wealth effects, treasury bill financing, and stability

Journal of Public Economics 21 (1983) 397403. North-Holland

WEALTH EFFECTS, TREASURY BILL FINANCING, AND STABILITY

David CURRIE*

Department of Economics, Queen Mary College, London El 4NS, U.K.

Shaziye GAZIOGLOU

Department of Economics, Birkbeck College, London WIP IPA. U.K.

Received February 1981, revised version received December 1981

This note examines the stability of government financing through capital-certain, variable interest bonds in the context of a fixed price macromodel. In contrast to the financing by perpetuities, it is shown that a wealth effect on expenditures may be destabilising, particularly if the interest elasticity of money demand is low.

It is familiar from the literature dealing with the government budget constraint that instability may result from debt-financing of fiscal deficits.’ The bulk of this literature assumes that government debt comprises perpetuities.’ In practice, of course, much government financing takes place through the issue of much shorter maturity debt, and it is of interest to enquire whether the stability results of the existing literature are altered when financing is in this form. The purpose of this note is to point out one difference between these cases. We show that, when financing is by the issue of variable-interest/capital-certain debt, a wealth effect on expenditures may be destabilising. This contrasts with the case of financing by perpetuities, where a wealth effect on expenditures assists stability.3

Our model is a simple fixed price model, formulated in continuous time, and given by the following seven equations:

*David Currie gratefully acknowledges the financial support of the SSRC (grant no. HR 8029). ‘See, for example, Blinder and Solow (1973) Currie (1976) Pyle and Turnovsky (1976), Infante

and Stein (1976) Turnovsky (1976) Christ (1978, 1979), and Smyth (1980). For a survey of much of this literature, see Currie (1978).

‘For an exception, see Smyth (1980). %ee, for example, Blinder and Solow (1973). It would, of course, be of interest to consider the

case of fixed coupon bonds of finite maturity, but this would require an analysis using mixed difference/differential equations, the analytical solution of which are much more complex. Intuitively, however, it seems probable that features of our analysis would carry over to the more general case.

0047-2727/83/$3.00 0 1983, Elsevier Science Publishers B.V. (North-Holland)

398 D. Currie and S. Gazioglou, Wealth effects

y=x+g,

x=x(yd,r,m-tw), X1,XJ>O, x,<Q

s=s(y+n), s,>Q

n=wr.

ni+ti=g-s+n,

(1)

(2)

(3)

(4)

(5)

(6)

(7)

where the following notation is used:

g = government expenditure, n =interest payments on government debt, s = tax revenues, w = government debt (= net non-monetary financial wealth), y =gross national product, x = private sector expenditures, yd = disposable income, r =rate of interest, m = high-powered money stock.

The model is entirely standard. Eq. (1) is the condition for equilibrium in the output market. Eq. (2) makes private sector expenditures a positive function of disposable income and wealth and a negative function of the interest rate. Eq. (3) specifies that the money market clears instantaneously, so that the supply of money is equal to the demand for money. Money demand is assumed to depend positively on income, negatively on the rate of interest, and positively on outstanding government debt.4 Eq. (4) defines disposable income, while (5) specifies the tax function. Eq. (6) defines interest payments on government debt, which is assumed to be entirely in the form of variable-coupon/capital-certain bills (which, for convenience, we refer to as treasury bills in what follows). Finally, eq. (7) defines the government budget constraint.

We may conveniently represent the model in IS/LM terms as in fig. 1. The

*The derivative I, captures not only wealth effects on money demand but also substitution effects, and so will be non-zero even if government debt is not net wealth. As Tobin (1971) observes, 1, may be negative if government debt is a close substitute for money. [See also Currie (1979).] However, empirical support for this possibility is absent, and it is less probable when the representative rate of interest is a short rate, as in our analysis [see Currie (1979)].

D. Currie and S. Gazioglou, Wealth effects 399

Fig. 1. Wealth effect on expenditures stabilising

LM curve in differential form may be derived from (3) as:

dy= -l~‘l,dr-l~~l,dw+l~ldm, (8)

which has the conventional positive slope. As is familiar from the literature on the government budget constraint [see, for example, Blinder and Solow (1973)], the issue of additional government debt shifts the LM curve to the left by increasing the demand for money, since 1, > 0.

Goods market equilibrium may be obtained by eliminating x, yd, and s from eqs. (l), (2), and (4x6), yielding a relationship between y, r, w, h and g which in differential form is given by:

dy=y,[(x,(l-s,)w+x,)dr+(x,(l-s,)r+x,)dw+x,dm+dg], (9)

where y1 =(I -x,(1 -si)))l. It will be noted that the slope of the IS curve is ambiguous, since the direct interest sensitivity of private sector expenditures may be offset by the effect of interest rate changes on interest payments, disposable income and hence expenditures.5 Since it is familiar that a positively sloped IS curve with slope less than the LM curve necessarily gives rise to instability for reasons quite independent of the government budget constraint, we assume that this is not the case. Thus we assume that x1(1-s,)w+x,+y;‘l,l;‘<O, which ensures that the government expenditure multiplier has the conventional positive sign. Irrespective of the slope of the IS curve, an increase in government debt outstanding shifts the IS curve to the right.

5This effect is also a feature of a number of the large econometric models of the U.K. economy. [See Artis (1978).]


Finally, we may depict by BB the locus of points where the government budget is in the balance. From (6) and (7), this is given by:

(10)

The dependence of interest payments on the rate of interest means that this locus is positively sloped. Inspection of (9) and (10) makes it clear that BB is flatter than the IS curve (if this is positively sloped), but may be either flatter or steeper than the LM curve. An increase in non-monetary government debt shifts the BB curve to the right if, as we assume in the following, the real interest rate, r, is positive.6

In what follows, we treat g and m as exogenous, and focus exclusively on treasury bill financing [thus setting ni=O in (7)]. Thus, to the left of BB the government budget is in deficit, and we assume that this is financed by the issue of a larger volume of treasury bills; to the right of BB the budget is in surplus, permitting the stock of treasury bills outstanding to be run down.

The two cases of interest are depicted in figs. 1 and 2. In fig. 1 the BB curve is steeper than the LM curve. The instantaneous equilibrium (y,r) is such that the budget is in deficit. The resulting issue of treasury bills shifts the curves in the directions indicated by the arrows. Clearly the shifts of the LM and BB curves are destabilising, in that they tend to generate a larger budget deficit.’ The shift of the IS curve is, by contrast, stabilising, tending to move the system along the (shifting) LM curve towards a position of

Y

Fig. 2. Wealth effect on expenditures destabilising.

61f r<O, an increase in w shifts the BE curve laterally and uniformly but also rotates it in a clockwise direction. It may well be that the net result is a rightward shift of the BB curve in the neighbourhood of equilibrium, even though r<O, so that our analysis is more generally applicable. All that is required is that total debt interest should rise with w (holding m constant).

‘This is true even if the IS curve is positively sloped (but steeper than the LM curve), because it is necessarily steeper than the BB curve.


balanced budget. A sufficiently large wealth effect on expenditures can therefore stabilise the system. This result accords with that obtained for financing by perpetuities. [See, for example, Blinder and Solow (1973).]

In fig. 2 the BB curve is flatter than the LA4 curve and, as before, the shifts of the LM and BB curves are destabilising. For this case, however, the shift of the IS curve is also destabilising, tending to shift the economy along the (moving) LM curve away from the position of balanced budget. In this case, the system is necessarily unstable. A larger wealth effect on expenditures adds to this instability, in the sense that it increases the speed of divergence of the system. This is because in this case a rise in income, unaccommodated by any increase in the money supply, raises interest payments by more than the induced rise in tax revenues, widening the budget deficit and requiring an added issue of treasury bills. A low interest elasticity of money demand implies a steep LM curve, making this second case more probable.

To demonstrate these conclusions formally, we solve the system around its

long-run equilibrium in terms of the state variable, w. Thus, setting dm=dg =0 in (8) and (9) and eliminating dr, the instantaneous equilibrium for output may be obtained from the IS and LM curves as:

dy=y,[x,+x,(l-s,)r-(x,(l-ss,)w+x,)l~ll,]dw, (11)

where y2=[1-x1(1-s1)+(x1(1-s1)w+xz)Z~1Z1]~1~0 by the requirement that the IS curve (if positively sloped) has slope greater than the LM curve.

Similarly, we may eliminate r from the LM and BB curves [eqs. (8) and

(lo)] to give:

dti=(l-s,)(r-~l,‘l,w)dw-(s,+(l-s,)l,ll,w)dy.

Eliminating dy from (11) and (12), we then obtain:

(12)

dti -=yyzr(l--s,)(l-x,+x,l;1ll)-y,(sl+(1-s,)l;1ll~)~, dw

-yJ,‘((l-s,)(l-x,)w-s,x,)l,. (13)

For local stability around equilibrium, we require dti/dw < 0, while dti/dw > 0 implies that the system is locally unstable.

If I > 0, the first main term in (13) is positive, confirming Smyth’s finding that treasury bill financing is necessarily unstable in the absence of wealth effects.’ The third main term in 1, is necessarily positive, confirming that a

*Note, however, that the dynamics of our model are very much simpler than those of Smyth, demonstrating that some of the dynamic features of his model are superfluous to his main result. Note, also, that if real interest rates are negative, instability does not result for this special case of no wealth effects (I, =x3 = 0).


wealth effect on money demand is destabilising. The second main term in xj is of ambiguous sign. If si +(l -s,)l; ‘I,w > 0, it is negative, so that the wealth effect on expenditures, if it is sufficiently large, can stabilise the system. But if si +(I -s,)I,‘I, w < 0, this term is positive, so that the wealth effect on expenditures adds to instability. In this latter case, the system is necessarily unstable.’ It is straightforward to check that this latter condition is simply that the BB curve should be flatter than the LM curve, as in fig. 2. In this case, the rise in interest rates induced by the wealth effect on expenditures increases interest payments faster than tax revenues. The government budget deficit therefore widens, adding to instability.

Although our analysis has been conducted in the context of a deterministic model, it is clear that the stability analysis carries over to the case where additive stochastic disturbances are included in the model. It is therefore directly applicable to the case where monetary targets are adhered to, and residual financing of stochastic fluctuations of the government budget is by government debt sales.

The case where the wealth effect on expenditures is destabilising is more likely to occur the greater is the outstanding stock of debt and the lower the interest elasticity of money demand. These conditions seem relevant to the U.K. where the ratio of government debt to GDP is high and where the tendency of the own rate of interest on money to move in line with parallel market rates results in a low effective interest elasticity of broadly defined money (&M3). Thus, the result may be of more than simply theoretical interest.

‘Subject to the qualification of the previous footnote that r>O; if r<O, instability in this case is very likely, but not inevitable.

References

Artis, Michael J., 1978, Fiscal policy and crowding out, in: Michael Posner, ed., Demand management (Heinemann).

Blinder, Alan S. and Robert M. Solow, 1973, Does fiscal policy matter? Journal of Public Economics 2, 319-337.

Christ, Carl F., 1978, Some dynamic theory of macroeconomic policy effects on income and prices under the government budget restraint, Journal of Monetary Economics 4, 45-70.

Christ, Carl F., 1979, On fiscal and monetary policies and the government budget restraint, American Economic Review 69, 526538.

Currie, David A., 1976, Optimal stabilization policies and the government budget constraint, Economica 43, 159-167.

Currie, David A., 1978, Macroeconomic policy and government financing: A survey of recent developments, in: M.J. Artis and A.R. Nobay, eds., Studies in contemporary economic analysis (Croom Helm).

Currie, David A., 1979, Portfolio and wealth effects of bond finance and the stability of the monetarist policy rule, Economics Letters 44, 163-168.

Infante, Eltore F. and Stein, Jerome J., 1976, Does fiscal policy matter?, Journal of Monetary Economics 2,473-500.


Pyle, David H. and Stephen J. Turnovsky, 1976, The dynamics of government policy in an inflationary economy: An intermediate run analysis, Journal of Money, Credit and Banking 8,411437.

Smyth, David J., 1980, Treasury bill financing in a dynamic macroeconomic model with a government budget constraint, Economics Letters 5, 2255229.

Tobin, James, 1971, An essay on the principles of debt management, in: Essays in economics, vol. 1, Macroeconomics (North-Holland, Amsterdam).

Turnovsky, Stephen J., 1976, Macroeconomic analysis and stabilization policy (Cambridge University Press, Cambridge).

wealth effects, treasury bill financing, and stability

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