The liquidity effects of foreign exchange intervention

The liquidity effects of foreign exchange intervention

Journal of International Economics 63 (2004) 179 – 208 www.elsevier.com/locate/econbase The liquidity effects of foreign exchange intervention Wai-Mi...

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Journal of International Economics 63 (2004) 179 – 208 www.elsevier.com/locate/econbase

The liquidity effects of foreign exchange intervention Wai-Ming Ho* Department of Economics, York University, 4700 Keele Street, Toronto, ON M3J 1P3, Canada Received 24 February 2000; received in revised form 30 December 2002; accepted 21 January 2003

Abstract This paper examines the effectiveness of foreign exchange intervention in a two-country, twocurrency, general equilibrium model that allows for liquidity effects. Both sterilized and nonsterilized intervention operations have significant impacts on the allocation of liquidity in international financial markets. Whether intervention is successful in moving the exchange rate in the desirable direction depends upon the degree of sterilization of intervention and the intratemporal elasticity of substitution of the consumption goods. The model shows that there exist circumstances in which the response of exchange rate to intervention is ‘perverse’ as documented in the empirical literature. D 2003 Elsevier B.V. All rights reserved. Keywords: Foreign exchange market; Sterilized and non-sterilized intervention; Liquidity effects JEL classification: F31; F41

1. Introduction In order to affect the exchange rates, monetary authorities intervene in foreign exchange markets by buying or selling foreign exchange, normally against their own currency. There are two types of interventions: non-sterilized intervention and sterilized intervention. Nonsterilized intervention affects the supply of domestic currency in the foreign exchange market, and results in a change in the domestic monetary base. Its effect on the nominal exchange rate is therefore analogous to that of a change in domestic monetary policy. Sterilized intervention neutralizes the effect of foreign exchange intervention on the domestic monetary base by an offsetting open market operation of domestic-currency* Tel.: +1-416-736-2100; fax: +1-416-736-5987. E-mail address: [email protected] (W.-M. Ho). 0022-1996/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0022-1996(03)00041-2

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denominated bonds, and causes only a ‘pure’ change in the currency denomination of assets held by the public. Hence, sterilized intervention is independent of monetary policy, and if it is an effective instrument for exchange rate management, monetary authorities can maintain greater flexibility of their monetary policy. Because of this reason, there has been a large research effort on the effectiveness of sterilized intervention in theory and practice. In the literature, sterilized intervention has been viewed as having effects on exchange rates through either of two channels: the portfolio-balance channel and the signaling channel.1 However, the evidence on the effectiveness of intervention via the two channels is inconclusive. Given the data showing that interventions in the markets for major currencies have been substantial and frequent in recent years, there is a clear need to provide a satisfactory explanation of why central banks engage in foreign exchange interventions to such a large extent. As both sterilized and non-sterilized intervention operations result in changes in asset supplies, such changes can have significant impact on liquidity in international financial markets. When economic agents are subject to liquidity constraints, liquidity effects induced by official intervention should be taken into account. The analyses of the effectiveness of intervention via the portfolio-balance channel and the signaling channel have ignored the crucial function of international financial markets in allocating liquidity across market participants. Hence, it will be beneficial to investigate theoretically the impacts of intervention within the context of a two-country, two-currency, general equilibrium model that allows for liquidity effects. Recent work on liquidity effects of monetary policy shocks in closed economy settings by Bernanke and Blinder (1992), Christiano and Eichenbaum (1995), and Strongin (1995) have provided strong empirical support for liquidity effects.2 Eichenbaum and Evans (1995), and Grilli and Roubini (1995) extend this line of research to open-economy settings and find that expansionary shocks to US monetary policy are followed by sharp declines in US interest rates and sharp depreciations in US nominal and real exchange rates.3 These findings are consistent with the predictions of the open-economy models allowing for liquidity effects studied by Grilli and Roubini (1992), Ho (1993), and Schlagenhauf and Wrase (1995a,b). By following Lucas (1990)’s approach to modeling an asymmetry of monetary injections, these theoretical models examine the liquidity effects of monetary shocks on the world economy.4 As economic agents are affected by the

1 See Edison (1993) and Dominguez and Frankel (1993) for detailed surveys of the empirical research on the effectiveness of intervention via the two channels documented in the earlier literature, and see Sarno and Taylor (2001) for a survey of the more recent literature on official intervention. 2 These papers find that positive shocks to money lead to reductions in the short-term nominal interest rates and increases in output in the United States. 3 Grilli and Roubini (1995) examined data of the G-7 countries and found that while US interest rates rise and the US dollar appreciates significantly on impact following a positive interest rate shock in the US, such shocks in the non-US G-7 countries are often associated with an impact depreciation of their currency value relative to the US dollar. However, they showed that after controlling for US monetary policies and expected inflation, the response of exchange rates to positive interest rate shocks was a persistent currency appreciation in most of the G-7 countries. 4 Fuerst (1992) is the first paper to introduce production into Lucas (1990)’s closed-economy model.

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liquidity shocks asymmetrically, the redistribution of liquidity in international financial markets not only causes fluctuations in exchange rates and interest rates but also has real effects on the world economy. Given that intervention can affect the allocation of liquidity in international financial markets substantially, further research on the liquidity effects induced by intervention may provide new insight into a better understanding of the effectiveness of foreign exchange intervention. The purpose of this paper is to reexamine the effects of foreign exchange intervention in a two-country, two-currency, general equilibrium model that allows for liquidity effects. The world economy is a monetary economy in which money is introduced by imposing cash-in-advance constraints on all transactions. Economic agents of the two countries are linked together by trade in goods and financial assets. The limited participation assumption implies that different economic agents face different trading opportunities. Shocks to the world economy will induce a reallocation of liquidity across different types of market participants and therefore generate liquidity effects. The nominal exchange rate is determined by the demands and supplies of the two currencies in the foreign exchange market, which reflect both the liquidity of the foreign exchange market and the relative liquidity of the home-currency-denominated asset market and the foreign-currencydenominated asset market. This paper presents an alternative channel of influence of foreign exchange intervention that emphasizes the role of international financial markets in allocating liquidity. To make the analysis more transparent, assumptions are made to ensure that both the portfolio-balance channel and the signaling channel are absent in the model. When the domestic monetary authority conducts an official sale of domestic currency so as to keep the domestic currency from appreciating, the supply of domestic currency to the foreign exchange market increases. In order to clear the market, the nominal exchange rate rises, and the sellers (buyers) receive (pay) more home currency for each unit of foreign currency traded. In addition to this direct impact on the liquidity in the foreign exchange market, the relative liquidity of the two asset markets are affected by the resulting adjustments of the domestic monetary authority’s asset holding. In the case of nonsterilized intervention, the domestic monetary authority uses the proceeds of foreign currency from the official sale of domestic currency to purchase the foreign-currencydenominated bonds. This increase in the supply of liquidity causes a decrease in the interest rate on the foreign-currency-denominated assets and a reallocation of liquidity in this market. In the case of sterilized intervention, the domestic monetary authority not only purchases the foreign-currency-denominated bonds but also conducts an open market sale of the domestic-currency-denominated bonds to sterilize the effect of intervention on the domestic money supply. As the demand for liquidity in the homecurrency-denominated asset market rises, the interest rate on these assets rises, and the allocation of liquidity changes. These liquidity shocks to the asset markets affect the economic activities of the market participants, which, in turn, generate downward forces on the nominal exchange rate. Hence, whether an intervention operation can move the exchange rate in the desirable direction depends upon the relative strength of all of these liquidity effects. The effects of foreign exchange intervention on exchange rate and interest rates can be summarized as follows. First, non-sterilized intervention is always effective in

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affecting an exchange rate as it is analogous to a change in monetary policy. However, the impact of a non-sterilized intervention operation and that of an open market operation on interest rates are different qualitatively. Although both non-sterilized intervention and monetary policy involve monetary injections to the economy, the injections are channeled through different markets. As the induced liquidity shocks occur in different markets, these two policies will have different impacts on the interest rates. Second, even though sterilized intervention is less effective than non-sterilized intervention, it can influence an exchange rate in the desirable direction when the consumption goods are substitutes in consumers’ preferences. This implies that sterilized intervention can be undertaken independently for exchange rate management, allowing monetary authorities to have greater flexibility of their monetary policy. Third, when intervention is sterilized and when the goods are not substitutes in consumption, the liquidity effect in the foreign exchange market will be dominated by the liquidity effects in the asset markets so that the equilibrium effect of sterilized intervention on the exchange rate will be insignificant or even in the wrong direction. This result is consistent with the empirical evidence that intervention either had no insignificant effect or moved the currency significantly in the wrong direction. Kaminsky and Lewis (1996) document that in 1987, dollar buying interventions led to a significant depreciation in the US dollar; and during 1988 and 1989, the official sales of the US dollar led to an appreciation in the dollar. Bhattacharya and Weller (1997) presented a theoretical explanation for these puzzling ‘perverse’ responses of exchange rates documented in the empirical literature on intervention by examining the signaling channel in an asymmetric information model that characterizes the strategic interactions between the central bank and speculators. In contrast, this paper stresses the allocative function of international financial markets and presents an alternative explanation for the empirical puzzle by using a two-country, two-currency, general equilibrium model with liquidity effects. The remainder of the paper is organized as follows. Section 2 describes the model. Section 3 presents a stationary equilibrium of the world economy. The effects of foreign exchange intervention on the world economy are discussed in Section 4. Section 5 concludes the paper.

2. The model Consider a monetary model of a world economy with two countries, home and foreign. Each country is inhabited by N identical, infinitely-lived, multi-member households. N is assumed to be large enough that every individual acts as a pricetaker in the markets for goods, services and financial assets. Transactions in all of these markets are subject to cash-in-advance constraints; and payments must be made in terms of the sellers’ currency. As the world economy can be considered as an economy with two heterogeneous households, all variables will then be expressed in per (own country) household terms. The foreign variables and parameters are indexed with asterisks.

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2.1. The households Each household consists of five members: a shopper, a worker, a firm, a financial intermediary, and an importer. The preferences of the home representative household is characterized by the additively time-separable utility function, l X U¼ bt uðCxt ; Cyt ; Gt ; ht Þ; ð1Þ t¼0

where 0 < b < 1 and uðCxt ; Cyt ; Gt ; ht Þ ¼ ln½Cxta þ Cyta 1=a þ ln Gt þ v½1  ht ; v > 0: The instantaneous utility function uðCxt ; Cyt ; Gt ; ht Þ is discounted by the subjective discount factor b. The household is endowed with one unit of time in every period. In period t, it supplies ht units of work effort to the labor market in the home country and enjoys 1  ht units of leisure. v is a positive parameter measuring the constant marginal utility of leisure. The household’s consumption of good j, j ¼ x; y; in period t is denoted by Cjt , and the elasticity of (intratemporal) substitution in consumption between the two goods, ru1=1  a , is constant over time. In addition to the private consumption, the household can consume the public services, Gt, which are provided by the government of its own country.5 For simplicity, the representative households of the two countries are assumed to have identical preferences. Firms in the home country produce only good x, while those of the foreign country produce only good y. Each home firm faces the production function, Qxt ¼ Fðht ; lt Þ ¼ ht lt ;

ð2Þ

where the output of good x, Qxt , depends on the input of labor, lt , and the country-wide productivity shock, ht. Similarly, the foreign firm’s production function of good y is given by Qyt* ¼ Fðht* ; lt* Þ ¼ ht* lt*. Given that there is a complete specialization in production but each household consumes both goods, the importers of each country purchase goods produced abroad and then sell to the domestic residents. The cash-in-advance constraints on all transactions assign financial intermediaries a role in financing production and international trade. 2.2. The governments Each country has a government that consists of two branches, a fiscal authority and a monetary authority. In period t, the fiscal authority of the home country determines its fiscal spending, Bt units of home currency, and finances by issuing Bt units of the oneperiod, home-currency-denominated bonds.6 Using the funds obtained from bond sales, the home fiscal authority hires ltg units of labor from the home labor market to produce the public services for the consumption of its residents, subject to the technological constraint, Gt ¼ dltg , where d is a positive constant. At the end of period t, for the redemption of its 5

The consumption of public services is assumed to be non-rival and non-exclusive. For simplicity, it is assumed that each fiscal authority issues bonds denominated in the currency of its own country only. 6

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bonds, the home fiscal authority imposes a lump-sum tax of Tt units of home currency on its residents. Each monetary authority has responsibility for the monetary policy and foreign exchange policy of its own country. Each monetary authority conducts its monetary policy by way of trading the one-period bonds denominated in its own currency. In period t, the home monetary authority purchases Bm t units of home-currency-denominated bonds from the home fiscal authority and/or the financial intermediaries. The bond purchase 7 results in a temporary injection of Bm t units of home currency to the economy. For the international monetary arrangement, a flexible exchange rate regime is adopted by the monetary authorities of the two countries. Although the monetary authorities do not use administrative controls to fix the exchange rate directly, each of them may intervene in the foreign exchange market with the aim of moving the exchange rate in its desired direction. Each operation of foreign exchange intervention conducted by the home monetary authority is characterized by two policy variables—the volume of intervention (Zt ) and the degree of sterilization (zt ). To keep the home currency from appreciating, the home monetary authority sells Zt units of home currency in the foreign exchange market; the proceeds of foreign currency will then be used to purchase the one-period, foreigncurrency-denominated bonds. The intervention operation (the official sale of Zt units of home currency in the foreign exchange market) effectively increases the quantity of home currency in circulation. To sterilize the positive effect of intervention on its money supply, the home monetary authority performs an open market sale of zt units of home-currencydenominated bonds to absorb the extra liquidity.8 The intervention is fully sterilized (unsterilized) when zt ¼ Zt (zt ¼ 0); and a partially sterilized intervention (0 < zt < Zt ) results in an increase in the supply of home currency by Zt  zt units.9 Let Mt denote the aggregate (per own-country household) home money stock at the beginning of period t. By implementing the monetary policy and foreign exchange policy, the home monetary authority sets the quantity of home currency in circulation during period t at the level of Mt þ Bm t þ Zt  z t . 2.3. The timing of information and transactions The timing of information and transactions is shown in Fig. 1. The representative household of the home country enters period t with cash balances carried over from the last period, which include mht units of home currency and mft units of foreign currency. At the 7

As will be described below, at the end of period t, after the home fiscal authority redeems the bonds, the home monetary authority rebates the interest income to its residents. As a result, the end-of-period (beginning-ofperiod) aggregate home money stock will not be affected by this monetary injection. 8 In the case in which Zt is negative, the home monetary authority purchases Zt units of home currency in the foreign exchange market by using foreign currency. It is assumed that the home monetary authority has large foreign reserve holdings so that the feasibility of intervention is not an issue. To sterilize the negative effect of this intervention operation on the home money stock, the home monetary authority uses home currency to purchase home-currency-denominated bonds from the market. 9 As will be shown in Section 2.2, even though intervention is fully sterilized (Zt ¼ zt ) and has no effect on the quantity of home currency in circulation during period t, the stock of home currency will still be affected when the home-currency-denominated bonds mature and their interest payments are made.

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Fig. 1. The timing of transactions of the home representative household.

beginning of period t , the household deposits nt units of home currency in the home financial intermediary and allocates the remaining mht  nt units of home currency to the shopper and mft units of foreign currency to the importer. Transaction costs are assumed to be prohibitively high that once the deposit is made, it cannot be withdrawn until the end of the current period. For simplicity, each household is allowed to hold deposits denominated

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in the currency of its own country only.10 After the deposit is made, the household separates. Household members have different tasks to perform in the markets for labor, consumption goods, and financial assets. Once the household is separated, the state of the world is revealed to everybody. The state of the world, st, is independently and identically distributed across time, and its probability density function Gðst Þ is public knowledge.11 The realization of st determines the values of the country-wide productivity shocks, ht and h*t ; the fiscal m spending, Bt and B*t , the monetary injections, Bm t and Bt *, and the foreign exchange * * intervention and sterilization, ðZt ; zt Þ and ðZ t ; z t Þ, of the two countries.12 In the financial markets, both home-currency-denominated assets and foreign-currency-denominated assets are traded.13 In period t, the nominal interest rates on the oneperiod, home-currency-denominated assets and foreign-currency-denominated assets are denoted by it and i*t , respectively. Each intermediary can trade bonds denominated in either currency but is allowed to make loans denominated in its own country’s currency only. In addition, firms and importers are allowed to borrow only from the intermediaries of their own country.14 The allocation of liquidity in the financial markets during period t, after st is revealed, is presented in Fig. 2. Given the deposit of nt units of home currency, the representative home intermediary faces the following cash-in-advance constraint,

nt z Lxt þ Lyt þ bht þ et bft :

ð3Þ

Taking as given the demand for funds of the borrowers, the interest rates, it and i*t, the spot currency exchange rate, et , and the one-period, forward currency exchange rate, e ft , the home intermediary allocates the loans Lxt and Lyt to the home firm and the home importer, respectively, and purchases bht units of home-currency-denominated bonds and bft units of foreign-currency-denominated bonds.15,16 The home intermediary is required to use foreign currency to purchase the foreigncurrency-denominated bonds; and the home importer must pay for its imports in foreign

10 This restriction will not make any qualitative difference to the results, while helping to economize on the notations and to reduce the accounting procedures. 11 It can be shown that the results of this paper remain valid if we allow the state of the world to be positively, serially correlated by assuming that st follows a two-state Markov process. 12 The assumption that st is independently distributed across time implies that foreign exchange intervention does not provide a signal about the future stance of policy. Hence, official intervention operations do not affect the exchange rate through the signaling channel. 13 Since perfect competition implies that intermediaries, firms and importers earn zero profits, without loss of generality, trading of shares in these entities are ignored. 14 These assumptions are for simplicity. Allowing the intermediaries to borrow from the intermediaries of another country and lend to the borrowers of either country will not affect the equilibrium of the world economy, but many accounting procedures will be involved. 15 In the case of bj < 0, j ¼ h; f , the home intermediary raises funds by selling bonds. 16 The exchange rates et and e ft are the prices of the foreign currency in terms of the home currency.

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Fig. 2. Cash flows in the financial markets of the world economy during period t after st is revealed.

currency. Their foreign counterparts also face a similar problem. At this time, the currency exchange markets are opened. The intermediaries and the importers of both countries can trade for the desired currency in the spot exchange market at the exchange rate, et. In order to cover the foreign exchange risk, in the forward exchange market each intermediary can sell its future receipt of foreign exchange at the forward exchange rate, e ft , for delivery at the end of period t. Under a flexible exchange rate regime, the spot exchange rate, et , and the oneperiod, forward exchange rate, e ft , are determined by the market forces. However, as described above, the monetary authority of either country may affect the equilibrium exchange rates indirectly by foreign exchange intervention. The home monetary authority sells Zt units of home currency in the foreign exchange market and then purchases Zt =et units of foreign-currency-denominated bonds from the bond market. In order to sterilize the effect of its intervention on the supply of home currency, it sells zt units of home-currency-denominated bonds to the market.17 Labor is internationally immobile. In the home labor market, the representative worker of the home country sells ht units of labor effort at the market wage rate of Wt units of home currency. After issuing Bt units of home-currency-denominated bonds, the home fiscal authority can hire ltg units of labor to produce the public services, subject to the cash-in-advance constraint, Bt zWt l gt :

ð4Þ

17 Sterilized foreign exchange intervention results in a swap of currency denomination of assets in the monetary authority’s portfolio.

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By borrowing Lxt units of home currency from the home intermediary, the home firm hires lt units of labor to produce good x, and its cash-in-advance constraint is given by,

Lxt z Wt lt :

ð5Þ

In the foreign goods market, the home importer uses the cash balance of mft þ Lyt =et units of foreign currency to purchase IMyt units of good y at the price of P*yt units of foreign currency, facing the cash-in-advance constraint,

mft þ

Lyt z P*yt IMyt : et

ð6Þ

The imports will then be shipped to the home country. In the goods market of the home country, the home firm sells its output of good x to the home shopper and the foreign importer at the price of Pxt units of home currency, and the home importer sells its import of good y to the home shopper at the price of Pyt units of home currency. Taking the prices as given, the home shopper’s purchases of goods for consumption are subject to the cash-in-advance constraint,

mht  nt z Pxt Cxt þ Pyt Cyt :

ð7Þ

At the end of the period, loan repayments are made; and bonds are redeemed. Given that the public services are provided to its residents free of charge, in order to maintain a balanced budget, the home fiscal authority finances its redemption of bonds by imposing a lump-sum tax of Tt ¼ Bt ð1 þ it Þ units of home currency on the representative home worker (household).18 By collecting the returns from its portfolio, the home intermediary has ðbht þ Lxt þ Lyt Þð1 þ it Þ þ bft ð1 þ i*t Þeft units of home currency and pays out its deposits, nt ð1 þ it Þ. After all transactions are completed, the household is reunited, all remaining cash is pooled, and goods purchased by the shopper are consumed. The cash flows in the world economy at the end of period t are summarized in Fig. 3. It is noted that because some of the home-currency-denominated bonds issued by the home fiscal authority are held by the monetary authorities of the two countries, the imposition of the lump-sum tax, Tt, and the redemption of bonds, Bt ð1 þ it Þ, result in a * withdrawal of ðBm t  zt þ et Z t Þð1 þ it Þ units of home currency in circulation; and the 18

It is noted that perfect competition implies that firms, importers, and intermediaries earn zero profits.

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Fig. 3. Cash flows in the world economy at the end of period t.

m * aggregate home money stock is now equal to Mt þ Bm t þ Zt  zt  ðBt  zt þ et Z t Þ 19 m ð1 þ it Þ. If Zt  ðBt  zt Þit  et Z *t ð1 þ it Þ is negative (positive), then the aggregate home money stock at the beginning of period t þ 1, Mtþ1, will be lower (larger) than Mt, which will have a deflationary (an inflationary) effect on the world economy.20 In order to eliminate the deflationary (inflationary) effect and focus our attention on the liquidity effect induced by foreign exchange intervention and sterilization, the home monetary authority is assumed to keep the beginning-of-period, aggregate home money stock equal to unity over time, Mt ¼ M ¼ 1; b t; by making a lump-sum transfer of * ðBm t  zt Þit þ et Z t ð1 þ it Þ  Zt units of home currency to the home representative * household.21,22 Let the lump-sum transfer be denoted by dt uðBm t  zt Þit þ et Z t ð1 þ it Þ Zt .23

19 The returns on holding the home-currency-denominated bonds received by the home monetary authority * and the foreign monetary authority are ðBm t  zt Þð1 þ it Þ and et Z t ð1 þ it Þ, respectively. 20 This deflationary/inflationary effect exists even though the intervention operations are fully sterilized, Zt ¼ zt and Z t* ¼ z*t . 21 The assumption of M ¼ 1 is just for convenience. 22 It is noted that the imposition of this lump-sum transfer eliminates completely any dynamic considerations, allowing us to focus on the liquidity effects on current economic activity. Given that generally the internal propagation mechanisms in the models examining liquidity effects are fairly weak, and the dynamic effects are therefore short-lived, relaxing this assumption would not alter the essentials of the model. 23 If dt < 0, this is instead a lump-sum tax.

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After receiving the lump-sum transfer dt, the household holds the cash balances mhtþ1 and mftþ1 for next period, where 24     mhtþ1 ¼ mht  nt  Pxt Cxt  Pyt Cyt þ nt  Lxt  Lyt  bht  et bft   þ½Lxt  Wt lt  þ ½Pxt Qxt  Lxt ð1 þ it Þ þ Pyt IMyt  Lyt ð1 þ it Þ h i  þ Lxt þ Lyt þ bht ð1 þ it Þ þ bft etf ð1 þ i*t Þ þ Wt ht  Tt þ dt ¼

mht  Pxt Cxt  Pyt Cyt  Wt lt  Lyt þbht it þ bft ðe ft ð1 þ i*t Þ  et Þ þ Pxt Qxt þ Pyt IMyt þ Wt ht  Tt þ dt ; ð8Þ

mftþ1 ¼ mft þ

Lyt  Pyt* IMyt : et

ð9Þ

The activities of the household members and government of the foreign country are analogous to their counterparts in the home country. Hence, the foreign variables and parameters are defined in a similar way. 2.4. The optimization problem of the home representative household The home representative household maximizes the expected lifetime utility with preferences given by Eq. (1), subject to the technology constraint [Eq. (2)], the cashin-advance constraints [Eqs. (3) and (5) – (7)], and the two evolution equations of the household’s beginning-of-period cash balances [Eqs. (8) and (9)]. The household’s optimization problem can be solved by applying dynamic programming. V ðm; s˜ Þ ¼ max

0VnVmh

Z max

Cx ; Cy ; h; bh ; bf ; Lx ; Ly ; l; IMy

fuðCx ; Cy ; G; hÞþbV ðmV; sÞgGðsÞ ds; ðP1Þ

subject to mh  nzPx Cx þ Py Cy ;

ð3VÞ

nzLx þ Ly þ bh þ ebf ;

ð5VÞ

24 Eq. (8) is derived from summing up the unspent balances of home currency held by the shopper, financial intermediary, and firm, the profits of the firm and importer, the revenue of the financial intermediary, the wage income of the worker, and the net transfer from the government. Eq. (9) gives the unspent balance of foreign currency held by the importer.

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ð6VÞ

Lx zWl;

Ly z P*y IMy ; e

mf þ

191

ð7VÞ

mVh ¼ mh  Px Cx  Py Cy  Wl  Ly   þbh i þ bf e f ð1 þ i*Þ  e þ Px Qx þ Py IMy þ Wh  T þ d;

mfV ¼ mf þ

Ly  Py* IMy ; e

ð8VÞ

ð9VÞ

where the time subscripts for current period have been dropped while those for the next period have been denoted by primes. The value function V ðm; s˜ Þ is a function of the collection of the beginning-of-period money holdings of the home and foreign representative households, m ¼ ðmh ; mf ; m*h ; m*f Þ, and the realization of last period’s state of the world, s˜. The first-order conditions for Eq. (P1) are presented in Appendix A. The foreign representative household has an analogous optimization problem. From the first-order conditions of the two representative households, it can be shown that because of perfect competition, all firms, intermediaries, and importers earn zero profits. Hence, the marginal revenue and marginal cost of labor facing each firm are equalized, W ð1 þ iÞ ¼ Px h;

  W * 1 þ i* ¼ P*y h*;

ð10Þ

and the arbitrage conditions hold,   eð 1 þ i Þ ¼ e f 1 þ i * ;

P*x ¼

  Px 1 þ i* ; Py ¼ P*y eð1 þ iÞ: e

ð11Þ

ð12Þ

The arbitrage condition for the financial markets, Eq. (11), states that each intermediary must be indifferent between holding bonds denominated in either currency of the two countries.25 As shown in the arbitrage conditions for the goods markets, Eq. (12), if the interest rates are positive, the presence of the cash-in-advance constraint on each importer

25 Since the foreign exchange risk of holding an asset denominated in the currency of another country can be eliminated completely, and the (covered) effective rates of return on the domestic and foreign assets are equalized, the two assets are perfect substitutes in asset-holders’ portfolios. Hence, the portfolio-balance channel is absent in the model.

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will cause imports to be sold at higher prices in the imported country, and the consumption ratios of the two representative households will be different even though they have identical preferences. As illustrated in Appendix A, solving the first-order conditions for consumption of each household gives the expenditure share of good j, j ¼ x; y, in each shopper’s budget. Sj u

Pj1r Pj Cj P*j C *j Pj*1r i ; Sj* u ; ¼h ¼  1r mh  n m*f  n* Px* þ Py*1r Px1r þ Py1r

j ¼ x; y:

ð13Þ

It is noted that Sx þ Sy ¼ S *x þ S *y ¼ 1:

3. Stationary rational expectations equilibrium In the stationary rational expectations equilibrium of the world economy, the prices and decision rules are fixed functions of the current state of the world, s ¼ ðh; h*; B; B*; Bm ; Bm *; Z; z; Z *; z*Þ: Given that the deposit decisions, n and n* , are made before the realization of the cu rrent state of the world, s, they are independent of s. In the following discussion, our attention will be restricted to situations in which the interest rates i and i * are strictly positive. This implies that all of the cash-in-advance constraints always bind; and the borrowers borrow only what they plan to spend. In this equilibrium, the following conditions must be satisfied in each period. First, the home representative household solves its optimization problem [Eq. (P1)], taking as given the technology shock, h, the government’s decisions, G, T, and d, and the pricing functions, i, i *, e, e f , Px , Py , W , and Py*. The foreign representative household solves an analogous optimization problem. Second, each fiscal authority’s budget constraints are satisfied. Finally, all markets clear. Labor markets : h ¼ l þ l g ; Goods markets :

h* ¼ l * þ l g *;

Cx þ C *x ¼ Qx ¼ h l;

IM *x ¼ C *x ;

Cy þ C *y ¼ Q *y ¼ h *l *; Money markets : mh þ m*h ¼ 1;

Loan markets :

ð14Þ

IMy ¼ Cy ;

mf þ m*f ¼ 1;

ð15Þ ð16Þ

n  bh  ebf ¼ Wl þ eP*y Cy ;

n* 

b*h Px C *x  b*f ¼ W *l * þ ; e e

ð17Þ

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193

Bond markets : B þ z ¼ Bm þ bh þ b*h þ eZ *; Z B * þ z * ¼ B m * þ bf þ b*f þ ; e Spot currency exchange market :

ð18Þ

ebf þ e P*y Cy þ Z ¼ b*h þ Px C *x þ e Z *; ð19Þ

Forward currency exchange market : e f bf ð1 þ i *Þ ¼ b*h ð1 þ iÞ: It is noted that substituting Eq. (11) into Eq. (20) yields ebf ¼ b* h:

ð20Þ

ð21Þ

The covered interest parity condition [Eq. (11)] shows that intermediaries are indifferent between holding bonds denominated in either currency of the two countries. However, purchasing bonds denominated in the currency of another country requires the intermediaries to trade for the desired currency in both the spot and forward currency exchange markets, and that their purchases of foreign exchange in the spot market correspond with the sales of their future receipts of foreign exchange in the forward market. Given that the relation between the transactions of the home and foreign intermediaries in the forward foreign exchange market is represented by the equilibrium condition for the forward currency exchange market [Eq. (20)], together with Eq. (11), we can derive Eq. (21) to represent the relation between the transactions of the two intermediaries in the spot currency exchange market. By substituting Eqs. (18) and (21) into Eqs. (17) and (19), we can obtain Eqs. (22) – (24) that characterize the ultimate allocations of liquidity in the home-currency-denominated asset market, the foreign-currency-denominated asset market, and the spot currency exchange market, respectively.26 n þ Bm þ ðZ  zÞ ¼ B þ Wl þ Px C *x ;

ð22Þ

n* þ Bm * þ ðZ *  z *Þ ¼ B* þ W * l * þ P *y Cy ;

ð23Þ

eP *y Cy þ Z ¼ Px C *x þ eZ *:

ð24Þ

Eq. (22) states that the supply of liquidity in the home-currency-denominated asset market are from three sources. The first one, n, is the deposit of the home household. The 26 As shown by Eqs. (17), (18) and (22) – (24), the equilibrium values of bh, bf , bh*, and b*f are indeterminate, indicating that the composition of each intermediary’s bond holding does not play any role in the determination of the ultimate allocations of liquidity in asset markets in equilibrium. There is a continuum of equilibria which have identical pricing rules, real allocations, and ultimate allocations of liquidity in financial markets. Each of these equilibria is characterized by a distinct vector of equilibrium values, ½bh , bf , bh*, b*f ].

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second one, Bm, is the monetary injection of the home monetary authority by way of open market purchases of home-currency-denominated bonds. The third one, Z  z , is the monetary injection resulting from the foreign exchange intervention operation conducted by the home monetary authority.27 The liquidity in this market is ultimately allocated to finance the fiscal spending of the home fiscal authority, B, the wage bill of the home firm, W l, and the purchases of good x of the foreign importer, Px C *x . Similarly, Eq. (23) illustrates that in the foreign-currency-denominated asset market, the sources of liquidity are from the foreign household’s deposit, n* , the foreign monetary authority’s open market purchases of foreign-currency-denominated bonds, Bm *, and the foreign monetary authority’s official sales of foreign currency in the foreign exchange market, Z *  z*, while the ultimate uses of the liquidity are to finance the fiscal spending of the foreign fiscal authority, B* , the wage bill of the foreign firm, W *l * , and the purchases of good y of the home importer, P *y Cy . Eq. (24) is derived by substituting Eq. (21) into Eq. (19). Eq. (19) states that in the spot currency exchange market, the demands for home currency are from the foreign importer for the purchase of good x, Px C *x , the foreign financial intermediary for the purchase of bh* units of home-currency-denominated bonds, and the foreign monetary authority for the official purchase of eZ * units of home currency; while the supplies of home currency are from the home importer for the purchase of good y, eP *y Cy, the home financial intermediary for the purchase of bf units of foreign-currency-denominated bonds, and the home monetary authority for the official sale of Z units of home currency. Since ebf ¼ b *h , we can rewrite Eq. (19) as Eq. (24). 3.1. Solving for an equilibrium Using the binding cash-in-advance constraint of each importer and the money market clearing conditions, we can show that at the beginning of each period, the home (foreign) currency is held entirely by the home (foreign) representative household. Given that mh ¼ m *f ¼ 1 , m *h ¼ mf ¼ 0 , and s is independently and identically distributed across time, the equilibrium values of n and n* are fixed numbers which are between zero and one. As illustrated in Appendix A, the stationary equilibrium can be characterized by a simultaneous equation system of three equations [Eqs. (22V) –(24V)], in three unknowns, i, i * and e.   n ¼ B  Bm þ ZR þ z  ð1 þ RÞeZ * þ ð1  nÞ 1 þ R Sy R;

n* ¼ B *  Bm * þ Z *R * þ z *  ð1 þ R *Þ

  Z þ ð1  n *Þ 1 þ R *S *x R *; e

ð22VÞ

ð23VÞ

27 As discussed in Section 2, if the home monetary authority conducts an operation of foreign exchange intervention that is characterized by ðZ; zÞ, the supply of home currency will be increased by Z  z units.

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Z þ ð1  nÞRSy ¼ eð1  n *ÞR *S *x þ eZ *;

195

ð24VÞ

where Ru

1 ; 1þi "

Sy ¼

S *x ¼

R *u

1 ; 1 þ i*

ð1  nÞb *h *R * ð1  n *Þbhe

"

ð1  nÞ b *h * ð1  n *Þ bheR

Px ð1  nÞb *h *R * ¼ ; Py ð1  n*Þbhe

P *x ð1  nÞb *h * ¼ : P *y ð1  n*ÞbheR

#1

1r þ1

;

and

#1

r1 þ1

:

ð13VÞ

From Eqs. (22V) –(24V), it is clear that the equilibrium values of the interest rates i and i*, and the spot exchange rate e depend on the deposit decisions of the two representative households, n and n*, and the realization of the current state of the world, s ¼ ðh; h *; B; B *; Bm ; Bm *; Z; z; Z *; z *Þ: Once the equilibrium values of i, i * and e have been obtained by solving Eqs. (22V)– (24V), the equilibrium values of all other variables of interest can be derived.

4. Effects of policy shocks on interest rates and exchange rate As stated in Eqs. (22V) –(24V), changes in the domestic fiscal policy, B, the foreign fiscal policy, B*, and the foreign monetary policy, Bm *, lead to changes in the spot exchange rate. In response to these policy changes, the home monetary authority could intervene in the foreign exchange market so as to prevent wide fluctuations in the spot exchange rate. Given that sterilized and non-sterilized intervention have different implications on the money supply of the home country and the allocation of liquidity in international financial markets, it is of interest to study the impacts of foreign exchange intervention on the world economy and to compare the effectiveness of sterilized and non-sterilized intervention operations. Some comparative statics exercises across states of the world will now be performed to analyze the impacts of the foreign exchange intervention and sterilization conducted by the home monetary authority. For simplicity, it is assumed that the foreign monetary authority does not undertake foreign exchange intervention to affect the exchange rates, Z * ¼ z * ¼ 0. By totally differentiating Eqs. (22V)– (24V), the effects of changes in B, B *, Bm , Bm *, Z and z on the equilibrium values of i, i *, and e can be derived. It is noted from the expressions of Sy and S *x in Eq. (13V) that the directions of the equilibrium effects may depend on the substitutability of the two consumption goods in

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households’ preferences. In the case of r ¼ 1, the two consumption goods have a unit elasticity of substitution, and the expenditure shares Sy and S *x are always equal to 1=2. However, in the case of r p 1, each household adjusts its expenditure shares of the two goods in response to the changes in the interest rates and the spot exchange rate. Given that Sy and S *x are non-linear in i, i * and e, the comparative statics results are complicated by the presence of the induced adjustments of Sy and Sx*. Hence, we simplify the analysis by proceeding in the following two steps. First, we examine the comparative statics results of the model in the case of r ¼ 1. By isolating the adjustments of Sy and Sx* , we can provide some insight into understanding of the effects of foreign exchange intervention. Second, based on the analytical results obtained from the case of r ¼ 1, we can conjecture how the home monetary authority’s foreign exchange intervention affects the world economy when r p 1; and some numerical examples will be presented to confirm our conjecture. 4.1. The model with r ¼ 1 By setting r ¼ 1 and Z * ¼ z* ¼ 0, Eqs. (22V) –(24V) can be rewritten as

 R n ¼ B  Bm þ Z R þ z þ ð1  nÞ 1 þ R; 2

n* ¼ B*  Bm *  ð1 þ R* Þ

ð22WÞ

 Z R* * þ ð1  n Þ 1 þ R *; e 2

ð23WÞ

1 1 Z þ ð1  nÞR ¼ eð1  n*ÞR*: 2 2

ð24WÞ

The results of the comparative statics exercise on Eqs. (22W) –(24W) are presented in Section A.2 of Appendix A. A summary of these results is presented in Table 1.

Table 1 Summary of the results in Section 4.1a Shocks

Dh* DB* DBm * Dh DB DB DBm DBm Dz DZ DZ ðZ ¼ 0Þ ðZ p 0Þ ðZ ¼ 0Þ ðZ p 0Þ ðZ p 0; dZ ¼ 0Þ ðz ¼ 0Þ ðDZ ¼ DzÞ

Effects D i 0 D i* 0 De 0 a

0 + +

0  

0 0 0

+ 0 

Assume that r ¼ 1 and Z * ¼ z* ¼ 0.

+  signZ 0  +

 sign Z +

+ sign Z 

+  +

+  ?

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197

4.1.1. The effects of fiscal policies Consider a larger realization of the volume of the home-currency-denominated bonds issued by the home fiscal authority. Since the home government finances its spending by issuing bonds, the supply of home-currency-denominated bonds increases, generating an excess demand for liquidity in the bond market. In order to clear the market, the interest rate i increases. The increase in the cost of financing causes the home firms to increase the home price of good x, Px , and the home importers to raise the home price of good y, Py. Given that r ¼ 1, the expenditure shares Sy and S *x are constant across states. If e and i * remain unchanged, an increase in Py will reduce the home shopper’s demand for good y, Cy , and the home importer’s demand for loans, eP*y Cy ¼ ð1  nÞ=ð2ð1 þ iÞÞ ; and an increase in Px will reduce the foreign shopper’s demand for good x, C *x, while having no effect on the foreign importer’s demand for loan, Px C *x =e ¼ ð1  n *Þ=ð2ð1 þ i *ÞÞ. Hence, in the foreign exchange market, the demand for foreign currency of the home importer drops, but the supply of foreign currency of the foreign importer remains unchanged. The spot exchange rate, e, falls to clear the market; and the home currency appreciates. It is noted that the decrease in e induces the home importer to increase his demand for good y, Cy , which may offset the initial decrease in Cy . As stated in Eqs. (22V) and (23V), in the absence of foreign exchange intervention, Z ¼ Z * ¼ 0, an increase in B causes ð1 þ iÞ to rise and e to fall by the same proportion, P *y Cy ¼ ð1  nÞ=ð2ð1 þ iÞeÞ remains unchanged, and the liquidity in the foreign-currency-denominated asset market is unaffected. Hence, the equilibrium value of i * does not change. Using a similar explanation, one can show that a smaller volume of bonds issued by the foreign fiscal authority, B * , will reduce both the interest rate on the foreign-currencydenominated assets, i *, and the spot exchange rate e. In addition, it will have no effect on the interest rate on the home-currency-denominated assets, i , if there is no foreign exchange intervention, Z ¼ Z * ¼ 0. 4.1.2. The effects of monetary policies Suppose that there is a larger realization of the volume of the home-currencydenominated bonds purchased by the home monetary authority using newly created home currency, Bm . For any given level of fiscal spending of the home government, B , an increase in Bm is an expansionary monetary policy of the home monetary authority because it injects newly created home currency into the home-currency-denominated asset market.28 As the demand for the home-currency-denominated bonds increases, the supply of liquidity in the market for these bonds increases, causing the interest rate i to fall. The reduction in the cost of financing facing the firm and importer of the home country leads to decreases in the home goods prices, Px and Py. If e and i * remain unchanged, the decreases in Px and Py imply that in the foreign exchange market, the home importer’s demand for foreign currency, P *y Cy, increases, while the foreign importer’s demand for home currency, Px C *x , remains unchanged. The excess demand for foreign currency causes the home

28 As shown in Eqs. (22W) – (24W), B and Bm enter the simultaneous equation system in a similar way so that the effects of an increase in Bm on i, i and e are identical to those of a decrease in B.

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currency to depreciates and e to rise. As shown in Eqs. (22V) and (23V), if there is no foreign exchange intervention, Z ¼ Z * ¼ 0, an increase in Bm raises e and reduces ð1 þ iÞ by the same proportion so that P *y Cy ¼ ð1  nÞ=ð2ð1 þ iÞeÞ does not change, and the equilibrium value of the interest rate on foreign-currency-denominated assets is not affected by a change in Bm. However, in the presence of foreign exchange intervention, Z p 0, the rise in e changes the home monetary authority’s demand for foreign-currency-denominated bonds, Z=e, leading to a change in the allocation of liquidity in the foreign-currencydenominated asset market. Consequently, e and ð1 þ iÞ do not offset each other completely, and there are changes in the equilibrium values of P *y Cy and i *. It is found that an increase in Bm causes i * to rise (fall) if Z is positive (negative). Similarly, we can conclude that if the foreign monetary authority conducts a contractionary monetary policy by purchasing a smaller volume of the foreign-currencydenominated bonds, B m *, the interest rate on the foreign-currency-denominated assets, i* , and the spot exchange rate, e, will increase. However, there will be no effect on the interest rate of the home-currency-denominated assets, i, if Z * ¼ 0. 4.1.3. The effects of non-sterilized foreign exchange intervention Consider a larger non-sterilized purchase of foreign currency by the home monetary authority, Z . Non-sterilized intervention consists of two transactions. First, the home monetary authority purchases the foreign currency using Z units of newly created home currency. As the supply of home currency in the foreign exchange market increases, the spot exchange rate, e, rises, and the home currency depreciates. Second, with the Z=e units of foreign currency acquired through the foreign exchange market, the home monetary authority purchases Z=e units of foreign-currency-denominated bonds. A higher demand for the foreign bonds implies a larger supply of liquidity to the market, and results in a fall in the interest rate i *. The adjustments of e and i * will induce a change in the allocation of liquidity in the home-currency-denominated asset market. If the interest rate i remains unchanged, the changes in e and i * will have no effects on the home importer’s demand for loan, eP *y Cy ¼ ð1  nÞ=ð2ð1 þ iÞÞ, while increasing the foreign demand for good x, C x*, and leading to an increase in the home firm’s demand for loan, W l. In response to the excess demand for liquidity in the home-currency-denominated asset market, the interest rate i rises. This result is in sharp contrast to the conventional view that a non-sterilized official sale of home currency in the foreign exchange market is equivalent to an expansionary monetary policy action of the home country. As discussed above, an expansionary monetary policy of the home country (an increase in Bm ) also causes the home currency to depreciate, but it reduces the equilibrium value of the interest rate i. The difference in the equilibrium effect on i of a non-sterilized sale of home currency in the foreign exchange market and that of an open market purchase of home-currencydenominated assets can be explained as follows. Both of these policy actions involve monetary injections to the economy. However, the injections are channeled through different markets so that the induced liquidity shocks occur in different markets. Given that different economic agents face different trading opportunities, how the monetary injections are channeled to the economy plays an important role in the determination of the effects of the policies.

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199

In the case of an expansionary monetary policy, the newly issued home currency is injected through the home-currency-denominated asset market. In order to eliminate the excess supply of liquidity in the market, the interest rate i falls to encourage the borrowers to absorb the extra liquidity. Hence, the borrowers of the home intermediary—the home firm and the home importer—can have direct access to the newly injected home currency through the home intermediary. As the home importer sells the home currency in the foreign exchange market, the foreign intermediary and the foreign importer can then have access to the newly injected home currency indirectly through currency trade. In contrast, in the case of a non-sterilized intervention, the monetary injection occurs through the foreign exchange market. When the spot exchange rate, e, rises to clear the market, the newly issued home currency is absorbed solely by the buyers of home currency. The increases in the quantities of home currency that the foreign intermediary and the foreign importer can obtain through currency trading have two opposing effects on the liquidity of the home-currency-denominated assets market. First, an increase in e lowers the cost of importing good x measured in terms of foreign currency and therefore increases the foreign demand for good x, C x*. Facing an increasing demand for its output, the home firm’s demand for loan increases, which increases the demand for liquidity in the market for home-currency-denominated assets. Second, as the foreign intermediary uses home currency to purchase homecurrency-denominated bonds, a fraction of the newly injected home currency is channeled to the home-currency-denominated assets market, which increases the supply of liquidity of the market. These two effects on the liquidity of the homecurrency-denominated asset market are in opposing directions. However, given a fixed supply of home-currency-denominated bonds, the magnitude of the second effect is constrained, and is shown to be dominated by the first effect. Hence, the non-sterilized intervention generates an excess demand for liquidity in the market for home-currencydenominated assets. To clear the market, the equilibrium level of i rises. Similarly, although the home monetary authority’s non-sterilized intervention operations are analogous to its open market operations, foreign-currency-denominated bonds rather than home-currency-denominated bonds are bought and sold. As the liquidity shocks induced by these two policies occur in different asset markets, they would have different effects on the interest rate on the foreign-currency-denominated assets, i *. 4.1.4. The effects of sterilization Consider a larger volume of sterilization conducted by the home monetary authority, z , for any given volume of foreign exchange intervention, Z . After the home monetary authority intervenes the foreign exchange market by selling Z units of newly issued home currency, it can sterilize the positive effect on the home money stock by selling z units of home-currency-denominated bonds to the market. This open market sale of home-currency-denominated bonds is a contractionary monetary policy of the home country. Using Eqs. (22W) –(24W), it is clear that the equilibrium effects of an increase in z on i, i * and e are identical to those of a decrease in Bm . By increasing the supply of home-currency-denominated bonds, the sterilization increases the demand for liquidity in the home-currency-denominated asset market, and results in a rise in the interest rate i. The rise in i causes the home goods prices to

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increase. In the foreign exchange market, although the increase in Px does not affect the foreign importer’s demand for home currency, Px C *x , the increase in Py results in a decrease in the home importer’s demand for foreign currency, P*y Cy. Hence, the home currency appreciates and e falls. With the presence of foreign exchange intervention conducted by the home monetary authority, Z > 0, the fall in e increases the home monetary authority’s demand for foreign-currency-denominated bonds, Z=e . To eliminate the excess demand for foreign-currency-denominated bonds, the equilibrium interest rate i* falls. 4.1.5. The effects of sterilized foreign exchange intervention Based on the discussions in Sections 4.1.3 and 4.1.4, we could now consider the impact of sterilized intervention conducted by the home monetary authority, Z ¼ z. A sterilized intervention operation involves two policy actions—intervention plus sterilization. As discussed above, a non-sterilized official sale of home currency by the home monetary authority results in increases in i and e and a decrease in i*; and sterilization that takes the form of an open market sale of home-currency-denominated bonds leads to an increase in i and decreases in i* and e. We can then conclude that the sterilized intervention conducted by the home monetary authority has a positive equilibrium effect on i but a negative equilibrium effect on i*. However, its equilibrium effect on the spot exchange rate, e, is ambiguous because the two policy actions affect e in opposing directions. It is obvious that it is the offsetting effect of sterilization on e that makes sterilized intervention less effective than non-sterilized intervention. Furthermore, if the offsetting effect of sterilization is strong enough to dominate the desirable effect of intervention, sterilized intervention operations aimed at decreasing (increasing) the value of the home currency will indeed lead the home currency to appreciate (depreciate). 4.2. The effects of intervention in the model with rp1 As discussed in Sections 4.1.3 and 4.1.5, in the case of r ¼ 1, both non-sterilized and sterilized intervention operations of the home monetary authority cause the interest rate i to rise and the interest rate i* to fall. Taking these results as a benchmark, we can now investigate how the changes in i and i* lead the shoppers to alter their expenditure shares, Sy and S *x, and then discuss how the adjustments of Sy and S *x will, in turn, induce further adjustments of i; i* and e. Eq. (13V) states that in response to an increase in i, the relative goods price faced by the foreign shopper, Px*=Py*, rises. In the case of r > 1 (0Vr < 1), the rise in Px*=Py* results in a decrease (an increase) in the expenditure share of good x in the foreign shopper’s budget, S *x. Therefore, the foreign importer’s demand for loan, Px C *x =e, decreases (increases), and generates a downward (an upward) force on i* . In the foreign exchange market, the decrease (increase) in the demand for home currency of the foreign importer, Px C *x , will induce a positive (negative) effect on the exchange rate, e. In addition, Eq. (13V) shows that in response to a decrease in i*, the relative goods price faced by the home shopper, Px =Py, rises, which causes the expenditure share of good y in the home shopper’s budget, Sy , to increase (decrease) in the case of r > 1 (0Vr < 1).

W.-M. Ho / Journal of International Economics 63 (2004) 179–208

201

Hence, the home importer’s demand for loan, ePy*Cy, increases (decreases), generating an upward (a downward) force on i. In the foreign exchange market, the increase (decrease) in the demand for foreign currency of the home importer, P*y Cy , will induce a positive (negative) effect on the exchange rate, e. Given that a non-sterilized official sale of home currency by the home monetary authority has a positive effect on the equilibrium value of e when r ¼ 1, and that the adjustments of Sy and Sx* strengthen (weaken) the positive effect on e when r > 1 (0 < r < 1), we could then conjecture that in the case of r p1, the equilibrium effect on e will also be positive. In the case of r > 1, it is obvious that the adjustments of Sy and S *x reinforce the upward force on e. In the case of 0 < r < 1, although both of the changes in Sy and S *x have offsetting effects on e , neither of them is large enough to have a determinant impact, and the equilibrium value of e is expected to rise. As the equilibrium effect on e of a sterilized official sale of home currency by the home monetary authority is ambiguous when r ¼ 1, the adjustments of Sy and S *x may have a dominant role in determining the equilibrium effect on e when r p 1. Given that the adjustments of Sy and S *x have an upward (a downward) force on e when r > 1 (0 < r < 1 ), it is expected that the equilibrium effect of the sterilized intervention operation on e tends to be positive (negative). To confirm our conjecture, the equilibrium values of the interest rates, i and i*, and the exchange rate, e, will be numerically calculated by using Eqs. (22V) –(24V). For simplicity, assume that there are only four possible states of the world, represented by sa and sbj, j ¼ o; NI; SI. The only differences among these four states are with regard to the realizations of the home-country fiscal policy variable, B , and intervention policy variables, Z and z. In state a (bj), the fiscal spending of the home government is Ba (Bb ). Suppose that Ba < Bb . A switch from Ba to Bb will cause an appreciation of the home currency. The home monetary authority does not intervene the foreign exchange market in states a and bo, while it uses non-sterilized intervention in state bNI and sterilized intervention in state bSI.29 As shown by the results of the numerical examples presented in Table 2, our conjecture of the effects on e of intervention in the case of r p1 is confirmed. In all cases, an increase in B results in an appreciation of the home currency and a fall in e; and an official nonsterilized sale of home currency by the home monetary authority is effective in keeping the home currency from appreciating. That is, ebo < ebNI < ea, b r. In the cases of r > 1, an official sterilized sale of home currency by the home monetary authority can also have a positive effect on e , even though the effect is weaker than that of non-sterilized intervention, ebo < ebSI < ebNI < ea . However, in the cases of 0 < r < 1 , sterilized intervention not only fails to accomplish the policy goal but also reinforces the appreciation of the home currency, ebSI < ebo < ebNI < ea . The result that sterilized intervention may move the exchange rate in the wrong direction is consistent with the evidence of the puzzling ‘perverse’ response of exchange rates documented in the empirical literature on intervention (for example,

29 It should be mentioned that the aim of the numerical exercises in this paper is to illustrate the theoretical properties of the model rather than to match observed data.

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Table 2 The computed equilibrium of the numerical exercise in Section 4.2a

ia ibNI ibSI ibo i*a i*bNI i*bSI i*bo ea ebNI ebSI ebo

r ¼ 0:2

r ¼ 0:5

r ¼ 0:8

r¼1

r ¼ 1:2

r ¼ 1:5

r¼2

0.0319 0.0515 0.0581 0.0446 0.0436

0.0303 0.0529 0.0607 0.0454 0.0455

0.0295 0.0537 0.0621 0.0457 0.0466

0.0291 0.0540 0.0628 0.0459 0.0472

0.0288 0.0543 0.0632 0.0460 0.0476

0.0285 0.0546 0.0638 0.0460 0.0481

0.0282 0.0550 0.0643 0.0460 0.0488

0.0336 0.0362 0.0494 1.0546

0.0320 0.0332 0.0483 1.0207

0.0312 0.0315 0.0475 1.0086

0.0308 0.0306 0.0472 1.0038

0.0304 0.0300 0.0468 1.0003

0.0301 0.0292 0.0464 0.9965

0.0297 0.0282 0.0459 0.9923

1.0122 0.9896 1.0088

0.9972 0.9826 0.9914

0.9957 0.9856 0.9884

0.9958 0.9878 0.9878

0.9961 0.9897 0.9875

0.9967 0.9921 0.9874

0.9976 0.9952 0.9875

a b ¼ b* ¼ 0:96 . There are four possible states of the world, a , bo , bni , and bsi . Prob(s ¼ aÞ ¼ 1=2 , Prob(s ¼ bjÞ ¼ 1=6, j ¼ o; ni; si, hi ¼ h*i ¼ 1, B*i ¼ 0:2, i ¼ a; bo; bni; bsi, Ba ¼ 0:2, Bbj ¼ Bb ¼ 0:21, j ¼ o; ni; si, Za ¼ za ¼ 0, Zbo ¼ zbo ¼ 0, Zbni ¼ 0:005, zbni ¼ 0, and Zbsi ¼ zbsi ¼ 0:005:

Kaminsky and Lewis, 1996). Hence, this paper offers a theoretical explanation of the empirical puzzle by studying the liquidity effects generated by foreign exchange intervention.

5. Conclusion This paper presents a two-country, two-currency, general equilibrium model to study the effectiveness of foreign exchange intervention by examining the liquidity effects generated by intervention. In the model, the influence of intervention on the exchange rate is through neither the portfolio-balance channel nor the signaling channel. By assuming the existence of a forward exchange market, the foreign exchange risk of holding an asset denominated in the currency of another country can be eliminated completely. As the (covered) effective rates of return on the domestic and foreign assets are equalized, economic agents are completely indifferent as to whether they hold the domestic or foreign assets. In addition, by assuming that intervention policy is independent of both the current and future monetary policy variables, intervention does not provide a signal of future monetary policy. Hence, neither the portfolio-balance channel nor the signaling channel are present in this model. In contrast, this paper emphasizes the role of international financial markets in allocating liquidity. Both sterilized and non-sterilized intervention operations have significant impacts on the allocation of liquidity in international financial markets. Whether intervention is successful in moving the exchange rate in the desirable direction depends upon the degree of sterilization of intervention and the intratemporal elasticity of substitution of consumption goods.

W.-M. Ho / Journal of International Economics 63 (2004) 179–208

203

As intervention not only affects asset prices but also influences real activity, it is obvious that the economic welfare of each country will be affected, implying the incentives for monetary authorities to behave strategically when conducting foreign exchange intervention. A complete investigation of the strategic interaction of the monetary authorities in a general equilibrium framework would be an interesting topic for future research.

Acknowledgements I wish to thank Mick Devereux, an anonymous referee, and conference and seminar participants at the Bank of Canada, the University of Toronto, the Canadian Economics Association Meeting, and the Midwest Macroeconomics Conference for helpful comments and suggestions. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.

Appendix A A.1 . Solving for the equilibrium The first-order conditions for the optimization problem [Eq. (P1)] Let k1 , k2 , k3 and k4 be the multipliers associated with the cash-in-advance constraints, Eqs. (3V), and (5V)(7V), respectively. These multipliers are positive as the cash-in-advance constraints are assumed to be binding.

R

R

k1 GðsÞds ¼ k2 GðsÞds; uy ux ¼ ¼ k1 þ bVmh V ; Cx ; Cy : Px Py h : v ¼ bVmh V W ; n :

bh : k2 þ bVmh V i; h i bf : k2 e ¼ bVmh V e f ð1 þ i* Þ  e ; Lx : k 2 ¼ k 3 ;

 1 Ly : k2 þ bVmh V ¼ k4 þ bVmf V ; e l : k3 W ¼ bVmh V ½Px h  W ;   * P ¼ bV P ; IM : k þ bV y

4

mf V

y

mh V y

where uj u

AuðCx ; Cy ; G; hÞ ; ACj

j ¼ x; y;

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W.-M. Ho / Journal of International Economics 63 (2004) 179–208

Vmh u

Vmf u

Z Z AV ðmh ; mf ; mh* ; mf* ; s˜ Þ ux ¼ ½k1 þ bVmh V GðsÞds ¼ GðsÞds; Amh Px AV ðmh ; mf ; mh* ; mf* ; s˜ Þ Amf

¼

Z



 k4 þ bVmf V GðsÞds

Solving these first-order conditions, the optimal levels of the household’s deposit, the shopper’s consumption demand, the worker’s labor supply, and the firm’s labor demand can be characterized by Eqs. (A.1)– (A.4), respectively.

E



 ux uVx ¼ b E½1 þ iE ; Px P Vx

Cj ¼

ðmh  nÞPjr ½ Px1r þ Py1r 

Sj ¼

;

ðA:1Þ Pj1r Pj Cj ¼ 1r ; mh  n ½ Px þ Py1r 

j ¼ x; y;

ðA:2Þ

vðmh  nÞ ; b

ðA:3Þ

W ð1 þ iÞ ¼ hPx ;

ðA:4Þ

W ¼

Eq. (A.1) states that the home household chooses n such that the expected marginal utility loss of reducing the shopper’s cash balance by one unit is equal to the discounted expected future marginal utility gain from increasing the intermediary’s cash balance by one unit. That is, the home currency is expected to be equally valuable in the goods market and in the financial market. In equilibrium, the arbitrage conditions facing the home intermediary and the home importers are respectively given by, e ð1 þ iÞ ¼ e f ð1 þ i* Þ;

Px* ¼

Px ð1 þ i* Þ; Py ¼ Py* e ð1 þ iÞ: e

ðA:5Þ

ðA:6Þ

In addition, from the equilibrium conditions for the goods markets, we get l¼

Cx þ Cx* ; h

l* ¼

Cy þ Cy* : h*

The derivation of the simultaneous equation system [Eqs. (22V) –(24V)]

ðA:7Þ

W.-M. Ho / Journal of International Economics 63 (2004) 179–208

205

Using mh ¼ mf* ¼ 1, Eqs. (A.2)– (A.4) and (A.6), and the analogous equations of the foreign household, we can get Eq. (13V). Then, from Eqs. (A.2), (A.4), (A.6), (A.7) and (24), we have " # hPx Cx þ Cx* * Wl þ Px Cx ¼ þ Px Cx* 1þi h ¼ Px Cx R þ Px Cx* ð1 þ RÞ ¼ Sx ð1  nÞR þ ðePy* Cy þ Z  eZ * Þð1 þ RÞ ¼ Sx ð1  nÞR þ ½Sy ð1  nÞR þ Z  eZ * ð1 þ RÞ: Similarly, for the foreign country, we can get W * l * þ P* C y

y

¼

" # hPy* Cy þ Cy* þ Py* Cy * 1 þ i* h

¼ Py* Cy* R* þ Py* Cy ð1 þ R* Þ 1 ¼ Sy* ð1  n* ÞR* þ ðPx Cx*  Z þ eZ * Þð1 þ R*Þ e

 Z * * * * * * ¼ Sy ð1  n*ÞR þ Sx ð1  n ÞR  þ Z ð1 þ R* Þ: e Substituting these results into Eqs. (22) and (23) yields Eqs. (22V) and (23V). In addition, we can use Eqs. (A.2) and (A.6) to get ePy* Cy ¼ Sy ð1  nÞR and Px Cx* ¼ eSx* ð1  n* ÞR* ; and rewrite Eq. (24) as Eq. (24V). The simultaneous equation system, Eqs. (22V)– (24V), is in three unknowns, R; R* ; and e, which are functions of s, n and n* only. After solving the simultaneous equation system for R; R* ; and e, the equilibrium values of n and n* can be derived by solving Eqs. (A.1V) and (A.1W) simultaneously. h i 1 E 1 þ iðn; n* sÞ ¼ ; b

ðA:1VÞ

h i 1 E 1 þ i* ðn; n* sÞ ¼ : b*

ðA:1WÞ

Once the equilibrium values of n; n* ; R; R* ; and e have been obtained, the equilibrium values of all other variables of interest can be derived. A.2 . The results of the comparative statics exercises in Sections 4.1 When r ¼ 1, we have Sj ¼ Sj* ¼ 1=2; j ¼ x; y: Eqs. (22V) –(24V) can be rewritten as Eqs. (22W) –(24W). Taking n and n* as given, totally differentiating Eqs. (22W)– (24W) yields

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dB  dBm þ ZR

 dR dZ þ þ dz þ ð1  nÞ ½1 þ R dR ¼ 0; R Z

" ! # Z R* dR* dZ de * m* *  dB  dB  ð1 þ R Þ þ e Z e 1 þ R* R* h i þð1  n* Þ 1 þ R* dR* ¼ 0; " #  1 dR 1 de dR* * * ð1  nÞR ¼ e ð1  n Þ R þ : dZ þ 2 R 2 e R*

ð22aÞ

ð23aÞ

From Eqs. (22a)(24a), we can get dR ¼ 

dR* R*

dB  dBm þ RdZ þ dz ; ð1  nÞ ð1 þ RÞ þ Z

h i e dB*  dBm * ¼

ð1  nÞRð1 þ R* Þ þ Z  dZ dR  ; R ½ð1  nÞR þ 2 Z½ð1  nÞRð1 þ R* Þ þ Z Z Zð1  nÞRð1 þ R* Þ

þ

and



 de 2 1 dR dR* ¼ ð1  nÞR dZ þ  : e 2 R e ð1  n* Þ R* R* Hence, we have di di di ¼ m ¼ dB dB dz di dZ

j

dz¼0

> 0;

j

di dZ

dZ¼0

j

> 0;

dZ¼dz

di di ¼ m ¼ 0; * * dB dB

> 0;

di* di* 1 þ i* de 1 þ i* de ¼ m ¼ ¼ > 0; dB* dB * e dB* e dBm *

ð24aÞ

W.-M. Ho / Journal of International Economics 63 (2004) 179–208

207

 di* di* di* 1 ð1  nÞRð1 þ R*Þ Z ¼ m ¼ ; ¼ dB dB dz dZ¼0 D 2R* e 

de de de  1 ð1  nÞR ¼  m ¼ dZ¼0 ¼ ½eð1  n*Þð1 þ R*Þ  ZR* < 0: dB dB dz D 2

j

di* dZ

j

dz¼0



ð1 þ R*ÞR2 1n 1 < 0; ½ð1  nÞð1 þ RÞ þ 2Z ¼ 2 e DR*



 R*R 1  n eð1  n*Þ ½eð1  n*Þð1 þ R*Þ  2Z þ Z ¼ > 0; D 2 2

de dZ

j

dz¼0

di* dZ

j

dZ¼dz

¼

di* dZ

j

dz¼0

þ

di* dz

j

dZ¼0



ð1 þ R*ÞR 1n 1 ½ð1  nÞRð1 þ RÞ þ ð1 þ 2RÞZ < 0; ¼ DR* 2 e de dZ

j

dZ¼dz

de ¼ dZ

j

de þ dz¼0 dz

j

dZ¼0

 R*R eð1  n*Þ 1  n  ¼ Z; D 2 2

where ð1  n*Þ e R* 2



 ð1  n*Þ R* Z m*  n*  B* þ B þ R* < 0: 2 e

D ¼ R½ð1  nÞð1 þ RÞ þ Z 

After we have derived the effects of changes in B, B*, Bm, Bm *, Z and z on the equilibrium values of other variables of interest can be derived.

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