DAVID CURRIE Queen Mary College

University of London

ELIAKIM KATZ Bar llan University, lsrael

A Reconsideration of the Balanced Budget Multiplier

This paper examines the effect of balanced budget fiscal policy within a model which explicitly incorporates the asset adjustment view of income determination. In this context it

is demonstrated that, in the absence of supply constraints, the balanced budget multiplier has continuing validity, though the size of the multiplier depends on the particular nature of the government expenditure in question.

The concept of the balanced budget multiplier commands an exten- sive literature and is an established part of Keynesian macroeconomics.’ However, its Keynesian basis, that an equal increase in government ex- penditure and taxes will raise national income by reducing private sector saving as a proportion of national income, has been increasingly chal- lenged by recent analysis which emphasizes the role of saving in private sector portfolio adjustment towards desired wealth holdings. The purpose of this short paper is to examine the effects of balanced budget fiscal policy within a model which explicitly incorporates the asset adjustment view of income determination. Our conclusions are that, in general, balanced budget fiscal measures will influence aggregate demand, although the extent and sign of the effect may depend on the particular nature of the government expenditure in question.

Our argument is based in essence on the point that changes in the relative levels of private and public sector activities affect the portfolio equilibrium of the economy. We consider the effect of a balanced budget increase in public spending on the demand for three types of assets: money, non-monetary financial assets, and physical assets.

Regarding financial assets, both monetary and non-monetary, it seems reasonable to assume that the shift in disposable income from the private to public sector associated with the balanced budget fiscal change will reduce private net demand for financial assets.2 However, the effect

‘See Haavelmo (1945), Musgrave )1945), Baumol and Peston (1955), Peacock (1956), and Peston (1958). For a symposium on the early history of the balanced budget multiplier see Salant et al. (1975).

ZFor the dependence of money demand on post-tax income, see Holmes and Smyth (1972). Some dependence on total income must, however, be expected: this is particularly so for the demand for money if a narrow definition of money is adopted, so that the transactions demand assumes primary importance.

Journal of Macroeconomics, Summer 1979, Vol. 1, No. 3, pp. 309-313. 309 @ Wayne State University Press, 1979.

David Currie and Eliakim Katz

on private sector demand for physical assets may not be as clear-cut. While government spending on public consumption or investment in areas competitive with private sechr activity will reduce private demand for physical assets, spending in complementary areas may increase it by raising private sector profitability [see Buiter (1977)].

Using these assumptions, a formal model may be set up, using the following notation:

Y= a* =

a= t= ?-=

- k: :

k= b= n=

m=

national income; desired private sector financial wealth; actual private sector financial wealth; taxation (equal to government expenditure);3 rate of interest; total private sector wealth; desired capital stock; actual capital stock; quantity of government bonds outstanding; value of government bonds outstanding; money stock.

Desired private sector financial wealth, a*, is given by

a* = f(y, t, f-, w) fu, fr, fw 2 0; ft s 0 . (1)

Ceteris paribus, desired financial wealth of the private sector may be viewed as a function of a weighted average of disposable and national income.4 In the one extreme when only disposable income has an effect, fV = -ft; in the other extreme, ft = 0.

The desired private sector capital stock is given by

k* = g(y, t, r, w) g,, g, 2 0; g, $2 0; g, 6 0. (2)

In view of the accounting identity that

w=a+k, (3)

we also impose the behavioral constraint onfand g that 0 s fw + g, s 1.

aSince we assume a balanced budget throughout, we adopt the convention that the derivative with respect to t represents the joint effect of equal changes in taxes and govern- ment expenditure.

We assume throughout that the public sector’s demand for its own assets remains un- changed.

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Net private sector financial wealth is the sum of the money stock, m, and the value, n, of outstanding government bonds which in turn is a function of the quantity, b, of outstanding bonds and of the rate of inter- est:

a=m+n(b,r) nb>O;n,dO. (4)

The final equation is a portfolio allocation equation specifying how finan- cial wealth is allocated between money and non-monetary assets:

m = h(y, t, r, a) h,, h, 3 0; ht, h, d 0. (5)

An explicit bond demand function is, of course, implicit in (5). In long-run equilibrium, the desired and actual asset stocks will be

equal. Hence, setting a* = a and k* = k and eliminating w by use of (3), the long run comparative statics of the system are given by:

and hence the balanced budget multiplier is given by

$ = - D-%+h,n,) (l-g,)& - D-l(h,+h,n,)fwg,

+ D-’ {M -(I-fwhl Cl-gw) + (a + gEOn,.)jJht , (7)

where it can be shown that

D = -h, {(l-gw)[f, -Cl-f,hl + fw kr + GW)) + (hr+ha4Kl-gw)f, + f&,1 (8)

must be negative for stability. From (7), it is clear that it is not possible to establish an unambigu-

ous sign for the balanced budget multiplier since, although the first term is clearly positive, the second and third terms may be either positive or negative. The effect of balanced budget fiscal changes is ambiguous be- cause the impact on the velocity of circulation may be ambiguous. From (5), it is clear that money velocity is an increasing function oft and r and a decreasing function of w. Hence, with m constant, the change in y de-

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pends on the changes in t, r, and 20. Ceteris paribus, the increase in t increases the velocity of circulation. If the balanced budget fiscal change also raises r, this reinforces the rise in velocity, both directly, via the interest rate effect in the money demand function, and indirectly, since the lower valuation of non-monetary financial assets lowers the desired capital stock and therefore total wealth holdings. Thus a sufficient (but by no means necessary) condition for a positive long-run multiplier is that the fiscal change raises interest rates. If, however, interest rates fall (a possi- bility that cannot be excluded a priori), the consequent effect on velocity may outweigh the direct effect of t on money demand, so that the multi- plier may be negative. This effect may be seen if we rewrite (6) as

2 = -h,‘h, - h;‘(h,+han,)$ .

In view of the discussion in the earlier literature of the size of the balanced budget multiplier, it is of interest to note that a multiplier of unity can be obtained from our model in the particular case where the demand for money is insensitive to the interest rate (h, = h, = 0) and depends on disposable, rather than national, income (h, = -h,). More generally, the impact of balanced budget fiscal policy depends on the effects of fiscal parameters on all of the asset demand functions, not simply the money demand function5

Received: December 1977 Revised version received: February 1979

References Baumol, W. J., and M.H. Peston. “More on the Multiplier Effects of a

Balanced Budget.” American Economic Review 45 (March 1955): I40- 48.

Buiter, W.H. “Crowding Out and the Effectiveness of Fiscal Policy.” Journal of Public Economics 7 (June 1977): 309-28.

Haavelmo, T. “The Multiplier Effects of a Balanced Budget.” Economet- rica 13 (October 1945): 311-18.

Holmes, J. M. and D. J. Smyth. “The Specification of the Demand for

5The balanced budget multiplier therefore seems to be alive and well on a wide range of assumptions, including those that may be dubbed “monetarist.” Of course, we are coo- cerned with the effects of fiscal policy on aggregate demand; capacity constraints, which we neglect here, may dissipate its expansionary effects by induced price rises.

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Money and the Tax Multiplier.” Journal of Political Economy 80 (Janu- ary-February 1972): 179-85.

Musgrave. R.A. “Alternative Budget Policies for Full Employment.” American Economic Review 35 (June 1945): 387-400.

Peacock, A.T. “A Note on the Balanced Budget Multiplier.” Economic Journal 66 (June 1956): 361-65.

Peston, M.H. “Generalizing the Balanced Budget Multiplier.” Review of Economics and Statistics 40 (August 1958): 288-91.

Salant, W.S. et al. “Origins of the Balanced Budget Multiplier Theorem.” Symposium in History of Political Economy 7 (Spring 1975): 3-43.

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