1. The consumer’s problem and the government

Consider a two-period, two-country, general equilibrium model of the world economy. In each country, there exists a representative consumer who maximizes an intertemporal utility function subject to a sequence of two budget constraints (one corresponding to each period of the agent’s life). The resources available to this agent take the form of endowments of three commodities: importables, exportables and nontradables. Agents are assumed to have access to an integrated world capital market through which all borrowing and lending takes place at the world rate of interest.

In each country, there is a government that levies lump sum taxes and spends the proceeds on various goods. The government has access to the world capital market and can borrow and lend at the same interest rate as the private sector. The horizon of the government is identical to that of private individuals. The model is therefore completely Ricardian so that the real equilibrium is independent of the timing of taxes. ^7/

We abstract from monetary considerations in the model and focus instead only on real quantities and prices. There is no uncertainty and individuals are assumed to have perfect foresight.

We assume that preferences may be represented by a weakly time separable utility function with homothetic subutilities. The agent’s optimization problem may then be viewed as taking place in two stages. ^8/ In the first stage, the agent allocates within-period spending across the three goods in order to minimize the total expenditure necessary to achieve a given level of subutility. The solution to this problem yields demands, c_it, i = x (exportable), m (importable), n (nontradable), and the consumption based price index, P_t, t = 0, 1. Demands are functions of the temporal relative prices, P_mt and P_nt and within period spending, P_tC_t, where pit is the relative price of good i, and C_t represents subutility or real spending in period t. Home country exportables serve as numeraire. All foreign economy variables will be denoted by an asterisk.

In the second stage, the agent maximizes an intertemporal utility function, U(C₀, C₁), subject to the constraint that lifetime expenditure not exceed lifetime wealth, W₀, defined as the present value of the endowment stream net of historical debt commitment and lump sum taxes. The intertemporal budget constraint can therefore be written as:

where α_x1 represents the world discount factor equal to (1 + r_x0)^-1 and r_xt is the rate of interest prevailing between periods t and t+1; Ȳ_it is the endowment of good i; T_t represents lump sum taxes in period t = 0,1 and ${\text{B}}_{-1}^{\text{P}}$ represents the private sector’s initial debt commitment.

The government’s consolidated budget constraint is given by:

where G_it denotes government consumption of good i in period t, i = x, m, n and t = 0,1 and ${\text{B}}_{-1}^{\text{P}}$ is the government’s initial debt commitment.

The representative consumer sees through equation (2) and incorporates the government budget constraint into his own. Accordingly, the equilibrium value of wealth for the consumer is given by:

where ${\text{B}}_{-1}={\text{B}}_{-1}^{\text{P}}+{\text{B}}_{-1}^{\text{g}}$, denotes the economy’s external debt commitment. Note that, when the definition of equilibrium wealth is substituted into the consumer’s budget constraint (equation (1)), the latter becomes equivalent to the condition that, over the lifetime of this economy, namely during periods 0 and 1, the present value of the sum of the trade account surpluses must equal the economy’s initial debt commitment.

It will prove useful to rewrite equation (1) in real terms; that is, in terms of period 0 subutility. Dividing through by P₀, we obtain:

where α_c1 = α_x1P₁/P₀, W_c01 - W₀/P₀ represent the consumption based discount factor (equal to (1+r_c0) where r_c0 is the consumption interest rate ^9/ prevailing between periods 0 and 1) and consumption based lifetime wealth, respectively. The optimization problem and constraints faced by the foreign country are completely analogous to those presented here for the home country.

2. The general equilibrium

An equilibrium is defined as a set of prices, P_m0, P_m1, P_n0, P_n1, ${\text{P}}_{\text{n0}}^{*},{\text{P}}_{\text{n1}}^{*}$, and a_x1, together with an allocation, which satisfy any seven of the following eight market clearing conditions, as well as the requirements that agents in each country maximize utility subject to constraint (1) and an analogous equation for the foreign economy:

Equations (4) and (5) state that the world demand for the exportable good must equal the world supply, net of government purchases, in each of the two periods while equations (6) and (7) state the corresponding condition for the importable commodity. Equations (8) and (9) specify zero excess demand for the home country’s nontradable good in each of the two periods while equations (10) and (11) express the corresponding condition for the foreign economy’s nontradable commodity. The specific form of the demand functions given in equations (4) through (11) follows from the earlier assumptions made concerning preferences. The exogenous variables in equations (2) through (9) are the endowments and the levels of government consumption. The equilibrium conditions demonstrate clearly, in this Ricardian setting, the equivalence between supply shocks and changes in government spending.

Figure 2 illustrates the equilibrium configuration of relative prices around an initial equilibrium of zero government consumption, i.e., G_it - 0, ∀ i, t. Consider the left-hand panel (panel a) first. The NN (N^*N^*) schedule represents the locus of combinations of the domestic (foreign) real exchange rate ratio, ^10/ P_n0/P_n1 (${\text{P}}_{\text{n0}}^{*}/{\text{P}}_{\text{n1}}^{*}$), and terms of trade ratio, P_m0/P_m1, along which there is zero excess demand for the domestic (foreign) nontradable good in periods 0 and 1. The Appendix shows that the slopes of these schedules are given by: ^11/

where β_i (${\beta }_{\text{i}}^{*}$) is the domestic (foreign) expenditure share of good i, σ_ij (${\sigma }_{\text{ij}}^{*}$) is the domestic (foreign) Allen elasticity of substitution between goods i and j, σ (σ^*) is the domestic (foreign) intertemporal elasticity of substitution, and Δ₁, ${\mathrm{\Delta }}_1^{*}$ are positive constants.

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The general equilibrium configuration of relative prices: The world rate of interest, terms of trade and domestic and foreign real exchange rates

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

Data. σ_ij > σ

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The intuition of equation (12) is as follows: suppose there is a rise in the relative price of importables in period 0. This leads to substitution among importables, exportables and nontradables within period 0. If importables and nontradables are Hicksian substitutes (complements), there is excess demand (supply) for nontradables at the initial price and a real appreciation (depreciation) is necessary to restore equilibrium in the home goods sector. This is the intratemporal substitution effect. Now suppose that P_m0 and P_m1 both rise but that P_m0 rises by more than P_m1 so that the ratio, P_m0/P_m1, rises. In this case the magnitude of the intratemporal substitution effect in period 0 exceeds that in period 1 and the price ratio, P_n0/P_n1, rises in order to maintain market clearing if importables and home goods are Hicksian substitutes, and conversely if they are complements. The magnitude of this intratemporal substitution effect is governed by σ_nm (${\sigma }_{\text{nm}}^{*}$), ^12/ the domestic (foreign) elasticity of substitution between importables and nontradables, which enters with a positive sign in equation (12).

On the other hand, the rise in P_m0/P_m1 raises the cost of current relative to future consumption, i.e., raises the consumption rate of interest. Agents substitute their expenditures from the current to the future period, part of which fall on nontradables. This intertemporal substitution effect therefore lowers the real exchange rate ratios, P_n0/P_n1 and ${\text{P}}_{\text{n0}}^{*}/{\text{P}}_{\text{n1}}^{*}$. The magnitude of this effect is governed by σ (σ^*), the domestic (foreign) intertemporal elasticity of substitution, which enters with a negative sign in equation (12). ^13/

Thus, equation (12) states that the terms of trade and real exchange rate ratios will be positively correlated if and only if the intratemporal elasticity of substitution between importables and nontradables exceeds the intertemporal elasticity of substitution. In Figure 1, the slopes of the two schedules reflect this assumption. When performing the comparative statics exercises, however, both the case of relatively large intertemporal elasticities of substitution and the case of relatively large intratemporal elasticities of substitution will be considered.

Consider now the right-hand panel (panel b) of Figure 2. The MM schedule represents the locus of combinations of the world discount factor, α_x1, and world terms of trade ratio, P_m0/P_m1, which equilibrates the world market for good m in periods 0 and 1 while the XX schedule represents the corresponding market clearing locus for good x. These schedules represent a reduced form relationship in the sense that they already incorporate the relationships embodied in equation (12). Their intersection at point A therefore represents the equilibrium value of the world discount factor and terms of trade ratio.

Consider first the slope of the MM schedule. ^14/ A rise in the world discount factor, α_x1 (a fall in the world rate of interest), causes aggregate spending in both countries to be brought forward and therefore raises the world importables consumption ratio, ${\text{c}}_{\text{m0}}^{\text{w}}/{\text{c}}_{\text{m1}}^{\text{w}}$, holding other prices constant. In order to eliminate the resulting excess demand, the terms of trade ratio, P_m0/P_m1, must rise. This suggests that the MM schedule is positively sloped.

One complication arises, however, because the rise in α_x1 raises the domestic and foreign real exchange rate ratios, P_n0/P_n1 and ${\text{P}}_{\text{n}\text{0}}^{*}/{\text{P}}_{\text{n1}}^{*}$. The reason is that the fall in the world interest rate creates excess demand for current relative to future goods (including nontradables) which requires a rise in their current relative to their future price to maintain market clearing.

The new real exchange rate ratios alter the world importables consumption ratio through two channels. The intratemporal substitution effect raises the consumption ratio, ${\text{c}}_{\text{m}\text{0}}^{\text{w}}/{\text{c}}_{\text{m1}}^{\text{w}}$, if home goods and good m are Hicksian substitutes in both countries, and lowers ${\text{c}}_{\text{m}\text{0}}^{\text{w}}/{\text{c}}_{\text{m1}}^{\text{w}}$ if the goods are complements. The intertemporal substitution effect always lowers ${\text{c}}_{\text{m}\text{0}}^{\text{w}}/{\text{c}}_{\text{m1}}^{\text{w}}$. This is because the rise in P_n0/P_n1 and ${\text{P}}_{\text{n}\text{0}}^{*}/{\text{P}}_{\text{n1}}^{*}$ raises the consumption rate of interest in both countries.

This suggests that if intratemporal elasticities of substitution exceed intertemporal elasticities (as in Figure 2), the endogenous response of the real exchange rate reinforces the direct effect of a rise in α_x1 on ${\text{c}}_{\text{m}\text{0}}^{\text{w}}/{\text{c}}_{\text{m1}}^{\text{w}}$ whereas if the intertemporal elasticities are sufficiently large, real exchange rate effects mitigate the direct effects. The following section considers a special case for the utility functions in which the real exchange rate effects cannot outweigh the direct effects so that the MM schedule is necessarily upward sloping. ^15/

Consider now the slope of the XX schedule. A rise in α_x1 creates excess demand for exportables in period 0 relative to period 1. How can this excess demand be eliminated? There are two effects. If importables and exportables are Hicksian substitutes, a fall in P_m0/P_m1 reduces the demand for good x in period 0 relative to period 1, and conversely in the case of complements. This is the intratemporal substitution effect. In addition, however, the fall in P_m0/P_m1 lowers the consumption rate of interest and thereby raises the demand for c_x0 relative to c_x1 in both countries. This is the intertemporal substitution effect. This argument suggests that--depending on the relative magnitudes of these two effects--the XX schedule may be either positively or negatively sloped. ^16/ The appendix shows that provided the intratemporal elasticities of substitution exceed the corresponding intertemporal elasticities (as assumed in Figure 2), the XX schedule is negatively sloped. The opposite case of relatively large intertemporal elasticities is considered below.

Figure 2 provides a complete characterization of relative prices in the initial equilibrium. Point A gives the equilibrium value of the terms of trade ratio and world discount factor while points a and a* give the values of the domestic and foreign real exchange rates along the NN and N^*N^* schedules. Note finally that these schedules are drawn for the equilibrium value of α_x1 at point A in Figure 2.

1. Government spending on nontradables

Consider first the effect of government consumption of nontradable goods. Using the diagrammatic apparatus developed in Figure 2, the vertical shifts of the equilibrium schedules in response to a rise in the discounted sum of government spending, G, are given by:

where k₁, k₂ are positive constants ^20/ and γ^g is the government’s average saving propensity defined as the ratio of future government spending to the discounted sum of government spending.

Equations (16) and (17) reveal that the direction in which the equilibrium schedules shift in response to changes in government spending depends on two factors: first, a transfer-problem criterion involving relative magnitudes of public and private sector spending propensities; second, the relative magnitudes of the intratemporal and intertemporal elasticities of substitution.

Consider first the transfer problem criterion. A rise in government spending on nontradables redistributes aggregate spending between the public and private sectors. Insofar as the (intertemporal ^21/) spending propensities differ between these two groups, aggregate demand will change and, given supply, the time profile of the equilibrium real exchange rate will be altered.

Specifically, if the private sector saving propensity (γ) exceeds the saving propensity of the government (γ^g), then the rise in government spending redistributes aggregate spending on nontradables in favor of a unit with a relatively large spending propensity in period 0, and vice-versa. In the first case, the rise in G raises the equilibrium real exchange rate ratio, P_n0/P_n1, and conversely.

Consider the case in which γ > γ^g (as when the government increases spending temporarily, in the current period) so that the direct impact of the rise in G is to raise the equilibrium value of P_n0/P_n1. The new time profile of the real exchange rate has two effects. First, the intratemporal substitution effect implies that agents substitute away from nontradables in favor of tradables. The magnitude of this effect is governed by the intratemporal elasticity of substitution, σ_jj > 0, in the CES case. Second, the rise in P_n0/P_n1 raises the cost of current in terms of future consumption, i.e., raises the consumption interest rate. This intertemporal substitution effect tends to lower consumption of tradables in the current relative to the future period. The magnitude of this effect is governed by σ > 0, the intertemporal elasticity of substitution in consumption.

The previous discussion suggests that if the intratemporal substitution effect is large relative to the intertemporal substitution effect, then a temporary rise in government spending on home goods creates excess demand for current relative to future period tradables, and conversely. How can this excess demand (supply) be eliminated? Consider first the case in which σ_ij > σ. In this case, the excess demand for importables (in period 0 relative to 1) requires a rise in the terms of trade ratio, P_m0/P_m1, to clear world markets so that, as indicated by equation (16), there is an upward displacement of the MM schedule. The excess demand for exportables requires a fall in P_m0/P_m1 to maintain market clearing in the world market for good x so that, as indicated by equation (17), the XX schedule shifts down.

It is also easy to verify that if σ > σ_ij, the XX schedule also shifts down. This is because the excess supply for good ξ in period 0 relative to period 1 requires a fall in P_m0/P_m1 to restore market clearing. The mechanism is straightforward: the fall in P_m0/P_m1 lowers the consumption rate of interest, thereby stimulating current relative to future period demand for good x via an intertemporal substitution effect. The intratemporal substitution effect operates in the opposite direction but is weak because σ > σ_ij. The same argument reveals that the MM schedule also shifts down In this case.

The two cases are illustrated in Figures 3 and 4. In both figures, the original world equilibrium is given by point Ã. In Figure 3, which corresponds to the large intratemporal elasticity of substitution case, the shifts in the MM (MʹMʹ) and XX (to XʹXʹ) schedules result in a new equilibrium at point $\tilde{\text{B}}$ and the world rate of interest necessarily rises (i.e., the world discount factor, α_x1, falls). In Figure 4, which corresponds to the large intertemporal elasticity of substitution case, the equilibrium moves from point à to point $\tilde{\text{B}}$ʹ, and the world rate of interest falls. Further, it can be shown that in both cases, the terms of trade ratio is unaffected by the change in government spending on home goods. ^22/

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The effect of a temporary increase in government spending on home goods: The case of large intratemporal substitutability.

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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The effect of a temporary increase in government spending on home goods: The case of large intertemporal substitutability

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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Consider now the behavior of real exchange rates. In the case in which σ > σ_ij (Figure 4), the results are clear cut. Because the world rate of interest falls, agents in both countries substitute spending from the future to the current period, part of which falls on home goods. A rise in both real exchange rate ratios, P_n0/P_n1 and ${\text{P}}_{\text{n0}}^{*}/{\text{P}}_{\text{n1}}^{*}$, is therefore required to maintain market clearing. This is reflected by the leftward displacement of the NN (N^*N^{* 23/}) schedules to NʹNʹ (N^*ʹN^*ʹ) respectively. Note that the magnitude of the shift in the NN schedule exceeds that of the N*N* schedule because the increase in government spending originates in the home country. This implies that the new home country equilibrium, given by point aʹʹ lies to the left of the foreign economy’s equilibrium, given by point a^*ʹʹ, and that both lie to the left of the original equilibrium given by point a. Real exchange rates are positively correlated across countries in response to the increase in government spending. Furthermore, because the short run (period 0) response exceeds the long run (period 1) response, the temporary rise in government spending generates overshooting of the equilibrium real exchange rate.

Consider now the case of relatively large intratemporal elasticities of substitution (Figure 3). In this case, the behavior of the foreign real exchange rate is opposite to the previous case, i.e., there is a real depreciation in the current relative to the future period. The reason is of course that with σ_ij > σ, the rise in government spending results in an increase in the world rate of interest which in turn generates excess supply of nontradables in the current relative to the future period and a fall in ${\text{P}}_{\text{n0}}^{*}/{\text{P}}_{\text{n1}}^{*}$. This is reflected by a rightward displacement of the N*N* schedule and a new equilibrium of the foreign economy at point a*’ in Figure 3. Note that at this point, the short run response of the real exchange rate falls short of the long run response, so that we may refer to this situation as one of equilibrium undershooting.

When σ_jj > σ, the domestic real exchange rate is influenced by two opposing forces: the increase in government spending requires a rise in P_n0/P_n1 to clear the nontradables sector whereas the rise in the world interest rate requires a fall in the nontradables price ratio. It can be shown, however, that in the case of identical CES preferences, the former influence always dominates so that P_n0/P_n1 rises, i.e., the behavior of the equilibrium real exchange rate is characterized by overshooting, and the new domestic economy equilibrium is given by a point such as a’ in Figure 3. It is also noteworthy that in this case (σ_ij > σ), domestic and foreign real exchange rates are negatively correlated (in contrast to the previous case in which they are positively correlated).

Table 2 summarizes the main results of this section. It can be seen that, under the assumption of identical CES utilities across countries, the behavior of the interest rate and the domestic and foreign real exchange rates depend both on a transfer problem criterion relating government and private sector saving propensities and on the relative magnitudes of the intratemporal and intertemporal elasticities of substitution in consumption. Finally, note that, as alluded to previously, the absence of movement in the terms of trade resulting from an increase in government spending on home goods depends critically on the specification of preferences. As shown in the Appendix, if elasticities of substitution differ across goods within a period (as with the more general utility function of Section II), the terms of trade will not in general remain constant. Moreover, their response can be shown to depend on whether home goods are more closely substitutable for importables or exportables in consumption. In contrast, in the following section, it is shown that changes in government expenditures on tradable goods will in general lead to fluctuations in both the terms of trade and real exchange rates of both countries even with preferences as specified in equations (13) and (14). Thus, in this case, we can also examine the determinants of the comovement between the two temporal relative prices, namely the terms of trade and the real exchange rate.

Table 2.

The Effect of a Rise in the Discounted Sum of Government Spending on Nontradable Goods

Table 2.

The Effect of a Rise in the Discounted Sum of Government Spending on Nontradable Goods

Relation Between Intratemporal and Intertemporal Elasticities of Substitution	Intertemporal Allocation of Government Spending
	γ > γg				γ < γg
	${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$				${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$
σij > σ	+	0	-	+	-	0	+	-
σij < σ	-	0	+	+	+	0	-	-

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Table 2.

The Effect of a Rise in the Discounted Sum of Government Spending on Nontradable Goods

Relation Between Intratemporal and Intertemporal Elasticities of Substitution	Intertemporal Allocation of Government Spending
	γ > γg				γ < γg
	${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$				${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$
σij > σ	+	0	-	+	-	0	+	-
σij < σ	-	0	+	+	+	0	-	-

2. Government spending on tradable goods

In subsections a and b, we consider the effects of increased government consumption of exportables and importables on world relative prices and domestic and foreign real exchange rates. Subsection c goes on to consider some possible implications of the analysis for the behavior of various macroeconomic aggregates of interest including consumption, investment, and employment. An attempt is also made to compare the various results concerning government expenditures on tradables versus nontradable goods.

a. Exportables

Consider now the effect of a rise in the discounted sum of government consumption of good x. The vertical displacement of the XX schedule is given by: ^24/

$\begin{array}{cc}\frac{\text{d}\text{log}({\text{P}}_{\text{m}\text{0}}/{\text{P}}_{\text{m}\text{1}})}{\text{dG}}{|}_{\text{XX}}={\text{k}}_3(\gamma -{\gamma }^{\text{g}})(\sigma -{\sigma }_{\text{ij}})& \left(18\right)\end{array}$

where k₃ is a positive constant. ^25/ As before, the direction in which the XX schedule shifts in response to an increase in government spending on the exportable good depends on a transfer problem criterion involving the relative magnitudes of the public and private sector saving propensities, γ and γ^g, and an additional condition involving the relative magnitudes of the intratemporal and intertemporal elasticities of substitution in private consumption. ^26/ The logic is similar to what was described in the previous section. If γ > γ^g (as with a temporary current increase in government spending), the transfer problem criterion dictates that the redistribution of aggregate spending between the public and private sectors creates excess demand in the current relative to the future period. In order to eliminate this excess demand, the consumption rate of interest must rise in both countries. In the case under consideration, the rise in the consumption rate of interest is accomplished by a combination of a rise in the world rate of interest (i.e., a decline in the world discount factor, a_x1) and an improvement in the terms of trade in the current relative to the future period (i.e., a decline in P_m0/P_m1). These results are illustrated in Figures 5 and 6 (for the case γ > γ^g) where it is seen that, qualitatively, the direction in which the world temporal and intertemporal terms of trade moves in response to the change in government expenditures does not depend on the relative magnitudes of the intra- and intertemporal elasticities of substitution. Note also that the improvement in the terms of trade implies that the rise in consumption rates of interest in both countries is smaller than the rise in the rate of return on real bonds, r_x0.

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The effect of a temporary increase in government spending on exportables: The case of large intratemporal substitutability.

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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The effect of a temporary increase in government spending on exportables: The case of large intratemporal substitutability.

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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The behavior of domestic and foreign real exchange rates depends only on movements in world temporal and intertemporal terms of trade. This is because, with shocks originating in the tradables sector, there is no direct impact on the relative price of home goods. In Figures 5 and 6, it is shown that the nontradables equilibrium locus shifts rightward, reflecting the rise in interest rates in world markets. The interest rate effect therefore favors a real depreciation in the current relative to the future period in both countries. However, in addition to this effect, the fall in the terms of trade ratio, P_m0/P_m1, reinforces the interest rate effect in Figure 5 (in which intratemporal elasticities of substitution are relatively large) but mitigates the effect of rising world interest rates in the large intertemporal elasticity of substitution case (Figure 6). The reason for the latter, as already noted, is that if σ > σ_ij, the intertemporal substitution effect associated with the fall in P_m0/P_m1 (which reduces the consumption rate of interest and thereby tends to raise current period nontradables consumption) outweighs the intratemporal substitution effect which favors consuming more (relatively cheaper) exportables (i.e., less nontradables) in period 0. However, it can be shown that the interest rate effect always dominates so that, qualitatively, a current increase in government consumption of exportables must generate a real depreciation of the (exportables ^27/) real exchange rate (a fall in P_n0/P_n1 and ${\text{P}}_{\text{n0}}^{*}/{\text{P}}_{\text{n1}}^{*}$), in the current relative to the future period, in both countries, irrespective of the relative magnitudes of the intra- and intertemporal elasticities of substitution (see appendix). The analysis therefore suggests comovements consisting of improving terms of trade and real depreciations resulting from a temporary increase in government consumption of good x. Moreover, along the adjustment path to the new long run equilibrium, the real exchange rate will exhibit equilibrium undershooting.

b. Importables

A rise in the discounted sum of government spending on good m shifts the MM locus by an amount equal to: ^28/

$\begin{array}{cc}\frac{\text{d}\text{log}({\text{P}}_{\text{m}\text{0}}/{\text{P}}_{\text{m}\text{1}})}{\text{dG}}{|}_{\text{MM}}={\text{k}}_4(\gamma -{\gamma }^{\text{g}})& \left(19\right)\end{array}$

where k₄ is a positive constant. ^29/ Thus, as in the previous cases, the direction in which the MM schedule shifts depends on a transfer problem criterion involving differences between public and private saving propensities. Accordingly, if γ > γ^g (γ < γ^g), the rise in government spending raises aggregate demand for good m in the world economy in the current (future) relative to the future (current period), and a rise in the terms of trade ratio, P_m0/P_m1, is necessary to clear world markets. The upward displacement of the MM schedule is portrayed in Figures 7 and 8. There, it is seen that, irrespective of the relative magnitudes of the intratemporal and intertemporal elasticities of substitution, a temporary rise in government spending on good m causes a deterioration in the terms of trade in the current relative to the future period. In contrast to the case of government spending on good x, it is also apparent that the behavior of the world rate of interest is ambiguous: it rises if σ > σ_ij but falls if σ > σ_ij.

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The effect of a temporary increase in government spending on importables: The case of large intratemporal substitutability.

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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The effect of a temporary increase in government spending on importables: The case of large intratemporal substitutability.

Citation: IMF Working Papers 1989, 028; 10.5089/9781451981094.001.A001

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To understand this result, recall that a temporary rise in current government spending on any tradable good creates excess demand for current relative to future tradables, the elimination of which requires a rise in the consumption rates of interest in both countries to restore market clearing. When the government biases its spending toward good x, the terms of trade improve in the current relative to the future period (which tends to lower consumption interest rates) so that, in order for consumption rates of interest to increase, the world rate of interest must necessarily rise. In contrast, when the government biases its spending toward good m, the terms of trade ratio, P_m0/P_m1, necessarily rises, thereby contributing to the required increase in consumption rates of interest in both countries. The direction in which the rate of return on the internationally traded bond must move in order to eliminate world deceiving is therefore ambiguous. If σ > σ_ij, the intertemporal effect associated with the terms of trade deterioration is more than sufficient to suppress world borrowing at the initial interest rate. It follows that in this case, the world discount factor actually rises (the world interest rate falls) as shown in Figure 8. In contrast, when σ_ij > σ, the intertemporal substitution effect associated with movements in the terms of trade is rather weak and, therefore, in order to eliminate excess demand for current tradables (i.e., desired world borrowing), a rise in the world rate of interest becomes necessary (Figure 7). One conclusion of the above analysis is that independent of whether the government consumes tradable or nontradable goods, the world rate of return on internationally traded bonds may either rise or fall as a result of a temporary rise in government spending. Such a result, which contrasts with the usual prediction of neoclassical macro- models, demonstrates the importance of intertemporal movements in other macroeconomic relative prices (in this case, the terms of trade and the real exchange rate) for the determination of macroeconomic equilibrium. It also argues in favor of a modelling strategy that allows for the endogenous determination of these relative prices (i.e., a three sector model) in response to macro-disturbances, at least until empirical research demonstrates that movements in the time paths of the terms of trade and the real exchange rate are quantitatively unimportant for the determination of agents’ intertemporal consumption decisions.

Having determined the behavior of world temporal and intertemporal terms of trade, we can now ask how real exchange rates react to a temporary increase in government spending on importables. In Figure 7, the rise in the world rate of interest shifts the nontradables equilibrium locus rightward, i.e., for given terms of trade, there is a real depreciation in the current relative to the future period. In contrast, in Figure 8, the fall in the world rate of interest shifts the NN and N*N* loci leftward, and there is a real appreciation in the current relative to the future period, at initial terms of trade. The movement in the latter always dampens the effect of changes in the world interest rate on the domestic and foreign real exchange rate. ^30/ Specifically, if σ_ij > σ (Figure 7), the deterioration in the terms of trade favors an appreciation in the current relative to the future period (corresponding to the northwest movement along the NʹNʹ locus). In contrast, when σ > σ_ij, the effect of the fall in the world interest rate on domestic and foreign real exchange rates is mitigated by the rise in P_m0/P_m1 which favors a real depreciation in the current relative to the future period (corresponding to a north-east movement along the nontradables equilibrium locus in Figure 8).

In fact, it can be shown (see the Appendix) that the overall effect of movements in the temporal and intertemporal terms of trade is to leave both the domestic and foreign exportables real exchange rate ratios unchanged. Before concluding anything from this result, however, the following two points should be kept in mind. First, the result is essentially an artifact of the choice of numeraire. Specifically, because a temporary rise in government consumption of any tradable commodity must raise the consumption rate of interest, it follows that spending on all goods will be tilted toward the future so that a consumption based measure of the real exchange rate must depreciate in the current relative to the future period. ^31/ Second, although the real exchange rate ratio is unaffected by the temporary change in fiscal policy, the level of the real exchange rate does in fact change, period by period. Specifically, it can be shown that there is a real depreciation both in periods 0 and 1, and that the magnitudes of these depreciations are equal to each other. Therefore, in this case, the (exportables) real exchange rate exhibits neither equilibrium under- nor overshooting (in contrast to the cases considered in the previous two subsections) along the adjustment path but instead adjusts instantaneously to its new long run equilibrium value.

Table 3 summarizes the main results concerning the relative price effects of government spending on tradable goods. First, it can be seen that a temporary increase in government spending on tradable goods need not increase the rate of return on internationally traded bonds if spending is relatively biased toward the importable commodity and elasticities of substitution are relatively large intertemporally. Second, in three of the four cases, movements in the temporal and intertemporal terms of trade exert conflicting influences on the foreign economy, so that it may be of some importance, in evaluating the size of comovements induced by changes in fiscal policy, to relax the assumption of a composite tradable commodity. Third, the analysis suggests that real depreciations of the (consumption based) measure of the real exchange rate and equilibrium undershooting are the likely outcomes resulting from temporary government expenditures on tradable goods, which are opposite to the predictions for nontradables. Fourth, the comovement between the terms of trade and the real exchange rate depends on the intratemporal allocation of government expenditures, being positive in the case of government spending on exportables and negative in the case of government spending on importables. Fifth, with shocks originating in the tradable rather than the nontradable sector, the main determinant of both domestic and foreign real exchange rates are movements in the world temporal and intertemporal terms of trade, which are of course common to both countries. Therefore, the expected correlation between domestic and foreign real exchange rates is positive when the government spends on tradables. This contrasts with the case of government spending on home goods in which the comovement of domestic and foreign real exchange rates would be negative for sufficiently small values of the intertemporal elasticity of substitution in consumption.

Table 3.

The Effect of a Rise in the Discounted Sum of Government Spending on Tradable Goods

Table 3.

The Effect of a Rise in the Discounted Sum of Government Spending on Tradable Goods

	Allocation of Government Expenditures:
	Intratemporally	Intertemporally
Relation Between Intratemporal and Intertemporal Elasticities of Substitution		γ > γg				γ < γg
		${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$				${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$
σij > σ	importables	+	+	0	0	-	-	0	0
	exportables	+	-	-	-	-	+	+	+
σij < σ	importables	-	+	0	0	+	-	0	0
	exportables	+	-	-	-	-	+	+	+

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Table 3.

The Effect of a Rise in the Discounted Sum of Government Spending on Tradable Goods

	Allocation of Government Expenditures:
	Intratemporally	Intertemporally
Relation Between Intratemporal and Intertemporal Elasticities of Substitution		γ > γg				γ < γg
		${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$				${\text{r}}_{\text{x0}}\frac{{\text{P}}_{\text{m0}}}{{\text{P}}_{\text{m1}}}\frac{{\text{P}}_{\text{n0}}^{*}}{{\text{P}}_{\text{n1}}^{*}}\frac{{\text{P}}_{\text{n0}}}{{\text{P}}_{\text{n1}}}$
σij > σ	importables	+	+	0	0	-	-	0	0
	exportables	+	-	-	-	-	+	+	+
σij < σ	importables	-	+	0	0	+	-	0	0
	exportables	+	-	-	-	-	+	+	+