1. Perfect capital mobility

Under perfect capital mobility, the domestic real interest rate (in terms of tradables) equals the international one (i.e., ρ-r). Furthermore, the supply of money, m^s, is endogenous, implying that equilibrium condition (9) always holds. Therefore, under perfect capital mobility, equations (6), (7) and (8) are reduced to (recall that β = r):

Consider first steady-state solutions. By equation (12), a constant real exchange rate is obtained if, and only if, c^* is constant over time; which, by equation (11), implies that the monetary authority must engineer a constant nominal interest rate. Since in this case i_t = r + ∊_t, where ∊ is the rate of devaluation, we have that a constant i implies a constant rate of devaluation. In turn, by the overall budget constraint (10), a constant c^* implies c^* = y^*, which is independent of the nominal interest rate, i, and, therefore, of the rate of devaluation, ∊. Hence, by (12),

We have thus obtained the intuitively plausible implication that the steady-state real exchange rate is independent of (permanent changes in) the rate of devaluation. ^18/ In other words, the real exchange rate will be given by (13) for any constant level of the rate of devaluation and thus of the nominal interest rate. Furthermore, since the utility function is assumed to be strictly concave, it can be verified that a constant-c^* path is a necessary and sufficient condition for a social optimum. Hence, in this economy it is socially optimal to have a constant rate of devaluation and, consequently, to generate the (unique) real exchange rate which can be kept constant over time. Any departure from this constant-real-exchange-rate path will be non-optimal, which proves, for the case of perfect capital mobility, that any attempt to depreciate the real exchange rate by monetary policy (or, to be sure, by any other means) is bound to be socially costly. ^19/

Suppose that the government attempts to depreciate the real exchange rate over and above the level achieved on the steady-state path. By previous considerations, such a policy can only attain its objective for a limited period of time (since we have shown that the steady state is unique). Since the utility function is strictly concave, it follows from equation (12) that e rises if, and only if, c^* falls. By the resource constraint (10), the latter requires c^* to rise over its present steady-state level sometime in the future.

For the sake of clarity, consider the case in which the government sets the real exchange rate at e¹, exceeding its present steady-state level, from time 0 to time T > 0 (referred to as the “first period”) and, thereafter (referred to as the “second period”), the economy settles to its new steady state, indicated by e² (see Figure 3, Panel A). ^20/ Thus denoting the corresponding consumption of traded goods by c^*1 and c^*2, we have, by equation (12), c^*1 < y^*; and, by the resource constraint (10), c^*1 < y^* < c^*2 (see Figure 3, Panel B). Hence, by equation (12), e² is lower than initial e. Such a path of c^* implies, using (11), that i¹ > i² or, equivalently, that ∊¹ > ∊² (see Figure 3, Panel C). ^21/ Since within each period the relative price of traded goods in terms of home goods, e, is constant, it follows from the above analysis that the rate of inflation in period 1 exceeds that of period 2. Under perfect capital mobility, therefore, the model implies that in order to depreciate the real exchange rate over and above its current steady-state level, present inflation should be (and expected to be) higher now than in the future (i.e., inflation is higher in period 1 than in period 2).

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Effects of Real Exchange Rate Targeting

Citation: IMF Working Papers 1994, 022; 10.5089/9781451921212.001.A001

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Notice that the above result is not tantamount to saying that the current rate of inflation has to increase relative to its past level. Rather, the result says that the policy must be such that the public expects inflation to fall over time. Here is where credibility issues come into play. For example, a present real exchange rate depreciation could be achieved with lower inflation today, if such action led the public to expect that inflation will continue falling in the future. However, in practice, this can only be achieved if the government engages in a credible adjustment that lowers the fiscal deficit. ^22/ Hence, a present unsustainably low inflation will lead the public to expect higher, rather than lower, inflation in the future which, as argued above, would not be consistent with a real exchange rate depreciation today. Consequently, in the absence of a credible fiscal adjustment, a policy aimed at depreciating the real exchange rate is likely to jack up the rate of inflation (i.e., set present inflation higher than before).

Finally, note that the central result that real exchange rate targeting is inflationary would remain valid under a PPP-type of rule whereby the real exchange rate is kept constant in the face of external shocks. Specifically, consider an initial equilibrium in which foreign inflation is positive so that i = i* + ∊, where i* = r + π*. Further, suppose that there is a temporary fall in foreign inflation and, thus, in the world nominal interest rate; that is, i^*1 < i^*2. In the absence of any policy response, this positive external shock would lead to a temporary fall in the domestic nominal interest rate (i.e., i¹ < i²), which increases consumption of traded goods (i.e., c^*1 > y^* > c^*2) and causes the real exchange rate to appreciate (i.e., e¹ falls below its initial level). The authorities can prevent this by setting ∊¹ higher than ∊¹ so as to exactly offset the changes in the world nominal interest rate. In other words, policymakers set i¹ (= i^*1 + ∊¹) equal to i² (= i^*2 + ∊²). By so doing, consumption of traded goods and, thus, the real exchange rate remain unchanged with respect to the initial equilibrium (i.e., before the external shock hit). Hence, the policy is successful in preventing the real exchange rate from appreciating, but at the cost of higher inflation (i.e., ∊¹ > ∊²) relative to the situation in which the authorities would not have responded to the external shock. ^23/

2. No capital mobility

Consider now the case in which capital controls are in place. It will be assumed that such controls can be perfectly enforced so that the stock of foreign assets in the hands of the public remains constant over time. ^24/ It will be shown that, unlike the case of perfect capital mobility, a temporary real exchange rate depreciation can be obtained with zero inflation and a constant nominal exchange rate.

Unlike the case of perfect capital mobility, the domestic real interest rate (in terms of tradables), ρ, can transitorily differ from the international one. ^25/ Once again, consider the experiment of setting e_t = e¹ for 0 ≤ t < T. Since, by assumption, the nominal exchange rate is fixed (i.e., ∊ = 0), i = ρ. ^26/ Furthermore, equilibrium condition (10) still holds in this case, implying that c^*_t = c^*1 < y^* during the first period. Thus, as before, if the economy settles down to a steady state after time T, we have c^*_t = c^*2 > y^*, for t ≥ T. ^27/ Moreover, by equations (6) and (7), it is straightforward to show that in a steady state with fixed exchange rates i = ρ = β. We will now show that, during the first period the money supply can be manipulated in order to generate e = e¹ and c^* = c^*1.

By first-order condition (6), it follows that

where

Therefore, recalling equation (2) and that with fixed exchange rates i = ρ, we have

Thus, by equations (14) and (18), it follows that

By definition (recall equations (14) and (15)), λ is continuous with respect to time. Moreover, from (15), it follows that λ must attain a well-defined level at time T. Formally, then, the equilibrium solution is associated with the continuous path of λ that satisfies dynamic equation (19) and terminal condition (15). We now have the basic elements to proceed with the substantive part of the analysis.

We first show that λ decreases over time. Suppose, to the contrary, that λ increases over time. This implies, from equation (19), that (1/α + β)λ₀ > u_c^*(c^*1, y)/α. Then, since λ_T > λ₀ and c^*1 < c^*2, it follows, using (12), that (1/α + β)λ_T > u_c^*(c^*1, y)/_α > u_c^*(c^*2, y)/α, which contradicts terminal condition (15). Therefore, (1/α + β)λ₀ < u_c^*(c^*1, y)/α which implies, by equation (19), that λ decreases over time. ^28/ Consequently, by equation (14), the nominal interest rate increases over time. Moreover, by equation (14) and the above finding that (1/α + β)λ₀ < u_c^*(c^*1, y)/α, it follows that

implying that i₀ > β. Therefore, if before the attempt to raise the real exchange rate the economy was in steady-state equilibrium, an overdepreciated real exchange rate can be sustained by a jump in the nominal/real interest rate, followed by further rises until the policy is abandoned at time T (and i goes back to its steady-state level β), as illustrated in Figure 3, Panel D. ^29/

In sum, the analysis has shown that, under no capital mobility, a temporary depreciation of the currency in real terms can be achieved without affecting the inflation rate if it is accompanied by a temporarily tight credit stance. As expected, tight credit is achieved by lowering real monetary balances. To prove it, notice that the cash-in-advance constraint (4) and equilibrium condition (8) imply

Hence, m falls at time 0 because e rises and c^* increases and remains constant in each of the periods. Consider the domestic credit policy that supports such a path of the money supply. At time 0, domestic credit is reduced to engineer the drop in the money supply. Thereafter, and for the rest of the first period, the monetary authorities fully sterilize the reserve inflow that results from the current account surplus, so as to keep the money supply constant. At time T, domestic credit is increased to support the higher consumption of traded goods and lower real exchange rate.

The above result testifies to the much greater power that monetary policy has under imperfect capital mobility. In our example, the real exchange rate can be changed by manipulating the supply of money but, remarkably enough, without having to change the rate of inflation. It should be pointed out, however, that even in the extreme case of no international capital mobility, temporary changes in the real exchange rate are socially costly. Actually, our example dramatizes this point since the associated social costs of temporary changes in the real exchange rate are identical to those borne under perfect capital mobility. ^30/

The power of monetary policy is undermined also in this case if government policy is not fully credible. Consider, for example, the case discussed above, in which the public expects high inflation in the future, irrespective of government announcements. Under those conditions, the expected future interest rate is largely independent of present announcements. Hence, in order to provoke a temporary depreciation of the real exchange rate, the government will be forced to increase current interest rates even further than it would under perfect credibility. In a more realistic model in which there is a positive stock of short-term government debt, higher interest rates would worsen the fiscal balance, possibly generating the high inflation expected by the public.

1. Perfect capital mobility

Taking into account equations (22) and (23), first-order conditions (11) and (12) become:

Using (24), (25), and resource constraint (10), a closed-form solution for c^* can be derived:

where

To simplify notation, equation (27) defines the effective price of consumption, while equation (28) defines the intertemporal elasticity of substitution relevant for traded goods. ^33/ Note that if i, and thus p, are constant over time, then the term that multiplies y^* on the right-hand side of equation (26) is unity, which implies that ${\mathrm{c}}_{\mathrm{t}}^{*}={\mathrm{y}}^{*}$ for all t. If i, and thus p, vary over time, then c^* will also vary over time. In this case, the parameter η* plays a key role in determining the response of c^*. Specifically, if p is higher in the present than in the future, then today’s consumption of traded goods is lower than in the future. The higher is η*, the smaller will be today’s consumption relative to future consumption.

To make equation (26) operational, we need to make explicit the path of i and thus p. Following the theoretical example, suppose that i_t = i¹ for 0 ≤ t < T and i_t = i² for t > T, where i¹ > i². Then, denoting by p¹ and p² the respective effective prices (i.e., p¹ = 1 + αi¹ and p² = 1 + αi², where p¹ > p²), equation (26) reduces to:

where p and η* are defined in equations (27) and (28), respectively. (An analogous expression holds for t≥T.)

Using equations (25), (27), (28) and (29), we can compute the nominal interest rate which is needed to generate a given depreciation of the exchange rate. ^34/ Assuming that i² = r = 0.03, Table 1 shows the nominal interest rate (in monthly effective terms) which generates during period 1 a real depreciation of 5, 10, and 15 percent for different values of η and T (expressed in years). ^{35/ 36/} For example, if η = 0.4 and T = 1/2 (half a year), then the nominal interest rate needs to be 4.97 percent per month (or 79.0 percent per year) for the real exchange rate to depreciate by 5 percent.

Table 1.

Nominal interest Rate Needed to Generate a Given Depreciation

(In percent per month)

Table 1.

Nominal interest Rate Needed to Generate a Given Depreciation

(In percent per month)

	Intertemporal elasticity of substitution	Depreciation of real exchange rate
		5 percent	10 percent	15 percent
T=0.5	0.15	10.57	23.35	39.26
	0.4	4.97	10.07	15.55
	0.8	3.43	6.73	10.15
T=1	0.15	10.75	23.78	40.06
	0.4	5.05	10.22	15.81
	0.8	3.48	6.83	10.31
T=2	0.15	11.10	24.67	41.74
	0.4	5.20	10.55	16.34
	0.8	3.58	7.05	10.63

View Table

Table 1.

Nominal interest Rate Needed to Generate a Given Depreciation

(In percent per month)

	Intertemporal elasticity of substitution	Depreciation of real exchange rate
		5 percent	10 percent	15 percent
T=0.5	0.15	10.57	23.35	39.26
	0.4	4.97	10.07	15.55
	0.8	3.43	6.73	10.15
T=1	0.15	10.75	23.78	40.06
	0.4	5.05	10.22	15.81
	0.8	3.48	6.83	10.31
T=2	0.15	11.10	24.67	41.74
	0.4	5.20	10.55	16.34
	0.8	3.58	7.05	10.63

Four observations follow from the figures reported in Table 1:

a. The inflationary consequences of engineering a temporary depreciation of the real exchange rate are likely to be substantial. Even though these figures should be viewed as an upper bound—given that in practice capital mobility is less than perfect—the order of magnitude is large enough to suggest that the inflationary effects would still be large under less than perfect capital mobility.

b. The real exchange rate target has a substantial effect on the inflation upsurge. In other words, for a given value of the intertemporal elasticiy of substitution (say, 0.4), targeting a real depreciation of 15 percent during one year results in considerable more inflation (a nominal interest rate of 15.55 percent per month) than targeting a real depreciation of 5 percent (a nominal interest rate of 4.97 percent per month).

c. The intertemporal elasticity of substitution plays a key role. Since the mechanism through which the real exchange rate depreciation is effected is intertemporal consumption substitution, it is not surprising that the magnitude of this parameter critically affects the inflationary consequences of real exchange rate targeting. For instance, for T=l and a real exchange rate depreciation of 10 percent, the nominal interest rate varies from 23.78 to 6.83 percent per month as η varies from 0.15 to 0.8. As reported in Reinhart and Végh (1993), intertemporal elasticities of substitution in developing countries such as Argentina, Brazil, Chile, Israel, Mexico, and Uruguay are clustered around 0.20. ^37/ Hence, these low values of η are likely to exacerbate the inflationary consequences of real exchange rate targeting.

d. The time period during which policymakers seek to maintain a more depreciated exchange rate level is relatively unimportant. As Table 1 shows, the values of the parameter T make little difference to the inflationary effects. For instance, for a real depreciation of 5 percent and η = 0.15, the nominal interest rate varies only from 10.57 to 11.10 percent per month as T varies from half a year to two years. Hence, what matters is not so much the time period during which the more depreciated real exchange rate is maintained, but rather the desired target level.

2. No capital mobility

In spite of having intrinsic dynamics, the model with capital controls model is simple enough to lend itself to an easy numerical solution. Our objective is to compute the initial and final values of the real interest rate path (i.e., ρ₀ and ρ_T^-), depicted in Figure 3, Panel D, that generates a temporarily depreciated real exchange rate. The values of c^*1 and c^*2 are the ones that follow from the perfect capital mobility case since, by construction, the policy under capital controls studied in Section 3 supports such a path.

Since no additional insights are derived from solving the model, we will only indicate how the model is solved without reporting the solution itself. The linear differential equation (19) can be solved to obtain λ₀ as a function of λ_T and c^*1. Since we know both λ_T (which follows from equation (15) using equations (22) and (23)) and c^*2, λ₀ can be computed. Given λ₀ and c^*1, i₀(= ρ₀) can be computed from equation (14), using equations (22) and (23). The value of i_T^- can be computed in the same way by recalling that λ is continuous at t=T.

The results of the simulation are reported in Table 2. Each entry reports two values of the real interest rate path depicted in Figure 3, Panel D: the first is the value of the real interest rate at time 0, while the second is the value at time T^- (i.e, just before the real exchange rate falls). In general, the initial increase in real interest rates is rather small. ^38/ However, the real interest eventually reaches high, and in some cases exorbitant, levels. Note that the final value taken by the real interest rate (or the nominal interest rate) coincides with the value that the nominal interest rate takes in the perfect capital mobility case, as a comparison of Tables 1 and 2 reveals. This should not come as a surprise since terminal condition (15) also holds under perfect capital mobility, which implies that ${\lambda }_{\mathrm{T}}=\overline{\lambda }$. Hence, since consumption is the same in both cases, ρ_T^-(= i_T^-) (under no capital mobility) equals i¹ (under perfect capital mobility).

Table 2.

Real Interest Rate Needed to Generate a Given Depreciation

(In percent per month)

Table 2.

Real Interest Rate Needed to Generate a Given Depreciation

(In percent per month)

	Intertemporal elasticity of substitution	Depreciation of real exchange rate
		5 percent	10 percent	15 percent
T=0.5	0.15	0.55-10.57	0.79-23.35	0.99-39.26
	0.4	0.40-4.97	0.53-10.07	0.65-15.55
	0.8	0.35-3.43	0.45-6.73	0.53-10.15
T=1	0.15	0.26-10.75	0.27-23.78	0.27-40.06
	0.4	0.26-5.05	0.26-10.22	0.26-15.81
	0.8	0.25-3.48	0.26-6.83	0.26-10.31
T=2	0.15	0.25-11.10	0.25-24.67	0.25-41.74
	0.4	0.25-5.20	0.25-10.55	0.25-16.34
	0.8	0.25-3.58	0.25-7.05	0.25-10.63

View Table

Table 2.

Real Interest Rate Needed to Generate a Given Depreciation

(In percent per month)

	Intertemporal elasticity of substitution	Depreciation of real exchange rate
		5 percent	10 percent	15 percent
T=0.5	0.15	0.55-10.57	0.79-23.35	0.99-39.26
	0.4	0.40-4.97	0.53-10.07	0.65-15.55
	0.8	0.35-3.43	0.45-6.73	0.53-10.15
T=1	0.15	0.26-10.75	0.27-23.78	0.27-40.06
	0.4	0.26-5.05	0.26-10.22	0.26-15.81
	0.8	0.25-3.48	0.26-6.83	0.26-10.31
T=2	0.15	0.25-11.10	0.25-24.67	0.25-41.74
	0.4	0.25-5.20	0.25-10.55	0.25-16.34
	0.8	0.25-3.58	0.25-7.05	0.25-10.63

The same observations made for the case of perfect capital mobility apply here. In particular, the key parameters are the intertemporal elasticity of substitution and the target level of the real interest rate. The time frame during which the more depreciated real exchange rate is in effect plays a minor role.

In conclusion, it should be borne in mind that Tables 1 and 2 represent two extreme situations—perfect capital mobility and perfect capital immobility—neither of which is likely to hold in practice. In the real world, the applicable scenario will be somewhere in between, even when it has been moving towards the perfect capital mobility case during the last 20 years. Therefore, in practice, targeting a over-depreciated real exchange rate for a limited period of time is bound to result in both higher inflation and higher real interest rates. Under this interpretation, Tables 1 and 2 suggest upper bounds for the order of magnitudes involved.

1. Temporary shocks to the real exchange rate

To determine how important a role temporary shocks play in explaining real exchange rate variability, we employ Cochrane’s (1988) methodology, which provides a measure of the persistence of shocks to a variable by examining the variance of its long differences. Specifically, if the variable ξ has the following representation,

then if δ=1, x follows a pure random walk and the variance of its k-differences grows linearly with the difference

If δ < 1 and x is a stationary process, the variance of its k-differences is given by

Therefore, the ratio (1/k)var(x_t-x_t-k)/var(x_t-x_t-1) is equal to one if x follows a random walk process and converges to zero if x is stationary. If x has both permanent (random walk) and temporary (stationary) components, the ratio will converge to the ratio of the variance of the permanent shock to the total variance of x. Thus, the closer that ratio is to unity, the lower is the relative importance of temporary shocks.

Table 4 summarizes the main results. The values of k range between one and ten years. In all three countries considered, temporary shocks account for a sizable share of the variance of the real exchange rate. Temporary shocks are most important for Chile (62 percent of the variance) and least important (43 percent of the variance) for Brazil. Colombia falls in the middle of the range with temporary shocks accounting for about 54 percent of the variance of the real exchange rate.

Table 4.

1/k Times the Variance of k-differences of the Real Exchange Rate

^1/Quarterly data was used. The real exchange rate indices are from the Information Notice System, IMF. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n=62 and k=32 and 40, under the null hypothesis of a random walk.

Table 4.

1/k Times the Variance of k-differences of the Real Exchange Rate

σk2/σ12 various k (Quarters)
8	16	24	32	40
Brazil
1.07	0.64	0.75	0.47
(0.015)	(0.021)	(0.028)	(0.030)
Chile
1.041	0.863	0.704	0.513	0.376
(0.017)	(0.027)	(0.031)	(0.031)	(0.012)
Colombia
1.494	1.217	0.953	0.687	0.465
(0.017)	(0.027)	(0.031)	(0.031)	(0.012)

^1/Quarterly data was used. The real exchange rate indices are from the Information Notice System, IMF. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n=62 and k=32 and 40, under the null hypothesis of a random walk.

View Table

Table 4.

1/k Times the Variance of k-differences of the Real Exchange Rate

σk2/σ12 various k (Quarters)
8	16	24	32	40
Brazil
1.07	0.64	0.75	0.47
(0.015)	(0.021)	(0.028)	(0.030)
Chile
1.041	0.863	0.704	0.513	0.376
(0.017)	(0.027)	(0.031)	(0.031)	(0.012)
Colombia
1.494	1.217	0.953	0.687	0.465
(0.017)	(0.027)	(0.031)	(0.031)	(0.012)

^1/Quarterly data was used. The real exchange rate indices are from the Information Notice System, IMF. Standard errors are in parentheses. The standard errors were tabulated from Monte Carlo simulations (600 replications) for n=62 and k=32 and 40, under the null hypothesis of a random walk.

On balance, these results would seem to indicate that, for these countries, temporary shocks play an important role in the behavior of real exchange rates. Hence, at least in this respect, the theoretical framework outlined in sections 2 and 3 is not devoid of empirical content. Our results contrast with those of Edwards (1989), who tentatively concludes temporary shocks play a relatively small role in determining the behavior of real exchange rates.

Edwards’ (1989) conclusion is based on the results of a regression which has the level of the real exchange rate as the dependent variable, and includes as explanatory variables both permanent and temporary components of the terms of trade, government spending, and other “real” variables (see Edwards (1989)). The main problem with that approach is that not all variables appearing in the regression are integrated of the same order, which will bias the results towards finding no role for temporary shocks. Note that both the real exchange rate and, by construction, the “permanent component” of all the explanatory variables are non-stationary. ^42/ However, also by construction, the “temporary component” of all explanatory variables is stationary. Hence, regression methods, such as OLS, will attach zero coefficients to all the stationary variables appearing in the right hand side, since asymptotically there can be no relationship between a nonstationary and stationary variable. However, such lack of statistical significance of the temporary components was taken as evidence that temporary shocks were not an important factor in real exchange rate behavior.

The methodology outlined here is more direct and does not require any estimation. However, it is important to note that this methodology does not discriminate among “types” of temporary shocks. It does not distinguish between a “temporary policy shock”, such as the one considered in the previous exercise, from say, a temporary terms-of-trade shock, which underlies Edwards’s (1989) exercise.

2. Inflation and the real exchange rate

The theoretical model suggests that inflation will accelerate when the authorities attempt to depreciate the real exchange rate beyond its equilibrium level. To examine this proposition we follow a two-step approach. First, employing the Beveridge-Nelson technique (Beveridge and Nelson (1981)) as modified by Miller (1988), we decompose the exchange rate into its “permanent” (or steady-state) component and “temporary” (or cyclical component). As discussed above, the identifying criteria for this technique is that the former captures the nonstationary component of the variable, while the latter captures its stationary element. Table A.1, in the Appendix, provides details about the ARMA processes that best described the real exchange rate for the three countries in our sample, while Appendix A.2 discusses the links between the “economic fundamentals” and the trend and cycle. Second, we examine the pairwise correlations between the cyclical component of the real exchange rate and inflation (which was also shown to be a stationary variable).

The inverse of the IMF index of the real exchange rate is used; hence, as in the theoretical model, an increase in the index denotes a real depreciation. When the cyclical component is negative, the actual exchange rate is “overvalued” relative to its equilibrium steady-state level. Hence, the model suggests that we should observe a positive correlation between inflation and the cyclical or temporary component of the real exchange rate. The corresponding correlations and their standard errors are reported in Table 5. In all three cases considered, the correlation has the anticipated sign and is significant at the 10 percent confidence level or higher. In all cases, the correlation is relatively low (0.26 to 0.42 range), suggesting that there are also important differences in the driving forces behind these two variables. This low correlation is evident from Figure 4, which plots inflation and the cyclical component of the real exchange rate.

Table 5.

Pairwise Correlations ^1/ 1979: IV-1992: 2

^1/Standard errors of the correlation coefficients are in parentheses.

^2/The correlations with the real exchange rate are only meant to be illustrative. Inference-making cannot proceed as usual given that the real exchange rate is 1(1) and inflation is 1(0). Such problems do not arise with the correlations involving the cyclical component of the real exchange rate, which by construction is 1(0),

Notes: The real exchange rate is in logs while inflation is measured as the first difference of the log of the price level. The trend-cycle decomposition of the real exchange rate was obtained using the Beveridge-Nelson technique. The ARMA processes that model the change in the permanent component are presented in Table A.1 in the Appendix. Since inflation was found to be stationary around a deterministic trend, the bottom panel of the this table reports the correlations for the cyclical deviations from trend.

Table 5.

Pairwise Correlations ^1/ 1979: IV-1992: 2

Country	Brazil	Chile	Colombia
	Inflation
Real Exchange Rate 2/	0.092	0.066	0.324
	(0.148)	(0.146)	(0.135)
Cyclical Component of the Real Exchange Rate	0.257	0.293	0.333
	(0.144)	(0.139)	(0.134)
	Cyclical Component of Inflation
Real Exchange Rate	-0.224	0.415	0.196
	(0.145)	(0.133)	(0.140)
Cyclical Component of the Real Exchange Rate	0.265	0.423	0.362
	(0.144)	(0.132)	(0.133)

^1/Standard errors of the correlation coefficients are in parentheses.

^2/The correlations with the real exchange rate are only meant to be illustrative. Inference-making cannot proceed as usual given that the real exchange rate is 1(1) and inflation is 1(0). Such problems do not arise with the correlations involving the cyclical component of the real exchange rate, which by construction is 1(0),

Notes: The real exchange rate is in logs while inflation is measured as the first difference of the log of the price level. The trend-cycle decomposition of the real exchange rate was obtained using the Beveridge-Nelson technique. The ARMA processes that model the change in the permanent component are presented in Table A.1 in the Appendix. Since inflation was found to be stationary around a deterministic trend, the bottom panel of the this table reports the correlations for the cyclical deviations from trend.

View Table

Table 5.

Pairwise Correlations ^1/ 1979: IV-1992: 2

Country	Brazil	Chile	Colombia
	Inflation
Real Exchange Rate 2/	0.092	0.066	0.324
	(0.148)	(0.146)	(0.135)
Cyclical Component of the Real Exchange Rate	0.257	0.293	0.333
	(0.144)	(0.139)	(0.134)
	Cyclical Component of Inflation
Real Exchange Rate	-0.224	0.415	0.196
	(0.145)	(0.133)	(0.140)
Cyclical Component of the Real Exchange Rate	0.265	0.423	0.362
	(0.144)	(0.132)	(0.133)

^1/Standard errors of the correlation coefficients are in parentheses.

^2/The correlations with the real exchange rate are only meant to be illustrative. Inference-making cannot proceed as usual given that the real exchange rate is 1(1) and inflation is 1(0). Such problems do not arise with the correlations involving the cyclical component of the real exchange rate, which by construction is 1(0),

Notes: The real exchange rate is in logs while inflation is measured as the first difference of the log of the price level. The trend-cycle decomposition of the real exchange rate was obtained using the Beveridge-Nelson technique. The ARMA processes that model the change in the permanent component are presented in Table A.1 in the Appendix. Since inflation was found to be stationary around a deterministic trend, the bottom panel of the this table reports the correlations for the cyclical deviations from trend.

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Temporary Component of Real Exchange Rate and Inflation

Citation: IMF Working Papers 1994, 022; 10.5089/9781451921212.001.A001

Source: IMF, International Financial Statistics and Fund staff estimates.Note: A decrease in the real effective exchange rate index denotes an appreciation. Inflation is computed as the change in the CPI over the previous quarter for Brazil and over the previous four quarters for Chile and Colombia.

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By contrast, no systematic relationship is evident from the correlations of the (log) level of the real exchange rate and inflation in two of the three countries (see Table 5). ^43/ This lack of a systematic relationship between inflation and the real exchange rate has fueled the observation that Chile represents a case of successful real exchange rate targeting, in the sense that a policy of targeting the real exchange rate coexisted with declining inflation rates (see Edwards (1991)). The above results would suggest, however, that the lack of inflationary pressures in the case of Chile possibly stemmed from having a real exchange rate target that was, in effect, closely tracking the equilibrium real exchange rate. However, as in Brazil and Colombia, the evidence suggests that in periods when the real exchange rate was depreciated relative to its steady-state level inflation did tend to accelerate. ^44/

In sum, the empirical exercises summarized in this section yield two main observations, both of which are consistent with the theoretical model: (i) temporary shocks play an important role in explaining real exchange rate behavior, and (ii) there appears to be a systematic relationship between real exchange rate disequilibria and inflation.

3. Implications of other models

The theoretical model outlined in this paper has stressed the relationship between the temporary or cyclical component of the real exchange rate and inflation. However, other models (see Lizondo (1991, 1993) and Montiel and Ostry (1991, 1992)) have focused on the relationship between inflation and the “permanent” or steady-state real exchange rate. Specifically, the relationship between these two variables implied by these models is an indirect one (in the sense that there is an implied relationship between revenues from the inflation tax, rather than inflation, and the real exchange rate), and comes through from wealth effects. ^45/ In these models, the steady-state real exchange rate is determined by market clearing in the nontraded good sector. Demand for the nontraded good depends on its relative price (i.e. the real exchange rate), and wealth, which, in turn, depends on the inflation tax. Changes in the inflation tax affect household wealth because it is assumed that the government does not return revenues from the inflation tax to the household via a lump-sum transfer. Rather, the government uses these revenues to either increase spending on traded goods or accumulate international reserves. Hence, these models predict that the steady-state real exchange rate can be depreciated by permanently increasing the inflation rate. ^46/ An increase in inflation reduces households’ wealth and decreases their demand for the nontraded good. As a result, the real exchange rate must depreciate to restore equilibrium in the market for home goods.

The empirical examination of a steady-state relationship between inflation and the real exchange rate is far from trivial because, in principle, there are a host of other variables (terms of trade, government spending, etc) that affect the steady-state real exchange rate, and which should be incorporated into the empirical analysis. At the very least, however, and given that we have in mind the equilibrium in the home goods market, the supply of home goods must be taken into account. Hence, to explore some of the empirical implications of these models we proceed in two steps. First, we establish the time series properties of the inflation tax and GDP (the latter will serve as a proxy for output of the nontraded good). As is well known, a steady-state relationship can only exist among variables which are integrated of the same order. Hence, the inflation tax and real GDP must be difference stationary (same as the real exchange rate) if the steady state relationship postulated by these models is to have empirical content. Second, for the cases where the all the variables are integrated of the same order, we proceed to examine via cointegration tests if a steady-state relationship among them can be identified.

Applying the same battery of tests as before, in all three countries considered, GDP per capita and the inflation tax (also on a per capita basis) were found to be nonstationary (however, the inflation tax as a percent of GDP is stationary). ^47/ Hence, based on the individual unit root tests there is no a priori basis for ruling out the steady-state relationship postulated by Lizondo (1991, 1993) and Montiel and Ostry (1991, 1992).

To examine whether output and the inflation tax are sufficient to pin down the steady-state behavior of the real exchange rate we performed the cointegration tests of Johansen (1988, 1990). The results summarized in Table 6 report the λ-max and trace statistics, as well as their respective critical values. In addition, the estimated parameters for the cointegrating vectors (if these exist) are also reported at the bottom of the table. Cointegration among the real exchange rate, real GDP per capita (a proxy for output of nontraded goods), and the inflation tax per capita was only detected for Colombia. If the assumption of a single traded good is relaxed, and a distinction is made between importables and exportables, the equilibrium real exchange rate also depends on the terms of trade (see for example, Edwards (1989)). Including the terms of trade in the vector of variables was particularly important for Chile. Once the terms of trade are included, cointegration obtains (see Table 6 and critical values for n=4). Hence any meaningful inference will be limited to those two cases.

Table 6.

Cointegration Tests for the Real Exchange Rate, the Inflation Tax, and Real GDP ^1/

^1/Coefficients are only reported when cointegration obtains.

Notes: Standard errors are in parentheses. The number of lags in the vector autoregression is three. The critical values are those under the null of no cointegration. The source of the critical values is Osterwald-Lenum (1992). For the specification that includes the terms of trade, the λ-max and trace statistics for Brazil are 25.08 and 50.44, respectively.

Table 6.

Cointegration Tests for the Real Exchange Rate, the Inflation Tax, and Real GDP ^1/

Country	Brazil	Chile	Colombia
λ-max	11.530	36.410	30.068
Trace	15.904	60.769	43.917
Coefficient estimates:
Inflation tax		0.102	0.130
		(0.034)	(0.024)
Real GDP		0.747	2.445
		(0.223)	(0.426)
Terms of trade		-0.312
		(0.040)
		n=3	n=4
Critical values for λ-max:
at 95 % confidence level =		25.54	31.46
at 90 % confidence level =		23.11	29.12
Critical values for trace:
at 95 % confidence level =		42.44	62.99
at 90 % confidence level =		39.06	59.14

^1/Coefficients are only reported when cointegration obtains.

Notes: Standard errors are in parentheses. The number of lags in the vector autoregression is three. The critical values are those under the null of no cointegration. The source of the critical values is Osterwald-Lenum (1992). For the specification that includes the terms of trade, the λ-max and trace statistics for Brazil are 25.08 and 50.44, respectively.

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Table 6.

Cointegration Tests for the Real Exchange Rate, the Inflation Tax, and Real GDP ^1/

Country	Brazil	Chile	Colombia
λ-max	11.530	36.410	30.068
Trace	15.904	60.769	43.917
Coefficient estimates:
Inflation tax		0.102	0.130
		(0.034)	(0.024)
Real GDP		0.747	2.445
		(0.223)	(0.426)
Terms of trade		-0.312
		(0.040)
		n=3	n=4
Critical values for λ-max:
at 95 % confidence level =		25.54	31.46
at 90 % confidence level =		23.11	29.12
Critical values for trace:
at 95 % confidence level =		42.44	62.99
at 90 % confidence level =		39.06	59.14

^1/Coefficients are only reported when cointegration obtains.

Notes: Standard errors are in parentheses. The number of lags in the vector autoregression is three. The critical values are those under the null of no cointegration. The source of the critical values is Osterwald-Lenum (1992). For the specification that includes the terms of trade, the λ-max and trace statistics for Brazil are 25.08 and 50.44, respectively.

The Stock-Watson (1991) estimates of coefficients of the cointegrating vectors, which deal with the biases introduced in the cointegrating regressions by simultaneity and serial correlation in the errors, indicate that the variables enter significantly and with the anticipated signs. Hence, an expansion in output depreciates the real exchange rate, implying a positive coefficient; similarly, an increase in the inflation tax depreciates the equilibrium real exchange rate. An improvement in the terms of trade, other things equal, tends to appreciate the equilibrium real exchange rate (a negative coefficient). For the case of Brazil, little inference is possible as cointegration did not obtain. ^48/ The persistent lack of cointegration for Brazil is likely indicative of a misspecification problem, possibly due to omitted variables or perhaps to the linearity imposed in the cointegration tests. The relationship among the real exchange rate and the explanatory variables indicated by these models may simply be nonlinear. As suggested in Lizondo (1991), a leading candidate in this list of potential omissions is public expenditure on nontraded goods. ^49/

Our results tend to suggest that there is potential for quantitatively important indirect links between inflation and the equilibrium real exchange rate. However, the evidence is not conclusive, which suggests that a more comprehensive model of equilibrium real exchange rate determination may be needed to be able to quantify the relationship between the real exchange rate and the inflation tax.