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The viability of an "indirectly convertible" gold standard: comment.

I. Introduction

In a recent article in this journal, Dowd |1~ considers a monetary system which is a modification of the gold standard. In common with the gold standard, the value of currency is tied to that of gold at some given parity. But instead of undertaking to exchange its currency for gold, the currency issuing bank maintains the gold value of its issue by "indirect convertibility": redeeming its notes not into gold itself but into some other good known as a "redemption medium." The quantity of redemption medium offered for a unit of currency is equal in market value to the gold which would have been obtained in a direct conversion of a unit of currency at the given parity. The redemption medium could be any good other than gold and Dowd suggests that shares in some company might be convenient for this purpose.(1)

The virtue of this arrangement, it is claimed, is that it overcomes the weakness of a direct gold standard, that the currency issuing bank's fractional gold reserves may be insufficient to sustain convertibility. An indirectly converting bank does not redeem into gold, so that it need not carry gold reserves. And exhaustion of reserves of redemption medium would not imply suspension of convertibility because the bank (provided that it was solvent) would apparently be able to purchase redemption medium as needed in the market. As a result, so Dowd argues, the indirectly convertible gold standard would be less prone to banking panics than the direct standard, and would also exhibit less volatile interest rates.

In this paper we cast doubt on the viability of Dowd's scheme on the grounds that indirect convertibility could not be practiced by a bank whose currency is a medium of account for quoting prices of goods.(2)

II. Identification of the Medium of Account

Dowd's description of his scheme implies that there are several banks whose private currencies simultaneously coexist as media of exchange. For the purposes of this appraisal, however, it is the identification of the medium of account which is of importance. What unit is commonly used for expressing prices of goods, in particular the price of gold?

If indirect convertibility succeeds in tying the value of all currencies to gold, then any one of these currencies could be considered as the medium of account, as could gold itself. Our purpose here, however, is to investigate the viability of this method of ensuring the values of the currencies. This exercise requires that we allow the value of a currency to deviate from its chosen parity relative to gold, and then consider the dynamic process by which this deviation may be corrected. To assume that all currencies and gold are media of account would defeat this purpose.

Addressing this question of the identification of the medium of account forces us to engage in some discussion of trading behavior. We shall make the plausible assumption that there is one "dominant" currency in which prices quoted by traders are understood to be measured. Prices are not understood as expressing amounts of gold, since gold is not a medium of exchange. The price tag put on an article by a trader refers to the quantity of paper dollars of this currency, or paper claims (checks) on this currency, which he would be prepared to accept in exchange for his article.(3) It is, moreover, this currency price of the article which the trader adjusts in the face of changed supply or demand for his article, and he does not adjust this price unless induced to do so by changed supply or demand.

If some currency other than the dominant medium of account is tendered in exchange for an article, the traders' action is to convert the posted or contracted medium of account price at the moment of the transaction according to the observed market exchange rate between the currencies.

III. Indirect Convertibility for the Medium of Account

Consider then the operation of indirect convertibility for the bank whose currency, according to our above discussion, is the medium of account. Quoted market prices of goods are expressed in this bank's currency, and henceforth we shall use the term "dollar" to denote this currency exclusively.

Let the bank's chosen parity (the price of a unit of gold measured in its dollar currency) be |P*.sub.g$~. If the bank were practicing direct convertibility, it would offer conversion of each of its paper dollars into 1/|P*.sub.g$~ units of gold. Under indirect convertibility, the bank is committed to offer conversion of each of its paper dollars into an amount of redemption medium whose value, in the market, is equal to 1/|P*.sub.g$~ units of gold. Formally, this obliges the bank to observe the market price of redemption medium measured relative to gold, |P.sub.rg~, and to calculate its conversion rate of dollars to redemption medium |R.sub.r$~ as

|R.sub.r$~ = |P*.sub.g$~ |center dot~ |P.sub.rg~. (1)

The bank's dollar price of redemption medium, |R.sub.r$~, is thus its instrument which it adjusts continuously in order to compensate for observed changes in |P.sub.rg~.

By assumption, however, market prices of goods including gold and redemption medium are expressed in dollars, hence the bank cannot make direct observation of the relative price |P.sub.rg~. The bank must rather derive this price from observations of the market dollar prices of gold |P.sub.g$~ and redemption medium |P.sub.r$~ as

|P.sub.rg~ = |P.sub.r$~/|P.sub.g$~. (2)

Substituting equation (2) into equation (1), the bank's operating rule is |R.sub.r$~ = |P.sub.r$~(|P*.sub.g$~/|P.sub.g$~). (3)

Equation (3) shows that whenever the market dollar gold price |P.sub.g$~ deviates from the set parity |P*.sub.g$~, the dollar issuing bank sets its conversion price of redemption medium |R.sub.r$~ different from the market price of redemption medium |P.sub.r$~. To confirm that equation (3) correctly reflects indirect convertibility, suppose that |P.sub.g$~ has risen above |P*.sub.g$~, which implies that |R.sub.r$~ |is less than~ |P.sub.r$~. An agent could still buy gold indirectly at |P*.sub.g$~; he would do this by buying redemption medium (with his dollars) from the bank at |R.sub.r$~ then reselling the redemption medium at the higher market price |P.sub.r$~. The extra cash he receives in this way is exactly sufficient to compensate him for the price rise in |P.sub.g$~. Obviously, however, there is an opportunity for riskless arbitrage. An agent could multiply his stock of dollars by "round tripping" between the bank and the market for redemption medium.

Any difference between |P.sub.r$~ and |R.sub.r$~ would therefore be unsustainable. Assuming that the bank's indirect convertibility commitment is credible, the market price |P.sub.r$~ will always converge on |R.sub.r$~. With the bank offering sales of redemption medium at |R.sub.r$~, no market dealer in redemption medium would be prepared to buy at some higher price; conversely nobody would be prepared to sell at a lower price than the bank's. There is thus no scope for some dollar price of redemption medium to prevail which differs from |R.sub.r$~: the market "price takes" the bank's price.

We therefore have the circumstance that, when |P.sub.g$~ |is not equal to~ |P*.sub.g$~, the bank is obliged to hold |R.sub.r$~ different from |P.sub.r$~, yet the "market" ensures that |P.sub.r$~ is not different from |R.sub.r$~. It follows that, unless there is some mechanism by which changes in |R.sub.r$~ instantly cause correction of |P.sub.g$~ back to parity, the bank would be unable precisely to satisfy indirect convertibility as embodied in equation (3). In the absence of such a mechanism, if the bank insisted on trying to maintain indirect convertibility continuously, the above arguments imply that there would be unlimited changes in the price of redemption medium (both |R.sub.r$~ and |P.sub.r$~) when |P.sub.g$~ |is not equal to~ |P*.sub.g$~. If |P.sub.g$~ |is less than~ |P*.sub.g$~, both |R.sub.r$~ and |P.sub.r$~ would increase without limit as the bank tried to hold |R.sub.r$~ above |P.sub.r$~ to satisfy equation (3). Similarly, the situation |P.sub.g$~ |is greater than~ |P*.sub.g$~ would imply unlimited decreases in |R.sub.r$~ and |P.sub.r$~.

In fact there is a correction mechanism for |P.sub.g$~. Starting from a situation in which |P.sub.g$~ = |P*.sub.g$~, suppose that reduced demand for gold causes |P.sub.g$~ to fall. The rule of equation (3) then requires the bank to raise |R.sub.r$~, which also causes |P.sub.r$~ to rise. This reduces demand for redemption medium which, amongst the consequent general equilibrium adjustments and to the extent that redemption medium and gold are substitutes, raises the demand for gold. An alternative standard explanation would be that the increase in |R.sub.r$~ causes net sales of redemption medium to the bank in exchange for its currency, and that this increase in "money supply" raises demand for other goods, gold included. In any event, the raised demand for gold causes gold traders to respond by raising the gold price, |P.sub.g$~.

Whilst this mechanism works in the right direction to restore |P.sub.g$~ to parity, it relies as it must do on supply and demand induced adjustments to |P.sub.g$~ which presumably take time to occur. The success of indirect convertibility (equation (3)) therefore depends on the bank's ability to hold |R.sub.r$~ different from |P.sub.r$~ for sufficiently long for this correction process to run its course. Unless one is prepared to adopt the unrealistic assumption that the "law of one price" in the market for redemption medium is defective, allowing changes in |P.sub.r$~ consistently to lag changes in |R.sub.r$~,(4) one must accept that indirect convertibility cannot be practiced because it would imply the unlimited changes to |R.sub.r$~ which have been described above.

IV. An Alternative: Gold Price "Targeting"

The solution to this difficulty seems to be to release the bank from rigid commitment to equation (3) and rather to permit it to make slower adjustments to its price of redemption medium, thereby allowing time for the gold price to respond. This would be achieved if the rule of equation (3) were modified so that the bank makes its observations in one time period and then adjusts |P.sub.r$~ in a later period:

|P.sub.r$~(t + 1)= |P.sub.r$~(t)(|P*.sub.g$~/|P.sub.g$~(t)) (3a)

where t refers to time, and we are now recognizing the equality |P.sub.r$~ = |R.sub.r$~ and considering |P.sub.r$~ as the bank's instrument. According to this rule, during periods in which |P.sub.g$~ |is less than~ |P*.sub.g$~, |P.sub.r$~ would be increased each period, but there would be no unlimited rise as there was under equation (3).

This operating rule would obviously not succeed exactly in maintaining the desired gold/dollar parity, and it therefore does not constitute indirect convertibility; nor is it, we believe, what Dowd had in mind. If the bank's adjustments are sufficiently infrequent, the general equilibrium responses of the economy may be such that deviations in |P.sub.g$~ are corrected over time, thus providing for stable control over the dollar gold price. The system might be described as a redemption medium standard in which the gold price is the "target."(5)

The stability of this system will depend on the bank's speed of adjustment of its instrument, |P.sub.r$~, as compared with the speed at which the markets respond in adjusting |P.sub.g$~. The bank has to allow time for changed supplies and demands in the economy to impact on the gold market. The faster the bank changes |P.sub.r$~, the more likely it is that the system will be unstable. The extreme case, in which the bank allows no interval between its adjustments to |P.sub.r$~ is indirect convertibility. In this extreme, as discussed above, if the bank attempts to bring about immediate corrections of deviations of |P.sub.g$~ from parity, the only consequence will be an unlimited rise or fall in the value of the bank's instrument, |P.sub.r$~.

V. Indirect Convertibility for Other Currencies

Thus far, we have argued that indirect convertibility is unviable for the currency which is the medium of account for quoting prices of goods. There would, however, be no difficulty in applying indirect convertibility to a currency which floats against the medium of account. Suppose a new bank begins issuing currency denoted n whilst the prevailing medium of account is still $, and that this bank attempts indirect convertibility. From equation (1), the new bank must calculate its redemption rate as

|R.sub.rn~ = |P* |center dot~ |P.sub.rg~ (4)

where |R.sub.rn~ is the bank's conversion rate to redemption medium, |P* is its chosen parity and |P.sub.rg~ is, as before, the observed market cross-price of redemption medium relative to gold. Given that market prices are still in $, equation (2) remains appropriate for the bank to derive the value of |P.sub.rg~ from observations of |P.sub.g$~ and |P.sub.r$~. In line with our previous arguments it is also true that, given the new bank's convertibility commitment, the market "price-takes" the bank's choice of |R.sub.rn~ so that |P.sub.rn~ = |R.sub.rn~. Substituting equation (2) into equation (4), the new bank's rule becomes

|P.sub.rn~ = |P.sub.r$~(|P*|P.sub.g$~). (5)

In contrast to equation (3), there would be no difficulty in applying equation (5). Changes by the new bank in the value of its currency relative to the redemption medium, |P.sub.rn~, cause instantaneous proportional changes in the value of its currency relative to dollars and to all goods including gold, leaving dollar-measured prices unaffected.

VI. Are Stocks of Redemption Medium Necessary?

As noted in our introduction, Dowd argues that depletion of an indirectly converting bank's reserves of redemption medium would not be a problem since the bank can purchase redemption medium in the market. Indeed, he describes |1, 720-21~ a process in which, if the banks collectively buy redemption medium in the market, the consequent demand raises its market price with the happy result that any stocks of redemption medium, which a bank has in its possession, rise in value.

Notwithstanding our criticism of indirect convertibility itself, we mention as a final point that this argument is in error. As has been shown above, the value of redemption medium relative to a bank's currency is set by that bank: there is no independent market price of redemption medium, hence the bank's demand for purchases of redemption medium cannot alter its value. Moreover for a given net demand by the market for bank redemptions at the bank's given price, if the bank were to buy in redemption medium from the market (at that same price) this would only cause further redemptions so that this could not save a bank with insufficient stocks.

It is well known that under a "direct" gold standard, the currency issuing central bank needs gold reserves sufficient to make its convertibility commitment credible; that is, it must potentially be able to satisfy all foreseeable demands for redemption into gold from its own stocks. A central bank whose ability to uphold convertibility is in doubt is vulnerable to speculative attack. This argument would also apply to the stocks of redemption medium held by a bank attempting to practice indirect convertibility.

VII. Closing Remark

We have assumed above that there is some bank whose currency is used as the medium of account for quoting prices of gold and the redemption medium, and we have argued that this bank would be unable to fix the value of its currency to gold by means of indirect convertibility. On the other hand, a bank whose currency is not used for quoting prices would be able to practice indirect convertibility.

These results can, in fact, be construed as statements about indexing and they become more transparent when cast in this context. The indirect convertibility rule amounts to an obligation on a bank to index the value of its currency to gold: as the market value of gold (measured in some unit) rises, the bank must arrange that the value of its currency (measured in this same unit) rises in proportion. This is impossible when the unit in which the value of gold is measured in the market is the currency whose value is to be indexed.

1. It may be noted that if the redemption medium is a company share, when the bank changes its redemption rate this amounts to changing the interest yield on this share and, by substitution, on other assets as well. The bank's instrument is thus an interest rate. This observation does not materially alter any of the following analysis.

2. We have elsewhere |4~ presented a fuller criticism of indirect convertibility in the context of a proposal of Greenfield and Yeager |2~. Their scheme aims to use indirect convertibility of currency to a redemption medium for the purpose of tying the value of the currency to a defined basket of goods.

3. This natural association between medium of account and medium of exchange has been pointed out by White |5~.

4. It would be in the interests of dealers in redemption medium to anticipate changes by the bank in |R.sub.r$~ which implies that, even if there are lags in the observation of |P.sub.g$~, changes in |P.sub.r$~ would not consistently lag changes in |R.sub.r$~.

5. A close relative of this scheme is Fisher's |3~ "Compensated Dollar" in which the redemption rate of convertibility to gold is manipulated so as to 'target' a given dollar price of a basket of goods.


1. Dowd, Kevin, "Financial Instability in a 'Directly Convertible' Gold Standard." Southern Economic Journal, January 1991, 719-26.

2. Greenfield, Robert L. and Leland B. Yeager, "A Laissez-Faire Approach to Monetary Stability." Cato Journal, Fall 1989, 405-21.

3. Fisher, Irving. Stabilizing the Dollar. New York: Macmillan, 1920.

4. Schnadt, Norbert and John Whittaker, "Inflation-Proof Currency? The Feasibility of Variable Commodity Standards." Journal of Money, Credit, and Banking, May 1993, 214-21.

5. White, Lawrence H., "Competitive Payments Systems and the Unit of Account." American Economic Review, September 1984, 699-712.

The Viability of an "Indirectly Convertible" Gold Standard: Reply

I. Introduction

The experience of continuing inflation makes it increasingly difficult to deny that fiat monetary regimes have an inbuilt inflationary bias. If there is such a bias, no amount of "tinkering" with fiat monetary rules will solve our inflation problem, and monetary reformers who wish to end inflation need to think in terms of establishing convertible monetary systems instead. The only systems that have been tried historically are monometallic gold or silver standards, or bimetallic standards, and neither of these can be relied on to produce the degree of price-level stability we might desire. If we wish to stabilize the price level by (re-)establishing currency convertibility, we presumably need some other form of convertibility that has not yet been tried in practice. We must therefore think in more abstract terms about convertibility issues than we normally do, and given the potential dangers involved in putting "untested" convertibility schemes into operation, any schemes we suggest need to be subjected to careful scrutiny.

I therefore welcome Schnadt and Whittaker's |4~ critical comments on my earlier paper |1~ on indirect convertibility. Nonetheless, I believe they are wrong on both their key points: They are mistaken when they say that indirect convertibility is not feasible in practice, and the 'compensated dollar' type of system they discuss as an alternative to indirect convertibility is itself subject to flaws that rule it out as unworkable. In short, the system they dismiss as unworkable could be made to work in practice, and the one that they suggest might be workable is not.

II. The "Paradox" and the Feasibility of Indirect Convertibility

In any system of convertibility the value of currency is (perhaps implicitly) defined in terms of a given quantity of some 'anchor' commodity (or commodity-basket). The convertibility rules are meant to ensure that the nominal price of this anchor is held (at least approximately) fixed, and other nominal prices can then be thought of as tied down by the combination of these rules and the "real" conditions that determine relative prices. Under indirect convertibility, the issuer(s) of currency redeem their currency with media of redemption (MOR) that are different from, but have the same market value as, that given quantity of the anchor commodity |1; 4; 5~. Suppose that the anchor is gold, and the value of the dollar is defined as equal to that of a unit of gold. If the MOR is silver, a bank would exchange each $1 note it issues for silver of the same market value as a unit of gold.

Assume now that the market price of a unit of gold deviates from its "par" value of $1 to $1.20. A bank would then have to hand over more silver for each dollar note than it previously did. The bank price of silver--the rate of exchange (at the bank) of notes per unit of silver--now falls below the prevailing market price of silver (see, e.g., equation (3) in Schnadt and Whittaker |4~). Arbitrage opportunities then open up for agents to make profits by buying silver from the banks (ie, by redeeming notes) to sell it on the market. The market price of silver falls, and the banks are obliged to hand over more silver for each dollar note to compensate noteholders for the fail in the market price of silver. The bank price of silver therefore falls pari passu with the market price, and the gap between the market and bank prices of silver cannot be closed for as long as the market price of gold remains above $1. The arbitrage opportunity thus remains, arbitrage operations continue, and the market price falls further. The bank price again falls with it, and both prices keep chasing each other downwards. If it occurs and is not corrected reasonably rapidly, an increase in the market price of gold thus leads the price of silver, and with it the supply of currency, to collapse |2; 7~. And conversely, a fall in the price of gold below par leads the price of silver and the supply of currency to rise without limit. We thus arrive at the "paradox" result emphasized by Schnadt and Whittaker.

Yet it would be wrong to conclude as Schnadt and Whittaker do that the "paradox" result makes indirect convertibility unworkable. One could only arrive at that conclusion if the price of the anchor both deviated from par and was relatively slow returning to it. A system of indirect convertibility in which the price of the anchor was prevented from deviating from par, or one in which deviations from par were corrected "rapidly," would therefore be able to avoid paradox-related problems, provided such a system could be found. An example of such a system is provided by Sumner |6~ and Dowd |3~ who suggest that currency issuers peg the prices of CPI-futures (or related) contracts. Every month the central bank (or, under free banking, the banks of issue) would peg the prices of contracts that are to mature the next month. The zero-arbitrage equilibrium condition would ensure that the CPI expected next month was "close" to being constant, and the actual (ex post) CPI delivered next month would then be reasonably stable. The "anchor" in this system would be the future basket of goods and services represented by the CPI-futures contract, and the rule to peg the price of the futures contracts would tie down the anchor's nominal value. Indirect convertibility could be established by having the central bank or banks of issue observe "over the counter" indirect convertibility for the general public on those days when the price of the futures contract was pegged. The proposed system would be indirectly convertible because members of the public could redeem banknotes for (or buy banknotes with) MOR of the same market value as the "anchor" whose price was being pegged, but the rule to peg the futures price would ensure that the price of the anchor was always at par on those days when the central bank or banks of issue were committed to converting their notes on demand. Since the price of the anchor would always be at par on those days, the paradox situation described above would never arise. We would thus have a practicable system of indirect convertibility that would be immune to the paradox problem--and a counter-example to the Schnadt-Whittaker claim that indirect convertibility cannot be made to work.

III. The Impracticality of "Compensated Dollar" Schemes

Schnadt and Whittaker suggest as a possible alternative system a "compensated dollar" type of rule (or, in their terminology, a gold price targeting rule) which requires the central bank not to peg the price of an anchor as such, but to peg the price of the MOR and periodically alter that price in response to the deviation of a chosen price index from its target value. If gold were the MOR and the price index were above (below) par, the rule would oblige the central bank to reduce (increase) the price of gold by some stated percentage. The lower price of gold would stimulate purchases of gold from the central bank, money supply would fall, and the price index should be pushed back toward par. If the price index fell below par, on the other hand, the central bank would raise the price of gold to encourage agents to sell gold to it, the money supply would rise, and the price index should be pushed back up. The underlying idea is that the rule would have the central bank alter the price of the MOR in an automatic way intended to reduce the supply of money if the price index is too high and increase the supply of money if the price index is too low.

This type of rule is open to serious objections. One problem is that it is vulnerable to much the same sort of speculative attack as exchange rates under a crawling peg exchange rate regime. In each case the relevant price--the price of the MOR, or the exchange rate--is temporarily pegged, and then periodically altered. However, in the period before the price changes occur, interim information will become available that will enable agents to predict at least the direction of the price change. As the time for the price change approaches, agents can make arbitrage profits by going short, if the price is expected to fall, or long, if the price is expected to rise, and they will make a capital gain when the price change occurs. The rational arbitrage strategy for each agent involved is to sell or buy as much as possible, and since the central bank would be the counterparty that took the losses from such operations, it is very doubtful that a central bank in practice would be able to withstand the strain and stick to its announced rule. The experience of crawling peg exchange rate regimes leaves one with little confidence that central banks can withstand such pressure, and should a central bank try to implement such a rule in practice, the most likely outcome would be a withering speculative attack that ultimately led to the rule being abandoned.

But even if this kind of rule were immune to speculative attack, it is still far from clear that it would generate the desired degree of price-level stability. The basic rule that every so often the central bank should lower (raise) the price of the MOR by x percent of the deviation of the chosen price index above (below) target creates pressures to push the price level in the direction needed to restore equilibrium, but creating such pressures is not sufficient to stabilize the price level. If x is too high, a small deviation of the price index above its target value will lead to a relatively large change in the price of the MOR. The danger is that this latter change might lead to a relatively large fall in the money supply which in turn produces a large fall in prices. A small positive deviation of the price index above target would thus be converted into a large deviation of the price index below target. The latter would then lead to an even larger deviation of the price index above target, and so on. Each time the price index would be pushed in the right direction, but with so much force that each deviation would be overcompensated and the price level would oscillate more and more wildly around its target value. If x were too small, on the other hand, it might take a long time for the price of the MOR to alter to a point where it had a significant effect. The price level could therefore fluctuate very considerably around its target value, and the economic force of gravity that pulled it back toward that value would operate only weakly and slowly. There is nothing to tell the designer of such a rule what the "right" value of x should be, and all the central banker or legislator can do in practice is guess the answer and hope it works. Since one of the arguments for this type of rule is to eliminate (or at least reduce) the need for central bank discretion, the chosen value of x would also be difficult to alter later on. The designer must not only guess the answer, but he must also get it right the first time and hope that his answer continues to be right in the light of the economy's subsequent evolution. I simply do not believe that any legislator or central banker has the knowledge or expertise to tackle this problem with any reasonable expectation of success. But then again, I see no reason why he should want to try. Why choose such a flawed system when one can adopt indirect convertibility instead?


1. Dowd, Kevin, "Financial Instability in a 'Directly Convertible' Gold Standard." Southern Economic Journal, January 1991, 719-26.

2. -----, "The Mechanics of Indirect Convertibility." Journal of Money, Credit, and Banking, 1994, forthcoming.

3. -----. "A Proposal to Eliminate Inflation." Mimeo, University of Nottingham, 1992.

4. Schnadt, Norbert and John Whittaker, "The Viability of an 'Indirectly Convertible' Gold Standard: Comment." Southern Economic Journal, October 1993.

5. ----- and -----, "Inflation-Proof Currency? The Feasibility of Variable Commodity Standards." Journal of Money, Credit, and Banking, May 1993, 214-21.

6. Sumner, Scott, "Using Futures Instrument Prices to Target Nominal Income." Bulletin of Economic Research, April 1989, 157-62.

7. Yeager, Leland B. and William W. Woolsey, "Is There a Paradox of Indirect Convertibility?" Paper presented to the Durell Foundation Conference, American Money and Banking: Financial Fitness for the 1990s, Scottsdale, Arizona, May 1991.
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Title Annotation:includes reply; response to Kevin Dowd, Southern Economic Journal, January 1991
Author:Dowd, Kevin
Publication:Southern Economic Journal
Date:Oct 1, 1993
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