DAVID WEINBERG Xavier Uniwersity

Cincinnati, Ohio

Monetary Versions of the Balanced Budget Multiplier*

This paper examines the impact of varying the specihcation of the demand for money on the size of the balanced budget multiplier. The money demand may shift au- tonomously following a balanced budget change in government spending if private money demand is dependent on disposable rather than total income or if, due to a lag in the government spending process, a nonzero incremental governmental money demand exists. The implications of these assumptions are determined in a pure monetary model and then in an IS-LM model. In each case the balanced budget multiplier differs from the conventional result,

The literature on the balanced budget multiplier, voluminous though it is, remains, with a notable exception,’ incomplete in that it ignores the possibility that the policy may create autonomous changes in equilibrium in the money market. To the extent that this occurs, I argue in this paper, a monetarist would accept a non- zero balanced budget multiplier.2 In the coming era of Gramm- Rudman-Hollings, it is relevant to pursue the subject once again.

In this note I make two points. First, I point out that there are two conceptually independent effects of a balanced budget change in government spending. The first of these, the orthodox Keynesian

*I wish to thank William Shropshire of Oglethorpe University, three referees, and the editor of this journal for their helpful comments on previous versions of this paper. As always, all remaining mistakes are my own.

‘Haberler (1946) explicitly discusses the monetary behavior implied by Haavel- mo’s result. He considers both the case of no time lag and the case of lag between revenue collection by the government and government spending. He takes the ba- sic case to be the one I analyze when I assume money demand to be dependent on disposable income and no lag. He intuits the correct result, except that he as- serts there will be a shift in private money demand with respect to net income, by which I take his meaning to be disposable income. I believe that the correct analysis, as explained in this paper, is that there will be a shift in private money demand with respect to total income, not with respect to disposable income.

*A very different argument in the monetarist tradition is made by Martin Bailey [(1971), pp. 153-551: that real crowding-out will occur. The argument here concerns an entirely different matter: the effects of changes in money demand on aggregate economic activity.

Journal of Macroeconomics, Summer 1987, Vol. 9, No. 3, pp. 429-438 429 Copyright 0 1987 by Louisiana State University Press 0164-0704/87/$1.50

David Weinberg

analysis, results from an exogenously caused change in equilibrium in the goods market. The second of these-what is novel here- results from an exogenously caused change in equilibrium in the money market. I work through the comparative statics of this mon- etary analysis. The results of this exogenous change I call the “mon- etary balanced budget multiplier.” My second point is that, rather than being inconsistent, the monetary and orthodox Keynesian ap- proaches are complementary and can be integrated, using the stan- dard IS-LM framework. I then work through this integration.

1. The Basic Point The orthodox Keynesian balanced budget multiplier has the

numerical value of one,3 given the appropriate assumptions, be- cause a rise in the government budget financed by taxation transfers income from a group, private consumers, whose average marginal propensity to consume (MPC) is assumed to be between zero and one, to another group, the government, whose MPC is assumed to be equal to one. Less well known is the analysis of the effect of lags between the initial change in taxation and the change in gov- ernment spending. As first shown by Richard Goodwin (1946), the size of the Keynesian balanced budget multiplier in equilibrium is unaffected by payments lags, although the path of adjustment is dependent on the lag structure.

From a purely monetary perspective, a balanced budget change in spending will have an impact to the extent that it creates an exogenous shift in money demand. Depending on the assumption, an increase in taxes and accompanying expenditures can alterna- tively raise, lower or leave unchanged the money demand. It is helpful to explain how each of these three alternatives is plausible.

First, why might the demand for money rise? When the gov- ernment raises taxes with the intent of also raising spending, the government might very likely wish to keep greater working trans- actions balances. While at first glance this may seem inconsistent with an incremental balanced budget, the two can be reconciled by assuming that there is a payments lag between receipt of tax rev-

3This result is originally attributed to Haavelmo (1945). However, it was inde- pendently anticipated by William Salant, Samuelson, and Somers earlier in the 1940s. See Salant and Samuelson in the Spring 1975 issue of the History of Political Econ- omy, which discusses this, and also see in this issue Gelting, Goodwin, Hansen, and Walter Salant. The Somers contribution is discussed in the Fall 1977 History.

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enues and spending of the revenues.4 If this happens, then the ag- gregated demand for money will rise. It is also possible that gov- ernment payments lead government revenues. In this case, money demand declines. (This case of falling money demand is not dis- cussed further.)

Secondly, why might money demand decline? Many econo- mists have argued that private money demand is a function of dis- posable income.5 Holmes and Smyth (1972) have worked out the comparative statics of this case for a tax change in general but not specifically for a balanced budget change. If this is the case, then a balanced budget increase will, by creating an autonomous fall in disposable income, cause a fall in money demand.

Finally, orthodox Keynesian analysis implicitly assumes that there will be no autonomous shift in money demand-that there will be no change in the government money demand and that pri- vate money demand depends on total, rather than disposable, in- come.

In all cases, changes in money demand will a.fFect nominal economic activity. For this to be fully translated into an impact on real economic activity, it must be assumed that aggregate supply is perfectly elastic. I assume this.

2. The Pure Monetary Balanced Budget Multiplier In this section I work through the comparative statics that re-

sult from the autonomous shifts in money market equilibrium ac-

“Implicitly, I am assuming an unorthodox definition of money demand and sup- ply. Usually, government money holdings are not counted as money. An alternative approach would be to think of this behavior as a reduction in the supply of money. The results should be no different. The one thing that would cause a different analysis would be if it were assumed that the central bank offset any change. in government cash holding.

‘Several empirical studies, including de Leeuw (1965), Hamburger (1966), and Motley (1967), use disposable income. These are cited by Holmes and Smyth (1972). McGibany and Nourzad (1985) offer some evidence that total income is less satis- factory than disposable income. Mankiw and Summers (1986) also suggest that dis- posable income is preferable to total income but that consumption is better than either. I argued in an earlier version that Rtcardo was implicitly arguing something like this in his treatment of the price effects of indirect taxes. This appears both in his Principles of Political Economy and Taxation (1953) and his Notes on Prices and Taxation [(1953); Sraffa edition (lQ61)]. Finally, the same idea is implicit in more modern public finance treatments of indirect taxes including Brown (1939), Due (1949). Rolph (1956) and Musgrave (1959).

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companying balanced budget changes in government spending. Since I do not include the effects of autonomous shifts in the goods mar- ket equilibrium, the analysis of this section can be thought of in one of two ways: as a prelude to a more realistic analysis, in which shifts in both markets are modelled, or alternatively, as a pure monetarist analysis, in which it is assumed that the interest elas- ticity of demand for money is zero.

To analyze the impact of an incremental balanced budget change, I develop two separate variants. In the first, private money demand is dependent on total income; in the second, it is depen- dent on disposable income.

To see the pure monetary balanced budget multiplier for- mally, consider the following simple money supply and demand model.

L, = L,(Y) .

The private money demand, L,, is a function of total income, where Lpy(Y), the derivative with respect to income, is assumed to be a constant, 4, and greater than zero. (Superscripts are used through- out to designate the arguments of derivatives.)

Lg = L,(T) . (2)

The government’s money demand is a function of total tax revenue, where LRT(T), the derivative with respect to tax revenue, is as- sumed to be a constant, Kg, and greater than or equal to zero.

M=fi’. (3)

The supply of money is constant. Equilibrium in the money sector requires:

M = Lp + Lg . (4)

Taking the differential of Equation (4) and rearranging leads to the following for the pure monetary balanced budget multiplier:

dY/dT = -Kg/& . (5)

The standard implicit assumption in the balanced budget mul- tiplier model is that Kg = 0. In this case the pure monetary mul-

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tiplier, dY/dT, degenerates to the numerical value of zero. On the other hand, if there is a payments lag, K,: will exceed zero rather than be equal to zero. Therefore, in this case, the pure monetary balanced budget multiplier will be less than zero.

If, on the other hand, the private money demand is a function of disposable rather than total income, the simple model must be modified by altering the specification of private money demand to be:

LP = L&Y - T) , 0’)

where the derivative, with respect to disposable income, is assumed to be a constant, I$,, and greater than zero. Once again, take the differential of Equation (4). Assume that the private and govern- ment money demand functions are linear, so that the first deriva- tive of private money demand is a constant, z<p, and the first deriva- tive of government money demand is a constant, KR. Rearranging gives:

dY/dT = [K,, - &J/K,. (5’)

In this case, as long as Z$ > K,, which seems most likely, dY/dT will exceed zero. In the special case in which K,: = 0, we coincidentally discover that the monetary balanced budget multi- plier will take on the numerical value of one, the same as in the case of the simple Keynesian balanced budget multiplier.

3. Integrating the Monetary and Keynesian Approaches The Keynesian and monetary balanced budget approaches both

produce nonzero multipliers, but they arise from analytically dis- tinguishable behavior. The Keynesian multiplier arises from an ex- ogenously caused change in equilibrium in the goods market; the monetary multiplier arises from an exogenously caused change in equilibrium in the money market. Rather than being inconsistent, the two are integrable within a standard IS-LM model, which I now work through. Of course, the orthodox analysis of the balanced budget multiplier in a model that includes a money market differs from the result in the goods-only elementary model, since the in- crease in income induces a higher demand for money, reducing the numerical value of the multiplier.

Formally, assume:

David Weinberg

IS Y = C(Y - T) + Z(i) + G ; (6)

LM M = L,(Y,i) ; (7)

where consumption, C, depends on disposable income; planned in- vestment, I, depends on the rate of interest, i; and government spending, G, is exogenous. Assume consumption to be linear with respect to income, so that Cy = CT, and assume both are constant. Assume Lpy to be independent of the interest rate, and L,’ to be independent of the level of income. Introducting a small balanced budget change, dG = dT, taking differentials of Equations (6) and (7) and rearranging yields the conventional result

dY/dT = [l - CT]

[l - cy + Z’(L,y/L,‘)] . (8)

Since, generally,

-w<Z’<O,

03 > L,,’ > 0 , and

--m<Lpi<O,

then, 1> dY/dT > 0.

Using this model, I proceed to analyze the impact of the mon- etary effects that I discussed in Section 2 of the note. Again, two variants of the model are solved. The first assumes that private money demand depends on total income; the second, that private money demand depends on disposable income.

The IS equation6 remains Equation 6; the LM equation be- comes an interest-sensitive variant of Equation 4. Assuming, for simplicity, that the government demand for money is independent of the interest rate, LM becomes:

LM M = L&i, Y) + L,(T) . (7’)

6No time periods are included in the specification of the IS equation because I am interested only in comparative statics rather than in dynamics.

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The Balanced Budget Multiplier

Solving the differential of (7’) for di and substituting it into the differential of (6) yields:

dY,dT = [l - CT - 1’ (~gT&‘)I [l - cy + I” &Y/L,‘)]

(9)

This is the standard IS-LM result except for the addition of the last term in the numerator. The implicit standard assumption is that the incremental demand for money by the government, LgT is equal to zero. If this is true, the third term in the numerator of (9) equals zero, and the balanced budget multiplier degenerates to the orthodox IS-LM result. If, however, 4’ > 0, as it would be were there a payments lag, and if I’ and L,’ are both negative as economic theory would suggest, then the last term in the numer- ator will be greater than zero. In this case, dY/dT will be less than the orthodox IS-LM result.

In the second variant, private money demand is a function of disposable income rather than total income. IS will still be given by Equation 6, but LM becomes:

M = L&Y - T,i) + L,(T) . (7”)

A solution technique analogous to that which led to (9) yields

dr,dT = u - CT + Km,‘) (LpT - q-m [l - cy + I’ (L//L,‘)] .

This expression, too, is the orthodox IS-LM balanced budget multiplier except for the addition of the third term in the numer- ator. Economic theory again leads us to believe that I’ and L,’ are each negative. Casual empiricism leads us to believe that LPT is greater than LgT. As a result dY/dT will typically exceed the or- thodox IS-LM result.

In the special case in which LgT equals zero, if we assume that consumption is a linear function of disposable income and if we assume that private money demand is also a linear function of in- come, then, Cr equals Cy and LPy equals L,T. In this special case, the balanced budget multiplier once again takes the numerical value of one.

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4. Concluding Remarks The essential point of this note is not that the value of the

balanced budget multiplier is one particular numerical result rather than another. Clearly, the unrealistically rigid assumptions are what produce simple results. Instead, the basic point is a conceptual one. The proper analysis of a balanced budget policy must recognize that a balanced budget change might cause autonomous change in the equilibrium of the money market. By the rationale of this argu- ment, even someone who believes that the interest elasticity of the demand for money is zero would predict that a balanced budget change in spending will have a nonzero impact on aggregate eco- nomic activity.

For an entirely a priori argument such as this, empirical work is in order to determine the practical significance of the argument. Two points are open for empirical investigation: first, measurement of the government’s demand for money under incrementally bal- anced budget spending regimes; and, second, further determination of the relative usefulness of total versus disposable income as the basis for private money demand. In the past two years, McGibany and Nourzad (1985) have offered preliminary evidence that total in- come is a less satisfactory determinant of money demand than dis- posable income. Mankiw and Summers (1986) offer evidence that consumption is a better determinant than either total or disposable income. However, they make a stronger case for rejecting total in- come than for rejecting disposable income. The empirical issue is not settled. As far as I know, no use of microeconomic evidence has been brought to bear on this issue.

Received: August 1986 Final version: March 1987

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