# Currency preferences and the Australian dollar

## Currency preferences and the Australian dollar

**Currency preferences and the Australian dollar Geoffrey Kingston*, Martin Melecky School of Economics, University of New South Wales, Kensington, NSW 2052, Australia Abstract We investigate currency substitution and currency complementarity in the case of the Australian dollar. Data spanning 1984e2003 contain evidence of the Australian dollar’s substitution for the Deutschmark and complementarity with the yen and the US dollar, consistent with the theory that international variables will in general affect the demand for domestic money. Atemporally nonseparable preferences also give rise to the possibility of third-currency effects. **

Our regressions find some evidence of these. For example, a rise in the US federal funds rate has been associated with rises in the value of the Australian dollar against the mark and yen, controlling for changes in other interest rates and in money supplies and real outputs.

Ó 2007 Elsevier Ltd. All rights reserved. JEL codes: E41; F31; F36 Keywords: Substitution; Complementarity; Money demand; Third-currency effects; Exchange rate dynamics 1. Introduction This paper reports the results of regression tests for multilateral influences on the demand for and value of the Australian dollar over the period 1984e2003. Its theoretical basis is atemporally nonseparable preferences. Specifically, this paper builds on the currency substitution literature and introduces the possibility of currency complementarity. Either feature of currency preferences implies international scale variables and opportunity-cost variables in the domestic * Corresponding author.

Tel.: þ61 2 9 385 3345; fax: þ61 2 9 313 63. E-mail address: g.kingston@unsw.edu.au (G. Kingston).

0261-5606/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jimonfin.2006.11.001 Journal of International Money and Finance 26 (2007) 454e467 www.elsevier.com/locate/jimf

money demand function; moreover, there will generally be third-currency effects in exchangerate determination. Money demand regressions give evidence of significant substitution between the Australian dollar and the Deutschmark,1 and significant complementarity of the Australian dollar with the Japanese yen and the US dollar. Regressions that seek to explain changes in the external values of the Australian dollar in terms of changes in money supplies, interest rates and GDPs give further indications of complementarity between the Australian dollar and the yen.

The paper is organized as follows. Section 2 relates our research to previous work, including an update of a landmark comparison of income velocities of circulation (Brittain, 1981). Section 3 outlines a theory of currency substitution and currency complementarity. Section 4 investigates the associated empirics. It re-examines the demand for the Australian dollar, and investigates third-currency effects on its external value. Section 5 summarizes and concludes. 2. Antecedents Theory typically postulates that the demand for a nation’s money is wholly determined by two domestic macroeconomic variables.

Thus the textbook condition for equilibrium in the market for the Australian dollar is M P ¼ LðY;RÞ; ð1Þ where M is the outstanding stock of Australian money, P is the general level of prices of Australian-produced goods and services, Y is the general level of real economic activity and R is some measure of short-term interest rates in Australia. If prices are assumed sticky, we describe Eq. (1) as the ‘‘LM curve’’. If not, the term ‘‘portfolio balance schedule’’ is often used instead. We assume vL/vY > 0 and vL/vR < 0; Y is the ‘‘scale variable’’, and R is the ‘‘opportunity-cost’’ variable in the money demand function.

Tobin (1969) added bond and stock returns to the menu of opportunity-cost variables, with bills, bonds and stocks all assumed to be ‘‘gross substitutes’’ for money. This has no deep theoretical rationale. By contrast, the unaugmented money demand function on the righthand side of Eq. (1) is readily given a theoretical justification; candidate microfoundations for money demand have included money directly in the utility function (Lucas, 2000), and money indirectly in the utility function via a cash-in-advance constraint (Lucas, 1984; Lucas and Stokey, 1987). Whether the resulting demand for money is direct or derived matters little in applications.

These include estimating money demand functions (Mark and Sul, 2003) and explaining the behavior of exchange rates (Obstfeld and Rogoff, 1996). The standard model of the money market [i.e., Eq. (1)] is restrictive compared to treatments of some other markets. A case in point is alcoholic beverages (Clements and Selvanathan, 1991; Clements et al., 1996). Holding constant the total consumption of alcohol in Australia, there is evidence of substitution across beer and wine in the sense that the two relevant cross-price elasticities are negative, consistent with the fact that a fall in beer consumption per head has gone hand in hand with a rise in wine consumption per head.

**On the other hand, there is evidence of complementarity between beer and spirits in the sense that if we hold constant the marginal utility of income, then a rise in the relative price of spirits has been associated with a fall in 1 Beginning in 1999 the Deutschmark was supplanted by the euro. 455 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467**

the consumption of beer, a finding that has been rationalized by the ‘‘formal dinner model’’2 of an evening meal that kicks off with beer and finishes with spirits. In this case, wine is neither a substitute nor a complement for the other two beverages, in the sense that if we again hold constant the marginal utility of income then a change in the relative price of wine does not induce a significant change in the consumption of either beer or spirits. A challenge for monetary economics is to match this level of analytical sophistication. 2.1. Currency substitution Theoretical and empirical research on money demand has given consideration to the possibility of currency substitution (related to the concept of ‘‘dollarization’’).

The pioneering contribution was made by Boyer (1970), and an influential survey was conducted by Giovannini and Turtelbloom (1994).

For developed-world currencies the evidence from money demand regressions has been mixed. Among the pound, the mark and the US dollar, for example, only German M0 and M1 can be regarded as having shown anything like persuasive evidence of substituting for some other currency (Brittain, 1981; Cuddington, 1982; Traa, 1985). In the case of Canada, for example, scant evidence has been found, despite the plausibility of the hypothesis that US dollars are substitutes for Canadian ones (Bordo and Choudri, 1982; Traa, 1985). Since the 1990s, research on currency substitution has continued apace, but has largely been confined either to pure theory or to the empirics of transition economies; see, e.g., Trejos and Wright (2000) and Liviatan (1993), respectively.

Moreover, the possibility of currency complementarity seems never to have been considered in any setting. The present paper allows for nonseparable currency preferences in the case of developed-world currencies, including the possibility of complementarity, and with special reference to the Australian dollar. 2.2. Velocity comparisons Brittain’s (1981) evidence of substitution between the Deutschmark and the US dollar included a graphical comparison of income velocities of money in Germany and the United States. Rising velocity of US M1 contrasted with falling velocity of German M1, suggesting that there had been substitution of Deutschmarks for US dollars.

While never represented as more than a prelude to formal regression tests, Brittain’s graphical exercise shed light, and proved to be influential.

This subsection updates Brittain’s V1 comparisons to the period spanned by our regressions, namely 1984e2003, and broadens the scope of the exercise by bringing in Japan and Australia. Additionally, we calculate pairwise correlation coefficients, across the four countries just mentioned. The coefficients include logged and differenced V0, as well as logged and differenced V1. For details see Figs. 1 and 2. Fig. 1 compares the logs of V1 in Germany, Japan and the United States over the period 1985 to the turn of the century (v denotes logs).

Brittain’s finding that German and US V1 are negatively correlated is confirmed by Fig.

**1. However, the extent of negative correlation between logged and differenced V1 in the two 2 This is sometimes described as the ‘‘barbecue’’ model of the demand for alcoholic beverages. 456 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467**

- countries is only
- 0.05. The relevant correlation coefficient for logged and differenced V0, namely
- 0.01, is even smaller in absolute value, although it too has a negative sign. For the GermanyeJapan pairing we get a mixed message; the correlation is negative for V1 but positive for V0. Accordingly, Fig. 1 sheds little light on whether there has been either substitution or complementarity between the mark and the yen. By contrast, there are two positive coefficients for the JapaneUS pairing, consistent with complementarity between the yen and the US dollar. In this study, formal multivariate tests for substitution and complementarity are confined to pairs involving the Australian dollar. At this point we give an informal indication; see Fig. 2. Fig. 2 suggests that the Deutschmark substituted for the Australian dollar; the relevant correlation coefficients are
- 0.03 and
- 0.08. By contrast, Fig. 2 suggests also that the yen complemented the Australian dollar; the relevant coefficients are 0.04 and 0.23. Both pairs 1985 1990 1995 2000 -.25 -.2 -.15 -.1 -.05 .05 .1 .15 .2 corr(jap, us) corr(ger, jap) corr(ger, us) Fig. 1. Comparison of V1 velocity for the US, Japan and Germany. Source: Reserve Bank of Australia; International Financial Statistics (IMF). Notes: The figure shows pairwise correlations of Dv1 velocities in Germany, Japan and the US calculated stepwise. v1 is the log of quarterly GDP expressed as a fraction of the volume of M1 for each country. In 1999:1 euro M1 is spliced to German M1.

1985 1990 1995 2000 -.5 -.4 -.3 -.2 -.1 corr(au, ger) corr(au, jap) corr(au, us) Fig. 2. Pairwise comparison of V1 velocity for Australia to V1 for the US, Japan and Germany. Source: Reserve Bank of Australia; International Financial Statistics (IMF). Notes: See the notes to Fig. 1. The pairwise correlations between Dv1 in Australia and in Germany, Japan and the United States calculated stepwise. 457 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467

of results are broadly consistent with regression results in Section 4 (which warrant more weight than Figs.

1 and 2). Likewise, the US dollar appears to have complemented the Australian dollar, and the regressions in Section 4 corroborate this. 3. Theory 3.1. Money demand Eq. (1) is supplanted here by the general formulation M1 P1 ¼ L1ðY;RÞ; ð2Þ where Y h (Y1,.,Yn) is a vector of n GDPs measured in constant dollars, and R h (R1,.,Rn) is a vector of n short-term nominal interest rates. In other words, there are n scale variables and n opportunity-cost variables.

- As in standard theory we predict vL1/vY1 > 0 and vL1/vR1 < 0. We have vL1=vR2W0 ð3Þ according to whether currency 2 is a substitute for or complement with currency 1. The intuition for the case of substitutes (vL1/vR2 > 0) is as follows. Imagine that the representative agent is a ‘‘citizen of the world’’ e a cosmopolitan individual without any particular national habitat. Suppose further that currency 2 is a substitute for currency 1 in the Edgeworth sense, that is, the two currencies satisfy similar wants or needs.3 If R2 rises then standard theory holds that vL2/vR2 < 0; there will be a fall in the equilibrium real quantity of currency 2. Having relinquished some of the liquidity services provided by currency 2, the representative agent in the world economy will substitute towards one or more other currencies generating similar services. Given Covered Interest Parity we can use the forward discount on currency 1, D h R1
- R2, as the ‘‘international’’ opportunity-cost variable in Eq. (2), instead of R2. If D falls while R1 remains constant then there must be an equal rise in R2. The demand for currency 1 is again predicted to rise. To the extent that Uncovered Interest Parity holds, the fall in D represents an expectation of appreciation of currency 1 against currency 2. That currency 1 will appreciate against currency 2 is plausible without being compelling. What is essential is that we include more than one opportunity-cost variable in Eq. (2), thereby controlling for the money/discount bill margin and the domestic money/foreign money margin.

Intuition for the case of complements follows readily. Suppose that currency 2 complements currency 1 in the Edgeworth sense; in other words, the two monies are used in conjunction with 3 An extended version of this paper (available from the authors on request) derives microfoundations for currency substitution and complementarity by generalizing single-currency models of cash and credit goods (see Lucas, 1984; Lucas and Stokey, 1987; Boyer and Kingston, 1987). Roughly speaking, the condition for substitution between currencies i and j (in the Edgeworth sense) on the cross-partial derivative of the period utility function U of the representative agent in the world economy is v2 U=ðv cash good i$v cash good jÞ < 0.

In equilibrium, however, additional consumption of any cash good requires a matching reduction in the consumption of the credit good denominated in the same currency, for a given level of output. This is consistent with Eq. (3). On the other hand, it is not strictly consistent with Edgeworth concepts of substitution and complementarity, which are purely partial-equilibrium concepts, and so do not impose this material-balance condition. Because pure Edgeworth concepts of currency substitution and complementarity are not readily testable, this paper utilizes condition (3).

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each other. Once a rise in R2 has shrunk the real stock of currency 2, the representative agent no longer has the same need for currency 1, and the demand for it will fall. The interplay between foreign scale variables and domestic real balances is less straightforward. On the one hand, one might expect the effect on the demand for currency 1 of a change in Y2 to be similar to that of Y1. A counter-argument is that a Y2 rise, having induced a rise in M2/P2, might lead to less need for currency 1.

This counter-argument has less force in the case of complements. Overall, we settle for vL1=vY2X 0 ð4Þ with a presumption that the sign is more likely to be positive in the case of complements.4 3.2. Restrictions One would expect the effects of multiple changes in scale or opportunity-cost variables to be constrained by suitable multivariate analogues of the standard conditions vL/vY > 0 and vL/vR < 0. For example, a 1% rise in all national GDPs would be expected to raise the demand for currency 1, notwithstanding the ambiguity suggested by Eq. (4). Likewise, a one percentage point rise in all national interest rates would be expected to reduce the demand for currency 1, even in the case of substitution between currencies 1 and 2.

- 3.3. Third-currency effects Now introduce the simplifying assumption of purchasing power parity between currencies 1 and 2, that is, P1 ¼ SP2, where S stands for units of currency 1 per unit of currency 2.5 In this case we have S ¼ M1=L1 M2=L2 ð5Þ so that Dln S ¼ Dln M1
- Dln M2
- Dln L1 þ Dln L2zDln M1
- Dln M2 þ bDln Y þ cDR; ð6Þ where D is the first-difference operator, b is a vector of coefficients defined by the vector of differences between income elasticities of money demands, and c is a vector of coefficients defined by the vector of differences between interest semi-elasticities of money demands. For example, the first element of b is defined as Y1vL1=L1vY1
- Y1vL2=L2vY1. The coefficients b and c can be interpreted in terms of the previous discussion. Suppose initially that there are no relationships of currency substitution or complementarity in the 4 The extended version of this paper analyzes this ambiguity in the context of a two-country analysis of a model with cash goods and credit goods. The ‘‘perverse’’ outcome of a negative elasticity of demand for domestic money with respect to some foreign scale variable is promoted by Edgeworth substitution between domestic cash goods and foreign credit goods, Edgeworth complementarity between domestic and foreign credit goods, and substitution between domestic and foreign monies.

5 The extended version of this paper does not impose purchasing power parity. 459 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467

system. A rise in the interest rate denominated in currency 1 will lower the demand for currency 1 without any effect on the demand for currency 2. It will therefore be associated unambiguously with a depreciation of currency 1 against currency 2.6 Now suppose that currencies 1 and 3 are substitutes and there are no other relationships of currency substitution or complementarity elsewhere within the system.

Then a rise in the interest rate denominated in currency 3 will raise the demand for currency 1. It will therefore be associated with a higher value of currency 1, other things equal.

4. Empirics This section presents our empirical findings on currency preferences and the Australian dollar. 4.1. Money demand We employ M0 (monetary base) and M1 (narrow money) measures in order to lessen the interest-bearing components of the monetary aggregates that are used as dependent variables, thereby making it reasonable to use interest rates as opportunity costs. Cash-in-advance theory suggests a beginning-of-period dating for money stocks rather than end-of-period or periodaverage dating. Similarly, the interest rates (opportunity costs) are dated on a beginning-ofperiod basis. Cash-in-advance theory suggests also that GDP deflators should be used for the purpose of transforming nominal money balances into real ones.

Our data are quarterly and span 1984:1e2003:3. The choice of start date represents a compromise between minimizing measurement difficulties arising from the financial innovations and deregulations that occurred during the first half of the 1980s in Australia (Milbourne, 1990) and maximizing the available span of data. It implies that our sample falls entirely within the post-1983:4 era of floating exchange rates. The transition in 1999:4 from Deutschmarks to euros is handled by dummy variables. All the variables employed in our analysis are seasonally adjusted whenever a seasonal is present.

The money demand regressions reported below are estimated by the Johansen technique, which is regarded as being more efficient than dynamic OLS or the ARDL method assuming the diagnostics are sound.

The estimated equation is mkt ¼ a þ pt þ b ln Yt þ gRt þ dDt þ 3t; ð7Þ where mkt (k ¼ 0,1) is the log of either Australia’s monetary base (k ¼ 0) or volume of M1 (k ¼ 1), a is the intercept term, pt is the log of Australia’s GDP deflator, b h (bAUD, bDEM, bJPY, bUSD) is a row vector of coefficients showing elasticities with respect to scale variables, Yt is a column vector of GDPs and g h (gAUD, gDEM, gJPY, gUSD) is a row vector of coefficients showing semi-elasticities with respect to opportunity-cost variables in Rt. For example, bAUD is the elasticity with respect to Australia’s GDP, and gAUD is the semi-elasticity with respect to Australia’s 90-day Bank-Accepted Bill rate.

The variable Dt is a shift dummy such that 6 Recall that this mental experiment holds constant the nominal quantity of currency 1, thereby controlling for any liquidity effect (specifically, monetary contraction) associated with the postulated rise in the interest rate denominated in currency 1.

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Dt ¼ I (>1998:Q2) to eliminate the detected instability in M1 money demand. The error term is 3t. Results are set out in Table 1. Both estimations carried out satisfy common diagnostic tests as reported in the last three rows of Table 1. We tested for whether the demand for money is linear homogeneous in the general level of prices. This restriction was accepted in the case of M0 and M1 alike. Consider now the scale variables. Domestic GDP has a significant influence on the demand for the Australian dollar as measured by either M0 or M1, as one would expect.

On the other hand, German GDP has a significantly positive effect on the demand for Australian M0 even while it has a significantly negative effect on the demand for M1. Then Japanese GDP has a significantly negative effect on the demand for Australian M0 but not on M1; these disparities are puzzling. US GDP has no significant effect on the demand for the Australian dollar. Consider next the opportunity-cost variables. The domestic opportunity costs of holding M0 and M1 confirm the significantly negative signs predicted by standard theory. The absolute size of the M0 semi-elasticity is small, consistent with the low volatility of V0 over the sample period.

The German opportunity-cost variable is insignificant in the case of M0. On the other hand, it is significant and positive in the case of M1. Hence, there is evidence for substitution between the Deutschmark and the Australian dollar in the case of M1. By contrast, the Japanese opportunity-cost variable is significant and negative; there is evidence for complementarity between the Japanese yen and the Australian dollar in the case of M1. Currency complementarity is consistent with the observation that the real economy of Japan is a commodity-importing one that is exceptionally complementary with commodity-exporting Australia.7 The coefficient on the US federal funds rate is insignificant in the case of M0.

But it is significant and negative in the case of M1, although the estimated US semi-elasticity is smaller in absolute value than its Japanese counterpart. This is evidence for complementarity between the US dollar and its Australian counterpart. Intuition suggests that the two currencies would be substitutes, given the similarities between the structures of the two economies. One possible explanation is multicolinearity involving the US and Australian opportunity-cost variables, owing to the considerable influence of US monetary policy on Australian monetary policy. Another explanation runs as follows: As one of the very few first-world commodity exporters, the Australian economy tends to be complementary with the developed-world economy that accounts for the bulk of Australia’s international trade and payments, yet it is scarcely an exaggeration to say that the United States is the developed-world economy.

During the 1990s, for example, the United States was the destination of over half the world’s international portfolio investment. In this way the Australian dollar may have been pushed off its natural relationship of being a substitute for its US counterpart.

4.2. Restrictions An equiproportionate increase in the vector of outputs, at home and abroad, should raise the demand for domestic money (here, the Australian dollar). Similarly, an equal increase in the vector of interest rates should reduce the demand for domestic money e recall Section 3. Accordingly, we investigate ‘‘global’’ scale and opportunity-cost coefficients e sums of income elasticities, and sums of semi-elasticities with respect to interest rates. 7 Without ruling out the possibility of a capital-account explanation. 461 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467

- A preliminary exercise based on Table 1 is to calculate the global scale and opportunity-cost coefficients implied by it. In the case of M0 the relevant global coefficient for scale variables is given by 0.981 þ 0.608
- 0.421 ¼ 1.168. Likewise, the global coefficient for the opportunity cost of holding Australian M0 is given by
- 0.004. In the same way, the global scale variable for M1 is given by 2.531
- 1.182 ¼ 1.349, and the global opportunity-cost variable for M1 is
- 0.027 þ 0.023
- 0.031 ¼
- 0.035. Each of the global coefficients therefore has the expected sign. Moreover, each is of a magnitude that is no less reasonable than its domestic counterpart. Notably, the global scale variables are close to one. Unity is a plausible value for the income elasticity of demand for money in the long run.

Table 2 reports results of likelihood-ratio tests of hypotheses that global scale variables and opportunity-cost variables are not different from zero. The first row reports the results of tests of the hypothesis that the global scale variables sum to zero. This hypothesis is rejected at the 10% level in the case of M0 and the 1% level in the case of M1. The second row reports the results of tests of the hypothesis that the global opportunity-cost variables sum to zero. This hypothesis is seen to be rejected at the 1% level for M0 and M1 alike.

- Table 2 Restrictions Hypothesis Likelihood-ratio tests M0 M1 P g
- i ¼ 0 3.5502 [0.0595]* 12.765 [0.0004]*** P b
- i ¼ 0 9.3944 [0.0022]*** 21.121 [0.0000]*** Notes * indicate rejection of the null at the 10%, 5% and 1% significance level, respectively. Each result corresponds to the relevant LR statistic with the p-value reported in squared brackets. Table 1 Demand for the Australian dollar Independent variables (logs except for interest rates) Dependent variables (logs) M0 M1 AUD gdp deflator Restricted to 1 Restricted to 1 0.25136 [0.6161] 0.63842 [0.4243] AUD gdp 0.981 (0.429)** 2.531 (0.287)*** DEM gdp 0.608 (0.174
- 1.182 (0.380)*** JPY gdp
- 0.421 (0.163)** e USD gdp e e AUD 90-day BAB rate
- 0.004 (0.002)**
- 0.027 (0.006)*** DEM call money rate e 0.023 (0.012)** JPY call money rate e
- 0.031 (0.015)** USD federal funds rate e
- 0.018 (0.008)** Constant
- 7.107 (0.429
- 17.399 (2.036)*** Dummy 98Q2-end NA
- 0.409 (0.070)*** Residual AR (1e3) F-test 0.98302 [0.4068] 0.95779 [0.4185] Residual normality c2 -test 1.213 [0.5453] 2.0404 [0.3605] Residual heteroscedastity F-test 1.2346 [0.2749] 0.70048 [0.8297] Source: RBA, IMF * e stand for significance at 10%, 5% and 1% level, respectively. Standard errors are in parentheses.

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- 4.3. Exchange rates Nonseparable currency preferences imply that there will generally be third-currency effects in exchange-rate determination, yet the bulk of the pre-existing literature employs bilateral models. One exception is the analysis of Hodrick and Vassalou (2002) based on interest rates with multiple maturities. Bilateral modeling is found to be inadequate for the major currencies. For example, they have found that UK interest rates have affected DEM/USD and DEM/JPY exchange rates. Likewise, Nucci (2003) finds third-currency interest-rate effects in the determination of major exchange rates. This section tests for third-currency effects on the external values of the AUD over the period 1984:1e2003:3 (1998:4 for DEM/AUD). In contrast to previous investigations we examine the effects of third-currency outputs as well as those of third-currency interest rates, consistent with the analysis of Section 3. Moreover, the estimates here represent an ex post accounting for exchange-rate changes rather than the predictive frameworks employed by Hodrick and Vasssalou, and Nucci.8 Our estimated equation was derived in Section 3. It is reproduced below, with slightly different notation and with the addition of an intercept term a, dummies Dt for the introduction of the euro, and an error term ht 9 : sjt ¼ a þ Dln Mt
- Dln Mjt þ bDln Yt
- cDRjt þ dDt þ ht: ð8Þ The dependent variable sjt is the annual depreciation of the Australian dollar against currency j, where j denotes marks, yen or US dollars. The intercept term a on the right-hand side of Eq. (8) is predicted to be zero. The coefficient on the annual change in the log of the Australian money supply, Dln Mt, is restricted to equal 1. Likewise, the coefficient on the annual change in the log of the money supply of country j, Dln Mjt, is restricted to equal
- 1. The vector Dt includes shift and impulse dummies to account for the introduction of the euro in 1999:Q4. Table 2 found ‘‘international’’ interest-rate effects to be present only in the case of M1. Accordingly, Table 3 confines attention to results for M1 measures of monetary aggregates.10 The dependent variable in the regression results reported in the first panel of Table 3 is the annual rate of decrease in value of the Australian dollar against the mark. Likewise, the dependent variable in the second panel is the annual rate of decrease in value against the yen, and the dependent variable in the third panel is the annual rate of decrease in value against the US dollar. In all three cases we have imposed the restriction of a unit coefficient on the relative rate of money supply growth, in accord with Eq. (8).

Each of the three columns of figures in Table 3 is consistent with the hypothesis of an insignificant constant term. Likewise, each contains a positive coefficient on the change in the Australian 90-day Bank Bill rate, consistent with the standard prediction of a negative domestic semi-elasticity of money demand.11 Moreover, two of the three estimates are significant at the 5% level. On the other hand, only one of the three coefficients corresponding to foreign 8 We anticipate from, e.g., Faust et al. (2003) that the goodness of fit of such regressions will be mediocre at best, even ex post, possibly because of the difficulties in identifying or measuring exchange-rate fundamentals.

9 The error term should be interpreted as a consequence of measurement error rather than the arrival of new information.

10 The inclusion of M1 money only is also dictated by unavailability and inconsistency of M0 money measures across the countries considered. 11 This result is also consistent with those of Table 1. 463 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467

- semi-elasticities of money demand is significant at the 5% level. Specifically, the third panel reports a coefficient on changes in the US federal funds rate of the predicted negative sign; the associated t statistic is
- 3.14. Another puzzling set of results is that all but one of the coefficients on the change in the log of domestic or foreign GDP is insignificant.12 This is inconsistent with the prediction of monetary models of the exchange rate e including the variant here e that currency depreciation is associated with low domestic output growth and high foreign output growth.
- The first column of figures in Table 3 contains a negative coefficient on changes in the US federal funds rate. Specifically, the coefficient is
- 0.238, and the associated t statistic is
- 2.655. That the Australian dollar has tended to gain in value against the mark when US interest rates are raised is inconsistent with either a dominant effect of complementarity between the US dollar and its Australian counterpart, or a dominant effect of substitution bet ween the US dollar and the mark. Hence the negative coefficient in question is at odds with two empirical findings reported earlier in this paper.
- The second column of figures in Table 3 again contains a negative coefficient on changes in the US federal funds rate. The coefficient is
- 0.192, and the associated t statistic is
- 2.412. That the Australian dollar has tended to gain in value against the yen when US interest rates are raised is inconsistent with a dominant effect of complementarity between the US dollar and its Australian counterpart, but consistent with a dominant effect of complementarity between the US dollar and the yen. Hence the negative coefficient in question is at odds with one empirical finding reported earlier in this paper while being consistent with another. The third column of figures in Table 3 reveals no significant third-currency interest-rate effect on the rate of exchange between the US dollar and its Australian counterpart. This result Table 3 Third-currency effects Independent variables Depreciation of the Australian dollar less relative money growth AUD/DEM AUD/JPY AUD/USD DRAUD 0.2013 (0.1076)* 0.3005 (0.0811)*** 0.2067 (0.0667)*** DRDEM
- 0.1404 (0.1252)
- 0.1174 (0.0973) 0.0903 (0.0970) DRJPY 0.0947 (0.1276) 0.0058 (0.0133) 0.0188 (0.0141) DRUSD
- 0.2382 (0.0897
- 0.1920 (0.0796)**
- 0.2698 (0.0859)*** Dln YAUD
- 26.417 (27.886)
- 32.247 (27.083)
- 11.600 (18.4830) Dln YDEM 1.8196 (5.9621) 2.3347 (3.4357) 0.6009 (2.5993) Dln YJPY
- 4.0180 (5.6858)
- 5.0964 (3.7583)
- 7.0524 (2.9507)** Dln YUSD 2.6271 (11.629) 6.7888 (7.0019) 3.6986 (4.0835) Constant 11.046 (10.673) 8.0108 (8.1573) 1.5420 (5.5968) D99i NA 21.7160 (4.2808)*** 10.3030 (3.7140)*** D99 NA 0.9677 (5.6780)
- 9.0873 (3.6278)** R2 adjusted 0.1134 0.2002 0.2676 Dependent variables: Depreciation of the Australian dollar less relative money growth (% pa). Source: RBA, IMF; D99i e impulse dummy I(99Q1), D99 e shift dummy I(>99Q1). Notes: The data span 1984:1e2003:3, except in the case of positions in DEM, in which case the data end in 1998:4. NeweyeWest HAC standard errors are shown in parentheses * and *** e indicate significance at 10%, 5% and 1% level, respectively. Estimation is by OLS.

12 Specifically, there is a significant coefficient on the rate of growth of Japanese GDP in the equation for the rate of loss of value of the Australian dollar against the US dollar. 464 G. Kingston, M. Melecky / Journal of International Money and Finance 26 (2007) 454e467

can be interpreted as being inconsistent with the findings reported earlier in this paper, which found evidence for substitution or complementarity involving the US dollar and the other three currencies under consideration here. Or it could be interpreted in the case of German interest rates as evidence for substitution between the mark and the Australian dollar that is exactly offset by substitution between the mark and the US dollar.

The positive sign on the coefficient for Japanese interest rates is consistent with our earlier finding of complementarity between the Australian dollar and the yen, but the associated t statistic of 1.333 is too low for significance at the 5% level.

5. Summary and conclusions Atemporally nonseparable currency preferences can be classified under the broad headings of currency substitution and currency complementarity. Substitution and complementarity can each be defined either in utility terms or in terms of the cross-elasticity of money demand with respect to a foreign interest rate. Specifically, substitute currencies serve similar wants and needs in trade and payments, and are evidenced by negatively correlated velocities or positive cross-interest elasticities in a money demand regression. By contrast, complementary currencies are used in conjunction with each other and are evidenced by positively correlated velocities or negative cross-interest elasticities in a money demand regression.

Velocity correlations for the period 1984e1999 corroborated Brittain’s (1981) finding that the Deutschmark and US dollar were substitutes. They also suggested the novel generalization that the yen is a prime candidate for complementarity with other currencies. Money demand regressions were consistent with our preliminary findings based on velocity correlations. They provide a more rigorous basis for inferences about substitution and complementarity. Over the period 1984:1e2003:3, a one percentage point rise in the German call money rate raised the demand for Australia’s M1 in real terms by an estimated 2.3% e almost the same as the absolute value of the semi-elasticity for the Australian 90-day Bank Bill rate, i.e., 2.7%, although much less well determined.

On the other hand, there was no significant effect of the German rate on the demand for M0, even though coefficients on the Australian Bank Bill rate had the standard negative signs for M0 and M1 alike. On balance, then, there is some evidence for substitution between the mark and the Australian dollar. There was a significantly negative coefficient on both the Japanese call money rate and the US federal funds rate in our M1 regression, suggesting complementarity between the Australian dollar and the yen, and also the Australian dollar and its US counterpart. As was noted above, this type of result is new.13 Tests for global restrictions on the demand for the Australian dollar found that the income elasticity of demand for M1 with respect to a global scale variable was much closer to one than the income elasticity of demand with respect to Australian GDP.

Tests for third-currency effects over the period 1984:1e2003:3 were generally difficult to reconcile with our results from money demand regressions. Moreover, the tests did not overturn the standard empirical result that changes in exchange rates are difficult to account for even on an ex post basis. On the other hand, significant third-currency effects were found, and this represents an extension over the standard bilateral model of exchange-rate determination. 13 Bordo and Choudri (1982) report results we would interpret as evidence that the Canadian dollar was neither a substitute nor a complement with its US counterpart.

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Notably, rises in the US federal funds rate were associated with rises in the value of the Australian dollar against both the Deutschmark and the yen. Overall there is considerable evidence for offshore influences on the demand for the Australian dollar and for third-currency effects on its external value. This paper employed singleequation regressions and focused on a small currency. It has therefore scarcely scratched the surface of what atemporally nonseparable preferences might imply for systematic interactions between the major currencies.

One topic for future research is the money-demand analogue of the cross-equation ‘‘symmetry restriction’’ from standard demand analysis. Another topic is moving beyond a bilateral setting when investigating the implications of the ‘‘forward discount puzzle’’. If third-currency effects are present then the forward discount on a currency is not a sufficient statistic for the conditional expectation of its rate of depreciation. Finally, currency substitution can lessen the volatility of exchange rates and is therefore a candidate explanation for the ‘‘excess smoothness’’ of currency depreciation rates relative to stock returns.

Acknowledgements We would like to thank participants in seminars at the University of New South Wales and the University of Sydney, and a session of the 31st Australian Conference of Economists, for helpful comments. Special thanks are due to Kenneth Clements, Lance Fisher and Adrian Pagan. Three referees provided helpful feedback. Carol White provided editorial assistance. Financial assistance from the Australian Research Council is gratefully acknowledged. References Bordo, M.D., Choudri, E.U., 1982. Currency substitution and the demand for money: some evidence for Canada. Journal of Money, Credit and Banking 14, 48e57.

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