Fiscal Deficits Interest Rates and Inflation

7/29/2019 Fiscal Deficits Interest Rates and Inflation

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Economic and Political Weekly July 22, 2000 2537

Special articles

Fiscal Deficits, Interest Rates

and InflationAssessment of Monetisation Strategy

The relationship between budget deficits, money creation and debt financing suggests thatinterest rate targeting and inflation control are both monetary and fiscal policy issues. Thepaper formalises these links within two analytical frameworks, static as well as dynamic,

which by highlighting the concepts of the high interest trap and the tight money paradox,respectively, suggests that, for any given deficit, there exists optimal levels of monetisation

and market borrowings. The model is then applied to evaluate the implications of the unionbudget 2000-01 and the results indicate that unless government borrowings are reducedsubstantially, and about 40 per cent of the deficit is monetised, the inflation rate as well as

the interest rate could be much higher than what they fundamentally ought to be.

rate reduction becomes questionablebecause of the implications of the en-suing fiscal arithmetic on inflation andinterest rates.

Nevertheless, both the finance minister

and the RBI seem to be confident that thetiming of government debt issues as wellas the cluster of other measures announced such as the cut in the cash reserve ratio(CRR) which would release an additionalRs 7,200 crore into the system would

be such as to ensure that interest rates donot rise. However, the issue is not thatsimple because the mere timing of govern-ment debt issues cannot bridge the fun-damental gap between resources and re-quirements, nor can a one-off infusionameliorate the impact of sustained and

large-scale borrowings on inflation andinterest rates.

In this context, it would be interestingto quote from one of the finance ministerspost-budget interviews: Excessive domes-tic borrowings to finance current expen-ditures has resulted in debt service pay-

ments approaching unsustainable levels. Ifwe do not raise resources and instead takerecourse to even higher borrowing nextyear, we will jeopardise our prospects forgrowth, re-ignite the flames of inflation,sow the seeds of another balance of pay-

ments crisis and place an unfair burden onthe next generation. Implicit in thismessage seems to be the underlying caveatthat unless fiscal deficits are substantiallyreduced, monetisation of these deficits on

a scale much larger than that which isexisting presently may soon become ab-solutely necessary.

All this suggests that targeting interestand inflation rates would depend criticallyon both the size of the deficit and, equallyimportant, on the respective shares ofmonetisation and market borrowings inthis overall deficit which implies thereforethat interest rate targeting as well as in-flation control are ultimately both mon-etary and fiscal policy issues.

IUnpleasant Fiscal Arithmetic

Milton Friedmans famous statementthat inflation is always and everywhere amonetary phenomenon is correct. How-ever, while rapid money growth is con-ceivable without an underlying fiscal

balance, it is unlikely. Thus rapid inflationis almost always a fiscal phenomenon[Fischer and Easterly 1990: 138-39]. Thisinteraction between monetary and fiscalpolicy exemplified by the relationship

The Reserve Bank of Indias recentdecision to reduce the bank rate isseen by many as an attempt to drive

down interest rates to near global levelsto ensure that the recovery process cur-

rently under way is further stimulated. Thisreduction was long overdue in view of thelow prevailing inflation rate (below 4 percent) which implied that India claimedthe dubious distinction of having one ofthe worlds highest real, or inflation-

adjusted, lending rates (of about 8 percent) as well as tactically feasible giventhe stability of the Indian currency (whichdepreciated by just over 2 per cent during1999-2000).

However, the broader strategy behindsuch a reduction of trying to help a debt-

ridden government to borrow cheaply fromthe market must eventually address itselfto the fact that any success in sustaininga lower interest rate structure would hingecrucially on the complementarity of fiscalpolicy as reflected both in the fiscal deficitas well as the government borrowings

programme. In such a context, once theprojected fiscal deficit for 2000-01ofRs 111,275 crore of which a staggeringRs 108,746 crore will be financed throughmarket borrowings is factored into theanalysis, the sustainability of the interest

M J MANOHAR RAO


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Economic and Political Weekly July 22, 20002538

between fiscal deficits and inflation is oftenconsidered the heart of macroeconomicsand has been the focus of extensiveempirical research [Agnor and Montiel1996]. One of the commonest explana-tions for the inflationary consequences offiscal deficits in developing countries isthat the central bank, being under the directcontrol of the government, often passively

finances deficits through money creation.On a theoretical plane, however, there

is an appealing argument which relies onthe existence of strong expectational ef-fects linked to perceptions about futuregovernment policy. Private agents in aneconomy with high fiscal deficits may atdifferent times form different expectationsabout how the deficit will eventually beclosed. For instance, if the public believesat a given moment that the governmentwill attempt to reduce its fiscal deficitthrough inflation (thus eroding the real

value of the public debt), current inflation which reflects expectations of futureprice increases will rise. If, later, the

public starts believing that the governmentwill eventually introduce an effective fis-cal adjustment programme to lower thedeficit, inflationary expectations will ad-just downwards and current inflation willfall [Drazen and Helpman 1990].

In this context, a particularly well knownexample of the role of expectations aboutfuture policy is provided by the monetar-ist arithmetic or the so-called tight money

paradox. In a seminal contribution, Sargentand Wallace (1981) showed that when afinancing constraint forces the governmentto finance its deficit through the inflation

tax, any attempts to lower the inflation ratetoday, even if successful, will require ahigher inflation rate tomorrow. For a givenlevel of government spending and con-ventional taxes, the reduction in revenuefrom money creation raises the level ofgovernment borrowing. If a solvencyconstraint imposes an upper limit on publicdebt, the government will be forced to

eventually return to money financing. Atthat stage, however, the rate of moneygrowth required will be much higher as itwill have to finance not only the originalprimary deficit that prevailed before theinitial policy change, but also the higher

interest payments due to the additionaldebt accumulated as a result of the policychange.

In their theoretical analysis of the inter-action between monetary and fiscal policy,Sargent and Wallace focus primarily onthe case where the time paths of both

government spending and tax revenues arefixed a situation in which it is the centralbank that must, by design, eventually givein to the fiscal authority. However, thesame framework is equally applicable tothe case where the central bank moves first

and sets monetary policy independently.Here, lower rates of money growth sooneror later require lower fiscal deficits and,

in this modified framework, it is thereforethe fiscal authority that must capitulate tothe central bank [Burdekin and Langdana1992].

The importance of such a reverse direc-tion of influence was originally suggestedby Sargent (1985) who characterised thecombination of tight money and largedeficits during the Reagan administrationas a game of chicken. Here, if the

monetary authority could successfully stickto its guns and forever refuse to monetiseany government debt, then eventually thearithmetic of the governments budget

constraint would compel the fiscal autho-rity to back down and to swing its budgetback into balance [Sargent 1985:248].Under such circumstances, if the centralbank does not yield by monetising(a proportion of) the deficit, and if nofurther borrowings from domestic or for-eign sources are available, then fiscal policymust necessarily be constrained.

Admittedly, both situations where oneof the authorities must eventually give into the other are rather extreme. What ismore likely is that for any given deficit,there would exist optimal levels ofmonetisation and borrowings. Thus, sol-

vency and macroeconomic consistencywould impose constraints, in terms of sucha choice, if both fiscal and monetary policyoptions are to be synchronised in an at-tempt to reduce the inflation rate.

Based upon these implications, we setout two analytical frameworks static as

well as dynamic which examine the natureof the relationship between deficits, sei-gnorage and debt which has long beenconsidered the central elements in theorthodox view of the inflationary pro-cess in developing countries. We then apply

both these models in the current Indiancontext and examine whether the fiscalstance as reflected in the union budget2000-01 is consistent with the proposedmonetary stance of trying to reduce infla-tion and interest rates.

IIHigh Interest Trap

When an economy, in the process ofliberalisation, encounters inflation rateswhich are sticky downwards, the problemin most cases lies in the government fiscal

deficit. However, the destabilising effectsof a budget deficit in an open economyare not confined to inflation alone. Thebudget deficit, which constitutes negativepublic sector savings, increases the current

account deficit (when it is viewed as thedifference between domestic investmentand savings). Thus, inflation and BOPcrises often go hand-in-hand with budgetdeficits. It is thus a necessary condition forstabilisation to close the budget deficit asrapidly as possible. However, the elimi-nation of budget deficits is not a sufficient

condition for stabilisation from an initiallyhigh-inflation trap because, although thesource of prolonged inflationary pressuresis in most cases a large budget deficit,elements of inertia in the dynamics ofinflation often give inflation a life of itsown after a certain period of high inflation

has elapsed. Thus, for example, inflationmay accelerate in response to certain otherfactors, for example, external price shocks,even when the government budget deficithas been reduced or has not risen.

The dynamics of such inflationary

Figure 1: High Interest Trap

InflationRate ()

Interest Rate (i)

MM1 MM2 MM0MM3 EE

H1

H

B

T

L

O

A


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processes usually manifest themselves indiscrete jumps in the inflation rate. Whilesuch inflation rate jumps are often influ-enced by the size of the fiscal deficit, theymay not be directly correlated with it: ineffect, an economy may be stuck at a highinflation equilibrium because of a givenhigh budget deficit although, with the samebudget deficit, it could have been at a

lower level.Such a phenomenon was formally

modelled by Bruno and Fischer (1990)who highlighted the role of inflationaryexpectations and the potentially destabi-lising effects of fiscal rigidities to explainthe concept of the high inflation trap. Inthis paper, we extend their basic moneyonly model by considering both moneyfinancing as well as debt financing anddemonstrate the existence of dual equili-bria under which the economy may finditself in a high interest trap if the govern-

ment resorts to excessive market borrow-ings in order to finance its fiscal deficit.

Assume that the demand for real money

balances (M/P) takes the semi-logarithmicform given by:M/P = Ayei ...(1)where M is nominal money supply, P is

the price level, y is real output, i is thenominal interest rate, is the incomeelasticity of real money demand, and isthe interest rate (semi-) elasticity of moneydemand.

Decomposing the fiscal deficit (FD) into

interest payments on the domestic debt andthe primary deficit, we have:FD = (i+)D + x. Py ...(2)

The first term on the right-hand-side ofeq (2) denotes interest payments, where(i+) is the average nominal interest rateon public debt1 and D is the total debtstock; and the second term denotes theprimary deficit, where x is the ratio of theprimary deficit to nominal income (Py).

Given the financing rule that this fiscal

deficit can be financed either by money-financing (M) or debt-financing (D), we

have (with a dot for the time derivative):FD = M + D ...(3)

Linking together eqs (2) and (3), anddividing throughout by nominal income(Py), yields:M/Py + D/Py = FD/Py

= (i+)(D/Py) + x ...(4)which can be rewritten as:

(M/M).(M/P).(1/y) + (D/D)d

= f = (i+)d + x ...(5)where f (=FD/Py) is the ratio of the fiscaldeficit to nominal income and d (=D/Py)is the debt-income ratio.

Letting (=M/M) denote the rate ofmoney growth, (=D/D) the rate of growthof borrowings, substituting eq (1) intoeq (5) and re-arranging terms yields:

Aya-1e-i = (i + e d)d + x ...(6)Differentiating eq (1) logarithmically

with respect to time and assuming steadystate (i e, i = 0) yields: = + g ...(7)where (= P/P) is the inflation rate andg (= y/y) is the real growth rate. Substi-tuting eq (7) into eq (6) and rewriting theresultant expression in terms of the infla-tion rate yields: = [(i+-)d+x]/[Ay1ei] g ...(8)

Eq (8) is plotted in Figure 1. The curveMM0 represents all combinations of and

i for which the monetised deficit is con-stant: hence MM0 represents an iso-

(monetised)-deficit line which is upwardsloping because a rising interest rate (whichwould increase the deficit and decrease themonetary base) must be offset by (anincrease in money growth which entails)a rising inflation rate to keep the monetiseddeficit constant. Given a constant f and ,the economy is always located on the MM0curve, since the government is bound byits budget constraint. However, any in-crease in would shift MM0 rightwards,

and vice versa.Invoking the Edwards-Khan interest rate

determination equation (Edwards and Khan1985) which states that, in a semi-openeconomy, the nominal interest rate is aweighted average of the closed economy

Fisherian equation and the open economyuncovered interest rate parity equation, wehave:i = (1 ) (r + ) + (if + e

e) ...(9)where r is the domestic real rate, if is theforeign interest rate; ee is the expected rateof depreciation; and is an index mea-

suring the extent of financial openness of

the economy.Eq (9) can be rewritten as: = i/(1) [/(1)](if+e

e) r ...(10)

Eq (10) is represented by the straight lineEE in Figure 1 and, as depicted, the MM0curve and the EE line intersect twice,implying two potential steady state equi-libria: the low interest equilibrium at L andthe high interest equilibrium at H.

If there is no debt financing, the curveshifts upwards (say, to MM1) and theremight be no steady state solution implyingthat the economy degenerates into hyper-inflation because of excessive moneycreation. However, with an optimal amountof debt financing, there would be a unique

steady state at T (denoted by the point oftangency between the curve MM2 and the

line EE) at which both inflation and in-terest rates could be stabilised. The exist-ence of two steady state equilibria in thecase of the original MM0 curve thus sug-gests that an economy, with a more thanoptimal level of borrowings, may find itselfat the high interest trap H, rather than atthe low interest trap L. Whether this islikely to happen would depend on therelative stability of the respective equilib-rium points.2

Is the reduction of the monetised deficita sufficient condition for stabilisation ata lower level of inflation? The answer isa qualified negative. Consider, for example,in Figure 1, the effect of a decrease inmoney financing (implying an increase in

debt financing) when the economy is ina steady state at point H. The curve MM0shifts rightwards to MM3 implying aninstantaneous increase in the interest ratefrom H to A, and a gradual further upwardmovement of (and i) from A to H asthe government prints money rapidly to

Figure 2: Sub-Optimal Monetisation of Deficit

Inflation

Rate

H

0.2

0.15

0.1

0.05

0

0.05 0.075 0.1 0.125 0.15 0.175Interest Rate

EE

MM

L


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offset a shrinking monetary base. Thus, asstated earlier, while the source of an in-flation could be a large monetised deficit,the dynamics of inflation and interest ratesmay be such that they could refuse torespond to lower monetisation rates unlessaccompanied by special stabilisationmeasures.

Translated into stabilisation policy for

inflation control, this theory thereforesuggests that for any given fiscal deficit,there exists an optimal level of monetaryaccommodation at which both the infla-tion rate as well as the interest rate couldbe stabilised. If there is excessivemonetisation, there would be no steadystate, and inflation could continue to in-crease indefinitely. On the other hand, ifthere is insufficient monetisation, imply-ing a high level of market borrowings, theeconomy could find itself in a high infla-tion/high interest equilibrium. The impor-

tant implications of these results is that byensuring such an optimal degree of mon-etary accommodation, the government can

avoid the danger of inflation and interestrates being higher than what the funda-mentals require them to be.

IIIStatic Optimisation

Estimated ModelAs a first step to obtaining policy guide-

lines in the current Indian context based

upon the above model, we provide belowthe estimated version of eq (1):M/P = 0.0513y1.2298e3.2267i ...(11)where M is broad money supply (M3), Pis the GDP deflator (1980-81 = 1), y isGDP at factor cost at constant (1980-81)prices, and i is the 1-year term deposit rate.

The parameters of the above equationwere estimated using annual time seriesdata over the 10-year period 1990-2000.The time-varying parameter estimates were

obtained using the Kalman filtering andsmoothing recursion algorithms [Rao

1997). We have provided above only thefinal Kalman smoother estimator of eq (1)for 1999-2000 which would forecast theconditional mean of (M/P) for 2000-01based on the complete data set. It is thusseen that: A=0.0513, =1.2298 and=3.2267.

Assuming an output growth of 6 per centin 2000-01, i e, g = 0.06, implies that GDPat factor cost (at 1980-81 prices) wouldincrease to Rs 371,483 crore, i e, y =371483.Substituting all these values into eq (8)yields its following estimated form:

= [(i+-)d+x]/[0.9774e3.2267i] 0.0738 (12)Assuming that, in 2000-01, the foreign

interest rate (proxied by the 1-year LIBOR)would be 6 per cent and the expected rateof depreciation would be 5 per cent, i e,if= 0.06 and e

e = 0.05, yields the followingestimated version of eq (10): = 1.25i 0.0437 ...(13)

where, based on Rao (2000), we have set: = 0.20 and r = 0.0162.

Eqs (12) and (13) comprise a set of twoequations in two unknowns (i and ) andin order to solve the model, we needestimates of x, d, and . The union budget2000-01 projects a gross fiscal deficit(GFD) of Rs 1,11,275 crore of whichRs 1,08,746 crore would be financedthrough (gross) market borrowings.Decomposition of the GFD indicates thatinterest payments would amount toRs 1,01,266 crore leaving behind a re-

sidual primary deficit of Rs 10,009 crore.As the GFD is assumed to be 5.1 per centof GDP, it implies that the projected es-timate of GDP at market prices in 2000-

01 is Rs 2,181,863 crore, representing a12.2 per cent increase over its previouslevel of Rs 1,944,607 crore in 1999-2000.Finally, it is estimated that the total do-mestic liabilities of the centre would bearound Rs 908,131 crore by the end of1999-2000.

Based upon all these indicators, thefollowing four required parameter esti-

mates emerge: (1) The primary deficitwould be 0.46 per cent (=10009/2181863) of GDP in 2000-01, i e, x =0.0046. (2) Total domestic liabilities were46.7 per cent (= 908131/1944607) of GDP

in 1999-2000, i e, d = 0.467. (3) Internaldebt would increase by 11.97 per cent(=108746/908131) in 2000-01, i e, =0.1197 (almost equal to the projectedgrowth rate of nominal GDP in 2000-01).(4) Considering that the implicit interestrate on public debt is around 11.15 per cent(=101266/908131) and that the 1-year term

deposit rate is currently about 8 per cent,it implies that the interest rate differentialin 2000-01 would be approximately 315basis points, in i e, = 0.0315.

Substituting all these estimates intoeq (12) yields:

= [0.4670i0.0366]/[0.9774e3.2267i]0.0738 ...(14)

Optimal Market Borrowings

Eq (14), plotted by the curve MM inFigure 2, represents all combinations ofand i for which the growth rate of debt ()

would be constant at 11.97 per cent. Eq (13)is represented by the straight line EE inFigure 2, with slope equal to 1.25 andintercept equal to -0.0437 on the -axis.As depicted in the figure, the MM curveand the EE line intersect twice: the low levelequilibrium at L (i = 0.070 and = 0.044)and the high-level equilibrium at H(i = 0.160 and = 0.156).

It is extremely interesting to note in thiscontext that despite the simplicity of themodel, as well as the absence of severalother important factors affecting interestand inflation rates, the current inflationrate (4.6 per cent) and the current interestrate (8 per cent) are very much in the near-neighbourhood of the low level equilib-rium, clearly highlighting the practicalas well as the policy relevance of thisframework.

However, despite the accuracy of thesepredictions, simulations indicated that this

low level equilibrium solution was un-stable.3 While these results cannot bedirectly construed to imply that the infla-tion and interest rate could increase to theextent suggested by the stable solution atpoint H, they do suggest the possibilitythat, if the fiscal stance remains unaltered,

then there could be a discrete jump in theinflation rate which, as mentioned earlier,is often influenced by the magnitude andfinancing pattern of the fiscal deficit. Thehigh level equilibrium predictions aretherefore more indicative of the general

direction, if not exact magnitude, of changelikely as a result of the proposed govern-ment borrowings programme.4

The important question therefore iswhether an increase in monetisation wouldlead to a higher level of inflation. To answerthis, consider, for example, in Figure 1, theeffect of an increase in money financingwhen the economy is at point H. The curveMM0 shifts leftwards to MM2 implying afall in the interest rate from H to B, anda gradual further downward movement of

because the rise in the monetary base

reduces the need to increase (and i)from B to T. Thus, if high interest ratesare the result of a high level of governmentborrowings, then the dynamics of inflation

Table: Optimal Market Borrowings underAlternative Scenarios

Expected Rate Growth Rate

of Depreciation (Per Cent)

5.0 6.0 7.0

4.0 97170 80370 63569

5.0 100803 84002 672026.0 104435 87635 70834


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and interest rates could be such that theyrespond favourably only to higher levelsof monetisation.

In the context of our model, this impliesthat the growth rate of market borrowingsshould be decreased to an optimal level(*) at which the iso-deficit curve MMwould be tangential to the interest rate lineEE. Numerical simulations indicated thatat * = 0.0925 there would be such atangential solution. Given the current debtstock, a 9.25 per cent increase in borrow-ings rather than the budgeted 12 per cent implies that, for the given fiscal deficitof Rs 111,275 crore, the optimal level of(gross) market borrowings in 2000-01

should be about Rs 84,002 crore whichis about Rs 24,744 crore less than the

budgeted amount at which point, theinterest rate and inflation rate would beabout 10 per cent and 8.13 per cent, respec-tively. The important implications of theseresults is that by ensuring this optimal levelof monetisation which is about 24.5 percent of the fiscal deficit the governmentcan avoid the danger of the interest andinflation rates being trapped at the stablehigh level equilibrium solution, regardlessof where precisely it may lie.

Growth, Depreciation andMarket Borrowings

Needless to say, the optimal financingpattern would depend crucially on thegrowth rate and the expected depreciationrate. If the money demand function is stable,then high growth rates would invoke higher

levels of monetisation to prevent interestrates from rising. Contrariwise, high ratesof depreciation would, by increasing in-terest rates, reduce money demand, thereby

allowing the government to raise moreresources from the market without putting

further pressure on interest rates.

Based on numerical simulations, weprovide, in the Table, the optimal levelsof (gross) market borrowings (in Rs crore)for alternative growth and exchange ratedepreciation scenarios.

The results indicate that for every per-centage point increase in the growth rate,gross market borrowings need to be redu-ced by about Rs 16,800 crore; and that forevery percentage point increase in the rateof depreciation, gross market borrowingscan be stepped up by about Rs 3,600 crore.This implies that if the economy grows at

7 per cent in 2000-01, as is optimisticallyexpected, then monetisation should bemuch higher: of the order of about 39.6per cent of the GFD.5 Thus, avoiding theperils of the high interest trap would in-

volve balancing the needs of the govern-ment vis-a-vis the needs of the economy.

IVTight Money Paradox

How reliable are the above results interms of analysing the impact of

monetisation and market borrowings oninflation and interest rates in the long run?In order to answer this question, we needto extend the above static framework byincorporating dynamic ingredients fromthe monetarist arithmetic model ofSargent and Wallace (1981). Howeverbefore doing so, it would be useful if weinitiate the discussion by providing a brief

restatement of the basic Sargent-Wallace(SW) results.

In their paper, SW consider two simplemacroeconomic models. The first consists

of two equations, one being the govern-ment budget constraint given by (seeeq (3)):FD = M + D ...(15)where FD is the fiscal deficit (net of in-terest payments), M is the monetary base,and D is the stock of privately held govern-

ment debt. The second equation of the SWModel I is the simplest version of the

quantity theory, i e,P = Mv/y ...(16)where P is the price level, v is the (assumedconstant) velocity of money, and y is realGNP. In the SW Model 2, this equationis replaced by the money demand function:M/Py = ...(17)where is the rate of inflation.

In the case of their first model, a rea-sonable translation of the SW results yields(SW Result 1): If the real rate of interestis a constant r, output is growing exoge-nously at a given rate g, and the steady state

debt income ratio is constant, then it mustbe true that high deficits lead to highinflation. The proof is that in steady state,the growth rate of debt () equals theinflation rate plus the real growth rate, i e, = + g. By the quantity theory, it mustalso be true that = + g, where is thegrowth rate of money. Consequently, itfollows that = and = g in steadystate and, therefore, if large deficits cause to be high, then and must also belarge in steady state.

In their second model, the SW results

can be split up into two parts. The first partreads (SW Result 2): Given a constantexogenous real rate of interest r which isgreater than the exogenous natural rate ofgrowth g, a constant debt-income ratio insteady state, and some regularity condi-tions that resolve problems of non-exist-ence and uniqueness, then one can deter-mine the steady state value of inflation.This result is arrived at thus: Mimickingthe solution strategy in SWs Appendix B,we obtain the following non-linear differ-ential equation in inflation: .

= 1[f (rg)d + g +(g) ] ...(18)

where f and d represent constant steadystate deficit-income and debt-income ra-tios, respectively. One can then derive asteady state value of that will be thesmallest possible sustainable value in steadystate. Denote this value by *(d).

The final claim of the SW paper makesuse of the second model (SW Result 3):Consider a situation where the initial stockof debt and money supply is given, andthe time path of deficits (net of interest)

Figure 3: Potential Instability of Debt Finance

Inflation

Rate

0.12 -

0.1 -

0.08 -

0.06 -

0.04 -

0.02 -

0 -0 50 100 150

Time Periods

Optimal monetisation Sub-optimal monetisation


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is fixed and positive for time between 0and T, and fixed at zero for all time beyondT. Then a low initial path for money supply(i e, for M(t), 0 t T), can lead to a highervalue for *[D(T)/P(T)y(T)] than a higherinitial path for money supply. This resultis proved via numerical simulations.

Despite the widespread interest that thispaper has generated in the literature,6 the

fact remains that the essence of the basicSW result has been ignored in Indian policy-

making circles, where thinking has beenlargely dominated by traditional mone-tarist concerns regarding the direct impactof money growth on inflation, overlookingin the process the indirect effects of lowmonetisation on the evolution of the debt-income ratio and its subsequent and irre-vocable impact on future fiscal deficits.

These results lead us to view the currentcombination of relatively tight money andlarge deficits as an unsustainable policy

stance. While it is true that if the RBIrefuses to monetise any debt, then thefinance ministry might be compelled toswing its budget back into balance, it is

undeniable that if political compulsions donot permit a fiscal reduction, then it is theRBI which would be eventually forced tomonetise a much larger proportion of thedeficit than what would have been neces-sary had it embarked on an optimalmonetisation programme right away. Thisis why the SW result that a low initialpath for money supply can lead to a higher

level of inflation assumes paramountimportance. Thus, fiscal solvency andmonetary accommodation are inter-dependent and impose hard constraintswhich need to be dynamically evaluatedwhile exercising the choice between money

or debt financing.To extend the static framework devel-

oped in Section III which indicated thatan optimal monetisation level was neces-sary to avoid the high-inflation trap andestablish the SW results, we need toformalise the dynamic nature of the link-

ages between money, inflation, interest,deficits and debt.

To do so, we follow the SW traditionand invoke the quantity theory equation(see eq 16) from which we obtain thefollowing long run relationship betweenthe rate of inflation (), money growth ()

and real output growth rate (g): = g ...(19)where we have set velocity shocks (v/v)to be equal to zero.

The interest rate determination equation(see eq (9)) remains unchanged and con-

tinues to be given by:

i = (1 )(r + ) + (if+ ee) ...(20)

where, as before, r is the domestic real rateof interest, ifis the nominal foreign interestrate, ee is the expected rate of depreciation,and is the financial openness index.

In order to fully capture the dynamicnexus between deficits and the inflation-ary process, we incorporate the Aghevli-

Khan hypothesis [Aghevli and Khan 1978]and the Tanzi-Olivera effect [Olivera 1967,

Tanzi 1988] into the model. As such, wenow assume that x (the primary deficit-income ratio) which was hitherto aconstant in the static framework is anincreasing function of the inflation rate.This implies that:x = Be, > 0 ...(21)

Substituting the above expression, whichincorporates fiscal erosion or the widen-ing gap between government expendituresand revenues due to inflation, into eq

(5) yields:f = (i+)d + Be ...(22)

Given the government budget constraint(see eq (3)) and writing for the proportionof the fiscal deficit monetised by themonetary authorities, we have:M = FD, 0 1 ...(23)

We now modify the money demandfunction (see eq (1)) by setting =1.7 Thisyields:M/Py = Aei ...(24)

Dividing eq (23) by Py; rewriting M/Pyas the product of (M/M) and (M/Py); and

then invoking eq (24) to replace M/Py,yields the following solution for the rateof money growth (): = (1/A)ei f ...(25)From eqs (3) and (23) we have:D = (1-)FD ...(26)

Differentiating the identity d=D/Py withrespect to time, and ignoring second- andhigher-order interaction terms, yields:dPy + dPy + dPy = D ...(27)

Dividing both eqs (26) and (27) by Py;

and linking them together yields thefollowing expression for the evolution of

the debt-income ratio:d = (1)f (+g)d ...(28)

Eqs (19), (20), (22), (25) and (28) cons-titute the model defining inflation, inter-est, deficits, money and debt; and it is seenthat the evolution of these five interactingvariables is governed entirely by whichis the only instrument in the framework.To establish the essence of the SW con-tention, we have to show that sub-optimalmonetary accommodation (i e, too low avalue of) can destabilise the model by

increasing the level as well as the variabil-

ity of the long run rate of inflation. If thisis borne out, then there could just aboutexist an optimal level of monetary accom-modation (*) which stabilises inflationprecisely at that rate which satisfies thesustainability condition for public debt.8

V

Long-Term Fiscal StanceEstimated Model

In order to obtain policy guidelines basedupon the above dynamic model, we needestimates of its six parameters and fourexogenous variables. As a first step todoing so, we provide below the estimatedversions of eqs (24) and (21):M/Py = 0.8867e3.1185i ...(29)x = 0.006743e8.6478 ...(30)

As before, the time-varying parametersof the above equations were estimated

using the Kalman filter algorithm whichwas applied to annual time series data overthe 10-year period 1990-2000.9 We haveprovided above only the final Kalmansmoother estimators of eqs (24) and (21)

which would forecast the conditional meansof (M/Py) and x for 2000-01 and beyond.Thus, it is seen that: A=0.8867, =3.1185,B=0.006743 and =8.6478.

As far as the remaining two parameterswere concerned, we assumed that the indexof financial openness would remain atabout 20 per cent, i e, = 0.2; while the

differential between the average interestrate on public debt and the 1-year termdeposit rate would stabilise at 300 basispoints, i e, = 0.03.

As far as the four exogenous variableswere concerned, we assumed that: (i) real

output would grow at 6 per cent, i e,g=0.06; (ii) the foreign interest ratewould be 6 per cent, i e, i f = 0.06;(iii) expected rate of depreciation would

be 5 per cent, i e, ee= 0.05; and (iv) domesticreal rate of interest would be 2 per cent,i e, r = 0.02

Based upon the above set of estimates,the structural form of the dynamic modelcan be set out as follows: = 0.06 ...(31)i = 0.038 + 0.8 ...(32)f = (i + 0.03)d + 0.006743e8.6478 ...(33) = 1.1278e3.1185i

f ...(34)d = (1)f ( + 0.06)d ...(35)

Eqs (31)-(35) thus comprise a set of fiveequations in five unknowns (, i, f, and d)and the model can be closed and simulatedby choosing a value for which, in ourframework, is assumed to be a constant


7/9


over the entire period of simulation.Before we initiate the simulations, it

would be interesting to see if we can actuallyanticipate the behaviour of the model. Weinitially set out below the relationshipbetween the real rate of interest on publicdebt (rd) and the real growth rate (g) whenthese two variables are equal:rd = (i + ) = g ...(36)

Substituting eq (32), as well as thenumerical estimates of and g, into the

above expression yields:[(0.038 + 0.8) + 0.03] = 0.06 ...(37)which indicates that rd g only if 0.04.As such, a low value of which depressesthe rate of inflation below 4 per cent wouldyield rd > g and thus violate the sustain-ability condition for debt. Consequently,there would be a steady rise in d and asubsequent increase in f. This, in turn,would increase and the resulting in-crease in would imply that eventually

rd < g. This turnaround would, by the samereasoning, ultimately result in falling in-flation rates, leading once again to rd > g.Thus, these results suggest that cyclicalvariations in inflation can be damped downonly by an optimal level of monetisation.

Optimal Monetisation

Considering that over the period 1991-2000, the monetised deficit was approxi-mately 11 per cent of the GFD, in the initialsimulation, we set = 0.11. The results

which are set out in Figure 3 (patternlabelled sub-optimal monetisation) indicate, just as anticipated, that for suchan extremely low value of, the inflationrate is relatively high and volatile, settlingdown finally to the range between 1.2 percent and 9.2 per cent, with no evidenceof a steady state solution.

The interesting aspect of these results isthat they seem to replicate fairly well the

general pattern of actual inflation over thisperiod: a steady decline from a high of 13.7per cent in 1991-92 to an all-time low of

just under 1.7 per cent in the second halfof 1999-2000 and then a sudden upturnto about 4.6 per cent currently. While itwould be rather premature to suggest thatthe model is mimicking the actual datapattern, the facts are inescapable: sub-optimal levels of monetisation can yieldhigher and more volatile inflation rates.

To try and damp down the inflation rateto its optimal level given by eq (37), wegradually increased the value of and the

calibration results which are set out inFigure 3 (the pattern labelled optimal mon-

etisation) indicated that at * = 0.43,the inflation rate would stabilise at justover 4 per cent. Thus, the model indicatesthat by monetising about 43 per cent of

the GFD, the government would not only

be able to reduce the inflation rate to areasonably low level, but also satisfy thestability condition for public debt, therebyensuring the long run sustainability of thefiscal stance.

Velocity Shocks, InstrumentInstability

Logarithmically differentiating eq (24)with respect to time, setting g = 0.06 and = 3.1185 yields the following relation-ship incorporating velocity shocks that

were ignored hitherto between inflation,money growth and output growth: = 0.06 + 3.1185i ...(38)which replaces eq (31) in the model duringthe simulation.

The results (Figure 4) obtained by set-ting = 0.11 once again are dramaticbecause they indicate that sub-optimal

monetisation coupled to any instability, inthe form of velocity shocks, can increasethe level as well as the variability of in-flation rather drastically. It is seen that foran identical value of, the inflation rate

is now extremely high and volatile, oscil-lating violently from 7.6 per cent to 43.6per cent. Moreover, in keeping with theobserved patterns of disinflation after aprolonged period of hyperinflation, it isseen that the inflation rate, after attainingits peak, dissipates very rapidly beforerising up once again.

As before, we gradually increased themonetisation level and it was seen that at

* = 0.36, the long run inflation rate at-tained a steady state of just over 4 per centwithout any oscillatory behaviour whatso-

ever. Thus, the results indicate that if thereare any inherent instabilities in the dynam-ics of inflation, then the optimal value ofthe instrument variable () is damped down

considerably (to 36 per cent of the GFD

as against 43 per cent in the earlier ex-periment), which is a direct corollary ofthe famous instrument instability prob-lem first alluded to in the literature byHolbrook [1972].10

VIConclusions

The basic notion of the sustainability offiscal deficits centres around the issue ofwhether the existing split between moneyfinancing and debt financing, if pursued

indefinitely, can ensure that the debt-in-come ratio stabilises around a reasonablesteady state equilibrium solution. The sus-tainability condition under an accountingapproach indicates that real output growth(g) should exceed the real rate of interest

on public debt (rd) for ensuring the stabilityof the debt-income ratio. If g > rd, even

a persistent rise in the debt-income ratiodue to primary account deficits may nothave any adverse implications from theviewpoint of fiscal sustainability. All thiscan be easily ascertained by substituting

eqs (5) and (36) into eq (28) to yield:d = (rd g)d + x f ...(38)implying that for given levels of the fiscaldeficit (f), primary deficit (x) and mon-etary accommodation (), the larger thegap between rd and g, the higher will bethe increase in the debt-income ratio (d).The above analysis indicates that if rd > g,then even with a primary account balance(i e, x = 0), the interest burden on theexisting debt would translate itself into aperpetual growth in the debt-GDP ratio,

unless there is a sufficiently high level of

Figure 4: Explosive Instability of Debt Finance

Inflation

Rate

0.6 -

0.4 -

0.2 -

0 -

0.2 -Time Periods

0 50 100 150 200


8/9


monetary accommodation. If this is notforthcoming, there would be no alternativeother than primary surpluses, which shouldbe adequate to offset the differential be-tween rd and g. Viewed from this angle,the size of market borrowings, which de-termines the interest rate structure, turnsout to be the principal fiscal variable inthe quest for debt-income stability.

The sustainability of debt in the Indiancontext, therefore, needs to be assessed

within the perspective of the debt servicingburden of the deficits. During the 1980s,interest rates were mainly administeredand the adoption of repressionary financ-ing implied that interest rates did not fullyreflect the pressure of government debt onfinancial markets and on the interest ratestructure. Naturally, therefore, the sus-tainability condition, i e, rd < g, was satis-fied in an accounting sense for most of theyears over this period. In such circum-

stances, the primary account balancesoffered a better indicator for assessingfiscal sustainability and, viewed from thisangle, the fiscal structure remained unsus-tainable. The relatively high primary defi-cits of 4.1 per cent and 4.8 per cent during

the first and second half of the 1980s,respectively, led to a secular increase inthe debt-GDP ratio from 45.8 per cent to57.0 per cent, what with the annual growthrate of domestic debt at 19.4 per cent beingmuch higher than the annual growth rateof nominal GDP at 14.9 per cent.

In the 1990s, as a result of fiscal con-solidation, there was a distinct reversal inthese trends, as a result of which the debt-GDP ratio declined from 58.7 per cent in1990-91 to 47.9 per cent in 1996-97.However, in 1997-98, we once againwitnessed the phenomenon of crossover ofdebt growth over GDP growth, and it is

distressing that no attempt has been madein the millennium budget 2000-01 to arrestthis upward spiral and prevent it fromescalating to unsustainable levels. In otherwords, the current evolution of govern-

ment debt which is almost tantamountto a Ponzi scheme type of debt financing is not consistent with the medium-termsustainability of fiscal policies.

Despite such warning signals, there existsa misplaced concern in policy circles thatmonetisation of the fiscal deficit is boundto be inflationary per se. However, ourresults suggest that an optimal expansion

in money supply can be absorbed by theeconomy without causing inflation, as in1999-2000 when despite an M3 growth ofover 14 per cent and a real output growth

of about 6 per cent, the inflation rate waswell below 4 per cent.

With the current low rate of inflation,many indicators suggest that long-terminterest rates (which reflect inflationaryexpectations) could fall still further. Thus,the fiscal stance, in terms of its borrowingsstrategy, as well as the monetary stance,in terms of its monetisation strategy, must

be to ensure that interest rates at the shorterend do not rise too much as this couldflatten or even invert the yield curve in thecoming year, which is often a leadingindicator of a recession.

On a theoretical plane, this implies thata slower increase in the money stock thataccompanies a high government borrow-ings programme will result in high interestrates which would create a budget deficitthat could be unsustainable in the long run.If the resulting solvency constraint thenforces the government to eventually resort

to large-scale monetisation of such defi-cits, then this could take away the inde-pendence of the central bank to follow a

monetary policy attuned towards domesticstabilisation.

In conclusion, by ensuring an optimalsplit between monetisation and borrow-ings in the present, it would be possibleto balance the future needs of the economyvis-a-vis the needs of the government andthereby avoid the high interest/inflationtrap and the subsequent spectre of aneconomic slowdown.

Notes

1 While the theoretical literature assumes that

the interest rate used in the money demand

function is identical to the rate of interest paid

on public debt, in actual empirical applications

this equality is not borne out. Therefore,

is specifically introduced as a measure of the

interest rate differential.

2 The stability of the high inflation trap largely

depends on the degree of accommodation to

the price level of the nominal magnitudes,

such as money supply, the exchange rate and

the wage rate. Such an accommodation is

either built in endogenously (the wage-price

spiral) or through policy design (the crawling

peg exchange rate system), both of which

contribute to the dynamics of inflation.

However, as a result of such accommodation,

once inflation starts accelerating, the economy

loses its nominal anchor, and there is nothing

left to hold down prices.

3 Numerical simulations indicated that the

assumption of rapid asset market adjustment

was sufficient to ensure that the low level

equilibrium solution was unstable.

4 This is an implication of the well known

Lucas critique which states that a regime

switch could invalidate the parameters of an

estimated model. Translated in terms of our

framework, it implies that because the model

was estimated using data over the period

1990-2000, the low equilibrium solution (L)

would be more accurate because the resulting

estimates of i and lie within the range

suggested by the sample space. On the other

hand, if i and were to move towards the

neighbourhood of the high equilibrium

solution (H), this would entail a regime switchnecessitating a re-estimation of the parameters

of eq (11), notably which is the principal

determinant of the curvature of the MM curve.

If now this revised estimate were to increase,

then it would imply a steeper MM curve and,

consequently, the second intersection point

between the MM curve and the EE line, i e,

the stable solution (H), would necessarily be

at a lower level of i and than what is

predicted by the existing model. Thus, the

results do not directly suggest that i and

would increase to 16 per cent and 15.6 per

cent, respectively.

5 It is interesting to note that even the dynamic

version of the present static model, developedin Sections IV and V, predicts an optimal

monetisation level of about 40 per cent of

the GFD.

6 The assumption that r is a constant (and

greater than g) is necessary for the SW results

to pass through. However, an analysis along

the lines of the Mundell-Tobin real balance

effect [Mundell 1963, Tobin 1965] and the

Darby-Tanzi tax adjusted Fisher effect

[Darby 1975, Tanzi 1976] have indicated

that the original Fisher equation: i = r + ,

which is invoked in the SW model, should

be modified to: i = r + , where 1. For

the Mundell-Tobin effect, > 1 implying that

r/ > 0; while for the Darby-Tanzi effect, > 1 implying that r/ > 0. Thus, in both

cases, the assumption of a constant r is

violated.

However, as has been shown by Rao (1998):

(1) even if r > g, the SW results will not pass

through ifr/ (= -1) is small enough as

a result of the Mundell-Tobin effect to yield

r* < g in steady state, and (2) even if r < g,

the SW results will still pass through pro-

vided r/ is sufficiently large enough as

a result of the Darby-Tanzi effect to ensure

that r* > g in steady state (where r* = r +

(r/)).

7 Apart from simplifying the ensuing analysis,

this ensures that income drops out of the

money growth equation (see eq (25)). This

is essential because the presence of y which

would be increasing over time in eq (25)

would have ruled out the possibility of long

run steady state solutions for the model.

8 The sustainability condition which has been

discussed in Section VI states that the real

rate of interest on public debt (rd) should not

exceed the real growth rate (g), i e, rd g.

9 It needs to be noted, however, that the dynamic

evolution of the parameters indicated that

eq (30) was not very stable.

10 Instrument instability refers to the possibility

EPW


9/9


that the adjustment path of the control variable

may be unstable. However, the existence of

stochastic elements or shocks in the model

exerts an inhibiting influence on the adjust-

ment of policy instruments, making it optimal

to adjust them more cautiously. Thus, the

adjustment path is damped down, making

it stable.

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Documents

Fiscal Deficits Interest Rates and Inflation