Dalida Eini - boi.org.il Review/reveiw 73/surv073_1e.pdf · 2 BankofIsraelEconomicReview73 rate has been managed within acrawling band, in accordance with which gradual, predetermined,andpreannouncedadjustmentsof

Bankof Israel Economic Review 73 (2001), 134

A REEXAMINATION OF THE COMPOSITION OF THE OPTIMALCURRENCY BASKET FOR ISRAEL

Dalida Eini *

This paper presents a method of calculating the currency basket directly, without makingany piror assumptions regarding the importanceofany one currency in trade. This contrastswith the method currently prevalent in Israel (and the world), which uses the geographicalcomposition of trade as a basis for determining the relative importance of the vairouscurrencies, arbitrairly dividing 'the world' into five currencies.The currency basket is an exchangerate policy instrument for minimizing the volatilityof trade pirces (imports and exports) in localcurrency terms. Using a simple theoreticalmodel, it can be demonstrated that the target of minimizing volatility is attained when thecomposition of the currency basket reflects the distirbution of the trade prices of thepirncipal competitors. In this article the distirbutionof pirces is deirved from an examinationof the development of the pirces of Israel's imports and exports: the share of the vairouscompetitors in Israel's trade was calculated by compairng the pirces of its imports andexports with those in the currencybasket countires.The empiircal examinations show that the pirces of exports from the currencybasketcountires provide the best explanation of the price of Israel's trade. From an examinationof the price of Israel's merchandise exports it can be concluded that some 60 percentcompete with US products, about 5 percent with Japanese products, and the rest withthose from Europe. The distirbution of import pirces is about 50 percent from the US, 10percent from Japan, and the rest from Europe. One of these combinations, or a mixture ofthem, will be chosen to constitute the currency basket, in accordance with the objectivesof the policymakers.

INTRODUCTION

In Israel, as in dozensofother (mainly developing) countries, exchangerate policy is managedin relation to a basket of currencies.1 Since 1986 the exchange rate has been managed inrelation to a basket of ifve currencies, in varying forms.2 Since December 1991 the exchange

* Until her untimely demise, the late Dalida Eini was an economist in the Research Department ofthe Bankof Israel.

The author is grateful to Zalman Shiffer and participants in the Bank of Israel's Research Departmentseminar for their valuable comments.

' The main countires that link their currency to a basket are Chile, Columbia, the Czech Republic,Hungary, Poland, Iceland, Morocco, Thailand, and Cyprus. Jamaica, Jordan, Bahrein, and Saudi Arabialink their currencies to SDR. Several developing countries, including El Salvador, India, and Jamaica,have a floating exchange rate (see IMF, 1993).

2 For details of Israel's actual exchangerate policy, see Foreign Currency Exchange Rates in Israel,1995, Bank of Israel, Foreign Currency Department, Economic Unit.

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2 Bank of Israel Economic Review 73

rate has been managed within a crawling band, in accordance with which gradual,predetermined, and preannounced adjustments of the midpoint rate visavis the basket andof the width of the exchangerate band are made. Given this exchangerate policy, there isroom to discuss the composition of Israel's currency basket, and this composition assumesgreater significance as the exchangerate band becomes narrower and more rigid. Until 1995the exchange rate was set within an internal band, so that the compositionof the basket had amarked effect on monetary policy. Once the exchangerate band was widened and the exchangerate made more flexible, this effect weakened.

Underlying the theoretical literature on the composition of the currency basket is theconsensus that the geographical distribution of trade best represents the optimal weights ofthe currency basket. Thus, most of the countries that manage their exchange rates in relationto a basket of currencies determine the weights in accordance with the weights of trade.3 Inthis article the drawbacks of this approach are described, and a theoretical and empiricalalternative is presented. The question of the composition of the desired currency basket wasalso discussed extensively in Israel,4 and here, too, it was finally concluded that the mainconsideration would be the distirbution of trade. The question is, however, whether it is possibleto determine the weightof the European currencies in the basket on the basisof the weight oftrade with the European countries, even though some of this trade is conducted in dollars. Inother words, can it be said, for example, that an exporter to Germany is affected solely bychanges in the Deutschmark when some of his transactions are implemented in dollars? Andwhat about the small countries with which Israel trades, and whose share is increasing? Intrade with the countiresof eastern Europe which currency is relevant, the European one or thedollar? This paper represents an attempt to answer these questions.

We ifrst show that what is important is neither the geographical area nor the currency oftrade but the way trade pirces are determined in Israel. The fact that the composition of thecurrency basket is actually determined on the basisof the geographical distirbutionof trade isa direct result of an assumption regarding the pircing mechanismofgoods traded in internationalmarkets: the market for a specific item is identical with the geographical area in which it issold. This means that the pirce of an Israeli export item that is sold in Germany is determinedin accordance with the pirce of the Germanmade item rather than with that of the USmadeone. Consequently, the proceeds (pirce in local currency) of Israeli exports to Germany aredetermined on the basisofthe pircesofGerman goods and the DM/NIS exchange rate. However,since the proceeds obtained by some exporters to Germany are denominated in dollars, theseproceeds are affected by the NIS/DM exchange rate. Thus, data about the geographical areado not provide sufficient information about the relative importance in trade of each currency,and the same can even be said about the distirbution of the currency in which the transactionis made. If the dollar is expected to weaken against the mark, the exporter who sets the pircesof the goods he sells in Germany in dollars can raise these pirces, i.e., he can respond tochanges in cross rates by alteirng the pirces of his goods, thereby neutralizing the relative

3 See IMF (1993) and Branson and KatseliPapaefstratiou (1981), pp. 398400.4 These include Gottlieb and Galyam (1981), Galyam (1985), Galyam and Halevi (1989), Roth

( 1994), Shiffer ( 1993), Flanders and Helpman ( 1 979), and Banders and Tishler(1981). Fora discussionof the impotrance of capital flows in determining the composition of Israel's currency basket, seeBenBassat(1995(.

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a ReExamination of the Composition of the Optimal Currency Basket for Israel 3

decline in proceeds (relative to exporters whose transactions are conducted in marks). If theexporter alters his prices even though the transaction is undertaken in dollars, his proceedswill be determined by the pircesof the Germanmade goods, i.e., they will be similar to thoseofthe exporter whose pirces are in marks, and are hence affected by the exchange rate againstthe mark. On the other hand, if the exporter cannot alter the pirces of his goods because theycompete with othergoods whose prices are denominated in dollars, his proceeds will be affectedby thelocalcurrency/dollar exchange rate.5

This article is based on an approach that is consistent with the new theory of internationaltrade: there are different markets/pirces for different brandsof the same product, and the priceof each brand is determined by prices in the leading country that produces the item. Everysmall producer of the same brand faces a world price that is exogenous to him and is set by theleading producer. Thus, for example, an Israeli exporter chooses which brand of the product toproduce one that competes with the German brand or one that competes with the Ameircanitem. The pirce is determined according to this choice, irrespective of the area in which theproduct is sold,6 and the importance of the currency for the exporter/importer is determinedcorrespondingly. Hence, in each geographical areathere are different pirces for the same product,and the way pirces are determined in Israel can be determined by an empiircal examination.

The correct definitionof the connection between trade pirces and domestic prices shifts theemphasis from geographical areas of trade to the competing products traded, and from thegeographical distirbutionoftrade to the distirbution of its prices. As the theoretical partof thisarticle will show, in order to stabilize export pirces or the prices of goods that compete withimports, the composition of the currency basket has to be set on the basis of each country'sshare in determining prices of imports/exports. In the empiircal part of the article we willpresent a method for directly calculating the shareofthe main countires participating in Israel'strade in determining pirces of its imports/expotrs.

As stated, the distirbution of currencies in the basket should be determined in a way that isidentical with the distirbution of trade pirces but the distirbution based on export pircesdiffers from that based on import pirces. Each of these distributions is suited to a differentpolicy instrument and acts differently to attain the ultimate goal of growth. When the stabilityofexport pirces is chosen as the principal aimof the currencybasket policy, the compositionof the basket should represent the distirbution of export pirces; when the pirce stability ofgoods that compete with imports is selected as the policy focus, and hence economic unitsi.e., consumers and producers of import substitutes are affected directly by these pirces, thecomposition of the basket will be determined by the distirbution of import pirces; and whenthe policy is to stabilize inlfation via tradables prices, the composition of the basket shouldrepresent the distirbution of both import and export pirces (as together they constitutegoodstraded in the domestic market). In order to decide which composition of the currency basket

5 When there is PPP, i.e., when there is a high correlation between the prices and exchange rates ofthe various countries, the currency in which the prices are determined is not relevant. See also thediscussion in the following section.

6 This does not mean that there is no price discrimination between areas. A large producer can pricediscriminate between areas, but this makes no difference for the Israeli exporter. If the price of the USbrand in Germany behaves in the same way as those of the German products, the mark will have to begiven greater weight in the currency basket (see below(.


to choose, a decision has to be made as to the relative importance of the economic units thatare affected by the volatility of these prices in attaining the targetof growth.7

The structure of the article is as follows: Section 1 focuses on the importance of randomchanges in the exchange rate for the composition of the currency basket; in Section 2 threesalient concepts regarding the compositionofthe currency basket geographical distirbution,currency distirbution, and trade market distirbution are clairfied and the connections betweenthem descirbed; this leads to the conclusion that only trade markets are relevant for determiningthe compositionofthe optimal currency basket. In Section 3 we review the theoretical literatureon the composition of the optimal currency basket, and present a model for determining it;this leads to the conclusion that when the policy objective is the stabilization of export prices,the composition of the currencies in the basket should be identical with that of the exportmarkets. In Section 4 we present a method for determining the composition of the basket inaccordance with the conclusion deirved from the theoretical model, and estimate desiredcurrencybasket compositions in accordance with the objectives of stabilizing export pircesand stabilizing impotr pirces. Section 5 contains a summary and conclusions.

1. THE SIGNIFICANCE OF RANDOM CHANGES IN CROSS RATES AND WORLDPRICES

The need to determine a currency basket, and the effect of its composition on economic vairables,depends on the volatility of the exchange rate and the resulting depatrure from PurchasingPower Pairty (PPP). If PPP exists in the world, then all the vairous kinds of indexation haveidentical effects on domestic markets, so that the compositionof the currency basket is irrelevant.As is claimed by Turnovsky (1982), Flanders and Helpman (1977), Rao and Magee (1980),and others, were it not for the stochastic volatility of cross rates, world exchange rates (net ofpirce changes) would move together, and the questionofchoice between them would not airse.When there is depatrure from PPP pirces of tradables from cetrain countires irse more thanothers, thereby influencing the profitability of trade (impotrs and expotrs) with each country.

Neither the theoretical debate on the existenceofPPP nor the empiircal studyof the subjecthave led to any consensus on the subject. Currently the discussion appears to focus on whetherPPP exists in the long term, it being agreed that it does not explain shotrterm movements.Dornbusch(1987) reviews the literature and concludes that there is no hard empiircal evidencefor PPP, in either the shotr or the long run.8 Studies that reject the existence of PPP includeCorbae and Ouliairs (1991), Edison and Klovland (1987), Edison (1987), Mark (1990), andFrenkel (1981), inter alia, while leaving room for a discussion of the composition of theoptimal currency basket.

י Naturally, indirect pirce effects also play a part. Thus, for example, import pirces have a directeffect on the proiftability of the producers whose products compete with imports, but an indirect effecton production costs in general, including thoseofexporters. Since the direct and powerful effectof tradepirces which are determined exogenouslyis on producer proiftability, we have concentrated hereonly on that aspect of pirces.

8 See also Edison (1987) for a review of the debate and a bibliography of empiircal studies. Fewerstudies suppotr PPP and they do so with some reservations (see, for example, Fischer and Park (1991).

A ReExamination of the Composition of the Optimal Currency Basket for Israel 5

2. THE GEOGRAPHICAL, CURRENCY, AND TRADE COMPOSITION OF MARKETS

In this section we review the conceptual problem associated with the use of the compositionof trade to determine the composition of the currency basket, and offer a solution for it. Inorder to do this a distinction must be made between three concepts connected with foreigntrade: the geographical region in which the product is sold, the currency of payment, and thecurrency in which prices are determined (the product's market). The fact that the compositionof the basket is actually determined on the basisof the geographical distribution of trade is adirect result of the assumption made regarding the pricing mechanism of products traded ininternational markets: the market for a specific product is identical with the geographicalregion in which it is sold. This means that the price of an Israeli export item that is sold inGermany is set in accordance with the price ofthe German item, and is not affected by that ofthe American one. Consequently, the proceeds (the price in local currency) of an Israeli exporterwho exports to Germany are determined on the basisof the pricesofthe German products andthe mark/shekel exchange rate. However, according to the literature as well as to Israel's tradedata, this connection would not seem to be exact as most international deals are made indollars. Grossman (1973) was the ifrst to note that most interbank payments are in US dollars,whether the US is directly involved in them or not. As Krugman ( 1980) pointed out, thehegemony of the dollar as the currency of payment can be explained by the efficiency ofconducting international transactions in a single currency, just as the use ofa single currencyreduces the costs of a transaction in the domestic market. In Israel, too, there is a gap betweenthe geographical and the currency compositionof trade: the shareofthe dollar in merchandisetrade payments is 75 percent in exports and 60 percent in imports, while the share of the US intrade is 27 percent of exports and 23 percent of imports (Tables A1 and A2). It can be concludedfrom these data that not only are the transactions of.small countries implemented in dollars,but this is also the case with some of those involving large European ones.

Thus, the localcurrency proceeds of some exporters to Germany are affected by the NIS/dollar exchange rate. Consequently, while data about geographical area do not provide suiffcientinformation about the share of each currency in trade, nor does information about the distributionof the currencies of transaction. If the dollar is expected to weaken against the mark, theexporter can denominate the prices of the products he sells in Germany in dollars in order toincrease their price i.e., to respond to changes in cross rates by altering the pricesof productsand thereby neutralize the fall in relative proceeds (relative to exporters whose transactionsare in marks). This ability of the exporter to alter his prices depends on which products competewith his. If the exporter competes with American products he cannot alter his prices, and sohis proceeds in shekels per unit exported will decline in accordance with the extent to whichthe dollar weakens. Butif the exporter competes with German products he can alter his pricesin dollars, so that his shekel proceeds per unit exported will not be affected. Hence, it can beconcluded that the relevant parameter for defining the optimal weights of currencies in thebasket is not the geographical regionor even the currency in which transactions are implementedbut the prices of the goods in the country with which the products exported by the smallcountry competes, in this case the exports of Germany or the US.

In the wake of the marked expansion of intraindustry trade (bidirectional trade in thesame products) between industrial countries, a new theoretical literature has emerged stressingthe differentiation between various kindsofthesame product as a sourceoftrade, i.e., perceiving


specialization, the traditional reason for trade (according to the HeckscherOhlin model), asmarginal in trade between industrial countries (countries which are similar to one another asregards the composition of factors of production), its place being taken by the consumers'desire for variety.9 In this context it is appropriate to assume that the price of an Israeli exportitem is determined by that of the brand set by the producer with which itcompetesi.e., theleading producer in theworldthis price being uniform for all the geographical regions inwhich it is sold, changing along with shifts in the prices of the exports of the country withwhich it competes.

Flanders and Helpman (1977) write (p.15) that the factor determining the weight of aspecific currency in the basket is not its weight in a country's trade but the substitutabilitybetween its exports and the exports of the currencybasket country. The closer substitutes theproducts are for one another, the greater is the effect of the change of price on domesticexports, and hence the greater is the weight that should be ascribed to that currency in thebasket. This article seeks to examine directly whether the productsofcertain countries competewith Israeli exports, and if their prices determine those of Israel's impotrs.

3. REVIEW OF LITERATUREAND PRESENTATION OF THE MODEL

The composition of the currency basket in effect influences the rate of depreciation againsteach currency, given the changes in cross rates and the slopeof the band. Thus, for example,if there are two currencies, the dollar and the mark, the basket consistsof one dollar unit (100percent dollar), the slope ofthe band is set at 10 percent, and the dollar is expected to strengthenby 10 percent against the mark, the local currency will depreciate by 10 percent against thedollar and 0 percent against the mark (since both the local currency and the mark have weakenedby 10 percent against the dollar, the ratio between them is unchanged). If, however, the basketcomprises one dollar unit and one mark unit (50 percent for each currency, assuming that theirinitial value against the local currency is equal), the rate of depreciation will be 5 percentagainst the mark and 15 percent against the dollar, so that the average rateof depreciation willbe 10 percent, according to the slopeof the band. There will still be a 10 percent gap betweenthe depreciation against the mark and that against the dollar, but in that case the 'realappreciation' (the fall in the priceofthe product on the domestic market relative to the nominalexchange rate) in termsof the mark is smaller and the 'real depreciation' in termsof the dollaris greater. Thus, the compositionof the basket does not affect the average change in the pricesof the various countries, but can influence the variance of these changes in shekels.

This variance in prices has a real cost, and the composition of the basket is chosen so as tominimize it. Thus, the purposeof the pioneering work by Black (1976) was to minimize thevolatility of the prices of tradables in the domestic market. Although Lipschitz andSundararajan (1980) chose to minimize the volatilityof the real exchange rate, they assumedthat the pirces ofnontradables were determined exogenously, and hence focused on the relationbetween the composition of the basket and prices of tradables. Not all the studies of thissubject concentrate on this pirmary link between the composition of the basket and pricevairance, and some of them focus on more distant intermediate targets. These include the

' See, for example, part III ofHelpman and Krugman (1985(.


stabilization of the production of tradables (Edison and Vardal, 1 989) or of GDP (Home andMartin, 1989). Flanders and Helpman (1977) discuss the optimal compositionof the basketin the light of three objectives: minimizing fluctuations in the balance of payments,employment, and social welfare (the net effect of the terms of trade). Branson and KatseliPapaefstratiou ( 1 980, 1981) select the minimizationof the volatilityof the real exchange rateand of the balance of payments as a target.

Most studies in the field, like those mentioned above, focus on real mechanisms, and virtuallyignore the nominal implicationsof the exchange rate. Turnovsky (1982) and Connolly (1982)were among the first to develop a model that included a monetary mechanism, though only inthe former was the exchange rate set endogenously through capital flows and expectations ofinterestrate changes. Connolly (1982) incorporates monetary considerations, as the objectiveis to stabilize inflation, but exchange rates are determined exogenously, and there are nocapital flows of interestbearing assets. For a comparative analysis of articles in this ifeld, seeWilliamson (1982).

The prime objective of all macroeconomic policy is sustainable growth. As the review ofliterature has shown, the relation between the compositionof the basket and stable growth isnot unequivocal, and there are many and varied passthrough mechanisms between the two.This paper focuses on the price variance of the tradables imports and exports that aredirectly affected by exchangerate policy.

The basic assumption thatdistinguishes the model used here concerns the way Israeli export/import prices are determined. As described in the preceding section, we assume that the priceof an Israeli expotr good is determined by the pirce set by the leading producer in the world,and that this price is uniform in all the geographical regions in which it is sold. Domesticexpotrs can thus be presented as consisting of n products, which differ from one another onthe basis of the products of the large country with which they compete. Thus, for example, theexpotrerof Israeli cars produces products that compete with cars made in the US, and whosepirce is therefore determined in accordance with the priceof cars expotred from the US, evenif they are sold in Germany. This price is not affected (in the short term) by changes in thepirces of German cars.10

Here and in the empiircal section below we assume that there is one aggregate product thatcompetes with the expotrs of each of the large countries. This aggregate product is similar incomposition to the product expotred by the country with which it competes, and its pirce canhence be represented by the pirce of the product expotred by that country. The empiircalexaminations yielded a larger than expected correlation, thereby beairng out this assumption(see the empiircal section below). The localcurrency proceeds received by each expotrer perunit expotred are the pirce of the product in the currency against which it competes, in localcurrency terms (for a full mathematical formulation of the problem, see Appendix 1). Theexpotr pirce is a weighted average of the prices of all these products, which are determinedabroad, in accordance with the weights of each of those products in Israeli expotrs:

10The way export prices adjust to changes in competitors' prices is not within the realmofthe presentanalysis, but is connected with priceadjustment models. To avoid departing from the frameworkof thisdiscussion, reference here is to annual prices, assuming that this is a long enough period for priceadjustment, whatever the nature of the process.


d) n,=£w,(A, + eu)

lnP.' p.r the competing export pirce with country / in the currency of country i at time t.ln£.' = e. the exchange rate of the home country visavis country i at time t.w.the weightof the competing expotr with country i in total exports: 'Lwi = 1 . These weightscould change over time as a resultofchanges in the relative profitabilityof different products(positive supply elasticity). Appendix 2 contains the formulationof the problem in this instance,and the results are identical in both cases.

The proiftofeach expotrer depends on the cost function, which is derived from the product'sproduction function. This expenditure, which is expressed in local currency, also depends onthe currency basket, which affects the rateof nominal depreciation, and hence on the prices ofimpotred raw mateirals, and because of the indexationmechanismson the rate at whichnominal wages rise. The different weights of raw materials and labor (and the varyingcompositionof raw mateirals) in the production costs of the vairous products will thereforecause the compositionof the basket to have diffeirng effects on the production costsof differentproducts. Hence the composition of the basket, in a generalequilibrium model, will haveindirect effects on the profitof each expotrer. As these effects are far more indirect than that ofthe exchange rate on the expotrer's proceeds, we will ignore them at this stage and focus onthe objective of expotr pirce stability.

The valueofthe currency basket at every peirod St (discrete time) is known and determinedin accordance with exchangerate policy:

(2)S,= !*,*,,

x. the weights of the currencies in the basket.S the value of the basket at every time t, which changes at a regular and known pace.Note that the compositionof the basket is determined by the quantityof currencies in it, ratherthan by their weights. Hence, x. refers to the weight of the currencies in the first peirod, asdeirved from the desired quantityofeach currency. Substituting (2) in (l)and minimizing thepirce vairance yields the optimum weight of a currency in the basket that is equal to theweight of the expotrs whose pirce is denominated in that currency:

)3( w= x_

In pirnciple there is no reason to assume that the share of each currency will be positiveand less than 1. According to Turnovsky (1982), the share of a currency can be negative, ofrexample if holding it rather than other currencies leads to a sharp fall in foreign demand ofrdomestic product. Edison and Vardal (1990) do not restirct the signof the weights, claimingthat there is a technical logic in assigning a negative weight to a currency whose exchangerate moves in the opposite direction to that of the basket, and adding to the weights of thecurrencies that are consistent with the basket in order to compensate for this. Flanders andHelpman (1977) also note that the weight of a currency can be negative (as sometimes occurswhen the objective is welfare). Lipschitz and Sundararajan (1980), on the other hand, maintainthat when adding a specific currency increases the variance of the real exchange rate, its


weight should be negative, but since within the conceptual frameworkofthe model it is dififcultto explain the significance of negative weight, positive weights are necessary for theoptimization process. Thus, here, too, since the weightsof the currencies are equal to those ofthe various products exported, there is no significance to negative weights. Nevertheless, thisassumption is discarded later on, and is revealed to be ineffective.

Note that the minimization of volatility could come at the expense of the average level ofthe variable. Flanders and Helpman (1977) as well as Lipschitz and Sundararajan (1980)minimize the varianceof the target variable under the constraintofmaintaining (or improving)its average level. This is done because there is substitutability between improving the targetvariable and its variance. For defining this problem under a constraint, see Appendix 3. Inorder to keep the analysis simple, we remain within the boundaries of the local formulation.

4. THE OPTIMAL COMPOSITION OF CURRENCIES FOR ISRAEL

The optimal weights of baskets of currencies for vairous countires have been calculated inseveral studies, in attempts to show that these are preferable to trade weights for stabilizingthe macroeconomic variables chosen as target vairables. The methods used in these studiesdiffer from one another. Lipschitz and Sundararajan (1980), for example, arbitrairly chosetrade elasticities for imaginary countires on the basis of which they constructed an optimalcurrency basket. Edison and Vardal (1990), on the other hand, ran a regression for the tradedata of Finland, Norway, and Sweden, while Home and Martin (1989) used Kalman's filtertechnique, applying it by means of an autoregressive model.

The current study directly estimates the optimal weights for Israel's economy byexamining the distirbutionof its trade markets. By comparing Israel's trade prices (importsand exports) with the pirces of competing goods we find the weights of trade pirces: weexamine the proportion of Israel's goods exports that competes with those of each of thecurrencybasket countires (so that its pirces are determined according to that country'sexport pirces), and the optimal weights of the currency basket are derived from theseproportions, the policy target being the stabilityofexport pirces. Similarly, it is possible todetermine the composition of the import markets, which serves as an indication of theweights that will lead to price stability of goods that compete with imports. This yields twooptimal currency baskets, one based on exports and the other on imports. In accordancewith the target function of policymakers, i.e., the relative importance they ascirbe to eachof the economic units affected by these pirces, it is possible to deirve the optimal compositionof the currency basket."For this purpose it is necessary to make an assumption (and examine it) about which pirces

are the closest competitors of Israeli exports, and which are the closest competitors of Israeliimports. The main contenders are the export pirces, import pirces, and wholesale pircesof theifve currencybasket countires, which are Israel's pirncipal trading partners. The examinationswere made with and without the condition that weights be positive.

" For the sources of the data and the method of calculation, see Appendix 4.


a. Positive weights1

(i) MethodThe trade pricesof the currencybasket countries in each year between 1986 and 1995 weregiven various positive weights adding up to 1. This yielded a weighted pirce for each year,which was compared with Israel's actual trade pirce. The weights that led to the closest fitbetween the weighted pirces and Israel's export pirces were those that form the optimal currencybasket when the target is the stabilizationof export pirces, and those that led to the closest iftwith Israel's import pirces were the weights that form the optimal currency basket when thetarget is the stabilization of import pirces.

The extent of fit is usually measured via the correlation coefficient. Because of thedisadvantages of calculating this index, I have decided here to adopt the method used in theexact sciences and use the average of the absolute difference (see Appendix 5): for each yearthe absolute difference between the actual and the calculated pirce was calculated, and thedifferences averaged over the entire peirod; the weights that minimize the average of theabsolute difference are the optimal ones.

The optimal weights were found in two stages. At the ifrst stage, the weights of the USand Japan were altered at intervals of 5 percent, the total weights of the pirces of Germany,England, and France constituting the residual of l.The internal distirbutionof the Europeancurrencies was assumed as given according to the average for 1 994. The number of vairableswas thus restricted to two, the weights of pirces in the US and in Japan. This simpliifes theanalysis and the visual representation without detracting from the main points. At the secondstage, the assumption regarding the ifxed ratio between the weightsof the European currencieswas removed. ;

Assume, for example, that the basket consistsof two currencies only, the dollar and the yen.We multiply the pirce ofUS exports by weight*, and thatofJapan's by weight (1jc), to obtain '

the weighted pirce that is calculated for each year. We thus obtain a vector of weighted pirces(of Israel's trading partners) for each weight*. From this vector we deduct the vectorofIsrael'sexport pirces, and add up the absolute value of these differences. This is the average absolutedifference given weights x and (1*). These weights range from zero to one at intervalsof0.05.The weights for which the average absolute difference is minimal are the optimal weights.

n=noofyearsMinx J[jUSt x + Japan, . (1 x)\ Israel, |

1=1

where USt, Japan., and Israel. are, respectively, the export pirces of the three countires.

(11) Stabilityofexport pricesThe prices of exports are best represented by the expotrs of the currency,basket countires(Table 1), but the extent of ift of the import pirces of those countires is also high, and thecomposition of the resulting currency basket is similar to that resulting from the expotr pircesofthe currencybasket countires 65 percent dollar and a low yen weight. The extent of ift ofthe wholesale prices of the currencybasket countires is far lower.

Figures la and lb show the average difference between the actual price of Israel'smerchandise expotrs in 198695 and the weighted pirce of those of the currencybasket


Table 1The Fit Between Israel's Export Prices and Other Prices, and the ConsequentOptimal Composition of the CurrencyBasket

Averageminimum Weight of currency in basket (percent)difference $US ¥ DM £UK FFr

Prices in currencybasket countires

5651.06Exports0651.21Imports0802.20Wholesale5550.67Exports 25 10

countries as a function of the weights of the export prices of the US and Japan. Note thatthese weights are equal to those of the dollar and the yen in the optimal currency basket. Atevery line the weight of the dollar is constant, and that of the yen shifts along it, so that thevariableofthe weightofthe European currencies changes accordingly, the proportions betweenthem (mark, pound, and franc) remaining constant relative to the 1994 average. The figureclearly shows the continuity of the target function and one optimum point, convergence towhich is gradual, so that there are no radically different compositions of baskets that willlead to optimal results.

The average difference is maximal when the currency basket consists entirelyofyen (Figurela). The smaller the weight of the yen in the basket, the greater the ift; this holds up to aweight of'5 percent, where the weight of the dollar is 65 percent (Figure lb). The averagedifference is very small when the weight of the yen is between 0 and 5 percent and that of thedollar is between 65 and 70 percent.

Removing the restriction on the European currencies improves the extent of fit betweenprices, so that the average difference falls to only 0.7 percentage points. As expected, removingthe restriction causes the weight of the European currencies to rise, but their compositionchanges in an unexpected way: England and France have a larger share in determiningIsrael's export prices than Germany, contrary to the prevailing view. Because of the highcorrelation between price changes in Europe, the distinction between the various Europeancurrencies may not be very significant: the correlation between price changes in Germanyand France in 1 98695 is greater than 99 percent, and that between Germany and England isabout 53 percent.

Thus, the results indicate that the expotrs of the currencybasket countries are very closecompetitors with Israel's expotrs. This appears to be because the expotrs of these countriesconsist of manufactured goods, as do Israel's. Although the ift with the impotr prices andwholesale prices of the currencybasket countries is also high, it is clear that Israel's expotrsdo not compete with all tradable goods worldwide, but with a subgroup characterized mainlyby a low propotrion of raw materials. Due to the higher shareofraw materials in the wholesaleproduct or impotrsof the currencybasket countries, their prices are less representativeof thepricesofproducts that compete with Israel's expotrs than thoseof the expotrsof the currencybasket countries.


Figure laFit Between Prices ofMerchandise Exports in Israel and in theCurrencyBasket Countries, for Various Baskets

כדa>a>SI

0.0

Q

a**ss§s eK8**

8™o"< Weight of dollar

Weight of yen

Figure lbSegment of Fit Between Prices ofMerchandise Exports in Israel and inthe CurrencyBasket Countries, for Various Baskets

20

75

65

Weight of dollar

Weight of yen


Figure lc(1) Relation Between Correlation and Average Difference of Export Pricesof CurrencyBasket Countries and of Israel

£ 4T5

>0 J

2

1

0

D םם

#1

ם ם ם o agn a

20 40 60Correlation

80

Point A

Point B

Weightof yen

5o/o

0o/o

Weightof$65O/800/

Averagedifference

1.061.46

Correlation

92.3o/o97.3o/o

(2) Relation Between Export Prices and CurrencyBasket Countries' ExpotrPrices, Weighted by Two Sets of Weights11.0

[] Point A0 Point B

9.0

e"it45O lin

0n

7.0

F

\A5 1.0

1.0

etual averacxport price

Ace

3.0

5.05.0 3.0 1.0 1.0 3.0 5.0

Actual export price7.0 9.0 11.0


Figure IdIsrael's Actual Export Price visavis CurrencyBasket Countries'Export Price, Based on Optimal Weights0/o

12

10

8

6

2

0

2

4

Actual priceWeighted price

L L1986 1987 1988 1989 1990 1991

Years1992 1993 1994 1995

, According to the cirteiron of exportpirce stability, the weight of the dollar in the currencybasket should be set at 5560 percent, and thatof the yen at 5 percent. The distirbution amongthe European currencies should also be changed, particularly by increasing the weight of theEnglish pound. Because of the high correlation between pirces in France and Germany, thedistirbution between those two currencies is less significant. Thus, it appears that most ofIsrael's exports compete with US brands, even though exports toAmeirca constitute less thana third of goods exports. The low share of the yen indicates that Israel's exports to the newmarkets ofEast Asia, which have grown continuously in the last few years, is not affected bypirces and exchange rates in Japan, but rather, it would seem, by those in the US.

Table 2The Fit Between Israel's Import Prices and Other Prices, and the ConsequentOptimal Composition of the Currency Basket

Averageminimumdifference

Weight of currency in basket (percent)$US DM £UK FFr

Prices in currencybasket countries

15451.77Exports0801.93Imports0552.56Wholesale goods15401.74Exports 20 15 10

a reExamination of the Composition of the Optimal Currency Basket for Israel 15

Figure 2aFit Between Prices of Merchandise Imports in Israel and in theCurrencyBasket Countries, for Various Baskets

Weight of dollar20 510י 'Too

Weight of yen

Figure 2bin Israel andImportsSegment of Fit Between Prices ofMerchandise

Basketsfor Variousin the CurrencyBasket Countries,

1 1

.n4.0 jU 1/MA3.5

7MMfm3.0

>v

JSF\a>rtz Ml2.5 שCO

ש2.0 ^^1.5

Mi^^. 1Wm1.0 I ^^3050 ^^^B ^045 ^*^Weight of yen

^^^1035 0

40Weight of dollar


(iii) Stabilityof importpricesThe correlation between the pircesofgoods impotrs in Israel and vairous prices in the currencybasket countires is lower than it is with Israel's expotr pirces, and here too the highest correlationis with the pirces of exports of the currencybasket countires (Table 2). The reason for this isunclear, but may revolve round the lack of correlation in their composition: the share ofunfinished manufactured goods in Israel's impotrs is greater than it is in the impotrs of theindustiralized countires, most of whose impotrs are of finished manufactured goods.

Figures 2a and 2b show that the average difference between the pircesof goods impotrs inIsrael and those of goods expotred by the currencybasket countires narrows as the share ofthe yen in the currency basket declines down to 1015 percent. Within this range of yenweights the average difference is the lowest when the weight of the dollar is 4550 percent.

The removalof restirctions from the European currencies does not significantly change theweights, but as with expotrs albeit to a lesser extent here, too, what is notable is the largershare of the franc and the pound than is traditionally attached to them. The large shareof theyen compared with the shareof expotrs from Japan (about 5 percentof merchandise impotrs)is also marked. Flanders and Helpman (1977), whose object was to minimize the volatility ofthe balance of payments, also found that in some instances the weight of a currency in thebasket may be greater than the relative share of trade of that country, because its expotrs are aclose competitor with domestic expotrs. In Israel this was known as the Spanish Effect, asthere was a time when Spain did not trade with Israel but competed with it for expotr markets.The higher weightofthe dollar than the US shareofboth expotrs and impotrs is hardly surpirsingin view of the leading role played by US products in international markets. Impotrs to Israel

Figure 2cIsrael's Actual Import Price visavis CurrencyBasket Countries'Import Price, Based on Optimal Weighting0/o

12

10

8

6

2

0

2 V^^~ Actual price

Weighted pirce

J I I L

1986 1987 1988 1989 1990 1991

Years

1992 1993 1994 1995


Table 3Regression Results: Israel's Export Prices visavis Export Prices ofCurrencyBasket Countries, 198695

Regression 4Regression 3Regression 2Regression 1

Coefficient WeightCoefficient WeightCoefficient WeightCoefficient Weight93.294.294.693.6RsqAdj.

US 1.03 73 1.03 72.5 1.08 76.6 1.34 84.3(99.1) (99.4) (99.8) (100)

Japan 0.07 5 0.07 4.9 )74()68.6(

15.70.2513.50.1910.60.15120.17Germany)100()99.5()97()43.9(

9.90.1412.00.17120.17UK)83.9()88()77.3(

_20.03France

)4.5(Note: Figures in parentheses denote level of significance.

also appear to compete with Japanese goods, even when they originate from other countires,possibly becauseofJapan's growing importance in world markets. This also seems to explainat least in part the nature of impotrs from East Asia, which have accounted for an increasingshare of imports in recent years, irsing from 3 percent in 1986 to 7 percent in 1995.

b. Unconstrained weights

The share of a currency in the basket ofcurrencieswhen the weights can be negativeiscalculated by means of a regression. The drawback of this method is explained in Appendix 5as the motive for using the average difference index. Nonetheless, a regression is still thesimplest method available to us. In effect, we would like to specify the regression in such away that its constant is 0 and its slope 1 , but because of the paucity of observations (10 years)we had to be satisfied with running a regression without a constant, after an examination hadshown that the constant was not significant, and that the Adj Rsq of the regression without aconstant was higher.

The resultsof the regression for exports are given in Table 3.12 Only the coefficient ofthe US was significant, and only that of France was negative. Because of the high multicolineairty between prices in France and Germany, French pirces which have the lowestsignificance level were removed from the regression. This served to raise the explanatorylevel of the regression, leaving the weight of the European currencies unchanged andincreasing the significance of all the other variables (Regresssion 2). From these results itcan be concluded that a negative weight should not be ascirbed to any currency accordingto the cirteironof stabilizing export pirces.The large weightof the dollar is consistent w'th

12 The regressions were run only with the export data of the currencybasket countries, as they hadthe best Fit with the prices of Israel's imports and exports.


Table 4Regression Results: Israel's Import Prices visavis Import Prices ofCurrencyBasket Countries, 198695

Regression 4Regression 3Regression 2Regression 1

Coefficient WeightWeightCoefficientWeightCoefifcientWeightCoefifcient90.189.089.287.1Adj. Rsq

1.16 70.670.71.1674.01.2673.71.28US(99.8)(99.3)(97.9)(96.3)0.14 8.68.60.147.90.137.90.14Japan

(82.0)(76.9)(74.4)(71.5)0.34 20.621.20.3421.50.3713.10.23Germany

(99.9)(54.9)(99.9)(24.9)__3.30.064.90.08UK

(25)(27.2)_0.50.01_10.10.18France

(1.0)(15.5)Note: Figures in parentheses denote level of significance.

the results presented in the preceding section, as well as with the positive weights at themaximum point of the correlation coefifcient (see Figure lc), where the weight of thedollar is 80 percent and that of the yen is 0. These conclusions reinforce the calculationspresented in the preceding section.

Identical conclusions can be reached regarding the quality of the results in the precedingsection for prices of Israel's impotrs. Here, too, the regression without a constant yielded ahigher level of explanation, and this is presented in Table 4. In Regression 1 , which includesall the currencies, only the US coefficient is significant, and only that of the UK is negative)and not significant). In order to improve the level of significance of the coefifcients, thevariable with the lowest significance level France was removed from the regression. Thisslightly improved the explanatory level of the regression, mainly due to the greater significanceof German prices, but the negative English coeiffcient remained nonsigniifcant. Removingthe UK from the regression maximizes the explanatory level of the regression, improves thesignificance levelof the other variables, and leaves the weightsofthe US and Japan unchanged)Regression 4). Here, too, the weight of the dollar is very similar to that obtained under theconstraintofthe positive coeiffcients when the aim is to maximize the correlation coeiffcienteven though the weight of the yen here is slightly lower. It appears that in this case, too, theconstraint of positive coeiffcients is not effective, so that the results of the preceding sectionregarding the weightsof the currencies when the aim is to minimize the average difference arealso valid when there is no constraint on the sign of the coeiffcients.

c. Some expansions of the model

The conceptual and empirical framework can be expanded in several ways. Three kinds ofexpansion are given here: ifrst, alternative tests were run regarding prices other than trade prices;second, the tests were run at the quatrerly level; third, the timeframeof the tests was expanded.


Table 5Examination of Fit Between Various Prices in Israel and inCurrencyBasket Countries

Weight (percent(Average¥$USminimum difference

102530

454535

2.253.123.57

Inflation*1Prices AbPrices Bc

a Prices (CPI) in currencybasket countries and in Israel.b Wholesale prices in currencybasket countries, tradables prices in Israel (based on CPI).c Wholesale pirces in currencybasket countries, wholesale pirces in Israel.

1. Alternative testsThere are two reasons for running alternative tests. First, there are other intermediate targetsforemost among them the real exchange rate that reflect general economic equilibrium betterthan changes in import or export prices. Second, since the extent of passthrough from importprices to those of tradables and from them to those of all productsis not clear, it should beexamined. These alternative tests give rise to two main problems: ifrst, since the transmissionmechanism from tradables prices to nontradables prices is complex and controversial, studiesthat minimize the volatilityof the real exchange rate assume pricesofnontradables to be constant,so that they do not affect the optimal weights (see, e.g., Black, 1976, in which the variance oftradables prices is minimized, and Branson and KatseliPapaefstratiou, 1980, where the

5 3aon Between Wholesale Prices in Israel and in the CurrencyBasketries

FigunRelatiCouni

7.0 ;

rנ=

| |o.o

\=

g 6.0 |c £ i£ 5.5

§> 5.0

< 4.5

4.0

=1

===

==1

=

1J ±

.

0 10 20 30 40 50 60 70 80 90 100

Weight of dollar


minimization of the vairance of the real exchange rate is defined, and in effect this is donesolelyviapirces oftradables). Second, any testof domestic pirces is biased as these are influencedby the existing composition of the currency basket: the pirces of tradables in localcurrencyterms and their effect on the pirces of nontradables depend directly on the exchangerate policyin force at the timeof the estimation. The conversionofthese pirces into a numeraire currency,e.g., the dollar, will also be directly affected by the compositionof the currency basket and theshare of the dollar in it, as this determines the rate of nominal depreciation visavis the dollaragainst the nominal depreciation visavis the other currencies. For these reasons all tests basedon domestic pirces are problematic, and it is difficult to draw any conclusions from them.

Despite these reservations, several relations were examined between domestic pirces inIsrael and those in its main trading partners, as can be seen in Table 5 and Figures 3a, 3b, and3c. In all the compairsons higher average differences were found than in the direct compairsonof Israel's trade pirces with the export pirces of the currencybasket countires, even though acompairson of the inflation rates in Israel and those countires showed that these differencesare not much higher. In effect, we found that the most reliable relation between domesticpirces in Israel and those in its trading partners was between inflation rates rather than betweenpirces oftradables. This relation between changes in pircesof nontradables in Israel and in thecurrencybasket countires, which goes beyond that between pirces of tradables, is surpirsingand requires further investigation.

Outstanding among the compositionof currencies is the relatively low weightof the dollarcompared with its average weight in the currency basket in the relevant peirod. This is apparentlythe result of factors that work in opposing directions regarding the relative importance of thevairous currencies in determining the pirces of nontradables in Israel. On the one hand, asstated, special importance is attached to the dollar in determining some nontradables pirces in

Figure 3bRelation Between Tradables Prices in Israel and Wholesale Prices in theCurrencyBasket Countries

6.5

6.0

10 20 30 40 50 60

Weight of dollar

70 80 90 100


Figure 3cRelation Between Inflation in Israel and in CurrencyBasket Countries

O)2s>

]

i: ::1

J\1||11

! 1111

111l

10 20 30 40 50 60Weight of dollar

70 80 90 100

Israel; on the other, the threat to imports comes mainly from Europe. Thus, for example, thepotential impotrs that compete with Israeli agricultural products, which are nontradableeither because ofquotas and administrative restrictions or because of natural protection (milk)and transpotration costs are primarily from Europe. The Spanish Effect that operates in thiscase on competing impotrs in Israel comes more from Europe and Japan than from the US.

2. Quarterly testsThe main advantageof running quatrerly tests is the large number of observations, which canimprove the quality of the results. The disadvantage is the problem of the timing of pricechanges in Israel and abroad; for example, if there is a change in the prices of products withwhich expotrs compete, it takes time until the expotrer adjusts his prices, and it is not clearwhether the adjustment is made in the same or the subsequent quatrer. Consequently, thepresent study is based on annual data.

After ascetraining that the rates of changeof all prices were stationary, we ran a regressionto explain the priceof Israel's expotrs by the priceof the currencybasket countries' expotrs.The Adj Rsq of the regression was negative (3 percent), and all the coefficients were nonsignificant. Different vairations ofthe regression, with lagged vairables and/or omitted vairableswith low significance, led to a maximum explanatory levelof about 13 percent for a regressionin which the explanatory variables are pirces in the equivalent quatrer with a onequatrer lag.

3. Longterm testsThe first question that airses in the context of longterm tests is the extent to which the resultsare sensitive to the years chosen; in other words, if the calculations had been made for thepreceding year, i.e., for the 198594 peirod, would the results have been substantially different.


Table 6Goodnessof Fit Over Time Between Israel's Export and Import Prices andExport Prices of CurrencyBasket Countries

Israel's imports,exports,Israel'sexpotrsCB countries'CB countries' expotrs

¥$USAverage difference¥Average difference $US

15401.740.050.550.6719869510601.580.050.550.831985945701.550.050.550.7219849320551.830.050.550.8619839245251.940.050.551.151982915020y 1.880.050.551.5319819015301.850.050.551.57198089

Note: Iterationsof5 percent for positive weights.

/As the ifrst partof Table 6 shows, the relation between the export prices of the currency

basket countries and those of Israel is very stable over time, and the average difference evendeclines. Figure Id also shows that since 1989 the extentof ift between Israel's export pircesand the weighted priceof the expotrsof the currencybasket countries is almost the maximum.These results raise additional questions about the quality of expotrs and changes in it overtime, especially as to whether the composition of expotrs changes over time so that thepropotrion of goods that are 'unique' to Israel, such as the product of the defense industry,declines and that of products that compete on the free market rises. The results presented heresuppotr that hypothesis.The second patrof Table 6 shows the instabilityof the link between Israel's impotr pirces

and those of the expotrs of the currencybasket countries. This instability is another aspect ofthe lower explanatory level of impotr prices. The separation between world pirces and thepriceof Israel's impotrs may also be a resultof the political limitations that were imposed onIsrael and the administrative restirctions and quotas that Israel imposed on itself. The gradualand regionallyoirented relaxation of the restirctions and quotas, which began in 1975 whenthe free trade agreement with the EU was signed, apparently caused fluctuations in the sourcesof Israel's impotrs.

5. SUMMARYAND CONCLUSIONS

In this atricle we have presented a new wayof calculating the weightsof the currency basket.Its main advantage lies in the absenceof any assumptions regarding the relative impotrance ofany currency in trade. This contrasts with the method currently prevailing, in which 'the world'is divided arbitrarily and without prior knowledge into 5 currencies. This method, whichrelies primarily on the availability of data rather than on an accepted theory, has becomedififcult to apply because of the increased impotrance of new trade areas, and ignorance as towhich currency 'bloc' these regions should be ascirbed. In this study the composition of thebasket which is optimal for Israel is deirved from a direct examination of the behavior of


Israel's export and import prices. This kind of examination is required because neither thegeographical nor the currency composition of trade are sufficiently indicativeof the nature ofthe markets with which Israel trades and the way Israel's trade prices are determined in them,and that is the main variable in determining the compositionof the currency basket. The shareofthe various competitors in Israel's trade was calculated by comparing Israel's import/exportprices with those in the currencybasket countries, and it was found that those countries'export prices provided the best explanation of Israel's trade prices. The strong relations thatwere found between Israel's trade prices and 'world' prices support the hypothesis underlyingmostof the empirical studiesof this subject that the Israeli economy is a small and open onein which the prices of tradables are determined exogenously.

The weights were estimated here according to two aims: the stability of export pirces andthe stability of import pirces. For each target different weights were obtained: for the exporttarget the optimum weight of the dollar was 60 percent, and 5 percent for the yen, while forthe import target the optimumweight of the dollar was 50 percent, and 10 percent for the yen.The optimum weights are within a certain range, as two cirteira were used in making thechoice, and precise weights could be deirved from the decision regarding the relative importanceof each cirteiron. Note, too, that the weights deirved from the geographical distirbution oftrade are not precise. The weights of exports to and imports from the US are about 27 and 23percent respectively. Any other weightof the dollar deirves from an assumption regarding thenatureof trade with other geographical areas, so that the range of considerations is very wide.

The weightof the dollar obtained from this examination is greater than it is on the basis ofthe geographical data on trade, for both imports and exports, and is nearer to its weight on thebasis of the currency distirbution of trade. An examination of the composition of the optimumbasket for stabilizing pirces on the basis of localcurrency domestic pirces shows that theweight of the dollar in it45 percentis lower than that obtained from tests based on dollarpirces, while the yen maintained its relatively high weight of 1020 percent. This result issurpirsing, both because of the importance of the dollar in determining localcurrency pircesin Israel and because it is not clear how important the yen is.


Appendix 1 : Formulation of the Optimization Problem

The priceof exports is the weighted averageofthe pricesof products on intenrational markets,determined exogenously, according to the weightsofeachof these products in Israeli exports:

(1)rX = Ew,(p, , + eit)

The value of the basket of currencies at every St period (discrete times) is known and isdetermined exogenously on the basis of the exchangerate management policy:

(2) Sl=Jdxiei,

In effect, the rate of depreciation/appreciation is determined in relation to one currency, andvisavis all the rest it is determined by cross rates, which are given:

(3) el,=S,T.xie[,

eu the exchange rate of the shekel against the numeraire, say the dollar',ei't = In E, the exchange rate of the numeraire (dollar) against the currency of country i,whereE, =£'£,, .

Transposing (1) in (3) yields:

(4) IT,=XwiPit+I(w,*, ) + S,/ i

This means that from the irse in pirces of products abroad, pP the average exporter earns thechange in the exchange rate against the numeraire, e', as well as the rateof depreciationof thecurrency basket, S. While the proift from the change in pirce abroad is weighted by exportweights, which are given exogenously, the profit from the change in cross rates also dependson the weight of the currency in the basket.

(5) Var(U) = £wfVar(Pi) + Var(S) +£ (w'. xf Vare') + 2^^wiWj.Cov(Pi, Pj)i*< '

+ 2^WiCovp.,S) +^^,w^x^Covip^ + l^îw.x^Wjx^Covie'êj' )

+ 2Jj(wix.)Cov(e;,S)

The decision vairable, the policy instrument, determines the weights of the currency basketthat will minimize the vairance:

(6) _^tW = I(Wj Xj )Cov(e'm,e'( + I WjCov(e'm,pj) + Cov(S,e'm) = 0OXm j*m


Wegetn 1 equations with n 1 unknowns, because the equation does not exist for thenumeraire (ej' = 0). The weightof the numeraire currency is the residual of 1 (the sumof theweights is 1). The last covariance in equation (6) is between the valueof the basketofcurrenciesand the exchange rate of country m against the dollar. Given the policy of the crawling band,the basket increases at a fixed and known rate, so that it should be regarded as a constantrather than as a stochastic variable. Henceits joint variance with a stochastic variable is 0. Inthe wake of other theoretical and empirical studies, we assume that changes in the exchangerate and in prices are distributed independently, or that the relation is not stable over time, sothat Cov(e'm ,pj) is negligible. Thus, when acurrency is at its optimum weight in the basketthis will be equal to its weight in imports that compete with producers who determine theirprices in the same currency:

(7) wm xm

Appendix 2: Formulation of the Model with Positive Supply Elasticity

In the bodyof the article and in Appendix 1 we presented the problemofthe optimal compositionof the currency basket in its simplest form in order to clarify the nature of the problem. Herewe present one expansion of the problem, with positive export supply elasticity; thus, thequantity of exports of a product whose pirce is denominated in a specific currency will risewhen the pirce of that currency irses in terms of the numeraire currency (either the pirce ofthis product irses in terms of the currency in which it is denominated, or the exchange rate ofthe currency strengthens visavis the numeraire). Note that these changes do not affect thetotal amount of the economy's exports over time because the amount of sources directed toexpotrs is obtained from the economy's general equilibirum, and this allocation changes overtime only when shifts in economic parameters, such as world demand for expotrs of a cetrainproduct, are perceived as permanent. Changes in the relative profitability of expotrs of acetrain product do not meet this cirteiron. Thus, the localcurrency pirceof total expotrs is theweighted average of the pirces of all the products expotred:

(1) p^ÎewEX 1=1

If we normalize all the pirces in the ifrst peirod, we get the rateof change in the pirceof totalexpotrs over time as a function of:

)2(^"^XX7^^ frln^>=1 ) ;=<

../ז the elasticity of supply of product / relative to the pirce of product/.uEX

= vv; the weight of product 1 in total expotrs.EX


As stated, in this framework there is no change in the total amounts expotred, meaning thatEX = £ EX. is constant, so that for the rate ofchange of expotrs over time to be 0 (dln£X 0),for each /= 1, ...,71 we need:

(3) Xv^=0The total elasticity of supply relative to the price of a certain product is therefore zero; in otherwords, the sumof elasticitiesof all products relative to the priceof product / weighted by theirrelative share in expotrs is zero. We transpose this in equation (2), which presents the changein the expotr pirce, and get:

(4) dlnP^^WidlniP

The pirce each expotrer obtains in localcurrency terms is determined by the world pirce andthe domestic exchange rate relative to the market currency:

(5)iP = Pei

d\niP=d\nP*+d\nei

where P. is the pirce of the product in local currency, P' is its pirce in the market currency,and e. is the exchange rate of the local currency visavis the market currency. The basket isdefined as:

(6) S,=2>,.lne,

We choose currency 1 as the numeraire, and define all the exchange rates in relation to it,ei e'ei , where e[ is the exchange rate ofcurrency i against the numeraire, and by transposingthe currencybasket equations we get:

(7) lne,=S,^Xilne'1=2

n

t>l.*lne, =5, +\nej''_^1xi\aei'

We differentiate the exchangerate equations and remember that we normalized pirces in theifrst peirod:

)8( dlne1=X^ln<n

/>!.> dine,. =d\nei'^1xjd\ne'i=2


By transposing the overall pirce equation (4), we get:

n n 1

(9) d\nPx =^Wid\nP* +YJ(wi x^dlnel,1 ' 1=2

Equation (9) presents the rateof changeof the pirceof exports as a functionof the world pirceand of cross rates against the numeraire. The vairance of the rate of change of the pirce is:

nn n

(10)Var(dlnPx) = ^w?Var(dlnP' ) +2^Y,wiwjCov(dlnP''dlnPî=l ' j=2 i=\

+]T(w,.Jt,. )2ofrf*/ In e[)+ 2£ ^(w.x^Wjx^Covidlne'^dlne)i2 j=l 1=2

+JT ^w^w. jey)Cov(dln P*,dlne'(J=2 '=1

According to accepted assumptions, we expect a nonsigniifcant relation between changes inthe vairous exchange rates (covairance close to zero), as well as an unstable or nonsigniifcantrelation between changes in pirces and exchange rates. Thus, in order to minimize the vairanceofthe rateof changeofexport pirces, the deirvatives with respect to the decision vairable (i.e.,the weights of the currencies in the basket) have to be equated to zero:

(n) dVard\nPx) = 2t(w. Xi)Var(dlne;)= 0^w, = Xj

dx Sf

Appendix 3: Optimization Under Constraint

We present the problem of maximization for three currencies, so as to be able to illustrate theproblem on a twodimensional graph. The mathematical description of the problem ofoptimization under a constraint is:

MmfVarll, ] = Min[(w2 x2 f Var(e2'( +(n' 3 x3)2 Var(e3')\s.t.1.a<n1wlpl+W2(p2+e2') + w3(p3+e^)x2e2x3e3+St2.n <a3.x2 + x3=l xt

From an initial observation it is obvious that the minimum vairance will be at point (w2,w3),where the vairance is 0.

The chart below shows the problem in graphic form, where the circles represent the objectivefunction, and the lines theconstraints. The larger the circles the greater the vairancethey represent.Lines (1) and (2), which represent constraints 1 and 2, have the same slope, and the distancebetween them is 2a. The line representing constraint 3 passes through the minimum vairance


point, where x. = w., i = 1,2,3. Thus, in the optimization without a constraint on the average ofthe target variable (without constraints 1 and 2), we must get the minimum global value of theobjective functio. This is also the case when the constraint is applied to the average of the targetvariable, but the constraint is not binding or does not exist, i.e., when the global minimum pointis in the area between lines (1) and (2). The position of the constraints relative to the point)w2,h'3) is not unequivocal, and depends on the relations between the level of the currencybasket and thatof export prices (in currencybasket terms) visavis a. In other words, the relativepositionofthe constraints depends on the level of 'basic proiftability' from which the deviationis measured (the level that determines the position of the constraints) and on the percentage ofthe deviation that is permitted (which determines the distance between the constraints).

According to the KuhnTucker optimization conditions, if one of the constraints obtains,we will be on oneof the dotted lines: the constraint is binding and hence we will not be at theglobal minimum of the objective function. Similarly, the cases in which the weight of one ofthe currencies is zero can be derived from these conditions.

Appendix 4: The Data and the Method of Calculation

The change in the price of an Israeli import/export product, AP, is the weighted changes in theprices of competing products, AP1, translated into dollars by changes in the appropriate crossrate, AE1, and in accordance with the weights of these products w.v

l + AP = £(l + A/>i)a+AEOwi

The objective is to find the weights that lead to the maximum ift between the two parts of theequation , once for Israel's export prices and once for its import prices. These weights vary


between 0 and 100 percent at 5 percent intervals, for the US, Germany, England, France, andJapan (for wholesale prices except for France). The weighted price of the currencybasketcountries for the 10 observations between 1986 and 1995 is calculated on the basis of eachrow of weights. These weighted prices are compared with Israel's import and export prices.The rowofweights that leads to the best ift, i.e., the smallest average deviationofthe calculatedprice from the actual price over time, represents the optimal composition of the currencybasket that is appropriate for the policy target: the stabilization of import or export prices.

The data on export prices, import prices, wholesale prices, and inflation in the currencybasket countries (the US, Germany, England, France, and Japan) between 1986 and 1995were taken from IFS, where they appear in their local currencies.13 A change in these prices istranslated into dollar terms in accordance with the change in the annual average cross rate.The frequencyof the data is annual, in order to overcome the possibilityof irgidityofcontracts,so that there is enough time for market prices to adjust. The rates of change in the prices ofIsrael's goods imports and exports are calculated on the basis of a Pasche Index of prices, sothat they ift the IMF's indicesofUnit Import/Export Value. The pirce indicesofIsrael's tradablesare taken from the Consumer Price Index.

Appendix 5: The Considerations for Choosing the Criterion ofGoodness of Fit

In order to reach a conclusion as to which set of weights is the most suitable for thecomposition of the prices of Israel's imports/exports, the extent of ift of the various setsshould be ranked. The extent of ift is usually quantified by a correlation coefficient. Thewidespread use of the correlation coefficient deirves from the advantage of the regressionmethod in ifnding a linear relation between vairables, where the correlation coefficient isthe R of the regression:

where S^ isthejoint varianceofthe explanatory variables, x, and the dependent variable, y, Sand S)y are the variances of the independent variables and the dependent variable, and P is thevectorofcoefficients estimated by the regression method. The correlation coefifcient measuresthe percentage of vairance of the variable y, which is explained by x, where /iS is the absolutepart that is explained. The parameters that are calculated in this way are known as BLUE(Best Linear Unbiased Estimates). In other words, in the group of unbiased linear estimatesthe estimates of least squares are characteirzed by minimal variance (Maddala, 1977). Thedrawback of this index is that it ascribes excessive weight to the adjustment of observationsthat are far from the average, because the calculationof the correlation coefifcient is based onmeasuring the squareof the deviation from the average. Consequently, outlying observationsare given greater weight and can bias the results.

" The data on wholesale prices are for 198594.


An alternative index used mainly in research in the exact sciences is the average of thepercentageof the absolute deviation (and not the squared deviation) between the actual variableand the values of the calculated variables. This index, known as FOM (Figure of Merit) wasifrst defined by Balian and Eddy (1977) and Misra and Eddy (1979) as follows:

FOM^"^^!A

where FOM is the percentage of the deviation between the values of the dependent variable,y ., and those of the independent vairable obtained from specific variables, x., that the researcherhas chosen in accordance with the theory on the basisofwhich he seeks to explain the behaviorof y.. A is the totality of values that have to be explained. When the difference is below acertain percentage, usually 5 percent, it can be said that the variables selected on the basis ofthe theory do in fact explain the dependent variable.

The characteristics of BLUE that have made the method of the regression and correlationcoefficient useful are based on assumptions about the vairances and distirbutions of thevairables. The FOM index is not restricted to variables that uphold these assumptions, and soit need not display those characteirstics.

In the present study I have used that formula while omitting the denominator. First of all, Ais the sum of values that have to be explained, and is relevant for calculating the percentage ofdeviation, but its omission does not have an adverse effect on the ranking of the extent of fitobtained from different independent variables. Second, the value of the dependent variable inthis study is in rates of change, so that the relevant index is not the rateof deviation but theabsolute deviation (for rates that are close to zero, small deviations will be translated intolarge numbers that will bias the results). Consequently, using the FOM index, the averagedifference in this study is calculated as follows:

. 10

FOMi=£|PISR; PISR(n',.,PSALy(|

For every set of weights /, the FOM index equals the average of the differences betweenIsrael's actual import/export prices, PISR, at every yearj, and the price calculated on the basisof the set of weights, w, and pirces in the currencybasket countries, PSAL, each year. Theperiod for which the examination is undertaken is 198695, so that the amount is divided by10. The weights for which the minimal average FOM difference is obtained are optimal.

The difference between the correlation coeiffcient and the minimum average difference isdemonstrated in Figure 3c. Every point in the ifrst part of the figure represents the relationbetween the correlation coefficient and the average difference for a specific set of weights.The composition of the weights at point B maximizes the correlation coefficient, and thecomposition represented by point A minimizes the absolute average difference between achange in Israel's export pirce and a change in the weighted pirce of the exports of the currencybasket countires. In mostofthe range the relation between the two is negative: as the correlationbetween the calculated and the actual pirce irses, the average difference between the twodeclines. Only at high levels of correlation, above 95 percent, is there substitution between


the two, so that a rise in the correlation is at the expense ofan increase in the average difference.Although for both compositions the difference between the correlation coefficients is small,they represent differing explanations, as can be seen in the second part of Figure lc. Thefigure shows Israel's export pirces at each year (10 years, hence 10 points). 8of the 10 pointsrepresenting the composition of weights at point A are closer to the 45 degree line than thepoints representing B. However, the points representing B are nearer to the regression line,which is nonsigniifcant in this examination. As we are trying to ifnd a maximum explanationfor the yearly change in trade prices, whatever it may be, there is no reason to stress any oneyear more than another, so that the cirteironofminimizing the average difference was preferred.

Table AlGeographical Distribution ofMerchandise Trade, by Principal Region

(current dollars, percent"(1995199419931992199019881986198419801974

Sources of imports46504850495050454250l.EU8899910109882. EFTA222323222321232928223. US45775543244. Japan7655 4431115. RestofAsia148881010101318146. Other

535857595960605450587. Europe6363130303332344246378. US and other

Destinations ofexports3632333941403636' 4543l.EU33334445782. EFTA

272728282726252313143. US33222221114. Japan998655133125. Restof Asia222626222123333131236. Other

393536424544404252517. Europeb495354504849585444368. US and other

9. Europe as share47495252515351495156of total tradeb

10. US and other as42403839423944474537share of total trade

a Excluding oil and diamonds.b EU and EFTA.Source: Central Bureau of Statistics.


Table A2Merchandise Imports and Exports, by Pirncipal Currencies, 198594

(percent)19941993199219901988198719861985

Imports58.561.259.169.067.966.865.971.8$US4.13.83.73.23.74.24.04.0£UK2.42.21.91.71.71.82.01.6SFr15.915.216.613.212.913.915.211.9DM1.91.81.81.61.61.71.81.6DF1

3.93.23.32.52.42.41.91.2Lit4.63.74.43.13.83.02.82.6FFr3.04.04.01.81.81.91.91.3¥

94.395.194.896.195.895.795.596.0Cumulative32.829.931.725.326.127.027.722.9of which European currencies

Exports75.974.672.776.477.076.077.277.2$US5.35.55.75.25.25.45.45.6£UK1.10.81.20.81.11.00.80.8SFr6.97.88.97.67.88.27.67.5DM2.32.42.52.12.02.02.22.0DF11.01.11.30.90.80.80.80.8Lit3.43.53.53.42.83.52.83.0FFr1.41.51.30.91.00.70.60.7¥

97.397.297.197.397.797.697.497.6Cumulative20.021.123.120.019.720.919.619.7of which European currencies

Source: Foreign Exchange Control Department, Bank of Israel.


References

Balian, H.G. and N.W. Eddy ( 1 977). "Figure of Merit (FOM), an Improved Criterion over the NormalizedChiSquared Testfor Assessing GoodnessofFitofGamma Ray Spectra Peaks,"Nuclear InstrumentMethods, 145, 389395.

BenBassat, I. (1995). "Choosing the Optimal Currency Basket, and Capital Flows," Bank of IsraelResearch Department, internal memorandum, February (Hebrew).

Bhandair, J.S.(1985). "Expeirments with the Optimal Currency Composite," Southern Economic Journal,51,711730.

Black, S.W. (1976). "Exchange Rate Policies for Less Developed Countries in a World of FloatingExchange Rates," Princeton Essays on International Finance, 1 19, International Finance Section,Pirnceton University.

Branson, W.H. and L.T. KatseliPapaefstratiou (1980). "Income Instability, Terms of Trade, and theChoice of Exchange Rate Regime," JournalofDevelopment Economics, 7 (March), 4976.(1981). "Exchange Rate Policy for Developing Countries," in S. Grossman and E. Lundberg

(eds.), The World Economic Order: Past and Prospects, Macmillan, London.Connolly, M. (1982). "The Choice ofan Optimum Currency Peg for a Small Open Country," Journal of

International Moneyand Finance, 1, 153164.Corbae, D. and S. Ouliairs(1991)."ATest ofLongRun Purchasing Power PairtyAllowing for Structural

Breaks," Economic Record, 196, 2633.Dornbusch, R. (1987). "Purchasing Power Parity," in J. Eatwell, M. Milgate, and P. Newman (eds.), The

New Palgrave, a DictionaryofEconomics, Stockton, New York, 10751085.Edison, H.J. (1987). "Purchasing Power Parity in the Long Run: A Testof the Dollar/Pound Exchange

Rate (18901978)," JournalofMoney, Credit and Banking, 19(3), 376387.and J.T. Klovland (1987). "A Quantitative Reassessment of the Purchasing Power Parity

Hypothesis: Evidence from Norway and the United Kingdom," JournalofApplied Econometrics,2, 309333. and E. Vardal (1990). "Optimal Currency Basket for Small, Developed Economies," ScandinavianJournalof Economics, 92(4), 559571.

Fischer, E. and J.Y. Park (1991). "Testing Purchasing Power Pairty under the Null Hypothesis of Cointegration," Economic Journal, 101 (November), 14761484.

Flanders, M.J. and E. Helpman (1977). Optimal Currency Basket, Working Paper No. 577, TelAvivUniversity.and E. Helpman ( 1 979). "An Optimal Exchange Rate Peg in a World of General Floating," ReviewofEconomic Studies, 46(3), 533542. andA. Tishler (1981). "The Role ofElasticity Optimism in Choosing an Optimal Currency Basketwith Applications to Israel," JournalofInternational Economics, 11(3), 395406.

Frenkel, J.A. (1981). "The Collapseof Purchasing Power Parities during the 1970s," European EconomicReview, 16, 145165.

Galyam, Z. (1985). "Determining the Currency Basket for Conducting the Exchange Rate Policy: TheCase of Israel," Bank of Israel Research Department, internal memorandum, July (Hebrew).( 1 986). "Choosing the Currency Basket for the Coming Year," Bankof Israel Research Department,internal memorandum, March (Hebrew). and A. Halevi ( 1 989). "Changes in the 5Currency Basket," Bank of Israel Research Department,internal memorandum, December (Hebrew).

Gottlieb, D. and Z. Galyam (1981). "Choosing the Currency Basket for Israel," Bank of Israel ResearchDepartment, internal memorandum, February (Hebrew).

Grossman, S. (1973). "A Fundamental Symmetry in International Payment Patterns," Journal ofInternational Economics, 3, 105116.


Helpman, E. and P.R. Krugman (1985). Market Structure and Foreign Trade, The MIT Press.Home, J. and V. Martin (1989). "Exchange Rate Indicators and Optimal Currency Baskets: A

Macroeconomic Analysis with Application to Developing Countries," Applied Economics, 21,11371151.

IMF (1993). Annual ReportofExchange Arrangements.Krugman, P.( 1980). "Vehicle Currencies and the Structure of International Exchange," JournalofMoney,

Credit,and Banking, 12, 513526.Lipschitz, L. and V. Sundararajan (1980). "The Optimal Basket in a World of Generalized Floating,"

IMFStaffPaper, 80100.Maddala, G.S. (1977). Econometrics. Economics Handbook Series, McGrawHill Book Company.Mark, C.N. (1990). "Real and Nominal Exchange Rates in the Long Run: An Empirical Investigation,"

JournalofInternational Economics, 28, 115136.Misra, S.K. and N.W. Eddy (1979)."IFOM,A Formula for Universal Assessment ofGoodnessofFit of

Gamma RaySpectrd"Nuclear Instrument Methods, 166, 537540.Rao, R.K.S. and S.P. Magee (1980). "The Currency of Denomination of International Trade Contracts,"

in Levich, R.M. and C.G. Wihlborg (eds.), Exchange Risk and Exposure, Lexington: Mass., 6179.Roth, J. (1994). "An Examination of Changes in the Currency Basket," Bank of Israel Research

Department, internal memorandum, November (Hebrew).Shiffer, Z. (1993). "Regarding the Composition of the Currency Basket," Bank of Israel Research

Department, internal memorandum, December (Hebrew).Takagi, S. (1985). Pegging to a BasketofCurrencies: Conceptualand Operational Issues, IMF Research

Department.Turnovsky, S.I. (1982). "A Determinationof the Optimal Currency Basket: A MacroeconomicAnalysis,"

JournalofInternational Economics, 12 (i4), 333354.Williamson, J. (1982). "A Survey of the Literature on the Optimal Peg/1 Journalof Development

Economics, 11 , 3962.

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Dalida Eini - boi.org.il Review/reveiw 73/surv073_1e.pdf · 2 BankofIsraelEconomicReview73 rate has been managed within acrawling band, in accordance with which gradual, predetermined,andpreannouncedadjustmentsof