Chapter

Chapter4. Equilibrium Real Exchange Rate in Paraguay

Author(s):
Jeffrey Franks, Randa Sab, Valerie Mercer-Blackman, and Roberto Benelli
Published Date:
September 2005
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A. Background

In recent years, Paraguay's real exchange rate has exhibited large fluctuations. From end-2000 through end-2002, a period characterized by subsequent banking crises and a deep recession, the real effective exchange rate shed about one-third of its value, which it recovered only slightly during 2003 and early 2004. Fluctuations in the real exchange rate were even larger in the earlier part of the 1980s. As shown in Figure 4.1, these fluctuations took place around a declining long-term trend.

Figure 4.1.Real Exchange Rate and Terms of Trade

(1995:Q1=100)

Sources: International Monetary Fund; and Fund staff estimates.

As the economy emerges from its 2002 recession, the appropriate level of the real exchange rate is an overarching policy question. Besides affecting external competitiveness, the recent developments in the real exchange rate have complicated the conduct of monetary policy, as large inflows of official reserves have forced the Central Bank of Paraguay to issue—at a large quasi–fiscal cost—large amounts of debt paper to sterilize the impact of reserve accumulation on money growth. These developments in turn raise the question of whether the optimal policy is to allow a gradual real appreciation of the guaraní, which would be justified if the recent crises have left the guaraní undervalued in real terms. The answer to this question requires an assessment of the magnitude of the misalignment of the real exchange rate from its equilibrium value.

The purpose of this chapter is to estimate the long–term equilibrium real exchange rate at the end of 2003 and, as a result, the misalignment in the real exchange rate. We use a variety of potential explanatory variables for the equilibrium real exchange rate, which we define as the level toward which, absent new shocks, the real exchange rate converges in the long run. Our estimates of the misalignment vary somewhat across different empirical specifications, possibly owing to the short sample size. However, these estimates consistently show that the real exchange rate was undervalued at the end of 2003, by a magnitude ranging between 3 and 10 percent.

The literature on estimating equilibrium real exchange rates is vast. Some recent papers that adopt the same methodology used in this chapter include Clark and MacDonald (2000), MacDonald and Ricci (2003), and Alberola, López, and Servén (2003). Readers are referred to these papers for thorough reviews of the theoretical and empirical literature.

The chapter is organized as follows. Section B briefly presents the empirical methodology that we use in this study. Section C presents our findings on the role of the terms of trade and regional factors using quarterly data. Section D performs some robustness exercises using annual data. Section E concludes.

B. Empirical Methodology

We use co–integration techniques to identify a long–run co–integration relationship between the real effective exchange rate and its determinants.73 As common in several other studies, we interpret this co–integration relationship as the long–run equilibrium relationship between the real exchange rate and its determinants (the “fundamentals”). We follow the methodology proposed by Johansen (1995) to investigate the existence of long–run co–integration relationships. This methodology is briefly described in this section.74

Our approach can be summarized as follows. We denote by xtthe vector containing the real effective exchange rate and its determinants; the series in this vector are integrated of order one (denoted by I(1)). A co–integrating vector b(of the same order as Xt) has the property that bxtis stationary, that is, integrated of order zero (I(0)). Intuitively, this property implies that any deviation from the long–run equilibrium is a stationary variable and therefore cannot diverge for too long from zero (or a constant value), that is, the variables in xtare nonstationary but tend to move “together” around an equilibrium relationship. Provided that the vector process xtadmits a vector autoregression (VAR) representation, it can be reparameterized in terms of a vector error correction model (VECM) as follows:

where Δ denotes the difference operator and η and π are a vector and a matrix of parameters, respectively. By defining β, the matrix whose columns consist of all the linearly independent co–integration vectors, the VECM can be rewritten as

where α is a matrix of adjustment coefficients, that is, the parameters that measure the speed at which the disequilibrium from the long–run equilibrium is eliminated (if the coefficients turn out to be negative).

We use standard tests to detect co–integration. Johansen (1995) provides two tests to detect the existence of co–integration relationships among the variables in xt, the trace test and the maximum–eigenvalue test. In our study we employ these tests.

C. Role of Terms of Trade and Regional Factors

It is a well documented fact that, for commodity–producing countries, the terms of trade explain a large portion of the variation in the real effective exchange rate. This fact has recently been documented for industrial countries (Chen and Rogoff, 2002) and developing countries (Cashin, Cespedes, and Sahay, 2002).

Paraguay easily fits the definition of a commodity–producing economy. In fact, Paraguay stands out in Cashin, Cespedes, and Sahay's (2002) data set of 58 commodity–producing developing countries as one of the countries that can best be qualified as a “commodity currency,” with three agricultural commodities—soybeans, cotton, and soy meals—accounting for about 80 percent of its exports.75 Therefore, it is worth starting the analysis by investigating the relationship between the real exchange rate and the terms of trade.

It is reasonable to presume that an improvement in terms of trade would raise the real exchange rate. This is because, although the effect of terms of trade on the real exchange rate is ambiguous on theoretical grounds, an improvement in terms of trade would tend to increase domestic wages, and with them the demand for and the price of nontradable goods. Indeed, Cashin, Cespedes, and Sahay (2002) find that, for most countries in their sample, a rise in real commodity prices increases the long–run equilibrium real exchange rate. In particular, for the 22 countries for which they accept the null hypothesis of co–integration between the real exchange rate and the terms of trade, for only three do they estimate a negative elasticity of terms of trade on the real exchange rate; for the other countries, the estimated elasticity ranges between 0.2 and 2.

For the sake of comparability, we construct Paraguay's terms of trade index using the export shares provided by Cashin, Cespedes, and Sahay (2002). Following a common practice in this literature, we define the terms of trade as the weighted average of world commodity prices weighted by export shares, deflated by the world price of manufactured goods (proxied by the price of industrial country exports). This real price of commodities is more precisely described in the literature as “commodity terms of trade,” but, for brevity, we will refer to it as “terms of trade.” This definition ensures that the terms of trade are an exogenous variable from the perspective of Paraguay because it prevents changes in the nominal exchange rate from affecting the real exchange rate. Data sources and definitions are provided in the appendix to this chapter.

The strength of the positive co–movement between the real effective exchange rate and the terms of trade is striking in Paraguay (Figure 4.1). Nonetheless, the figure also shows that the real exchange rate and the terms of trade can diverge for prolonged periods of time. In particular, this diverging behavior was observed starting from end–2001, when commodity prices began to rise sharply while the real exchange rate continued its downward movement as subsequent waves of crises hit Paraguay and the region.

The first part of this section investigates more formally the role of the terms of trade for the real exchange rate. Our sample consists initially of quarterly data covering 1980 through 2003. Although using quarterly data reduces the set of variables for which data are available, we begin our analysis with quarterly data to raise the number of observations used to estimate the dynamic structure of our empirical models. In Section D we perform some robustness exercises on these initial estimates using annual data.

Test for nonstationarity

The preliminary requirement for co–integration that the univariate time series be integrated of order one is met. To test this property, Table 4.1 presents the Augmented Dickey–Fuller test and the Phillips–Perron test of the null hypothesis that the univariate time series are I(1). Both tests show the null hypothesis of unit roots in the real exchange rate (in logs) and the terms of trade (in logs) cannot be rejected. The two tests also do not reject the null hypothesis for Argentina's and Brazil's real effective exchange rates (in log), which we use below in our empirical analysis.

Table 4.1.Unit Root Tests
Augmented Dickey-Fuller1Phillips-Perron1
LagDWAdj.Band-
t-statp-value2length3 statistict-statp-value2width4
Real effective exchange rate (log)
Paraguay-1.2250.6651.82-1.2040.678
Argentina-1.8050.3701.87-1.9400.312
Brazil-1.7800.3801.93-1.8550.352
Terms of trade (log)-2.0360.2701.64-2.2010.204
Sources: International Monetary Fund; and Fund staff estimates.

Null hypothesis is that the series has a unit root.

One-sided p-values.

Automatic based on SIC (Schwartz information criterion).

Newey-West using Bartlett kernel.

Sources: International Monetary Fund; and Fund staff estimates.

Null hypothesis is that the series has a unit root.

One-sided p-values.

Automatic based on SIC (Schwartz information criterion).

Newey-West using Bartlett kernel.

Role of terms of trade

The simplest model relates the real exchange rate to the terms of trade. Column 1 in Table 4.2 presents selected results from estimating a vector error correction model on the real exchange rate and the terms of trade. We find that a high number of lags (11) are required to eliminate serial correlation from the residuals.76 The trace test shows that we cannot reject, at the 5 percent confidence level, the null hypothesis that there is one co–integration relationship between the real exchange rate and the terms of trade (both in logs).

Table 4.2.Selected Results from VECM Estimation(Quarterly data)
(1)(2)(3)(4)
Number of co-integrating vectors
Trace test5 percent1122
1 percent0122
Max-eigenvalue test5 percent0122
1 percent0012
Co-integration vector1
REER (-1)1111
TOT (-1)-1.40-1.37-1.99-4.76
(0.16)(0.19)(-0.17)(1.61)
REER Brazil (-1)-0.5313.1
(0.28)(1.8)
REER Argentina (-1)-0.42-5.12
(0.1)(1.16)
Adjustment coefficient2-0.20-0.18-0.170.003
(0.08)(0.06)(0.08)(0.008)
Lags in VECM311111111
N (after adjusting for endpoints)84848484
Sources: International Monetary Fund; and Fund staff estimates.

Standard errors in parentheses.

Coefficient on the co-integrating equation in the ECM representation for Paraguay's log real effective exchange rate.

Number of lags in first differences in VECM representation.

Sources: International Monetary Fund; and Fund staff estimates.

Standard errors in parentheses.

Coefficient on the co-integrating equation in the ECM representation for Paraguay's log real effective exchange rate.

Number of lags in first differences in VECM representation.

The long–run elasticity of the real exchange rate with respect to the terms of trade is high but reasonable. While high, 1.4, it is not out of line with the estimate for Paraguay reported by Cashin, Cespedes, and Sahay (2002), 0.99, which is itself one of the highest estimates for commodity–producing countries. The estimated adjustment coefficient shows that the adjustment toward the long–term equilibrium is quite rapid, 20 percent per quarter, implying that the half–life of the adjustment to the long–run equilibrium is just over three quarters. This estimate is reasonable and compares with the estimates reported by Cashin, Cespedes, and Sahay (2002), who find that the median half–life for commodity–producing countries is eight months.

However, the evidence of co-integration is not unquestionably strong, possibly because other variables that affect the long–term equilibrium real exchange rate have been omitted from the empirical relationship. Unit root tests on the residuals from regressing the real exchange rate on the terms of trade (in logs) support this interpretation, as the null of a unit root in the residuals cannot be rejected.77 This suggests that some persistent real exchange rate determinant may have been omitted, a problem that Chen and Rogoff (2002) also find and refer to as “nagging persistence.”

Role of regional factors

For a small economy such as Paraguay's, regional factors are natural first candidates as additional determinants of the real exchange rate. A simple way to take regional factors into account is to include the real effective exchange rates of the two largest economies in the region which are Paraguay's main trading partners, Argentina and Brazil. Besides cyclical conditions, real exchange rates in the neighboring economies could indirectly capture the effect of productivity developments in the region on the real exchange rate—under the assumption that productivity in Paraguay reflects to some extent productivity in its large neighboring countries. Figure 4.2 shows that indeed the real exchange rates of Paraguay, Argentina, and Brazil tend to move closely together.

Figure 4.2.Real Effective Exchange Rates for Paraguay, Argentina, and Brazil

(1995:Q1=100)

Sources: International Monetary Fund; and Fund staff estimates.

We find stronger evidence of co–integration when we add Brazil's real effective exchange to our empirical specification (Table 4.2, column 2). The estimates of the long–run effect of terms of trade on Paraguay's real exchange rate are similar to our previous estimates. However, we find that Brazil's real exchange rate also has a strong and statistically significant long–run effect on Paraguay's real exchange rate. The estimate in column 2 shows that a 1 percent depreciation in Brazil's real effective exchange rate causes a real effective depreciation in the guaraní of 0.5 percent. The adjustment to the long–run equilibrium also remains similar to our previous estimate (implying a half–life of the disequilibrium of 3.5 quarters).

We find similar results using Argentina's real exchange rate (Table 4.2, column 3). The co–integration tests indicate a second co–integration relation (not reported in the table), whose coefficients, however, do not appear reasonable on economic grounds. The estimate of the effect of the terms of trade is higher(close to 2), and Argentina's real exchange rate is found to have a strong long–run effect on Paraguay's real exchange rate (the elasticity is about 0.4).

We do not find sensible results when we use both Brazil's and Argentina's real exchange rates (Table 4.2, column 4). Using both Argentina's and Brazil's real exchange rates together with the terms of trade does not yield sensible results in terms of the magnitude and sign of the coefficients in the long–run relationship and in the adjustment coefficient—the latter is positive but not statistically significant—possibly reflecting multicolinearity between Brazil's and Argentina's real exchange rates.

Misalignment from long–run equilibrium

We use the previous estimates for a first assessment of the misalignment in Paraguay's real effective exchange rate at the end of 2003. The results from the empirical model with the terms of trade only and the models that add Brazil's and Argentina's real effective exchange rate in turn (corresponding to columns 1–3 in Table 4.2) are plotted in Figure 4.3. In each panel, we compute Paraguay's long-run real effective exchange using the coefficients from the co–integration vectors reported in columns 1–3 of Table 4.2.

Figure 4.3.Actual and Long–Run Equilibrium Real Effective Exchange Rate

Sources: International Monetary Fund; and Fund staff estimates.

As a preliminary step, we need to compute the long–run values of the determinants of the real exchange rate. This is because, to compute the long–run equilibrium real exchange rate, we need to evaluate the co–integration relationship using the long–run equilibrium values for the determinants of Paraguay's real exchange rate, that is, the terms of trade and the real exchange rates of Brazil and Argentina. More precisely, denoting by bthe long–run coefficients on the determinants of the real exchange rate78 and by f^ the long–run values of the fundamental determinants of the real exchange rate, we define the long–run equilibrium real exchange rate as bf^ To compute the long–run value of the fundamentals, we follow the simple approach suggested by MacDonald and Ricci (2003) of smoothing the real exchange rate determinants with the Hodrick–Prescott filter.79

This method of defining long–run values of the fundamentals has shortcomings. The main limitation is likely to be that, being completely statistical in nature, this method is sensitive to persistent departures of the smoothed series from their long–run equilibrium values, because the filter tends to interpret these departures as shifts in the long–run trends. This problem is likely to be particularly severe when smoothing the real exchange rate of the neighboring economies, since real exchange rates are known to exhibit long–lasting departures from their equilibrium values. For example, Alberola, López, and Servén (2003) show that the Argentine peso underwent a prolonged and growing real appreciation away from its long–term equilibrium during the second part of the 1990s through the end of 2001.

When computing the end–2003 misalignment, it is critical to control for regional factors (Figure 4.3). The top panel, based on the model with terms of trade only, shows that the drop in the real value of the guaraní starting from the beginning of 2002 produced a widening misalignment in the actual real exchange rate from its long–run equilibrium value, as the latter increased as a result of the ongoing improvement in the terms of trade (as shown in Figure 4.1). According to this first model, at the end of 2003 the real effective exchange rate was undervalued by about 27 percent. However, this model, by including the terms of trade only, does not take into account the developments in the neighboring countries, which were simultaneously experiencing a rapid real depreciation in their currencies (as shown in Figure 4.2). When these real depreciations are taken into account, the long–run equilibrium value of the guaraní continued to declineafter 2001, implying that the undervaluation in real terms at the end of 2003 was much smaller, 3 and 2 percent using the model with Brazil's and Argentina's real effective exchange rates, respectively (as shown in the second and third panel of Figure 4.3.).

D. Robustness

To check the robustness of the previous results, we turn to annual data. A larger set of variables is available at the annual frequency. However, the drawback of using annual data is that the number of observations falls dramatically.

Besides terms of trade and regional factors, some common determinants considered in the literature are the following:80

  • Productivity differentials (the Balassa-Samuelson effect). An increase in productivity (relative to trading partners) in tradable goods raises the relative price of nontradable goods and thus raises the real exchange rate. We measure this effect by introducing real per capita GDP relative to the United States’ real per capita GDP.

  • Trade openness. A more open trade regime increases competition in tradable goods, reducing their price and thus lowering the real exchange rate. As is commonly done, we measure trade openness as the sum of exports and imports in percent of GDP.

  • Fiscal balance. An improvement in fiscal balance tends to reduce the demand for nontradable goods and thus lower the real exchange rate. We measure the fiscal balance as central government balance in percent of GDP.

  • Current account balance. By definition, the current account balance determines the change in a country's stock of net foreign assets. Thus, an increase in capital inflows that is reflected in a worsening current account balance may cause an appreciation of the real exchange rate as demand for nontradables increases.81 We measure the current account balance in percent of GDP.

  • Net foreign assets. Higher net foreign assets allow a higher level of consumption and therefore tend to raise the price of nontradable goods and the real exchange rate. We measure net foreign assets as the sum of official reserves and the banking system's foreign assets in percent of GDP.

Figure 4.4 plots these potential determinants of the real effective exchange rates, together with the annual series of the terms of trade and the real exchange rates of Brazil and Argentina.82

Least-square estimates of long-run equilibrium

We start by estimating the long-run equilibrium relationship directly (Table 4.3). As the reason for this is that the number of observations falls sharply with annual data (we have 24 annual observations in our sample), it is convenient to estimate the long-run equilibrium relationships directly by regressing Paraguay's real exchange rate on its determinants.83

Table 4.3.Least-Square Estimates of Long-Run Equilibrium
Dependent variable: REER
(1)(2)(3)(4)(5)
Terms of trade (log)1 11***1.09***1.17***0.31**0.22
(0.17)(0.18)(0.17)(0.14)(0.14)
REER Brazil0.110.0030.2
(0.17)(0.13)(0.18)
REER Argentina0.14*0.10.06
(0.08)(0.06)(0.05)
Current account balance-0.016***-0.014**
(0.01)(0.01)
Fiscal balance-0.018-0.054**
(0.01)(0.02)
Foreign assets-0.001**0.005
(0.01)(0.00)
Openness-0.003**0.001
(0.00)(0.00)
Relative GDP per capita1.12**-0.60
(0.48)(1.15)
Linear trend-0.037**
(0.02)
Constant-0.52-0.87-1.40-5.777.44
(0.80)(0.97)(0.92)(3.29)(8.48)
R-squared0.660.660.70.950.96
Adjusted R-squared0.640.630.670.930.94
Durbin-Watson stat0.991.011.092.762.85
N2424242424
Sources: International Monetary Fund; and Fund staff estimates.Standard errors in parentheses (not corrected for co-integration) in columns. Newey-West heteroscedasticity and autocorrelation consistent (HAC) standard errors in column 5.*, Denotes significance at the 10 percent level; **, at the 5 percent level; and ***, at the 1 percent level.
Sources: International Monetary Fund; and Fund staff estimates.Standard errors in parentheses (not corrected for co-integration) in columns. Newey-West heteroscedasticity and autocorrelation consistent (HAC) standard errors in column 5.*, Denotes significance at the 10 percent level; **, at the 5 percent level; and ***, at the 1 percent level.

We first replicate the results found on quarterly data (Table 4.3, columns 1–3). Table 4.3 reports the regressions corresponding to the VECM representations estimated on quarterly data (reported in columns 1–3 of Table 4.1). The terms of trade and the real exchange rates of the neighboring countries explain about two- thirds of the annual variation in Paraguay's real exchange rate over 1980–2003. While roughly in line with the co-integration vectors reported in Table 4.2, the coefficients on the terms of trade and Brazil's and Argentina's real effective exchange rates are somewhat smaller. The low values of the Durbin-Watson statistics show that the residuals exhibit some serial correlation, indicating that other relevant variables may have been omitted from these specifications.

Figure 4.4.Determinants of the Real Effective Exchange Rate, 1980–2003

Sources: International Monetary Fund; and Fund staff estimates.

From a general specification that includes other potential explanatory variables we find the following results (Table 4.3, column 4):

  • The coefficient on the terms of trade remains positive but falls sharply when more fundamentals are included in the equation—the elasticity of the real exchange rate is 0.3—and continues to be statistically significant at the 5 percent confidence level.84

  • The real effective exchange rates for Brazil and Argentina are no longer significant, indicating that in the previous regressions they may have proxied for other omitted variables. In particular, they may have proxied for the long-term decline in relative productivity, the Balassa-Samuelson effect, picked up by relative GDP per capita. As expected from inspecting Figure 4.4, this has a large positive coefficient that implies that a 1 percent fall in GDP per capita lowers the real effective exchange rate by about 1 percent.

  • The current account balance has a negative small coefficient. As noted above, the negative sign may reflect reverse causality, that is, the fact that a rise in the real exchange rate causes a worsening in the current account balance by negatively affecting competitiveness and net exports.

  • As expected, the fiscal balance has a negative sign, indicating that an increase in fiscal deficit by 1 percent of GDP appreciates the real exchange rate by about 2 percent. This effect is not statistically significant, however.

  • Trade openness has a small negative effect on the real exchange rate, showing that trade openness works as a tariff: an increase in external competition tends to lower the price of tradable goods and thus the real exchange rate.

  • Foreign assets do not have a quantitatively nor statistically significant effect. This finding is not surprising, given the small role of capital account transactions in Paraguay. This contrasts, for example, with the important role of net foreign assets found for emerging market economies such as Argentina (Alberola, López, and Servén, 2003) and South Africa (MacDonald and Ricci, 2003).

We find that our results are broadly robust to the introduction of a linear time trend (Table 4.3, column 5). This is the specification estimated that would be appropriate if the data were trend-stationary. The estimates in column 5 remain broadly in line with those in column 4. The coefficient on terms of trade falls relative to column 4 (to 0.22) and is not significant at the 10 percent confidence level (its p-value is 0.14). The real exchange rates of Brazil and Argentina continue to be statistically insignificant, and the coefficient on the current account and fiscal balances remain negative—both are now statistically significant at the 5 percent level. The main difference with the specification in column 4 is the role of relative GDP per capita, which has now a negative (but statistically insignificant) coefficient. This difference is not surprising, given that the long-term decline in productivity is now captured by the linear trend, which indicates that over the sample period the real exchange rate has declined on average by almost 4 percent a year.85

The general model implies that the real exchange rate was undervalued in 2003. Figure 4.5 provides a visual summary of the goodness of fit of the general model estimated in column 4. The residuals from this model (based on the actual values of the explanatory variables) indicate that in 2003 Paraguay's real exchange rate was undervalued by about 3 percent, an estimate that is close to the estimates found in the previous section. The figure also plots the misalignment from the long-run real effective exchange rate computed by smoothing the determinants of the real exchange rate with the Hodrick-Prescott filter (using a factor of 100). According to this estimate, the misalignment for 2003 is higher, about 15 percent.

It is useful to investigate the sources of this undervaluation (Table 4.4). Using the estimates of our general specification (column 4 of Table 4.3), Table 4.4 breaks down the misalignment into the portion that is accounted by the misalignment of the fundamentals from their long-run trend and the portion that cannot be explained by observed variables (this latter portion corresponds to the estimated regression residual for 2003). When we evaluate the fundamentals at their actual 2003 values, the real exchange rate turns out to be 2.6 percent undervalued (this misalignment is plotted as the residual in Figure 4.5). However, when we adjust the fundamentals to their long-run values (defined as their Hodrick-Prescott trends), the misalignment rises to 15 percent. This is because the estimate of the equilibrium real exchange rate is 12.5 percent higher—and as a result the undervaluation is higher—when all the fundamentals are evaluated at their long- run values rather than at their actual values. More specifically:

  • Adjusting the current account balance to its trend value in 2003 (lower than its actual value) raisesthe equilibrium real exchange rate by 4 percent.

  • Adjusting the fiscal balance to its trend value in 2003 (lower than its actual value) raisesthe equilibrium real exchange by 4 percent.

  • Adjusting Argentina's real exchange rate to its trend value in 2003 (higher than its actual value) raisesthe equilibrium real exchange rate by 3 percent.

  • Adjusting the terms of trade to their trend value in 2003 (lower than their actual value) lowersthe equilibrium real exchange rate by 3 percent.

  • Adjusting openness to its trend value in 2003 (lower than its actual value) >raisesthe equilibrium real exchange rate by 2 percent.

  • Adjusting relative real GDP per capita to its trend value in 2003 (higher than its actual value) raises the equilibrium real exchange rate by 1.5 percent.

  • Adjusting net foreign assets and Brazil's real exchange rate at their trend values does not have any quantitatively relevant effect on the equilibrium real exchange rate.

Figure 4.5.Fitted Real Exchange Rate and Misalignment from Long-Run Equilibrium

(Estimated from static long-run relationship)

Source: International Monetary Fund; and Fund staff estimates.

Our method of computing long-run values for the fundamentals tends to overestimate the misalignment in 2003. This is because the Hodrick-Prescott filter, which is used to compute the long-run fundamental values, may fail to capture important developments that occurred at the end of our sample period,86 a point that is particularly relevant when computing the long-run fiscal balance.

Table 4.4.Breakdown of Misalignment in 2003 (In percent of long-run equilibrium)1
Misalignment2-15.1
Accounted by fundamentals3-12.5
Current account-4.1
Fiscal balance-4.3
REER Argentina-3.4
REER Brazil0.0
Terms of trade3.1
Net Foreign Assets-0.1
Openness-2.2
Relative GDP per capita-1.5
Unaccounted by fundamentals4-2.6

Based on the estimates of the general model in column 4 of Table 4.3.

Difference between actual REER and long-run equilibrium. The latter is computed by evaluating the regression in column 4 of Table 4.3. at the long-run value of the fundamentals (according to the HP filter).

Difference between actual and long-term value of the fundamental (according to the HP trend) multiplied by respective coefficient in column 4 of Table 4.3.

Residual for 2003 (in percent of long-run trend).

Based on the estimates of the general model in column 4 of Table 4.3.

Difference between actual REER and long-run equilibrium. The latter is computed by evaluating the regression in column 4 of Table 4.3. at the long-run value of the fundamentals (according to the HP filter).

Difference between actual and long-term value of the fundamental (according to the HP trend) multiplied by respective coefficient in column 4 of Table 4.3.

Residual for 2003 (in percent of long-run trend).

The large fiscal deficits prior to 2003 imply that the long-run fiscal balance for 2003 computed using the Hodrick-Prescott filter is also large. However, this procedure ignores that Paraguay's new government started an ambitious fiscal consolidation program in the second half of 2003. If the fiscal balance for 2003 is considered to be more indicative of the trend in government finances than the recent past (as it seems likely), then the misalignment of the real exchange rate implied by the fiscal balance is much smaller, bringing down the overall real misalignment toward 10 percent.

Conversely, other factors could raise the long-run value of the real exchange rate in the near future. In the short run, the most important factor in this sense is related to the size of the current real underappreciation of the Argentine peso. If the long-term real value of the Argentine peso were even higher than implied by the Hodrick-Prescott trend (because its value at end-2003 is excessively sensitive to the large 2001 depreciation), then the long-run value of the guaraní would be higher, and with it the resulting estimated misalignment.87 Similarly, if the recent increase in terms of trade proved to be persistent, the long-run value of the guaraní would be higher.88 Finally, if sustained growth were to return to Paraguay, raising relative per capita GDP, the long-run value of the guaraní would also be higher.

Error correction models

To check robustness, we also estimate error correction models on annual data (Table 4.5). The small number of observations constrains the dynamic structure of the models that we can estimate. As a result, we start with small models (which allow for some dynamics) and we add potentially omitted variables in light of the previous results.

Table 4.5.Selected Results from VECM estimation(Annual data)
(1)(2)(3)(4)(5)(6)
Number of co-integrating vectors5 percent103220
Trace test1 percent003220
Max-eigenvalue test5 percent103201
1 percent001000
Co-integration vector1 REER (-1)111111
TOT (-1)-1.37 (0.13)-1.33 (0.14)-1.86 (0.11)-0.91 (0.27)-0.55 (0.13)-0.22 (0.06
REER Brazil (-1)-0.12 (0.22)
REER Argentina (-1)-0.37 (0.08)
Relative per capita GDP-1.02 (0.65)-1.61 (0.35)-1.47 (0.15
Current account0.02 (0.00)0.02 (0.00
Fiscal balance0.08 (0.01)0.04 (0.00
Openness0.00 (0.00
Adjustment coefficient 2-0.62 (0.24)-0.49 (0.19)-0.52 (0.17)-0.74 (0.21)0.47 (0.33)-0.14 (0.33
Lags in VECM 3222210
N (after adjusting for endpoints)212121212223
Sources: International Monetary Fund; and Fund staff estimates.

Standard errors in parentheses.

Coefficient on co-integrating equation in the ECM representation for Paraguay's log real effective exchange rate.

Number of lags in first differences in VECM representation.

Sources: International Monetary Fund; and Fund staff estimates.

Standard errors in parentheses.

Coefficient on co-integrating equation in the ECM representation for Paraguay's log real effective exchange rate.

Number of lags in first differences in VECM representation.

We find evidence of co-integration in most specifications. We find some evidence of co-integration in all but the specification that includes the terms of trade and Brazil's real exchange rate as determinants of the real exchange rate (column 2). For some specifications the co-integration tests show that we cannot reject the presence of more co-integration relationships (we report only the first one). The half-life of the misalignment from the long-run equilibrium implied by the adjustment coefficients range between 6 (column 2) and 9 months (column 4) and are roughly in line with the findings on quarterly data (ranging from 9 to 12 months). Only in the specification in column 5 does the adjustment coefficient turn out positive (but statistically insignificant). The estimates of the coefficients on terms of trade in the co-integration relationships across the various relationships are also in line with the findings on quarterly data and from estimating the long-run relationship directly, except in columns 5 and 6, for which the estimates are slightly lower.

We also broadly replicate our earlier results found on quarterly data. With regard to the models that were also estimated on quarterly data, the co-integration equations for the models with the terms of trade only and with the real exchange rates for Brazil and Argentina (columns 1–3) replicate well the findings on quarterly data (columns 1–3 of Table 4.2). In column 4, we replace relative per capita GDP (as a proxy for the Balassa-Samuelson effect) to Brazil's and Argentina's real exchange rates as a measure of productivity pressures on the real exchange rate. As in the long-run equation presented in Table 4.4, we find that relative per capita GDP has a quantitatively strong long-run effect on the real exchange rate, since a 1 percent fall in relative GDP per capita lowers the real exchange rate by 1 percent.89 In column 5 of Table 4.5 we add current account balance and the fiscal balance (in percent of GDP) to the specification in column 4 and we find effects similar to what was previously found for the long-run relationship (column 4 of Table 4.3). In particular, worsening the current account balance or the fiscal balance raises the real exchange rate.90 Column 6 of Table 4.5 presents the most general error correction model (ECM) representation, corresponding to the most general specification for the long-run relationship in column 4 of Table 4.3, except for the exclusion of Brazil's and Argentina's real exchange rates and net foreign assets (which were found to play a negligible role).91 All the estimates have values in line with the previous findings.

The estimated misalignment in the real exchange rate in 2003 is also consistent with previous findings. The general model in column 6 implies that when all the determinants of the real exchange rate are evaluated at their long-run equilibrium (according to the Hodrick-Prescott filter), the real exchange rate in 2003 was about 17 percent below its long-run equilibrium (Figure 4.6). Deviations of the fundamentals from their long-term values account for 14 percent of this misalignment, with the fiscal balance in turn accounting for more than half of this. This implies that if the fiscal balance in 2003 were regarded as a long-term measure of fiscal policy, the misalignment would fall below 10 percent92.

Figure 4.6.Actual and Long-Run Real Effective Exchange Rate

(Estimated from VECM representation)

Sources: International Monetary Fund; and Fund staff estimates.

E. Conclusions

Our estimates showed a real undervaluation in the guaraní at the end of 2003 in the range of 3–10 percent. We estimated several empirical models and found a range of estimates of the real misalignment in the guaraní at the end of 2003. Although these estimates are consistent in pointing out an underappreciation in real terms, the range of the estimated misalignment is relatively large, between 3 to 15 percent, possibly as a consequence of the small size of our sample. However, we argued that we can narrow this range to 3–10 percent once we take into account the fiscal consolidation that was started by the new government in the second half of 2003.

Other factors could, in the near future, raise the long-run value of the real exchange rate and thus the size of the misalignment. In the short run, the most important factor in this sense could be the magnitude of the current underappreciation in real terms of the Argentine peso, whose recovery could pull up the long-term equilibrium value of the guaraní. Similarly, persistently high commodity prices and the return of sustained growth to Paraguay would raise the long-term real value of the guaraní, raising in turn the magnitude of the misalignment in 2003.

Appendix 1. Data Sources and Definitions
VariableSourceCodeComment
Paraguay real effective exchange rateInternational Financial Statistics288..RECZF…Real effective exchange rate based on relative consumer prices (normalized to 1995=100 for annual data and 1995:Q1 for quarterly data).
Cotton price indexInternational Financial11176F.DZFM40
Statistics
Soybean price indexInternational Financial Statistics11176JFDZF
Soybean meal price indexInternational Financial Statistics11176JJDZF…
Industrial countries export price indexInternational Financial11074..DZF…
Statistics
Paraguay export price indexWeighted average of soybean, cotton and soybean meal price indexes using shares of 44, 26, and 9, respectively (provided by Cashin, Cespedes, and Sahay (2002)).
Paraguay terms of tradeComputed by dividing Paraguay export price by industrial countries export price (normalized to 1995=100 for annual data and 1995:Q1=100 for quarterly data).
Argentina real effective exchange rateInformation Notice SystemI213EREERReal effective exchange rate based on relative consumer prices (normalized to 1995=100 for annual data and 1995:Q1 for quarterly data)
Brazil real effective exchange rateInformation Notice SystemI223EREERReal effective exchange rate based on relative consumer prices (normalized to 1995=100 for annual data and 1995:Q1 for quarterly data).
Paraguay GDP at current pricesWorld Economic OutlookW288NGDP
Paraguay GDP at constant pricesWorld Economic OutlookW288NGDP_R
Paraguay real GDP per capitaWorld Economic OutlookW288NGDPRPC
United States real GDP per capitaWorld Economic OutlookW111NGDPRPC
Relative GDP per capitaLog difference between Paraguay real GDP per capita and United States GDP per capita.
Current account balanceWorld Economic OutlookW288BCA
Imports of goods and servicesWorld Economic OutlookW288BM
Exports of goods and servicesWorld Economic OutlookW288BX
Central government fiscal balanceWorld Economic OutlookW288GCBUsed in percent of GDP.
Trade opennessSum of imports and exports in percent of GDP.
Net international reservesInternational Financial Statistics28811…ZF…
Bank foreign assetsInternational Financial Statistics28821…ZF…
Net foreign assetsSum of net international reserves and bank foreign assets in percent of GDP.
References

    AlberolaEnriqueHumbertoLópez and LuisServén2003Tango with the Gringo: The Hard Peg and Real Misalignment in Argentina”(unpublished; Washington: World Bank).

    CashinPaul A.LuisCespedes and RatnaSahay2002Keynes, Cocoa, and Copper: In Search of Commodity CurrenciesIMF Working Paper 02/223 (Washington: International Monetary Fund).

    ChenYu-chin and KennethRogoff2002Commodity Currencies and Empirical Exchange Rate PuzzlesIMF Working Paper 02/27 (Washington: International Monetary Fund).

    ClarkPeter B.RonaldMacDonald1998Exchange Rates and Economic Fundamentals—A Methodological Comparison of BEERs and FEERsIMF Working Paper 98/67 (Washington: International Monetary Fund).

    ClarkPeter B.RonaldMacDonald2000Filtering the BEER—A Permanent and Transitory DecompositionIMF Working Paper 00/144 (Washington: International Monetary Fund).

    JohansenSoren1995Likelihood-Based Inference in Cointegrated Autoregressive Vectors (Oxford: Oxford University Press).

    MacDonaldRonald and Luca A.Ricci2003Estimation of the Equilibrium Real Exchange Rate for South AfricaIMF Working Paper 03/44 (Washington: International Monetary Fund).

    StockJamesMarkWatson1993A Simple Estimator of Cointegrating Vectors in Higher Order Integrated SystemsEconometrica vol. 61 No. 4 pp. 783820.

Using co-integration techniques is not the only possible approach, as determining the nonstationarity of macroeconomic time series in finite (and possibly very short) samples is difficult. On these grounds, Chen and Rogoff (2002) choose to work mainly with trend-stationary series. However, we take assurance from the large number of papers that conclude in favor of the existence of co-integration techniques among the real exchange rates and their determinants. For example, Cashin, Cespedes, and Sahay (2002) conclude that the real exchange rate and the commodity terms of trade are co-integrated in the case of Paraguay.

75

Out of 58 commodity-exporting countries, Paraguay is the seventh country in terms of share of commodity exports in total exports. Soybeans, cotton, and soy meals account for 44, 26, and 9 percent, respectively, of its exports.

Although this number could be reduced further by dropping recursively insignificant lags from the VECM, we maintain 11 lags to ensure that the residuals do not display any significant autocorrelations. We also include centered seasonal dummies.

77

A word of caution: this test on the residuals is not conclusive, as its distribution is not entirely correct when the test is performed on residuals from a first-stage regression.

These coefficients are obtained by changing the sign of the parameters in the co-integration vector.

We use the smoothing factor of 1,600, the recommended factor for quarterly data.

This discussion follows MacDonald and Ricci (2003), who provide further references to theoretical papers underpinning these channels.

However, the negative association between the current account balance and the real exchange rate may simply reflect reverse causality, as a lower real exchange rate may stimulate more exports and discourage imports.

For some series we also plot the Hodrick-Prescott trend (using a smoothing factor of 100).

If the variables included in the regression are co-integrated, the least-square estimates are “super-consistent.” However, the least-square standard errors are not correct, since they need to be corrected for the nonstandard distribution of the estimator in the presence of nonstationary time series. A procedure that corrects for this problem, the dynamic least squares proposed by Stock and Watson (1993), requires introducing leads and lags of the right-hand side variables, further reducing the size of the sample available for estimation.

As remarked in the previous footnotes, statements about the statistical significance have to be handled with care, since the standard errors in columns 1–4 are not corrected for the nonstationarity of the included variables.

A simple regression of relative per capita GDP on a linear trend shows that relative GDP per capita has fallen on average by 1 percent a year over our sample period. The trend accounts for almost 80 percent of the variation in relative GDP per capita.

This is the well-known end-point problem of the Hodrick-Prescott filter.

According to the Hodrick-Prescott filter, in 2003 the Argentine peso was 35 percent below its trend value.

However, the latest World Economic Outlook projections suggest that the current upturn in terms of trade may not be a long-term phenomenon.

The estimated coefficient is close to being significant at the 5 percent significance level.

However, the “wrong” positive sign of the adjustment coefficient suggests that this model is not well specified.

This specification could be estimated only after eliminating all the lags on differenced variables.

The same caveat with regard to the long-term values of the terms of trade and relative per capita GDP applies in this context.

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