-19-

next section, such ambiguity can lead to significant problems in
simulation exercises. Moreover, international capital flows may not
capture total changes in holdings of foreign currency, since home
residents can hold foreign currency bonds issued at home LL/ In brief,
when the currency denomination assumption does not hold, the link between
capital flows and exchange market pressure is broken.

Available data suggest that the assumption is violated
significantly in some cases. As indicated in Table 2, nearly 75 percent
of Germany's private claims on foreigners are denominated in marks, while
nearly 40 percent of its liabilities to foreigners are denominated in
currencies other than marks. Other data indicate that well over 80
percent of U.S. private claims on foreigners are denominated in
dolars.22/

This evidence alone does significant damage, but the estimation
of separate capital account equations for changes in claims on foreigners
and liabilities to foreigners faces yet another problem. In many cases
it is not realistic to assume that these gross flows as recorded in the
balance of payments accounts are independent of each other. Banks and
corporations are both the major holders of claims and issuers of
liabilities and the two sides of the same institution's balance sheet are
likely to be interrelated. For example, the rapid growth of U.S. bank
loans to nonoil LDC's after 1973 was related to the inflow of OPEC
deposits. Another example is the frequent booking of loans by hanks to
residents of the same country at their offshore offices, which inflates
both capital inflows and outflows. Such transactions, termed "round
tripping", are generally influenced by institutional factors that are not

readily quantifiable.


-40-

Definitions
CDUM Canadian Political Dummy Variable
CUMBB Cumulated Canadian Basic Balance
CER Canadian Dollar Exchange Rate
CNETPK Canadian Stock of Net Short Term Private Liabilities To
Foreigners
CNW Canadian Wealth (Net Worth)
CRS Canadian Short Term (3 month) Interest Rate

ECUMBBAL UK Cumulative Current Account Balance

EDNETPK Change in Net UK Private Liabilities To Foreigners
EER Dollar/UK Pound Exchange Rate
EERFW Weighted Average Yen Exchange Rate, Using FRB Multilateral

Trade Weights
= (BER*23 . (EER/CER)*°9 . (EER/JER)*14 . (EER/JER)*25)1-492

EFINFFW Expected Foreign Inflation Rate, (UK Model), One Quarter
Ahead, Based on Fixed FRB Trade Weights

“

(EFPFW1/EFPFW1_4 - 1) . 100

EFPFW UK Weighted Average Price Level, Based on FRB Multilateral
Trade Weights

(up+23 , cp+99 , gp+21 , gps 14)1.492
EFPFW1 Expected Value of EFPFW One Quarter Ahead
= -0.001 + 1.554 EFPFW - 9.162 EFPFW_y + -9.40EFPFW_ 5
- 0.027 EFPFW_3 - 0.184 EFPFW_, + 9.224 EFPFW_.

EFRSFW Foreign Short Term Interest Rate (UK model), Based on
Multilateral FRB Trade Weio'’s


-36-

Pp _ pP*

+ (Boe - Fg )

Finally, we add and subtract from the right-hand-side of (A.3') each of

the following terms: FR home private holdings of foreign currency bonds
issued by the home government, Fe, home government holdings of foreign
currency bonds issued by home residents, and Bh and Bees the analogous

terms for foreigners. Rearranging again, yields:

" _ ogP P PP OG
A.3" NETCF = (Foy + Fox + Fg - Fp ~ Fp)
pe Pe pk PG
- (Bp + By + Boy - Box - Box)
P | ape a
+ [(Bge + Box) - (Fa + Fg) - Boe + Fp |

The first group of terms on the right-hand side of (A.3") can be
modeled as the total home private demand for foreign currency bonds minus
the home private supply of foreign currency bonds. (Note that foreign
currency bonds both issued and held by the home private sector, FP
cancel out and do not appear in this net demand expression.) This net
demand varies positively with the foreign interest rate and negatively
with the home interest rate and expected appreciation of the home
currency. The second group of terms on the right hand side of (A.3")
equals the net foreign private demand for home currency bonds, which
varies in just the opposite direction with the rate of return variables.
Since foreign net demand enters negatively into the equation, however, no

ambiguity with respect to signs on rates of return arises between the

first two groups.


is net private demand for home currency bonds (B), and SBg is equal to D
-L+FYS.

5/ This assumes that the government deficit is financed by bonds and
high powered money, and abstracts from changes in government liquid
assets (deposits at banks, etc.).

6/ Capital gains are limited to foreign exchange gains or losses. For
simplicity bonds are measured at nominal values rather than market
prices.

7/ This model abstracts from private fixed capital, which can affect the
results to the extent that private equities are substitutable for
government bonds in private portfolios. This abstraction is generally
adopted in empirical applications, due to the absence of data on rates of
return on private fixed capital (equities).

8/ To show that the balance of payments identity is not a necessary
equilibrium condition but an ex-post identity that holds by definition
when all markets are in equilibrium, we need only derive that identity
from the other equations in the model. This is done as follows: First,

substitute equation (12a) into the first difference of (13a) for AW, to
obtain the home private sector's budget constraint:

(F.5) PY-T-C+Z = AR+AF/S+ AL +Z

(Note that A(F/S) = AF/S + Z, where Z is limited to foreign exchange
gains or losses). Second, solve the first difference of the bond market
equilibrium condition (2a) for AL, and substitute the result into (F.5):

*
(F.6) AaB + AF/S + D + AFS/S ~ aB - aBY - AB +Z=PY-T-C+#Z

Next, substitute into (F.6) both the right hand side of (11a) for D and
the solution for PY obtained in the goods market equilibrium condition

(la), yielding:

(F.7) AB + AF/S + G@ - T + AFS/S ~ aB - Bt - ABO + Z= C+

- M/S + X¥-T-C+Z
which collapses to

(F.8)  AF/S + AFS/S - Be - ABS* = -M/S + X*


-13-

holder.2/ The wealth constraint is imposed on the asset demand equations
in estimation to ensure consistency between private savings and asset
accumulations in the model.

Of the six market equilibrium conditions in the model (la -
3b), five are independent (by Walras' law). The five independent markets
determine five market prices: P, P*, R, R* and the spot exchange rate,
S. When the sixth market is dropped two behavioral equations identifying
home and foreign demands in that market are dropped along with the market
equilibrium condition. Those two demands are still identified, however,
given the wealth constraints (13a) and (13b). The remaining 15
endogenous variables in the model: C, C*, M, X*, F, B*, L, L*, s°, Wy
W*, T, T*, D and D*, are identified by the remaining 15 equations
included in (4a) -(12b).

The balance of payments conditions (14a and 14b) are
satisfied, ex-post, when all markets are in equilibrium. That is, when
the goods, bonds and money markets are in equilibrium, the net flow of
goods and assets, both private and official, must sum to zero. Hence,
the balance of payments holds implicitly and is not needed explicitly to
identify any variables in the model A! (Note that one of the two balance
of payments equations is redundant in any case.) As we shall see,
however, under some of the approaches considered below, the balance of

payments plays a more central role as an ex-ante equilibrium condition.

Structural Balance of Payments

As shown by Stevens (1976), the balance of payments equation
can be substituted as an ex-ante equilibrium condition for any of the
other equilibrium conditions in the model. When this substitution is

made, two markets are dropped from the model, one by Walras' law and the


-23-

across bonds issued in different currencies, and to net privately issued
home currency bonds against home holdings of home currency bonds issued
in other countries.

Our experience with the various approaches to exchange rate and
capital flow determination in working with the MCM is summarized in the

next three sections.

IV. Exchange Rate and Capital Flow Determination in the Early Version
of the MCM.

As discussed in the previous section, the original version of
the MCM employed the structural balance of payments approach. The V.S.
bond market was dropped by Walras' law, and in each of the other country
models the balance of payments equation was substituted for the domestic
bond market. In each case, equations for nondirect capital flows
generally were disaggregated by short term and long term claims and
liabilities of the bank and nonbank sectors. Direct investment flows
were modeled separately. Official capital flows were identified in most
cases by intervention reaction functions (which performed a smoothing
role) 22/ The exchange rate was identified implicitly -- it essentially
adjusted to clear the balance of payments.

The nondirect capital flow equations were derived as first
differences of the following stock-demand functional forms for claims and

liabilities:


-41-
= 0.343 URS + 0.134 CRS + 0.313 GRS + 0.21 JRS
EINF Expected UK Inflation Rate, One Quarter Ahead
= (EP1/EP1_4 - 1).100

EP UK Absorption (Total Expenditure) Deflator
EP1 Expected Value of EP, One Quarter Ahead

= = 0,01 + 1.36 EP - 0.476 EP_, + 1.379 EP_p + 0.196 EP_s
- 0.875 EP_g + 0.438 EP_s

ERS Short Term (3 month) UK Interest Rate

GCCURAB Cumulative German Current Account Balance

GDNETPK Change in Net German Private Liabilities To Foreigners

GER Dollar/Mark Exchange Rate

GERFW Weighted Average DM Exchange Rate, using FRB Multilateral
Trade Weights

(GER*25 . (GER/CER)*°9 . (GER/EER)*12 . (GER/JER)*4)1+72

GFINFFW Expected Weighted Average Foreign Inflation Rate, German
Model ~*

= ((GFPFW1/GFPFW1_,) - 1) + 100

GFPFW Expected Foreign Price Level (German Model), Based on Fixed
FRB Trade Weights

(up+23 , cp-09 , epel2 , gpeldy 1.724

GFPFW1

Expected Value of GFPFW, One Quarter Ahead

- 0,002 + 1.647 GFPFW - 0.542 GFPFW_, + 9.005 GFPFW_»


-4

The present paper serves two purposes. The first is to outline
the theoretical basis for alternative approaches to exchange rate
determination in a general-equilibrium multicountry model and to describe
the empirical considerations that impinge upon the selection among
alternative approaches. The second is to document the current process of
exchange rate and capital flow determination in the MCM, while relating
it to the previous version of the model as well as to further
developmental work currently in progress.

The paper is organized as follows. Section II presents a brief
overview of the MCM for those not familiar with its structure. Section
III outlines the theoretical basis for three alternative approaches to
exchange rate determination: the structural balance of payments approach
(employed in the early version of the MCM), the net private capital or
inverted capital account approach (used in the current MCM), and the bond
market approach (which is the focus of our current research). This
section establishes that all three approaches are theoretically
consistent in that they can be derived from a common general equilibrium
portfolio balance model. It also considers some of the empirical factors
that have led us to select one approach over another. Section IV then
summarizes our experience with the structural balance of payments
approach in the early version of the MCM. Section V and Appendix B
document the current version. Our conclusions and a brief description of

work currently in progress are presented in Section VI.

II. Overview of the Multicountry Model
The Multicountry Model is a large-scale econometric model

developed by the staff of the Division of International Finance at the


=34-

Subscripts denote the sector issuing the bond and superscripts the sector
holding the bond; "*" denotes foreign sectors; absence of “*" denotes
home sectors. For convenience, foreign currency bonds (F) as well as
home currency bonds are valued in home currency units. Note that each
sector's holdings of bonds issued by itself net out; also we abstract
from government holdings of own-currency private bonds, which do not
affect the results discussed below.

Home private claims on foreigners (CF) and home liabilities to
private forigners (LF), as defined in the balance of payments accounts,

are written:

Private claims on foreigners

A.l CFp = Foy + FR

>. oP
p= Fox + Fox + Box + Bex

Liabilities to private foreigners

When separate demand functions for LF, and CF, are estimated
the signs of the rate of return variables are ambiguous because demand
for bonds denominated in different currencies are mixed together. To
show how modeling net claims minus liabilities can avoid this ambiguity,
the terms in equations A.1 and A.2 must be rearranged and supply
functions must be used instead of demand functions for certain
components. This substitution is permissible if markets are assumed in

equilibrium: quantity supplied will equal quantity demanded.


-20-

Table 2

Currency Denomination of German Foreign Claims & Liabilities
(Stock at end of 1980, billions of DM)

Denominated in

Claims on Foreigners
Short Term Bonds
Long Term Bonds
Short Term Domestic Enterprises
Long Term Domestic Enterprises
Credit Terms & Advance Payments

Total Claims

Liabilities to Foreigners
Short Term Bonds
Long Term Bonds
Short Term Domestic Enterprises
Long Term Domestic Enterprises

Credit Terms & Advances Payments

DM Other Currencies
28.7 29.2
90.3 7.5

6.6 6.1
4.7 4.2
68.3 25.3

198.6 72.3
43.8 34.1
52.8 11.8
33.1 9.4
15.8 11.2

39.7 25.1
185.2 91.6

Total Liabilities

Source: Statistical Supplement to the Monthly Report of the Deutsche

Bundesbank Series 3 Balance of Payments Statistics lables 7 & 8

December 1980.


~26-

official intervention functions. The Japanese EPA World Economic Model
has employed this technique, as described in Amano et.al. (1981). When
exchange rate changes reach a given value per quarter, official
intervention cuts in to eliminate further change. This solution had the
appeal of stabilizing simulations without having to undertake structural
reforms of the model. However, if the intervention constraint was
binding, exchange rate determination ultimately would be in official
hands, which returns us to a more or less fixed exchange regime. This
might have been a plausible assumption in some cases but to the extent
that the intervention rule masked structural errors in the model, it
would have yielded misleading signals about the amount of intervention
required in the case of particular policy shocks. The second solution,
adopted in the MCM, was to begin to reestimate and restructure certain

parts of the model, as described in the next section.

Vv. Exchange Rate Determination in the Current Version of the MCM.
Revision of the process of exchange rate and capital flow

determination in the early version of the MCM has gone through several
phases. First, an attempt was made simply to update the existing
equations in the model, estimating them over the managed floating rate
period since 1973Q2 (the starting point was somewhat earlier for Canada).
The original equation specifications generally performed poorly over this
period -- signs of key coefficients were often reversed and statistical
significance fell. The second step was to impose a number of constraints
on the gross flow equations. In particular, the components of relative
rates of return were constrained to be the same (with appropriate signs),

the lags on interest rates and the forward premium were dropped, and


-22-

flows as defined in the balance of payments can be derived from the bond
market approach without introducing ambiguity into the coefficients on
relative rates of return. This is shown in Appendix A. By netting
claims against liabilities, this approach, too, solves the problem
concerning institutional factors that cause claims and liabilities to
grow jointly.

While the second, third and fourth solutions all handle the
round-tripping problem (an advantage over the first, which does not),
they also have a drawback. Under these three approaches the stocks of
claims on foreigners and liabilities to foreigners are not identified
separately. These stocks are needed in order to determine investment
income receipts and payments. Some approximation would have to be made
in order to determine these receipts and payments. One possibility is to
model net investment income receipts as a function of net claims. The
costs of doing so might not be significant, since gross receipts and
payments are not required for income determination. In cases where
capital account data disaggregated by currency of denomination are not
available, some approximation of this disaggregation, based on whatever
information is available (intermittent survey data, etc.), would have to
be made.

Finally, in order to net bond supplies against demands, as is
done in the latter three solutions, it must be assumed that bonds
denominated in the same currency are perfect substitutes, even if issued
in different countries. That is, differences in political risk or
default risk across countries are not significant. This may not be too
strong an assumption for the group of major industrial countries included

in the MCM. The assumption allows us to aggregate behavioral equations


-35-

(Note that in principle, the ambiguity of signs on the rate of
return variables in the claims equation (A.1), for example, could be
eliminated by treating that equation as an aggregation of home demand for
foreign currency bonds plus foreign supply of home currency bonds.
However, this specification would require identifying the separate scale
variables for both home country gross demand and foreign country gross
supply. It is unclear which scale variables are appropriate for
determining each gross flows because the scale of assets and liabilities
is interrelated. By contrast, in the net capital account approach
outlined below we can assume that the private net demand (demand minus
supply) of each country for assets denominated in the other country's
currency is a function of its own wealth.)

The net capital account approach involves subtracting (A.2) from

(A.1) to derive an equation for net claims minus liabilities (NETCF):

_ P,P. oP
A.3 NETCF = Fo, + Fox + Box + Bow
p* p* p* p*

- Bl - BE - Fp - Fe

Next, rearranging the right-hand side of A3 into three groups of terms

yields:

\ cP og gP pe
A.3! NETCF = (Foy + Faw - Fp )

pe ge

p*
- (B, + By px)


equations for both home and foreign holdings of home bonds, (6a) and
(7b), must be modeled explicitly. The home bond market equilibrium
condition then serves to determine one of the five market prices
including the exchange rate (hence the label "bond market approach"). In
this approach the balance of payments equation per se does not play a
role in determining the exchange rate or any other market price. It
could not in any case, since one of the components of the capital account
(F/S) is not modeled explicitly. Both F/S and Fare identified
implicitly, however, by the home and foreign wealth constraints so that
the balance of payments identity does hold implicitly.

A simplification of the bond market approach applied to the
above example involves aggregating bond demands to estimate a single
behavioral equation for total domestic and foreign demand for home bonds.
This approach has been outlined by Frankel (1982). (For future reference
we label this the “aggregate bond market approach".) The home and

foreign demand equations, (6a) and (7b), are rewritten:

+ -

- + + - - =
(17) B=.B(R, R's S, S° W, Y, P,P)

+ + - + + - - -
(18) BY = BY (R, RY, S, SW, YY, Py OP)
Aggregation yields:
* Lae ee A ee
(19) B+B =B' (R,R,S,S,W,W, Y, ¥, Ps P )


-9-

(Table 1 continued)

Definitions

Home private holdings of home-currency bonds, net of home private

*
supply of those bonds; B is foreign private holdings of home
*
a is foreign official holdings of home currency

currency bonds; B
bonds.

Private expenditures (consumption)

Government budget deficit

Home private holdings of foreign currency bonds (stock); Fr is
foreign private holdings of foreign currency bonds, net; Fa is home
official holdings of foreign currency bonds

Government expenditures

Stock of high-powered money (currency plus reserves)

Home purchases of foreign goods and services (valued in foreign
currency )

Price of home goods; > = price of foreign goods (in foreign
currency)

Interest rate

Exchange rate, in terms of foreign currency/home currency

Tax receipts (net of transfers)

Private wealth

Foreign purchases of home goods and services (valued in home
currency)

Output (real income)

Capital gains on holdings of foreign assets; Z = Fa(t); 7" = BAS;

G

2% = FSa(h; z*8 = Bas


-32-

Second, several alternatives to the structural balance of
payments approach exist, some of which involve aggregation (such as
estimating net capital flow equations), and some of which involve a more
fundamental restructuring of the underlying model (such as specifying a
domestic bond market explicitly). In cases where capital account data
disaggregated by currency of denomination are not available, interest
income receipts and payments cannot be modeled explictly, and some
approximation must be made in estimation.

Third, work has progressed on the approach of estimating net
capital account equations normalized on the exchange rate. The results
of this work to date, as reflected in the current (interim) version of
the MCM, suggest that shifts in asset supplies (portfolio balance
considerations) do not have a significant, lasting effect on exchange
rates. However, the results are not internally consistent. Whereas
intervention does not have a significant impact on exchange rates,
current account deficits do.

For this reason work is currently underway to pursue some of
the other approaches in this paper. In particular, for countries for
which data are available (Germany and possibly Japan) a disaggregated
bond market approach is being tested. In addition, an aggregate bond
demand equation is being estimated for all of the MCM countries, using
available data on the total outstanding stocks of government bonds.
Other refinements being undertaken include an effort to take into account
changes in the market prices of bonds in calculating bond stocks and
wealths, and further experimentation with exchange rate expectations

equations.


-29-

* *
+ 6, ~ 5, (B= F/S)

Our linear approximation in the rational expectations case is written:

* * *
(27) log S=0 +0, (R-R + S,1) - Op W + 03 W ~ 0, (B

0
- F/S)

S still appears in the last term on the right hand side of (26) and (27)
because net liabilities to foreigners are computed from balance of
payments data in which claims on foreigners are denominated in the home
currency. It can be shown that if home and foreign assets are perfectly
substitutable, the last three terms on the right-hand side of both
equations drop out. (This implies that changes in asset supplies (e.g.,
through intervention) and wealth have no effect on the exchange
rate.28/)

A number of alternative versions of (26) and (27) were
estimated for each country paralleling the alternatives tried for (25) as
discussed above. In addition, two-step two-stage least squares, as
described in Cumby et.al. (1982) was employed in estimation.

The results of this round of estimation for equation (26)
produced the equations that are employed in the current interim version
of the MCM. These equations are reported in Appendix B in the same form
in which they appear in the model. (Nefinitions of variables are given
at the end of the appendix.)

In three of the four countries (except Canada) weighted
averages were used for exchange rates and other foreign data. The

weights are proportional to each country's share of total world trade.


-6-

III. Theoretical Basis for Alternative Approaches to Exchange Rate
and Capital Flow Determination

This section outlines the theoretical basis for the alternative
approaches to the determination of exchange rates and capital flows
embodied in the original, current (revised) and prospective future
versions of the MCM. For convenience, we have labeled the approaches
respectively: 1) the structural balance of payments approach, 2) the net
private capital or inverted capital account approach, and 3) the
structural bond market approach. It is shown that all three approaches
are theoretically consistent in that they can be derived from the same
underlying model. The selection of one approach over another, which has
been governed largely by empirical considerations -- data availability,
etc. -- and the "realism" or plausibility of simplifying restrictions,
is also considered in this section, as well as in following sections.

To describe the three approaches and illustrate their
theoretical consistency, we have written down a two-country model of
markets for goods (and services), bonds (interest bearing financial
assets) and money. The model is presented in Table 1, with definitions
Provided at the end of the table. The model is a simple extension of
small open economy portfolio balance models that have become familiar in
the literature over the past two decades .2/ It serves our purposes as an
abbreviated version of the theoretical structure underlying the MCM. The
major simplifications include: 1) the labor market has been dropped, 2)
total output is held exogenous, 3) private investment is assumed to be
zero, 4) demands are aggregated over a number of components and 5) the
model is reduced from five countries to two countries. None of these

abstractions materially affect the theoretical results drawn below. In


-5-

Federal Reserve Board. It consists of quarterly macro models of five
countries -- Canada, Germany, Japan, the United Kingdom and the United
States -- as well as abbreviated OPEC and rest-of-world sectors.
Particular attention has been paid to international aspects of the model,
but each country model is sufficiently developed to be used individually
as well as fully linked with other countries in the model.

The single country models vary in size from 200 to 300
behavioral equations and identities, each including a domestic goods
market (determining domestic income and expenditure components, potential
output and the price level), a labor market, a money market and a
complete international accounts sector. Within the international
accounts, trade flows are disaggregated by country or region and
commodity (between oi] and other), while service transactions and capital
flows are determined multilaterally.

When the country models are linked together and simulated, economic
impulses are transmitted from one country to another through both goods
markets (via trade flows, prices and exchange rates) and financial
markets (via asset demands or capital flows, interest rates and exchange
rates). Four bilateral exchange rates are determined in the model: the
U.S. dollar rates of the Canadian dollar, pound sterling, Deutschemark
and Japanese yen. In some cases (in the current version) weighted
average or effective rates of a given currency against the other four are
modeled explicitly. Each exchange rate is one of a number of price
variables in the model that simultaneously clear all goods and asset
markets. The process of exchange rate determination is examined in

considerable detail in the following sections.


-18-

This approach has an appeal for cases in which data on the
supply (stock) of government bonds are more readily available than data
on home and foreign private holdings of bonds, which is often the case.
However, by dropping one of the bond demand equations, and removing the
distinction between B and B, F and F* cannot be identified through the
home and foreign wealth constraints. F and B* are still needed to
determine investment income receipts and payments, which enter into
income determination. This can be achieved by adding the balance of
payments equation (to determine changes in the stock of net private
foreign assets A(F-B*)) and a behavioral equation for either B* or F.
While this could still result in significant errors in the predicted
scale of F and B*, the error in the net stock (F-B*) would be limited to
cumulative errors in the prediction of other components of the balance of

Payments, which may be easier to model.

Relaxing the Currency Denomination Assumption.

To this point we have assumed that bonds are denominated only
in the currency of the country in which they are issued. If this
assumption holds, it allows us to employ capital account data from the
balance of payments in estimating equations (7a) and (7b), so that aF/S
is equal to changes in private claims on foreigners and AB” is equal to
changes in liabilities to private foreigners. However, when residents of
one country issue debt denominated in foreign currency the concepts
measured in the balance of payments do not conform to the theoretical
model. In this case claims on foreigners may include home currency bonds
as well as foreign currency bonds, while liabilities to foreigners may
include foreign currency bonds as well as home currency bonds. In bond
demand equations estimated with this data, the expected signs of
coefficients on relative rate of return variables (interest rates and

expected exchange rate changes) become ambiguous 20/ As discussed in the


10.

C.

-8-

(Table 1 continued)

Taxes

a) T= (PY)

Identities

ll.

12.

Government Neficits

a) D=G-T
Wealth Accumulation

a) AW= PY-T-C+#Z

Other Conditions

13.

14,

Wealth Constraints
a) W=B+F/S#L
Balance of Payments
a) xX - M/S +B” - aF/s + aBe

- aF Sys = 0

b)

b)

b)

b)

b)

x o* * *
W=BS+F 4#L

* * G
XS -M+ SAB - AF + SaB

- AF

G

4
1

4
*

~
*

~<
*

=0

*


-24-
Claims on Foreigners
(20) (F;/S)/W = ag - a (L)Rg - ay (L)R, + 03 (L)RE + aq (LYRE
- ag (S° - S)/S = ag (s - 3)/s + ay rar

Liabilities to Foreigners

* * * *
(21) B/W = By + By (L) Re + Bo (L) Rr - 83 (L) Re - By (L) Ry
+8, (8° - S)/S +8, (S* - S)/S +B, NS/W*,

where F; and 8 are disaggregated claims and liabilities, (L) denotes a

lag operator, Ry and R, are short-term and long-term interest rates,

f

L
is the forward exchange rate and other variables are as defined in

Ss
Table 1. The coefficients are included with their expected signs.

In most cases foreign variables were defined as U.S. variables;
in some cases weighted averages of four countries (including the US) were
employed. Homogeneity of responses to changes in the components of the
relative rates of return was not imposed, and separate interest rate
terms were included with lags of up to 10 quarters in some cases. The
import and export variables were included to capture trade credit.
Exchange rate expectations were proxied by relative prices (assuming
expected long run purchasing power parity) and in some cases changes in
official reserves. Note that both the expected change in the exchange

rate and the forward premium were included. The empirical implementation

of these equations varied across countries. In some cases they were


International Finance Disucssion Papers
Number 213

December 1982

ALTERNATIVE APPROACHES TO GENERAL EQUILIBRIUM MONELING OF
EXCHANGE RATES AND CAPITAL FLOWS: THE MCM EXPERIENCE

by

Peter Hooper
Richard D. Haas
Steven A. Symansky
Lois Stekler

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.


-47-

13/ In most cases changes in reserves were expressed as a function of
exchange rate changes and lagged reserves.

14/ Exchange rate and capital flow determination in the original version
‘Of the MCM are described in considerable detail in Stevens et.al.

(1982). See also Stevens et.al. (1980).

15/ With exchange rate expectations relatively sluggish in the model, the
appreciation of the home currency induced an expected depreciation, which
tended to offset the rise in home interest rates.

16/ See Hooper et.al (1981) for details.

17/ See Haas et.al (1980) for a sample of these results.

18/ See Hooper et.al. (1981) or Symansky et.al. (1981).

19/ See, for example, Roley (1980).


-l-

particular, the results obtained for the two-country case can be
generalized for models with more than two countries. However, several
additional underlying assumptions do have a bearing on the results.
First, high powered money (currency plus reserves) is assumed
to be held only in the country of issue. Second, all bonds denominated
in a particular currency are assumed to be perfect substitutes, whether
issued by the private sector or the government. Third, bonds are assumed
to be issued in the currency of the home country only (i.e., residents of
one country do not issue bonds denominated in the currency of another
country). The last assumption is relaxed below, and as we shall see, it
is especially important to selecting among the three modeling approaches.
The model consists of market equilibrium equations for domestic
and foreign goods (equations 1a and 1b), domestic and foreign bonds (2a
and 2b) and domestic and foreign currency (3a and 3b). Demand for goods

(including services) includes private consumption plus government

expenditures, C + G minus demand for foreign goods, M/S, plus foreign
demand for domestic goods, x. The goods market in the foreign country
is symmetrical, expressed in foreign currency (abstracting from c.i.f. -
f.o.b. differentials on trade flows).

In the home bond market equilibrium (2a) home net private
*
demand, B, plus foreign private and government demand, Bt + Bo » is

equated with the outstanding stock of home government bonds. Net private
demand in this case is defined as total private holdings of bonds minus
bonds issued by the private sector.4/ The stock of home government bonds
is given by the cumulative home government deficit plus home government
holdings of foreign currency bonds, minus high powered money minus

cumulative capital gains on government holdings of foreign currency


-10-

Superscript denotes foreign country variable
Superscript denotes expectations

Superscript denotes official holdings
Denotes exogenous variables

Denotes cumulation of flow (stock)

Denotes change in stock (flow)


-43-

= (up-23, cp+09 , Epel2 | gp-21)1-538

OFPWL Expected Value of JFPFW, One Quarter Ahead
- 0.006 + 1.439 JFPFW - 0.202 UFPFW_y - 9.168 JFPFW 5
+ 0.277 JFPFW_ 3 - 0.781 JFPFW_, + 0.448 JFPFW_.

JFRSFW Weighted Average Foreign Short-Term Interest Rate, Using
Multilateral Trade Weights, Japanese Model

= 0.354 URS + 0.138 CRS + 0.185 ERS + .323 GRS

JINF Expected Japanese Inflation Rate, One Quarter Ahead

(JP1/JP1_4 - 1) .100
JP Japanese Absorption (Total Expenditure) Deflator

JPL Expected Value of JP, One Quarter Ahead

0.0048 + 1.901 JP - 1.052 JP_y + 0.385 UP_> - 0.464 JP_,

+ 0,191 JP_g + 0.040 JP_s

URS Japanese Short Term (3 month) Interest Rate
ONW Cumulative OPEC Current Account
UNW US Wealth (Net Worth)

URS US 3 Month CN Interest Rate


~31-

others, In this case net private capital flows would be determined
residually by the balance of payments equation (with perfect
substitutability of assets, any shock to the current account would be
automatically financed by private capital flows).

This view is troublesome for two reasons. First, not only does
the portfolio balance model have a strong theoretical appeal, but it has
also been applied empirically with some success to domestic financial
market's 22/ Second, and of more immediate importance to the present
case, is the significance of cumulative current accounts in determining
exchange rates in the estimated equations. If assets were perfect
substitutes at all horizons (the assumption underlying the monetary
approach), it would be irrational for market participants to expect the
current account to affect the exchange rate. The results shown in the

equations in Appendix B are in this sense contradictory.

VI. Conclusions and Plans for Future Research
We conclude, first, that there are potentially severe

conceptual problems with implementing the structural balance of payments
approach to modeling exchange rates and capital flows. Except in one or
two countries for which requisite data are available, separate equations
for claims and liabilities in the capital account cannot be estimated in
a fashion that is consistent with underlying theory. This conclusion is
based on 1) our experience with such capital account equations in the
early version of the MCM, 2) our assessment of effects of bonds being
issued in more than one currency and 3) the effects of institutional

factors (“round-tripping", etc.) that are difficult to model.


-48-
References

Amano, Akihiro, Akira Sadahiro, and Takahiro Sasaki, “Structure and
Application of the EPA World Economic Model" EPA Discussion paper
#22, August 1981.

Rerner, Richard, Peter Clark, Howard Howe, Sung Kwack and Guy Stevens,
"Modeling the International Influences of the U.S. Economy: A
Multi-Country Approach," FRB, International Finance Discussion
Paper No. 93, November, 1976.

Branson, William H., Financial Capital Flows in the United States Balance
of Payments, Ansterdam: North Holland Publishing Company, 1968.

Bryant, Ralph C. and Patric H. Hendershott, “Financial Capital Flows in
the Balance of Payments of the United States: An Exploratory
Empirical Study," Princeton Studies in International Finance, No.
25, June 1970.

Cumby, R. E., J. Huizinga and M. Obstfeld, "Two-Step Two-Stage Least
Squares in a Model with Rational Expectation," Columbia University
Discussion Paper No. 71, June 1980.

Dooley, Michael P., "A Model of Arbitrage and Short-Term Capital Flows,"
FRB, International Finance Discussion Paper No. 40, January 1974.

Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics". Journal
of Political Economy, Vol. 84 pp. 1161-1176, December 1976.

Fleming, J. Marcus, "Domestic Financial Policies Under Fixed and Under
Floating Exchange Rates," International Monetary Fund Staff Papers,
Vol. 9, No. 3, pp. 369-380, November 1976.

Frankel, Jeffrey A., "On the Mark: A Theory of Floating Exchange Rates
Based on Real Interest Differentials," American Economic Review,
Vol. 69 pp. 610-622, September 1979.

Frankel, Jeffrey A., "Estimation of Monetary and Portfolio-Balance Models
of Exchange Rates," paper written for NBER, Bellugio, Italy,
January 1982,

Haas, Richard and William Alexander, "A Model of Capital Flows and
Exchange Rates: The Canadian Floating Exchange Rate Experience,"
The Journal of Money, Credit and Banking, Vol XI, No. 4, pp. 467-
482, November 1979.

Haas, Richard, Peter Hooper, Richard Meese, Guy Stevens and Ralph Tryon,
“Exchange Rate Determinationin a Multicountry Model," FRB, August
1980.


-30-

The interest rate and expectations variables (relative prices, inflation
rates and cumulative current accounts) generally yielded coefficients
with the expected sign and at least marginal significance. The UK was an
exception; therefore a number of the coefficients were constrained based
on the results obtained for other countries. The long run relative price
coefficient was constrained to 1.0 in all cases (based on theoretical
priors). The cumulative current account term varied across countries.
In the Canadian case the cumulative basic balance was used, and in other
cases the cumulative OPEC current account (weighted by factors equal to
one-half of each country's share in OPEC's imports) was added to the
cumulative current account to adjust for transitory savings in current
accounts due to oi] price shocks.

However, the coefficients on wealth variables and net foreign
liabilities were generally statistically insignificant, often with the
wrong sign. However, when the net foreign liabilities variable was
included in flow form it yielded the expected sign, although still with
low statistical significance. (In this case official intervention, which
is reflected in changes in net private liabilities, has only a transitory
one period impact on the exchange rate.) These results are consistent
with the perfect substitutability of assets--except in the short run,
perhaps reflecting adjustment lags--and therefore tend to reject the
portfolio balance theory underlying the model. In this case selection
among the alternative approaches to modeling exchange rates and capital
flows outlined in Section III is irrelevant, since all of these are based
on the portfolio balance view. One is tempted to conclude that exchange
rates should be modeled explicitly as a function of interest rates and
factors affecting expectations alone. This would be consistent with the

monetary approach, as developed by Dornbusch (1976), Frankel (1979) and


-7-

Table 1. Two Country Model of Goods, Bonds and Money.

Home Country Foreign Country
Market Equilibrium Conditions

Demand Supply Demand Supply

1. Goods Markets

- * * * *~
C+G-M/S +X = PY b) C +G@ -XS+#M=PY
2. Bond Markets

G Gi

-,* - -
papi seo exp-LaFeys-s2o by Peer a Fo = cp eb + BOs - se

3. Money Markets

*
Loe - bd) Doo= 8
Behavioral Equations
4, Private Expenditures
* * * * *
a) C= C(Y, P, P, S, R) b) C (Y, P, P, S, R )

5. Demand for Other Country's Goods

* * * * * * *
a) M/S = M(Y, P, P, S, R, B ) b) XS =X (Y, P, P, S, Rs F)
6. Demand for Own-Currency Bonds

a) B= B(R, R. S, S°W, PY) b) FY = F(R, Ry S, SO We P*Y")

7. Demand for Other-Currency Bonds

* e * * * e *  **
a) F/S = F(R, R, S, SS W, PY) b) BS=B (R, R, S, SSW, PY)

8. Money Demand

*

* e * * * e
a) L=L(R, R, S, Ss W, PY) b) L L'(P, PR, RS, SS

* *
Ww, PY)
9. Exchange Rate Expectations

e

s® = s®(...)


In brief, these empirical problems raise significant doubts
about any approach to general-equilibrium exchange rate modeling that is
based on the estimation of traditional gross structural capital account
equations. This points to the structural balance of payments approach in
particular, but could also affect the bond market approach, since it too
requires the estimation of home demand for foreign assets.

Several possible solutions exist. First, in the structural
balance of payments approach, one could estimate equations for capital
flows disaggregated by currency of denomination. This would remove the
ambiguity of signs on coefficients, but it would not get around the
institutional or round-tripping problem. In any event, this approach is
feasible for only one or two countries for which such disaggregated data
are available (Germany and perhaps Japan).

A second alternative is to employ the disaggregated bond market
approach. Since bond demands are expressed net of bond supplies, this
avoids the round-tripping problem as well as the currency denomination
problem. However, since it requires data on bond holdings disaggregated
by currency, it too can be applied only in one or two cases.

A third alternative is to use the aggregate bond market
approach, which does not require estimation of any capital account
equations. The only adjustments to the model (in addition to those
outlined above for this approach) involve: 1) defining foreign private
demand for home bonds as net foreign private supply of those bonds, and
2) adding foreign government supply of home bonds to the right hand side
of equation (2a).

A fourth alternative is the net private capital or inverted

capital account approach. A behavioral equation for net private capital


-38-

Appendix B
Estimated Exchange Rate Equations (Based on Inverted Capital Account
Approach) used in Current Version of the MCM,
(t-ratios in parentheses)

1. US Dollar/Canadian Dollar Exchange Rate Equation.

LOG(CER) = .427-  .9026 CDNETPK + .0063 (CRS - URS)
(3.75) (-1.30) (4.23)
+ 885 LOG(CER ,) - «272 LOG(CER_») - 4.00 (CNW,
(6.15) (-2.40) . (-3.97) ‘UNW

+

-00204 CUMBB + .018 CDUM
(1.23) (1.89)

Sample Period 1970 04 - 1980 Q2

R= 0.98 SER = 0.010 DW = 2.37

2. Weighted Average German Mark Exchange Rate Equation.

LOG(GERFW) = 9.010 + LOG(GFPFWI 7 /6P1 )) + 0.009 (GRS - GINF
(-.11) - ° (1.63)

GFRSFW + GFINFFW) + 0.091 (GCCURAR , + 9.055 ONW ,+2.2)
(2.56) 7 |

- 0.9001 GDNETPK + 4
(9.456)

Sample Period 1973 QI - 1980 04

R = 0.792 SER = 0.039 DW(0) = 1.87 RHOT = 0.432


-39-

3. Weighted Average Japanese Yen Exchange Rate.

LOG(JERFW) = 233"%8)* LOG(JFPFW1_1/JP1_,) + 9.0025(JRS - JINF

JFRSFW + JFINFFW) + 0 902(SCCURAB_y

9.00
(1.72

+

0.075 ONW_}/0.033) - (28289) JNNETPK

Sample Period 1973 02 - 1980 93
R2 = 0.089 SER = 0.048 W(0) = 1.32  RHM1 = 0.825

4, Weighted Average UK Pound Exchange Rate

ALOG(EERFW) 939892? + A(LOG(EFPFW1_,/EP1_,)) + 0.0025a(ERS - EINF

(i.

(EFRSFW - EFINFFW)) + 0,00164(ECUMBBAL_, + 0.00450NW_)

+ 0,474) - 4A EDNETPK

Sp

Sample Period 1973 Ql - 1980 Q4

R2 = -0.471 SER = 0.0449 DW(0) = 2.15 RHO1 = 0.257


-27-

alternative expectations variables were tested. These changes still
failed to yield reasonable results.

In light of these empirical results and an increasing awareness
of some of the theoretical problems with the estimation of gross capital
account equations discussed in Section III, we adopted the net private
capital approach, which led to the inverted capital account
specification. The explicit theoretical derivation of this approach was
as follows. Equations for total gross nondirect claims and liabilities
were written:

W- a,

(22) F/S=a R= R + log (S°/S))W

1 2 (

(23) B= 6, W'/S +8, (R- RTM + log (s/s) )W"/s

Under the assumption that a, = By (the home response to a change in
relative rates of return is the same as the foreign response), the
following equation for net liabilities to foreigners can be derived by

subtracting (22) from (23):

*

(24) B + F/S= - a, N46, W'/S +a, (RR + LOG (S°/5))
*
(W +W /S)
Equation 24 was estimated for each of the four non-U.S.

countries in the MCM (Canada, Germany, Japan and the U.K.). Foreign

variables were defined alternatively as U.S. variables and as weighted


~3-

The third factor is our experience to date in attempting to
estimate gross capital flow equations over the floating rate period. The
early version of the MCM was estimated over a period of predominantly
fixed exchange rates (1960-1975). The results, in terms of signs and
significance of coefficients, generally conformed to theoretical priors,
but in some cases the estimated equations led to implausible simulation
properties in the model a Attempts to update the capital flow equations
with data for the floating rate period alone (1973-81) were generally
unsuccessful. Signs on coefficients frequently were inconsistent with
theoretical priors.

In light of these factors, we have adopted as an interim
measure an approach similar to Haas and Alexander's (1979) method of
aggregating private capital flows into a net private capital flow
equation, solving for the exchange rate, and estimating the resulting
equation with the exchange rate as the dependent variable. While this
approach, as embodied in the current version of the MCM, yields much more
plausible simulation properties, it too has its drawbacks. In
particular, gross claims and liabilities, which are needed to determine
investment income payments and receipts, are not identified
explicitly.2/

Qur research on exchange rate determination and capital flows
is therefore still actively in progress. Current efforts center on what
would seem at first glance to be a quite different approach, involving
the explicit modeling of domestic financial asset markets, as applied
recently to the German case by Obstfeld (1982), as well as a more

aggregated approach than Obstfeld employed.


~46-

rearranging, we have the balance of payments identity:

(13a) -X* = M/S + AB* = AF/S + ABS -aF Sys = 0
This issue has been considered elsewhere in Stevens (1976) and Dooley
(1974).
9/ In fact, among the five countries included in the MCM, the balance of
Payments substitution was made for four of the countries and the bond
market in the fifth country (the United States) was dropped by Walras'
law.
10/ To see this, suppose, that claims on foreigners (CF) consist of home

currency bonds issued abroad (Bs) as well as foreign currency bonds
issued abroad (F), so that:

(F.9) CF = F/S + By
Behavioral equations for F/S and Ry are much the same as (7a) and (7b):

— + + +
(F.10)  F/S = F (R, R*, S, S°, W, PY)

“a

+ — — +, + —
(F.11) By = Ba (R, R*, S, S®, W, PY)

Substituting (7a) and (F.11) into (F.10) yields:

202. 2, + =
(F.12) CF = CF (R, R*, S®, W, PY)

See Appendix A for more on this point.

11/ This is a problem only to the extent that the foreign bonds were
issued by the home government (as in the Canadian case in particular),
since privately issued bonds would be netted out of private home demand
in the net private demand specification.

12/ At the end of 1980, 97 percent of U.S. bank and nonbank claims on
Foreigners (excluding stocks and long term bonds) were denominated in
dollars. These claims accounted for 89 percent of total portfolio
(nondirect) claims, and it is likely that a significant portion of the
remainder (largely long term bonds) also were dollar denominated.

Source: Federal Reserve Bulletin, July 1982, and Department of Commerce,
Survey of Current Business, August 1981.



-44-
Footnotes

1/ For example, relatively small monetary shocks were observed to induce
extremely large, and in some cases explosive exchange rate movements in
the model. See Hooper et.al. (1981).

2/ The balance of payments condition identifies only net private foreign
assets. The stocks claims on foreigners and liabilities to foreigners
still must be identified in order to determine the investment income
receipts and payments on those stocks. For this Purpose the current MCM
retains the earlier version of either the claims or liabilities equation,
depending upon the particular country. With one side (eg. claims) thus
identified, the other side (liabilities) is then derived from the
cumulative flow of net private foreign assets.

3/ Such models were introduced in the early 1960's by Mundel (1963) and
Fleming (1962); see Henderson (1982) for a more recent example.

4/ Home private bond demand, B, expressed net of home private bond
supply. To see that net home private demand plus foreign demand for home
currency bonds is equal to the supply of home government ("outside")
bonds, the market for private home currency bonds can be written:

*
* GL
(F.1) DB, + D8) + DBC = SB,

where DB, is gross,home demand for privately issued domestic currency
bonds, DB5 and peg are foreign private and official demands, and SB, is

total supply (based on the assumptions that B, is supplied domestically
only and is not held by the home government).' Similarly, the market for
government home currency bonds is:

*
(F.2) DBg + DBG + DBE = SRe

Summing (F.1) and (F.2) to get total demands and supplies of home
currency bonds yields:

*

* *
* G GL
pt DBg + DBD + DBE = SBy + SBg

(F.3) DB, Pp

p + DB + DB

Next, aggregating demands for government and private bonds and
rearranging yields:

Gt
(F.4) DB 4 g- SB, + DB y G+ DBA*, G = SBg,

which is equivalent to equation (2a) in Table 1, given that DB #G7 SB,


-14-

other by substitution for the balance of payments equation. However, any
transaction in either of the two dropped markets that appears in the
balance of payments must still be modeled explicitly in order to identify
all of the components of the balance of payments ex-ante.

In the early version of the MCM, the balance of payments was
substituted for the domestic bond market equilibrium condition (2a), and
the foreign bond market equilibrium condition was dropped by Walras'

9/

law.— Neither of the own-currency bond demand equations (6a) and (6b)
was estimated. However, equations for both domestic holdings of foreign
bonds (7a) and foreign holdings of domestic bonds (7b) were estimated in
order to identify ex-ante the capital flow components of the balance of
payments. (These bond holdings were also needed to identify interest
Payments and receipts in equations (5a) and (5b).

In brief, the structural balance of payments approach involves
estimating behavioral equations for each of the components of the balance
of payments, while dropping demand equations for own-country bonds. The
balance of payments equation becomes an equilibrium condition that
identifies one of the five market clearing prices in the model. While
prices are determined simultaneously by the five equilibrium conditions,
the exchange rate has its greatest impact on transactions that enter into
the balance of payments. It is thus convenient to think of the exchange
rate as adjusting primarily to clear the balance of payments. However,
significant problems can arise in structural modeling of the balance of

payments, as discussed below.


-16-

are expected to vary negatively with own real income and prices (which

determine transactions demand for money) and positively with own wealth.
Subtracting (7a) from (7b') yields an equation for private

liabilities to foreigners net of private claims on foreigners (hence "net

private capital"):

+ =
(15) BY - F/S = BF (R, R

- + +. Ex +
> S,S,W,W, PY, PY)
The “inverted capital account approach" involves solving (15) for S,
to obtain:
‘* tYoo + -
(16) s=s (RR, S°, WY, Wy PY’, PY, (BY-F/S)),
The selection between (15) and (16) is based largely on empirical
considerations, as discussed in Section V.

When either (15) or (16) is added to the model, it replaces the
capital account equations for claims and liabilities (7a) and (7b). In
this case, if the stocks of claims and liabilities are to be identified
separately (e.g., for purposes of identifying investment income receipts

and payments), another equation must be added to the model.

Bond Market Approach.

In terms of the model presented in Table 1, this approach is
straightforward. It involves dropping one of the markets by Walrus's law
and estimating all the behavioral equations in the model. For example,
the foreign bond market (including the equilibrium condition (2b) and the
demand equations determining F/S and F*) can be dropped. In this case,

the home bond market equilibrium condition remains and behavioral


-2-

rate determination. As described in Berner et.al. (1976), each of the
components of the balance of payments (including imports and exports of
goods and services, as well as the various private and official gross
capital flows) was modeled behaviorally, as a function of the exchange
rate and other variables. The exchange rate, in turn, adjusted to
equilibrate the balance of payments. A similar approach was adopted in
the EPA World Economic Model, as described by Amano et.al. (1981).

Several factors have led us to reconsider this theoretical basis
for exchange rate determination in the MCM. First, an important
assumption underlying the structural modeling of the gross private
capital flow components of the balance of payments is that financial
assets are denominated in the currency of the country in which they are
issued. That is, claims on foreigners must be denominated in foreign
currency and liabilities to foreigners must be denominated in the home
currency if capital account data in the balance of payments is to conform
to the theory underlying asset demand equations. However, the rapid
growth of Euro-currency markets and other financial developments during
the 1970's has made this assumption increasingly untenable.

Second, a further problem facing structural modeling of gross
capital flows is that a substantial part of the growth in gross claims
and liabilities over the past decade has been the result of
intermediation by residents of one country through the books of financial
institutions located in another country, as reflected in the rapid growth
of Euromarkets. Not only is it misleading to treat such claims and
liabilities independently, but it is also difficult to quantify the
institutional factors influencing changes in the scale of these

transactions.


-37-

The third group of terms includes the foreign-currency bonds issued
by each government ("Carter bonds" for example) and official holdings of
foreign currency denominated claims on their own private sectors. For
analytical purposes these terms should be combined with official monetary
capital flows reported in the balance of payments accounts. The terms
could be treated exogenously or modeled as part of intervention policy.

Data on Carter-type bonds are available in some but not all cases.


-25-

estimated in stock form as shown, in other cases in flow form (by
multiplying the equation by wealth and taking the first difference of the
equation). Some of the determinants were dropped in various cases;
dummy variables were added in a number of cases 14/

In simulation exercises with the early MCM, several exchange
rates exhibited dynamic instability, particularly in the absence of
intervention reaction functions. This behavior was traced to estimated
coefficients in both the current account and capital account equations.
Private foreign asset demands (as well as current account flows)
generally had very low responsiveness to changes in exchange rates.
Meanwhile, coefficients on interest rates were proportionately greater
than those on exchange rates. In addition the distributed lags on
interest rates meant that an interest rate shock had continuing effects
on asset demands. To illustrate the effects of these properties on
exchange rate and capital flow determination, a monetary shock that
raised interest rates induced a large (and continuing) incipient capital
inflow. This potential inflow had to be either accomodated by large-
scale official intervention or offset by an appreciation of the home
currency proportionately much greater than the rise in the domestic
interest rate 22/ In the absence of the smoothing effects of endogenized
official intervention, the Canadian model, as well as the German and
Japanese models, exhibited exchange rate behavior that seemed implausible
and in some cases explosive in longer run (7-8 year) simulations.26/
This exchange rate behavior, of course, had significant impacts elsewhere
in the model.

Two possible solutions to those simulation properties were

considered. The first was to mask the instability by tightening the


Alternative Approaches to General Equilibrium Modeling of Exchange

Rates and Capital Flows: The MCM Experience.

I. Introduction

Nearly a decade has passed since the international monetary
system shifted from a regime of relatively fixed exchange rates to one of
relatively flexible exchange rates among major industrial countries.
Until recently any historical sample period long enough to provide
meaningful statistical inference for quarterly macroeconomic modeling of
open economies had to contend with this major shift in regimes.
Sufficient data is available now to focus on the determination of
quarterly movements in exchange rates in the present environment of
relatively flexible rates. However, some theoretical issues concerning
the structural modeling of exchange rates in macroeconometric models are
yet to be resolved.

During the Bretton Woods era (pre-March 1973 for most
countries) exchange market pressures particularly during "speculative"
periods were manifest in large private capital flows that were financed
by changes in official reserves. This close association between exchange
market developments and capital flows had a lasting influence on modeling
even after the regime changed and rates became more flexible. Models of
exchange rate determination have focused on the balance of payments as a
convenient empirical statement of changes in demand for and supply of
foreign exchange. Following upon the earlier empirical work of Branson
(1968) and Bryant and Hendershott (1970), among others, the initial
version of the Federal Reserve Board Staff's Multicountry Model (MCM)

modeled capital flows explicitly as an input into the process of exchange


~49-

Henderson, Dale, “Balance of Payments Analysis, Fiscal Policy and the
Boyer Paper; A Comment" in Purvis, editor, The Canadian Balance of
Payments: Perspectives and Policy Issues, Institute for Research
on Public Policy, Ottawa, 1982.

Hooper, Peter, Richard Haas, and Steven Symansky, "Revision of Exchange
Rate Determination in the MCM," Paper prepared for International
Workshop on Exchange Rates in Multicountry Models, University of
Leuven, November 1981.

Hooper, Peter and John Morton, “Fluctuations in the Dollar: A Model of
Nominal and Real Exchange Rate Determination", Journal of
International Money and Finance, Vol. 1, No. 1, pp. 39-56, April
1982.

Kouri, Pentti J. and Michael J. Porter, “International Capital Flows and
Portfolio Equilibrium," Journal of Political Economy, Vol. 82, No.
3 pp. 443-467, 1974.

Leamer, Edward E. and Robert M. Stern, Quantitative International
Economics, Boston: Allyn and Bacon, Inc. 1970.

McCallum, B. T., "Rational Expectations and the Natural Rate Hypothesis:
Some Consistent Estimates," Econometrica, LXIV, pp. 43-52, January
1976.

Mundell, Robert A., "Capital Mobility and Stabilization Policy Under
Fixed and Flexible Exchange Rates," Canadian Journal of Economics
and Political Science, Vol. 29, No. 4, pp. 475-485, November 1963.

Obstfeld, Maurice, “Exchange Rates, Inflation, and the Sterilization
Problem: Germany, 1957-1981", paper delivered at NBER and Manheim
West Germany, May 1982.

Roley, V. Vance, "The Role of Commercial Banks' Portfolio Behavior in the
Determination of Treasury Security Yields," Journal of Money,

Credit and Banking, Vol. XII, No. 2, May 1980.

Stern, Robert M., The Balance of Payments, Chicago: Aldine Publishing
Company 1973.

Stevens, Guy V. G., Richard Berner, Peter Clark, Ernesto Hernandez-Cata,
Peter Hooper, Howard Howe, Sung Y. Kwack and Ralph Tryon, "Modeling
Bilateral Exchange Rates in a Multicountry Model," FRB,
International Finance Discussion Paper No. 167, July 1980.

Stevens, Guy V. G., Richard Berner, Peter Clark, Ernesto Hernandez-Cata,
Howard Howe and Sung Y. Kwack, The U.S. Economy in an
Interdependent World: The Multicountry Model. Federal Reserve
Board, Washington, ). C. (forthcoming).



-33-

Appendix A

The purpose of this appendix is to show that an equation for net
private capital flows (ie., changes in claims on foreigners net of
liabilities to foreigners), is consistent with an aggregation of net
private bond demands, and therefore avoids the problem of ambiguity of
signs on coefficients that can arise in the structural capital account
approach (ie., modeling changes in claims and liabilities separately)
when data on claims and liabilities disaggregated by currency of
denomination are not available.

To show this, we adopt a two-country model in which private
residents and governments of both countries can issue and hold bonds
denominated in the currencies of both countries. The various bond

holding and issuing possibilities are summarized in the following chart.

Sector Sector Holding Bond

Issuing Bond Home Priv. Home Govt. For. Priv. For. Govt.

A G pe P* G*

Home Priv. -- -, Fp Bp > Fp Bos -
. P oP p* Pp G*

Home Govt. Boe Fa -3- Boe Fe Boe -
*

For. Priv. Boas Foe -> Fee -- Bees -

p* *
For. Govt. Bees Foe “> Foe Bowe ee --



GFRSW

GINF

GP

GP1

GRS

JCCURAB
JDNETPK
JER

JERFW

JF INFFW

JFPFW

~42-
+ 9.163 GFPFW_3 - 0.725 GFPFW_, + 9.460 GFPFW 5

Weighted Average Foreign Short Term Interest Rate, German
Model, Using FRB Multilateral Trade Weights

= 0.40 URS + 9.155 CRS + 0.21 ERS + 0.241 JRS

Expected German Inflation Rate, One Quarter Ahead

(GP1/GP1_4 -1) + 100

German Absorption (Total Expenditure) Deflator

Expected Value of GP, One Quarter Ahead
= 0.002 + 1.004 GP + 0.30 GP_, - 0.248 GP_, + 9.095 GP_3

Short Term Interest Rate (3 month Frankfurt Money Market
Rate)

Cumulative Japanese Current Account Balance
Change in Net Japanese Private Liabilities To Foreigners
Dollar/Yen Exchange Rate

Weighted Average Yen Exchange Rate, Using FRB Multilateral
Trade Weights
(JER*23- (JER/CER)*°9 ~—-« (JER/EER) #2

+ (JER/GER) +21) 1.538

Expected Foreign Inflation Rate, One Quarter Ahead Japanese
Model

= (JFPFW1/JFPFW1_4 - 1) + 100

Weighted Average Foreign Price Level, Using FRB Multilateral
Trade Weights, Japanese Model


-28-

averages of four other countries (including the U.S.). Two alternative
approaches were employed to identify the expected exchange rate: 1)
using the realized future spot exchange rate (based on McCallum's (1976)
rational expectations approach) for estimation purposes, and 2)
specifying expectations structurally using Hooper and Morton's (1982)
approach. The expected exchange rate in the latter case is specified as
a function of relative prices, relative expected inflation rates and the

home country's cumulative current account lagged one period:

*
(25) LOG S° = vq + y, LOG (P*/P) + (B° - BP) + yy Z(M/S - XF)_,

where P is the inflation rate and definitions are otherwise the same as
in Table 1, Finally, (24) was estimated using ordinary least squares,
and instrumental variables.

The results were generally disappointing. The key coefficient
a was never significant with the expected sign Z/ It was recognized
that if domestic and foreign bonds are perfectly substitutable, (24)
could not be estimated because Yo would be infinite. To test for this
case the equation was inverted by solving for S. The result for the
structural expectations case (after substituting (25) into (24)) was a

complex nonlinear specification, of which we took the following linear

approximation:

*

(26) log S = 8) + 8, (R- RY + BE ~ P°) + 6,5 (W/S = x") ~ 8M

3


-12-

5/

bonds.’ Increases in home official holdings of foreign bonds, Fo, net.
*
of foreign official holdings of home bonds, BS, are the counterpart of

combined intervention of the two countries to support the foreign
currency. The money markets (3a and 3b) are represented by demands for
and supplies of own-country high-powered money (currency plus reserves).
Official intervention and money supplies are assumed exogenous in this
simplified model; these variables can be endogenized through the
introduction of policy reaction functions.

Equations (4a - 8b) are behavioral demand equations for goods,
bonds and money. Goods demands are functions of own income and relative
prices. In addition, home purchases of foreign goods’ and services, M/S,
include interest payments to foreigners, so that their determinants
include the home interest rate and the stock of home bonds held by
foreigners. Foreign purchases of home goods and services are treated
symmetrically. Bond and money demands are functions of expected relative
rates of return on home and foreign assets (including expected exchange
rate changes), own wealth, and a transactions demand variable (own
nominal. income).

Equation (9) identifies exchange rate expectations, which are
discussed in detail in later sections. Government tax receipts and
deficits are defined in equations (10a - 11b). Equations (12a) and (12b)
define changes in home and foreign wealth as private savings (disposable
income minus consumption) plus capital gains on the existing wealth
stocks (z) 8/ Equations (13a) and (13b) are home and foreign wealth
constraints, equating private portfolio wealth with net private holdings

of money and bonds valued in terms of the currency of the wealth


~50-

Stevens, Guy V. G., "Balance of Payments Equations and Exchange Rate
Determination," FRB, International Finance Discussion Paper No. 95,
December 1976.

Symansky, Steven, Richard Haas, and Peter Hooper, "Empirical Tests of
Exchange Rate Determination in a Portfolio Balance Model Under
Alternative Expectations Hypotheses," FRB, December 1981.


-15-

Net Private Capital or Inverted Capital Account Approach.

The net or inverted capital account approach is a simple
extension of the structural balance of payments approach. This involves
making the same balance of payments substitution as outlined above. It
then goes at least one and possibly two steps further by: 1) aggregating
foreign demand for home bonds minus home demand for foreign bonds into a
single equation for net home private liabilities to foreigners, and 2)
solving t:hat equation for the exchange rate.

The underlying asset demand equations, (7a) and (7b), written

with the expected signs of coefficients over corresponding variables are:

Home claims on foreigners

- +, + - + -
(7a) F/S =F (R, Ry S, S°, W, PY)

Home liabilities to foreigners

+

4 toe - +.
(7b') BY = BY (R, RY, S, Se, Ww

Py")
(where, S, which appears on the left-hand side of (7b) in Table 1, has

been moved to the right-hand side in (7b').

Home demand for foreign bonds is expected to vary directly with the
foreign interest rate and inversely with the home interest rate and the
expected appreciation of the home currency (s°/s). The expected signs on

foreign demand for home bonds is just the opposite. Both bond demands