Earlier versions of this paper were published in (a) the Proceedings of the International Electronic and Electrical Engineering (IEEE) Engineering Management Society Conference, in Albuquerque, New Mexico (August 2000), and (b) the Conference on Computing in Economics and Finance (CEF) in Washington, DC, sponsored by George Washington University and the US Federal Reserve Board (June 2005).

Abstract: Reciprocal credit and exchange networks or "barter rings" do billions of dollars of trade each year within the rich countries of the world. Their turnover is shown to be highly counter-cyclical. Most studies of the internet's macroeconomic impact have focused on price and inventory flexibility. There has been little study, however, of the macroeconomic impact of reciprocal exchange networks like the Swiss Wirtschaftsring (“Economic Circle”), founded in the early 20^th century. The experience of this network suggests that the credit it provides during recessions is highly stabilizing. This has important implications for monetary theory and policy.

I. Introduction

Faster and cheaper information on the internet means greater macroeconomic stability. That, at least, is a well-publicized view of internet-based commerce. By making it possible for purchasing firms and households to compare prices more widely, e-commerce has forced better price flexibility and greater resistance to inflation (Greenspan, 1999). Better supply tracking and demand estimation also helps keeps inventories lean, thus tamping down unplanned inventories (Wenninger 1999), an important precursor of recession.

But this literature on price and inventory flexibility has ignored another way that better information can be macro-stabilizing. As any loan-officer or central banker can attest, the prudent allocation of credit is both knowledge-intensive and highly uncertain. What if, instead of trying to estimate the proper amount of money and credit to complete all transactions, current values bid by each potential purchaser, and asked by each potential seller, were precisely known by a central clearing house? The problem of how much money-stuff to create to balance aggregate supply and demand would largely disappear; money in the conventional sense would no longer exist.

Such moneyless exchange took place in the ancient storehouse economies of the Middle East and the Americas (Polanyi 1947), and in the simplified models of microeconomic exchange -- both under conditions where the relevant information is centralized. The ancient storehouse economies collapsed, and monetary[1] systems evolved because the information required to coordinate a complex economy was far too great to be centralized (Stodder 1995). The internet is once again making large-scale information-centralization efficient, however and centralized barter is a new form of e-commerce. Barter clearing-houses are growing with internet companies like swap.com, BarterTrust.com, and uBarter.com (Anders 2000).

The implications of moneyless business are neither straightforward, nor without controversy. A few prominent economists have speculated that computer-networked barter might eventually replace our decentralized money -- as well as its centralized protector, central banking. Such questions have been asked by leading macroeconomists like Mervyn King, presently the Governor of the Bank of England (King 1999, Beattie 1999), and Benjamin Friedman of Harvard (1999).

Friedman's view that central banking may be seriously challenged was a lead topic at a World Bank conference on the "Future of Monetary Policy and Banking" (World Bank 2000). His warnings sparked a pair of skeptical reviews in the Economist Magazine of London (2000a, 2000b). But no one, as far as I know, has looked at the direct evidence on this issue, the large-scale barter networks in existence for decades.

II. Statement of the Argument

If barter is informationally-centralized - on a network where, via a central resource, all parties can scan each other's bids and offers - it will tend to be counter-cyclical. The central record of the value of such barter will track the bids (unmet demands) and asks (excess supplies) of all agents on the network. For a simple model of informationally centralized barter, consider firms, A, B, and C, each of which lacks one input -- a, b, and c, respectively. Let us say that A currently holds c, B holds a and C holds b. This is shown in Figure 1 below.

[ Please place Figure 1 about here.]

If prices are set at unity, Pa = Pb = Pc = 1, the direction of mutually improving trade is obvious from the picture: A gives a unit of c to C, C gives a unit of b to B and, and B gives a unit of a to A. But if these are the only inputs of interest to each firm, then there are no bilaterally improving trades. Without a sufficient value of decentralized money-stuff, some form of centralized credit accounting is necessary. In the simplest economies – a few households linked by long-term kinship relations – such centralized credit accounting can be each household’s reputational ‘capital’. But in larger and more complex societies this is unfeasible. In traditional and primitive economies, centralized ‘big-man’ or ‘storehouse’ households have been designated to keep these credit accounts (Stodder, 1995).

The WIR bank in Switzerland can be seen as a more sophisticated answer to the same information problem, with centralized credit accounts for each household and firm, and a record of all unmet bids and asks. This is far more knowledge than is available to any "central" bank -- the knowledge it has to set the money-supply basis of exchange. Its broad monetary aggregates sit atop the decentralized "real" data in which investors and central bankers are interested. To get at this information, the bank can only scan indirect monetary indicators -- ratings of credit-worthiness, and statistical leading indicators. Of course a centralized barter administration can still make mistakes, extending credit too much or too little. Credit "inflation" was indeed evident in the early history of the world's largest barter exchange, the "Economic Ring" (Wirtschaftsring, or WIR) of Switzerland (Defila 1994, Stutz 1994). Such a centralized barter exchange, however, will have a better knowledge base on which to extend credit than any central bank.

The WIR was inspired by the ideas of an early 20^th-century economist, Silvio Gesell (Defila 1994). Keynes devotes a chapter of his General Theory (1936; Book VI, Chapter 23) to Gesell’s ideas. Despite criticisms, Keynes acknowledges that this “unduly neglected prophet” anticipated some of his own ideas. This link with Keynesian monetary theory should have made Gesellian banking of some interest to macroeconomists.^{^[2]} Only one contemporary economist, however, seems to have studied the macroeconomic record of WIR, the largest and most long-lived bank of this sort. Studer (1998) finds positive correlation between WIR credits advanced and the Swiss money supply, M1. This suggests that WIR follows a counter-cyclical credit "policy," one parallel to the monetary policy of the Swiss central bank itself. The data used in Studer's study, however, go back only as late as 1994. The present study has access to 9 more years of data, and makes use of cointegration-based methods of time series analysis.

The present paper examines the historic data on a large barter exchanges -- the WIR, founded in 1930s Switzerland. These data will show that the economic activity of this exchange is counter-cyclical, rising and falling against, rather than with, the business cycle.

III. Data and Regression Results

Because the financial record of these exchanges is not widely known, I provide the basic data. The Swiss banking tradition is well-known for the quality of its private records. The WIR bank gives us 56 years of data on Participants (numbers of household or firm members), Turnover (account activity), and Credit advanced (in the form of credit to one’s reciprocal exchange account, not in terms of Swiss currency):

[Place Table 1 about here.]

As Figure 2 below shows, growth in the number of WIR Participants has tracked Swiss Unemployment very closely indeed, consistently maintaining a rate of about one-tenth the increase in the number of unemployed. Indeed, in the following regressions, the Unemployment term is the only one with strongly significant coefficients. The importance of Unemployment to WIR's Participant trend probably reflects its exclusion of "large" businesses, as established in the bank's rules since 1973 (Defila 1994). Employees in smaller, less diversified firms are probably more subject to unemployment risks.

[Place Figure 2. about here.]

In Table 2 below, it is clear that the long-term relationship between the number of WIR Accounts, Unemployment, and the Money Supply is positive, from the cointegrating equation, in column (a):

LnACCTS = 4.026392 + 0. 0998● LnUE + 1.132●LnMON, (3)

[5.158]*** [7.193]***

where both coefficients are significant at the 0.1 percent level. [3] LnACCTS, LnUE, LnMon, and all the other Swiss time series to be considered here can be shown by Augmented Dickey-Fuller (A.D.F.) tests to be I(1) at the 5 percent level of significance, so cointegration is possible.[4] The Johansen test results in column (a) of Table 2 show that cointegration is more likely when both LnUE and LnMON are used.

[Place Table 2. about here.]

Now Unemployment and Money Supply are almost certainly highly collinear. Note that by isolating them, as in Table 2, columns (b) and (c), the Johansen cointegration test is only significant at the 10 percent level. It is seen, however, that their coefficient signs do not change in the cointegrating equation.

Whenever we add a variable to an Error Correction Model, there is a potential for one more cointegrating equation. In the present context, however, it seems reasonable to assume that the most important arrows of causality run from the Swiss macroeconomic variables to the still small Swiss WIR-Bank, and not in the opposite direction. The obvious test here is for Granger causality. In Table 3, we can reject the null hypotheses that

a) the Money Supply and Unemployment variables, LnMon and LnUE, do not reciprocally Granger-cause each other; and that

b) LnUE does not Granger-cause Turnover, LnACCTS.

We cannot, however, reject the hypothesis that LnMON and LnACCTS do not Granger-cause each other. In summary, there is little doubt that Turnover is more affected by, rather than affecting, the other economy-wide macro-economic variables – as is only reasonable. Consequently, the cointegrating equation can reasonably be written in the form of (3) above.

[Place Table 3. about here.]

It is interesting here to look at the short-term and medium-term effects of Money Supply and Unemployment upon the number of Participants, as given both by the coefficients on the first lagged terms of each, and the summation of their lagged coefficients, as shown in Table 4. Even though the long-term cointegrating relationship seen in equation (3) has been seen to be a positive association between all three terms, the short-term and medium-term effects are seen to be largely negative.[5]

This is a necessary condition for stability in an error correction model of this type. Note that the coefficient on the error-correction term is always negative in all regressions. In Table 2, column (a), for example, a negative coefficient on the error term means that the number of Participants in WIR will grow when Unemployment and Money Supply are ‘too large’; i.e., when the error-correction term is itself negative. Since the medium-term effect of lagged Participants upon growth of Participants is also positive, we must have some negative feedback from Unemployment or Money supply if we are not to have an explosive system. Note in Table 2 (and all other regression Tables) that such negative feedback is provided by a negative sign not only on the coefficients for the short-term lagged variables, but on those coefficients’ summation as well.

From Figure 2 one can see that the number of WIR accounts has been, for over 50 years, roughly half as large as the number of unemployed workers in Switzerland.[6] While WIR account holders and the unemployed are not likely to often be the same people, this close fit between the two series is clearly an important counter-cyclical trend. WIR accounts are also sufficiently numerous, relative to the Swiss labor force, for this trend to have substantial counter-cyclical impact.

We now consider the positive association between WIR Turnover on Accounts, and the Swiss Money Supply as a whole, as measured by M2. Their long term common trend is seen in Figure 3:

[Place Figure 3. about here.]

The log of Money Supply (LnMON) and Total Turnover (LnTURN) in the WIR bank are positively associated in the long term, from the first two cointegrating equations estimated in Table 4. [7] In column (c), this is of the form:

LnTURN(-1) = -16.479 + 1.830●LnMON(-1) (4)

[6.091]

where the coefficient on LnMON is significant at the 0.1 percent level.

[Place Table 4. about here.]

Overall goodness of fit is comparable, however, by both R-squared and Aikake or Schwartz criteria, if we include GDP along with Money Supply as an independent variable determining Turnover. In column (b) this gives the cointegrating equation:

LnTURN(-1) = 59.278 + 8.244●LnMON(-1) - 12.546 ●LnGDP(-1) (5)

[5.116] [-4.390]

with both coefficients significant at 0.1 percent. Note in column (e), however, that when Money Supply is left out of the cointegrating equation (and thus allowing us to use a longer time series), the sign on GDP would becomes positive, and thus apparently pro-cyclical. This makes sense as a secular rather than cyclical effect – simply the long term trend for WIR Turnover to expand along with the Swiss economy as a whole. (Note that this positive secular association is very close indeed, as reflected by both the significance of the cointegrating relationship in the Johansen test, and by the goodness of fit statistics.)

Turning to the effects of Money Supply and GDP on Turnover, columns (a) and (b) of Table 4 show the coefficient on the first lag of each significant at the 10 and 5 percent levels, respectively. The medium-term effects of Money Supply and GDP are shown by their summation terms, which are significant at the 10 or 5 percent levels, depending on how many lags we use.

As was argued with equation (3), there is little question about the direction of causality. Granger causality results, shown in Table , are less ambiguous for the 3 lag specification. These results imply that (a) LnMON and LnTURN may well Granger-cause each other, with P-values slightly greater than 5 percent; (b) LnGDP Granger-causes LnTURN, but not the reverse, and (c) LnMON almost certainly Granger Causes LnGDP, but not the reverse. We need not accept at face vale the seemingly incredible claim of (a), that the movement of a few billion Swiss Francs in WIR accounts could determine the monetary policy of the Swiss central bank. We should recall the interpretation of Robert Shiller and Campbell (1998): that Granger causality may mean only that one time series accurately anticipates or predicts variation in a second series, without causing that variation, even a stochastically deterministic sense.

[Place Table 5. about here.]

In Table 6 we turn to the third of the Swiss WIR-Bank time series: the total value of Credit extended as part of the Bank’s operations; i.e., part of the foregoing statistic of annual Turnover. It will be seen that Credits are even more counter-cyclical than the total volume of Turnover itself. With LnCRED as the logged value of Credit, the form of the cointegrated equation in column (a) is:

LnCRED(-1) = 15.410 + 5.380●LnMON(-1) – 6.221●LnGDP(-1) (6)

[4.649] [2.923]

[Place Table 6. about here.]

with the coefficients on LnMON and LnGDP significant at the 0.1 and 0.5 significance level, respectively. From Table 7, we see that

(a) LnMon almost certainly Granger-causes LnGDP, but not the reverse;

(b) lnMON and lnCRED do not appear to Granger-cause each other; while

Again, the Shiller-Campbell (1998) interpretation of (c) is suggested: prediction, rather than deterministic causality. The log

[Place Table 7. about here.]

form allows us to interpret coefficients in elasticity terms. Our tentative empirical conclusions from Tables 5 and 7 are that:

· A 1 per cent increase in the long-term money supply (M2) is reflected in a long-term increase of between 4.9 to 8.2 per cent in the annual Turnover of WIR accounts (Table 7: a) and b)), and between 5.4 to 9.4 percent in the Credits advanced on that Turnover (Table 9: a) and b)).

· A 1 percent decrease in long-term GDP is reflected in a long-term counter-cyclical increase of between 5.8 to 12.5 percent in WIR Turnover (Table 7: a) and b)), and between 6.2 to 14.2 percent in the Credits advanced on that Turnover (Table 9: a) and b)).

These estimates show that WIR-Bank pursues a counter-cyclical policy that is very aggressive. Since M2 is defined as currency in circulation and most forms of ordinary bank money (checking deposits and savings accounts), these estimates imply that WIR-Bank’s creation of money and credit is many times more sensitive to economic conditions than is M2 itself. WIR increases its turnover by a money-multiplier several times higher than the ratio of the broadest measure of money, M3 over M2, in the Swiss monetary system. Over the past 20 years, the Swiss National Bank (the central bank) ratio M3/M2 has never been greater than 3.2.[8] WIR-Bank Turnover shows M2 income elasticity that is perhaps twice this ratio. Furthermore, WIR extends its credit even more aggressively than its Turnover, as has been seen.

The counter-cyclical trend of Turnover and Credit is far more pronounced than that of M2 itself. Preliminary estimates on this same Swiss National Bank data indicate that M2 itself has a positive income elasticity of about 2, a figure in line with a recent survey of the literature (Gerlach-Kristen, 2001). This must be compared with a long-term income elasticity of WIR Turnover and Credits that is not only negative (and thus counter-cyclical) when used as an independent variable alongside M2, but is also about twice as great in absolute value as the consensus income elasticity on M2.

V. Conclusions and Implications

There is substantial evidence for the general form of our hypothesis, that centralized barter exchange is highly counter-cyclical. There remains the vital question, however, as to why this counter-cyclicity occurs. A basic difference of opinion exists within macroeconomic theory as to whether instability is more due to price rigidity, or to inappropriate levels of money and credit. Keynes (1936) recognized that both conditions can and do apply, and that either can lead to instability.

The reigning macroeconomic consensus, as represented by Mankiw (1993), puts the blame more on rigid prices; economists like Colander (1996) stress monetary and credit conditions. Reflecting the "sticky price" consensus of macroeconomics, most commentary on the impact of e-commerce has concentrated on prices, as we have seen. But if a barter exchange's members charge prices that do not diverge significantly from its cash prices -- those charged to their non-members -- then counter-cyclicity may derive from barter's ability to create credit.

WIR activities are highly public and centralized, subject to the scrutiny of other customers, and so unlikely to allow confidential discounts. Also, prices for goods and services advertised in the WIRPlus magazine (2000-2005) are regularly quoted in WIR-credit prices that are higher than their price in Swiss Francs, so this does not seem to be downward price flexibility. Lower prices on barter than cash would tend to divert trade to the former. This would be undesirable for most businesses, since cash is almost always more fungible than exchange credits (Healey 1996).[9]

The possibility remains that barter may have forced greater flexibility in network members' cash prices. But since WIR's bylaws restrict membership to small and medium businesses (Defila 1994), members will usually have comparatively little price-setting power. Thus, the counter-cyclical history of WIR is likely due more to its credit creation than its added price flexibility. Inventory flexibility, however, could also be a factor, even before wide-scale use of computers. If such network exchanges are indeed counter-cyclical, this is emphatically not the case for all "network economies". Telecommunications networks are highly subject to increasing returns to scale, unlike older industries – and unlike neoclassical theory (Romer 1997, Howitt and Phillipe 1998, Arthur 1996). Such industries are therefore likely, especially as their importance to the economy increases, to fuel greater pro-cyclical instability.

Reciprocal exchange networks like those studied here also have increasing returns and "network externalities," yet they appear strongly counter-cyclical. It may be important to understand why. To quote Mervyn King (1999), now Governor of the Bank of England, electronic exchange may build a world in which "central banks in their present form would no longer exist; nor would money….The successors to Bill Gates could put the successors to Alan Greenspan out of business."

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FIG. 1.

Table 1: Participants, Total Turnover, Credit, and Credit/Turnover, WIR-Bank, 1948-2003

(Total Turnover and Credit Denominated in Millions of Current Swiss Franks)

Year	Participants	Turnover	Credit	Credit/ Turnover	Year	Participants	Turnover	Credit	Credit/ Turnover
1948	814	1.1	0.3	0.2727	1976	23,172	223.0	82.2	0.3686
1949	1,070	2.0	0.5	0.2500	1977	23,929	233.2	84.5	0.3623
1950	1,574	3.8	1.0	0.2632	1978	24,479	240.4	86.5	0.3598
1951	2,089	6.8	1.3	0.1912	1979	24,191	247.5	89.0	0.3596
1952	2,941	12.6	3.1	0.2460	1980	24,227	255.3	94.1	0.3686
1953	4,540	20.2	4.6	0.2277	1981	24,501	275.2	103.3	0.3754
1954	5,957	30.0	7.2	0.2400	1982	26,040	330.0	127.7	0.3870
1955	7,231	39.1	10.5	0.2685	1983	28,418	432.3	159.6	0.3692
1956	9,060	47.2	11.8	0.2500	1984	31,330	523.0	200.9	0.3841
1957	10,286	48.4	12.1	0.2500	1985	34,353	673.0	242.7	0.3606
1958	11,606	53.0	13.1	0.2472	1986	38,012	826.0	292.5	0.3541
1959	12,192	60.0	14.0	0.2333	1987	42,227	1,065	359.3	0.3374
1960	12,567	67.4	15.4	0.2285	1988	46,895	1,329	437.3	0.3290
1961	12,445	69.3	16.7	0.2410	1989	51,349	1,553	525.7	0.3385
1962	12,720	76.7	19.3	0.2516	1990	56,309	1,788	612.5	0.3426
1963	12,670	83.6	21.6	0.2584	1991	62,958	2,047	731.7	0.3574
1964	13,680	101.6	24.3	0.2392	1992	70,465	2,404	829.8	0.3452
1965	14,367	111.9	25.5	0.2279	1993	76,618	2,521	892.3	0.3539
1966	15,076	121.5	27.0	0.2222	1994	79,766	2,509	904.1	0.3603
1967	15,964	135.2	37.3	0.2759	1995	81,516	2,355	890.6	0.3782
1968	17,069	152.2	44.9	0.2950	1996	82,558	2,262	869.8	0.3845
1969	17,906	170.1	50.3	0.2957	1997	82,793	2,085	843.6	0.4046
1970	18,239	183.3	57.2	0.3121	1998	82,751	1,976	807.7	0.4088
1971	19,038	195.1	66.2	0.3393	1999	82,487	1,833	788.7	0.4303
1972	19,523	209.3	69.3	0.3311	2000	81,719	1,774	786.9	0.4437
1973	20,402	196.7	69.9	0.3554	2001	80,227	1,708	791.5	0.4634
1974	20,902	200.0	73.0	0.3650	2002	78,505	1,691	791.5	0.4681
1975	21,869	204.7	78.9	0.3854	2003	77,668	1,650	784.4	0.4754

Sources: Data to 1983 are from Meierhofer (1984). Subsequent years are from the annual Rapport de Gestion and communi-

cations with the WIR public relations department (2000, 2004). The first three series names (Participants, Turnover, and Credit) are given in the annual report in French as Nombre de Comptes-Participants, Chiffre (o Volume) d'Affaires, and Autres Obligations Financières envers Clients en WIR, respectively. Both Turnover and Credit are denominated in Swiss Francs, but the obligations they represent are payable in WIR-accounts. In the regressions, all monetary series were deflated by the1990 GDP deflator.

Table 2: Account Activity in WIR Exchange Network, as Explained by Unemployment and Money Supply 1960-2002*

[t-stats] in parentheses, ***: p-value < 0.001, **: p-value < 0.01, * : p-value < 0.05, ^oo: p <0.1; ^o: p <0.15

Cointegrating Eq:	(a)	(b)	(c)	(d)
Johansen Cointegration Test, P-Value:	.01	.10	.10	.20
LnACCTS(-1)	1.000000	1.000000	1.000000	1.000000

LnUE(-1)	-0.099794		-0.229313	-0.279225
	[-5.158]***		[-14.210]***	[-5.067]***

LnMON(-1)	-1.131793	-1.852541
	[-7.193]***	[-14.646]***

C	4.026392	12.90664	-9.958488	-9.633628
Error Correction:	D(LNACCTS)	D(LNACCTS)	D(LNACCTS)	D(LNACCTS)
CointEq1	-0.099030	-0.061111	-0.046168	-0.021387
	[-4.530]***	[-2.509]*	[-4.189]***	[-1.680]^oo

D(LnACCTS(-1))	0.786376	0.912327	0.709588	0.728941
	[6.128]***	[6.419]***	[ 5.099]*	[ 5.476]***

D(LnACCTS(-2))	0.011106	0.071534	0.186215	-0.029469
	[0.073]	[0.389]	[ 1.131]	[-0.184]

D(LnACCTS(-3))	0.016312	-0.164988	-0.082101	0.326010
	[0.108]	[-0.968]	[-0.503]	[ 2.268]*

D(LnACCTS(-4))	0.201309	0.151225	0.137935	-0.346573
	[1.783]^oo	[1.040]	[ 1.104]	[-3.106]**

∑_t D(LnACCTS(-t))	1.01510	0.970097	0.951636	0.678909
	[13.392]***	{10.395]***	[11.925]***	[7.930]***

D(LnUE(-1))	0.003822		4.393E-03	7.167E-03
	[0.801]		[ 1.156]	[ 0.967]

D(LnUE(-2))	-0.018154		-0.016161	-0.015226
	[-3.219]**		[-3.839]***	[-1.971]^oo

D(LnUE(-3))	-0.000628		-4.846E-03	-2.387E-03
	[-0.115]		[-1.139]	[-0.302]*

D(LnUE(-4))	-0.013051		-0.015700	-7.389E-03
	[-3.444]**		[-3.699]***	[-1.016]

∑_t D(LnUE(-t))	-0.02801		-0.032315	-0.017835
	[-2.455]*		[-3.930]***	[-1.405]

D(LnMON(-1))	-0.122727	-0.103439
	[-2.852]**	[-2.043]^oo

D(LnMON(-2))	-0.051672	-0.085094
	[-0.948]	[-1.642]^o

D(LnMON(-3))	-0.118640	-8.616E-03
	[-1.398]	[-0.168]

D(LnMON(-4))	-0.039625	-3.743E-03
	[-0.490]	[-0.054]

∑_t D(LnMON(-t))	-0.332664	-0.200892
	[-1.870]^oo	[-1.384]

Constant	0.010038	4.566E-03	5.096E-03	0.019485
	[1.254]	[0.730]	[ 1.078]	[ 2.213]*
Observations	39	39	39	50
R-squared	0.926	0.859	0.879	0.859
Adj. R-squared	0.886	0.815	0.842	0.827
Log likelihood	117.969	107.929	111.685	104.540
Akaike AIC	-5.472	-5.022	-5.215	-3.782
Schwarz SC	-4.869	0.905	-4.788	-3.399
P-val. LM test (1)	0.986	0.951	0.397	0.000
P-val. LM test (2)	0.613	0.159	0.131	0.133
P-val. LM test (3)	0.148	0.073	0.457	0.065
P-val. LM test (4)	0.243	0.476	0.083	0.008
P-val. LM test (5)	0.820	0.905	0.624	0.973

* Note: For Column (d), which only includes Accounts and Unemployment, sample is extended to its maximum, 1948-2002.

Sources: WIR Annual Reports (Rapport de Gestion), World Bank Development Indicators, 2004.

Table 3: Pairwise Granger Causality tests: WIR Accounts, Unemployment, and Money Supply (M2), 1960-2002

Lags: 4
Null Hypothesis: No Granger Causality of	Obs.	F-Statistic	P-value
LnUE upon LnACCTS	50	1.16002	0.34209
LnACCTS upon LnUE		0.93729	0.45176

LnUE upon LnACCTS	43	2.33012	0.07577
LnACCTS upon LnUE		1.94024	0.12620
LnMON upon LnACCTS	40	0.93776	0.45511
LnACCTS upon LnMON		1.23926	0.31474
LnMON upon LnUE	39	6.32342	0.00082
LnUE upon LnMON		2.74761	0.04650
Lags: 3
LnUE upon LnACCTS	43	2.44883	0.07940
LnACC upon LnUE		2.24093	0.10019
LnMON upon LnACCTS	41	2.23398	0.10207
LnACCTS upon LnMON		1.41519	0.25524
LnMON upon LnUE	40	7.07425	0.00084
LnUE upon LnMON		3.32948	0.03130

Table 4: Turnover in the WIR Exchange Network, as Explained by Money Supply (M2) and GDP, 1960-2003

[t-stats] in parentheses; ***: p-value < 0.001, **: p-value < 0.01, * : p-value < 0.05, ^oo: p <0.1; ^o: p <0.15

Cointegrating Equation:	(a)	(b)	(c)	(d)	(e)
Johansen Cointegration Test, P-Value:	0.10	0.05	0.10	0.01	0.05
LnTURN(-1)	1.000000	1.000000	1.000000	1.000000	1.000000

LnMON(-1)	-4.874644	-8.244366	-1.830236
	[-3.586]***	[-5.116]***	[-6.091]***

LnGDP(-1)	5.760765	12.54567		-5.997376	-3.430694
	[ 2.300]*	[ 4.390]***		[-5.758]***	[-8.093]***

Constant	-17.08268	-59.27782	16.47885	68.250310	36.04694
Error Correction:	D(LnTURN)	D(LnTURN)	D(LnTURN)	D(LnTURN)	D(LnTURN)
Coint. Equation	-0.079224	-0.040163	-0.076565	-4.023E-03	-0.044820
	[-2.644]*	[-2.771]**	[-2.906]**	[-0.27497]	[-2.388]*

D(LnTURN(-1))	0.573234	0.589409	0.686543	0.766490	0.585649
	[3.247]**	[3.737]***	[4.693]***	[ 4.87723]	[ 4.372]***

D(LnTURN(-2))	0.323044	0.324488^oo	0.248226	0.128213	0.302734
	[1.595]^o	[1.94044]	[1.602]^o	[ 0.82271]	[ 2.281]*

D(LnTURN(-3))	0.072986
	[0.372]

∑_t D(LnTURN(-t))	0.96926	0.91390	0.93477	0.894704	0.888383
	[8.694]***	[9.741]***	[9.561]***	[8.767]***	[14.965]***

D(LnMON(-1))	-0.360272	-0.363954	-0.066805
	[-1.802]^oo	[-1.835]^oo	[-0.482]

D(LnMON(-2))	-0.193820	-0.186259	-0.313684
	[-0.938]	[-0.997]	[-2.361]*

D(LnMON(-3))	0.087171
	[0.462]

∑_t D(LnMON(-t))	-0.46692	-0.55021	-0.38049
	[-1.105]	[-1.825]^oo	[-1.948]^oo

D(LnGDP(-1))	-1.41559	-1.345752		-1.071322	-0.761633
	[-2.521]*	[-2.459]*		[-2.503]*	[-1.924]^oo

D(LnGDP(-2))	0.095148	0.233857		0.841125	0.686411
	[0.153]	[0.515]		[ 2.065]*	[ 1.957]^oo

D(LnGDP(-3))	0.089058
	[0.200]

∑_t D(LnGDP(-t))	-1.23139	-1.11189		-0.230197	-0.075222
	[-1.866]^oo	[-2.094]*		[-0.516]	[-0.177]

Constant	0.034573	0.038895	0.011874	5.738E-03	-3.128E-03
	[1.90229]^oo	[2.294]*	[1.194]	[ 0.433]	[-0.213]
Observations	40	41	41	41	53
R-squared	0.796	0.769	0.743	0.715	0.837
Adj. R-squared	0.726	0.720	0.706	0.675	0.820
Log likelihood	69.274	68.968	66.750	64.661	73.698
Akaike AIC	-2.914	-2.974	-2.963	-2.862	-2.555
Schwarz SC	-2.449	-2.640	-2.713	-2.611	-2.332
P-val. LM test (1)	0.970	0.557	0.707	0.179	0.517
P-val. LM test (2)	0.753	0.530	0.843	0.012	0.067
P-val. LM test (3)	0.367	0.711	0.905	0.936	0.518
P-val. LM test (4)	0.806	0.147	0.234	0.937	0.818

Sources: WIR Annual Reports (Rapport de Gestion), World Bank Development Indicators, 2004

Table 5: Pairwise Granger Causality tests: WIR Turnover, GDP, and Money Supply (M2), 1960-2003

Lags: 3
Null Hypothesis: No Granger Causality of	Obs.	F-Statistic	P-value
LnMON upon LnTURN	41	2.79406	0.05506
LnTURN upon LnMON		2.61596	0.06691
LnGDP upon LnTURN	44	3.71742	0.01966
LnTURN upon LnGDP		2.10155	0.11666
LnGDP upon LnMON	41	1.07191	0.37395
LnMON upon LnGDP		14.3525	3.3E-06
Lags: 2
LnMON upon LnTURN	42	0.77078	0.46994
LnTURN upon LnMON		1.26698	0.29362
LnGDP upon LnTURN	44	2.78191	0.07423
LnTURN upon LnGDP		2.87996	0.06814
LnGDP upon LnMON	42	0.86046	0.43126
LnMON upon LnGDP		20.5973	9.7E-07

Table 6: Credit in the WIR Exchange Network, as Explained by Money Supply (M2) and GDP, 1960-2003

(standard errors) and [t-stats] in parentheses, ***: p-value < 0.001, **: p-value < 0.01, * : p-value < 0.05, ^oo: p <0.1; ^o: p <0.15

Cointegrating Equation:	(a)	(b)	(c)	(d)	(e)
Johansen Cointegration Test, P-Value:	0.07	0.05	0.15	0.05	0.01
LnCRED(-1)	1.000000	1.000000	1.000000	1.000000	1.000000

LnMON(-1)	-5.379977	-9.364830	-2.393765		-3.307454
	[-4.649]***	[-4.930]***	[-10.275]***		[-9.373]***

LnGDP(-1)	6.221436	14.21366		-5.372218
	[2.923]**	[ 4.257]***		[-6.514]***

Constant	-15.41026	-64.91655	24.63596	61.54493	35.66864
Error Correction:	D(LnCRED)	D(LnCRED)	D(LNCRED)
CointEq1	-0.086261	-0.025332	-0.095920	-0.025688	-0.124612
	[-2.705]*	[-1.840]^oo	[-2.361]*	[-0.891]	[-3.686]***

D(LnCRED(-1))	0.530399	0.626873	0.692746	0.736722	0.263086
	[3.029]**	[3.682]***	[4.204]***	[ 4.265]	[ 2.012]^oo

D(LnCRED(-2))	0.080187	0.177155	0.053711	0.047170	0.484968
	[0.401]	[0.991]	[0.263]	[ 0.220]	[ 4.379]***

D(LnCRED(-3))	0.350244		0.148277	0.046772	0.150581
	[1.743]^oo		[0.850]	[ 0.260]	[ 1.189]^oo

∑_t D(LnCRED(-t))	0.96083	0.80403	0.894735	0.830665	0.898635
	[6.721]***	[6.640]***	[6.521]***	[5.700]***	[9.616]***

D(LnMON(-1))	-0.556649	-0.339104	-0.204543
	[-2.276]*	[-1.600]^o	[-1.262]

D(LnMON(-2))	-0.006542	0.099423	-0.081741
	[-0.030]	[0.468]	[-0.512]

D(LnMON(-3))	0.038870		-0.121267
	[0.187]		[-0.789]

∑_t D(LnMON(-t))	-0.52432	-0.23968	-0.407551
	[-1.108]	[-0.718]	[-1.293]

D(LnGDP(-1))	-1.439979	-1.000384		-0.128998	0.025940
	[-2.156]*	[-1.601]^o		[-0.261]	[ 0.046]

D(LnGDP(-2))	-0.362967	-0.019670		-0.156727	-0.386
	[-0.552]	[-0.039]		[-0.294]	[-0.631]

D(LnGDP(-3))	-0.075068			0.563805	-0.208374
	[-0.148]			[ 1.247]	[-0.425]

∑_t D(LnGDP(-t))	-1.87801	-1.02005		0.278079	-0.568319
	[-2.188]*	[-1.729]^oo		[0.083]	-0.872

Constant	0.049263	0.035872	0.014946	1.137-E3	0.010071