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Temporary and permanent government spending in a small open economy
Journal of Monetary Economics 43 (1999) 125—141
Temporary and permanent government spending in a small open economy Cem Karayalc7 in* Department of Economics, Florida International University, Miami, FL 33199, USA Received 9 December 1993; received in revised form 18 December 1997; accepted 21 January 1998
Abstract This paper studies a dynamic optimizing small open economy model that emphasizes the supply-side responses of labor and capital to changes in fiscal policy. The model used generates results that are consistent with a number of empirical regularities in small open economies. Furthermore, temporary fiscal shocks are shown to have permanent positive effects on output and negative effects on consumption and welfare. The strength of these effects are shown to depend on intertemporal elasticities of substitution and the persistence of policies. 1999 Elsevier Science B.V. All rights reserved. JEL classification: E62; F41 Keywords: Fiscal policy; Small open economy
1. Introduction This paper investigates the effects of temporary and permanent fiscal policies within an equilibrium model of a small open economy in which the intertemporal optimizing behavior of agents endogenously determines employment and investment. The paper is motivated by two central questions raised in recent macroeconomic literature: (1) what are the effects of permanent changes in
* E-mail: [email protected] For the closed economy literature, see, for instance, Barro (1989) and Baxter and King (1993). For the open economy literature, see Ahmed (1986), Baxter (1995), Karayalcin (1996), and Turnovsky and Sen (1991). 0304-3932/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 3 2 ( 9 8 ) 0 0 0 4 4 - 0
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government spending?; and (2) in what ways do the effects of temporary changes in fiscal policy differ from the effects of permanent changes? The paper shares with the recent closed and open economy literature the emphasis on the supply-side responses of labor and capital to changes in government spending and taxes. Four results that emerge in this paper, where such interactions are emphasized, conform with the findings of recent research (see Baxter and King, 1993; Baxter, 1995) and are supported by the empirical findings in small open economy setups (see Ahmed, 1986). First, increases in government spending financed by non-distortionary taxes cause a negative wealth effect which induces a rise in labor supply. Second, government spending crowds out private consumption. Third, permanent increases in government spending turn out to have stronger impact effects than temporary increases. Fourth, fiscal expansions have strong positive effects on domestic output. Further, the small open economy framework yields results that contradict those obtained in the closed economy setup: for instance, here government spending stimulates private investment. This conclusion is readily seen to be the consequence of the assumption of perfect international capital mobility, which implies that the interest rate in the small country, being fixed by the exogenously given world interest rate, does not rise in response to an increase in government spending. What, instead, takes place, in response to such an increase is a rise in labor supply (due to the negative wealth effect) which reduces the real wage rate and increases the profitability of firms, leading to a stock market and investment boom. In addition, a temporary increase in government spending leads to a permanent increase in domestic output. This result is important in two respects. First, it contradicts the conventional wisdom about the long-run effects of temporary fiscal shocks as well as the findings of closed economy (see, for example, Baxter and King, 1993) and small open economy (see, for instance, Karayalcin, 1996; Baxter, 1995), analyses of fiscal policy. Second, it is well-known that the time series of government spending for small open economies such as UK is dominated by large temporary increases corresponding to the two world wars, rendering the analysis of temporary rises in government spending especially important. The result that temporary fiscal policies have permanent effects is due to the by-now well-known (see Turnovsky and Sen, 1991) character of small open economy models in which the constant rate of time preference is set equal to the exogenously given world interest rate to ensure the existence of a well-defined steady state. Furthermore, it should be emphasized that this result is by no means confined to the model presented here. A straightforward extension of the In a two-country general equilibrium model with incomplete markets, Baxter (1995) obtains the result that temporary country-specific productivity shocks have permanent effects. This result differs from the one obtained here in that in the present setup it is temporary fiscal shocks that prove to have permanent effects in a global environment with complete markets.
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logic of the closed-economy, heterogeneous-agent analysis of Becker (1980) implies that temporary shocks will have permanent effects in any model where agents face the same rate of interest and possess identical pure rates of time preference. Thus, shocks will be hysteretic in two-country complete-markets models as well as in closed-economy heterogeneous-agent models if agents have the same rates of time preference. The framework for the analysis is discussed in the next section. In its barebone essentials the model is similar to that developed in Turnovsky and Sen (1991). One advantage of the framework provided here is that, unlike, for example Baxter (1995), it possesses an analytical solution. The consequences of temporary and permanent increases in government spending are studied in Section 3 which develops an analytical model and calibrates and simulates it. The last section provides some concluding remarks.
2. The model Consider a small open economy with a constant number (normalized, without loss of generality, to one) of identical households that possess perfect foresight. Suppose, in addition, that perfectly competitive firms in the economy produce a single traded good that can be used for consumption and investment. We now turn to a detailed analysis of household and firm behavior. 2.1. Households Household labor supply, ¸, is endogenous. One unit of labor services provided by households earns the real wage rate w in the competitive labor market. Households derive felicity from both consumption C and leisure. The government levies a lump-sum tax ¶ on each household to finance its spending G. Households allocate their portfolio across two assets, an internationally traded bond and equities issued by domestic firms. Since the assets are perfect substitutes, they earn the same rate of return: the exogenously given world interest rate r.
See Karayalcin (1996) for a two-country, perfect-capital-mobility model in which supply shocks are shown to be hysteretic. This model does not, however, endogenize the labor supply decisions of households. The present paper differs from Turnovsky and Sen (1991) in that it (i) extends the analysis to incorporate trend growth and introduces a specific felicity function to avoid trend growth in leisure in response to such growth in the real wage rate; (ii) calibrates and simulates this model; (iii) extends the model to differentiate analytically between the effects of temporary policies of different degrees of persistence.
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The representative household solves the following lifetime welfare maximization problem: max
u(C,¸)exp(!ot)dt
(1)
subject to AQ "rA #w ¸ !C !¶ , (2) R R R R R R A "A(0), (3) where t is a time index, and o and A denote the pure rate of time preference and the nonhuman wealth of the representative household. To avoid trend growth in leisure in response to trend growth in the real wage rate, the felicity function u(C,¸) is specialized to the following form C\Fexp[!(1!h) m¸>N]!1 u(C,¸)" , 1!h
for h'0, hO1,
"ln(C)!m¸>N, for h"1.
(4)
The felicity function has the properties u '0, u (0, and u (0. ! * !! In addition to Eq. (2), the solution of the welfare maximization problem can easily be shown to yield: CI \Fexp[!(1!h)m¸>N]"bI , CI ,Cexp(!xt),
(5)
w (1#p)m¸N" , CI exp (xt)
(6)
dbI /dt"bI (o#hx!r)NbI "bI H,
(7)
where * denote the steady-state equilibrium. The variable x represents the constant rate of labor-augmenting technological change. bI is the costate variable associated with constraint (2) and as such has the conventional interpretation of denoting the marginal utility of wealth. We assume that the effective rate of time preferenceo#hx equals the parametric world rate of interest r, for it is well known that in the absence of this assumption a well-defined steady-state fails to exist. Given this assumption, Eq. (5) implies that households smooth the This formulation follows that of Barro and Sala-i-Martin (1995). The condition u 40 holds if h51, which we assume. Similarly, u ]0 as h]1. ** !* Henceforth, time subscripts are dropped except when there is risk of confusion. The expression hx in the effective rate of time preference reflects the effect of diminishing marginal utility of consumption as C grows at the rate x. For a recent study imposing the same condition in a stochastic framework, see Correia et al. (1995). Note that if its rate of time preference does not equal the world rate of interest the small open country either grows without bound, eventually owning the entire wealth of the world or its wealth declines to zero.
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marginal utility from consumption. Note also that this assumption implies that the dynamic system possesses an eigenvalue equal to zero, the counterpart of which in a discrete-time system would be a unit root. Eq. (6) describes the condition that sets the marginal rate of substitution between consumption and leisure equal to the real wage rate. 2.2. Firms Perfectly competitive firms produce the single traded good by employing capital K and labor ¸ under constant returns to scale. The production function F(K,X¸), where X denotes the labor-augmenting technological progress, is of the conventional neo-classical type. Since installing investment goods is costly, it takes I[1#¹(I/K)] units of output to increase the capital stock by I units. The installation cost function ¹ is assumed to take the form ¹"(1/2c)(I/K) and adjustment costs depend on gross investment I and not on net investment I!dK (where d represents the constant rate of depreciation of capital). Firms choose the time path of investment I to maximize the present discounted value of net profits n"F(K,X¸)!I(1#¹)!w¸, subject to the constraint KQ "I!dK. The solution of this problem yields the following law of motion for Tobin’s Q QQ "(r#d)Q!f (KI ,¸)!(II /KI )¹ (II /KI ), (9) I where II ,Iexp(!xt), KI ,Kexp(!xt). Furthermore, Eq. (10) implies that net investment is the following function of Q dKI /dt"KI [c(Q!1)!(x#d)].
(10)
2.3. The current account To see how the traded bond holdings B of the representative household evolve, use A"B#QK, which says that the assets of this household comprise of (i) foreign bonds, B, and (ii) equities issued by domestic firms, the value of which equals QK. Together with this, Eqs. (2), (9) and (10) yield dBI /dt"(r!x)BI #f (KI ,¸)!II (1#¹)!CI !GI ,
(11)
where BI ,B exp(!xt), GI ,G exp(!xt). Thus, the detrended current account is equal to national income (r!x)BI #f (KI ,¸) less the sum of investment, consumption and government spending (where GI "¶I , ¶I ,¶ exp(!xt)). For notational ease it is assumed that investment is exclusively financed by retained earnings. It is well known that in certainty models, such as this, different forms of financing yield equivalent results.
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2.4. Equilibrium Specifying the production function as f (KI ,¸)"KI ?¸\? and using Eqs. (5) and (6) yields the solutions for c and l (henceforth lowercase letters denote the natural logarithms of variables, so, for instance, c"ln CI ) as c"g k#g b, AI A@ l"l(ak!c).
(12) (13)
where (e\!p) a !(p#a) , g , , g , * A@ AI h(e\ #a) (e\ #a) * * 1 e , . * p#h\ (h!1) (1!a) (½/C)
1 l, , (p#a)
The coefficients g and g denote the elasticities of consumption with respect to AI A@ the capital stock and the marginal utility of wealth, whereas e denotes the * bI -constant elasticity of labor supply. The intertemporal elasticity of substitution for consumption is given by 1/h, whereas the intertemporal elasticity of substitution for lesiure is given by 1/[p#(h!1)(1!a)(½/C)]. Thus, when utility is logarithmic (h"1), 1/p measures this intertemporal elasticity. The coefficient l measures the effect of changes in real wages and consumption in labor supply and takes into account the negative effect of an increase on labor supply on the real wage. Note that as the intertemporal elasticity of substitution for leisure falls (pPR), the coefficient l approaches 0. Eq. (12) indicates that whether consumption will fall or rise in response to an increase in the capital stock depends on the magnitude of e relative to p. In case * of logarithmic utility with h"1, preferences are separable in consumption and leisure (u "0) and smoothing the marginal utility of consumption implies that A* the (detrended) level of consumption remains constant [e\"p in Eq. (12)] as * the economy accumulates capital. If h'1, then e\'p and an increase in the * capital stock will lead to higher consumption. Intuitively, a rise in the capital stock increases the real wage rate and, thus, labor supply. The increase in labor supply raises the marginal utility of consumption (u '0 with h'1) and A* smoothing the marginal utility of consumption implies that changes in (detrended) consumption will be proportional to changes in labor supply: dc/dt"(e\!p)dl/dt. Now, for purposes of calibration take the realistic value * of 0.7 for the consumption-to-GDP ratio, C/½. Together with h"2, p"0.036 In setting up and discussing the equilibrium of the model, we follow Campbell (1994) and use loglinear approximations of relevant functions. In a stochastic model, this implies that the (detrended) level of consumption follows a random walk.
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Table 1 Consumption, employment, and output elasticites p
h
e *
g WE
g AI
g JI
g A@
g J@
p"0
h"1 h"2 h"5 hPR
R 2.15 1.35 1.08
R 0.26 0.26 0.26
0 0.20 0.25 0.25
1.00 0.43 0.27 0.27
!1.0 !0.21 !0.06 0
2.86 0.61 0.18 0
p"0.01
h"1 h"2 h"5 hPR
100 2.10 1.33 1.07
0.25 0.36 0.26 0.25
0 0.20 0.24 0.25
0.97 0.20 0.32 0.27
!1.0 !0.22 !0.07 0
2.78 0.61 0.18 0
p"1
h"1 h"2 h"5 hPR
1.00 0.68 0.57 0.52
0.12 0.12 0.12 0.12
0 0.09 0.12 0.14
0.26 0.19 0.17 0.15
!1.0 !0.37 !0.13 0
0.74 0.28 0.10 0
p"5
h"1 h"2 h"5 hPR
0.20 0.18 0.17 0.17
0.04 0.04 0.04 0.04
0 0.03 0.04 0.05
0.07 0.06 0.06 0.06
!1.0 !0.46 !0.18 0
0.19 0.09 0.03 0
p"20
h"1 h"2 h"5 hPR
0.05 0.05 0.05 0.05
0.01 0.01 0.01 0.01
0 0 0.01 0.02
0.02 0.02 0.02 0.02
!1.0 !0.49 !0.19 0
0.05 0.02 0.01 0
e denotes the real wage elasticity of labor supply. g is the elasticity of output with respect to * WE a permanent increase in government spending. g and g denote the elasticities of consumption and AI JI labor supply with respect to the capital stock. g and g denote the elasticities of consumption and A@ J@ labor supply with respect to the marginal utility of wealth b.
and a"0.35, this delivers a standard labor supply elasticity e of 2. Given these * values, since jc/jy"[(e\!p)/(1#p)] a 1% rise in GDP raises consumption * by 0.45%. Labor supply can also be expressed in terms of the capital stock and the marginal utility of wealth by substituting Eq. (12) into Eq. (13). This yields l"l(a!g )k!lg b,g k#g b. (13.1) AI A@ JI J@ A rise in the capital stock increases the real wage rate by the factor a which induces a rise in the labor supply, yet the increase in the capital stock stimulates consumption (if h'1) as well. This will have the opposite effect on labor supply. An increase in b raises the marginal utility of consumption (Eq. (5)) and gives rise to a substitution of labor services for consumption. Table 1 illustrates the values of g , g and e for different values of h and AI JI * p. When h"1, as mentioned above, smoothing the marginal utility of If h(1, we obtain the result that increases in income reduce consumption. This contradicts stylized facts.
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consumption implies that the (detrended) level of consumption remains constant, thus g "0. As the intertemporal elasticity of substitution for lesiure, 1/p, AI rises, the wage elasticity of labor supply e (which equals 1/p when h"1) does so * as well. The elasticity of labor supply with respect to the capital stock follows suit. When h'1, increases in 1/p raise e , g and g . In this case, as the * AI JI intertemporal elasticity of substitution for consumption, 1/h, rises, real wage and capital elasticities of labor supply (e and g ) rise, whereas consumption, as in * JI conventional analyses, becomes less responsive to changes in the capital stock (i.e., g falls). The table also shows the values of g and g which summarize the AI A@ J@ effects of changes in wealth on consumption and labor supply for different intertemporal elasticities. Substitution of Eqs. (12) and (13) into Eqs. (9) and (10) yields two differential equations. Loglinearizing the last two equations yields kQ "(x#d#c)q,
(14)
qR " k#rJ q, rJ ,r!x, I where "(1!a)u(1!g )exp(!qH)'0 (with u,f ) and measures the reI JI I sponsiveness of qR to changes in the capital stock. The system given in Eq. (14) has one positive and one negative eigenvalue given by
1 k " [rJ $(r#4 (x#d#c)]. I 2
(15)
Let k and k denote respectively the negative and positive eigenvalues. Since this subsystem has one jumping (q) and one predetermined (k) variable, it is locally saddle-path stable. Further, note that k measures the rate of conver gence to steady state. With our benchmark parameter values its absolute value equals 3.5% and falls well within the empirically plausible range as studied by Barro and Sala-i-Martin (1995). To obtain the law of motion of the representative household’s holdings of the traded asset along the convergent path, loglinearize Eq. (11) near a steady state, use Eq. (15) and invoke the familiar condition lim b B exp(!rJ t)"0 (16) R R R which prevents households from borrowing infinitely large amounts from the rest of the world to finance infinite levels of consumption. This yields b !bH"X(k !rJ )\(k !kH), R R X,g #[k /(x#d#c)]g , @I @O g ,exp(yH!bH)[a#(1!a)g !(exp(cH!yH)g @I JI AI !exp[(iH/kH)(kH/y*)](1#¹)], g ,!exp(kH!bH)c(exp qH), @O
(17)
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where X(k !rJ )\ is the elasticity of the (detrended) current account with respect to the capital stock of the economy. The expression g measures the @I elasticity of the current account with respect to the capital stock given Tobin’s Q. It thus summarizes the effect of a 1% change in the capital stock on GDP and the level of consumption. The expression g measures the effect of a 1% change @O in the capital stock on Tobin’s Q and, thus, on investment. Setting Eqs. (9)—(11) equal to zero, and using Eqs. (12) and (13) yields the steady-state of the system: exp(i!k)H"x#d,
exp qH"(x#d#c)/c,
(18)
u"f "(r#d)exp qH!(x#d)/2c, (19) I rJ exp bH"exp kH(x#d)(x#d#2c)/2c#exp cH#q!exp[f (kH,lH)], (20) b !bH"X(k !rJ )\(k !kH). (21) Note that steady-state levels of the investment—capital ratio and Tobin’s Q (Eq. (18)), and the capital-labor ratio Eq. (19) can be determined independently of the initial levels of the capital stock and the economy’s foreign asset holdings. However, this cannot be done for kH, bH or bH. In a similar (but stochastic) model Correia et al. (1995) interpret this result as implying that the steady state is compatible with any foreign asset-capital stock ratio. Yet, the analysis here shows that the steady-state levels of the variables are uniquely determined, inter alia, by the initial levels of the capital stock and foreign asset holdings of the economy. This result, which is an extension of the closed economy heterogeneous agent analysis of Becker (1980), is not confined to the small open economy setting and holds as well in n-country settings where agents in these countries have the same rate of time preference. It is useful, for future purposes, to solve the steady-state values of k, b, b in terms of q"g, k and b : kH"t g!t k !t b , t '0, i"g,k,b, (22) E I @ G bH"g g!g k !g b , g '0, i"g,k,b, (23) E I @ G bH"!f g#f k #f b , f '0, i"g,k,b, (24) E I @ G where t , g and f are positive constants. The dependence of the steady-state G G G levels of k, b and b on the initial values of the capital stock and the stock of holdings of traded bonds indicates that the economy’s adjustment to shocks will be hysteretic. This is the reason why temporary fiscal expansions have permanent effects, and is discussed below. Correia et al. (1995) also note this hysteretic adjustment result in their model, but suggest that this conclusion does not hold in two-country models. That this conclusion carries over to n-agent (n-country) models is shown in Becker (1980) and Karayalcin (1996).
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3. The effects of a fiscal expansion Consider now the effects of a balanced fiscal expansion dg"dq in this framework. To gauge the differential quantitative effects of the permanent and temporary policies to be explored, the model is calibrated and simulated. The calibration of the model follows the recent literature. Thus, the rate of growth of labor-augmenting technological progress x is 0.02; the rate of depreciation of capital d is set equal to 0.05; the world real rate of interest r equals 0.04; the adjustment cost parameters are chosen such that the steady-state level of Tobin’s q is 1.35. In addition, h is set equal to 1 for the simulation exercises, implying, as in the analysis of Baxter (1995), that consumption and leisure are separable in the felicity function. The single important consequence of this, as noted in Eq. (12) above, is that the consumption profile remains flat after an initial drop, instead of the path of consumption following that of k when h'1. It is useful to start by first focusing on a permanent unanticipated increase in government spending financed by lump-sum taxes. 3.1. A permanent fiscal expansion Across steady states, by increasing lump-sum taxes and thereby reducing the representative household’s after-tax lifetime income, the permanent balanced fiscal expansion (of one unit in terms of output in the simulation exercise) gives rise to a negative wealth effect. This leads to an increase in labor effort and a decline in consumption. The rise in labor effort increases the marginal productivity of capital, raising the yield on home equity above that of the international rate of return. This yield differential is eliminated by a rise in the home capital stock. Thus, by raising both the capital stock and employment, the fiscal expansion leads to a higher long-run level of domestic output. However, note that the combined effect of lower consumption and leisure leads to a reduction in long-run welfare. In addition, the fiscal expansion results in a steady-state decrease in b, since home households run down their holdings of the foreign bond in response to the rise in taxes. Table 1 shows the elasticity of output with respect to government spending. This elasticity is higher when labor supply is more elastic with respect to both wages and marginal utility of wealth. As comparison of elasticities with Campbell (1994) shows, output also tends to respond more to changes in
The upper limit for qH in the estimates of q by Blanchard et al. (1993) is 1.5. Note that the elasticities of labor supply, the capital stock, and output with respect to government spending coincide in the long run. This follows from two facts about the marginal productivity of capital: (i) it is homogeneous of degree zero in capital and labor, and (ii) it is fixed by the world real rental rate in the long run.
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government spending in the case of a small open economy. This follows from the fact that in such an economy, unlike in a closed one, increases in government spending would not cause an increase in real interest rates. The dynamic effects of this shock are best analyzed by means of Fig. 1, based on Eqs. (14), (18) and (22). The upper panel of Fig. 1 depicts the dynamics of k and q, while the lower panel shows that of k and b (in the figure the relevant steady-state levels of assets for this exercise are those denoted by k and b ). F F When the fiscal expansion takes place, say at time t"0, the stable arm of the saddle path of the system formed by Eq. (14) shifts from MM to M M due to the negative wealth effect. Consequently, labor supply increases. This, in turn, raises the marginal productivity of capital, and lowers the real wage rate. Hence, the fiscal expansion increases domestic output on impact. At t"0, the equity price q immediately jumps to point A, eliminating the yield differential between the home equity and the international rate of return. The jump in the home equity price gives rise to (correct) expectations of capital losses along the convergent path. Yet, in the medium run with the equity price q lying above the replacement cost of capital, there takes place an investment boom with firms accumulating capital. By increasing the real wage rate, this raises employment. As households smooth the marginal utility of consumption, the rise in labor effort is accompanied by higher levels of consumption (if h'1) along the convergent path. The new steady-state level of consumption will, however, be below its previous long-run level. This observation combined with the increase in labor supply throughout the adjustment process indicates, unsurprisingly, that the fiscal expansion financed by higher taxes unambiguously lowers the welfare of the households. The movement of the capital stock on the upper panel of Fig. 1 is reflected in the path ZZ (obtained from Eq. (17)) on the lower panel. The investment boom accompanied by the increase in consumption (if h'1) implies that households run down their holdings of foreign bonds and the economy runs a current account deficit along the convergent path. 3.2. A temporary fiscal expansion Consider now the effects of a temporary fiscal expansion financed by a temporary rise in lump-sum taxes. The experience of several small open economies, such as Canada, the Netherlands, Belgium and others in the EC, suggests that though there is substantial trend growth in government spending, it generally takes place on the background of temporary rises in expenditure, mostly during Conventional government spending multipliers can be obtained by multiplying the elasticities reported in Table 1 by ½H/GH (equal to, say, a stylized level of 7). If h"1, households smooth the consumption path such that it remains flat after an initial drop on impact.
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Fig. 1.
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137
wars. To gauge the implications of such policies, consider the following experiment. A balanced fiscal expansion (dg"dq'0) takes place at time t"0, but is correctly expected to last until time t"¹, at which point the policy is reversed. Thus, here the temporary change in government spending is defined as a change which will ultimately return government spending, however persistent it may be, to its constant mean. The question addressed here is the following: How does the short-run (impact) and long-run effects of temporary and permanent policies compare? Recent open (as well as closed) economy literature suggests that under complete markets as in here, permanent policies will have stronger short-run output effects, while temporary policies will have no permanent effect on output. Now consider the effects of the temporary fiscal expansion starting at time t"0. At this point the rise in taxes required to finance the higher level of government spending reduces household wealth. Households respond by increasing their labor effort and decreasing their consumption. The increase in labor effort reduces the wage rate and, thus, raises the marginal productivity of capital. This increased profitability of firms is immediately reflected in the jump of Tobin’s Q at time t"0. With Tobin’s Q now above the replacement cost of capital, firms start accumulating capital. With the rise in the capital stock, real wages increase, inducing households to increase their labor effort. Since households smooth the marginal utility of consumption, they simultaneously raise their (detrended) consumption levels if h'1. If preferences are separable in consumption and leisure (that is, if h"1) however, smoothing the marginal utility of consumption implies that the consumption level remains constant. The investment boom together with the rise in consumption leads to a current account deficit and households run down their holdings of the internationally traded bonds. As Fig. 1 reveals, the path that the economy traverses in the period 0(t(¹ depends on the persistence of the temporary policy. In Fig. 1 the paths BF and DG correspond respectively to policies of low and high persistence. If the policy is of high persistence (that is, lasts longer) it comes closer to being permanent and the path that the economy follows is closer to the path of a permanent policy. One consequence of this is that capital accumulation overshoots in the case of the high persistence policy. With the economy’s capital stock above its long-run level, the marginal productivity of capital will be too low. This pushes the stock market price of equity Q below the replacement cost This definition differs from the definition adopted by, for instance, Barro (1981) where a temporary policy is one in which current changes will be offset by future ones so as to leave the present discounted value unchanged. In this case, the policy will have no wealth effect, unlike the case discussed here. The downward sloping lines M M and M M correspond to the stable arms of the saddle-paths associated respectively with policies of low and high persistence.
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of capital, ushering in a period of capital decumulation. In response to the corresponding decline in the real wage rate, households reduce their labor effort. Smoothing of the marginal utility of consumption then implies a corresponding fall in consumption. The temporary policy is reversed, that is, government spending and the taxes required to finance it are reduced to their initial low levels, at time t"¹. Since foreward-looking agents knew of the timing and magnitude of this reversal at time t"0, there cannot be any discrete change in the stock market price Q or in consumption by households. Consequently, in the period t'¹, capital decumulation (in the case of the high-persistence policy) or accumulation (in the case of the low-persistence policy) continues till the new long-run equilibrium is reached. These changes in the capital stock are accompanied by the nowfamiliar changes in labor effort, consumption, and the current account. Note that the new long-run equilibrium that is reached in response to the temporary policy does not coincide with the initial steady-state level of the economy. The reason for this lies in the observation made earlier that the steady state of the economy depends on the initial levels of the assets its households hold. The temporary fiscal expansion raises the domestic capital stock (and ownership claims thereon) and reduces the foreign asset holdings of domestic households. Thus, when the policy is reversed at time ¹, the economy starts its adjustment from initial conditions (in Fig. 1, k and k respectively for policies 2. 21 of longer and shorter durations) different from those that prevailed (in Fig. 1, k ) when the fiscal expansion was first initiated at time t"0. Fig. 2 shows the adjustment paths of some of the variables when the policy is persistent (¹"10). Furthermore, as a comparison of the elasticities in Tables 1 and 2 shows, the temporary policy has, not surprisingly, a weaker long-run output effect than the permanent policy. This is because the former policy has a smaller negative wealth effect. Note that the more persistent the temporary policy is (that is, the longer is its duration), the closer it is to being permanent. The salient point of this analysis, however, is the fact that a temporary policy comes to have permanent effects. This result follows from the combination of perfect international mobility of capital and the constant effective rate of time preference equal to the world real rate of interest. The intuition for this result is well known. To see it, first consider a number of economies with different pure In Fig. 2, dashed lines indicate the initial values of the variables. In case of output and employment the horizontal axis fulfills the same function. As shown in Appendix A, the output elasticity of temporary increases in government spending depends on (i) the intertemporal elasticities of substitution in consumption and leisure in the same manner as does the similar elasticity for the permanent policy, and (ii) the duration of the policy. Thus, Table 2 concentrates on (ii) alone. See Becker (1980) and Lucas and Stokey (1984).
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Fig. 2. Table 2 Output elasticity of temporary increases in government spending h"1, p"0.036 ¹
1
3
5
10
20
40
g WER
0.01
0.01
0.02
0.03
0.04
0.05
rates of time preference and linked by perfect international capital mobility so that each economy faces the same rate of interest. In this case, either the most patient economy eventually owns the entire global stock of wealth, or, the long-run distribution of global wealth depends on initial conditions as when inhabitants of these economies possess the same rate of time preference. The consequence of this for the present analysis is that, by changing the initial conditions (recall k and b (i"S,P) above), a temporary balanced fiscal 2G 2G expansion comes to have permanent effects.
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4. Conclusion We have studied the effects of temporary and permanent increases in government spending in a small open economy model in which employment, investment and the current account are endogenously determined by the intertemporal optimizing behavior of infinitely-lived agents. The dynamic interaction between capital and labor has been shown to play a crucial role for the consequences of fiscal policy. The main results that emerge from the analysis are as follows. Permanent fiscal expansions have larger positive labor supply (due to the negative wealth effect) and output effects than temporary ones. Fiscal expansions crowd out private consumption, but give rise to stock market and investment booms, as the increase in labor supply lowers real wages and raises profitability in small open economies that face an exogenously given world interest rate. Most importantly, unlike in representative-agent closed economy analyses, temporary increases in government spending have permanent positive output and employment effects in the small open economy. The analysis in this paper can readily be generalized in several ways. The introduction of nontraded goods will enrich the model. Government expenditure can be assumed to affect the marginal utility of leisure and private consumption. The results will then hinge on whether private and public goods are Edgeworth complements or substitutes. One can also let government expenditures affect the marginal productivity of capital and labor (as in the closed economy model of Baxter and King (1993)). This will make the output effects of fiscal expansions stronger.
Acknowledgements I would like to thank the editor and an anonymous referee for helpful comments on both the content and the style of the paper.
Appendix A. Coefficients t "K\g, t "!XrJ (k !rJ )\exp(bH)K\, t "rJ n\t , (A.1) E I @ E g "pht , i"g,k,b, (A.2) G G f "!X(k !rJ )\t , f "K\XP(k !rJ )\, f "!K\P, E E I @ K,[X/(k !rJ )]exp(bH)rJ ]#P'0, (A.3) P,exp(bH)g #u'0, @I u,h\(e\!p)\(1!a)(1#g )(1!g )(g )\, n,exp(g!bH). * A@ JI J@
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The elasticity of output with respect to a temporary increase in government spending is given by g ,t /[H(exp k ¹!1)], WER E where !k g H, . rJ t exp (bH)(g #g /cQH) E @I @O References Ahmed, S., 1986. Temporary and permanent government spending in an open economy. Journal of Monetary Economics 17, 197—224. Barro, R., 1981. Output effects of government purchases. Journal of Political Economy 89, 940—971. Barro, R., 1989. The neoclassical approach to fiscal policy. In: Barro, R. (Ed.), Modern Business Cycle Theory, Cambridge, MA. Harvard University Press. Barro, R., Sala-i-Martin, X., 1995. Economic Growth, McGraw-Hill, New York. Baxter, M., 1995. International trade and business cycles. NBER Working Paper no. 5025. Baxter, M., King, R.G., 1993. Fiscal policy in general equilibrium. American Economic Review 83, 315—334. Becker, R., 1980. On the long-run steady state in a simple dynamic model of equilibrium with heterogeneous households. Quarterly Journal of Economics 95, 375—382. Blanchard, O., Rhee, C., Summers, L., 1993. The stock market, profit, and investment. Quarterly Journal of Economics 108, 115—136. Campbell, J., 1994. Inspecting the mechanism, an analytical approach to the stochastic growth model. Journal of Monetary Economics 33, 463—506. Correia, I., Neves, J., Rebelo, S., 1995. Business cycles in a small open economy. European Economic Review 39, 1089—1113. Karayalcin, C., 1996. Stockmarkets, adjustment costs, and international transmission of shocks. Economica 63, 599—610. Lucas, R., Stokey, N., 1984. Optimal growth with many consumers. Journal of Economic Theory 32, 139—171. Turnovsky, S., Sen, P., 1991. Fiscal policy, capital accumulation, and debt in an open economy. Oxford Economic Papers 43, 1—24.
Derivation of this result is available from the author upon request.
Temporary and permanent government spending in a small open economy Cem Karayalc7 in* Department of Economics, Florida International University, Miami, FL 33199, USA Received 9 December 1993; received in revised form 18 December 1997; accepted 21 January 1998
Abstract This paper studies a dynamic optimizing small open economy model that emphasizes the supply-side responses of labor and capital to changes in fiscal policy. The model used generates results that are consistent with a number of empirical regularities in small open economies. Furthermore, temporary fiscal shocks are shown to have permanent positive effects on output and negative effects on consumption and welfare. The strength of these effects are shown to depend on intertemporal elasticities of substitution and the persistence of policies. 1999 Elsevier Science B.V. All rights reserved. JEL classification: E62; F41 Keywords: Fiscal policy; Small open economy
1. Introduction This paper investigates the effects of temporary and permanent fiscal policies within an equilibrium model of a small open economy in which the intertemporal optimizing behavior of agents endogenously determines employment and investment. The paper is motivated by two central questions raised in recent macroeconomic literature: (1) what are the effects of permanent changes in
* E-mail: [email protected] For the closed economy literature, see, for instance, Barro (1989) and Baxter and King (1993). For the open economy literature, see Ahmed (1986), Baxter (1995), Karayalcin (1996), and Turnovsky and Sen (1991). 0304-3932/99/$ — see front matter 1999 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 3 9 3 2 ( 9 8 ) 0 0 0 4 4 - 0
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government spending?; and (2) in what ways do the effects of temporary changes in fiscal policy differ from the effects of permanent changes? The paper shares with the recent closed and open economy literature the emphasis on the supply-side responses of labor and capital to changes in government spending and taxes. Four results that emerge in this paper, where such interactions are emphasized, conform with the findings of recent research (see Baxter and King, 1993; Baxter, 1995) and are supported by the empirical findings in small open economy setups (see Ahmed, 1986). First, increases in government spending financed by non-distortionary taxes cause a negative wealth effect which induces a rise in labor supply. Second, government spending crowds out private consumption. Third, permanent increases in government spending turn out to have stronger impact effects than temporary increases. Fourth, fiscal expansions have strong positive effects on domestic output. Further, the small open economy framework yields results that contradict those obtained in the closed economy setup: for instance, here government spending stimulates private investment. This conclusion is readily seen to be the consequence of the assumption of perfect international capital mobility, which implies that the interest rate in the small country, being fixed by the exogenously given world interest rate, does not rise in response to an increase in government spending. What, instead, takes place, in response to such an increase is a rise in labor supply (due to the negative wealth effect) which reduces the real wage rate and increases the profitability of firms, leading to a stock market and investment boom. In addition, a temporary increase in government spending leads to a permanent increase in domestic output. This result is important in two respects. First, it contradicts the conventional wisdom about the long-run effects of temporary fiscal shocks as well as the findings of closed economy (see, for example, Baxter and King, 1993) and small open economy (see, for instance, Karayalcin, 1996; Baxter, 1995), analyses of fiscal policy. Second, it is well-known that the time series of government spending for small open economies such as UK is dominated by large temporary increases corresponding to the two world wars, rendering the analysis of temporary rises in government spending especially important. The result that temporary fiscal policies have permanent effects is due to the by-now well-known (see Turnovsky and Sen, 1991) character of small open economy models in which the constant rate of time preference is set equal to the exogenously given world interest rate to ensure the existence of a well-defined steady state. Furthermore, it should be emphasized that this result is by no means confined to the model presented here. A straightforward extension of the In a two-country general equilibrium model with incomplete markets, Baxter (1995) obtains the result that temporary country-specific productivity shocks have permanent effects. This result differs from the one obtained here in that in the present setup it is temporary fiscal shocks that prove to have permanent effects in a global environment with complete markets.
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logic of the closed-economy, heterogeneous-agent analysis of Becker (1980) implies that temporary shocks will have permanent effects in any model where agents face the same rate of interest and possess identical pure rates of time preference. Thus, shocks will be hysteretic in two-country complete-markets models as well as in closed-economy heterogeneous-agent models if agents have the same rates of time preference. The framework for the analysis is discussed in the next section. In its barebone essentials the model is similar to that developed in Turnovsky and Sen (1991). One advantage of the framework provided here is that, unlike, for example Baxter (1995), it possesses an analytical solution. The consequences of temporary and permanent increases in government spending are studied in Section 3 which develops an analytical model and calibrates and simulates it. The last section provides some concluding remarks.
2. The model Consider a small open economy with a constant number (normalized, without loss of generality, to one) of identical households that possess perfect foresight. Suppose, in addition, that perfectly competitive firms in the economy produce a single traded good that can be used for consumption and investment. We now turn to a detailed analysis of household and firm behavior. 2.1. Households Household labor supply, ¸, is endogenous. One unit of labor services provided by households earns the real wage rate w in the competitive labor market. Households derive felicity from both consumption C and leisure. The government levies a lump-sum tax ¶ on each household to finance its spending G. Households allocate their portfolio across two assets, an internationally traded bond and equities issued by domestic firms. Since the assets are perfect substitutes, they earn the same rate of return: the exogenously given world interest rate r.
See Karayalcin (1996) for a two-country, perfect-capital-mobility model in which supply shocks are shown to be hysteretic. This model does not, however, endogenize the labor supply decisions of households. The present paper differs from Turnovsky and Sen (1991) in that it (i) extends the analysis to incorporate trend growth and introduces a specific felicity function to avoid trend growth in leisure in response to such growth in the real wage rate; (ii) calibrates and simulates this model; (iii) extends the model to differentiate analytically between the effects of temporary policies of different degrees of persistence.
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The representative household solves the following lifetime welfare maximization problem: max
u(C,¸)exp(!ot)dt
(1)
subject to AQ "rA #w ¸ !C !¶ , (2) R R R R R R A "A(0), (3) where t is a time index, and o and A denote the pure rate of time preference and the nonhuman wealth of the representative household. To avoid trend growth in leisure in response to trend growth in the real wage rate, the felicity function u(C,¸) is specialized to the following form C\Fexp[!(1!h) m¸>N]!1 u(C,¸)" , 1!h
for h'0, hO1,
"ln(C)!m¸>N, for h"1.
(4)
The felicity function has the properties u '0, u (0, and u (0. ! * !! In addition to Eq. (2), the solution of the welfare maximization problem can easily be shown to yield: CI \Fexp[!(1!h)m¸>N]"bI , CI ,Cexp(!xt),
(5)
w (1#p)m¸N" , CI exp (xt)
(6)
dbI /dt"bI (o#hx!r)NbI "bI H,
(7)
where * denote the steady-state equilibrium. The variable x represents the constant rate of labor-augmenting technological change. bI is the costate variable associated with constraint (2) and as such has the conventional interpretation of denoting the marginal utility of wealth. We assume that the effective rate of time preferenceo#hx equals the parametric world rate of interest r, for it is well known that in the absence of this assumption a well-defined steady-state fails to exist. Given this assumption, Eq. (5) implies that households smooth the This formulation follows that of Barro and Sala-i-Martin (1995). The condition u 40 holds if h51, which we assume. Similarly, u ]0 as h]1. ** !* Henceforth, time subscripts are dropped except when there is risk of confusion. The expression hx in the effective rate of time preference reflects the effect of diminishing marginal utility of consumption as C grows at the rate x. For a recent study imposing the same condition in a stochastic framework, see Correia et al. (1995). Note that if its rate of time preference does not equal the world rate of interest the small open country either grows without bound, eventually owning the entire wealth of the world or its wealth declines to zero.
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marginal utility from consumption. Note also that this assumption implies that the dynamic system possesses an eigenvalue equal to zero, the counterpart of which in a discrete-time system would be a unit root. Eq. (6) describes the condition that sets the marginal rate of substitution between consumption and leisure equal to the real wage rate. 2.2. Firms Perfectly competitive firms produce the single traded good by employing capital K and labor ¸ under constant returns to scale. The production function F(K,X¸), where X denotes the labor-augmenting technological progress, is of the conventional neo-classical type. Since installing investment goods is costly, it takes I[1#¹(I/K)] units of output to increase the capital stock by I units. The installation cost function ¹ is assumed to take the form ¹"(1/2c)(I/K) and adjustment costs depend on gross investment I and not on net investment I!dK (where d represents the constant rate of depreciation of capital). Firms choose the time path of investment I to maximize the present discounted value of net profits n"F(K,X¸)!I(1#¹)!w¸, subject to the constraint KQ "I!dK. The solution of this problem yields the following law of motion for Tobin’s Q QQ "(r#d)Q!f (KI ,¸)!(II /KI )¹ (II /KI ), (9) I where II ,Iexp(!xt), KI ,Kexp(!xt). Furthermore, Eq. (10) implies that net investment is the following function of Q dKI /dt"KI [c(Q!1)!(x#d)].
(10)
2.3. The current account To see how the traded bond holdings B of the representative household evolve, use A"B#QK, which says that the assets of this household comprise of (i) foreign bonds, B, and (ii) equities issued by domestic firms, the value of which equals QK. Together with this, Eqs. (2), (9) and (10) yield dBI /dt"(r!x)BI #f (KI ,¸)!II (1#¹)!CI !GI ,
(11)
where BI ,B exp(!xt), GI ,G exp(!xt). Thus, the detrended current account is equal to national income (r!x)BI #f (KI ,¸) less the sum of investment, consumption and government spending (where GI "¶I , ¶I ,¶ exp(!xt)). For notational ease it is assumed that investment is exclusively financed by retained earnings. It is well known that in certainty models, such as this, different forms of financing yield equivalent results.
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2.4. Equilibrium Specifying the production function as f (KI ,¸)"KI ?¸\? and using Eqs. (5) and (6) yields the solutions for c and l (henceforth lowercase letters denote the natural logarithms of variables, so, for instance, c"ln CI ) as c"g k#g b, AI A@ l"l(ak!c).
(12) (13)
where (e\!p) a !(p#a) , g , , g , * A@ AI h(e\ #a) (e\ #a) * * 1 e , . * p#h\ (h!1) (1!a) (½/C)
1 l, , (p#a)
The coefficients g and g denote the elasticities of consumption with respect to AI A@ the capital stock and the marginal utility of wealth, whereas e denotes the * bI -constant elasticity of labor supply. The intertemporal elasticity of substitution for consumption is given by 1/h, whereas the intertemporal elasticity of substitution for lesiure is given by 1/[p#(h!1)(1!a)(½/C)]. Thus, when utility is logarithmic (h"1), 1/p measures this intertemporal elasticity. The coefficient l measures the effect of changes in real wages and consumption in labor supply and takes into account the negative effect of an increase on labor supply on the real wage. Note that as the intertemporal elasticity of substitution for leisure falls (pPR), the coefficient l approaches 0. Eq. (12) indicates that whether consumption will fall or rise in response to an increase in the capital stock depends on the magnitude of e relative to p. In case * of logarithmic utility with h"1, preferences are separable in consumption and leisure (u "0) and smoothing the marginal utility of consumption implies that A* the (detrended) level of consumption remains constant [e\"p in Eq. (12)] as * the economy accumulates capital. If h'1, then e\'p and an increase in the * capital stock will lead to higher consumption. Intuitively, a rise in the capital stock increases the real wage rate and, thus, labor supply. The increase in labor supply raises the marginal utility of consumption (u '0 with h'1) and A* smoothing the marginal utility of consumption implies that changes in (detrended) consumption will be proportional to changes in labor supply: dc/dt"(e\!p)dl/dt. Now, for purposes of calibration take the realistic value * of 0.7 for the consumption-to-GDP ratio, C/½. Together with h"2, p"0.036 In setting up and discussing the equilibrium of the model, we follow Campbell (1994) and use loglinear approximations of relevant functions. In a stochastic model, this implies that the (detrended) level of consumption follows a random walk.
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Table 1 Consumption, employment, and output elasticites p
h
e *
g WE
g AI
g JI
g A@
g J@
p"0
h"1 h"2 h"5 hPR
R 2.15 1.35 1.08
R 0.26 0.26 0.26
0 0.20 0.25 0.25
1.00 0.43 0.27 0.27
!1.0 !0.21 !0.06 0
2.86 0.61 0.18 0
p"0.01
h"1 h"2 h"5 hPR
100 2.10 1.33 1.07
0.25 0.36 0.26 0.25
0 0.20 0.24 0.25
0.97 0.20 0.32 0.27
!1.0 !0.22 !0.07 0
2.78 0.61 0.18 0
p"1
h"1 h"2 h"5 hPR
1.00 0.68 0.57 0.52
0.12 0.12 0.12 0.12
0 0.09 0.12 0.14
0.26 0.19 0.17 0.15
!1.0 !0.37 !0.13 0
0.74 0.28 0.10 0
p"5
h"1 h"2 h"5 hPR
0.20 0.18 0.17 0.17
0.04 0.04 0.04 0.04
0 0.03 0.04 0.05
0.07 0.06 0.06 0.06
!1.0 !0.46 !0.18 0
0.19 0.09 0.03 0
p"20
h"1 h"2 h"5 hPR
0.05 0.05 0.05 0.05
0.01 0.01 0.01 0.01
0 0 0.01 0.02
0.02 0.02 0.02 0.02
!1.0 !0.49 !0.19 0
0.05 0.02 0.01 0
e denotes the real wage elasticity of labor supply. g is the elasticity of output with respect to * WE a permanent increase in government spending. g and g denote the elasticities of consumption and AI JI labor supply with respect to the capital stock. g and g denote the elasticities of consumption and A@ J@ labor supply with respect to the marginal utility of wealth b.
and a"0.35, this delivers a standard labor supply elasticity e of 2. Given these * values, since jc/jy"[(e\!p)/(1#p)] a 1% rise in GDP raises consumption * by 0.45%. Labor supply can also be expressed in terms of the capital stock and the marginal utility of wealth by substituting Eq. (12) into Eq. (13). This yields l"l(a!g )k!lg b,g k#g b. (13.1) AI A@ JI J@ A rise in the capital stock increases the real wage rate by the factor a which induces a rise in the labor supply, yet the increase in the capital stock stimulates consumption (if h'1) as well. This will have the opposite effect on labor supply. An increase in b raises the marginal utility of consumption (Eq. (5)) and gives rise to a substitution of labor services for consumption. Table 1 illustrates the values of g , g and e for different values of h and AI JI * p. When h"1, as mentioned above, smoothing the marginal utility of If h(1, we obtain the result that increases in income reduce consumption. This contradicts stylized facts.
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consumption implies that the (detrended) level of consumption remains constant, thus g "0. As the intertemporal elasticity of substitution for lesiure, 1/p, AI rises, the wage elasticity of labor supply e (which equals 1/p when h"1) does so * as well. The elasticity of labor supply with respect to the capital stock follows suit. When h'1, increases in 1/p raise e , g and g . In this case, as the * AI JI intertemporal elasticity of substitution for consumption, 1/h, rises, real wage and capital elasticities of labor supply (e and g ) rise, whereas consumption, as in * JI conventional analyses, becomes less responsive to changes in the capital stock (i.e., g falls). The table also shows the values of g and g which summarize the AI A@ J@ effects of changes in wealth on consumption and labor supply for different intertemporal elasticities. Substitution of Eqs. (12) and (13) into Eqs. (9) and (10) yields two differential equations. Loglinearizing the last two equations yields kQ "(x#d#c)q,
(14)
qR " k#rJ q, rJ ,r!x, I where "(1!a)u(1!g )exp(!qH)'0 (with u,f ) and measures the reI JI I sponsiveness of qR to changes in the capital stock. The system given in Eq. (14) has one positive and one negative eigenvalue given by
1 k " [rJ $(r#4 (x#d#c)]. I 2
(15)
Let k and k denote respectively the negative and positive eigenvalues. Since this subsystem has one jumping (q) and one predetermined (k) variable, it is locally saddle-path stable. Further, note that k measures the rate of conver gence to steady state. With our benchmark parameter values its absolute value equals 3.5% and falls well within the empirically plausible range as studied by Barro and Sala-i-Martin (1995). To obtain the law of motion of the representative household’s holdings of the traded asset along the convergent path, loglinearize Eq. (11) near a steady state, use Eq. (15) and invoke the familiar condition lim b B exp(!rJ t)"0 (16) R R R which prevents households from borrowing infinitely large amounts from the rest of the world to finance infinite levels of consumption. This yields b !bH"X(k !rJ )\(k !kH), R R X,g #[k /(x#d#c)]g , @I @O g ,exp(yH!bH)[a#(1!a)g !(exp(cH!yH)g @I JI AI !exp[(iH/kH)(kH/y*)](1#¹)], g ,!exp(kH!bH)c(exp qH), @O
(17)
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133
where X(k !rJ )\ is the elasticity of the (detrended) current account with respect to the capital stock of the economy. The expression g measures the @I elasticity of the current account with respect to the capital stock given Tobin’s Q. It thus summarizes the effect of a 1% change in the capital stock on GDP and the level of consumption. The expression g measures the effect of a 1% change @O in the capital stock on Tobin’s Q and, thus, on investment. Setting Eqs. (9)—(11) equal to zero, and using Eqs. (12) and (13) yields the steady-state of the system: exp(i!k)H"x#d,
exp qH"(x#d#c)/c,
(18)
u"f "(r#d)exp qH!(x#d)/2c, (19) I rJ exp bH"exp kH(x#d)(x#d#2c)/2c#exp cH#q!exp[f (kH,lH)], (20) b !bH"X(k !rJ )\(k !kH). (21) Note that steady-state levels of the investment—capital ratio and Tobin’s Q (Eq. (18)), and the capital-labor ratio Eq. (19) can be determined independently of the initial levels of the capital stock and the economy’s foreign asset holdings. However, this cannot be done for kH, bH or bH. In a similar (but stochastic) model Correia et al. (1995) interpret this result as implying that the steady state is compatible with any foreign asset-capital stock ratio. Yet, the analysis here shows that the steady-state levels of the variables are uniquely determined, inter alia, by the initial levels of the capital stock and foreign asset holdings of the economy. This result, which is an extension of the closed economy heterogeneous agent analysis of Becker (1980), is not confined to the small open economy setting and holds as well in n-country settings where agents in these countries have the same rate of time preference. It is useful, for future purposes, to solve the steady-state values of k, b, b in terms of q"g, k and b : kH"t g!t k !t b , t '0, i"g,k,b, (22) E I @ G bH"g g!g k !g b , g '0, i"g,k,b, (23) E I @ G bH"!f g#f k #f b , f '0, i"g,k,b, (24) E I @ G where t , g and f are positive constants. The dependence of the steady-state G G G levels of k, b and b on the initial values of the capital stock and the stock of holdings of traded bonds indicates that the economy’s adjustment to shocks will be hysteretic. This is the reason why temporary fiscal expansions have permanent effects, and is discussed below. Correia et al. (1995) also note this hysteretic adjustment result in their model, but suggest that this conclusion does not hold in two-country models. That this conclusion carries over to n-agent (n-country) models is shown in Becker (1980) and Karayalcin (1996).
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3. The effects of a fiscal expansion Consider now the effects of a balanced fiscal expansion dg"dq in this framework. To gauge the differential quantitative effects of the permanent and temporary policies to be explored, the model is calibrated and simulated. The calibration of the model follows the recent literature. Thus, the rate of growth of labor-augmenting technological progress x is 0.02; the rate of depreciation of capital d is set equal to 0.05; the world real rate of interest r equals 0.04; the adjustment cost parameters are chosen such that the steady-state level of Tobin’s q is 1.35. In addition, h is set equal to 1 for the simulation exercises, implying, as in the analysis of Baxter (1995), that consumption and leisure are separable in the felicity function. The single important consequence of this, as noted in Eq. (12) above, is that the consumption profile remains flat after an initial drop, instead of the path of consumption following that of k when h'1. It is useful to start by first focusing on a permanent unanticipated increase in government spending financed by lump-sum taxes. 3.1. A permanent fiscal expansion Across steady states, by increasing lump-sum taxes and thereby reducing the representative household’s after-tax lifetime income, the permanent balanced fiscal expansion (of one unit in terms of output in the simulation exercise) gives rise to a negative wealth effect. This leads to an increase in labor effort and a decline in consumption. The rise in labor effort increases the marginal productivity of capital, raising the yield on home equity above that of the international rate of return. This yield differential is eliminated by a rise in the home capital stock. Thus, by raising both the capital stock and employment, the fiscal expansion leads to a higher long-run level of domestic output. However, note that the combined effect of lower consumption and leisure leads to a reduction in long-run welfare. In addition, the fiscal expansion results in a steady-state decrease in b, since home households run down their holdings of the foreign bond in response to the rise in taxes. Table 1 shows the elasticity of output with respect to government spending. This elasticity is higher when labor supply is more elastic with respect to both wages and marginal utility of wealth. As comparison of elasticities with Campbell (1994) shows, output also tends to respond more to changes in
The upper limit for qH in the estimates of q by Blanchard et al. (1993) is 1.5. Note that the elasticities of labor supply, the capital stock, and output with respect to government spending coincide in the long run. This follows from two facts about the marginal productivity of capital: (i) it is homogeneous of degree zero in capital and labor, and (ii) it is fixed by the world real rental rate in the long run.
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government spending in the case of a small open economy. This follows from the fact that in such an economy, unlike in a closed one, increases in government spending would not cause an increase in real interest rates. The dynamic effects of this shock are best analyzed by means of Fig. 1, based on Eqs. (14), (18) and (22). The upper panel of Fig. 1 depicts the dynamics of k and q, while the lower panel shows that of k and b (in the figure the relevant steady-state levels of assets for this exercise are those denoted by k and b ). F F When the fiscal expansion takes place, say at time t"0, the stable arm of the saddle path of the system formed by Eq. (14) shifts from MM to M M due to the negative wealth effect. Consequently, labor supply increases. This, in turn, raises the marginal productivity of capital, and lowers the real wage rate. Hence, the fiscal expansion increases domestic output on impact. At t"0, the equity price q immediately jumps to point A, eliminating the yield differential between the home equity and the international rate of return. The jump in the home equity price gives rise to (correct) expectations of capital losses along the convergent path. Yet, in the medium run with the equity price q lying above the replacement cost of capital, there takes place an investment boom with firms accumulating capital. By increasing the real wage rate, this raises employment. As households smooth the marginal utility of consumption, the rise in labor effort is accompanied by higher levels of consumption (if h'1) along the convergent path. The new steady-state level of consumption will, however, be below its previous long-run level. This observation combined with the increase in labor supply throughout the adjustment process indicates, unsurprisingly, that the fiscal expansion financed by higher taxes unambiguously lowers the welfare of the households. The movement of the capital stock on the upper panel of Fig. 1 is reflected in the path ZZ (obtained from Eq. (17)) on the lower panel. The investment boom accompanied by the increase in consumption (if h'1) implies that households run down their holdings of foreign bonds and the economy runs a current account deficit along the convergent path. 3.2. A temporary fiscal expansion Consider now the effects of a temporary fiscal expansion financed by a temporary rise in lump-sum taxes. The experience of several small open economies, such as Canada, the Netherlands, Belgium and others in the EC, suggests that though there is substantial trend growth in government spending, it generally takes place on the background of temporary rises in expenditure, mostly during Conventional government spending multipliers can be obtained by multiplying the elasticities reported in Table 1 by ½H/GH (equal to, say, a stylized level of 7). If h"1, households smooth the consumption path such that it remains flat after an initial drop on impact.
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Fig. 1.
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wars. To gauge the implications of such policies, consider the following experiment. A balanced fiscal expansion (dg"dq'0) takes place at time t"0, but is correctly expected to last until time t"¹, at which point the policy is reversed. Thus, here the temporary change in government spending is defined as a change which will ultimately return government spending, however persistent it may be, to its constant mean. The question addressed here is the following: How does the short-run (impact) and long-run effects of temporary and permanent policies compare? Recent open (as well as closed) economy literature suggests that under complete markets as in here, permanent policies will have stronger short-run output effects, while temporary policies will have no permanent effect on output. Now consider the effects of the temporary fiscal expansion starting at time t"0. At this point the rise in taxes required to finance the higher level of government spending reduces household wealth. Households respond by increasing their labor effort and decreasing their consumption. The increase in labor effort reduces the wage rate and, thus, raises the marginal productivity of capital. This increased profitability of firms is immediately reflected in the jump of Tobin’s Q at time t"0. With Tobin’s Q now above the replacement cost of capital, firms start accumulating capital. With the rise in the capital stock, real wages increase, inducing households to increase their labor effort. Since households smooth the marginal utility of consumption, they simultaneously raise their (detrended) consumption levels if h'1. If preferences are separable in consumption and leisure (that is, if h"1) however, smoothing the marginal utility of consumption implies that the consumption level remains constant. The investment boom together with the rise in consumption leads to a current account deficit and households run down their holdings of the internationally traded bonds. As Fig. 1 reveals, the path that the economy traverses in the period 0(t(¹ depends on the persistence of the temporary policy. In Fig. 1 the paths BF and DG correspond respectively to policies of low and high persistence. If the policy is of high persistence (that is, lasts longer) it comes closer to being permanent and the path that the economy follows is closer to the path of a permanent policy. One consequence of this is that capital accumulation overshoots in the case of the high persistence policy. With the economy’s capital stock above its long-run level, the marginal productivity of capital will be too low. This pushes the stock market price of equity Q below the replacement cost This definition differs from the definition adopted by, for instance, Barro (1981) where a temporary policy is one in which current changes will be offset by future ones so as to leave the present discounted value unchanged. In this case, the policy will have no wealth effect, unlike the case discussed here. The downward sloping lines M M and M M correspond to the stable arms of the saddle-paths associated respectively with policies of low and high persistence.
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of capital, ushering in a period of capital decumulation. In response to the corresponding decline in the real wage rate, households reduce their labor effort. Smoothing of the marginal utility of consumption then implies a corresponding fall in consumption. The temporary policy is reversed, that is, government spending and the taxes required to finance it are reduced to their initial low levels, at time t"¹. Since foreward-looking agents knew of the timing and magnitude of this reversal at time t"0, there cannot be any discrete change in the stock market price Q or in consumption by households. Consequently, in the period t'¹, capital decumulation (in the case of the high-persistence policy) or accumulation (in the case of the low-persistence policy) continues till the new long-run equilibrium is reached. These changes in the capital stock are accompanied by the nowfamiliar changes in labor effort, consumption, and the current account. Note that the new long-run equilibrium that is reached in response to the temporary policy does not coincide with the initial steady-state level of the economy. The reason for this lies in the observation made earlier that the steady state of the economy depends on the initial levels of the assets its households hold. The temporary fiscal expansion raises the domestic capital stock (and ownership claims thereon) and reduces the foreign asset holdings of domestic households. Thus, when the policy is reversed at time ¹, the economy starts its adjustment from initial conditions (in Fig. 1, k and k respectively for policies 2. 21 of longer and shorter durations) different from those that prevailed (in Fig. 1, k ) when the fiscal expansion was first initiated at time t"0. Fig. 2 shows the adjustment paths of some of the variables when the policy is persistent (¹"10). Furthermore, as a comparison of the elasticities in Tables 1 and 2 shows, the temporary policy has, not surprisingly, a weaker long-run output effect than the permanent policy. This is because the former policy has a smaller negative wealth effect. Note that the more persistent the temporary policy is (that is, the longer is its duration), the closer it is to being permanent. The salient point of this analysis, however, is the fact that a temporary policy comes to have permanent effects. This result follows from the combination of perfect international mobility of capital and the constant effective rate of time preference equal to the world real rate of interest. The intuition for this result is well known. To see it, first consider a number of economies with different pure In Fig. 2, dashed lines indicate the initial values of the variables. In case of output and employment the horizontal axis fulfills the same function. As shown in Appendix A, the output elasticity of temporary increases in government spending depends on (i) the intertemporal elasticities of substitution in consumption and leisure in the same manner as does the similar elasticity for the permanent policy, and (ii) the duration of the policy. Thus, Table 2 concentrates on (ii) alone. See Becker (1980) and Lucas and Stokey (1984).
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Fig. 2. Table 2 Output elasticity of temporary increases in government spending h"1, p"0.036 ¹
1
3
5
10
20
40
g WER
0.01
0.01
0.02
0.03
0.04
0.05
rates of time preference and linked by perfect international capital mobility so that each economy faces the same rate of interest. In this case, either the most patient economy eventually owns the entire global stock of wealth, or, the long-run distribution of global wealth depends on initial conditions as when inhabitants of these economies possess the same rate of time preference. The consequence of this for the present analysis is that, by changing the initial conditions (recall k and b (i"S,P) above), a temporary balanced fiscal 2G 2G expansion comes to have permanent effects.
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4. Conclusion We have studied the effects of temporary and permanent increases in government spending in a small open economy model in which employment, investment and the current account are endogenously determined by the intertemporal optimizing behavior of infinitely-lived agents. The dynamic interaction between capital and labor has been shown to play a crucial role for the consequences of fiscal policy. The main results that emerge from the analysis are as follows. Permanent fiscal expansions have larger positive labor supply (due to the negative wealth effect) and output effects than temporary ones. Fiscal expansions crowd out private consumption, but give rise to stock market and investment booms, as the increase in labor supply lowers real wages and raises profitability in small open economies that face an exogenously given world interest rate. Most importantly, unlike in representative-agent closed economy analyses, temporary increases in government spending have permanent positive output and employment effects in the small open economy. The analysis in this paper can readily be generalized in several ways. The introduction of nontraded goods will enrich the model. Government expenditure can be assumed to affect the marginal utility of leisure and private consumption. The results will then hinge on whether private and public goods are Edgeworth complements or substitutes. One can also let government expenditures affect the marginal productivity of capital and labor (as in the closed economy model of Baxter and King (1993)). This will make the output effects of fiscal expansions stronger.
Acknowledgements I would like to thank the editor and an anonymous referee for helpful comments on both the content and the style of the paper.
Appendix A. Coefficients t "K\g, t "!XrJ (k !rJ )\exp(bH)K\, t "rJ n\t , (A.1) E I @ E g "pht , i"g,k,b, (A.2) G G f "!X(k !rJ )\t , f "K\XP(k !rJ )\, f "!K\P, E E I @ K,[X/(k !rJ )]exp(bH)rJ ]#P'0, (A.3) P,exp(bH)g #u'0, @I u,h\(e\!p)\(1!a)(1#g )(1!g )(g )\, n,exp(g!bH). * A@ JI J@
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The elasticity of output with respect to a temporary increase in government spending is given by g ,t /[H(exp k ¹!1)], WER E where !k g H, . rJ t exp (bH)(g #g /cQH) E @I @O References Ahmed, S., 1986. Temporary and permanent government spending in an open economy. Journal of Monetary Economics 17, 197—224. Barro, R., 1981. Output effects of government purchases. Journal of Political Economy 89, 940—971. Barro, R., 1989. The neoclassical approach to fiscal policy. In: Barro, R. (Ed.), Modern Business Cycle Theory, Cambridge, MA. Harvard University Press. Barro, R., Sala-i-Martin, X., 1995. Economic Growth, McGraw-Hill, New York. Baxter, M., 1995. International trade and business cycles. NBER Working Paper no. 5025. Baxter, M., King, R.G., 1993. Fiscal policy in general equilibrium. American Economic Review 83, 315—334. Becker, R., 1980. On the long-run steady state in a simple dynamic model of equilibrium with heterogeneous households. Quarterly Journal of Economics 95, 375—382. Blanchard, O., Rhee, C., Summers, L., 1993. The stock market, profit, and investment. Quarterly Journal of Economics 108, 115—136. Campbell, J., 1994. Inspecting the mechanism, an analytical approach to the stochastic growth model. Journal of Monetary Economics 33, 463—506. Correia, I., Neves, J., Rebelo, S., 1995. Business cycles in a small open economy. European Economic Review 39, 1089—1113. Karayalcin, C., 1996. Stockmarkets, adjustment costs, and international transmission of shocks. Economica 63, 599—610. Lucas, R., Stokey, N., 1984. Optimal growth with many consumers. Journal of Economic Theory 32, 139—171. Turnovsky, S., Sen, P., 1991. Fiscal policy, capital accumulation, and debt in an open economy. Oxford Economic Papers 43, 1—24.
Derivation of this result is available from the author upon request.