A portfolio approach to international capital flows

A portfolio approach to international capital flows

Journalof IntesnationalEconomics 3 (1973) 135-160. 0 North-HollandPublishingCompany A PORTFOLIO APPROACH TO INTERNATIONAL CAPITAL FLOWS’ Polly Reyno...

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Journalof IntesnationalEconomics 3 (1973) 135-160. 0 North-HollandPublishingCompany


Polly Reynolds ALLEN hinmton Uniwsity

1. Introduction

The traditional view of international flows of portfolio capital assumes that capital flows are a function of relative interest rate levels.’ Portfolio theory postulates that demands for assets are demands for stocks rather than flows and that these stock demands depend not only on the relative rates of return but also on the size of the total portfolio. (See Markowitz, 1959, and Tobin, 1965). The implications for international capital flows of this kind of portfolio demand have been recognized in recent empirical work, where it is assumed that capital flows are a function of changes in, rather than levels of, interest rates.l But little theoretical work has been done to explain international capital flows in terms of portfolio adjustment.” That Is the purpose of this paper. A two-country stationary mode1 is developed in which the demands for financial assets - bonds and currency -- are.assumed to be demands for stocks rather than flows, dependent not only on income and the interest rate, but also on wealth. There is,perfect capital mobility and exchange rates are fixed. Comparisons are drawn between this portfolio* 1 wish to express my appreciationfor numeroushelpful comments on earlierdrafts of this paper to my colleagues, Stanley Black, WiHiamBaumol, William Branson, Peter Kenen and WallaceOates. * The traditional type of model is discussed and summarizedin Mundell(l968, ch. 18) and Whitman(1970). 2 The recent empiricalwork is summarizedin Branson(1970). 3 Meade (195 1, p. 103) briefly describessuch a process. Portfolio adjustment models of the same general approachas in this paper, but for small open economies, have been developed by Mcginnon and Oates (19663, McKinnon(1969), and Whitman(1970). The fact that these are one-country models for a small country limits their generality. An alternative approach to portfolio adjustmentand capital flows is that of Floyd (1969).


P.R. Akn, In twna tbnal capital jlo ws

balance model and a prototype of the traditional model, in which there is assumed to be a demand for money that does not depend on wealth and a flow demand for foreign bonds. One purpose of the paper is to show the relationships between a short-run market equilibrium and a long-run stationary portfolio equilibrium. The analysis is discrete and closely follows the formulation of Bushaw and Clower (1957)in its comparison of stocks and flows. Shortrun market equilibrium is made to obtain by assuming that markets adjust in each period to assure zero excess market demand for all goods and assets. This market equilibrium is consistent with changing levels of :;tocks in each country and, therefore, with changing levels of outputs, interest rate and the balance of payments. Long-run portfolio equiEbrium, by contrast, is reached only gradually, by moving through a sequence of market equilibria. It requires constant values of all variables and implies that persons are satisfied with existing, unchanging holdings of assets.4 Secondly, the paper derives the relationships that exist in portfolio equilibrium between the components of the balance of payments and the level and type of government budget financing. Portfolio equilibrium requires that a positive issuance of an asset by one government be offset by an equivalent withdrawal of the same asset by the other government, which requirement constrains the two countries’ fiscal policies5 In portfolio equilibrium the trade deficit equals the government budget deficit, the government issuance of new bonds equals the capital inflow, and government issu,ance of new currency equals the balance of payments deficit. Finally, the paper includes a comparative static analysis of the effects of two types of monetary disiurbance - an increase in one country in liquidity preference and a temporary increase in the rate of open. mIarket purchases in one country. For either disturbance there is no &g-run effect on the balance of payments. The effect on the distributil(3n of assets between countries depends on which country’s trade balance rises during the adjustment period. The country for which the trade balance temporarily improves gains both money and bonds from the other country. 4 Hereafter, market equiiibrium refers to a short-run flow equilibrium, in which markets are cleared of any fIows of goods or as!!;ets that are thrown upon the market in a given period. Portfolio equilibrium refers to ;Alongs-run stock equilibrium, in which the stock demand for each asset equals its suppty at the beginning of the period. ’ Under fixed exchange rates both currencies are regarded for this purpose as a single asset.

P.R. Allen, International cqhl



The major portion of the paper examines a Keynesian model in which there are constant prices and flexible output. These assumptions determine the specific conditions of some of the results of the exogenous disturbances. The model is then discussed in terms of classical assumptions of fixed output and flexible prices. A comparison of the results makes it possible to draw more general conclusions, which would apply to a model where adjustment in the goods markets falls somewhere between the classical and Keynesian extremes. Sect. 2 outlines hhe model, 3 discusses the relationship between the government budget and the balance of payments, 4 examines some implications of the traditional model, 5 works out the effects of the disturbances, and 6 examines the results for a classical model and other extensions of the model.

2. The model The model depicts a world of two countries, A and B, in which there are two consumption goods, each of which is produced by only one country. Since the major concern of the paper is with financial capital flows,the real-goods sector has been reduced to the simplest possible terms. It is assumed that there are no capital goods and thus no investment. This eliminates the necessity of considering the relationship between the capital stock and production of goods. In portfolio equilibrium private saving is zero, but, during the adjustment to equilibrium, saving (positive or negative) may occur, taking the form of changes in stock of financial assets. There is a single type of bond in the model. It is issued by private persons or the government of either country and is traded freely between countries at a single world rate of interest. The assumption of a single type of bond is made for simplicity and is not strictly required for the general conclusions of the model. The general conclusions, however, are based on the assumption of a high degree of international mobjlity of portfolio capital. A country’s aggregate stock demand for, or supply of, bonds refers to net ownership of ‘outside’ bonds, issued either by the government or foreigners. ‘Inside’ bonds, issued and held domestically by private persons, are cancelled by liabilities and do not appear in the aggregate bond stock of a country. While the world supply of bonds is assumed to be positive, the stock held by either one of the countries may be negative. The value of a bond is assume-d to


P.R. Allen, International capital 310ws

equal its face value and to be unaffected by the LGGof interest. This is an approximation which, to be strictly correct, would imply that bonds are of one-period maturity or always pay a coupon equal to the current market rate of interest. While it is assumed that interest is paid on bond holdings, interest payments are not explicitly considered here. For reasons of simplicity the standard assumption is made that such payments are sufficiently small to be ignored. Were they to be included, the definitions of disposable income, the government budget deficit, and the balance of payments surplus would be altered. Each country issues its own currency, and all money is outside money, issued by governments. Persons are assumed to demand only domestic, and not foreign, currency, eliminating private liquid capital flows between ‘countries. Country A is assumed to support the price of foreign exchange at unity by providing a perfectly elastic supply of foreign exchange (domestic currency) when it is demanded in exchange for domestic currency (foreign exchange). An implicit assumption of the model is that the government of A has sufficient foreign exchange reserves to carry out such a policy. It makes no difference for the results which government supports the exchange rate. The monetary value of the government budget deficit or surplus and the means of financing the budget are policy decisions of the govemment. Monetary policy consists of setting the rate of issuance of new money; debt policy, of setting the rate of issuance of new bonds. To the extent that the issuance of money is matched by government purchase of bonds, it occursthrough open market operations. Issuance of money in excess of bond purchases implies a government budget deficit, in the form of either government spending or transfer payments. A monetary policy of ongoing issuance or withdrawal of money results, in portfolio equilibrium, in the government sterilizing reserve flows, However, this occurs, not from a policy of accommodating monetary policy to the balance of payments, but rather from adjustment of the balance of payments to an independently determined rate of change of the money supplies. For the ith country, i = A, 8, in time period t, output is y’,, sold at price $ Private demand for all goods is &‘i,of which 44; is demand for the imported good. Government demand for goods is G: and taxes are denoted by 7$ Stock demand for bonds is Z”, with the world rate of interest, rt. The stock demand for domestic currency is Li. Stocks of bonds ldnd money existing at the beginning of the period are z:_~ and

PRAllen, Interntiriund capitalflows


$_r. Independent policy-determined issuances of bonds and money are represented by A$ and A$, reflecting the government’s debt and monetary policies. With the exception of real output, all quantities are given in monetary, or nominal, terms. When the government of A, in order to maintain the exchange rate, intervenes in the foreign exchange market by purchasing B’s currency with its own currency, thus increasing the privately-held stock of A’s currency and decreasing, by an equivalent amount, that of B’s currency, such intervention constitutes a balance of payments surplus for A, denoted by R,. On the other hand, when the intervention consists of A’s selling its reserves of B’s currency in exchange for its own currency, thus decreasing the privately-held stock of its own currency and increasing, by an equivalent amount, that of B’s currency, this constitutes a balance of payments deficit for A; a deficit is represented by a negative value of R,. These changes in the money supplies resulting from A’s intervention in the foreign exchange market occur in addition to the independent policy-determined issuances of currencies and do not influence the policy-determined issuances. The components of the balance of payments are the trade balance, RT, and the net capital flow, Rf .6 A country’s excess stock demand for bonds or currency is the difference between the stock demand for the asset and the stock .supply, Z$ - 2; 1 or Lf - v: 1, respectively. The country’s ‘investment’ demand for &&set, which% the demand for additional holdings of the asset, is a positive function of its excess stock demand. It is assumed here that the investment demand for an asset is some positive fraction, k’, of the excess stock demand. This fraction, the investment coefficient, is ’ assumed to be equal to or less than unity and to be the same for bond and currency demands in each country. Thus, the investment demands for bonds and currency in the ith country are k’[Z; - z:_r ] and k’[L; - v;_J .’ ’ The balance of payments is always expressed from the point of view of country A. For simplicity, whenever a statement refers to a value that can be either a surplus or a deficit, the following terminology will be used: the balance of payments refers to a balance of payments sur lus or deficit, Rt S 0; the trade balance refers to either a trade surplus or a trade deficit, RtIp2~0; and the net capital flow refers to a net capital inflow or outflow, Rf z 0. Similarly, the $vemment budget refers to a budget surplus or deficit. Strictly speaking, if the investment coefficient is less than unity, this proportional invertment function implies an infinite adjustment process, with the model never quite reaching equilibrium. With such an investment demand the stock of an asset is a function of present and past desired stocks, weighted by geometrically declining weights. (Continue on next page)

P.R, Allen, In ternatianalcapitalflows


Table 1 World excess market demands. B’s net market demand

#s net market demand


good A good B bonds

currencyA currency B

There may also be a flow supply (positive or negative) of each asset from the government, consisting of the independent policy-determined issuance of the asset, A$ or A$, plus, in the case of currencies, the endogenous flow supply from government A as a result of supporting the exchange rate. In each country the net market demand for an asset is the difference between the investment demand and the flow supply from its government. The net market demand for a good is simply private plus govemment consumption demands minus output. The world excess market demand foi each good or asset is the sum of the net market demands of the two countries. Market equilibrium guarantees zero world excess market demands, but does not guarantee that net market demands for goods and assets within a particular country will be zero. The five world excess market demands are shown in table 1, divided into net market demands for each country. The budget constraint for each country requires that the sum of the country’s net market demands must equal zero. ’ (continued from previous page) For example a0

v;=c [ki(l -ks,” .


Lt._,] + c,


where c is a constant representing new flow supplies. A failure of the model to reach equilibrium presents a problem in the discussion of comparative statics. This problem is scGed by assuming a finite adjustment process, such that

vi= 5 [w(n)Lt_,J + ..



where ?)t< -, cz!_o [w (n)] = I, and w(n) = ki (1 - ki)” for n < tn. Since the oroportional inir vestmen: function provides a close approximation of this finite adjustment process and makes no difference to the comparative static rest&s, it is retained in the text for simplicity.

P.R. Allen, International capital flows


The demand functions for goods and money in the ith country are as follows: > 0

E; =E’[y,d’,q]




G; = gip; ,

. (4)


where p/z+:





Pt=PAIPB t* tr

fixed level of prices,


disposable income,


terms of trade,



vreafth or total portfolio.


Private consumption demand for goods, eq. (2), is assumed to be positively related to disposable income and negatively related to the rate of interest and to be homogeneous of degree one in disposable income. Demand for imports, eq. (3), equals some portion of disposabie * In the Keynesian model, since neither the prices of goods nor the exchange rate change, the effect of the terms of trade on the marginal propensities to import is not a necessary piece of information. It is, however, necessary for the later extension to a classiczalmodel and makes the model more complete. Negatively sloped demand curves for imports require that

A > -mA/P mp


rn; < mBlp.


P.R. Allen, In ternatkmal capital flows

income, that portion depending on the relative prices of the IWO goods; the marginal propensity to import is assumed to be smaller than the marginal propensity to consume all goods. Government demand for goods, eq. (4), is a policy decision determined in real terms, in units of domestic goods. The demand for a stock of money, eq. (S), is always positive, is positively related to disposable income and to wealth and negatively related to the interest rate, and is homogene us of degree one in income and wealth; a shift parameter, indicating the degree of preference for money over bonds, is indicated by ai. The government deficit must be financed by the issuance of either new money or new bonds, so that

Government policy decisions affecting the budget include setting the real level of government spending, the nominal value of the budget deficit, and the means of financing the budget. These having been independently determined, eq. (10) defines the necessary level of taxes, for any given price level. Since government spending is determined in real terms and the total budget in nominal terms, an increase in the price level would raise nominal tsxes, but less than proportionately. The assumption that the governments independently determine the rates of issuance of bonds and money allows us to focus attention on the impact of monetary and debt policies. It is assumed that government demand for goods and the rates of issuance of bonds and money are constant, except for the disturbance discussed in sect. 5. A requirement of portfolio equilibrium in period t is that ongoing debt and monetary policies of the two governments exactly offset one another, such that Ai$ =-AP,a =AvA,

(1.1) (12)

for all n > k, assuming that t - k is a sufficient time for adjustment. Unless this ‘offsetting’ requirement is met, there exist no equilibrium values of the stocks of assets and the economy is continually adjusting to a moving target. Since the requirement is highly restrictive, a continually adjusting economy is probably more likely than one that

P.R. Allen, Intern&ma1 capitalflows


settles into a long-run portfolio equilibrium. However, in the subsequent comparative static analysis of long-run portfolio equilibria, it is assumed that eqs. ( J 1) and ( 12) are fulfilled. Since the net market demands for goods and currencies have been specified, the net market demand for bonds is defined by the budget constraint, eq. (1). Given our assumption that the investment demand for bonds is a fraction, kl, of the excess stock demand for bonds, (2” - & ), the demand for a stock of bonds can be derived by substitution of eqs. (7), (9), and ( 10j into ( 1),





Each country’s demand for a stock of bonds is seen to be positively related to the interest rate and to wealth and to be homogeneous of degree one in disposable income and weaIth. This is parallel to the assumptionsabout de-mands for money and constitutes a consistent portfolio approach to the demands for assets. The wealth effects on the demands for assets are the crux of the portfolio adjustment process upon which this paper is focused. The demands for both assets depend, not only upon the rates of return, but also upon the total size of the portfolio, or wealth, prevailing at the beginning of the period. A unitary increase in a country’s stock of either asset must produce an increase in net market demands for all goods and assets equal to the investment coefficient. Since there are; no wealth effects in the demands for goods, these wealth effects fall solely on the net market demands for financial assets (through the wealth effects on the stock demands for assets): It is assumed that an increase in the stock of either asset in a country will prodllce some increase in its stock demand for both assets, stimulating a readjustment in the country’s portfoiio. Market equilibrium consists of zero excess market demand for each good and asset and is achieved in each period by the adjustment of


P.R. Allen, International capital flows

outputs, the interest rate, and the balance of payments, $, $, rt, and R,. According to Walras’ law, zero excess demand in IF-~1 markets guarantees zero excess demand in the Nth, so any four of the five excess demands may be chosen to express market equilibrium. Here market equilibrium is expressed by zero excess demands for goods and currencies.

Ep;,:-G$ * -y;P;

+M; -M; = 0,


= 0, Ef+G,B--u,RP;+M; -j-f;


k* {Lk -Vt&)-Ai+Rt=O,



{LF -&)-Aij;+Rt=O.


Adjustment to portfolio equilibrium is accomplished through gradual changes in the holdings of assets, with markets adjusting immediately after each incremental change in stocks. Changes in a country’s stock -of an asset from one period to the next occur whenever there is a nonzero flow supply of the asset to the country. These flow supplies consist, firstly, of new issuances determined by government monetary and d&t policies, A$ and A#, and, secondly, of endogenous changes resulting from exchange with the other country - that is, net capital outflows, which produce an increase in a country’s stock of bonds, and a balance of payments surplus, which produces an increase in the money stock. The net capital inflow to country A, denoted as RF, equals A’s net market supply of bonds; alternatively, at the same time RF equals B’s net market demand for bonds and denotes a capital outflow from country B. The equality between A’s net market supply and B’s net market demand is guaranteed by market equilibrium.

The stock of an asset held by a country at the beginning of any period t equals the initial stock plus the sum of all flow supplies occurring since the initial period. t-l

$1 =v$+ c n=O

[AF;+R,] ,


P.R. Allen, international capital flows t-l


*+x = v()




pt=O t-1

A G-











n=O t-l


z; + c



[AZ; +R,K] .



To derive a long-run equilibrium solution of the model eqs. (19) and (20) should be first differenced and the results substituted into eqs. (16) and (IQ, respectively. A Vt


A 5




+R, = kAiLtA -vt+l},



(23’) (24’)

The equilibrium values of the variables are found by setting these first differences equal to zero, At* + R, = k* {Lt - vt ) = 0



and by summing (19) with (20) and (21) with (22), *

l-f +v,B=r,


where k

P= v;+v;+c




The zero first differences for A’s assets, (23) and (24), guarantee constant- stocks of assets in both countries, given fulfillment of the ‘offsetting’ requirement, (11) and (12); the combinations of the zero first differences with (16) and (18) show that constant stocks of assets . imply zero investment demands as well as zero flow supplies.

P.R. Allen, International capital flows


Given the definitional equations, the model c&nbe summarized by equations (14) through (17), the market equilibrium conditions, and (23) through (26), the additional conditions for long-run portfolio equilibrium. These eight equations can be solved for the eight long-run variables-y:, yf,r,, R,, $, “,B,qf.,and&9 3. The balance of payments and the government budget The balance of payments surplus in country A equals its trade surplus plus its net capital inflow, any of which may be positive or negative. In terms of the demands for goods and assets, the trade balance equals B’s demand for imports minus A’s demand for imports,

.RT=Mf'-Mp ;


the net capital inflow equals A’s net market supply of bonds; and the balance of payments surplus equals A’s investment demand for money minus the independent now supply. Combinations of eqs. (1 ), (14), (16), ( 18), and (30) yield these relationships, R, =R,T+R,K


kA {[P -- v&





They could alternatively be expressed in terms of B’s demands for bonds and’money. 9 Long-run portfolio equilibrium in any model requires that for each good or asset: (a) market excess demand equals zero; (b) flow demand (consumption) minus flow supply equals zero; (c) excess stock demand equals zero. If arry two are met, the third Js guaranteed, see Bushaw and Glower (1957). If one is also concerned about the distribution of assets, such as between countries in a two-country model, equilibrium requires zero excess stock demand in each cot .ntry. Requirement (c) is replaced by: (c’) excess stock demand equals zero in each country; (c”) the sum of all countries’ stocks equals the world stock. Fulftient of (c’) and {c”) plus (a) or (b) guarantees the remaining requirement. Given the constraint of a constant world stock of an asset, if requirement (a) or (b) is met, then zero excess stock demand in n-l countries guarantees zero excess stock demand in the nth. The stock of the asset in the nth country is defined by the .-Ad stock minus the stocks held by the other n-l countries. In our soiution of the model, eqs. (14) through (17) fulfill requirement (a); eqs. (23) and (24) fulfii I(c); and (25) and (26) fulfti (c”).

P.R. Allen, International capital flows


A nonzero balance of payments is sometimes referred to as balanceof-payments disequilibrium. Such an imbalance is a disequi.librium only as it is so defined by the government. Private demands are met in the markets; if they were not, outputs or prices would adjust, The exchange rate does not change precisely because the difference between the investment demand for money and the independent policy-determined flow supply is met by a perfectly elastic, endogenous flow supply produced by the government’s support of the exchange rate. The imbalance may or may not be consistent with portfolio equilibrium. But because these endogenous flow supplies of currencies are frequently inconsistent with the government’s desired levels of reserves, the imbalance of payments is itself defined as a disequilibrium. In portfolio equilibrium, where excess stock demands for assets equal zero, A’s balance of payments surplus equals her trade surplus plus her new issuance of bonds; it also equals her negative new issuance of money. Setting the excess stock demands in (3 1) equal to zero,

The long-run size and composition of the balance of payments are determined by the government’s monetary and debt policies. A country’s trade surplus (deficit) in portfolio equilibrium equals its government budget surplus (deficit). Combining eqs. (lo), (29) and (31),

(32) Whenever a government runs a budget deficit, it issues new flow supplies of some financial asset, creating additional disposable income. In portfolio equilibrium private saving is zero. People do not wish to increase their portfolios, so they spend this new disposable income for consumption goods, creating a trade deficit. To the extent that the government issues bonds to finance its budget deficit, the trade deficit is financed by loans from the other country, a capital inflow; to the extent that the; government issues new money, payment for the goods comes from the country’s reserves, creating a deficit in the balance of payments. Open market purchases or sales do not affect the size of disposable income, but do change its composition. In portfolio equilibrium persons do not wish to adjust the composition of their portfolios, so they


P.R. Allen, International



offset open market purchases (sales) by buying (selling) bonds from (to) foreigners, creating a balance of payments deficit (surplus), solely on capital account. 4. The traditional model The traditional approach to models of international capital flows differs in two basic ways from the portfolio-balance model developed here.” Firstly, the effects of wealth on demands for goods and assets are seldom explicitly considered. Usually, flow demands for goods and a stock demand for money are specified, and both are assumed to be independent of wealth. Bond demand of the home country is seldom explicitly examined. Secondly, in one-country models, the foreign demand for the home country’s bonds is assumed to be a flow demand dependent on the interest rate. Presumably, this would imply a flow demand in the home country for foreign bonds. In any model, for every asset for which there is a stock demand and supply, a unitary change in the country’s stock of that asset mutt produce a wealth effect on the country’s net market demands for all goods and assets equal to the investment coefficient. In the traditional model, since there is a stock demand and supply for money and since goods and money demands are specified as having no wealth effects, it fo1low.s that the wealth effect from changes in the money supply must fall solely on the unspecified demands for bonds. Two basic adjustments in the portfolio-balance model will convert it into a prototype of the traditional model described above. First, the wealth effect on the demand for money, Li, must be assumed tl~ equal zero. Second, instead of an excess stock demand, and the related investment demand, for bonds, there is simply a flow demand IL. additional bonds, g. Thus, the world excess market demand for bonds becomes KF - AZ; + KF - AZ!, and the budget constraint, eq. (l), is replaced by

lo An exampte of a two-country traditional model very close to the prototype described here cau be sound in Mundell (l”968, ch. 18, Aypendix). Whitman (1970) discusses a group of models that essentially falls int’o our category c:f traditional models, They differ from our prototype in that they are one-country models and they embody the assumption that monetary policy consists of setting the total supply of money by exogenous policy decision.

P.R. A llen, International capital jlo ws


The flow demand, K’, replaces the investment demand for bonds, k’(z:’ - zi_r } wherever the latter appears in the portfolio-balance model. The stock demand function for bonds, eq. (13), is replaced by the flow demand function, derived from (1’).



v~_+ ai3


The interesting c&aracteristic of this implied flow demand function is the effect of a rise in the money supply, v’_~. The larger a country’s money supply, the greater is its flow demand for bonds. However, a change in the stock of bonds will have n.o effect on the flow demand for bonds. These unusual features are applicable to the implied demand functions of most traditional models. Since the stock of bonds influences neither the investment demand for money nor the flow demand for bonds, the distribution of bond stocks between the two c!::;:ntries is no longer determined by the equilibrium conditions of tb~-dmodel. The stocks of bonds, & and z:_~, while still defined by eqs. (21) and (22), no longer interact with any other variables and can be ignored. Thus, eqs. (24) and (26) are eliminated from the long-run equilibrium conditions. The “offsetting’ requirement for government debt policies, eq. (12), also disappears. The balance of payments surplus and net capital inflows are now defined in terms of a flow demand for bonds R, = M;$:A4: - K; + &*t = kp jr;?- VP - ) - Ai+t 1


There is no reason to expect the flow demand for bonds to equal zero in long-run equilibrium; theye is no fixed long-run relationship between the net capital inflow and t he new issuance of bonds. The trade surplus equals the sum of the flow demand for bonds and the government


I?R. Allen, International capital flows

budget surplus. In long-run equilibriu.m, 4



(3 1’)

(32’) Portfolio equilibrium is not really an appropriate phrase to describe the equilibrium of the traditional model. The demands for assets are not based on, the desire to acquire a certain portfolio. While equilibrium does require a constant stock of money, it is consistent with continually changing bond stocks. Unless the flow demand for bonds equals zero, which would happen only coincidentally, bond holdings will be changing. 5. Effects of monetary disturbances

The first monetary disturbance is an exogenous increase in the demand for money in A, denoted by a rise in the shift parameter, a*. This indicates an increase in A’s liquidity preference, shifting A’s demands from bonds toward money. An intuitive reaction might be that in an open economy such an increase in money demand would result in an increased supply of money, as a result of a higher interest rate and an improved balance of payments. This reasoning is essentially borne out in the prototype traditional model and is also the initial effect of the disturbance in the portfolio balance model. IIowever, En the portfolio balance model each country’s stocks of assets, the levels of outputs, the interest rate and the balance of payments continue to adjust until the requirements of portfolio equilibrium are met. In long-run portfolio equilibrium the balance of payments .deCcit must equal the country’s new issuance of money, (23); the trade deficit must equal the government budget deficit, which is the sum of the new issuances of bonds and money, (32); and a country’s net market demand for all goods, E: + G/ - J#, must eiqual- its trade deficit, a requirement of .market equilibrium, (14) and (15). These requirements indicate, firstly, that there is no long-run change in the balance of payments nor in its components as a result of the disturbance, since the issuances of bonds and money are exogenously determined and are unaffected by the disturbance. Secondly, these four

P.R. Allen, Internatiomi capital jlows


equations simultaneously determine the: long-run equilibrium values of outputs, yf and y f, the interest rate, re, and the balance of payments, , Re, independently of the degree of liquidity preference or of the levels of assets in each country. Because there are no wealth effects on the demands for goods or on the policy decisions to issue bonds and money, the stocks of assets do not appear in these equations. Thus, the long-run values of outputs, the interest rate, and the balance of payments and its components are unaffected by the increase in liquidity preference.’ ’ The question remains how the stocks of assets are reallocated between countries in the process of adjustment to a new long-run equilibrium. Whenever a country’s balance of trade surplus exceeds (is less than) its government budget surplus or when its government budget deficit exceeds (is iess than) its balance of trade deficit, the country gains (loses) wealth, either bonds or money. Another way of saying this is that a country gains (loses) wealth, if its trade balance improves (deteriorates) relative to its long-run equilibrium level. Therefore, that country for which the increase in liquidity preference creates a temporary balance of trade surplus will gain wealth as a result of the disturbance, while th.e other country loses wealth. Furthermore, since an increase in a country’s supply of either asset raises its stock demand for both assets, a country must either gain or lose both bonds and money as a result of the disturbance. A transitional improvement (worsening) of a country’s trade balance relative to the long-run equilibrium level will therefore increase (decrease) the country’s stocks of both assets. An increase in liquidity preference is contractional in that it temporarily lowers outputs in both countries. As a result of the fall in o-&puts, A’s balance of. trade will temporarily improve (deteriorate), if the term, (mAE$sB - mBEtsA), is negative (positive).12 Thus, in the long run, if (mA EtsB - mBEfsA) is negative, the shift in A’s preferences from bonds toward money will cause A to gain both money and bonds from country B, in return for which it temporarily gives up ‘r Eqs. (23) and (33) imply eq. (24), as seen by subsiitution of eq. (31) into (33). The eight eqs. (14)-(17) and (23)-(26), summarize the solution of the model. Of these, (14), (15), (23) and (24) are determined independently of the levels of assets and are unaffected by the disturbance. Thus long-run equilibrium v&es of the four variables, [email protected], yf, Q, and R,, are unaffected by changes in levels of assets or by the disturbances. l2 The parameter s’ denotes the marginal propensity to save out of disposable income, such that si= 1 -Ef.

P.R. Allen, International capital flows


Table 2 Changes in the holdings of assets in response to a rise in liquidity preference in A and to a temporary rise in the rate of open market purchases in A. X:

dx _&A

dxa , dbA

A %

4 L$-L!j



A ze

A we






B ve

B ze

13 L3 --







as rnAE$a

B we 1 L&L?


- mBEgsA s 0 b

a Assuming b A = 0 initially, dbA = bA = dF = -dZ b Stability requires that (L$-L~(mAE~~

- mBEgsA) > 0.

more consumption goods to B. Conversely, if the term is positive, A will lose both money and bonds. These results are summarized in the first row of table 2.13 The second monetary disturbance is a temporary increase in the rate of open market purchases in country Al4 This occurs in period k, such that [email protected] - A# = - A$ + AZ! = 41” > 0, assuming the rates of issuance in B to be the same for all periods. This increase in open market purchases raises the world level of money, rii, and lowers the world stock of bonds, 2, by the amount bA. It is assumed that portfolio equilibrium prevails in period k-i. Since the change in the rate of open market purchases is only temporary, in long-run equilibrium the only parameters that are changed are the world stocks of currencies and bonds, F and Z. As in the case of a change in liquidity preference, the temporary increase in the rate of open market purchases has no long-run effect on l3 In table 2 aU the changes in stocks of assets arc expressed in terms of wealth effects on the stock demands for monay. They could alternatively be expressed in terms of the wealth effefc$ on the stock demands for bonds, since 25 = 1 -L$. Although fne disturbance is referred to as an increase in the rate of open market purchases, it should be understood to apply equally to a decline in the rate of open market sales, depending on whether the government was making open market purchases or sales prior to the disturbance.

P.R. Allen, In ternatbnal capitalflows


outputs, the interest rate, or on the balance of payments and its components. The disturbance is expansionary, in that it temporarily raises outputs in both countries. 2’~ a result of this expansionary disturbance A’s balance of trade temporarily improves (deteriorates), if the term (mAEis* - mBE:sA), is positive (negative); this is the reverse of the effect of the contractionary disturbance. In the long run, the temporary increase in A’s open market purchases, which raises the world stock of currencies and lowers the world stock of bonds, causes A to gain both money and bonds, if (mAE$sB - m* E!sA) is positive, and to lose both, if the term is negative. The latter case produces the rather surprising conclusion that a country attempting to increase its money supply through open market purchases may actually effect a long-run reduction in its money supply. These results are summarized in the second row of table 2. The effects of either disturbance on the stocks of assets are seen to depend on the relative size of the wealth effects, L$ -Lt. Furthermore, the necessary condition for local stability of the model is that the wealth effect on the stock demand for money be stronger in the country whose trade balance is initially improved by an expansionary disturbance. This is denoted by (mA Ets* - mBEgsA )(Lj - Lf) > 0



It should be remembered that L f - Lt indicates not only the difference of the wealth effect on A’s money demand minus the wealth effect on B’s money demand, but also the difference of the wealth effect on B’s bond demand minus the wealth effect on A’s bond demand, since 2; = 1 -L& The importance of the relative size of the wealth effects stems from their role in determining the impact on outputs of a redistribution of bonds or money. The effect of a redistribution of money or bonds is expansionary (contractionary), whenever the wealth effect on the demand for money, Lt, is stronger for the country losing (gaining) the asset. The mechanisms underlying this conclusion can be easily summarized. An increase in the supply of money in either country has an immediate expansionary effect 01. outputs in both countries. SOlution of the model shows that this expansionary effect is proportional to the wealth effect on the country’s demand for bonds, 1 - Li Therefore, a redistribution of money from A to I3 places conflicting pressures on outputs: the rise in & puts an upward pressure on l


P.R. Allen, Intematbnal capital flows

outputs proportional to 1 - Lf and the fall in I& puts a downward pressure on outputs proportions: to 1 - Lt. If the wealth effect on bond demand is stronger in g:ountry B - that is, the wealth effect on money demand is stronger in A, the country losing money - Lf > L! , then the upward pressure dominates and the overall effect is expansionary,. and vice versa, if L$ CL, B. The reverse would be true for a redistribution of money from B to A. In contrast, an increase in the supply of bonds in either country has a contractional effect on outputs, which is proportional to the wealth effect on the demand for money, L$. A redistribution of bonds from A to B will raise z? 1 , placing a downward oressure on outputs proportional to Lt , and will lower ztk l, placing ;;on.’ upward pressure on outputs proportional to Lt. If the wealth effect on money demand is stronger in country A, the country losing bonds, Lt > E,B 9 then the redistribution of bonds will have an expansionary effect on outputs. The reverse is true when bonds are distributed from B to A. We can now see how, if’ the model is stable, the redistribution of wealth resulting from either of the exogenous disturbances will return the outputs to their original levels. Consider the case where (mAEtsB mBE$* ) is positive. Firsts, an increase in A’s liquidity preference temporarily lowers outputs and worsens A’s trade balance, causing A to lose wealth to B. The required subsequent rise in outputs will occur if Lf > Lg , since a redistribution of assets is expansionary when the wealth effect on money demand is stronger in the country losing assets. Second, the temporary increase in the rate of open-market purchases in A is initially e:xpansionary, causing a temporary improvement in A’s trade balance an.d a flow of wealth from B to A. As a result of the ensuing redistribution of assets from B to A, the necessary contraction of outputs will occur, if L$ > LB, since a redistribution of assets is contractionary when the wealth effect on money demand is stronger in the country gaining assets. If, on the other hand, the stability conditions were not met and Lf were to exceed Lf , the redistribution of wealth in either disturbance would move outputs away from their equilibrium levels. For the opposite case from that discussed here, where (m* EtsB - mBEfs* ) is negative, the entire discussion would be reversed. These effects of wealth redistribution on outputs are the economic basis of the stability requirement. The more similar wealth effects are in the two countries, the smaller will be the effect on

P.R. Allen, Internatibnal capital flows


outputs of a given redistribution of money, and the larger will be the redistribution necessary to produce a new equilibrium. I5 A surprising result of this model is that neither a change in liquidity preferencenor a change in the world stocks of assets has any effect on the long-runlevelsof outputs. This is causedby the simplifying assumption that the levels of asset holdings have no effect either on the demands for goods or on the policy-determined issuances of new assets by the governments. If one does not believe in this long-run neutrality of money, this result suggests the desirability of including wealth effects in the long-run demands for goods? If there were positive wealth effects on the demands for goods, an increase in liquidity preference would be somewhat contractional and an open market purchase, somewhat expansionary, in the long-run. If the wealth effects on the demands for goods fell primarily on the demands for domestic goods, the country gaining wealth would experience a stronger expansionary impact and a smaller deflationary impact than the country losing wealth. The opposite would be true if the wealth effect on goods demands primarily affected demands for imported goods. If the wealth effects on goods demands dominated the wealth effects on assets demands, generalizations could no longer be made about the composition of the changes in the portfoiios. The country gaining wealth might gain money but lose bonds or vice versa, or could gain both assets. Another special assumption of the model is that monetary and debt policies, A$ and A$, are independent policy decisions, unrelated to the dependent variables of the model. This assumption is also made for simplicity. Given our assumptions about wealth effects, the relaxation of this assumption would have no effect on the comparative static results. If there were wealth effects either on the demands for goods or on the policy variables themselves, relaxing the assumption of rs By summing, from table 2, $.hechanges in money and the changes in bonds in the two countries, we can see that an increase in liquidity preference has no effect on the world stocks of money and bonds, while increased open market purchases raise the world stock of currencies and lower the world stock of bonds, When there is a change in liquidity preference, the distribution of the portfolio change between money and bonds depends on which country initiates the disturbance. However, it makes no difference to the end results which country initiates the increased open market purchases. l6 McKinnon (1969) and Whitman (1970), in their one-country portfolio-balance midels, bath find that monetary disturbances have no effect on output in the long run, even though they assume that there is a wealth effect on the (demand for goods. This results from the assumption that the world levels of output and world demand for the country’s imports are exogenous to the:model.

P.R. Allen, International capital flows


exogenous monetary and debt policies would produce new long-run levels of the balance of payments and its components as a result ,of the disturbances, in addition to new levels of outputs and the interest rate. However, unless these wealth effects were sufficiently strong to dominate the wealth effects on asset demands, conclusions about the direction of movement of assets would be unchanged. 6, Extensions of the model

The above model, through its assumptions of fixed prices and flexible outgirts, is Keynesizi. An alternative approach would be to specify a classical type of model in which prices are perfectly flexible and outputs are fixed at the full-employment level. In such a model, eq. (6) would be replaced by (6’), and prices, 8, would replace outputs as market variables. .




(6 1


All othe? equations remain unchanged. ‘Transitional changes in the trade balance as a result of the disturban!ces are dominated in the classical model by absolute changes in prices. A rise in liquidity preference has an initial deflationary effect on both prices and thus lowers the absolute value of the trade balance during the adjustment periods. The country with a trade surplus loses wealth, because the surplus declines, while the country with a trade deficit gains. Conversely, an open-market purchase is temporarily inflationary, raising the absolute level of the trade balance and causing the wealth of the trade-surplus (deficit) country to rise (‘all). In the classical model a trade surplus for country A is comparable to a positive value of the term (mAE$sB - [email protected] ) in the Keynesian model. Just as long-run outputs are unchanged in the Keynesian model, in the classical model long-run prices are unchanged. The effects of the disturbances on bond and money stocks are the same for the classical model as those shown in table 2, except that the direction of the changes apply as A’s trade balance is po:iitive or negative, M” ‘



2 0.


*’ Stability *jm the classid model requires that the Marshall-Werner(Continue on next page)

P.R. Allen, Internationalcapitalflows


In either model the long-run reallocation of bonds and money depends upon the transitional change in the trade balance. If the trade balance declines temporarily, the country loses wealth and vice versa. Since this conclusion applies for both a Keynesian and a classical model, one might interpolate and suggest that it would also apply in a model in which both price and output responded positively to excess market demand for a good. If there were wealth effects in the demands for goods and if monetary and debt policies were dependent on the market variables, the factor deciding the distribution of assets would be the change in the balance of trade relative to the government budget. Portfolio equilibrium, while requiring offsetting government budget policies in the two countries, is consistent with an ongoing nonzero issuance of both bonds and money. However, if capital were not perfectly mobile, or if both governments could not issue the same type of bond, portfolio equilibrium would require a zero issuance of bonds by each government. Similarly, if exchange rates were perfectly flexible, with no government intervention in the exchange market, portfolio equilibrium would require a zero issuance of new money by each government. In a stationary model in portfolio equilibrium a zero balance of payments surplus requires a zero issuance of new money in each country, and a zero net capital flow requires zero new issuance of government bonds. In a growing economy, portfolio equilibrium would require world issuance of new assets at the natural rate of growth of the world economy (which must be the growth rate for each country). Zero balance of payments and zero net capital flows would be consistent with new issuance of bonds and currency in each country sufficient to maintain the needed rate of growth of assets. ”

(continued from previous page) conditions for a nonzero trade balance be met and that (MtB-nf~,(L~-L;)>o,

instead of eq. (29). Since the trade surplus equals the government budget surplus in equllibrium, stability of the classical model requires a nonzero government budget surplus. These stability conditions are based on the assumption of no extreme asymmetries in behavior or size between the countries. There pre a few small terms in the Jacobian, resulting from the nonhomogeneity of disposable income with respect to price;, which conceivably could be destabilizing if there were extremely great differences in behaviorA responses in the two countries.

P.R. Allen, International capital flows


7. List of symbols used (hr the ith country at end of time period t)

expenditure demand for all goods demand for the imported good government expenditure demand taxes demand for a stock of bonds demand for a stock of domestic currency output disposable income stock of bonds owned by persons stock of domestic money wealth, equals bonds plus money, z: + $ total world supply of currency, I$ + V: total world supply of bonds, zt +zF price of the good produced in country i the terms of trade for country A, P.. /PF world interest rate on bonds balance of payments surp3us of A


trade balance of A, exports minus imports net capital inflows to country A independent new flow supply of bonds from government i independent new flow supply of currency i from government i flow demand for bonds in prototyye’traditional


investment coefficient marginal propensity to import out of disposable income marginal propensity to save out of disposable income

P.R. Alien, In ternatibnalcapitalflows


References Bramson,W.H., 1970, Monetary policy and the new view of international capital movements, in: A.M. Okun and G.L. Perry, eds., Brookings Papers in Economic Activity, Vol. 2 (The Brookings Institution, Washington, D.C.) 235-270. Bushaw, D.W. and R.W. Clower, 1957, Introduction to Mathematical Economics (Richard D. Irwin, Inc.) Floyd, I.E., 1969, International capital movements and monetary equilibrium, American Economic Review 59,472-492. McKinnon, RI., 1969, Portfolio balance and international payments, in: R.A. Mundell and AK Swoboda, eds., Monetary Roblems of the International IEconomy (University of Chicago Press) 199-234. McKinnon, RI. and W.E. Oates, 1966, The Implications of International Economic Integration for Monetary, Fiscal, and Exchange-Rate Policy, Princeton Studies in International Finance No. 16 (Princeton University). Markowitz, Harry M., 1959, Portfolio Selection: Efficient Diversification of Investments (John Wiley and Sons). Meade, J., 1951, The Balance of Payments (Oxford University Press). Mundell, R.A., 1969, International Economics (Macmillan). Tobin, J., 1965, The theory of portfolio selection, in: F. Hahn and F.P.R. Brechling, eds., The Theory of Interest Rates (Macmillan). Whitman, M. vN., 1970, Policies for Internal and External Balance, Special Papers in International Economics No. 9 (Princeton University).

Appendix Eqs. (2) through (13), (US), (27) and (28) define the fifteen variables: E:, M:, G:, L;, f$, y$ Pt, w:_~, c, AT: and AZ: (n > k), Z;, Rf , V, and Z, respectively. Eq. (1) is not independent but is the basis for eq. (13). Eqs. (14) through (17) and (19) through (22) can be solved for yp, y:, rt, R,, I&, vEl, ztl, and z?_~, for any period t. Alternatively, the equilibrium values of these eight variables can be found through solution of (14) through (17) and (23) through (26). Eqs. (23) through (26) are derived from (19) through (22) a.nd are not independent. Thus, there are 23 variables and 28 equations, 23 of which are independent. These equations complete the.model. Any subsequent equations either define additional variables or are derived from the above equations. The eight simultaneous equations are listed below. IInorder to express the investment demand for bonds in terms of the specified demands for goods and money, eq. (1) is substituted into eql. (24), producing (24*).

P.R. Allen, Internadonal capital flows



I,) +g*f$*


c, $,

k” {LB bp k*{L*l$?

a*] -v)j



+ rdqgy;* - mB[Pe Iy? = 0,

--- yfPf


5, q!? &I -I$)



- R,=O,


-SAFB +Re=O,





‘,1 -&?4A +v,Apb4- IPQLA[yedAp c, WA, a*1 - q*>+



-7 t - bf -If? =o,




. -z,B


Total differentiation of these eight equations, written in matrix form, yields the foliowing:


























kBJ.y J











[email protected]
































~ az,”

determinant of the above Jacobian matrix is Det= kAkB(L$ - Li)(mAEtsB -m*@@)> if (L$ - L$2


0 as fmAEt8 - mBEfsA) zz 0.

y use of Cramer’s rule the above system can be solved for the changes in the variables with respect to a change in a* or 6*.