.

(20) We find we can no longer access this website (http://www.edata.co.za.debeers/). However, these data are available on a piecemeal basis in the diamond industry press, as well as from the authors.

(21) Our price is an average of gem and near-gem prices because diamond mining yields far more near-gems than gem-quality stones; thus, both must be sold by the CSO. Because price increases are announced separately for gems and near-gems, we calculate a price by taking a weighted average of the prices for near-gems and gems, using weights based on those developed by von Saldem (1990).

(22) The final series was based on 12 different data sources (see Bergenstock [2005] for details).

(23) This section summarizes the results of the different parts of our analysis. Details of the econometrics and sources for the tests used can be found in the Appendix. All estimations were performed with Microfit 4.0 (Camfit Data, Ltd).

(24) Subtracting one standard error from the estimated coefficient on world production yields 0.95, a value that is perhaps more consistent with our intuition than a coefficient greater than one. But the point estimate of 1.26 is not unreasonable, given that world diamond production is larger than the production of the cartel.

(25) The Dickey-Fuller test rejects the null hypothesis of a unit root in the errors from Equation 3 at the 5% significance level. ADF(2) rejects at the 10% level. Thus, even though our [R.sup.2] is very small, these results conform to cointegration theory.

(26) There are two exceptions. Simulations not reported here indicate that the system is stable only when [ECQ.sub.t-1] and especially [ECI.sub.t-1] are included in the production equation, even though neither of these terms is statistically significant at the 10% level, so we include them.

(27) Our simulations revealed that the coefficient of 1.1295 on [ECP.sub.t-1] in the inventory equation did not cause long-run instability. But after a shock to the system, the return to equilibrium was somewhat faster if the said coefficient was 0.82 (i.e., the said point estimate less its standard error of 0.31).

(28) See, for example, Defterios (1996).

(29) An increasing share of the firm's equity was held by Americans, who were dissatisfied with the firm's long-run strategy and with the size of its inventory, which apparently cut into profits significantly (The Economist 1998; Harvard Business School 2000).

Donna J. Bergenstock, * Mary E. Deily, ([dagger]) and Larry W. Taylor ([double dagger])

* Muhlenberg College, 2400 Chew Street, Allentown, PA 18104-5586, USA; E-mail [e-mail].

([dagger]) Lehigh University, 621 Taylor Street, Bethlehem, PA 18015, USA; E-mail [e-mail]; corresponding author.

([double dagger]) Lehigh University, 621 Taylor Street, Bethlehem, PA 18015, USA; E-mail [e-mail].