A Portfolio-Balance Rational-Expectations Model of the Dollar-Mark Rate: May 1973 - June 1977

International Finance Discussion Papers Number 123

September 1978

A PORTFOLIO-BALANCE RATIONAL-EXPECTATIONS MODEL OF THE DOLLAR- MARK RATE: MAY 1973 - JUNE 1977

by

Michael P. Dooley and Peter Isard

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an

acknowledgment by a writer that he has had access to unpublished material) should be cleared with the author or authors.

A Portfolio-Balance Rational-Expectations Model of the Dollar- Mark Rate: May 1973 - June 1977

by

Michael P., Dooley and Peter Isard*

1. Introduction and Overview

This paper presents empirical evidence that month-to-month fluctuations in the dollar-Deutschemark exchange rate conform suitably to the predictions of a portfolio-balance model with rational expectations. Unlike monetarist models of exchange-rate behavior (e.g., Bilson, 1978; Dornbusch, 1976; Frenkel 1976; and Girton and Roper, 1977),|our approach emphasizes that the exchange rate between two currencies depends on the relative supplies of a wide range of financial assets denominated in those currencies, not only on the relative supplies of moneys. In this context we can distinguish between the impacts on asset supplies -- and hence on exchange rates -- of three different policy instruments: changes in the supply of base money, fiscal budget deficits, and official exchange-market interventions. .

Exchange rates depend as well on the relative demands for financial assets denominated in different currencies. In formulating the demand side of our model we follow Kouri (1976) and Branson (1976) by emphasizing the effects of the accumulation and shifting residence of wealth, and we pay particular attention to the dramatic growth of OPEC wealth since 1973, Currentaccount imbalances are viewed to affect exchange rates by shifting the residence of wealth between asset holders with --*/ The analysis and conclusions of this paper do not necessarily represent the views of the Federal Reserve System or anyone else on its staff. We would like to acknowledge enlightening discussions with

Dale Henderson and participants in the International Trade Workshop at the University of Chicago.

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different sets of portfolio preferences. Unlike the portfoliobalance models of Porter (1977) and Branson, Halttunen and Masson (1977), we retain wealth variables in our estimating equation.

The demand side of our model also allows for risk-averse behavior by portfolio managers. During our sample period, the absolute values of month-to-month changes in the spot rate exceeded 2 cents per mark (an annual rate of 60 per cent) for 6 out of 50 months, and exceeded 1 cent per mark during 20 months. Interest differentials were small relative to these exchange-rate movements. Thus, to the extent that such large exchange-rate movements were expected, market participants must have been strongly risk averse; otherwise they would have taken positions to prevent exchange rates from ever getting so far out of line with their expected future values. Obversely, to the extent that the large exchange-rate movements were unexpected, market participants were caught in a world in which they had good reason to be risk averse. Accordingly, we explicitly incorporate a risk-aversion parameter into our estimating equation, which predicts exchange-rate changes significantly better than the current one-month forward rate. This emphasizes the importance of filtering information on spot rates and interest differentials through a model that allows for risk aversion, rather than viewing the world as a risk-neutral environment in which forward rates

can be interpreted as expected future spot rates.

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One of our main objectives is. to move away from a model in which future (or current) spot rates are predicted from current (or lagged) spot or forward rates toward a model in which current and expected future spot rates are explained simultaneously and consistently. We do this by adopting an iterative estimation procedure. Our model provides an equation for estimating the current spot rate as a function of the expected future spot

rate and other variables that we either treat as exogenous or

replace with predetermined instruments. In our first iteration this equation is estimated under an arbitrary specification of the time

path of the expected future spot rate. In subsequent iterations, however, the time path of the expected future spot rate ig generated by applying the parameter estimates from the previous iteration to assumed expected future time paths of the other exogenous variables and predeterminedinstruments. (These latter expected future time paths are generated without sophistication from the in-sample time-series behavior of the

exogenous variables.) The details of this procedure are described

below. We continue to iterate until the predicted time path of

the spot rate is equal (within a tolerance limit) to the

time path of the expected future spot rate lagged one period.

This essentially forces the current spot rate and the expected

future spot rate to fit the same model, and in this sense our

expectations are "rational,"

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In order to be as consistent as possible with the portfoliobalance framework, we choose to observe the exchange rate at a single point in time at the end of each month, rather than averaging daily observations within each month. We know that our observed exchange rates are exchange rates that clear asset markets in a tautological sense, but we reject the assumption that asset holdings reflect continuous portfolio-balance equilibrium, and we do not attempt to model asset holdings as moving almost continuously along paths that adjust smoothly toward desired portfolio holdings. Instead, we assume that asset holdings fluctuate randomly about portfolioequilibrium levels” such that the difference between observed and equilibrium exchange rates is a serially-uncorrelated variable with zero mean (and constant variance). This assumption is implicit in the use of our exchange-rate observations as the dependent variable in a model of the exchange-rate path that would be consistent with continuous portfolio-balance equilibriun.

We use a nonlinear specification to estimate the equilibrium path of the exchange rate, and our iterative procedure for imposing rational expectations only converges to a sensible solution when we give strong weight to our prior notions about the parameters that determine portfolio shares .! Although we cannot provide theoretical justification for the modified-Bayesian approach and iterative

procedure that we adopt, our model correctly predicts the direction

1/ This view is also expressed by Christopher Sims in the general discussion of Kouri and de Macedo (1978).

2/ There is some precedent for imposing priors in exchange-rate estimation. Bilson (1978) gives strong weights to his priors, and Armington (1978) imposes priors on his portfolio-share matrix.

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of 35 out of 50 month-to-month changes in the observed exchangerate, as compared with 27 out of 50 changes (little better than a coin toss) that are correctly predicted by the forward rate. The coefficient of correlation between the changes predicted by our model and observed changes is .4l1,whereas the changes predicted by the forward rate have a small negative correlation with observed changes. In addition, our predictions of exchange-rate changes are more accurate -- albeit only slightly -- than predictions based on several measures of purchasing-power parity. Such results are nothing to crow too loudly about, but the portfoliobalance rational-expectations framework is much richer than either the forward-exchange or purchasing-power-parity theories, and there is scope for improving our empirical results by refining the model in several directions. 2. The Basic Framework Our portfolio model resembles Girton and Henderson (1976) in a number of its basic features. We assume a world with two currencies, called the dollar and the mark, and we divide the world into four "countries" or wealth-holding regions, called the United States (US), Germany (G), the oil-exporting countries.

(OPEC) and the rest of the world (ROW). We distinguish two types

of outside assets (or claims on official agencies) in each currency: the non-interest-bearing monetary base, and interest-bearing "bonds"

or government debt. Our exchange-rate equation is derived by

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focussing on the market-clearing condition for dollar-denominated assets. In theory we could just as well work with the market-clearing

condition for mark-denominated assets.

The supplies of U.S, base money and outside dollar -denominated bonds are assumed to be exogenously determined by the interaction of the Federal Reserve's monetary policy, the level of the U.S. government debt, and official U.S, and foreign exchange-market intervention involving dollar-denominated assets, This assumption of exogeneity . is strong, though conventional It implies that policy makers do not react systematically to the exchange rate or to variables that influence the exchange rate. We know, of course, that intervention policy can be viewed predominantly as a reaction to exchange rates, and that monetary policy and government-debt policy react to variables that influence exchange rates, However, it is difficult to model policy-reaction functions as systematic, and we have not attempted to do so. |

We let MB denote the U.S. monetary base and B denote the supply of outside dollar-denominated bonds, by which we mean the net stock of dollar-denominated bonds supplied by official institutions.

B is viewed to equal the cumulative U.S. budget deficit (DEF) minus

3/ Two exceptions that incorporate policy reaction functions are Artus (1976), who embeds the dollar-mark exchange rate in a model of Germany's monetary sector, and Branson, Halttunen and Masson (1977).

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the stock of bonds removed from private circulation through the openmarket operations of the Federal Reserve (which we take to equal MB), minus cumulative official intervention purchases of dollar-denominated bonds (INT).

(1) B= {DEF -MB -JINT

We assume that the U.S. monetary base is held entirely by U.S. residents, but that the supply of dollar bonds is allocated among (a) private U.S. wealth holders, (b) private German wealth holders, (c) private and official OPEC residents, and (d) private and official residents of ROW. The isolation of U.S. and German wealth holders is dictated by our focus on the dollar-mark exchange rate. The isolation of OPEC is based on the rapid increase in OPEC wealth during our sample period, combined with indications that OPEC has different portfolio preferences than other wealth holders. The inclusion of ROW is necessary to make the different components of demand add up to supply 2!

Before turning to our behavioral assumptions about d@mands £or

the two types of dollar assets, we can write the market-clearing conditions

4/ See Armington (1978) for an n-country model that is capable of estimating n-1 exchange rates simultaneously; and see Berner et al. (1977) for a 6-region model with 5 simultaneous ly-determined exchange rates.

for these assets as

d (2) MB = MB

US d dd d (3) Be Bio+ Bt Bopgc + Brow

where a superscript '"d" connotes demand and subscripts refer to the source of demand. Let ro denote private U.S. demand for interest-bearing assets denominated in marks (or for bonds denominated in currencies other than the dollar), let x denote the exchange rate in dollars per mark, and let W denote private U.S. wealth. Then by definition, the balance sheet of private U.S. wealth holders must satisfy the condition.>/ . “a _ : ee a (4) We MBs + Bis + Fs In order to derive a market-clearing condition for the two types of dollar-denominated assets combined, we add (2) and (3) and substitute from (4) to get:

d d d d (5) MB+B= (WexF 5) +B t B OPEC + Brow Alternatively, by combining (5) and (1): d d opec + Brow

We will substitute behavioral assumptions for the demand variables,

(6) fq@er-int) = (W-xFd) + Bg +B

and then manipulate condition (5) to yield an equation for the exchange rate, which is one of the arguments of our demand functions,

No information is gained by working with the market-

clearing condition for money and bonds combined, rather than

eee 5/ We make the standard assumption that private U.S. residents do not hold foreign non-interest-bearing money, and that the

U.S. monetary base is entirely held by U.S. residents.

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working with separate market clearing conditions, provided we introduce behavioral assumptions appropriately drawn from a portfolio-balance framework. The combined marketclearing condition is appealing, however, partly because of its broader scope and partly because of the symmetry

d d between F_ and B (FOREIGN = G, OPEC, ROW). us FOREIGN

3. Behavioral Assumptions

Let i and ig denote one-month own-currency rates of © interest on dollar-denominated and mark-denominated bends, let x° be the spot exchange rate (in dollars per mark) currently expected to prevail one month in the future, and let Y denote the nominal income of private U.S. wealth holders (measured in dollars), (Then a complete model of portfolio behavior for the U.S. private sector (relevant to the menu of assets that we are considering) can be specified as: |

(7) ma‘ = m(i,igt(x x) /x,¥/W, ...) .W US

d W (8) By. = b¢ ) d ).W (9) xF ys = £(

such that m+bt+f=1. We view (7)-(9) as a description of equilibrium

levels about which actual portfolio holdings are assumed to fluctuate

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randomly. The first two arguments of the functions m, b, and

f respectively represent the expected nominal dollar-equivalent yields on domestic bonds and foreign bonds; the nominal yield on base money is zero, The third argument, Y/W, is a transactions demand variable that allows the demand for money to increase (relative to wealth) as income increases (relative to wealth). Ideally, wealth, defined to satisfy condition (4), would also

be modeled as a portfolio choice variable rather than treated

as predetermined; but lack of appropriate data makes it difficult to treat wealth as endogenous, as will be discussed below.

[the specification of (7)-(9) in terms of nominal rather _ than real expected yields, which gives no explicit consideration to expected rates of inflation, implicitly assumes that portfolio choices between money and bonds are independent of the expected yields on stocks of goods or other assets. | We let r denote the expected differential yield on mark-denominated bonds relative to dollar-denominated bonds:

(10) r= ig + (x =x) /x -.i Since there is a one-to-one correspondence between (4, it (x=) /x)

and (i,r®), conditions (7)-(9) can be transformed into

(7a) MBs = m*(i,r°,Y/W,...).W

d (8a) Byg = b*( ).W (9a) xF4. = £°( ).W

1 BSS)

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Ideally we would like to estimate the complete U.S. portfolio model (7a)-(9a) together with analogous models for our three other regions, and to then solve our estimated structural equations for the relationship between the exchange rate and those variables that we assume to be exogenous. Unfortunately, data are not available on Bis and Fe’ Since we do not know exactly how much of the U.S. government debt is held by domestic residents, and neither do we know the currency composition of U.S. claims on foreigners. This lack of data motivates our approach of substituting a behavioral assumption for x into condition (5), along with behavioral assumptions for BC, BOPEC and Bow’ to arrive at a reduced-form relationship that can be manipulated to solve for the exchange rate as a function of other variables in the

model.

We do have data, however, on MBs} and the efficiency of our estimates may be increased by incorporating this information into our assumption about the behavior of Fic: Because we may also want to make use of estimated information about the relationship of MBS to i, Y and W, we assume that (7a). - (9a) have the specific simplified form

d (7b) MB /W =1- kG@,Y/W,...) (8) Bés/W =(1- ay - by Wr) -k( ) with b,>o

(9b) uF? woo (a, + bi?) .k( ) US

Condition (7b) simplifies condition (7a) by assuming that the allocation

e 2 2 of wealth between money and bonds is independent of r and, in particular,

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does not require knowledge of the expected rate of exchange-rate change. Given MB‘ /W and hence k , conditions (8b) and (9b) assume that the allocation between domestic and foreign bonds depends only on r, the expected differential yield between these two types of bonds, according to a functional form that is illustrated by Figure 1. With re = 0, U.S. private portfolio holders allocate the fraction ajk of their

wealth to foreign bonds, with k being a function of i and Y/W.as specified

Figure 1 e

in condition (7b), and with the parameter a, presumably valued between

O and 1. In the range r° >0, successive unit increments in r,

ceteris paribus, lead to positive but successively-smaller

increments in the share of U.S. private wealth allocated to foreign bonds, reflecting aversion toward risk in the home-currency valuation

of portfolio holdings. A symmetric assumption is made for the range

r©& <Q. The cubic-root equation is adopted as the simplest specification that exhibits the important properties of monotonicity and risk aversion.

Note that the ability to issue debt denominated in either foreign or

-13domestic currency makes it feasible to have either xFo/M <0 or xB tg /W > k. Note also that the greater is the parameter b,, the less is the degree of risk aversion; for b= ®, respresenting the case of risk neutrality, Fig would equal infinity whenever cr >O and minus infinity whenever r°< 0. Condition (9b) can be substituted into (5) to replace = a

In addition we require behavioral assumptions for Bes BOPEC and Bay

For Bo we assume the symmetric analog of (9b): d 3/6

(11) By/xW, = (ag + byWer )ekg( ) with by>0 d 3

(11a) Ba = (ay + bE) kg ( > HE

or

where Wo is German wealth measured in marks, we = xW, is German wealth

measured in dollars and -r° is the expected differential yield in favor

of dollar bonds. For OPEC and ROW we do not have data on supplies of

base money. Consequently, we assume

d (12) B® (a, + bre yw OPEC 3 3 OPEC

d 3/2 , S$ (13) B = (a, + b, -r ) «Wow

ROW

where the k functions are treated as constants and absorbed into the

$

a and b parameters, and where uw and W denote wealths denominated OPEC ROW

in dollars.

4. Graphical Illustration Substitution of (9b), la), (12) and (13) into (5) yields (14) MB + B= (1 -(a, + bee) w + (a, - byw dk We + (a3 - bs VF Wore + (ay = by VR

The four components of demand on the right-hand-side of (14) are illustrated

in Figure 2 for given values of the k and W variables. (In reality the relative positions and slopes of the four curves may be different than

this particular illustration. )

demand for dollardenominated assets

G

To illustrate the procedure we use to estimate the

determination of observed and expected exchange rates, Figure 3 shows aggregate supply (the SS curve) and demand (the DD curve) -- corresponding to the left and right*hand sides of condition (14) -- as functions of the observed exchange rate (x), for a given value of the exchange rate currently expected to prevail next month (x®). The transformation from Figure 2 to Figure 3 uses condition (10). The SS curve is vertical since MB + B is predetermined, independently of x.

We observe or introduce proxy time series on aggregate supply (MB + B), all variables other than x° that underlie the position of the DD curve in each time period, and the market-clearing exchange rate x. Accordingly, for any specified time series of x we can estimate the aggregate demand function, and (given the values of predetermined variables) we can plot the DD curve for each time period. Using our estimated values of the parameters of the aggregate demand function, together with assumptions about current expectations of next period's values of all predetermined variables, we can also plot the aggregate

supply and demand curves that currently are expected to prevail next

period -- represented in Figure 3 by s°s° and p°p°. Unless the intersection of s°s. and p°p” coincides with our specification of x, however, the estimated parameters of our aggregate demand function are not consistent with rational expectations. Accordingly, we estimate the aggregate demand function using an iterative procedure that begins

by adopting an arbitrary initial specification of x and then iterates through successive respecfications of x until we converge to estimated aggregate demand parameters that are consistent with rational expectations. The result is a model that simultaneously and consistently

explains the determination of observed and expected exchange rates, given observed and expected values of the predetermined variables that

enter the aggregate supply and demand functions.

Figure 3 pe

__value of x® that underlies the DD curve

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5. Data Inadequacies and Our Choice of Wealth Variables Our model is limited in a number of important ways by lack of data on the currency composition of international debts, and hence by lack of data on the currency composition of U.S. and foreign portfolio holdings £/ Without such data we cannot estimate a complete portfoliobalance model, and it is difficult to gear the model to a world with more than two currencies, Without such data we are also forced to adopt measures of wealth that cannot be revalued appropriately when exchange rates change. In other words, without data on Be and Fe we cannot construct W to satisfy condition (4) identically. Instead we have chosen to construct W from the national-income accounting identities. We know that private savings in any time period equals private investment plus the government budget deficit plus the current-account surplus on international transactions. Thus, abstracting from capital gains and losses, we generate our wealth variable (which excludes the value of equities) by estimating an initial value from the best information available and then adding in each period the cumulative value, since the beginning of the sample period, of private savings minus private investment--or the

cumulative sum of the government budget deficit plus the current-account

6/ Branson, Halttunan and Masson (1977) sidestep the problem by assuming that international debt is entirely denominated in a single currency

and can only be accumulated or reduced through current-account imbalances,

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surplus, Government budget deficits add to private wealth, and currentaccount imbalances shift the residence of wealth between countries — We construct data on Wo? the mark value of private German wealth, by the same method that we construct W. In estimating our model we adopt the strong but convenient assumption that the dollar value of private German wealth, constructed as

we = mW is predetermined and not influenced by the contemporaneous

exchange rate.

We construct WopEC by assuming an initial value of zero

at the beginning of the floating-rate period in March 1973--i.e., by assuming an initial balance between financial claims on and

debt to non-OPEC countries, Thereafter we increase W ec each

month by an estimate of OPEC's current-account surplus measured in dollars, To the extent that OPEC invests part of its current-

account surpluses in real assets or equities, W ec will overstate

OPEC's combined holdings of dollar-denominated and foreign-currency-

denominated bonds,

7/ Flow-of-funds data on the net financial worth of households and nonfinancial businesses (excluding their holdings of corporate equity) provide an alternative to constructing a U.S. wealth variable from data on budget deficits and current-account surpluses, Our suspicion, however, is that the flow-of-funds wealth variable contains more measurement error than our constructed wealth variable, so we have rejected this approach,

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We construct w as an initial value (to be described ROW below) plus the cumulative current-account balance of ROW since March 1973, The current-account of ROW is measured as the

balance that equates the global current account to

zero, given our estimates of the current-account balances for the United States, Germany and OPEC, To the extent that ROW "finances" part of its current~account deficits by selling real assets or equities, Wa will understate ROW's combined holdings of dollar-denominated and foreign-currency=denominated bonds, 6. The Fifst-Stage Estiation Procedure

In the empirical work reported in this paper we treat k and ke as endogenous, because in (7b) we view the shares of portfolios that are allotted to base-money holdings to be functions of the usual arguments of money demand functions, including interest rates, We are not willing to assume that interest rates are predetermined at the same time that we assume the stock of official dollar debt (MB+B) to be predetermined, We do assume, however, that policy variables, income levels and current-account balances are predetermined in the sense of responding to changes in exchange rates or interest rates with lags of at least one month,

Because we view interest rates as endogenous we have adopted a modified two-stage least-squares procedure, We thus sidestep the

specification and estimation of a full model of interest rates by

regressing i, ig, k and ko on the list of our predetermined variables,

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and by substituting fitted values for i, i, k and k, in the

second-stage estimation of our exchange-rate equation. In hopes

of increasing the efficiency of our estimates of i, ig, k andk ,

we modify the conventional first-stage procedure by

adding to the conventional list of regressors some predetermined variables that do not appear in our second-stage exchange-rate

equation, but that would appear in a full model of interest rates, Specifically, we regress i, ig, k and k, on the four wealth variables (wwe, We oc? DW ow)s four asset stock variables (MB, MB,, B,Bc ),

two scale-of-transactions variables (Y¥/W, Y,/W,) and constent terms, where

MB and B are the German analogs of MB and B, and where Dw G G g ROW represents the cumulative change in W from its base-period

8/ ROW value inMarch 1973,

7. The Second-Stage Estimation Procedure

Condition (14) can be manipulated to yield

$ $ $ 3 (lea k)W t+takWt+awWw aW - MB -B (5) r= 1 2GG 3 OPEC + 4 ROW bkW +bkW +bwW +b W 1 2GG 3 OPEC 4 ROW

AAR!

8/ We do not include expected rates of inflation among this list of regressors since we consider expected inflation rates to be themselves determined by the list of regressors, simultaneously with the determination of interest rates and exchange rates, We may nevertheless imagine that the regressors affect nominal interest rates in part by affecting expectations of inflation. Consider two equilibrium time paths of the world that differ only by the fact that on path 2 the nominal stocks of U.S, base money and outside dollar bonds grow g per cent per month faster than on path 1. There should be no real differences between these states of the world; and it may be instructive to note that none would arise in our model provided that the U.S. nominal interest rate was a uniform g per cent per month higher under state 2. For then a g per cent per month faster depreciation of the dollar in state 2 would be consistent with the same time paths of real variables as would emerge under state 1.

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and condition (10) can be manipulated to yield (16) x= x°/ (1tr'+i-i,) We can substitute (15) into (16) to obtain an expression for x in terms of x", a list of predetermined variables (Z) and the set of parameters to be estimated (p). Z includes the variables i, ioe k and ke» which henceforth denote the fitted (and thus predetermined) values of these variables based on the first stage regressions. With time subscripts added the model takes the general form (17) x= BCE, 47> Z., Pp) for tl, ...,T where x, and 2 are observed at the end of each month t and where Bex +1 » corresponding to x, is the unobserved expectation, held at the end of month t, of the value of x,4,. Rather than estimate (17) under an ad hoc specification of the time series tet! we adopt an iterative procedure intended to converge to a time series {E,x,,,} that is consistent with model (17) in the sense of satisfying 9! (18) Eyx i= 8X 40> E,Zet1,p) for tel,..., Te Here ? denotes the list of estimated parameter values that best fit model (17), Eee represents an assumption about period-t expectations of 2,,;, and E,x,42 is an assumption about period-t expectations of x49. Our particular choices for E,2.41 are based on the time-series history of Z. In particular, the predetermined

asset-supply, wealth and income variables are each regressed on

six lagged values of themselves (representing one to six-month

9/ Note that E.X,+, 1s a simplification of EE. .s%¢49-

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lags), and fitted values of Zt from those equations are adopted for Eee In addition, period-t expectations of the periodttl values of i,ig,k and Ko are generated from the first-stage estimates by replacing period-t+l values of predetermined asset~supply, wealth and income variables with their period-t expectations,

Our iterative solution procedure is as follows, We start with observations on the time series ix] and {2}, and with assumptions about the time series {E244} For the first iteration we begin with an arbitrary specification of the time series EEX yy bo call it fee he and we fit model (17) to obtain a vector of parameter estimates al We then generate a new time series Ete) using (18) subject to p= al and E.x,,5 =

ne %eH2" we continue in this fashion, using fx) to

generate {E Xa If the procedure converges in the sense

E

mt+1 m of reaching an m for which fe. Xa) and (Et

than a small tolerance Limit then the solution has the property

} differ by less

—T07 There are two exceptions here, E WCE) is based on the sixmonth history of WG, rather than we’, and E,WROW® | is constructed as a residual, consistent with the manner in which WROW is constructed to satisfy the global current-account adding-up condition.

lls We define convergence as an average absolute percentage

difference of less than one-tenth of one per cent, whith is less than .05 cents per mark,

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that

and (17a) X, = gE x7. ZeoP )

(18a) i I = CHEE EZ?) Thus, the fitted path of the exchange rate is based on exchangerate expectations that are themselves generated consistently from the same exchange-rate model and the same parameter values 2! Several points should be made about this iterative procedure, First, convergence is not guaranteed; and if convergence is achieved, it is important to check the sensitivity of the final parameter estimates.to the initial specification of (Exit Je Second, if the model does converge this procedure forces equality between expectations of future exchange rates and the exchange rates that the model predicts under a specific set of assumptions about the expected future values of the other variables in the model, Exchange-rate expectations can be wrong, but our procedure constrains them to be consistent with the model's estimates

of the exchange rates that are consistent with portfolio equilibrium,

~~ 12] It may be noted that the consistency here is based on using a x

E™ in place of E. ero a8 8 right-hand-side argument in condition

x ttl tt2 (18a). We lose generality but avoid an infinitely-recursive model by making this substitution. Our procedure thus ensures that Exot and % are estimated consistently, but stops short of attempting

to guarantee consistency between Exe and EXt+2? between E,x,;9 and

EXt43 and so forth ad infinitum, See Bilson (1978) for a different

empirical conceptualization of rational expectations.

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8. The First-Stage Estimation Results

The first-stage estimation results are shown in Table 1. Since our model imposes a loose correspondence between changes , $$ $ in the sum of the four wealth variables (WW pec WRoW and changes in asset supplies (MB+B, or MB, TB.) -- the correspondence would be tight if MBGtB, were measured in dollars -- we have

excluded B, from the i and k regressions and B from the i, and

G G Ko regressions, Thus, in the i and k regressions we view a change in Bo to be the counterpart to ceteris paribus changes in one of the wealth or asset-supply regressors, while changes in B are behind the scenes in the i, and ko regressions.

Our regression equations are not developed from a structural model, but we nevertheless have prior expectations about the signs of some of the parameters. In the k regression we expect an increase in the transactions variable Y/W to lower the ratio of bond holdings to wealth in U.S. portfolios (i.e., to

lower k), ceteris paribus; and we also expect k to rise in response

to increases in Wor reductions in MB, ceteris paribus, Our

results are consistent with these expectations and with similar expectations about the relationship of Ke to Y¢/Wes we, and MB, - The interest-rate regressions, however, are not as consistent with our prior expectations. While they confirm our expectation that increases in Y/W or Y¢/We> ceteris paribus, should raise both i and igs they do not entirely confirm our expectation

that an increase in any of the four wealth variables, ceteris paribus,

should reduce both i and i,. And it is especially disconcerting: (a) that

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- 24 i. is pushed up by an open market operation that increases MB, (holding constant MB ,+Bg) 3 and (b) that exchange-market intervention to increase B (sell dollar bonds) by reducing Bo (buying mark bonds) has the effect of pushing i down and i, up.

Although none of the estimated parameters with wrong signs is very significant, except perhaps for the coefficient of W in the i regression, our failure to estimate significant parameters with correct signs precludes the use of our model for estimating policy impacts. This underscores the importance of following Artus (1976) in embedding the exchange rate in a more adequate model of the monetary sector.

It should be emphasized that the shortcomings of our first-stage regressions do not affect the rationale for using first-stage fitted values as second-stage instruments for i, ig,

k and kg. Instruments of some sort are desirable to avoid inconsistent second-stage estimates, and we have extended our list of first-stage regressors in hopes of increasing the efficiency of our instruments relative to what would emerge from an unmodified two-stage least squares procedure, The use of actual values instead of instruments for i, ig; k and k, could further increase the efficiency of the second-stage estimates, but in view of the high zR measures associated with our first-stage results the

gain in efficiency would not be sufficient to warrant (under our

subjective preferences) the inconsistency that would be implied

- 25 -

by using the actual values of i, ig, k and Kg: All this is not to deny, however, that a more complete model of the monetary sector might result in more efficient instruments than those

provided by the first-stage results reported here.

9, The Second-Stage Results

The second-stage problem is to choose the ay and by parameters (for j=1,...,4) to minimize a sum of squared errors defined as 2 2 (19) fBerror =f (x - RHS (16)) t t t t t where x, is the exchange rate observed at the end of month t

and RHS,(16) is the value at the end of month t of the right-hand side of

equation (16), after substituting (15) for r® and first-stage fitted values (instrumental variables) for i, ig, k and k:

We have the following priors about the ay parameters ~--

i,e,, about the portfolio shares that market participants would choose

if they perceived a zero expected differential yield

between dollar-denominated and foreign-currency denominated bonds (i.e., when r°=0):

(20a) ay = 0 to .3 i.e., private U.S. residents would denominate 70 to 100 per cent of their interest-bearing portfolios in dollars

(20b) ay =0 to .3 i.e., private German residents would denominate 0 to 30 per cent of their interest-bearing portfolios in dollars

(20c) a3 ™ .5 to .8 i.e., residents of OPEC would denominate 50 to 80 per cent of their portfolios in dollars

(20d) a, = .15 to .45 i.e., residents of ROW would denominate 15 to 45 per cent of their portfolios in dollars

- 26 «~

The b, parameters describe how these shares change as r© moves away

from zero. Our priors are that all four groups of wealth holders

change their portfolio shares in the same preportion as r® changes (20e) b, = va; for j=1,...,4

where 13 /

(20f) v=Otol In the results reported below we impose (20e) as a constraint and

14/ estimate the five parameters a a,» a3, a, and vi

13/ Conditions (9b), (11), (12) and (13) assume that portfolio shares W/L e

vary in proportion to Vr rather than r~. Ex post differential yields during our sample period frequently turned out to be .02 to .04 per month (in absolute value), or to have cube roots in the range .27 to -34. To the extent that differential yields were expected to be in this range ex ante, our priors are that wealth holders would not have chosen dollar holdings that differed by more than 27 to 34 per cent from the levels they wuld desire at an expected differential yield of zero, Hence we expect vs 1.

14/ The initial value of We ova is also estimated (recall section 5) to equal that value for which the numerator of the right-hand side of condition (15) has a zero mean during the sample period. (The estimate ofthis initial value is adjusted after each iteration to be consistent with changing estimates of the a; parameters.) This procedure is almost equivalent to assuming that r® has a zero mean during

the sample period, although it ignores an upward trend in the denominator of the right-hand side of condition (15).

- 27 -

The minimand in our least-squares problem is a nonlinear. function of the parameters to be estimated, and when we give no 15/ weight to our priors our estimates are nonsense. § Accordingly

we adopt a modified Bayesian approach of asking the computer

to minimize each of two alternative loss functions:

(215 error t

2 _ _

) + )O if p,-m,<p, <ptm, for all

‘ Pym SPM 4 and ® otherwise

T 9 5 _ (22) g (error) + gt/5 2 ((p,-p,)/m y? +1 t jar. J J

Here the Py represent the five parameters a aos ay, ays and v3; the p j represent our "point priors" for the p 3? which we set equal to the

midpoints of the ranges (20a) - (20d) and (20f); the m in the "flat priors" case with minimand (21) define ranges for the Py within which we attach no loss to whatever parameter estimates emerge, but outside of which we attach an infinite loss; and g is a prespecified positive weight which, under minimand (22), imposes a loss pro-

portional to the eum of the squared percentage nomalized deviations

16/ between the estimated P; and our point priors.

j8/ Specifically, each of the five parameter estimates exceeds one million in absolute value for this case.

16/ Under minimand (22) the m, are set equal to the half widths of the ranges (20a)-(20d) and (266), thereby providing ~- ‘ normalized measures of the deviations between the p, and P .

Given the scale factor T/5 (the number of months divided by

the number of parameters), an average absolute error of one cent per mark conveys the same loss as an average absolute normalized difference of 100/Vg per cent between the estimated parameter values and our point priors.

- 28 -

For the case of flat priors, using minimand (21) and several alternative specifications of the ms, our iterative procedure only converged to solutions consistent with rational expectations when we constrained the parameters within relatively narrow bounds. In these convergent cases the estimated parameters all took boundary values and reflected local minima that were inferior to the interior solutions generated for the case of pointed priors. +

For the case of pointed: priors, using minimand (22), the procedure converged for values of gel. Results for g=1, 36 and 10,000 are shown in Tables 2-4, (Our choice of these particular values, and their translation, will be discussed below.) The first column of Table 2 shows the observed path of the exchange rate between May 1973 and June 1977. Columns 2-4 show the corresponding one-monthahead predictions that the model generates (with g=1,36 and 10,000 respectively) between April 1973 and May 1977 -- that is, the fitted values of the future spot rates that the model expected (one month ahead) to prevail between May 1973 and June 1977. It is noteworthy that fluctuations in the exchange rates that the model

expects have lower amplitudes than fluctuations in observed

17/ We tried four alternative specifications of flat priors, in each case constraining v to lie between 0 and 1 and alternatively allowing each of the a; to deviate from our point priors by an absolute value no greater than m.05, .1, .15 or .3. The model convergedto a boundary solution, but not a global interior minimun, for m=.05 and .1. The model failed to converge for m=.15 and .3.

May

1973

1974

1975

1976

1977

- 28a -

Table 2: (cents per mark)

Observed and Predicted Exchange Rate Levels

Lagged Observed Model Predictions Forward Spot Rate g=l g=36 g=1000 Rate XWPPP XCPPP EXWPPP EXCPPP 36.20 37.8] 40.19 40.25 35.38 36262 37-61 37-47 37.52 41.15 39223 40.92 40.34 36.34 37-18 37.61 38.03 37.57 435047 40037. 40292 41.02. 4428 .. 37073 37262 36074 37-60 40.63 41.20 40.90 40.99 43.254 36.93 37.61 40.22 38.86 41-4. 41.96 40.98 40091 40073 38697 38429. 37073. 38225. 41.19 42 264 41.09 41.00 41.63 38.25 38.37 37-11 38.19 38.12 42.96 41-09 41.01 41-30 | 37.75 38439 36238 37-89 37.201 43.00 40.97 40.90 37.98 37.46 38.19 39.41 38.213 _ 4026 ° ° -10 31.229 38-14 37.62 42.76 40.18 40.28 35.15 38.00 38.18 38.07 38.49 39048 420683 40603 40220 (37656 37273 38233 37288 38-93 40.46 42.87 39.89 40.11 39.47 37.72 38.64 37.87 38.46 39034 42.85 39-79 40605 40057 37.69 38-64 38-09 38.88 39.25 42.266 39-63 39.292 39-44 37.90 38.83 37.75 39.16 3 3 42.60. 39.66 39.94 39.36 38.01 39.04 39.78 39-24% 37.56 42244 39.76 39.98 39.20 39.03 39-24 41.38 39.87 37.63 41.89 39-83 39.99 37.69 40.25 39.69 39 244 £0.16 | 38.36 41.44 40.02 40.08 37.71 40.08 40.04 40.231 39.99 (40044 40.89 40.18 49-19 38.89 40.43 40.16 41.15 40.03

40-17 4 42.174 39.248 40.38 40.35 41.43 40.71 40.38 39.22 39.78 43.91 39.06 40.39 40.36 42.73 40.29 40.19 40.31 40.29 42.65 39.18 40.47 40.46 43.95 40.15 40.26 39 63 40.16 | 41.95 39.00 40.53 40.57 42.172 39.96 40.23 40.39 39.98 42.67 38.81 40.57 40.65 42-00 40.15 40.14 40.64 40.04 42.52 38.79 40.61 40.73 42.71 40.38 40.07 40.57 40.18 40264 40679 42-58 40650 40.10 41-32 40.96 38.74 38.82 40-68 40.86 39.66 40.93 40.53 41.3% 40.72 37252 38285 40.75 %0.96 38.85 41.14 40.71 41.17 40.45 39.10 38.79 40.79 41.01 37.61 41.25 40.70 41.58 40.91 _38.09 38.87 40.86 41.11 39.19 41.50 40.83 41.19 %0.98 38.30 38.87 40.89 41.15 38.18 41.36 40.96 41.24 40.87 9 41.20 38.36 41.39 41.01 40 .94 40.46 38.93 38.97 40.97 41.238 38.68 41.19 40.78 40.86 40.45 39218 39014 41.08 41-41 38.99 40.92 40.58 40.69 40.56 39-43 392.24 41015 41248 39.25 40.82 40.54 41.13 40.37 38.57 39.30 41.23 41.55 39.250 40.85 40.45 40.94 40.73 38.80 39.35 41234 41.62 38.65 40.82 40.54 41.10 40.77 39.33 39.40 41.4] 41.68 38.85 40.99 40.64 41.20 41.43 39.61 39.44 41.47 41.71 39.38 41.06 41.06 40.68 40.92 40.40 39.52 41-654 41.78 39-66 40.84 41.10 40.98 41.35 41.67 39.53 41.57 41.81 40.44 40.97 41.27 41.22 41.36 (41.56 39655 41.61 41.85 41.71 41.06 41.41 41.34 41.30 42.37 39.51 41.63 41.84 41.56 41.23 41.44 41.66 41.15 41.14 39.78 41.73 41.93 42.31 41.57 41.35 41.32 41.07 41.77 40.09 41.81 41.98 41.15 41.42 41.21 42.10 41.62 (41.82 405016 41289 42.05 41.78 41.14 41.38 42.22 41.58 42.48 40.45 41.98 42.11 41.82 42.04 41.49 42.84 41.64 42.41 40.68 42.07 42.18 42.49 42.39 41.62 42.42 41.67 42245 42.22 42.29 42.45 42.56 41.68 42.12

June

41-16

41.76

- 29 -

exchange rates. This relatively smooth nature of our particular description of expected exchange rates may be related to the time-series processes that we use to generate expected future values of our exogenous variables. To the extent that more realistic processes would generate more volatility in expected time paths of asset supplies and other exogenous variables,

the expected time path of the exchange rate might also be

more volatile.

Column 1 of Table 3 shows the month-to-month changes in the observed exchange rate, starting with the change between April and May 1973 and ending with the change between May and June 1977. Columns 2-4 show the corresponding changes expected by the model (under g=1,36 and 10,000 respectively) -- namely, the differences between columns 2-4 of Table 2 and the exchange-

rate path observed between April 1973 and May 1977.

- 29a - Table 3: Observed and Predicted Exchange Rate Changes

(cents per mark)

Model Predictions Forward Observed Rate Change gal g=36 g=1000 Change XWPPP XCPPP EXWPPP EXCPPP 4.95 3-03 4.72 4.14 214 98 1.41 1.83 1.37 = = = 3 73242. -3253 —-4%e41l —3-55 . -2-84 -2.27 -2.-57 -2.48 OT —-6.54 -5.86 —-3.25 -4.61 eSB 1.33. 035-28 #210 -1.66 -2.34 -2.90 -2.38 _7300T 177 ~el10 --18 ell 32644 -2.389 -4-81 —-3.39 -1.11 4.88 2.85 2-78 —-.14 -.66 207 1.29 eOl 1.80 5.90 32065 3.65 -.06_. _ 283 1.09 28 1.13 2-41 T7255 4-97 5.07 -.06 2.79 2.97 2.86 3.28 ___1.486 5.21 2-41 2-58 -.06 ell = e7l = =e 26-1 31 098 3039 41 63 -.01 -1.76 —-84 -1.-61 -1.02 = 039 ~2e67T -.41 211. H22TT = 1282 22037 2098 OT 4.33 2-27 2.43 213. 2-69 2.13 1-88 2-60 1.23 3281 2-39 2045 -08 2-45 2241 2.68 2-36 1.58 2-03 Le 32 1.33 = -: 9. 1.57 1.30 2.29 te 4’ = —.98 = 6 ~e “fe ~ie --70 -3-65 -2-e12 ~2.08 07 -2.69 -2. 342, 2.26 -2.67 2 -3.14 -1.38 -1.30 .05. 1.80 -1.81 -1.31 -1.91 -e15 -3.97 -2.06 -1.9% 004 —2.29 -2.60 -2.10 —-2.49 1975 —=229 —3275 -1.88 —-1.73 206 -2.02 -2.42 -1.20 -—1.56 —. 86 -.178 1.08 1.26 -06 1.33 93 1.74 1.12 1.58 1.27 3-27 3-49 -09 3.73 3.18 he 06 3.39 21 2178 2-80 3-06 09 3027 2-87 3. 15 2-78 30 34 2.34 2.65 205 2-56 2-15 2.23 1.82 225 _e2] 2015 2048 .06. 1299 1665 1676 1263 025 06 1.97 2.30 -O7 1.64. 1.36 1.95 1.19 | 1976 -.86 -.13 1.80 2012 .O7 4042-1602 «1651 =: 223 78 2eTT 3.05 -08 2225 1.97 2253 2.20 253 260 2061 2.88 .05_ 2.19 1.84 2.40 2.63. 79 --.09 14932617 05 1623, 1049 12371674 1.27 -.387 1.17 1.41 204 057 87 282 296 ell _=2212 _=2J6 _ 018 208 _ ve6h | 026 e033 eT __-.07_-1. 80 -e4l --30 .9O1 209 -.86 --06 81

June 005 1025 3-0 1D 04 e15 -.730 0 -e29 2 = 6 65

- 30 -

Columns 1-3 of Table 4 show the estimated values of the model parameters, the coefficients of correlation between the model's predictions and the actual observations of both exchangerate levels and changes, and the percentages of exchange-rate changes whose direction (sign) the model predicts correctly.

The results are quite insensitive to whether in the first iteration we specify the expected future spot rate as the forward rate or as the observed (perfect-foresight) future spot rate. (Tables

2-4 present results that correspond to the forward-rate setting.)

Recalling the discussion of minimand (22), it should be noted

that under the values g=1,36 and 10,000 respectively, an average absolute

difference of one cent per mark between observed and fitted exchange rates

conveys the same loss as average absolute normalized differences of 100 per

cent, 16-2/3 per cent and 1 per cent between the estimated parameter values

and our point priors, As g is reduced below 1 the estimated parameter values become more and more inconsistent with our priors

and the iterative procedure tends to converge very slowly. The

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- 31 -

value g=10,000 essentially imposes our point priors on the model. The value g=36 produced the best goodness-of-fit statistics out of a halfdozen specifications on a grid between 1 and 100, The parameter estimates, goodness-of-fit statistics and fitted exchange-rate paths varied smoothly as g was moved over this grid,

Table 4 indicates that our model does not yield high correlation coefficients by conventional standards, Nevertheless our results are slightly better than the predictions of several other popular models, One-month-ahead predictions based on 30-day forward rates are more highly correlated than our model's predictions with observed exchange rate levels. But the forward rate does miserably in predicting exchange rate changes, as indicated (a) by the goodness-offit statistics, (b) by infering from Table 3 that the forward rate predicts only small changes and therefore is always surprised by large changes, and (c) by discerning from Table 2 that the forward rate misses all the turning points,

The last four columns of Tables 2-4 refer to the exchange rate predictions consistent with alternative views of purchasingpower parity (PPP). XWPPP is a ratio of wholesale price indexes, scaled to be as favorable as possible to PPP, and prevailing onemonth in advance of the date for which the exchange-rate is being predicted; XCPPP is a similar ratio of consumer price indexes, EXWPPP is a one-month-ahead forecast based on a simple time-series

regression of XWPPP on six-lagged values of itself (representing

- 32 -

one to six-month lags); and EXCPPP is a similar forecast based on the time-series behavior of XCPPP, Thus EXWPPP and EXCPPP are constructed by the same procedure that we use to generate expected future values of the exogenous variables in our model.

Table 4 reveals that our model predicts only slightly better than the PPP models of equilibrium exchange-rate paths, Thus our particular empirical results should not be applauded too loudly, since PPP has been discredited as a hypothesis about the short-run behavior of exchange rates, We are quite encouraged, however, by the fact that we have found a procedure that is capable of providing estimates of the exchange-rate path consistent with both portfolio equilibrium and rational expectations, And we are hopeful that several refinements of our model will lead both to better second-stage goodness-of-fit statistics and to first-stage results that allow significant estimates of the impacts that various policy changes have on the path of exchange rates. 10. Conclusions

Our empirical results have demonstrated that exchange-rate behavior conforms suitably to the predictions of a portfolio-balance model with rational expectations, The retention of wealth variables in our empirical specification, the incorporation of rational expectations, and an explicit allowance for risk aversion represent important features that distinguish our exchange-rate model from others cited

in this paper,

- 33-

Our results nevertheless suggest several directions in which it would be interesting to extend the model before applying it to forecasting. The shortcomings of our first-stage results Suggest the desirability of extending the model to include at least a small-scale specification of the monetary sector, following the spirit of Artus (1976), since the model in its present state cannot provide sensible estimates of the impacts that policy actions have on interest rates and exchange rates. To the extent that policy-reaction functions are believed to be systematic or welldefined, they could in theory be easily incorporated into the model,

It would also be particularly interesting to explore more sophisticated specifications of the processes that are assumed to generate expectations of future asset stocks, wealths and incomes. Without a full model of the entire economy we cannot generate these expectations rationally, but by basing them on more relevant information than simple time-series behavior we may be able to attribute more of the variance in observed exchange rates to the variance in the exchange-rate levels consistent with portfolio

equilibrium.

- 34 -

11. Data Appendix

Exchange rates and interest rates are observed on the last Friday of each month (and for holiday Fridays, on the last previous day that markets were open). Spot exchange rates represent noon buying rates in New York, from Federal Reserve data.. Interest rates are l-month Eurodollar and Euromark bid rates in London as reported by Reuters (through September 1976) and various issues of Money Manager (beginning in October 1976). To avoid possible inconsistencies resulting from differences of several hours in the times that spot exchange rates and interest rates are observed, forward exchange rates are constructed to satisfy the interest-rate parity condition, Given that our interest rates reflect Eurocurrency

18:/ yields, the legitimacy of this procedure is well established.

End-of-month data on U.S. base money are from the Federal Reserve Board data bank, seasonally adjusted and also adjusted for reserve requirements, Data on German base money, seasonally adjusted, are from Bundesbank publications and are also adjusted for reserve requirements, Monthly budget deficits are measured as changes in public borrowings by the U.S. and German Federal Governments, from the Federal Reserve data bank and Bundesbank publications, We seasonally adjusted these deficits ourselves

using the Census X-11 program.

187 See Herring and Marston (1976).

-35-

Monthly data on U.S, and German current-account balances (in dollars and marks, respectively) are constructed from seasonallyadjusted quarterly current-account data by starting with seasonallyadjusted monthly data on merchandise trade balances and adding to each monthly trade balance one-third of the difference between the current-account and trade balances for the corresponding quarter, Monthly data on OPEC's current-account balances (in dollars) are based on internal Federal Reserve Board estimates (as of January 1978) of OPEC's annual current-account surpluses between 1973 and 1977; we assumed that each of these estimated annual surpluses was uniformly distributed over the months in the corresponding year, Monthly data on the current-account balances of ROW (in dollars) are constructed to be equal and opposite-in-sign to the sum of the estimated current-account balances of the United States, Germany and OPEC, after converting the German data into dollars at end-of-month exchange rates.

The construction of wealth variables is largely described in section 5 and footnote 14 of the text. The initial value of U.S. wealth (as of end-of-February 1973) is specified as $422,35 billion, which equals net Federal government debt (other than to the Federal Reserve System) plus total liabilities of the Federal Reserve System minus net U.S, liabilities to foreigners. The

initial value of net Federal debt, $387.49 billion, is also

-~ 36-

assumed to represent the initial supply of outside dollar-denominated bonds. (Sources are the Federal Reserve Board's Annual Statistical Digest: 1971-1975 and the April 1973 Federal Reserve Bulletin.)

We estimated the initial value of German wealth (as of end-of-February 1973) to be DM 205.83 billion, reflecting DM 147.36 billion of net Federal government debt (based on published Bundesbank statistics) and DM 82.9 billionof interest-bearing claims on foreigners (based on data from the Bundesbank Monthly Report for November 1974), We equated the initial value of the stock of outside mark-denominated interest-bearing debt to DM 48.36 billion, the net Federal debt minus the initial German monetary base,

Monthly data on U.S, and German income levels (in dollars and marks respectively) are based on quarterly seasonal ly-adjusted GNP data, The middle month of each quarter was assumed to have the same GNP (at an annual rate) as the quarter as a whole, and GNP levels for other months were based on linear interpolations between the mid-quarter months,

Our purchasing-power parity indexes are based on the U.S. wholesale price index for all commodities, the German producers price index for industrial production for the home market (excluding the tax on value added), the U.S, consumer price index, and the German CPI cost of living

index. These price data are not seasonally adjusted,

- 37 -

References

Armington, Paul, "Exchange Rates: the Model, the Evidence, and the Outlook," paper presented at the Wharton EFA Second World Outlook Conference, January 1978.

Artus, Jacques, R., "Exchange Rate Stability and Managed Floating: The Experience of the Federal Republic of Germany,"

IMF Staff Papers, 23, July 1976.

Berner, Richard, Peter Clark, Ernesto Hernandez-Cata, Howard Howe, Sung Kwack and Guy Stevens, "A Multi-Country Model of the International Influences on the U.S. Economy: Preliminary Results," International Finance Division Discussion Paper No. 115, Washington, Federal Reserve Board, December 1977.

Bilson, John F.0., "The Monetary Approach to the Exchange Rate: Some Empiricial Evidence," IMF Staff Papers, 25, March 1978.

Branson, William H., "Asset Markets and Relative Prices in Exchange Rate Determination," Seminar Paper No. 66, Stockholm, Institute for International Economic Studies, December 1976.

, Hannu Halttunen and Paul Masson, "Exchange Rates in the Short Run: The Dollar Deutschemark Rate," European Economic Review, 10, 1977.

Dornbusch, Rudiger, "Expectations and Exchange Rate Dynamics," Journal of Political Economy, 84, December 1976.

Frenkel, Jacob A., "A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence," Scandinavian Journal of Economics,78 (No. 2), 1976.

Girton, Lance. and Dale W. Henderson "Central Bank Operations in Foreign and Domestic Assets Under Fixed and Flexible Exchange Rates," in Peter B. Clark, Dennis E. Logue, and Richard James Sweeney, eds., The Effects of Exchange Rate Adjustments, U.S. Government Printing Office, Washington, D.C. 1977.

Girton, Lance and Don Roper, "A Monetary Model of Exchange Market Pressure Applied to the Post-War Canadian Experience,” American Economic Review, 67, September 1977.

- 38 -

Herring, Richard J. and Richard C. Marston, "The Forward Market and Interest Rates in the Eurocurrency and National Money Markets" in Carl H. Stem, John H. Makin, and Dennis E. Logue, eds., Furocurrencies and the International Monetary System, Washington, American Enterprise Institute for Public Policy Research, 1976.

Kouri, Pentti J.K., "The Exchange Rate and the Balance of Payments in the Short Run and in the Long Run: A Monetary Approach", Scandinavian Journal of Economics 78 (No. 2), 1976.

,» and Jorge Braga de Macedo, "Exchange Rates and the International Adjustment Process," Brookings Papers on Economic

Activity (No. 1), 1978.

Porter, Michael G., "Asset Markets and the Behavior of Exchange Rates - Some Preliminary Results," paper prepared for the Sixth Conference of the Economic Society of Australia and New Zealand, May 1977.