A structural portfolio balance model of the Sterling-Dollar exchange rate

A Structural Portfolio Balance

Model of the Sterling-Dollar Exchange Rate

By

Colm Kearney and Ronald MacDonald

C o n t e n t s : I. Introduction. - II. The Portfolio Balance Model. - I I I . Economet r i c Methodology. - IV. Estimation Results. - V. Simulat ion Results. - VI. S umma r y and Conclusions. - Data Appendix.

I. Introduction

S ince the move to a system of floating exchange rates in the early 1970s it has become fashionable to view the exchange rate as determined in asset markets 1. Within the asset approach to the exchange rate, however,

there are differing views as to which are the relevant assets and which simplifying assumptions one should invoke in an exchange rate model. One approach, the flex-price monetary approach, assumes that purchasing power parity holds and that non-money assets between countries are perfect substitutes. This approach concentrates on relative excess money supplies as the relevant determinants of exchange rates 2. Frankel [1979a], in his version of the monetary approach, retains the non-money asset substitutability assumption, but relaxes purchasing parity in the short run; the exchange rate is driven by a real interest rate differential. A third view within the asset approach, the portfolio balance approach (PBA), states that non-money assets are imperfect substitutes and that the exchange rate is only one of a number of prices that clears asset markets 3. Wealth effects also have a prominent role to play in this model.

Although a voluminous literature testing the two versions of the monetary approach has appeared 4 relatively little empirical work has been conducted on the portfolio balance view. Of the empirical evidence that has been conducted, reduced form modelling has been used and this has resulted in

The first major statements of the asset approach to the exchange rate appeared in the 1976 issue of the Scandinavian Journal of Economics. Further papers containing useful surveys of the asset approach are: Mussa [1979], Dornbusch [1980] and Frankel [1981].

2 This approach has been popularized by Frenkel [1976], Mussa [1976] and Bilson [1978].

3 Examples of the PBA may be found in Branson [1977], Girton, Henderson [1976] and Allen, Kenen [1980].

4 See, for example Frenkel [1976; 1981], Bilson [1978; 1979a; b; c], Hodrick [1978], Dornbusch [1976], Frankel [1979a; b; 1983].

The Sterling-Dollar Exchange Rate 479

much of the richness and realism of the asset approach being lost. For example, Branson, Haltunnen [1979] and Branson et al. [1977] consider a very simple empirical implementation of the asset approach where the exchange rate is regressed essentially on relative money supplies and relative cumulated current accounts. In this paper we adopt a different method of implementing PBA ~.

In particular, we estimate the model structurally using the Theil-Goldberger mixed estimation procedure for the sterling-dollar exchange rate over the period March 1973-1982. This we believe offers certain advantages in that it allows us to obtain unambiguous responses of the various interest rates to asset shocks and also to conduct some dynamic policy simulations. The latter is of interest since dynamics are often neglected in the analysis of portfolio balance models and emphasis is instead placed upon qualitative aspects which do not give a flavour of how the approach "works" over time.

The Theil-Goldberger procedure has been used extensively on U.S. data to estimate closed economy portfolio models, but it has not been used on U.K. data or to estimate an open economy portfolio model. Another innovative feature of our approach is the use of the new wealth data published by the Central Statistics Office. Although we believe our model has a number of interesting features, a limiting aspect is our treatment of expectations formation: Expectations are assumed throughout to be static. It is hoped to solve the model rationally in the future and to compare such solutions with the present results.

The outline of the remainder of this paper is as follows. In Section II we present a version of the portfolio balance model based upon the definition of private sector wealth for the U.K. This wealth definition differs from the usual one used in the PBA by its inclusion of bank lending. In Section III the methodology used to econometrically estimate our model is outlined. Section IV contains our econometric estimates and in Section V some simulation results are presented. Finally, we present a summary, some concluding comments and outline some points for future research.

II. The Portfolio Balance Model

In the monetary approach to the exchange rate the exchange rate is the price, and only price, that clears asset markets. Once one moves, however, from a world in which non-money assets are perfect substitutes to one in which they are imperfect substitutes the exchange rate becomes a price determined jointly with other asset prices (i.e. interest rates). Although the

5 Branson et al. [1977] have been criticised by Bisignano, Hoover [1983] for a failure to use strictly bilateral data and also for the exclusion of domestic non-monetary assets from their exchange rate equation.

480 Colm Kearney and Ronald M a c D o n a l d

extant empirical evidence does not shed much light on the issue of asset substitutability casual empiricism would suggest that non-money assets are imperfect substitutes and thus a broader PBA is the appropriate model with which to analyse the determination of the exchange rate 8.

In Branson [1977] a small country portfolio balance model of the exchange rate is presented where the assets chosen are home and foreign bonds and domestic money. Here we extend Branson's definition of wealth to include bank lending. Although the inclusion of bank lending in a model of the exchange rate may seem rather odd it does in fact result in a definition of wealth equivalent to that of the U.K. private sector, the relevant wealth definition used in our econometric analysis.

Our version of the PBA, which forms the basis of our econometric analysis, is given below.

A~ = al (r2, r3, r4 -{- ASe) w (1)

A~ = a2 (r2, r~, r4 + As~) w (2)

A3 ~ = a3 (r2, r3, r4 + Ase) w (3)

s . A~ = a 4 (r2, r3, r4 "~- ASe) w (4)

W = A I + A 2 + A 3 + s . A 4 (5)

Symbols have the following meanings: A~ = demand for money; A D = demand for bank loans; A~ = demand for domestic bonds; A4 D = demand for foreign assets denominated in foreign currency; W = net financial wealth; s = spot exchange rate, (s e = expected spot rate); r 2 = rate on bank loans; r 3 = yield on domestic bonds; r4 = yield on foreign assets (assumed to be determined exogenously: the small country assumption).

Eqs. (1) - (4) are the demands for money, bank loans (the negative of), domestic bonds and foreign assets, respectively. They are posited to depend upon wealth, the own rate and all cross rates. Since we are considering narrow money here, the own rate is set to zero for ease of exposition. Eq. (5) defines the net wealth constraint of the non-bank private sector as the sum of the four assets. The stocks of assets A 1 - A 4 are given historically at each point in time. Substituting these into (1) - (4) gives the market equilibrium conditions.

We assume that the assets are gross substitutes and this together with the balance sheet constraint implies that

Tests by Dooley, Isard [1979] and Frankel [1982] have failed to uncover a risk premium. However, tests of the efficiency of the forward exchange market strongly support the existence of a constant or variable risk premium (see inter alia Frankel [1979b], Hansen, Hodrick [1980], Ballie et

al. [1983]).


1~ I~ + 1~ + 1~ J~ I~ + 1~ + 1~ (6)

The four market equilibrium conditions contain three independent equations in r 2, r 3 and s, given the balance sheet constraint. Any three of (1) - (4) with wealth substituted from (5) can therefore be used to determine the short-run equilibrium of the three rates.

In the short run the exchange rate is determined by conditions of asset market equilibrium. But the value of the exchange rate so determined, given income, absorption and the price level, will generally yield a non zero current account balance. This must, with a flexible exchange rate, yield a non zero capital account of the opposite sign. For example, an increase in the money supply, resulting in an exchange rate depreciation, will lead to a current account surplus and the private sector accumulating foreign assets: A 4 is increasing, hence s must be changing. Thus the current account balance feeds holdings of net foreign assets, moving the exchange rate over time. In our example the rising exchange rate will reduce net exports. However, the increase in foreign assets will mean investment income is rising, pushing the current account further into surplus. For stability one has to assume that the income effect is outweighed by the trade balance effect which in turn requires that trade elasticities be sufficiently large.

The dynamics of current account adjustments are not included in our model. Instead we concentrate on a purely short-run horizon in which income and prices are exogenous and the exchange rate is determined simply by the interaction of asset markets. Exchange rate revaluation effects impinge upon financial wealth in our model, and this will have an important bearing on the results. Comparative statics are obtained by totally differentiating (1) - (3) with (5) written for W. They are written in matrix form below

Wa~r2 Walr3 ~ln4] [dr2]

Wa2r2 Wa2r3 a2A4] [dr3[ =

Wa3r2 Wa3r3 a3A4J ldsj

I 1 - al) - a 1 - a I - alS - Wa,r 4

a 2 (1 a2) 1212 - a2S Wa2r 4 (7)

a 3 a 3 (1 a3)- a3s Wa3r 4

dA1 I

dA2j

dA31

dA4 I

dr4

482 C o l m K e a r n e y and R o n a l d M a c D o n a l d

The determinant of the left hand side matrix is positive 7. Using Cramer's rule we can solve (7) to obtain the effects on the endogenous variables of the accumulation of assets and open market operations. These effects are summarised in the table below:

Table 1 - Effects of Increases in Asset Stocks on Interest Rates and the Exchange Rate

Effects on

Effects of a c c u m u l a t i o n of asset s tocks

~ 1 AA2 AA3 &A4

- + ? 0

- ? + 0 + ? ?

Effects of open m a r k e t s ope ra t ions

AA3 = - ~ 1 s ~ 4 = / k A 1

? +

+ +

The entries in Table 1 give the direction of change of interest rates and the rate of foreign exchange following: (i) an increase in one of the asset stocks holding the others constant (first four columns), and (ii) an expansionary open market operation, with money exchanged for either domestic bonds or foreign assets (last two colums).

Many of the effects are intuitive and are carried over from simpler specifications of the portfolio balance model. In particular, a monetary expansion will depreciate the exchange rate whereas a current account surplus will raise net foreign assets and result in appreciation. Accumulation of other assets has indeterminate effects on the rate of exchange, as does an open market operation in domestic bonds. This latter result does not replicate the results obtained in simpler specifications wherein the effects is unambig- uously to devalue the currency. More realistic modelling of portfolio behaviour is thus seen to render the monetary approach a special case.

III. Econometric Methodology

Our asset demand specifications are similar to those utilised by Backus, Purvis [1980], Backus et al. [1980], Smith, Brainard [1976] and Green [1982], and we will therefore only give a brief account of their derivation.

7 The determinant of the left hand side matrix in (7) on page 481 is positive as follows

A = A I + A 2 + A 3 > 0 w h e r e : + + - +

A 1 = alA4W (a2r 2 - a3r 3 - a3r 2 �9 a2r3) > 0 from (6)

A 2 a2A4W (a3r- 2 a i r 3 - a i r 2 . + = �9 a3r3) > 0 -- - - -F

A 3 = a3A4W (air 2 �9 a2r 3 - a i r 3 �9 a2r2) > 0


Treating the negative of bank loans as an asset, the long-run position of the i th asset is described by

n

a*/W= [~i0 +j~1~ii In r i (8)

where a~ ~ represents the desired stock of asset i (i = A 1, A 2, A3 and A4) and r i represents the relevant interest rate variables. The coefficients are subject to the adding-up restrictions across equations given by

n n

E 13~0 = 1 and Z IBii = 0 j = 1 . . . . . . n (9) i = 1 i = l

The asset demand functions take a familiar partial adjustment format in the short run. For example, the actual holdings of the i th asset are given by

11

fiai =i =ElVii (ai~t) - aj(t-1)) J = 1, . . . . . n (10)

The V~i's, the adjustment parameters, are subject to the cross-equation adding- up restrictions that

n

,EV i = = 1 j = l . . . . . . n (11)

By combining (8) and (10) we obtain

n n

fi a / W = CONSTANT -j =ElY i (ai (t_~)/W) +i=E1V~i~ j In ri (12)

Interest rates enter (11) logarithmically because of the finding by Smith, Brainard [1976] that the use of levels of interest rates often produces absurd simulations results.

Although the model is avowedly short run in nature, the asset demands are derived to be consistent with both short and long-run portfolio balance. In the econometric estimates of (12) we include variables which appear on the right hand side of any one asset demand equation in all others. Furthermore, we use the Theil-Goldberger mixed estimation to combine our subjectively held prior information with the data. Previous work by Smith, Brainard [1976] and Backus et al. [1980] demonstrates that the use of prior information eliminates many of the wrong signs that arise from ordinary least squares (OLS) estimation.

Using the Theil-Goldberger procedure to estimate a portfolio balance model stands the usual empirical implementation of such models on its head. Researchers commonly mine the data when they estimate asset demand equations or systems. Although this is not an illegitimate practice, it is important to

484 Colm K e a r n e y and R ona l d M a c D o n a l d

note that the iterative process which characterises a data mine implicitly involves the use of prior information. That is, certain variables or lags are rejected because the sign or the magnitude of the estimated coefficients conflict with the researcher's priors. The disadvantage of this procedure is that in simply reporting the "final" results, the researcher does not share with the reader the priors which were used to derive the estimates. In contrast, the Theil-Goldberger mixed estimation procedure makes the priors explicit at the outset and provides the reader with the opportunity to either agree or disagree with them (see Leamer [1978] for an excellent discussion of this issue).

The procedure can be summarily explained by representing the asset market model in matrix notation a

y = 13X + u (13)

The prior information is expressed as

r = R~ + v (14)

where r = a known g. I vector (g < k) with as many rows as restrictions; R = a known g. k matrix with as many rows as restrictions and as many columns as coefficients in the system; 13 = a vector formed from all the coefficients in the system; v = a vector of errors with E(v) = 0 and E(vv) = ~.

Combining (12) and (13) we obtain

where

E [ U ] = O a n d E [Uv] ,u'v',= L OF~

(15)

Since the variance-covariance is not O2In + g, a generalised least squares procedure must be used. We follow Smith, Brainard [1976] in assuming exchangeability

%~ / c~ = 0/j)/o~ (16)

Consider first the specification of the prior matrix. Priors on the long-run interest rate coefficients hre determined in the following way. First, we assume that the assets are gross substitutes so that, ceteris paribus, an increase in the own rate on an asset increases its demand and decreases, or leaves unaffected, the demand for other assets. Gross substitutability also implies that own rate effects will be greater than cross rate effects. It is further

a See Theil, Goldberger [1960] and Theil [1966]. On the application of the Theil-Goldberger methodology to a portfolio balance model see Smith, Brainard [1976].


assumed that assets which consti tute a large propor t ion of the portfolio have large interest rate responses. Finally two assets which are compat ible in terms

of liquidity will have larger cross effects than two assets that are relatively illiquid. Given these assumptions the long-run interest rate parameters are

reported in Table 2. They are clearly subjective but we would expect that most monetary researchers would find them compat ible with their priors.

Table 2 - L o n g - R u n C o e f f i c i e n t s

Asset (X/W) Procedure 1.0 r 1 r 2 r 3 r 4

P R I O R - 0.600 - 0.400 - 0.200 - 0.200 A 1 0.562 OLS - 7.147 0.216 - 1.336 3.879 0.241

MIXED 0.720 0.478 - 0.314 - 0.238 0.066

P R I O R - - 0.300 0.700 - 0.200 - 0.200 A 2 - 0.409 OLS 5.147 0.095 0.603 - 2.621 - 0.233

MIXED - 0.360 - 0.272 0.134 0.174 - 0.101

P R I O R - - 0.100 - 0.100 0.700 - 0.300 A 3 0.609 OLS 5.448 - 0.388 1.181 - 2.578 - 0.034

MIXED 1.080 - 0.162 0.099 - 0.066 - 0.170

P R I O R - 0.200 - 0.200 - 0.300 - 0.700 A 4 0.234 OLS - 2.448 0.780 - 0.448 - 1.340 0.034

MIXED - 0.490 - 0.061 0.098 0.132 0.050

The next stage is to specify the short-run adjustment coefficients. We

follow Backus et al. [1980] in defining the adjustment matrix with diagonal elements between 0 and 1, and with liquid assets adjusting more quickly than illiquid ones. Our short-run interest rate coefficients are derived as the

product of the long-run rate responses (Table 2) and the adjustment coefficients (given in the four columns on the right of Table 3(A)).

The prior var iance-covar iance matrix used to combine the a priori means

and the data is presented below. In determining the interest rate responses

.0306 0 0 0 0 0 0 0 0 .0480 0 0 0 0 0 0

0 0 .0361 0 0 0 0 0 0 0 0 .0961 0 0 0 0 0 0 0 0 .00563 0 0 0

0 0 0 0 0 .00563 0 0

0 0 0 0 0 0 .00563 0

0 0 0 0 0 0 0 .00563

we follow Backus, Purvis [1980] in assuming that the standard deviat ions are

one-half of the largest e lement in the column. The two standard deviat ion bands for the adjustment coefficients are assumed to be + 0.15. The

486 Colm Kearney and Ronald MacDona ld

off-diagonal elements are assumed to be zero in accordance with Smith [1981] who argues that a fully specified covariance matrix does not appreciably improve on results obtained using the above procedure.

IV. Estimation Results

A comprehensive description of the data sources and definitions employed in the econometric analysis is provided in the Data Appendix. It is worth noting here, however, that the U.K. private sector's net financial wealth is published in terms of the following identity:

W = A*+ A 2 + A 3 + s �9 A 4 + A 5 (17)

where W, A2, A3 and A 4 a r e as defined above and A~ ~= broad money and A5 = other private sector net assets.

The definition of financial wealth employed in the empirical analysis omits the As term. This causes (17) to resemble its theoretical counterpart given in (5). Since the remaining constituents account for almost 90 per cent of the variation in private financial wealth, this does not seem a restrictive exclusion. A further modification consists of using the sterling M3 definition of money in place of the broad money definition employed in the statistical sources referred to. This is considered appropriate in so far as the aggregate we use corresponds to that employed by the monetary authorities for targetting purposes, and because we are keen to estimate the wealth and interest rate elasticities for this measure within a portfolio balance context.

Consider first the short-run OLS estimates of the portfolio balance system, reported in Table 3. The equations appear to fit the data well. Durbin's h-statistic and the first order autocorrelation coefficient, Pl, (estimated by maximum likelihood) both indicate the absence of first order autocorrelation. The statistic x~20) is the Box-Pierce test for the whiteness of the residual correlogram, and the computed value is insignificant at the 95 per cent level in all four equations (• = 31.41 at 95 per cent level). Inspection of the residual correlogram reinforced the conclusion that the residuals are tolerably white. The statistic F(12,12) is the Chow test for parameter stability (which was computed by splitting the sample in half and re-estimating the equations for the sub-periods); in all cases this statistic is insignificant at the 95 per cent level (F(12,12) = 2.69 at 95 per cent level).

Notice that 11 (out of 16) interest rate responses and 4 (out of 16) adjustment coefficients have the wrong sign in the OLS estimates. In an attempt to improve upon these perversities, we applied the mixed estimation procedure. Before combining our priors with the data we checked that they were compatible by computing Theil's compatibility statistic

y = (r - R~[~) [ o "2 R (x' x) -1 R ' q- ~j[-1 (r - R~[3) '


Cl

I

,.ID

0 oO ~1 0 '~ID t'Xl 0 ",-"~ 0 0 ~ 0

I I

I

I I I I I

I I I I I

, - - ~ o o o o ~ o I I I I I I I I

o I I

~o.~ o~: ~o~ ~o~

~ ' ~

.~. r r.) .o

".~ .~ ~,

Q

~- . ~ . ~

0)

"-~ ~ "~

o,0 ch i i

o

t~

.z , ' , ' ~ .s E~

Wel twi r t s cha f t l i ches A r c h i v Bd. CXXII . 5

488 C o l m K e a r n e y and R o n a l d M a c D o n a l d

which has a chi-squared distribution with k (= 8) degrees of freedom. Since ~s) = 15.51 at the 95 per cent level and since our computed value of x 2 is considerably less, all four equations pass the compatibility criterion.

Applying the Theil-Goldberger procedure to our system we find that the results are more consistent with our priors. Now 9 out of the 16 interest rate coefficients have the correct a priori signs and of those that remain "per- verse", 3 move in the "correct" direction. T~vo of the adjustment coefficients also become consistent with the priors. In the equation for sterling M3, for example, the own rate and the bank lending rate are wrongly signed with the OLS estimate, but become correctly signed in the mixed estimates. In addition, the foreign rate moves in the correct direction and the bond rate mixed estimate is insignificantly different from its prior value.

The OLS long-run coefficients (which are derived from the estimated short-run equations reported in Table 3) are in some cases quite different in absolute terms from the priors. Now 9 out of 16 OLS coefficients have the "wrong" sign. One glaring perversity is the long-run OLS bond rate effect which implies that a 1 percent increase in that rate leads to an increase of 3.88 in the proportion of the portfolio held in money and a decrease of 2.58 in the proportion of that held in bonds. Although the long-run mixed estimates are more plausible, particularly in the case of the money and bank lending equations, 6 out of the 16 coefficients remain wrongly signed. The mixed estimates, however, imply a more sensible sign pattern with the private sector borrowing from the banks and the overseas sector in order to finance bond and broad money holdings.

V. Simulation Results

The model has been simulated to examine the qualitative and dynamic effects of the various policies considered within the theoretical framework. Before reporting the results of this exercise, it is worth noting that one of the disconcerting properties of many econometric models is their tendency to display slow or unstable adjustment towards equilibrium. The adjustment dynamics of the present model can be described as follows. With a given amount of wealth (W) and unchanged desired assets (a*), (18) describes the portfolio disequilibrium that exists T periods after an initial shock.

(a-a*) = (I-T) �9 (a_~ - a*)

= (I-r)' (a_l - a*) (18)

This system converges to equilibrium for all initial conditions if

lim (I-r)T = 0 T --~ oo


which is the case if the eigenvalues of (I-T) are all less than one in absolute value. The largest eigenvalues for the priors, the OLS and the mixed estimates are .50, .97 and .91, respectively.

Although the speed and pattern of convergence to equilibrium depends upon the type of shock, the speed of adjustment can be described by examining the largest possible difference between desired and actual holdings after T periods. This is obtained as the largest difference between any two elements in a row of (I-r) ~. The priors are the quickest to return to equilibrium, followed by the mixed estimates, while the OLS estimates are slow to converge, a finding that is consistent with the policy simulation properties which we now consider.

Figure 1 - 1 Per Cent Expansion in Money Stock

Per c e n t

d i f f e r e n c e

1.0 (A) PRIORS

0.5

0

-0.5 rz

-1.0 o ~ 1'o ,'s 2'0 2'5

10 (B)OLS .

. r~ 5

0

0 2 4 6 8 10 12 74 16 18 20 22

0

-0"5 I - 1.0

- 1.5

-0.2

-2.5 0

(C) MIXED

1'o ,'5 ~o 2's Quarter

Figure 2 - 1 Per Cent Expansion in Bank Lending

Per cent d i f f e r e n c e

0.5

0

-0 .5

- 1 . 0 �9

-1.5.

- 2.0

(A) PRIORS r3

5 10 15 20 25

- 2,5 [ r2v

5.o ; ,b ;5 2'o is

(C) MIXED

1'0 1'5 20 25 Quarter

5*

490 Colm Kearney and Ronald MacDonald

The following simulations are reported: Simulation 1: A one percent expansion in the stock of broad money (s Simulation 2: A one percent increase in bank lending to the domestic private

sector; Simulation 3: A one percent increase in the supply of domestic bonds; Simulation 4: A one percent increase in domestic holdings of foreign bonds; Simulation 5: An open market swap of domestic bonds for domestic money; Simulation 6: An equivalent open market swap of foreign bonds for domestic

money. Figures 1-6 present the response of domestic interest rates to these changes using respectively the priors, the ordinary least squares estimates and the mixed estimates. It is clear from the Figures that the least squares estimates

- 0.25

- 0 . 5 0

Figure 3 - 1 Per Cent Increase in Domestic Bonds

Per cent d i f f e r e n c e

0.25 (A) PRIORS

lO 1~ 2o 25

-4 -

- 6

0

(B ) OLS

r3

lO 1~ 2o 25 (C) MIXED

- 0 . 5

- 1 . 0

- 1 . 5

- 2.0 1'o 1`5 2'o 25 Q u a r t e r

Figure 4 - I Per Cent Increase in Foreign Assets

Per cent d if f e r e n c e

0

- 0.05

- 0.10

- 0.15

- 0.20

(A) PRIORS

15 1~ ~o 2~

- 0 . 5

- 1.0

0 ~

- 0.25

- 0.50

- 0.75

( B ) O L S

0 5 10 15 20 25

( C } M I X E D - ~ - -

. . P" '3"\ /

. . J /

/ f

/

1'0 1'5 20 25 Quar te r

T h e S t e r l i n g - D o l l a r E x c h a n g e Rate 491

Figure 5 - Open Market Swap of Domestic Bonds for Money

Per cent difference

O.:t (A) PRIORS r3----

-0"2 t -0 .4 -

- 0 . 6

Figure 6 - Open Market Swap of Foreign Bonds for Money

Per cent difference

0.1 (A) PRIORS

- 0 . 2

- 0 . 4

- 0 . 6

8 .

4-

0-

-4-

- 8 -

(B) OLS i . ~ / ~

r ~1 I ~'~

8

6

0

- 4 .

- 8

(B)OLS

r ,S '2

1.0-

0.5-

(C) MIXED

0 5 10 15 20 25 Quarter

0.5-

O-

- 0 . 5

(C)MIXED

s 1o is io ~ ' s Quarter

Figure 7 - Exchange Rate Consequences." Mixed Estimates

Exchanger ate

-1

(A) Asset supply changes 1 I " ~" %.

...,~ ~" ~" ~A 3 ~',,.

AA 1

" ~ . ~ AA 4 ~176176176 ~ "-- - ~ - ~... ~ . -~ . ..,,~176

�9 ... , . , . . ~ - ~ . . ~ . . . . . . . . . . . . . . . . . "~A;"

0 5 10 15 20 25 Quarter

Exchange rate (B) Open market operations I

AA3-AA 1

0

AA4-AA 1

1'o 1'5 ~o 2'~ QuQrter

492 Colm Kearney and Ronald MacDonald

imply slow and oscillatory dynamics. This finding concurs with our discussion of (18). We shall confine comment in what follows to the results obtained from employing the mixed estimates. Figure 7 provides the exchange rate dynamics of response in the simulations using the mixed estimates.

Consider first the effects of a one percent expansion in the stock of broad money (s The bond and bank lending rates fall whilst the exchange rate depreciates, as expected, and adjusts cyclically to its new equilibrium level. These results are consistent with those presented in Tables 1 and 3. The results of a similar expansion in the quantity of bank lending are interesting in so far as they shed light upon some of the indeterminacies of the theoretical model. In particular, rates of interest rise and the exchange rate appreciates as a consequence of these movements. The effects of a one percent expansion in the stock of domestic bonds are qualitatively opposite to those just men- tioned, and so cast additional light upon some of the ambiguities in Table 1. It is interesting to note that the interest rate effects of a one percent rise in domestic holdings of foreign assets has a moderate effect upon domestic rates of interest in comparison with the simulations discussed thus far. Also, the exchange rate appreciates as expected.

The final two simulations are perhaps the most interesting in so far as they correspond most closely to actual policy actions. Consider first the open market swap of domestic bonds for money depicted in Figure 5. The priors and mixed estimates result in higher bond and a lower bank lending rate of interest as expected. The net effect on the sterling-dollar exchange rate is shown on the bottom part of Figure 7 to involve a five percent deviation before commencing to converge cyclically. These results using the mixed estimates concur with those obtained in the theoretical model and in addition, cast light on the exchange rate effects which were ambiguous in that context. Finally, a swap of foreign bonds for domestic money results in exchange rate appreciation as expected, while the interest rate effects are divergent. In particular, the domestic bond rate declines in this case in contrast to the open market operation in domestic bonds.

VI. Summary and Conclusions

This paper has been concerned to improve upon the existing literature on empirical implementation of the PBA to modelling the exchange rate. In Section II we generalised the existing theoretical model to enable predictions to be made from a framework consistent with our econometric specification using the new private sector wealth data available in the U.K. We then estimated our empirical model of the sterling-dollar exchange rate using OLS and the Theil-Goldberger mixed estimation techniques. The latter was demonstrated to have been successful in moderating the peculiarities in the OLS results. In particular, a considerable number of "wrong" interest rate


responses were corrected as were incorrectly signed adjustment coefficients. Indeed, the equation estimates have an interest value in themselves in so far as they shed light on the usefulness of prior information and general partial adjustment in estimating asset demand functions. Finally, policy simulations were carried out to examine the effects of various policies on the exchange rate. Generally speaking the priors and mixed estimates were more stable and the OLS estimates demonstrated some peculiar responses.

The work suggests that explicit use of prior information is a useful alternative to standard econometric practice in estimating portfolio balance models. In particular, this study supports the contention that in many cases, data provides very little information on the dynamics of relationships between variables. Future work will involve rationalising the expectations formation mechanism and focusing more explicitly upon how capital gains are treated.

Data Appendix

This appendix describes, in alphabetical order, the data and definitions used in the study. The following abbreviations will be used: BEQB = B a n k of England Quarterly Bulletin; ET = Economic Trends; FS = Financial Stati- stics; IFS = International Financial Statistics.

A3: Domestic bonds held by the non-bank private sector. This series was calculated as the sum of (i) public sector long-term debt, (ii) national savings, (iii) treasury hills, (iv) local authority temporary deposits and bills together with tax instruments. The first two of these accounted for 94 per cent of A 3 at the end of 1980. Source: Appendix, ET, var. issues.

An: Foreign assets of the U.K. non-bank private sector. The data employed was from the series on "overseas assets" of the non-bank private sector. Source: Appendix, ET, vat. issues.

A 2 : Bank lending in sterling to the U.K. non-bank private sector. Source: FS, var. issues.

A1: Money, sterling M 3. Source: FS, various issues. r 1 : Rate on certificates of deposit. Source: FS. r 2 : Local authority rate on temporary loans. Source: BEQB. r 3 : Yield on government consols. Source: FS. r 4 : Eurodollar rate. Source: FS. S : Sterling-dollar exchange rate. Source: FS. W: Net financial wealth of the U.K. non-bank private sector. Source:

Appendix, ET, var. issues. A0: Other private sector assets. Calculated as the sum of (i) U.K. ordinary

and preference shares, (ii) other domestic and long-term loans and (iii) domestic trade and other credit. Source: Appendix, ET, var. issues.

494 Colin Kearney and Ronald MacDonald

A s : Other private sector liabilities. Calculated as the sum of (i) public sector loans, (ii) other domestic long-term loans and (iii) domestic trade and other credit. Source: Appendix, ET, var. issues.

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4 9 6 Colm Kearney and Ronald M a c D o n a l d The Sterling-Dollar Exchange Rate

Z u s a m m e n fa s s u n g: Ein Strukturmodell des verm6genstheoretischen Ansatzes zur Erkl~i- rung des Pfund-Dollar-Wechselkurses. - In diesem Aufsatz wird eine Variante des verm6- genstheoretischen Ansatzes zur Bestimmung des Wechselkurses in seiner Strukturform auf den Pfund-Dollar-Kurs des Zeitraums 1973-1982 angewandt. Dabei wird die Methodologie yon Brainard und Tobin benutzt, wodurch sichergestellt wird, daft die Koeffizienten bestimm- ten Restriktionen geniJgen. Gesch~itzt wird das Modell sowohl mit der Kleinst-Quadrate- Methode als auch mit dem Theil-Goldberger-Verfahren der gemischten Sch~itzungen. Meh- rere Aktiva-Schocks werden simuliert und die Reaktionen der Zinss/itze und der Wechselkurse aufgezeigt.

R6sum6: Un modble structurel de ,,portfolio balance,, du taux de change Sterling-Dollar. - Dans cet article les auteurs appliquent la structure d 'une version de l 'approche de ~,portfolio balance~ h la d6termination du taux de change sterling-dollar sur la p6riode 1973-1982. Dans le module, la m6thodologie de Brainard et Tobin est utilis6e qui garantit que les restrictions n6cessaires d'addition sont satisfaites. Les m6thodes des moindres carr6s ordinaires aussi bien que les proc6dures d'estimation mixte de Theil-Goldberger sont appliqu6es pour estimer le modble. Les auteurs simulent un nombre des chocs d'actif et illustrent la r6ponse des taux d'int6r~t et du taux de change.

Resu m en : Un modelo ,,portfolio balance~, estructural del tipo de cambio entre la libra esterlina y el d61ar. - En este trabajo se presenta una versi6n del modelo de ,,portfolio balance,, para determinar el tipo de cambio, que es implementado estructuralmente para el tipo libra esterlina - d61ar en el periodo 1973-1982. En la implementaci6n de este modelo se utiliza la metodologfa de Brainard y Tobin, que garantiza la consistencia de las restricciones. Con el fin de estimar el modelo se aplica tanto el m6todo de cuadrados minimos como tambi6n el m6todo mixto de Theil y Goldberger. Se llevan a cabo varias simulaciones a base de shocks de activos para ilustrar la reacci6n de las tasas de inter6s y del tipo de cambio.

Documents

A structural portfolio balance model of the Sterling-Dollar exchange rate