Fiscal Deficits Interest Rates and Inflation

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Special articles Fiscal Deficits, Interest Rates and Inflation Assessment of Monetisation Strategy The relationship between budget deficits, money creation and debt financing suggests that interest rate targeting and inflation control are both monetary and fiscal policy issues. The paper 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 union budget 2000-01 and the results indicate that unless government borrowings are reduced substantially, 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. M J MANOHAR RAO


he Reserve Bank of India’s recent decision to reduce the bank rate is seen by many as an attempt to drive down interest rates to near global levels to ensure that the recovery process currently under way is further stimulated. This reduction was long overdue in view of the low prevailing inflation rate (below 4 per cent) – which implied that India claimed the dubious distinction of having one of the world’s highest real, or inflationadjusted, lending rates (of about 8 per cent) – as well as tactically feasible given the stability of the Indian currency (which depreciated by just over 2 per cent during 1999-2000). However, the broader strategy behind such a reduction – of trying to help a debtridden government to borrow cheaply from the market – must eventually address itself to the fact that any success in sustaining a lower interest rate structure would hinge crucially on the complementarity of fiscal policy as reflected both in the fiscal deficit as well as the government borrowings programme. In such a context, once the projected fiscal deficit for 2000-01of Rs 111,275 crore of which a staggering Rs 108,746 crore will be financed through market borrowings is factored into the analysis, the sustainability of the interest

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rate reduction becomes questionable because of the implications of the ensuing fiscal arithmetic on inflation and interest rates. Nevertheless, both the finance minister and the RBI seem to be confident that the timing of government debt issues as well as the cluster of other measures announced – such as the cut in the cash reserve ratio (CRR) which would release an additional Rs 7,200 crore into the system – would be such as to ensure that interest rates do not rise. However, the issue is not that simple because the mere timing of government debt issues cannot bridge the fundamental gap between resources and requirements, nor can a one-off infusion ameliorate the impact of sustained and large-scale borrowings on inflation and interest rates. In this context, it would be interesting to quote from one of the finance minister’s post-budget interviews: “Excessive domestic borrowings to finance current expenditures has resulted in debt service payments approaching unsustainable levels. If we do not raise resources and instead take recourse to even higher borrowing next year, we will jeopardise our prospects for growth, re-ignite the flames of inflation, sow the seeds of another balance of pay-

July 22, 2000

ments crisis and place an unfair burden on the next generation.” Implicit in this message seems to be the underlying caveat that unless fiscal deficits are substantially reduced, monetisation of these deficits on a scale much larger than that which is existing presently may soon become absolutely necessary. All this suggests that targeting interest and inflation rates would depend critically on both the size of the deficit and, equally important, on the respective shares of monetisation and market borrowings in this overall deficit which implies therefore that interest rate targeting as well as inflation control are ultimately both monetary and fiscal policy issues.

I Unpleasant Fiscal Arithmetic “Milton Friedman’s famous statement that inflation is always and everywhere a monetary phenomenon is correct. However, while rapid money growth is conceivable without an underlying fiscal balance, it is unlikely. Thus rapid inflation is almost always a fiscal phenomenon” [Fischer and Easterly 1990: 138-39]. This interaction between monetary and fiscal policy exemplified by the relationship


between fiscal deficits and inflation is often considered the heart of macroeconomics and has been the focus of extensive empirical research [Agénor and Montiel 1996]. One of the commonest explanations for the inflationary consequences of fiscal deficits in developing countries is that the central bank, being under the direct control of the government, often passively finances deficits through money creation. On a theoretical plane, however, there is an appealing argument which relies on the existence of strong expectational effects linked to perceptions about future government policy. Private agents in an economy with high fiscal deficits may at different times form different expectations about how the deficit will eventually be closed. For instance, if the public believes at a given moment that the government will attempt to reduce its fiscal deficit through inflation (thus eroding the real value of the public debt), current inflation – which reflects expectations of future price increases – will rise. If, later, the public starts believing that the government will eventually introduce an effective fiscal adjustment programme to lower the deficit, inflationary expectations will adjust downwards and current inflation will fall [Drazen and Helpman 1990]. In this context, a particularly well known example of the role of expectations about future policy is provided by the ‘monetarist arithmetic’ or the so-called tight money paradox. In a seminal contribution, Sargent and Wallace (1981) showed that when a financing constraint forces the government to finance its deficit through the inflation tax, any attempts to lower the inflation rate today, even if successful, will require a higher inflation rate tomorrow. For a given level of government spending and ‘conventional’ taxes, the reduction in revenue from money creation raises the level of government borrowing. If a solvency constraint imposes an upper limit on public debt, the government will be forced to eventually return to money financing. At that stage, however, the rate of money growth required will be much higher as it will have to finance not only the original primary deficit that prevailed before the initial policy change, but also the higher interest payments due to the additional debt accumulated as a result of the policy change. In their theoretical analysis of the interaction between monetary and fiscal policy, Sargent and Wallace focus primarily on the case where the time paths of both


Figure 1: High Interest Trap MM1





H1 H B

Inflation Rate (π)



Interest Rate (i)

government spending and tax revenues are fixed – a situation in which it is the central bank that must, by design, eventually give in to the fiscal authority. However, the same framework is equally applicable to the case where the central bank moves first and sets monetary policy independently. Here, lower rates of money growth sooner or later require lower fiscal deficits and, in this modified framework, it is therefore the fiscal authority that must capitulate to the central bank [Burdekin and Langdana 1992]. The importance of such a reverse direction of influence was originally suggested by Sargent (1985) who characterised the combination of tight money and large deficits during the Reagan administration as a ‘game of chicken’. Here, “if the monetary authority could successfully stick to its guns and forever refuse to monetise any government debt, then eventually the arithmetic of the government’s budget constraint would compel the fiscal authority to back down and to swing its budget back into balance” [Sargent 1985:248]. Under such circumstances, if the central bank does not yield by monetising (a proportion of) the deficit, and if no further borrowings from domestic or foreign sources are available, then fiscal policy must necessarily be constrained. Admittedly, both situations – where one of the authorities must eventually give in to the other – are rather extreme. What is more likely is that for any given deficit, there would exist optimal levels of monetisation and borrowings. Thus, solvency and macroeconomic consistency would impose constraints, in terms of such a choice, if both fiscal and monetary policy options are to be synchronised in an attempt to reduce the inflation rate. Based upon these implications, we set out two analytical frameworks – static as

well as dynamic – which examine the nature of the relationship between deficits, seignorage and debt which has long been considered the central elements in the ‘orthodox’ view of the inflationary process in developing countries. We then apply both these models in the current Indian context and examine whether the fiscal stance as reflected in the union budget 2000-01 is consistent with the proposed monetary stance of trying to reduce inflation and interest rates.

II High Interest Trap When an economy, in the process of liberalisation, encounters inflation rates which are sticky downwards, the problem in most cases lies in the government fiscal deficit. However, the destabilising effects of a budget deficit in an open economy are not confined to inflation alone. The budget deficit, which constitutes negative public sector savings, increases the current account deficit (when it is viewed as the difference between domestic investment and savings). Thus, inflation and BOP crises often go hand-in-hand with budget deficits. It is thus a necessary condition for stabilisation to close the budget deficit as rapidly as possible. However, the elimination of budget deficits is not a sufficient condition for stabilisation from an initially high-inflation trap because, although the source of prolonged inflationary pressures is in most cases a large budget deficit, elements of inertia in the dynamics of inflation often give inflation a life of its own after a certain period of high inflation has elapsed. Thus, for example, inflation may accelerate in response to certain other factors, for example, external price shocks, even when the government budget deficit has been reduced or has not risen. The dynamics of such inflationary

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July 22, 2000

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Figure 2: Sub-Optimal Monetisation of Deficit 0.2


0.15 EE Inflation Rate

processes usually manifest themselves in discrete jumps in the inflation rate. While such inflation rate jumps are often influenced by the size of the fiscal deficit, they may not be directly correlated with it: in effect, an economy may be stuck at a high inflation equilibrium because of a given high budget deficit although, with the same budget 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 inflationary expectations and the potentially destabilising effects of fiscal rigidities to explain the concept of the high inflation trap. In this paper, we extend their basic ‘money only’ model by considering both money financing as well as debt financing and demonstrate the existence of dual equilibria under which the economy may find itself in a ‘high interest’ trap if the government resorts to excessive market borrowings in order to finance its fiscal deficit. Assume that the demand for real money balances (M/P) takes the semi-logarithmic form given by: ...(1) M/P = Ayαe–ßi where M is nominal money supply, P is the price level, y is real output, i is the nominal interest rate, α is the income elasticity of real money demand, and ß is the interest rate (semi-) elasticity of money demand. Decomposing the fiscal deficit (FD) into interest payments on the domestic debt and the primary deficit, we have: FD = (i+ε)D + x. Py ...(2) The first term on the right-hand-side of eq (2) denotes interest payments, where (i+ε) is the average nominal interest rate on public debt1 and D is the total debt stock; and the second term denotes the primary deficit, where x is the ratio of the primary 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), and dividing throughout by nominal income (Py), yields: ⋅ ⋅ M/Py + D/Py = FD/Py = (i+ε)(D/Py) + x ...(4) which can be rewritten as: ⋅ ⋅ (M/M).(M/P).(1/y) + (D/D)d = f = (i+ε)d + x ...(5) where f (=FD/Py) is the ratio of the fiscal deficit to nominal income and d (=D/Py) is the debt-income ratio.

0.1 MM 0.05 L

0 0.05



0.125 Interest Rate

⋅ Letting µ (=M/M) denote the rate of ⋅ money growth, δ (=D/D) the rate of growth of borrowings, substituting eq (1) into eq (5) and re-arranging terms yields: ...(6) µAya-1e-ßi = (i + e – d)d + x Differentiating eq (1) logarithmically with respect to time and assuming steady state (i e, i = 0) yields: µ = π + αg ...(7) ⋅ where π (= P/P) is the inflation rate and ⋅ g (= y/y) is the real growth rate. Substituting eq (7) into eq (6) and rewriting the resultant expression in terms of the inflation rate yields: π = [(i+ε-δ)d+x]/[Ayα–1e–ßi] – αg ...(8) Eq (8) is plotted in Figure 1. The curve MM0 represents all combinations of π and i for which the monetised deficit is constant: hence MM0 represents an iso(monetised)-deficit line which is upward sloping because a rising interest rate (which would increase the deficit and decrease the monetary base) must be offset by (an increase in money growth which entails) a rising inflation rate to keep the monetised deficit constant. Given a constant f and δ, the economy is always located on the MM0 curve, since the government is bound by its budget constraint. However, any increase in δ would shift MM0 rightwards, and vice versa. Invoking the Edwards-Khan interest rate determination equation (Edwards and Khan 1985) which states that, in a semi-open economy, the nominal interest rate is a weighted average of the closed economy Fisherian equation and the open economy uncovered interest rate parity equation, we have: i = (1 – Ω ) (r + π) + Ω (if + ee) ...(9) where r is the domestic real rate, if is the foreign interest rate; ee is the expected rate of depreciation; and Ω is an index mea-

July 22, 2000



suring the extent of financial openness of the economy. Eq (9) can be rewritten as: π = i/(1–Ω) – [Ω/(1–Ω)](if+ee) – r ...(10) Eq (10) is represented by the straight line EE in Figure 1 and, as depicted, the MM0 curve and the EE line intersect twice, implying two potential steady state equilibria: the low interest equilibrium at L and the high interest equilibrium at H. If there is no debt financing, the curve shifts upwards (say, to MM1) and there might be no steady state solution implying that the economy degenerates into hyperinflation because of excessive money creation. However, with an optimal amount of debt financing, there would be a unique steady state at T (denoted by the point of tangency between the curve MM2 and the line EE) at which both inflation and interest rates could be stabilised. The existence of two steady state equilibria in the case of the original MM0 curve thus suggests that an economy, with a more than optimal level of borrowings, may find itself at the high interest trap H, rather than at the low interest trap L. Whether this is likely to happen would depend on the relative stability of the respective equilibrium points.2 Is the reduction of the monetised deficit a sufficient condition for stabilisation at a lower level of inflation? The answer is a qualified negative. Consider, for example, in Figure 1, the effect of a decrease in money financing (implying an increase in debt financing) when the economy is in a steady state at point H. The curve MM0 shifts rightwards to MM3 implying an instantaneous increase in the interest rate from H to A, and a gradual further upward movement of π (and i) from A to H’ as the government prints money rapidly to


offset a shrinking monetary base. Thus, as stated earlier, while the source of an inflation could be a large monetised deficit, the dynamics of inflation and interest rates may be such that they could refuse to respond to lower monetisation rates unless accompanied by special stabilisation measures. Translated into stabilisation policy for inflation control, this theory therefore suggests that for any given fiscal deficit, there exists an optimal level of monetary accommodation at which both the inflation rate as well as the interest rate could be stabilised. If there is excessive monetisation, there would be no steady state, and inflation could continue to increase indefinitely. On the other hand, if there is insufficient monetisation, implying a high level of market borrowings, the economy could find itself in a high inflation/high interest equilibrium. The important implications of these results is that by ensuring such an optimal degree of monetary accommodation, the government can avoid the danger of inflation and interest rates being higher than what the fundamentals require them to be.

III Static Optimisation Estimated Model As a first step to obtaining policy guidelines in the current Indian context based upon the above model, we provide below the estimated version of eq (1): ...(11) M/P = 0.0513y1.2298e–3.2267i where M is broad money supply (M3), P is the GDP deflator (1980-81 = 1), y is GDP at factor cost at constant (1980-81) prices, and i is the 1-year term deposit rate. The parameters of the above equation were estimated using annual time series data over the 10-year period 1990-2000. The time-varying parameter estimates were obtained using the Kalman filtering and smoothing recursion algorithms [Rao 1997). We have provided above only the final Kalman smoother estimator of eq (1) for 1999-2000 which would forecast the conditional mean of (M/P) for 2000-01 based on the complete data set. It is thus seen that: A=0.0513, α =1.2298 and ß=3.2267. Assuming an output growth of 6 per cent in 2000-01, i e, g = 0.06, implies that GDP at factor cost (at 1980-81 prices) would increase to Rs 371,483 crore, i e, y =371483. Substituting all these values into eq (8) yields its following estimated form:


π = [(i+ε-δ)d+x]/[0.9774e–3.2267i] – 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 rate of depreciation would be 5 per cent, i e, if = 0.06 and ee = 0.05, yields the following estimated version of eq (10): π = 1.25i – 0.0437 ...(13) where, based on Rao (2000), we have set: Ω = 0.20 and r = 0.0162. Eqs (12) and (13) comprise a set of two equations in two unknowns (i and π) and in order to solve the model, we need estimates of x, d, δ and ε. The union budget 2000-01 projects a gross fiscal deficit (GFD) of Rs 1,11,275 crore of which Rs 1,08,746 crore would be financed through (gross) market borrowings. Decomposition of the GFD indicates that interest payments would amount to Rs 1,01,266 crore leaving behind a residual primary deficit of Rs 10,009 crore. As the GFD is assumed to be 5.1 per cent of GDP, it implies that the projected estimate of GDP at market prices in 200001 is Rs 2,181,863 crore, representing a 12.2 per cent increase over its previous level of Rs 1,944,607 crore in 1999-2000. Finally, it is estimated that the total domestic liabilities of the centre would be around Rs 908,131 crore by the end of 1999-2000. Based upon all these indicators, the following four required parameter estimates emerge: (1) The primary deficit would be 0.46 per cent (=10009/ 2181863) of GDP in 2000-01, i e, x = 0.0046. (2) Total domestic liabilities were 46.7 per cent (= 908131/1944607) of GDP in 1999-2000, i e, d = 0.467. (3) Internal debt would increase by 11.97 per cent (=108746/908131) in 2000-01, i e, δ = 0.1197 (almost equal to the projected growth rate of nominal GDP in 2000-01). (4) Considering that the implicit interest rate 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 differential in 2000-01 would be approximately 315 basis points, in i e, ε = 0.0315. Substituting all these estimates into eq (12) yields: π = [0.4670i–0.0366]/[0.9774e–3.2267i] –0.0738 ...(14)

Optimal Market Borrowings Eq (14), plotted by the curve MM in Figure 2, represents all combinations of π and i for which the growth rate of debt (δ)

would be constant at 11.97 per cent. Eq (13) is represented by the straight line EE in Figure 2, with slope equal to 1.25 and intercept equal to -0.0437 on the π-axis. As depicted in the figure, the MM curve and the EE line intersect twice: the low level equilibrium at L (i = 0.070 and π = 0.044) and the high-level equilibrium at H (i = 0.160 and π = 0.156). It is extremely interesting to note in this context that despite the simplicity of the model, as well as the absence of several other important factors affecting interest and inflation rates, the current inflation rate (4.6 per cent) and the current interest rate (8 per cent) are very much in the nearneighbourhood of the low level equilibrium, clearly highlighting the practical as well as the policy relevance of this framework. However, despite the accuracy of these predictions, simulations indicated that this low level equilibrium solution was unstable.3 While these results cannot be directly construed to imply that the inflation and interest rate could increase to the extent suggested by the stable solution at point H, they do suggest the possibility that, if the fiscal stance remains unaltered, then there could be a discrete jump in the inflation rate which, as mentioned earlier, is often influenced by the magnitude and financing pattern of the fiscal deficit. The high level equilibrium predictions are therefore more indicative of the general direction, if not exact magnitude, of change likely as a result of the proposed government borrowings programme.4 The important question therefore is whether an increase in monetisation would lead to a higher level of inflation. To answer this, consider, for example, in Figure 1, the effect of an increase in money financing when the economy is at point H. The curve MM0 shifts leftwards to MM2 implying a fall in the interest rate from H to B, and a gradual further downward movement of π – because the rise in the monetary base reduces the need to increase µ – (and i) from B to T. Thus, if high interest rates are the result of a high level of government borrowings, then the dynamics of inflation Table: Optimal Market Borrowings under Alternative Scenarios Expected Rate of Depreciation 4.0 5.0 6.0

Growth Rate (Per Cent) 5.0 6.0 97170 80370 100803 84002 104435 87635

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7.0 63569 67202 70834

July 22, 2000

Figure 3: Potential Instability of Debt Finance 0.12 -

0.1 -

Inflation Rate

0.08 -

0.06 -

0.04 -

0.02 -





Time Periods Optimal monetisation

Sub-optimal monetisation

and interest rates could be such that they respond favourably only to higher levels of monetisation. In the context of our model, this implies that the growth rate of market borrowings should be decreased to an optimal level (δ*) at which the iso-deficit curve MM would be tangential to the interest rate line EE. Numerical simulations indicated that at δ* = 0.0925 there would be such a tangential solution. Given the current debt stock, a 9.25 per cent increase in borrowings – rather than the budgeted 12 per cent – implies that, for the given fiscal deficit of Rs 111,275 crore, the optimal level of (gross) market borrowings in 2000-01 should be about Rs 84,002 crore – which is about Rs 24,744 crore less than the budgeted amount – at which point, the interest rate and inflation rate would be about 10 per cent and 8.13 per cent, respectively. The important implications of these results is that by ensuring this optimal level of monetisation – which is about 24.5 per cent of the fiscal deficit – the government can avoid the danger of the interest and inflation rates being trapped at the stable high level equilibrium solution, regardless of where precisely it may lie.

Growth, Depreciation and Market Borrowings Needless to say, the optimal financing pattern would depend crucially on the growth rate and the expected depreciation rate. If the money demand function is stable, then high growth rates would invoke higher levels of monetisation to prevent interest rates from rising. Contrariwise, high rates of depreciation would, by increasing interest rates, reduce money demand, thereby

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allowing the government to raise more resources from the market without putting further pressure on interest rates. Based on numerical simulations, we provide, in the Table, the optimal levels of (gross) market borrowings (in Rs crore) for alternative growth and exchange rate depreciation scenarios. The results indicate that for every percentage point increase in the growth rate, gross market borrowings need to be reduced by about Rs 16,800 crore; and that for every percentage point increase in the rate of depreciation, gross market borrowings can 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 optimistically expected, then monetisation should be much higher: of the order of about 39.6 per cent of the GFD.5 Thus, avoiding the perils of the high interest trap would involve balancing the needs of the government vis-a-vis the needs of the economy.

IV Tight Money Paradox How reliable are the above results in terms of analysing the impact of monetisation and market borrowings on inflation and interest rates in the long run? In order to answer this question, we need to extend the above static framework by incorporating dynamic ingredients from the ‘monetarist arithmetic’ model of Sargent and Wallace (1981). However before doing so, it would be useful if we initiate the discussion by providing a brief restatement of the basic Sargent-Wallace (SW) results. In their paper, SW consider two simple macroeconomic models. The first consists

July 22, 2000

of two equations, one being the government budget constraint given by (see eq (3)): ⋅ ⋅ FD = M + D ...(15) where FD is the fiscal deficit (net of interest payments), M is the monetary base, and D is the stock of privately held government debt. The second equation of the SW Model I is the simplest version of the quantity theory, i e, P = Mv/y ...(16) where P is the price level, v is the (assumed constant) velocity of money, and y is real GNP. In the SW Model 2, this equation is replaced by the money demand function: M/Py = α – ßπ ...(17) where π is the rate of inflation. In the case of their first model, a reasonable translation of the SW results yields (SW Result 1): If the real rate of interest is a constant r, output is growing exogenously at a given rate g, and the steady state debt income ratio is constant, then it must be true that high deficits lead to high inflation. The proof is that in steady state, the growth rate of debt (δ) equals the inflation rate plus the real growth rate, i e, δ = π + g. By the quantity theory, it must also be true that µ = π + g, where µ is the growth rate of money. Consequently, it follows that δ = µ and π = δ – g in steady state and, therefore, if large deficits cause δ to be high, then µ and π must also be large in steady state. In their second model, the SW results can be split up into two parts. The first part reads (SW Result 2): Given a constant exogenous real rate of interest r which is greater than the exogenous natural rate of growth g, a constant debt-income ratio in steady state, and some regularity conditions that resolve problems of non-existence and uniqueness, then one can determine the steady state value of inflation. This result is arrived at thus: Mimicking the solution strategy in SW’s Appendix B, we obtain the following non-linear differential equation in inflation: . π⋅ = ß–1[–f – (r–g)d + αg + ...(18) (α–ßg)π – ßπ²] where f and d represent constant steady state deficit-income and debt-income ratios, respectively. One can then derive a steady state value of π that will be the smallest possible sustainable value in steady state. Denote this value by π*(d). The final claim of the SW paper makes use of the second model (SW Result 3): Consider a situation where the initial stock of debt and money supply is given, and the time path of deficits (net of interest)


is fixed and positive for time between 0 and T, and fixed at zero for all time beyond T. Then a low initial path for money supply (i e, for M(t), 0≤ t ≤ T), can lead to a higher value for π*[D(T)/P(T)y(T)] than a higher initial path for money supply. This result is proved via numerical simulations. Despite the widespread interest that this paper has generated in the literature,6 the fact remains that the essence of the basic SW result has been ignored in Indian policymaking circles, where thinking has been largely dominated by traditional monetarist concerns regarding the direct impact of money growth on inflation, overlooking in the process the indirect effects of low monetisation on the evolution of the debtincome ratio and its subsequent and irrevocable impact on future fiscal deficits. These results lead us to view the current combination of relatively tight money and large deficits as an unsustainable policy stance. While it is true that if the RBI refuses to monetise any debt, then the finance ministry might be compelled to swing its budget back into balance, it is undeniable that if political compulsions do not permit a fiscal reduction, then it is the RBI which would be eventually forced to monetise a much larger proportion of the deficit than what would have been necessary had it embarked on an optimal monetisation programme right away. This is why the SW result – that a low initial path for money supply can lead to a higher level of inflation – assumes paramount importance. Thus, fiscal solvency and monetary accommodation are interdependent and impose hard constraints which need to be dynamically evaluated while exercising the choice between money or debt financing. To extend the static framework developed in Section III – which indicated that an optimal monetisation level was necessary to avoid the ‘high-inflation’ trap – and establish the SW results, we need to formalise the dynamic nature of the linkages between money, inflation, interest, deficits and debt. To do so, we follow the SW tradition and invoke the quantity theory equation (see eq 16) from which we obtain the following long run relationship between the rate of inflation (π), money growth (µ) and real output growth rate (g): π= µ – 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: ...(20) i = (1 – Ω)(r + π) + Ω (if + ee) where, as before, r is the domestic real rate of interest, if is the nominal foreign interest rate, ee is the expected rate of depreciation, and Ω is the financial openness index. In order to fully capture the dynamic nexus between deficits and the inflationary process, we incorporate the AghevliKhan hypothesis [Aghevli and Khan 1978] and the Tanzi-Olivera effect [Olivera 1967, Tanzi 1988] into the model. As such, we now assume that x (the primary deficitincome ratio) – which was hitherto a constant in the static framework – is an increasing function of the inflation rate. This implies that: ...(21) x = Beτπ, τ > 0 Substituting the above expression, which incorporates fiscal erosion – or the widening gap between government expenditures and revenues – due to inflation, into eq (5) yields: ...(22) f = (i+ε)d + Beτπ Given the government budget constraint (see eq (3)) and writingθ for the proportion of the fiscal deficit monetised by the monetary authorities, we have: ⋅ M = θFD, 0 ≤ θ ≤ 1 ...(23) We now modify the money demand function (see eq (1)) by setting α =1.7 This yields: ...(24) M/Py = Ae–ßi ⋅ Dividing eq (23) by Py; rewriting M/Py ⋅ as the product of (M/M) and (M/Py); and then invoking eq (24) to replace M/Py, yields the following solution for the rate of money growth (µ): ...(25) µ = (1/A)eßi θf From eqs (3) and (23) we have: ⋅ D = (1-θ)FD ...(26) Differentiating the identity d=D/Py with respect to time, and ignoring second- and higher-order interaction ⋅ ⋅ ⋅ terms, yields: ⋅ dPy + dPy + dPy = D ...(27) Dividing both eqs (26) and (27) by Py; and linking them together yields the following expression for the evolution of the debt-income ratio: ⋅ d = (1–θ)f – (π+g)d ...(28) Eqs (19), (20), (22), (25) and (28) constitute the model defining inflation, interest, deficits, money and debt; and it is seen that the evolution of these five interacting variables is governed entirely by θ which is the only instrument in the framework. To establish the essence of the SW contention, we have to show that sub-optimal monetary accommodation (i e, too low a value of θ) can destabilise the model by increasing the level as well as the variabil-

ity of the long run rate of inflation. If this is borne out, then there could just about exist an optimal level of monetary accommodation (θ*) which stabilises inflation precisely at that rate which satisfies the sustainability condition for public debt.8

V Long-Term Fiscal Stance Estimated Model In order to obtain policy guidelines based upon the above dynamic model, we need estimates of its six parameters and four exogenous variables. As a first step to doing so, we provide below the estimated versions of eqs (24) and (21): ...(29) M/Py = 0.8867e–3.1185i ...(30) x = 0.006743e8.6478 π As before, the time-varying parameters of the above equations were estimated using the Kalman filter algorithm which was applied to annual time series data over the 10-year period 1990-2000.9 We have provided above only the final Kalman smoother estimators of eqs (24) and (21) which would forecast the conditional means of (M/Py) and x for 2000-01 and beyond. Thus, it is seen that: A=0.8867, ß=3.1185, B=0.006743 and τ=8.6478. As far as the remaining two parameters were concerned, we assumed that the index of financial openness would remain at about 20 per cent, i e, Ω = 0.2; while the differential between the average interest rate on public debt and the 1-year term deposit rate would stabilise at 300 basis points, i e, ε = 0.03. As far as the four exogenous variables were concerned, we assumed that: (i) real output would grow at 6 per cent, i e, g=0.06; (ii) the foreign interest rate would be 6 per cent, i e, if = 0.06; (iii) expected rate of depreciation would be 5 per cent, i e, ee = 0.05; and (iv) domestic real 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 model can be set out as follows: π = µ – 0.06 ...(31) i = 0.038 + 0.8π ...(32) f = (i + 0.03)d + 0.006743e8.6478π ...(33) ...(34) µ = 1.1278e3.1185iθf ⋅ d = (1–θ)f – (π + 0.06)d ...(35) Eqs (31)-(35) thus comprise a set of five equations in five unknowns (π, i, f, µ and d) and the model can be closed and simulated by choosing a value for θ which, in our framework, is assumed to be a constant

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July 22, 2000

Figure 4: Explosive Instability of Debt Finance 0.6 -

0.4 -

Inflation Rate

over the entire period of simulation. Before we initiate the simulations, it would be interesting to see if we can actually anticipate the behaviour of the model. We initially set out below the relationship between the real rate of interest on public debt (rd) and the real growth rate (g) when these two variables are equal: ...(36) rd = (i + ε) – π = g Substituting eq (32), as well as the numerical estimates of ε and g, into the above expression yields: [(0.038 + 0.8π) + 0.03] – π = 0.06 ...(37) which indicates that rd ≤ g only if π ≥ 0.04. As such, a low value of θ which depresses the rate of inflation below 4 per cent would yield rd > g and thus violate the sustainability condition for debt. Consequently, there would be a steady rise in d and a subsequent increase in f. This, in turn, would increase µ and the resulting increase in π would imply that eventually r d < g. This turnaround would, by the same reasoning, ultimately result in falling inflation rates, leading once again to rd > g. Thus, these results suggest that cyclical variations in inflation can be damped down only by an optimal level of monetisation.

0.2 -






–0.2 Time Periods

etisation’) – indicated that at θ* = 0.43, the inflation rate would stabilise at just over 4 per cent. Thus, the model indicates that by monetising about 43 per cent of the GFD, the government would not only be able to reduce the inflation rate to a reasonably low level, but also satisfy the stability condition for public debt, thereby ensuring the long run sustainability of the fiscal stance.

ever. Thus, the results indicate that if there are any inherent instabilities in the dynamics of inflation, then the optimal value of the instrument variable (θ) is damped down considerably (to 36 per cent of the GFD as against 43 per cent in the earlier experiment), which is a direct corollary of the famous ‘instrument instability’ problem first alluded to in the literature by Holbrook [1972].10

Optimal Monetisation

Velocity Shocks, Instrument Instability

VI Conclusions

Considering that over the period 19912000, the monetised deficit was approximately 11 per cent of the GFD, in the initial simulation, we set θ = 0.11. The results – which are set out in Figure 3 (pattern labelled ‘sub-optimal monetisation’) – indicate, just as anticipated, that for such an extremely low value of θ, the inflation rate is relatively high and volatile, settling down finally to the range between 1.2 per cent and 9.2 per cent, with no evidence of a steady state solution. The interesting aspect of these results is that they seem to replicate fairly well the general pattern of actual inflation over this period: a steady decline from a high of 13.7 per cent in 1991-92 to an all-time low of just under 1.7 per cent in the second half of 1999-2000 and then a sudden upturn to about 4.6 per cent currently. While it would be rather premature to suggest that the model is mimicking the actual data pattern, the facts are inescapable: suboptimal levels of monetisation can yield higher and more volatile inflation rates. To try and damp down the inflation rate to its optimal level given by eq (37), we gradually increased the value of θ and the calibration results – which are set out in Figure 3 (the pattern labelled ‘optimal mon-

Logarithmically differentiating eq (24) with respect to time, setting g = 0.06 and ß = 3.1185 yields the following relationship – incorporating velocity shocks that were ignored hitherto – between inflation, money growth and output growth: π = µ – 0.06 + 3.1185i ...(38) which replaces eq (31) in the model during the simulation. The results (Figure 4) obtained by setting θ = 0.11 once again are dramatic because they indicate that sub-optimal monetisation coupled to any instability, in the form of velocity shocks, can increase the level as well as the variability of inflation rather drastically. It is seen that for an identical value of θ, the inflation rate is now extremely high and volatile, oscillating violently from –7.6 per cent to 43.6 per cent. Moreover, in keeping with the observed patterns of disinflation after a prolonged period of hyperinflation, it is seen that the inflation rate, after attaining its peak, dissipates very rapidly before rising up once again. As before, we gradually increased the monetisation level and it was seen that at θ* = 0.36, the long run inflation rate attained a steady state of just over 4 per cent without any oscillatory behaviour whatso-

The basic notion of the sustainability of fiscal deficits centres around the issue of whether the existing split between money financing and debt financing, if pursued indefinitely, can ensure that the debt-income ratio stabilises around a reasonable steady state equilibrium solution. The sustainability condition under an ‘accounting approach’ indicates that real output growth (g) should exceed the real rate of interest on public debt (rd) for ensuring the stability of the debt-income ratio. If g > rd, even a persistent rise in the debt-income ratio due to primary account deficits may not have any adverse implications from the viewpoint of fiscal sustainability. All this can be easily ascertained by substituting eqs ⋅ (5) and (36) into eq (28) to yield: ...(38) d = (rd – g)d + x – θf implying that for given levels of the fiscal deficit (f), primary deficit (x) and monetary accommodation (θ), the larger the gap between rd and g, the higher will be the 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 the existing debt would translate itself into a perpetual growth in the debt-GDP ratio, unless there is a sufficiently high level of

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July 22, 2000


monetary accommodation. If this is not forthcoming, there would be no alternative other than primary surpluses, which should be adequate to offset the differential between rd and g. Viewed from this angle, the size of market borrowings, which determines the interest rate structure, turns out to be the principal fiscal variable in the quest for debt-income stability. The sustainability of debt in the Indian context, therefore, needs to be assessed within the perspective of the debt servicing burden of the deficits. During the 1980s, interest rates were mainly administered and the adoption of ‘repressionary’ financing implied that interest rates did not fully reflect the pressure of government debt on financial markets and on the interest rate structure. Naturally, therefore, the sustainability condition, i e, rd < g, was satisfied in an accounting sense for most of the years over this period. In such circumstances, the primary account balances offered a better indicator for assessing fiscal sustainability and, viewed from this angle, the fiscal structure remained unsustainable. The relatively high primary deficits 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 in the debt-GDP ratio from 45.8 per cent to 57.0 per cent, what with the annual growth rate of domestic debt at 19.4 per cent being much higher than the annual growth rate of nominal GDP at 14.9 per cent. In the 1990s, as a result of fiscal consolidation, there was a distinct reversal in these trends, as a result of which the debtGDP ratio declined from 58.7 per cent in 1990-91 to 47.9 per cent in 1996-97. However, in 1997-98, we once again witnessed the phenomenon of crossover of debt growth over GDP growth, and it is distressing that no attempt has been made in the millennium budget 2000-01 to arrest this upward spiral and prevent it from escalating to unsustainable levels. In other words, the current evolution of government debt – which is almost tantamount to a Ponzi scheme type of debt financing – is not consistent with the medium-term sustainability of fiscal policies. Despite such warning signals, there exists a misplaced concern in policy circles that monetisation of the fiscal deficit is bound to be inflationary per se. However, our results suggest that an optimal expansion in money supply can be absorbed by the economy without causing inflation, as in 1999-2000 when despite an M3 growth of over 14 per cent and a real output growth


of about 6 per cent, the inflation rate was well below 4 per cent. With the current low rate of inflation, many indicators suggest that long-term interest rates (which reflect inflationary expectations) could fall still further. Thus, the fiscal stance, in terms of its borrowings strategy, as well as the monetary stance, in terms of its monetisation strategy, must be to ensure that interest rates at the shorter end do not rise too much as this could flatten or even invert the yield curve in the coming year, which is often a leading indicator of a recession. On a theoretical plane, this implies that a slower increase in the money stock that accompanies a high government borrowings programme will result in high interest rates which would create a budget deficit that could be unsustainable in the long run. If the resulting solvency constraint then forces the government to eventually resort to large-scale monetisation of such deficits, then this could take away the independence of the central bank to follow a monetary policy attuned towards domestic stabilisation. In conclusion, by ensuring an optimal split between monetisation and borrowings in the present, it would be possible to balance the future needs of the economy vis-a-vis the needs of the government and thereby avoid the high interest/inflation trap and the subsequent spectre of an economic slowdown. EPW



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, ε 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 π lie within the range suggested by the sample space. On the other hand, if i and π were to move towards the neighbourhood of the high equilibrium solution (H), this would entail a regime switch necessitating a re-estimation of the parameters of eq (11), notably ß 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 π than what is predicted by the existing model. Thus, the results do not directly suggest that i and π would increase to 16 per cent and 15.6 per cent, respectively. It is interesting to note that even the dynamic version of the present static model, developed in Sections IV and V, predicts an optimal monetisation level of about 40 per cent of the GFD. 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 + π, which is invoked in the SW model, should be modified to: i = r + ßπ, where ß ≠ 1. For the Mundell-Tobin effect, ß > 1 implying that δr/δπ > 0; while for the Darby-Tanzi effect, ß > 1 implying that δr/δπ > 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 if δr/δπ (= ß-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 provided δr/δπ is sufficiently large enough as a result of the Darby-Tanzi effect to ensure that r* > g in steady state (where r* = r + (δr/δπ)π). 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. 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. It needs to be noted, however, that the dynamic evolution of the parameters indicated that eq (30) was not very stable. Instrument instability refers to the possibility

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July 22, 2000

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 adjustment 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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Darby, M R (1975): ‘The Financial and Tax Effects of Monetary Policy on Interest Rates’, Economic Inquiry, 13. Drazen, A H and E Helpman (1990): ‘Inflationary Consequences of Anticipated Macroeconomic Policies’, Review of Economic Studies, 57. Edwards, S and M S Khan (1985): ‘Interest Rate Determination in Developing Countries’, IMF Staff Papers, 32. Fischer, S and W Easterly (1990): ‘The Economics of the Government Budget Constraint’, World Bank Research Observer, 5. Holbrook, R S (1972): ‘Optimal Economic Policy and the Problem of Instrument Instability’, American Economic Review, 62. Lonning, I M (1997): Controlling Inflation by Use of the Interest Rate: The Critical Roles of Fiscal Policy and Government Debt, Occasional Papers No 25, Bank of Norway, Oslo. Mundell, R A (1963): ‘Inflation and Real Interest’, Journal of Political Economy, 71. Olivera, J H (1967): ‘Money, Prices and Fiscal Lags: A Note on the Dynamics of Inflation’, Banca Nasionale del Lavoro Quarterly Review, 20. Rao, M J M (1997): ‘Financial Openness, Shadow Floating Exchange Rates and Speculative Attacks’, Economic and Political Weekly, XXXII (46).

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– (1998): ‘On Some Unpleasant Monetarist Arithmetic’, Working Paper No 3/98, Department of Economics, University of Mumbai. – (2000): ‘On Predicting Exchange Rates’, Economic and Political Weekly, Vol XXXV (3-4). Rao, M J M and R Nallari (1996): Macroeconomic Stabilisation and Growth-Oriented Adjustment, Monograph, Research Department, International Monetary Fund, Washington, DC. Sargent, T J (1985): ‘Reagonomics and Credibility’ in A Ando, H Eguchi, R Farmer and Y Suzuki (Eds), Monetary Policy in Our Times, MIT Press, Cambridge, Mass. Sargent, T J and N Wallace (1981): ‘Some Unpleasant Monetarist Arithmetic’, Federal Reserve Bank of Minneapolis Quarterly Review, 5. Tanzi, V (1976), ‘Inflation, Indexation and Interest Income Taxation’, Banca Nasionale del Lavoro, 116. – (1988), ‘Lags in Tax Collection and the Case for Inflationary Finance: Theory With Simulations’ in M I Blejer and K Chu (eds), Fiscal Policy, Stabilisation and Growth in Developing Countries, International Monetary Fund, Washington, DC. Tobin, J (1965): ‘Money and Economic Growth’, Econometrica, 33.


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