public sector borrowing, the money supply and interest rates

OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 47, 3 (1985)0305-9049 $3.00

PUBLIC SECTOR BORROWING, THE MONEYSUPPLY AND INTEREST RATES

Co/rn Kearney and Ronald MacDonald

I. INTRODUCTION

The Medium Term Financial Strategy (MTFS) of the ConservativeGovernment incorporated the assumption of a close relationshipbetween the public sector borrowing requirement (PSBR), the moneysupply and interest rates. A desire to avoid excessive reliance on highinterest rates in pursuit of monetary targets led the authorities tocurtail their borrowing requirement through fiscal restraint. The MTFSoutlined a path for the PSBR which was set to be consistent withachieving the planned reduction in the growth of the money supplyover the medium term with lower rates of interest. In what follows weinvestigate the basis for the view that fiscal policy needs to be 'dove-tailed' in with monetary targets. More specifically, we consider therelationship between the PABR, the money supply and interest rates.

Section II outlines the arguments for and against the existence of aclose relationship between these variables. The main argument used tosupport the existence of such a relationship has been in terms of port-folio balance between the stock of money and the outstanding stock ofpublic sector debt. Although there are theoretical and empirical reasonsfor being sceptical about the strength of this argument, there is littleconclusive evidence. In Section III we construct a portfolio balancemodel of the UK economy and estimate it on quarterly data over theperiod l972(l)-1982(4) using the TheilGoldberger mixed estimationprocedure. Given the authorities' fiscal stance, the model solves for themoney supply, interest rates and the rate of foreign exchange. InSection IV we simulate the model in order to provide evidence on thenature of the relationship which exists between the variables underdiscussion. The final Section summarizes the paper and concludes thata major element in the Government's economic and financial policyseems to be lacking in theoretical foundation and empirical support.

II. THEORETICAL CONSIDERATIONS

The role attributed to fiscal policy in the Conservative Government'santi-inflation strategy is based upon the proposition that a 'large'PSBR will induce either an increase in the rate of monetary growth or

249

250 BULLETIN

higher rates of interest. Speaking at a conference in January 1980, theFinancial Secretary to the Treasury stated:

the PSBR and the growth of the money supply and interestrates are very closely related. Too high a PSBR requires either thatthe Government borrow heavily from the banks - which addsdirectly to the money supply; or, failing this, that it borrows fromindividuals and institutions, but at ever-increasing rates of interest,which place an unacceptable squeeze on the private sector.

ETCSC (1980) p. 21

The rationale to the Government's financial strategy follows that ifmonetary control is to be secured at low rates of interest, the PSBRmust be reduced. The remainder of this Section considers the theoreti-cal basis for the existence of a close relationship between the variablesunder discussion and sets the scene for the econometric analysis whichfollows.

The issue is particularly important insofar as the recession caused theautomatic fiscal stabilizers to raise the PSBR above its 'consistent' pathand forced the following choice on the authorities: either raise interestrates (which was not desired and probably reduced output further byappreciating the exchange rate), reduce the PSBR by offsetting thefiscal stabilizers (which also depressed output further), or allow'cyclical' overshooting of the monetary targets. The issue is not apeculiarly British one. Large federal US deficits have rekindledAmerican concern about the interest rate consequences of both the sizeand the method used to finance these deficits. In this case analysts whobelieve that large deficits cause high interest rates claim that excessiveborrowing by the Federal Reserve kept market interest rates fromdeclining appreciably in the early 1980's when inflation and economicactivity were slowing down.

There are three basic routes through which the level of public sectorborrowing, the growth of the money supply and interest rates arerelated. These are the transactions approach, the portfolio balanceapproach and the expectations approach.

The Transactions Approach

In the standard closed-economy ISLM framework, an increase in tlieGovernment deficit will expand the level of income and raise thetransactions demand for money balances. This will cause the rate ofinterest on bonds to rise by an amount depending on the way in whichthe deficit is financed and on the interest elasticities of investmentexpenditure and the demand for money.' If the economy under

A money-financed deficit could result in lower bond interest rates. McCaleb and Sellon Jr.(1980) provide a neat discussion.

PUBLIC SECTOR BORROWING 25 1

discussion is open to foreign trade, the interest rate consequences arealso dependent upon whether the exchange rate is held fixed or allowedto float as well as on the degree to which capital is internationallymobile.

A number of relevant issues are appropriately raised here. First, itis crucial to co-ordinate 'the' interest rate used in the investment andmoney demand functions as otherwise the IS and LM curves exist ondiagrams with different vertical axes and their relative elasticities arenot comparable. The ISLM framework constitutes an over-simplifica-tion in this regard by focusing exclusively on 'the' rate of interest onbonds. It is generally accepted that the appropriate rate in the ISequation is the return to physical capital and/or some long-term bondrate, while both long and short rates have been used to estimate moneydemand equations. Also, the estimated interest elasticities in moneydemand equations have differed significantly with respect to the ratechosen, being larger for long-term than for short-term rates. In addition,empirical work indicates that the income elasticity of the demand formoney varies with the definition of money being used, the evidencesuggesting that it is greater for the broader definitions.2 The MTFStargeted on a broad measure of money, £M3, and this undoubtedlycontributed to the relationship between the PSBR and the level ofinterest rates.

The Portfolio Balance Approach

There exists a voluminous literature emanating from the work ofBlinder and Solow (1973) which focuses on the macroeconomic im-portance of the extent to which debt-financed Government deficitsincrease the private sector's perceived wealth. Insofar as anticipationsof future tax liabilities are less than perfect, increased wealth raises thedemand for financial assets including real balances. This shifts the LMcurve leftwards causing 'the' rate of interest on bonds to rise furtherthan that implied by consideration of the transactions effect inisolation.

Barro (1974) and Miller and Upton (1974) have emphasized theimportance of the future tax liabilities and the role of intergenerationaltransfers and bequests on individuals' wealth calculations. They showthat under certain conditions including a system of operative inter-generational transfers or bequests, there is no net wealth effect ofgovernment deficit finance. The degree of rationality, foresight andmarket perfection required by the Barro analysis clearly strains thecredibility of the analysis however. Also, as Feldstein (1982) pointsout, the 'optimal' bequest may well be negative and the form of the

2 Coghian (1980) pp. 130-38 contains a summary of the UK evidence.

252 BULLETIN

bequest may often involve current expenditure (on education, forexample). The Barro neutrality hypothesis has also been challenged onthe basis of empirical evidence. In this vein Butkiewicz (1979) showshow outside wealth is an important variable in a standard moneydemand equation.

The Expectations Approach

In addition to the transactions and portfolio balance approaches, thereare grounds for believing in the existence of an expectations routethrough which public sector deficits may impinge upon interest rates.This route could consist of one or more of the following:

a high PSBR may induce expectations of high interest rates in thefuture in order to finance the deficit in a non-monetary way;it may induce expectations of a rise in the money supply and highinterest rates in order to control monetary growth;there may be expectations that the PSBR is inherently inflationaryregardless of how it is financed and the inflation premium willthen be incorporated in nominal interest rates.

The first of these has recently been emphasized in an American contextby Blanchard and Dornbusch (1984). More generally, Turnovsky andMiller (1984) have extended the original Blinder and Solow (1973)model to analyse the effects of both anticipated and unanticipatedfiscal expansions on the term structure of interest rates. Feldstein(1982) also refers to a 'fiscal expectations effect' through which fiscalimpulses impinge upon the private sector's economic behaviour to anextent which depends upon the resulting change in agents' expectationsabout the Government's future fiscal actions. The change in expecta-tions and consequent behaviour that results from any given fiscalaction will differ over time in a way that depends on the entire historyof previous fiscal stances and the debates about how to manage them. Itfollows therefore, that it is extremely difficult to accurately predictthe private sector's behavioural responses to fiscal actions in anyparticular year.

In commenting upon the Conservative Government's anti-inflationstrategy, the Treasury and Civil Service Committee sought evidence onthe following possible relationships:

the size of the PSBR and the level of interest rates with a fixedrate of monetary growth;the size of the PSBR and monetary growth with fixed interestrates, andthe demand for money and the level of interest rates with a fixedPSBR.

PUBLIC SECTOR BORROWING 253

Evidence was submitted by HM Treasury and the Bank of England aswell as by many prominent economists which showed a broadconsensus on relationship (iii). Although the majority of commentatorsemphasized the importance of the portfolio balance approach inexplaining the first two relationships, a wide disparity of views wasexpressed.

Both HM Treasury and the Bank of England argued that conditionsof money market equilibrium imply a close relationship between thelevel of the PSBR, the level of interest rates and the growth of themoney stock in the medium term. The main argument used in supportof this thesis was that changes in the PSBR constitute the dominantsource of changes in private sector wealth and that the latter is aninfluential determinant of the demand for money. Thus monetarytargets together with a rising PSBR necessitate higher rates of interest.A corollary of this is that bond financed deficits require higher interestrates to induce the private sector to hold a higher proportion of itswealth in the form of Government securities. Thus monetary targetswith fixed interest rates necessitate reductions in the PSBR. Theseviews were supported by Professors Beenstock and Minford whoemphasize the portfolio balance nature of the argument.

The Government is quite correct to believe that in practice therate of growth of the money supply depends upon the PSBR. Inprinciple there need be no relationship between money supplyand the PSBR. If somehow the banks were prevented from buyingguts and the Government allowed real debt service costs to rise forever the PSBR could be completely funded. This immediatelydemonstrates why monetary growth is likely to depend uponPSBR. First, banks are in the market for gilts. Secondly, thepractical bounds to debt service costs imply that Governmentcannot indefinitely unbalance private sector portfolios in favourof gilts. The Government knows this and so does the privatesector. It is in this sense that one may speak of a portfolio balancerelationship between the stock of money and the outstandingstock of public sector liabilities generated by the PSBR in the past(cumulative PSBR). To deny this relationship is to imply theabsurdity that borrowing may grow for ever at finite interest rates.

[TCSC (1980) p. 57]

Many economists, including Professors Dornbusch, Friedman, Hahn,Kaldor and Laidler, submitted evidence to the Committee rejecting theexistence of close relationships described in (j) and (ii) above. Theformer offers data drawn from the UK in the 1970's to conclude that3

See TCSC (1980) p. 69. This quotation constitutes a summary of the elegant argumentsput forward by Professor Kaldor (ibid. p. 92).

254 BULLETIN

it is well established that there is no one-for-one link between thePSBR and money creation. Changes in international reserves,changes in private sector indebtedness or non-bank private sectorfinancing of deficits are the elements that break any tight linkbetween budget deficits and money creation.

Friedman summarizes his views on the matter quite clearly.4

There is no neccessary relation between the size of the PSBRand monetary growth. .. . The size of the PSBR does affect thelevel of interest rates. However, for given monetary growth, themajor effect on interest rates is exerted by the real PSBR not thenominal PSBR.

It is interesting to note, however, that Friedman's reliance upon the realborrowing requirement to influence interest rates has been explicitlyrejected by Professors Beenstock and Minford. Recent debate about thevalidity and usefulness of this distinction has generated more heat thanlight and it is not our intention to raise the temperature here. Suffice itto remark that it seems unreasonable to argue on portfolio balancegrounds for the existence of a close relationship between publicborrowing and interest rates on the one hand, and to deny the im-portance of measurements of the public sector's real indebtedness onthe other, since the latter will surely impinge upon market rates ofinterest to the extent that it causes portfolio substitution by changingreal private financial wealth.

III. THE MODEL AND ITS ESTIMATION

The model which forms the basis of our econometric analysis ispresented below:MD =m(rm,rl,rb,rf+ise)W (I)LD = l(rm,rl,rb,rf+ Ase) W (2)B' =b(rm,rl,rb,rf+zse)W (3)s.FD =f(rm,rl,rb,rf+zse)W (4)W M+B+s.FL (5)M =PSD_(B+B*)+L_BOF_X (6)

where;

M = broad moneyL = bank loansB = domestic bonds

= domestic bonds held by overseas residentsF = foreign assets denominated in foreign currencyW = net financial wealth of the non-bank private sector

See ibid. pp.56 and 57.


PSD = outstanding public sector debtBOF = balance for official financingX = banks 'switched' position plus their net overseas and non-

deposit liabilitiess = spot exchange raterm = own rate on moneyrl = rate on bank loansrb = yield on domestic bondsrf = rate of return on foreign assets

and superscripts D and e denote respectively the demand for and theexpected value of a variable.

Equations (l)-(4) are the demands for money, bank loans, domesticbonds and foreign assets respectively by the UK non-bank privatesector. They are posited to depend upon net financial wealth, the ownrate and all cross rates. Equation (5) defines the net wealth constraintof the non-bank private sector as the sum of the assets less debts.Equation (6) describes the accounting framework of the combinedpublic/banking sector. In first difference form it corresponds to thefamiliar presentation of the counter-parts to changes in the quantityof money, sterling M3. In this form, changes in the quantity of moneyare seen to result basically from three sources.

the unfunded public sector borrowing requirement,

PSBR(= PSD) - (B + B*)

sterling lending to the private sector, L, andchanges in reserves due to a non-zero BOF.

The design of the model reflects the prejudice inherent in the issues tobe addressed. To this end the portfolio behaviour of the private sectoris made explicit whereas the behaviour of the banks is not realisticallyanalysed.

The model constitutes a standard version of the portfolio balanceapproach to modelling the exchange rate made popular by Branson(1977). Equations (l)-(S) may be recognized as a straightforwardgeneralization involving an extra (negative) asset, bank loans. With thestocks of assets given at each point in time they can be substituted intoequations (l)-(4) to give the equilibrium conditions. In a previouspaper we have solved a model of this vintage5 to examine the effectson interest rates and the exchange rate of asset accumulation and openmarket operations.

Three approaches have hitherto been adopted in implementing port-folio balance models such as that contained in equations (l)-(6) above:the data can be mined for a satisfactory set of equations as in Lovell

See Kearney and MacDonald (1984).

256 BULLETIN

(1983); the general-to-specific modelling strategy proposed by Hendryand Mizon (1978) and developed for the portfolio balance model byDavidson and Keil (1983) and Davidson (1984) can be used; finally, theframework proposed and adopted by Backus, Brainard, Smith andTobin (BSST) (1980) can be applied.

The general-to-specific modelling strategy adopted by Davidson andKeil (1983) and Davidson (1984) incorporates error correctiorLmechanisms and is commendable insofar as the estimation results aredata coherent. In implementing the portfolio balance model, however,this approach leaves the money demand function as the unwrittenequation which forces the balance sheet constraint to hold in a rathercrude fashion. The stimulation properties of models which have beenestimated in this way are often fraught with peculiarities caused by theunwritten equation taking a form which is devoid of economic meaningand interpretation. Given the emphasis accorded to policy simulationsof the portfolio balance model in this paper, we were keen to adopt anapproach which avoids this problem. Furthermore, attempts to imple-ment a generalized autoregressive representation (including four lags onall relevant variables) proved unsatisfactory insofar as implausiblevalues were obtained for the long-run responses of asset holdings as aproportion of wealth. In implementing the model contained inequations (1)-(6) therefore, we adopted the BSST (1980) methodologywhich provides, we believe, data coherent equations, sensible long-runholdings of asset stocks, and in addition, satisfies the appropriateadding-up restrictions.

Since our asset demand specifications are similar to those employedby Brainard and Smith (1976), Backus and Purvis (1980), BSST (1980)and Green (1982), we shall accordingly be brief in describing theirderivation.

Treating the negative of bank loans as an asset, the long run positionof the ith asset is described by

a n

th13to+ ß11nr1/=1

where a7 represents the desired stock of asset j (j = M, L, B and F)and r1 represents the relevant interest rate variables. The coefficients aresubject to the adding-up restrictions across equations given by

= 1 (8)

jj0 j1,...,n

(7)


The asset demand functions take a familiar partial adjustment for-mat in the short run. For example, the actual holdings of the ith assetare given by

a1 =j1 yJ(a7() a/(_l)) j = 1,..., n (19)

The -y's, the adjustment parameters, are subject to the cross-equationadding-up restrictions that:

i1y= 1 /= l,...,n (10)

By combining (7) and (9) we obtain

a= constant - (t - 1) + 'y, 13,'j ln r1 (11)

w /=1 W /=1

Interest rates enter equation (11) logarithmically because of the findingby Brainard and Smith (1976) that the use of levels of interest ratesoften produces absurd simulation results.

Although the model is avowedly short-run in nature, the assetdemands are derived to be consistent with both short- and long-runportfolio balance. In the econometric estimates of equation (11) weinclude variables which appear on the right hand side of any one assetdemand equation in all others. Furthermore, we use the Theil-Gold-berger mixed estimation procedure to combine our subjectively heldprior information with the data. Previous work by Brainard and Smith(1976) and BBST (1980) demonstrates that the use of prior informa-tion eliminates many of the wrong signs that arise from ordinary leastsquares (OLS) estimation.

Using the Theil-Goldberger procedure to estimate a portfolio balancemodel stands the usual empirical implication of such models on itshead. Researchers commonly mine the data when they estimate assetdemand equations or systems. Although this is not an illegitimatepractice, it is important to note that the iterative process whichcharacterizes a data mine implicitly involves the use of prior informa-tion. That is, certain variables or lags are rejected because the sign orthe magnitude of the estimated coefficients conflict with theresearcher's priors. The disadvantage of this procedure is that in simplyreporting the 'final' results, the researcher does not share with thereader the priors which were used to derive the estimates. In contrast,the Theil-Goldberger mixed estimation procedure makes the priorsexplicit at the outset and provides the reader with the opportunity toeither agree or disagree with them.6

See Learner (1978) for an excellent discussion of this issue.

where

EIuu a2 I, O

1 = O and EI 1 [u'v'] =1[vi [vi L O 'I'

Since the variance-covariance is not a2I +g' a generalized least squaresprocedure must be used. We follow Smith and Brainard (1976) inassuming exchangeability."

1 1

2a, a1

Consider first the specification of the prior matrix. Priors on thelong-run interest rate coefficients are determined in the following way.First, we assume that the assets are gross substitutes so that, ceterisparibus an increase in the own rate on an asset increases its demand anddecreases, or leaves unaffected, the demand for other assets. Grosssubstitutability also implies that own rate effects will be greater thancross rate effects. It is further assumed that assets which constitute alarge proportion of the portfolio have large interest rate responses.Finally two assets which are compatible in terms of liquidity will havelarger cross effects than two assets that are relatively illiquid. Giventhese assumptions the long run interest rate parameters are reported inTable 1. They are clearly subjective but we would expect that manymonetary researchers would find them compatible with their priors.

This assumption is somewhat restrictive but Smith (1981) has shown that the use ofexchangeability in a system similar to ours does not distort the estimates and may be used as a'convenient approximation'.

(14)

(15)

258 BULLETIN

The procedure can be summarily explained by representing the assetmarket model in matrix notation

y = ßX + u (12)

The prior information is expressed as

r = Rß + y (13)

where;

r = a known g X 1 vector (g <k) with as many rows as restrictions.R = a known g X k matrix with as many rows as restrictions and as

many columns as coefficients in the system.ß = a vector formed from all the coefficients in the system.y = a vector of errors with E(v) = O and E(vv) = P.

Combining (12) and (13) we obtain

The next stage is to specify the short run adjustment coefficients. Wefollow BBST in defining the adjustment matrix with diagonal elementsbetween 0 and 1, and with liquid assets adjusting more quickly thanilliquid ones. Our short run interest rate coefficients are derived as theproduct of the long run rate responses (Table 1) and the adjustmentcoefficients (given in the four columns on the right of Table 2(a)).

The prior variance-covariance matrix used to combine the a priorimeans and the data is presented below. In determining the interest rateresponses

we follow Backus and Purvis (1980) in assuming that the standarddeviations are one-half of the largest element in the column. The twostandard deviation bands for the adjustment coefficients are assumed tobe ± 0.15. The off-diagonal elements are assumed to be zero in accor-

0.0306 0 0 0 0 0 0

o 0.0480 0 0 0 0 0

o o 0.0361 0 0 0 0

O 0 0 0.0961 0 0 0

O O 0 0 0.00563 0 0

O O O O O O O

O O O O 0 0.00563 0

O O O O O 0 0.00563

PUBLIC SECTOR BORROWING

TABLE 1Long Run Coefficients

259

Asset (d/W) 1.0 rm rl rb rf

M 0.562 Prior - 0.600 -0.400 -0.200 -0.200OLS -7.147 0.216 -1.336 3.879 0.241Mixed 0.720 0.478 -0.314 -0.238 0.066

L -0.409 Prior -0.300 0.700 -0.200 -0.200OLS 5.147 0.095 0.603 -0.621 -0.233Mixed -0.360 -0.272 0.134 0.174 -0.101

B 0.609 Prior - -0.100 -0.100 0.700 -0.300OLS 5.448 -0.388 1.181 -2.578 -0.034Mixed 1.080 -0.162 0.099 -0.066 -0.170

F 0.234 Prior - -0.200 -0.200 -0.300 0.700OLS -2.448 0.780 -0.448 1.340 0.034Mixed -0.490 --0.061 0.098 0.132 0.050

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262 BULLETIN

dance with Smith (1976) who argues that a fully specified covariancematrix does not appreciably improve on results obtained using theabove procedure.

Estimation Results

A comprehensive description of the data sources and definitionsemployed in the econometric analysis is provided in the data Appendix.It is worth noting here, however, that the UK private sector's netfinancial wealth is published in terms of the following identity:

W_M*+B+s.F+Y_L_Z (16

where W,B,s.FandL are as defined aboveand

= broad moneyY = other private sector assetsZ = other private sector liabilities

In our definition of wealth we have dropped the Y and Z terms. How-ever, since the remaining assets and liability account for almost 90 percent of the variation in private financial wealth, this does not seem arestrictive exclusion. A further modification we make is to use sterlingM3, (M3) instead of the broad money definition (M*) used in equation(16) above. This was done because £M3 has been the authorities'monetary aggregate for targeting purposes and because we were keento compare our estimated equation with single equation estimates ofthe demand for this money.

Consider first the short-run OLS estimates of the portfolio balancesystem, reported in Table 2. The equations appear to fit the data well.Durbin's h-statistic and the first order autocorrelation coefficient, p1,(estimated by maximum likelihood) both indicate the absence of firstorder autocorrelation. The statistic X2o) is the BoxPierce test for thewhiteness of the residual correlogram, and the computed value isinsignificant at the 95 per cent level in all four equations (X2o)3 1.41), at 95 per cent level. Inspection of the residual correlogramreinforced the conclusion that the residuals are tolerably white. Thestatistic F( 12, 12) is the Chow test for parameter stability (which wascomputed by splitting the sample in half and re-estimating theequations for the sub-periods); in all cases this statistic is insignificantat 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. Inan attempt to improve upon these perversities, we applied the mixedestimation procedure. Before combining our priors with the data wechecked that they were compatible by computing Theil's compatibilitystatistic


y=(rR3)[a2R(x'xy1R' + ]1(r_R)'which has a chi-squared distribution with k (= 8) degrees of freedom.Since x2(8) = 15.51 at the 95 per cent level and since our computedvalue of x2 is considerably less, all four equations pass the compati-bility criterion.

Applying the Theil-Goldberger procedure to our system we find thatthe results are more consistent with our priors. Now 9 out of the 1 6interest rate coefficients have the correct a priori signs and of those thatremain 'perverse', three move in the 'correct' direction. Two of theadjustment coefficients also become consistent with the priors. In theequation for sterling M3, for example, the own rate and the banklending rate are wrongly signed with the OLS estimate, but becomecorrectly signed in the mixed estimates. In addition, the foreign ratemoves in the correct direction and the bond rate mixed estimate isinsignificantly different from its prior value.

The OLS long-run coefficients (which are derived from the esti-mated short-run equations reported in Table 2) are in some cases quitedifferent in absolute terms from the priors. Nine out of 16 OLS co-efficients have the 'wrong' sign. One glaring perversity is the long-runOLS bond rate effect which implies that a I per cent increase in thatrate leads to an increase of 3.88 in the proportion of the portfolio heldin money and a decrease of 2.58 in the proportion of held in bonds.Although the long-run mixed estimates are more plausible, particularlyin the case of the money and bank lending equations, 6 out of the 16coefficients remain wrongly signed. The mixed estimates, however,imply a more sensible sign pattern with the private sector borrowingfrom the banks and the overseas sector in order to finance bond andbroad money holdings.

IV. SIMULATION RESULTS

In this section we conduct a number of policy simulations in order toexamine the implications of our econometric analysis for the questionsraised by the Treasury and Civil Service Committee about the relation-ship between the level of public sector borrowing, monetary growthand interest rates. More specifically, we shall introduce the followingpolicy shocks in order to examine the validity of the assertion that ifmonetary control is to be secured at low rates of interest, the level ofpublic sector borrowing must be reduced.

A once-for-all increase of £10 billions in the PSBR which isfinanced by monetary expansion;A similar increase in the PSBR which is financed by issuing debtwith a fixed quantity of money;

264 BULLETIN

(3) An open market switch of £10 billions worth of public sector debtfor money.

Before examining the specific policy simulation results, it is instruc-tive to consider the adjustment dynamics of the estimated model. Itis a disconcerting property of many econometric models that they tendto display inordinately slow or unstable adjustment towards equi-librium. Although the speed and pattern of convergence to equilibriumdepends upon the type of shock, the adjustment speed can be describedby examining the largest possible difference between desired and actualasset holdings after a given number of periods (r). With a given amountof financial wealth (W) and unchanged desired assets a*, equation (15)gives the portfolio disequilibrium that exists r periods after an initialshock.

(a _a*) = (I-F)T (a_1 _a*) (17)

The system converges to equilibrium for all initial conditions if

hm (I-F)T=01 -+

which is the case if the eigenvalues of (I - F)T are less than one inabsolute value. The largest eigenvalues for the priors, the OLS and themixed estimates of the estimated model are 0.50, 0.97 and 0.91 re-spectively. Table 3 below provides a description of the model's adjust-ment speeds by indicating the largest difference between any twoelements in a row of (I - F)T.

The priors are the quickest to return to equilibrium followed by themixed estimate and the OLS estimates are slowest to converge. Thisfinding is consistent with the policy simulation properties which wenow consider.

TABLE 3Model Adjustment Speeds

Quarters Priors OIS Mixed

1 0.500 0.981 0.8632 0.250 0.960 0.8003 0.125 0.938 0.7394 0.063 0.916 0.6805 0.03 1 0.894 0.6246 0.016 0.871 0.5727 0.008 0.849 0.5248 0.004 0.827 0.480

12 0.000 0.741 033616 0.000 0.662 0.23620 0.000 0.591 0.165


The simulation results for the three policy shocks outlined above arepresented in Figures 1-3. In each case we include the results obtainedfrom employing the priors and the OLS estimates in order to allowcomparison to be made with those obtained from the mixed estimates.

Consider first the effects of a monetary financed increase in thepublic borrowing requirement depicted in Figure 1. The mixed esti-mates in panel C illustrates that, in accord with intuition, the return toholding money rises by 10 per cent before returning to equilibriumwhile the Government bond rate initially declines by 50 per centrelative to base before converging monotonically to its new equilibriumlevel. The rate on bank loans converges after a period of mild oscilla-tions. It is interesting to compare this behaviour with the smoother andmore rapid adjustment obtained from the priors. By contrast, the OLSestimates indicate a large increase in both the own rate and the crossrates in the money demand function. This reflects the signs on thepurely data-determined least squares estimates and the gradual cyclicaladjustment towards the new equilibrium levels is consistent with thedynamic adjustment patterns contained in Table 3.

Consider next the results of a similar expansion in the public borrow-ing requirement which is now financed by issuing debt with a fixedsupply of money. Figure 2 presents the details. The mixed estimatesshow an initial reduction in the own rate on bonds relative to baseof 35 per cent along with mixed response of a lesser magnitude of thecross rates. Once more, the contrast between priors and the data-determined least squares estimates is substantial. The latter againexhibits slow and oscillatory dynamic adjustment in contrast to theother results. It is worth noting the extent to which the qualitativeeffects of monetary and bond financed increases in the public borrow-ing requirement on domestic rates of interest are different. Thedisparity is most notable in the OLS simulations and this contrasts withthe mixed estimation results which show similar effects. The latterresult is partly due to the influence of the priors but also reflects thedifficulties involved in obtaining intuitive results from empiricalGovernment debt equations in the UK.

Figure 3 depicts the results of an open market operation in whichthe authorities switch domestic bonds for money in the portfolios ofthe domestic non-bank private sector. This is perhaps the most interest-ing of the policy simulations considered insofar as it is the mostrealistic. It is indeed noticeable that the mixed estimates indicate anincrease in all rates of interest. This contrasts with the results obtainedfrom the priors which yields a higher bond rate and a lower return onholding money as expected. Once again the data-determined leastsquares simulation displays characteristically large interest rate effectswhich oscillate as expected while converging at a slow rate.

Before we turn to consider the implications of our analysis for thequestions raised by the Treasury and Civil Service Committee on the

266 BULLETIN

25

15

5----------------z

uu

270

u Ouu

70

30u

150

A : PRIORS

7'/\_J_

Legend

CDRAIEx LARAIED GBRAIE

5-15 I I I

25

B: OILS ESTIMA TES

C:MIXED ESTIMATES

O

10 x/20

30 j40 .

500 5 10 15 20 25

Quarters

Fig. 1. Money financed increase in PSBR (1Ob)

-5

- IS

0

- 100

200

20

lo

O


B: OILS ESTiMA TES

C: MIXED ESTIMATES

-x10 I-

- e-" -,30-40 I

0 5 10 15 20 25

Quarters

Fig. 2. Bond financed increased in PSBR (flOb)

LegendA PRIORS

CDRAIE1

7.'- X LARAIE

DGBRAIEf_J \/5'

o

- lo

20

30

800

600

400

200

O

200400600800

10

\/\.I\,

I ji

B: OILS ESTIMATES

C: MIXED ESTIMA TES

10 15

Quarters

Fig. 3. Open market switch of bonds for money (flOb)

o 5 20 25

268 BULLETIN

Legend

CDRAIEX LARAIE

A : PRIORSD GBRAIE


relationship between the PSBR, the money supply and interest rates, itis appropriate to mention how the policies considered here affect therate of foreign exchange of sterling. Figure 4 depicts the exchange rateconsequences of the three policy simulations conducted using themixed estimates. The most obvious point to emerge from the Figure isthat all three policies result in appreciation of the exchange rate. Thishappens in the case of monetary financing because the own rate onbroad money rises in all three simulations and this explains thedifference from analyses in which a narrow definition of money isemployed with no own rate. It is also worth noting that bond financeddeficits, in accord with intuition, result in greater and longer exchangerate overshooting than their monetary counterpart. This would implygreater losses in competitiveness and output if these effects wereallowed to feed through to a more general model of goods and factorsmarkets.

We now consider the implications of our analysis for the nature ofthe portfolio balance relationship which links the PSBR, the moneysupply and interest rates. Perhaps the most instantly observable con-clusion which emerges can be summarized in terms of recognizing thatthere exists many different rates of interest. This fact was recognizedby Professor Lord Kaldor in his evidence submitted to the Treasury and

Legend

Money Finance

X Bond Finance

D Open Market OperationQ

VV

30

VQV

20

10

O 5I I

10 15 20 25Quarters

Fig. 4. Exchange rate consequences of an increase in the PSBR (1Ob) - mixedestimates

50-

40 x

270 BULLETIN

Civil Service Committee, (TSCC (1980) PP. 119-121) but was notemphasized by other contributors. More specifically, the implicationsof our analysis may be case in a clearer light by using them to answerthe questions raised by the Committee outlined on page 252 above.

With a fixed supply of money, simulation (2) shows that a bond-financed increase in the PSBR will raise some rates of interest andreduce others. There is, therefore, no simple portfolio balance relation-ship linking high public sector borrowing with high rates of interest. Itis rather more likely that if such a relationship has recently beenobserved in the UK, it results from attempts to secure monetary controlby curtailing private demand for bank credit rather than attempting tooffload public debt to an unwilling private sector. Moreover, it should berecognized that public sector debt is not a homogeneous commodityinsofar as the Government can finance its deficit by varying the typesof asset it supplies towards those currently being demanded by wealth-holders, and it has done this over the 1970's and early 1980's. In short,the variety of public sector debt must be considered as contributing tothe weakness in the portfolio balance relationship between publicsector borrowing, the money supply and interest rates.8

The second question raised by the Committee concerned therelationship which exists between the PSBR and the money supplywith fixed rates of interest. Once more, the analysis presented hereconcludes that in terms of the portfolio balance approach, there is nosimple relationship between these variables which would correspond tothe views expressed in the MTFS. Rather, the present analysis suppliesevidence that the question is itself mis-placed insofar as it is impossibleto imagine such an event in practice.

It is appropriate to conclude this section by examining the implica-tions of our empirical analysis for the validity of this assertion.Monetary stringency accompanied by a tight fiscal stance which reducesthe level of public sector borrowing causes some rates of interest torise and others to fall. Conditions of portfolio balance cannot thereforebe relied upon as a sound rationale to a policy which attempts toreduce the level of public sector borrowing in order to secure monetarycontrol with low rates of interest.

V. SUMMARY AND CONCLUSIONS

The Government's strategy with respect to the PSBR is founded uponthe proposition that reductions in this variable are necessary in order toachieve lower monetary growth without exorbitant interest rates. Thosewho agree with this proposition have argued their case predominantlyin terms of a portfolio balance relationship between the PSBR, private

8 Llewellyn and Kearney (1984) expand on this issue.


wealth and the demand for financial assets by the non-bank privatesector. In Section II of this paper we outlined the arguments for andagainst this proposition. Subsequent sections developed, estimated andsimulated a portfolio balance model of the UK financial system in orderto cast light upon the validity of the proposition.

We conclude by noting firstly that there are strong reasons for beingsceptical about the strength of any portfolio balance relationshipbetween the PSBR, the money supply and interest rates. The formalanalysis abstracted from these caveats and found that although therelationship may emerge over long periods of time, conditions ofportfolio balance cannot be relied upon to provide a sound basis forrestricting the level of public sector borrowing in order to securemonetary control with low rates of interest. In short, a major elementin the government's economic and financial policy seems to be lackingin theoretical foundation and empirical support.

University of LoughboroughUniversity of AberdeenDate of Receipt of Final Manuscript: May 1985

DATA APPENDIX

This Appendix describes the data and definitions used in the study inalphabetical order. The following abbreviations are used: BEQB = Bankof England Quarterly Bulletin; ET = Economic Trends; FS = FinancialStatistics.

B Domestic bonds held by the non-bank private sector. This seriesis calculated as the sum of (i) public sector long term debt; (ii)national savings; (iii) Treasury bills; (iv) local authority temporarydeposits and bills together with tax instruments. The first two ofthese items accounted for 94 per cent of B at the end of 1980.Source Appendix, ET, various issues.

B* Domestic bonds held by overseas residents. Source FS, variousissues.

BOF Balance of official financing. Source FS, various issues.F Foreign assets of the UK non-bank private sector. The data

employed was from the series on 'overseas assets' of the non-bank private sector. Source Appendix, ET, various issues.

L Bank lending in sterling to the UK non-bank private sector.Source FS, various issues.

M Money, sterling M3. Source FS, various issues.M* Broad money (sterling and other currencies). Source Appendix,

ET, various issues.PSD Outstanding public sector debt. This series was calculated as

M + (B + B*) + BOF + X - L. This can be seen from identity

272 BULLETIN

(6) in the text. The resultant series is not appreciably differentfrom the figures for end-March published in BEQB.

rîn Rate on certificates of deposit. Source FS.rl Local authority rate on temporary loans. Source BEQB.rb Yield on government consols. Source FS.rf Eurodollar rate. Source FS.S Sterling-dollar exchange rate. Source FS.W Net financial wealth of the UK non-bank private sector. Source

Appendix, ET, various issues.X The sum of banks' 'switched' position plus their net overseas and

non-deposit liabilities. Source FS, various issues.Y Other private sector assets. Calculated as the sum of (i) UK

ordinary and preference shares, (ii) other domestic and long-termloans and (iii) domestic trade and other credit. Source Appendix,ET, various issues.

Z Other private sector liabilities. Calculated as the sum of (j) publicsector loans, (ii) other domestic long-term loans and (iii)domestic trade and other credit. Source Appendix, ET, variousissues.

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Barro, R. J. (1974). 'Are Government Bonds New Wealth?' Journal of PoliticalEconomy, Vol. 82, pp. 1095-18.

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Blinder, A. S. and Solow, R. M. (1973). 'Does Fiscal Policy Matter?', Journal ofPublic Economics, Vol. 2, pp. 3 19-38.

Brainard, W. C. and Smith, G. (1976). 'The Value of A Priori Information in Esti-mating a Financial Model', Journal of Finance, pp. 1299-322.

Branson, W. H. (1977). 'Asset Markets and Relative Prices in Exchange RateDetermination', Institute for International Economic Studies, Reprint SeriesNo. 48.

Butkiewicz, J. L. (1979). 'Outside Wealth, the Demand for Money and theCrowding Out Effect', Journal of Monetary Economics, Vol. 5, pp. 249-58.

Coghian, R. (1980). The Theory of Money and Finance, Macmillan Press.Davidson, J. E. H. (1984). 'Money Disequilibrium: An Approach to Modelling

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Feldstein, M. (1982). 'Government Deficits and Aggregate Demand', Journal ofMonetary Economics, Vol. 9, pp. 1-20.

Green, C. J. (1982). 'Preliminary Results from a Five Sector Flow of Funds Modelof the United Kingdom 1972-1977', Discussion Paper No. 26, University ofManchester.

Hendry, D. F. and Mizon, G. (1978). 'Serial Correlation as a Convenient Simplifi-cation, not a Nuisance: a Comment on a Study of the Demand for Money bythe Bank of England', Economic Journal, Vol. 88, pp. 549-70.

Kearney, C. and MacDonald, R. (1984). 'A Structural Portfolio Balance Model ofthe Sterling-Dollar Exchange Rate', AUTE Conference Paper, University ofBath.

Learner, E. E. (1978). Specification Searches, Wiley, New York.Llewellyn, D. T. and Kearney, C. (1984). 'The British Monetarist Experiment:

A Preliminary Assessment', Economics, Spring, pp. 15-22.Lovell, M. C. (1983). 'Data Mining', Review ofEconomics and Statistics, Vol. 65,

pp.1-12.McCaleb, T. S. and Sellon, G. H. Jr. (1980). 'On the Consistent Specification of

Asset Markets in Macroeconomic Models', Journal of Monetary Economics,Vol.6, pp.401-17.

Miller, M. H. and Upton, (1974). Macro-Economics: A Neoclassical Introduction,(Irwin, IL).

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