FRANK BARRY University College Dublin

BeIfield, Dublin, Ireland

Government Consumption and Private Investment in Closed and Open Economies*

Early versions of the equilibrium approach to fiscal policy implied that temporary increases in public consumption reduced investment while permanent expansions left it unchanged; current- account effects in the open economy were held to be analogous to these closed-economy in- vestment effects. It has been shown recently though that these investment results arise only under very restrictive assumptions. The present paper demonstrates this in a transparent fashion and extends the analysis to the open economy. Here the equilibrium approach has the implau- sible implication that fiscal expansions, whether temporary or permanent, should "crowd in" investment.

1. Introduction Traditional Keynesian analysis implied that fiscal expansions, even

while crowding out private investment, would nevertheless stimulate aggre- gate production. That this appeared to many as an accurate depiction of how real economies responded to fiscal stimuli was perhaps the most important factor in popularizing the Keynesian model.

Recent developments in macroeconomics have shown, however, that a purely equilibrium approach to the analysis of fiscal policy can replicate these results, though the factors driving economic behavior are very different from those postulated in the earlier models. The "new view," pioneered by Barro (1981a, 1989), Hall (1980) and Aschauer (1985, 1988), and drawing its inspiration from Bailey (1971), argues that the need to finance any in- crease in government consumption reduces the private sector's discounted disposable income and thereby reduces its consumption of all normal goods, including leisure. It is this impact on the labor/leisure decision that leads to the expansion in output.

Permanent increases in the size of the public sector are postulated to reduce private consumption by an equivalent amount both now and in the future, so that no excess demand emerges at the current interest rate; in-

*Helpful discussions with Michael Devereux, Colm Kearney and Ross Milbourne are grate- fully acknowledged.

Journal of Macroeconomics, Winter 1999, Vol. 21, No. 1, pp. 93-106 Copyright © 1999 by Louisiana State University Press 0164-0704/99/$1,50

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Frank Barry

vestment and the trade balance are therefore unaffected by these shocks. If the expansion is temporary, however, consumption-smoothing leads either to reduced investment (in a closed economy), or to foreign borrowing and a reduced trade balance surplus (with no effects on investment) in the small- open-economy case. 1

Myagari, Christiano and Eichenbaum (1992) and Baxter and King (1993) have shown however that under the assumption of a wealth effect on labor supply, which is crucial for the ability of the neoclassical model to explain how fiscal spending can be expansionary, many of the closed- economy results generated in the earlier literature are invalid. Specifically, permanent increases in government spending are found to raise investment, the output and employment effects can be larger than for temporary in- creases in government spending, and multipliers can be above unity.

Neither Myagari, Christiano and Eichenbanm (1992) nor Baxter and King (1993) extend their analyses to the open economy, In doing so here we are led to reject the assertion frequently made by writers in the tradition of the equilibrium approach that current-account effects mirror the investment effects found for the closed economy; this claim has been made for example by Aschaner and Greenwood (1985), Kimbrough (1985), Ahmed (1986, 1987) and Barro (1989). The belief that this is so seems to have deflected attention from the implications of the equilibrium approach for the impact of government consumption on private investment in the open economy.

Our strategy here is to set up a very simple closed-economy model that illustrates the defects of the original formulations of the equilibrium approach. Our transparent structure permits us to follow the earlier litera- ture in allowing government consumption to affect the marginal utility of private consumer spending and leisure. 2 The main benefit of the model's transparency, however, is the ease with which it can be extended to the open economy, allowing the results for the two types of economies to be com- pared. While temporary fiscal expansions crowd out investment in the closed economy, for example, we find that they raise private investment when in- terest rates are determined abroad. Government spending, whether tem- porary or permanent, we find, impacts on both the current account and on investment. The trade-balance effects no longer mirror the dosed economy's investment response.

Our most important finding is that the equilibrium approach, when

1Sachs (1981) and Ghck and Rogoff (1995) present small-open-economy models in which these resuhs appear explicitly.

2The numerical findings in Christiano and Eichenbaum (1992) indicate that the results of recent papers would be robust to this extension, The present paper provides a closed-form confirmation of this.

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Government Consumption and Private Inves tment

constant returns to scale and wealth effects on labor supply are taken into account, implies that both temporary and permanent government expansions should "crowd-in" investment in small open economies. That this does not show up in empirical studies across large samples of countries arguably casts doubt on the validity of the new view of fiscal policy.

The paper is organized as follows: The model is set up in the next section. The basic results for the dosed economy are first derived and the analysis is then extended to the open economy. Mathematical results are contained in an appendix.

2. The Model The points to be made here can be illustrated in a simple two-period

framework. (Periods are subscripted 1 and 2). The analytically convenient log,linear utility function is adopted as it emphasizes the wealth effects with which we are concerned, while still being sufficiently general that existing results on government consumption show up as special cases of the present modelP

The representative individual maximizes

U = [ctlnC~' + (1 - or) In(1 - L1) ]

+ B[o t lnC* + (1 - a) ln(1 - L2)], (1)

which depends on leisure, 1 - L i, and effective consumption, C*; i = 1, 2. The maximum amount of leisure is normalized at unity, L represents hours worked, and B is the discount factor. Effective consumption in period i consists of consumption goods purchased by the private sector, C i, plus that proportion, 13, of government consumption G~ which substitutes for private consumption:

c * = c , + p G , . (9,)

In line with the existing literature, 1~ is assumed to have a value of less than unity. 4 Utility is maximized subject to the intertemporal budget constraint

C1 + RC2 = F(K1, L1) + RF(K1 + I, L2) - I - T , (3)

3Baxter and King (1993) for the most part work with such a ul~lity function. 4Kormendi (1983), Aschauer (1985) and Ahmed (1986) report empirical findings that support

this.

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Frank Barry

which° taking (2) and the government budget constraint (T = G1 + RG2) into account, can also be written

CT + RC~ = F(K 1, L1) -b RF(K 1 + I, L2) - I - (1 - ~)G1

- R(1 - 13)G2 ~ Ao, (4)

where R is the interest factor (i.e., one divided by one plus the interest rate), T is the present discounted value of lump-sum taxes, and I is first-period investment. Capital must be installed one period in advance of use, and does not depreciate.

It is clear from (4) that Ricardian Equivalence holds and that how government spending is financed need not therefore concern us, a

The first-order conditions for the solution of the maximization problem a r e

c ~ = C * B / R ; (5)

C~' = FLi(1 -- L1)a/(1 - c~); (6)

C* = FL~(1 -- L2)a/(1 - or); (7)

and

R F ~ = 1; (8)

where FLi and Fza represent the marginal products of labor and capita] in period i. These conditions are standard and easily interpreted. Equations (5) and (8) are the intertemporal efficiency conditions for effective consumption and investment, while (6) and (7) are the intratemporal efficiency conditions relating effective consumption and leisure.

3. Investment Effects in a Closed Economy The goods market must clear each period in the closed economy,

entailing

F(K1, L1) = C1 + I + G1; (9)

5If lump sum taxes are not available, of course, fiscal expansions, particularly permanent ones, can reduce output (Baxter and King 1993). Barro (1981a) and Ahmed (1986) however estimate that permanent government purchases have a posil~ve output effect.

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Government Consumption and Private Investment

and

F(KI + I, L2) = Ca + G2 . (lO)

Equations (2), (9) and (10) can be used to substitute for C~" and C~' in Equations (5)-(7). I f the system is then differentiated and (8) is used to substitute for dR in Equation (5), we are left with three equations which de termine the behavior of the endogenous variables I, L t, and L2. The de- terminant of this system is positive (its value is given in the appendix) and is denoted ~ - 1. Consider first of all the effects of a temporary increase in government consumption6; dG 1 > O, dGa = 0, Since ~ < 1, the benefit to the private sector is less than the cost in terms of taxation, and private dis- counted wealth falls. 7 This reduces consumption in both periods and raises the per iod-one labor supply. The wealth effect also tends to raise labor sup- ply in period two, but since the second-period wage falls (as can be seen from the fact that the interest rate rises) there is a substitution effect op- erating in the opposite direction; the overall effect on second-period labor supply is therefore ambiguous.

dL1/dG 1 > O, dL~/dG1 ?

dL1/dG1 > dLz /dG 1 for R >-- B .

Because the private-sector response to the temporary shock is smoothed, excess demand would prevail in the goods market at the initial interest rate. This raises the interest rate and reduces investment:

dI /dG, = f~(1 - ~)(B/R)[cd(1 - a)g][FLI{FLL(1 -- L2)a - FL2 }

+ (1 - L1)FLL{FL2 -- FLLOL(1 -- Lz)}] < O. (11)

The temporary shock therefore raises first-period output, while second-period output falls since consumption is reduced and government spending returns to its initial level. All of these results for the temporary expansion are standard.

Now let us turn to the effects of a pe rmanen t expansion in government

%arro (1981) defines temporary changes in policy as changes in the timing of government purchases with the present value held constant; temporary changes therefore have no wealth effects. The present paper follows Aschauer and Greenwood's (1985) two-period formulation instead. The distinction clearly makes no difference to the results generated for permanent shocks, and it is easy to see how the effects of temporary shocks would change under Barro's formulation.

7The term A 0 in Equation (4) is a proxy for discounted wealth, The log specification allows us to write C~ and FL~(1 -- L~) as linear functions of A0, though we make use of this only in the open-economy section of the paper.

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consumption; (dG -~) dG1 = dG2 > 0, Intertemporal disposable wealth again falls, leading to reduced consumption and increased labor supply in each period. (There is no ambiguity about second-period labor supply in the present case because of the strength of the wealth effects).

The results reported on this experiment are based on an initial equi- librium in which the time preference and interest rates are equal (B = R), as in the steady-state equilibrium of dynamic optimization models. A wide range of effects is possible if this condition does not hold, and, as Aschauer and Greenwood (1985) remark, "concrete predictions outside of (this) benchmark case seem hard to obtain."

The impact on investment of a permanent increase in government consumption is given by

dI/dG = f~(1 - [~)C~B[1/(1 - c0]Fr.L JELl - - aFLL(1 -- L1)] > 0 . (12)

Investment rises because of the wealth effect on future labor supply, s Ceteris paribus this would generate excess demand in the present, so the interest rate must rise in this case also in order to shift consumption from the present to the future .9 With the interest rate rising along with investment and future labor supply, it is clear that the second-period capital labor ratio must decline, while output rises.

dL1/dG, dLz/dG > 0, with dL1/dG > dL2/dG ,

dR/dG < 0 .

(The interest rate moves in the opposite direction to the interest factor). Furthermore, with investment rising in the case of a permanent fiscal ex- pansion and falling when the expansion is temporary, while consumer spend- ing falls less than one-for-one with government consumption, it is clear that output can rise more in the case of the permanent expansion, and it is indeed easily verified that this occurs. 1°

SThis mechanism was recognized (in a footnote) by Barro and King (1984), though they suggest that it implies merely that investment is reduced less for permanent fiscal expansions than for temporary changes,

SThis effect arises in Aiyagari, Christiano and Eichenbaum (1992) also. In their model a high interest rate is associated with reduced investment if the fiscal shock is temporary and with increased investment if the fiscal shock is permanent.

l°Barro and King (1984) argue that "permanent and temporary movements in government purchases have identical effects on current quantifies of work, production and consumption when preferences are time-separable," We see here that this applies only when the labor-supply effect on investment is ignored, (Note Ahmed's 1986 empirical finding that permanent changes

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Government Consumption and Private Investment

These results contrast with those of Barro (1989) and Aschauer and Greenwood (1985), who find that a permanent increase in government con- sumption should leave investment unchanged. The present result arises for very straightforward reasons, however: government consumption raises hours worked in both periods, and an expansion in future hours worked, through its impact on the expected future marginal product of capital, stim- ulates current investment.

What then accounts for the results emerging from these earlier papers that dI/dG = 0? In Barro (1989) it arises because in the section of that paper in which the effects of temporary and permanent fiscal expansions are com- pared the supply of labor is held fixed. Since the present result arises because of the wealth effect on future labor supply it clearly will not emerge from that model. Aschauer and Greenwood (1985) allow labor supply to vary, but work with an unusual specification of the production function, one in which the second-period marginal product of capital depends on investment rather than on the capital-labor ratio as it would under constant returns to scale. 11 This is equivalent to setting F ~ equal to zero in the present model, in which case, as Equation (12) above reveals, the mechanism driving our results does not operate. ~2

4. Investment and Current Account Effects in an Open Economy The open economy literature, as mentioned earlier, has tended to ig-

nore investment in order to compare the response of the current account to the investment effects derived for the closed economy. Thus Kimbrough (1985) works with a fixed capital stock while Aschauer and Greenwood's analysis is restricted by their unusual investment function.

The last result derived above however has a particularly strong impli- cation for a competitive economy facing a given world interest rate, since

in government spending can affect output more than temporary changes). A multiplier can exist when the labor-supply effect is taken into account, as Aiyagari, Christiano and Eichenbaum (1992) and Baxter and King (1993) point out, and the interest rate impact of permanent fiscal expansions can be larger than for temporary expansions. These possibilities can arise here for particular parameter values although a multiplier is less likely than in their models because of the direct crowding-out effects of government spending on private consumer spending that are taken into account in the present case; i.e. as 13 ~ 1, dF(K1, L1)/dG 1 ~ O.

11See their Equation (7). IZlt is worth noting that the present result must also arise in an optimizing version of the

Solow growth model. The unique steady-state rate of return on capital in that model pins down the long-run capital-labor ratio. If a permanent fiscal expansion raises longqun labor supply it must also therefore stimulate capital accumulation; Barry and Deverellx (1994).

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the wealth effect on labor supply is now the only factor that effects how investment responds to government consumption. 13

In the open economy case, the first-order conditions (5)-(8) continue to hold, but goods market equilibrium as specified in Equations (9) and (10) need not hold in each period, since the economy can run a current account surplus or deficit.

The open-economy model can be solved as follows. Using the inter- temporal budget constraint (4) we can write (6) and (7) as

FLl(1 -- L1) = [(1 - a)/a][l/(1 + B)]Ao ; (13)

FL2(1 -- L2) = [(1 - oL)/c~][B/(1 + B)R]Ao; (14)

while (8) becomes RfF~ = 1 , (15)

where R f is now constant, as it refers to the fixed foreign interest rate. Plug- ging the value of L 1 from (13) into (4) yields three equations in the three unknowns Ao, L2 and I. The determinant of this system is denoted ® - 1 (its value is again given in the appendix), and is positive. A permanent increase in government spending has the same qualitative effect as in the closed economy, for the reasons identified above.

dI/dG = ®Fr, L[(1 -- oL)/a][B/(1 + B)Rf](1 - 13)(1 + R f) > 0 . (16)

The main result in the open economy case however is that since the interest rate is fixed, and the economy can adjust to a temporary period of excess demand through running a current account deficit, which a closed economy cannot do, the only factor impacting on investment in the case of a temporary fiscal expansion is the wealth effect on labor supply. A temporary fiscal ex- pansion also therefore raises investment:

dI/dG1 = ®Fr, L[(1 -- oL)/oL][B/(1 + B)Rf](1 - 13)> 0 . (17)

Because the negative wealth effects of a temporary expansion are smaller, future labor supply rises less than when the expansion is permanent, and the investment effects are accordingly less also.

This has interesting implications for the current account as well, rep- resented in the following equation:

13Sachs (1981) and Glick and Rogoff (1995) present small-open-economy models with in- vestment, but by assuming that labor is in inelastic supply they rule out the mechanism that allows fiscal policy to affect investment_

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Governmen t Consumpt ion and Private Inves tmen t

BT1 = F(K1, L1) - C1 - I - G1. (18)

The conventional wisdom is that temporary expansions worsen the trade balance while permanent expansions leave it unchanged. The investment effects identified here however mean that permanent expansions should also worsen the trade deficit. 14 The impact is as follows:

dBtl/dG = [@(1 - ~)/{FLI -- (1 -- L1)FLL}][(I - c~)/c~]

{-[FL1F~(1 - L~)Rf/(1 + B)] + FKL[FLL(1 -- LI) - FL1] } < 0. (1.9)

In fact, although it appears unlikely, the impact of a permanent shock may exceed that of a temporary one.

4, Concluding Comments The wealth effect on labor supply is the pivotal mechanism through

which, within the equilibrium approach, a fiscal expansion raises output. One implication of this mechanism has been downplayed in the literature to date however: this is that a fiscal expansion which raises future labor supply thereby enhances the expected marginal product of capital and so provides a stimulus to investment.

For the closed economy, a temporary fiscal expansion creates excess demand at the prevailing interest rate; the interest rate must therefore rise sufficiently to dominate this effect, and so investment falls. For a permanent expansion however the greater downward pressure (through the wealth ef- fect) on consumption and leisure allows investment to rise, while still forcing up interest rates.

For a small open economy facing a fixed world interest rate this mech- anism has even more dramatic effects. The only factor driving investment is now the wealth effect on future labor supply, so that both temporary and permanent fiscal expansions must "crowd-in" investment. If the equilibrium approach is correct, this implies that permanent as well as temporary expan- sions should generate current account deficits in the short run. The conven- tional view that the behavior of the current account of a small open economy replicates the response of investment to fiscal spending in the closed econ- omy is therefore invalid.

One further contrast between the closed and open economy cases is worth drawing out; while a temporary fiscal expansion in the former should

14Ahrned's (1986) findings on U.K. data are inconclusive on the question of whether per- manent government spending significantly affects the current account.

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Frank Barry

reduce future output (through the crowding-out effect on investment), ac- cording to the equilibrium approach it should raise both present and future output in a small open economy.

Finally, then, we must ask whether these crowding-in effects implied by the equilibrium approach occur in practice. I suggest that they do not, and that this casts doubt on the general validity of the new approach to fiscal policy.

We have seen that when the wealth effect is dominant, the equilibrium approach suggests that government consumption should stimulate private investment, for small open economies at least. Barro and Sala-i-Martin (1995; chapter 12) and Easterly and Rebelo (1993) employ large cross- country data sets to study these and other issues. Most of the countries in these data sets can plausibly be considered small open economies. The real government consumption variable used is measured net of spending on de- fense and education in order to isolate expenditures that do not directly affect productivity but that entail distortions of private decisions. Both sets of authors find that the ratio of this variable to real GDP is negatively as- sociated with the private investment ratio, contrary to the predictions of the equilibrium approach as derived in the present paper.

It could possibly be argued, though, that the (employment-increasing) wealth effects focused upon here are dominated by the employment-reduc- ing effects of increased income taxes, when non-distortionary taxation is unavailable. Indeed Baxter and King (1993) show that within a parameter- ized version of the basic neoclassical model the effects of the financing de- cision swamp all other considerations in determining the effects of fiscal policy.

If the distortionary effects of taxation dominate however, and are re- sponsible for our predictions not being borne out in the data, this should imply that permanent increases in fiscal spending reduce output and em- ployment. This however is not consistent with the findings of Barro (1981a) and Ahmed (1986).

Ahmed (1986) finds the effects on aggregate supply of permanent fiscal spending to exceed that of temporary spending, and identifies a wealth effect of the type focused upon here. Barro (1981a) identifies a significant expan- sionary effect of temporary defense purchases on real GNP, while perma- nent defense purchases have a significantly weaker, but still significantly positive, effect. The coefficient associated with permanent non-defense pur- chases, however, is imprecisely determined. 15

Summarizing the results from these two papers, Barro (1989) argues

15Neither Barro (1981a) nor Ahmed (1986) distinguish between productive government ex- penditures and government consumption.

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Government Consumption and Private Investment

that they support the hypothesis that "increases in government purchases lead to increases in real GNP, but by less than one-to-one." If such a positive relationship does exist, then the equilibrium approach pushed to its logical conclusion suggests that investment in small open economies should be found to be crowded-in rather than crowded-out.

Received: August 1995 Final version: December 1997

References Ahmed, Shaghil. "Temporary and Permanent Government Spending in an

Open Economy: Some Evidence for the U.K." Journal of Monetary Eco- nomics 17 (March 1986): 197-224.

. "Government Spending, the Balance of Trade, and the Terms of Trade in British History." Journal of Monetary Economics 20 (September 1987): 195-220

Aiyagari, S. Rao, Lawrence Christiano, and Martin Eichenbaum. "The Out- put, Employment, and Interest Rate Effects of Government Consump- tion." Journal of Monetary Economics 30 (October 1992): 73-86.

Aschaner, David A. "Fiscal Policy and Aggregate Demand." American Eco- nomic Review 75 (March 1985): 117-27.

~ . "The Equilibrium Approach to Fiscal Policy." Journal of Money, Credit and Banking 20 (February 1988): 41-62.

Aschauer, David A., and Jeremy Greenwood. "Macroeconomic Effects of Fiscal Policy." Carnegie-Rochester Conference Series on Public Policy 23 (Autumn 1985): 91-138.

Bailey, Martin. National Income and the Price Level, 2d. ed. New York: McGraw-Hill, 1971.

Barro, Robert. "Output Effects of Government Purchases." Journal of Po- litical Economy 89 (December 1981a): 1086-1121.

- - . "Intertemporal Substitution and the Business Cycle." Carnegie- Rochester Conference Series on Public Policy 14 (Spring 1981b): 237-68.

- - . "The Neoclassical Approach to Fiscal Policy." Chapter 5 in Modern Business Cycle Theory, edited by Robert Barro. Cambridge, Mass.: Har- vard University Press, 1989.

Barro, Robert, and Robert King. "Time-Separable Preferences and Inter- temporal-Substitution Models of Business Cycles." Quarterly Journal of Economics 99 (November 1984): 817-39.

Barro, Robert, and Xavier Sala-i-Martin. Economic Growth. New York: Mc- Graw-Hill, 1995.

Barry, Frank, and Michael B. Devereux. "The Macroeconomics of Govern-

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ment Budget Cuts: Can Fiscal Contractions be Expansionary?" In Deficit Reduction: Wha t Pain, What Gain?, edited by William Robson and Wil- liam Scarth. Toronto: C.D. Howe Institute, 1994.

Baxter, Marianne, and Robert King. "Fiscal Policy in General Equilibrium." American Economic Review 83 (June 1993): 315-34.

Christiano, Lawrence, and Martin Eichenbaum. "Current Real-Business- Cycle Theories and Aggregate Labour-Market Fluctuations." American Economic Review 82 (June 1992): 430-50.

Easterly, William, and Sergio Rebelo. "Fiscal Policy and Economic Growth: An Empirical Investigation." Journal of Monetary Economics 32 (Decem- ber 1993): 417-58.

Glick, Reuven, and Kenneth Rogoff. "Global versus Country-Specific Pro- ductivity Shocks and the Current Account." Journal o f Monetary Eco- nomics 35 (February 1995): 159-92.

Hall, Robert. "Labor Supply and Aggregate Fluctuations." Carnegie-Roch- ester Conference Series on Public Policy 12 (Spring 1980): 7-33.

Kimbrough, Kent. "An Examination of the Effects of Government Purchases in an Open Economy." Journal o f International Money and Finance 4 (March 1985): 113-33.

Kormendi, Roger. "Government Debt, Government Spending and Private Sector Behaviour." American Economic Review 73 (December 1983): 994-1010.

Sachs, Jeffrey. "The Current Account and Macroeconomic Adjustment in the 1970s.'" Brookings Papers on Economic Activity 1 (1981) 201-82.

Appendix

Closed-Economy Results The determinant of this system is

f1-1 = [od(1 - a)2]FLI{FL2FK2 + FL2(B/R) - or(1 - L2)FLL(B/R)}

+ [{FL2Fr~/(1 - a)} - Fr~F~][C*B/(1 - a)]

• [OLFLL(1 -- L1) - - EL1] - - [ { ( 1 - - L2)FL1/(1 - ct)}]

• FLLF~Od(1 -- or) + [Fr, LFLI(1 -- L~)][ot/(1 - et) ~]

• FL~ -- FLLF~[od(1 -- (x)]2FL2(1 -- L1) - [{FL2/(1 -- ix)}

-- {(1 -- L2)FLL(~/(1 -- ot)}](B/R)FLL(1 - L1){a/(1 - or)}

+ [FLLF~ - Fr.LFL2](1 - L1)(1 - L2)[a/(1 - a)]2Ff,L > 0.

The following are the effects of a temporary change in government spending.

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G o v e r n m e n t C o n s u m p t i o n a n d Pr iva te I n v e s t m e n t

dL1/dG1 = f~(1 - l})[{od(1 - a)}{FL~[Fra + (1 - L2)FrL] - F~FLL(1 -- L2)}

+ C~B(FrLFra - [1/(1 - a)][FLzFrn]}] > O.

d L z / d G 1 = f~(1 - ~) (B /R)[{a / (1 - ct)}{FL1 -- (1 -- L1)FLL}]

• [F r~ - {od(1 - a ) } ( 1 - L 2 ) F r L ] ,

T h e s i g n o f t h i s w h o l e e x p r e s s i o n is a m b i g u o u s (as d i s c u s s e d i n t h e t ex t )

b e c a u s e o f t h e a m b i g u i t y o f t h e f ina l t e r m in s q u a r e b r a c k e t s .

T h e i m p a c t o n t h e i n t e r e s t r a t e ( r a t h e r t h a n t h e i n t e r e s t f ac to r , R) is

dr/dG 1 = f~(1 - ~J)(B/R)[od(1 - a)]{[FrrFL2/(l - a)][Fa5(1 -- L1) - F51]

+ [FIaFr, L(FL1 - FLL(1 -- L1)}]} > 0 .

T h e e f f e c t s o f a p e r m a n e n t s h o c k a r e

dI /dG = f~(1 - 13){[1 - (B/R)][1/(1 - ct)]2[FL1 -- (1 -- LI)aFLL]

• [FL~ -- a (1 -- L2)FLL] + (B/R)FLI[1/(1 - a)J[FL2 -- a (1 -- Lz)FLL]

-- [FEe - C*BFKL][1/(1 - a)][FL1 - a (1 - L1)FLL]},

w h i c h is p o s i t i v e f o r B = R. (At t h i s in i t i a l e q u i l i b r i u m t h e p r e - s h o c k v a l u e s

o f L1 a n d L2 a r e a l so e q u a l ) .

F o r B = R , d L 2 / d G = f~(1 - ~)

• {(1 + F/~)[¢~/(1 - (g)][FL1 - - ( 1 - - L1)FLL ] -- C~BFr .x[1 / (1 - c~)]

• [FL1 -- a ( 1 -- L1)FLL ] + F L I [ a / ( 1 -- o0 ] (1 -- L2)Frx} > 0 .

d L J d G = d L 2 / d G + C ~ B F ~ [ 1 + F ~ - FKL(1 -- L2)od(1 - cQ] > 0 .

T h e i n t e r e s t - r a t e e f f e c t is

d r / d G = f~(1 - ~ ){FrL(1 + F ~ ) [ a / ( 1 - a ) ] [FL1 -- (1 -- L1)FLL]

+ F r L F L l [ a / ( 1 -- t~)](1 -- L2)Fr, L} > O.

O p e n - E c o n o m y Resu l t s

T h e d e t e r m i n a n t o f t h i s s y s t e m is

® - 1 = _ [1 + FL1DJ[FL2Fr.x] - [(1 - ct)/ct][B/(1 + B ) ] F L 2 F r x > O ,

w h e r e D = [(1 - a ) / o t ] [ 1 / ( 1 + B ) ] / [ E L 1 - F L L ( 1 - - L1)] > 0 .

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Frank Barry

dAo = O[Fr . rFL2](1 - [3)[dG1 + RfdG2] < O.

S i n c e dL1/dAo = - D i t is i m m e d i a t e l y c l e a r t h a t A0 falls m o r e , a n d L1 a n d

Y1 a c c o r d i n g l y r ise m o r e , fo r a p e r m a n e n t t h a n fo r a t e m p o r a r y f iscal

exp331sion.

dL~ = - O F ~ [ ( 1 - a)/et][B/Rf(1 + B)](1 - [3)[dG1 + RfdG2] > O .

d B T J d G 1 = 0 ( 1 - [~)B/(1 + B){(FL2Fra(/a) - [(1 - a)Fr, L/aRf]} < O .

dBT1/dG = [O(1 - I3)/{FL1 -- (1 -- L1)FLL}][(1 -- a) /a]

• {- - [FL1F~(1 - L2)Rf/(1 + B)] + Fr.L[FLL(1 -- L1) - FL1]} < O.

d B T J d G 1 - dBT1/dG has t h e s a m e s ign as

(FL1FL2Fr, r/et) - Fr, L{(1 - a ) / a } [ ( 1 - El)FEE - FEll - FLI(1 - L2)FZr..L,

w h i c h is a m b i g u o u s a p r io r i , w i t h m o s t e l e m e n t s nega t ive .

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