Information about Western Hemisphere Hemisferio Occidental
Journal Issue

chapter 3 Central America’s Regional Trends and U.S. Cycles

Dominique Desruelle, and Alfred Schipke
Published Date:
November 2008
  • ShareShare
Information about Western Hemisphere Hemisferio Occidental
Show Summary Details
Shaun K. Roache


The economies of Central America share a close relationship with the United States, with considerable comovement of GDP growth over a long period of time. The open nature of the region’s economies, combined with the geographical proximity to the United States, have produced a number of transmission channels through which U.S. cyclical fluctuations can affect Central America. The trade channel is particularly important, with more than half of all the region’s merchandise exports over the preceding five years destined for the United States, up from about one-third in the late 1990s. Other possible channels include the financial sector, and remittance flows from migrant workers in the United States, which accounted for 14 percent of regional GDP (excluding Panama) during 2006.

Figure 3.1 suggests that Central America and the U.S. economy are moving in tandem, but just how dependent is growth in the region on the United States? Is some part of the economic cycle uniquely Central American? If not, what explains the periods during which certain economies appear to have decoupled from the United States? These are some of the questions addressed in this chapter. An analysis of the linkages between the two regions is particularly timely given the protracted U.S. growth slowdown, which could pose challenges for policymakers in Central America. After a short description of the stylized facts about the economic linkages between Central America and the United States, the following analysis uses the common cycles method of Vahid and Engle (1993) to provide some answers to these questions.1

Figure 3.1.GDP Growth, 1970–2006

Sources: IMF, International Financial Statistics; and author’s calculations.

1Weighted average excluding Nicaragua and Panama.

2Residuals from an ordinary least squares (OLS) regression of country GDP growth on U.S. GDP growth.

Stylized Facts

Commonly, three channels of transmission are thought to explain the close economic relationship between Central America and the United States: trade, financial flows, and remittances.

Trade Linkages

Trade is likely to be the most important linkage. Since the early 1980s, the share of total merchandise exports from the region as a whole to the United States has averaged about 40 percent, ranging from 27 percent in Nicaragua to 53 percent in Honduras (Figure 3.2).2 The second largest share is exports to other Central American countries, which has averaged about 20 percent over the same period. Do exports to the region help to diversify exposure away from the U.S. economy? The answer would be “yes” in two circumstances: either there is a unique Central American business cycle or there is divergence in the long-run rate of trend growth between the region and the United States, an issue that will be explored below. The two possibilities would have very different implications for both the behavior of exports and the overall economy given that exports accounted for 20 percent of regional GDP in 2006.

Figure 3.2.Destination of Exports, 1986 Q1–2007 Q21

(Percent of total exports)

Source: IMF, Direction of Trade Statistics.

1Rolling five-year sum of quarterly export data.

Financial Linkages

Financial linkages are important, owing in part to the high—albeit varying—degrees of dollarization across Central America. Given that many transactions take place in U.S. dollars, financial conditions in the United States and the region should share some similarities, most obviously in terms of interest rates. The obvious rejoinder is that real interest rate parity, as described in theory, has little evidence to support it, in spite of open capital accounts.3 Indeed, complete interest rate synchronization rarely holds between Central America and the United States, even for officially dollarized economies such as El Salvador and Panama, reflecting some frictions and other imperfections in the financial sector.

Another, more direct linkage with U.S. financial conditions is through external debt. The debt owed to foreign banks that report to the Bank for International Settlements (BIS) by Central American borrowers from all sectors (excluding Panama) accounted for about 15 percent of GDP at the end of 2006.4 Although only 3 percent of GDP was directly owed to U.S. banks, the remainder was also likely to be U.S. dollar denominated, given the pattern of trade flows (Figure 3.3). In addition, loans with a maturity of less than one year—on which interest rates are set frequently and therefore reflecting prevailing global financial conditions—account for almost half of outstanding claims by BIS banks on Central America.

Figure 3.3.External Debt Owed to BIS-Reporting Foreign Banks by Domicile

(Percent of GDP, 1995–2006)

Source: Bank for International Settlements.

Foreign ownership of domestic banks, that is, ownership of domestic banks by institutions from outside of the region, may also introduce spillovers, particularly if these institutions take a global view of their portfolio and formulate their policies on the basis of financial conditions in their home economy. The degree of foreign ownership varies widely across the regions from less than 15 percent in Guatemala to more than 90 percent in El Salvador.5 However, the large-scale entry of foreign banks is still a relatively new development, so it is not yet clear how financial sector linkages will be affected.


Remittance flows sent by migrant workers to Central America have grown rapidly in recent years and, for some countries, now account for a significant share of GDP and rival or even dwarf foreign direct investment (FDI) as a source of external financing (Table 3.1). Over the long term, socio-demographic and institutional factors in the host and recipient countries are likely to have a dominant influence.6 In the short run, it would, however, be reasonable to presume that cyclical economic conditions in the host country would influence these remittance flows.

Table 3.1.Comparing the Size of Remittances, 2006
Billions of

U.S. Dollars

Change Since

Percent of

Exports of

Costa Rica0.5n.a.2.3744
El Salvador3.38918.166769
Sources: National authorities; IMF, International Financial Statistics (IFS); and author’s calculations.
Sources: National authorities; IMF, International Financial Statistics (IFS); and author’s calculations.

The empirical evidence, however, is somewhat ambiguous. Evidence from Roache and Gradzka (2007) suggests that remittances may not have been an important source of spillovers from the United States until now. This, of course, could be the result of weaknesses in the remittances data. It could also be due to migrant workers “smoothing” their remittance flows, for example, by sending a fixed U.S. dollar amount each month or quarter, irrespective of income fluctuations, at least within reason. Alternatively, immigrants might attach more weight to being employed than to the wage received, and thus are less likely to be unemployed (other things being equal) than their native-born counterparts.

Literature Review

The relevant literature for this chapter relates to the existing studies on Central American economic linkages and the ones that focus on the applications of the codependence methodology to business cycles.

Central America Linkages

Although the results from global and broader regional studies indicate that Central America is one of the more globally integrated regions of the world (see Desruelle and Schipke, 2007), little work has been done specifically on intraregional integration. One of the most comprehensive studies is Fiess (2007), which measures business cycle synchronization within the Central America region and sensitivity to the United States initially using simple correlations of band-pass filtered GDP data from 1965 to 2002. There is evidence of a close relationship among Costa Rica, El Salvador, Guatemala, and Honduras and between this group and the United States, suggesting that a significant portion of variability is being driven by external factors. The other two countries, Nicaragua and Panama, exhibit low or even negative correlations in most cases. Controlling for the common effect of the United States causes correlations to decline, although they remain fairly high between Costa Rica and Guatemala (0.48), Costa Rica and El Salvador (0.41), and Guatemala and Honduras (0.42).

The study also presents coherence measures over assumed business cycle frequencies of 6 to 32 quarters for Central America using industrial production and other monthly indicators from the 1995–2003 period. These results tend to confirm those from simple correlations. Business cycle synchronization was highest between Costa Rica and El Salvador (0.53), El Salvador and Guatemala (0.53), El Salvador and Nicaragua (0.51), and Honduras and Nicaragua (0.55). Comparing the CAFTA-DR (Central American-Dominican Republic Free Trade Agreement with the United States) trade blocs to others, it was shown that intra-CAFTA-DR coherence was lower than that seen within NAFTA (North American Free Trade Agreement) and the European Union but similar to that within Mercosur.

Kose and Rebucci (2005) estimate country-specific vector autoregressions for five Central American economies, the Dominican Republic, and Mexico using data from the period 1964–2003. Six shocks are assumed to drive business cycle dynamics, three domestic and three external. The domestic variables include real GDP growth, the consumer price index (CPI) inflation rate, and the trade bal-ance–to-GDP ratio. External variables include U.S. real GDP growth, a measure of the ex post U.S. real interest rate, and the ratio of oil to nonfuel commodity prices (a proxy for the terms of trade). External shocks accounted for one-third of output variance, with a wide range across economies from Costa Rica (67 percent) and Guatemala (55 percent) to the Dominican Republic (10 percent) and Nicaragua (18 percent).

Kose and Rebucci (2005) also present multicountry vector autoregressions (VARs) using GDP growth rates for the United States, Mexico, and the same six regional economies above, to assess the importance of regional shocks. The block recursive structure placed the United States and Mexico in the first block, the five Central American countries in the second, and the regional economy of interest in the final block. With this set-up, NAFTA shocks explained an average of 22 percent of output variance for regional economies, with Honduras (34 percent), Costa Rica, and El Salvador (both at 26 percent) showing most sensitivity. Regional shocks were more important, explaining on average one-half of output variance, with the range across countries much tighter. Domestic shocks explained the remainder (24 percent), with the Dominican Republic and Nicaragua most affected by idiosyncratic disturbances.

Common Business Cycles

Cerro and Pineda (2002) apply the codependent approach to investigate real output trend and cycle dynamics for 11 Latin American economies using quarterly constant price GDP data from 1960 to 2000.7 Tests indicated the existence of seven common trends and four common cycles, allowing the decomposition into trend and cycle components. The correlations of the cyclical components show that correlations across the region peaked in the 1970–80 decade, declined through 1980–90, but have been rising since then. Although intraregional correlations appear high compared to the results from other studies (often above 0.5), there was little evidence that either Chile or Mexico were influenced by the common regional cycle.

Hecq, Palm, and Urbain (2006) test for the presence of comovements in annual GDP series for five Latin American countries—Brazil, Argentina, Mexico, Peru, and Chile—for the period 1950–1999. The main purpose of this study is to develop a test for strong and weak form reduced rank structures, with the first referring to the existence of common cycles within first-differenced data and the latter within first differences adjusted for long-run effects. They find evidence for two to three cointegrating vectors and three codependent vectors (of each kind, strong and weak form), depending upon the specification, indicating linkages across the economies. The reduced form restrictions implied by a common cycles structure also appear to improve model accuracy, on the basis of root mean-squared errors.

Hecq (2005) uses annual GDP data from the period 1950–2002 for six Latin American countries (Brazil, Chile, Colombia, Peru, Mexico, and Venezuela), and finds three common trends and three common cycles. This paper provides an innovation by using an iterative approach to improve the performance of the Johansen test in small samples, and concentrates more on the method than the results.

Data and Common Cycle Methodology

The data used for the analysis is annual real GDP from the period 1950–2006 for six Central American countries—Costa Rica, El Salvador, Guatemala, Honduras, Nicaragua, and Panama—and the United States. The data are taken from the IMF’s International Financial Statistics and, for earlier periods, the Penn World Tables. Summary statistics for this data in annual percent changes are presented in Table 3.2 with a more detailed summary in Appendix Table 3.A1. For advanced economies, much use has been made of quarterly data; although these data are usually preferable for analyses of business cycles, it remains difficult to obtain data at this frequency that is both comparable across countries and available with a sufficient history for the Central America region.

Table 3.2.Real GDP Growth: Summary Statistics


Costa Rica5.44.118.4-
El Salvador3.34.012.0-
Sources: Heston, Summers, and Aten, Penn World Table Version 6.2 (2006); IMF, IFS; and national authorities.
Sources: Heston, Summers, and Aten, Penn World Table Version 6.2 (2006); IMF, IFS; and national authorities.

As the literature review shows, many methods are available to assess linkages and common cycles across economies. The focus in this chapter is on two particular methods: simple correlations, using a variety of cyclical decompositions; and the common cycles approach first described by Engle and Kozicki (1993) and Vahid and Engle (1993).

These two methods are intuitive and provide a clear description of the common forces that drive business cycle fluctuations. The results are easy to interpret, can be compared against those of other well-known methods of business cycle analysis, and allow for the testing of hypotheses. As with any methodology, there are drawbacks and the most important of these is the emphasis on association rather than causation. These methods have little, or nothing, to say explicitly regarding the underlying economic forces that drive synchronization. Some interpretation can be imposed upon the results, but this will be more conjecture than firm conclusion.

The common cycles technique is an extension of the cointegration framework outlined by Johansen (1988). Cointegration implies that one or more linear combinations of nonstationary variables can remove the trend from the data. As shown by Stock and Watson (1988), for n variables, the existence of r cointegrating vectors implies the existence of n - r common stochastic trends. For economic output series, one interpretation of this result could could be that, over the long run, there exist common forces driving the underlying growth process.

An analogous indicator of comovement among nonstationary series is codependence. A strong form of codependence is the serial correlation feature as described by Engle and Kozicki (1993). In this case, there exist some linear combinations of the variables that remove correlations, and hence predictability, based on the set of past values. These linear combinations are defined as cofeature vectors and may be compared to cointegration vectors for stationary data. The approach, briefly described in Appendix 3.1 borrows from Vahid and Engle (1993), where full technical details of the theory are presented.


Growth Correlations

Surprisingly, in many cases correlations of GDP growth rates are neither particularly high nor statistically significant (Table 3.3). A cluster of economies—Costa Rica, El Salvador, and Guatemala—correlate fairly closely, but the links do not appear to be too strong. Even to the United States, correlations appear to be low and, for some economies, have not risen in the most recent decade or so. One possible interpretation is that linkages are weak. A second, more plausible, alternative given the stylized facts presented before is that GDP growth rates are a combination of changes in the trend and cycle and that the linkages of both components differ.

Table 3.3.GDP Growth Correlations, 1950–2006 and 1995–2006
Correlation of GDP Growth Rates

Including the United States
Correlation of GDP Growth Rates

Controlling for the U.S. Effect1
Costa RicaEl SalvadorGuatemalaHondurasNicaraguaPanamaCosta RicaEl SalvadorGuatemalaHondurasNicaraguaPanama
El Salvador0.540.47
United States0.340.370.130.350.050.00
El Salvador0.470.30
United States0.490.210.320.010.590.63
Source: Author’s calculations.Note: Figures in bold are statistically significant at the 5 percent level.

These correlation coefficients use residuals from a regression of country i’s growth rate on a constant and the U.S. growth rate, over the same sample period.

Source: Author’s calculations.Note: Figures in bold are statistically significant at the 5 percent level.

These correlation coefficients use residuals from a regression of country i’s growth rate on a constant and the U.S. growth rate, over the same sample period.

Four Common Trends and Three Common Cycles

The first step in the common cycles approach is to select the lag order of the system by identifying the vector autoregression—using nonstationary level data—with the lowest Aikake information criteria (AIC).8 A five-lag system was selected by the AIC and other criteria (Appendix Table 3.A2). If the series are cointegrated, this implies an error-correction representation with four lags; this was used as the basis for the cointegration tests.

Cointegration tests, run on a number of lag specifications for robustness, suggest three cointegrating vectors, which implies four common trends among the GDP series. Appendix Table 3.A3 shows the results of the cointegration tests at the 5 percent level of significance and also indicates one weakness of the Johansen (1988) methodology with small samples and overparameterization (see Cheung and Lai (1993) and Ho and Sorensen (1996) among others). Often, the likelihood ratio tests are too liberal, leading to an overestimate of the number of cointegrat-ing vectors r. This bias is magnified as the lag length increases. The test for common cycles is based on calculating the canonical correlations of the (7 x 1) vector Δyt and its lagged values and the first lag of the three error correction terms. The value of the test statistic described by equation (8) are presented in Table 3.A3. In this test, the null hypothesis is that there are at least n - s common cycles and, at the 5 percent level of significance, it was not possible to reject the hypothesis of four common cycles among the GDP series. This conclusion was insensitive to the number of cointegrating relationships. Also, in most cases, the combined number of cointegration and cofeature vectors spanned R n, that is, r + s = n.

Trends and Cycle Decomposition

When the number of cycles and trends sum to the number of variables—that is, r + s = n—a special case allows the decompositon of each GDP series into a separate trend and cycle component. This Beveridge-Nelson-style decomposition of the γt vector into permanent (trend) and transitory (cyclical) components can be derived for each country, as shown by Vahid and Engle (1993) and extended in Gonzalo and Granger (1995).

The first step in recovering these components is to estimate the system described by equation (10). This was estimated using iterative three-stage least squares, which accounts for endogeneity of some regressors and provides efficiency gains over the two-stage procedure owing to the existence of common exogenous shocks—for example, the oil price—on output. This allows for the estimates for the cointegrating and cofeature vectors.

To see how these estimates may be used to recover the trends and cycles, it is important to recall that a cointegrating combination of I(1) variables eliminates the trend from the data, leaving only the cycle. By analogy, a codependent combination of the same variable eliminates the cycle, leaving only the trend9. Figures 3.4 through 3.6 show the derived trends and cycles to their Hodrick-Prescott (HP)-filter counterparts. One cautionary note regarding the common cycle model is the relatively high volatility of the trend component, a tendency also seen in the original application to U.S. consumption by Vahid and Engle (1993). Trend or underlying, GDP growth is often assumed to be smooth over time, with a lower frequency of perturbations.

Figure 3.4.Cyclical Components of GDP, 1960–20061

Source: Author’s calculations.

Note: HP=Hodrick-Prescott.

1There are two cyclical components from the common cycles model for each country. Cycle 1 is estimated from a model with 4 cofeature vectors (i.e., 3 common cycles and 4 common trends). Cycle 2 is estimated from a model with 3 cofeature vectors (i.e., 4 common cycles and 3 common trends).

Figure 3.5.Trend Components of GDP, 1960–20061

Source: Author’s calculations.

1There are two trend components from the common cycles model for each country. Trend 1 (solid line) is estimated from a model with 4 cofeature vectors (i.e., 3 common cycles and 4 common trends). Trend 2 (broken line) is estimated from a model with 3 cofeature vectors (i.e., 4 common cycles and 3 common trends).

Figure 3.6.Average Correlation of Cyclical GDP Component to the United States: Comparison of Methods1

Source: Author’s calculations.

1The methods include first-differenced log values, the first difference of the cyclical component from the Hodrick-Prescott filter, and the first difference of the common cycle factor recovered from the Vahid and Engle (1993) decomposition.

As a robustness check, the model was also run assuming four shared cycles and three shared trends. The results were not qualitatively different, although for some countries, the cycle tended to be somewhat more volatile. This is particularly true for Guatemala, for which the low volatility of the official GDP series tends to imply a very shallow cycle with this model.

Cyclical Correlations

Correlations of the cyclical part of GDP from this model are much higher than for the annual growth rate or the HP filter cycle (using three or four common cycles, see Appendix Figures 3.A1 and 3.A2). This is true for almost all economies. This result is not an inevitable outcome of the methodology; recall that there are three common cycles and it is conceivable that some economies would have exposure to some cycle, but not others. However, with this sample of countries, it appears that the exposure to these common cycles is similar. The results are stronger, but also similar in terms of the ranking of countries to the correlations of growth rates. Costa Rica, El Salvador, and Honduras appear to be the most sensitive to the U.S. business cycle.

Cyclical and Trend Elasticities to the United States

In the sample used, it is reasonably assumed that there is one truly exogenous cycle, that is, that of the United States (ignoring, for now, the possibility of common exogenous shocks, which could characterize the 1970s oil supply disruptions). Although correlations show that the cycles in most Central American countries and the United States tend to move in the same direction, it does not tell us anything about elasticities; that is, the extent to which growth in Central America would respond to a cyclical shock in the U.S. Assuming a one-way causality from the United States to Central America allows for the use of very simple methods to estimate elasticities, without running into all of the interpretation and estimation problems related to endogenous regressors.10

The results suggest that Central American is very cyclically sensitive to the United States, with elasticities highly significant for four countries (Guatemala’s elasticity is somewhat lower than the others, owing mostly to the low volatility of the historical GDP series).11 In contrast, long-run trend shocks in the United States have a lesser impact, indicating that trends are determined much more by regional developments. Running diagnostics for each of these estimations confirms that the model is well-behaved and supports our earlier assertions that this simple functional form captures the true cyclical elasticities (Appendix Table 3.A5).

Variance Decomposition by Factor

How much of the variation in GDP is due to the trend and how much to the cycle, at least as it is defined here? Previous research answered this question using a VAR approach (see Vahid and Engle (1993) and Cerro and Pineda (2002). Generally, it was found that one type of shock completely dominates variance and, using the same methods, similar results are obtained using this sample. However, the shock that dominates is very sensitive to the ordering. Without strong priors from theory to suggest which shock should be ordered first—such as cyclical or trend shocks—there would be a powerful incentive to identify a new decomposition method.12

The results suggest that for most Central American countries, the cycle contributes most to changes in GDP (see Figure 3.7). One exception is Honduras, for which the trend is more important and more closely linked to the U.S. trend than other countries. The other exception is Guatemala, with the cycle tending to dampen down changes in the trend; this can occur owing to the inclusion of co-variance terms in equation (16). Once again, as with the estimated elasticities, the curiously low volatility of the historical GDP series may be playing some role in this result.

Figure 3.7.Contribution of Cycle and Trend to GDP Growth: Common Cycles Method, 1950–2006

(Contribution to standard deviation of GDP growth in percentage points)

Source: Author’s calculations.

Strong Linkages and Policy Implications

Almost all of the countries in the sample—including the United States—share a common business cycle. Clearly, the United States is the dominant economy and, as a result, there is evidence of a powerful cyclical linkage running from the United States to Central America, a linkage that is stronger than simple regressions of GDP growth rates would imply.

Indeed, growth elasticities using GDP suggest a much weaker cyclical relationship. This is due to the weak links between long-run growth shocks in Central America and the United States, the most important of which are related to armed conflicts in particular countries but also common terms of trade shocks and poor policy responses (see Macías, Meredith, and Vladkova Hollar, 2007). If the longrun component of Central America’s GDP growth is not stripped out, reflecting these shocks, estimated cyclical linkages with the United States will seem lower than they really are, which could complicate the policy response.

How will these cyclical linkages evolve? They are unlikely to weaken in the absence of a significant diversification of exports and investment inflows, beyond the United States and, perhaps, the region itself. The CAFTA-DR trade agreement, the most important economic change in recent years, may play the pivotal role in determining how external linkages develop.

Most obviously, CAFTA-DR may encourage more integration with the United States not only through trade, but also through investment flows and the financial sector. This would tend to strengthen cyclical linkages. For example, Mexico’s experience under NAFTA suggests that trade flows between Centra America and the United States could increase rapidly as a result of CAFTA, while FDI from the United States would rise (Kose and others, 2005).

However, it is also conceivable that CAFTA-DR would have an externality effect that could weaken the dependence upon the U.S. cycle. It seems reasonable to assume that CAFTA-DR could have a positive effect on productivity growth, through higher investment and technology transfer. This in turn could encourage investment from new sources that have not been a strong presence in the region, such as Asia. Improved competitiveness may also increase the region’s penetration in other markets. In other words, CAFTA-DR could have positive externalities beyond the obvious linkages with the agreement’s members. Other bilateral trade agreements, including those currently being negotiated with the European Union, could also encourage cyclical diversification (Desruelle and Schipke, 2007).

The more difficult question is how long-run trend growth, which has been responsible for long periods of decoupling with the United States, will evolve across the region. The diversification of exports, with a greater share now destined for other countries in the region rather than the United States, suggests that Central America may be experiencing its own growth dynamic. Perhaps this is the early stage of the positive externality process from CAFTA mentioned earlier. How could this process provide some insulation against cyclical fluctuations in the United States? First, by encouraging linkages with new markets beyond CAFTA. Second, and less likely, by building the region’s critical economic mass to the point that it could generate its own economic cycle.

Whether a rise (or fall) in economic growth is due to the cycle or long-run structural factors should influence the public policy response. The clearest example is fiscal policy. Evidence suggests that government tax revenues in the region rise by more than one-for-one with growth in the economy.13 For example, if GDP growth over a year is 5 percent, tax revenues will grow by more than 5 percent, causing the tax-to-GDP ratio to rise (and vice versa for a decline).14

The decision to save or spend this additional income is a straightforward application of the permanent income hypothesis. If the rise in growth is due to permanent structural factors, then the optimal response would be for the government to fully “spend” it, either through higher expenditure or lower taxes.15 If the rise in growth is cyclical, and by definition temporary, it would be optimal to “save” most of it and spread the benefits of temporarily higher income through time. In other words, governments would be well advised to adjust their spending to the “structural” level of revenues; that is, the level explained by potential or long-run growth.

Appropriate policy settings rely upon a good understanding of the nature of growth. Although a simple trend-cycle analysis incorporating major trading partners cannot provide all the answers, it does provide some important clues. For Central America, the message seems to be that if regional growth is picking up (or falling) at the same time as it is in the United States, then it is reasonable to presume that some portion of that improved growth performance is due to temporary cyclical factors.


The economies of Central American and the United State are closely intertwined. The open nature of the region’s economies, combined with the geographic proximity to the United States, has resulted in a number of transmission channels through which U.S. cyclical fluctuations could impact the region. The main channels through which shocks are transmitted are trade, financial flows, and remittances. As the implementation of CAFTA-DR moves forward, the links between the two regions are likely to become even stronger.

Given these links, it should be no surprise that the Central American economies appear to be strongly influenced by cyclical fluctuation in the United States. Historical data show that business cycles in Central America move in the same direction as those in the United States. Based on empirical estimates a growth slowdown of 1 percentage point in the United States would typically be associated with a cyclical fall in output growth of 0.5 to 1 percentage points in most of the countries of the region. In light of this dependence, a prolonged downturn in the United States would be expected to have significant implications for the region.

Appendix 3.1. The Common Cycles Method

Let γt denote the (7 x 1) vector of log GDP series for the economies in our sample. As confirmed by standard tests (Table 3.A1), these data are I(1) while their first differences Δγt are I(0). As a result, Δγt has the following Wold representation:

where C(L) is a matrix polynomial in the lag operator and ε is an (7 x 1) vector of stationary innovations. Assuming that μ = 0 for algebraic convenience, the Beveridge-Nelson decomposition allows the original I(1) series to be expressed as the sum of a trend (T) and a cyclical (C) component.

Stock and Watson (1988) show that a number of common trends r may be shared among the variables in vector γ. In this case, the matrix C(1) may be decomposed into the product of an (n x (n - r)) matrix of rank n - r (A) with a ((n - r) x n) matrix of rank n - r(B) as follows:

where A is an (n x (n - r)) matrix of factor loadings with full column rank. Analogously, the vector γ may also share common cycles. If common cycles exist, then there must exist linear combinations of the γ vector that do not contain the cycle and for which history has no predictive power. This would imply that the following condition, for some set of linearly independent vectors α* known as cofeature vectors, will hold:

When applied to Δγ, the cofeature transformation α* eliminates all the positive powers of the lag operator; in other words, it removes the serial correlation of first differences. This same transformation, when applied to the levels, removes the common cycles.

We test for the existence of common cycles using the canonical correlation procedure outlined in Vahid and Engle (1993). The first step is to estimate a vector error correction model to recover the error correction series, otherwise known as the long-run relationship:

Then, defining two (7 x 1) random vectors ϱt and ηt, which are linear combinations of the (7 x 1) vector Δγt and the ((7 p + r) x 1) vector of lags and error correction terms (which will be termed xt):

The (n x n) matrix A and the (n x (np + r)) matrix B are chosen such that four conditions hold. The first two state that the individual elements of both ϱt and ηt have unit variance; the third condition states that the ith element of ϱt and the jth element of ηt are uncorrelated; and the final condition states that the elements of ϱt and ηt are ordered in such a way such that:

where the correlation ri is known as the ith canonical correlation between the two vectors Δγt and xt. The canonical correlations and the values of A and B can be calculated from the covariance matrices of Δγt and xt through eigenvalues and eigenvectors. The test statistic is analogous to the trace statistic from the Johansen (1988) procedure, with the null hypothesis that the dimension of the cofeature space is at least s (or equivalently that there are at most n - s common cycles) being:

where the λ2’s are the s smallest squared canonical correlations between ϱt and ηt. Under the null, this statistic is chi-squared with s2 + snp + sr - sn degrees of freedom.

Suppose there are s linearly independent cofeature vectors; in this case, the (s x n) matrix of cofeature vectors that has full column rank. Vahid and Engle (1993) suggest that these equations may be regarded as s pseudo-structural equations for the first s terms of the vector Δγ:

In other words, there are s linearly independent combinations of the elements of Δγt that have no dependence on the relevant past, such that the residual term is stationary, analogous to cointegration. The system is completed by including the unconstrained reduced form equations for the remaining (n - s) elements of the (n x 1) vector:

This system may then be estimated using maximum likelihood or other estimation procedures, such as iterative three-stage least squares.

Table 3.A1.Real GDP Summary Statistics(Using first-difference of log values, unless otherwise specified)


SkewnessUnit Root Test p-Values1
Costa Rica565.13.9-
El Salvador563.14.0-1.90.510.03
United States563.32.2-0.50.810.00
Source: Author’s calculations.

One-sided p-values from Augmented Dickey-Fuller unit root tests with lags selected usiing Aikake information criteria.

Source: Author’s calculations.

One-sided p-values from Augmented Dickey-Fuller unit root tests with lags selected usiing Aikake information criteria.

Table 3.A2.Vector Autoregression (VAR) Lag Order Selection Criteria1


Source: Author’s calculations.Note: Bolded figures identify the lag order selected by each criteria for the VAR in levels of all seven variables.

The criteria include: small-sample adjusted log likelihood ratio test; Aikake information criteria (AIC); Schwarz-Bayes information criteria (SBC); and the Hanan-Quinn information criteria (HQ).

Source: Author’s calculations.Note: Bolded figures identify the lag order selected by each criteria for the VAR in levels of all seven variables.

The criteria include: small-sample adjusted log likelihood ratio test; Aikake information criteria (AIC); Schwarz-Bayes information criteria (SBC); and the Hanan-Quinn information criteria (HQ).

Table 3.A3.Tests for the Number of Cointegrating Vectors: Probability Values
Null hypothesisTrace TestMaximum Eigenvalue Test
Lag orderLag order
r = 00.0290.0000.0000.0000.0000.0000.0000.0000.0000.000
r≤ 10.0450.0030.0030.0000.0000.0010.0000.0000.0000.000
Source: Author’s calculations.
Source: Author’s calculations.
Table 3.A4.Tests for the Number of Cofeature Vectors

Probability ValuesCanonical Correlation
Number of cointegrating vectorsNumber of cointegrating vectors
s> 00.98210.98660.95810.94640.940.950.950.95
s > 10.96570.96190.80090.75090.850.910.910.91
s > 20.69620.47560.26690.05970.730.760.850.85
s > 30.17760.09040.00730.00010.660.660.750.81
s > 40.00830.00200.00000.00000.550.620.630.72
s > 50.00000.00000.00000.00000.370.390.470.50
s > 60.00000.00000.00000.00000.
Source: Author’s calculations.
Source: Author’s calculations.
Table 3.A5.Growth Elasticity Models: Diagnostics




Cycle equations
Costa Rica560.811.840.14350.0487
El Salvador560.731.920.29710.2034
Trend equations
Costa Rica560.231.790.14350.0487
El Salvador560.401.430.29710.2034
Source: Author’s calculations.

Probability value of the test statistic if the null hypotheses (of no autocorrelation or heteroscedasticity) were true.

Source: Author’s calculations.

Probability value of the test statistic if the null hypotheses (of no autocorrelation or heteroscedasticity) were true.

Figure 3.A1.Average Correlation of Cyclical GDP Component to the United States: Comparison of Methods1

Source: Author’s calculations.

1The methods include first-differenced log values, the first difference of the cyclical component from the Hodrick-Prescott filter, and the first difference of the common cycle factor recovered from the Vahid and Engle (1993) decomposition.

Figure 3.A2.Average Correlation of the Cyclical Component of GDP to Other Central American Countries: Comparison of Methods1

Source: Author’s calculations.

1The methods include first-differenced log values, first-differences adjusted for the U.S. effect by running an OLS regression on contemporaneous U.S. first differences, the first difference of the cyclical component from the Hodrick-Prescott filter, and the first difference of the common cycle factor recovered from the Vahid and Engle (1993) decomposition.

Figure 3.A3Common Cyclical and Trend Factors

Source: Author’s calculations.


    Cerro, A.M., and J.Pineda,2002, “Do Common Cycles Exist in Latin American Countries?” Latin American Research Abstracts, No. 17 (Summer) (Dallas: Federal Reserve Bank of Dallas, Center for Latin American Economics).

    • Search Google Scholar
    • Export Citation

    Cheung, Yin-Wong, and Kon S.Lai,1993, “Finite-Sample Sizes of Johansen’s Likelihood Ration Tests for Cointegration,”Oxford Bulletin of Economics and Statistics, Vol. 55 (August), pp. 313–28.

    • Search Google Scholar
    • Export Citation

    Chinn, Menzie D., and GuyMeredith,2005, “Testing Uncovered Interest Parity at Short and Long Horizons During the Post-Bretton Woods Era,”NBER Working Paper No. 11077 (Cambridge, Massachusetts: National Bureau of Economic Research).

    • Search Google Scholar
    • Export Citation

    Cubero, Rodrigo, and RhiannonSowerbutts,forthcoming, “Growth Elasticities of Tax Revenues in Costa Rica,”IMF Working Paper (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Desruelle, Dominique, and AlfredSchipke,eds., 2007, Economic Growth and Integration in Central America, IMF Occasional Paper No. 257 (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Engle, Robert F., and SharonKozicki,1993, “Testing for Common Features,”Journal of Business and Economic Statistics, Vol. 11 (4), pp. 369–80.

    • Search Google Scholar
    • Export Citation

    Fiess, Norbert,2007, “Business Cycle Synchronization and Regional Integration: A Case Study for Central America,”World Bank Economic Review, Vol. 21 (1), pp. 49–72.

    • Search Google Scholar
    • Export Citation

    Gonzalo, Jesus, and Clive W.J.Granger,1995, “Estimation of Common Long-Memory Components in Cointegrated Systems,”Journal of Business and Economic Statistics, Vol. 13 (1), pp. 27–35.

    • Search Google Scholar
    • Export Citation

    Gonzalo, Jesus, and Jean-YvesPitarakis,2001, “Lag Length Estimation in Large Dimensional Systems,” Econometrics No. 0108003 (EconWPA).

    • Search Google Scholar
    • Export Citation

    Hecq, Alain,2005, “Common Trends and Common Cycles in Latin America: A 2-Step vs. an Iterative Approach,” Computing in Economics and Finance Paper No. 258 (Society for Computational Economics).

    • Search Google Scholar
    • Export Citation

    Hecq, Alain, Franz C.Palm, and Jean-PierreUrbain,2006, “Common Cyclical Features Analysis in VAR Models with Cointegration,”Journal of Econometrics, Vol. 132 (May), pp. 117–41.

    • Search Google Scholar
    • Export Citation

    Ho, Mun S., and BentSorensen,1996, “Finding Cointegration Rank in High Dimensional Systems Using the Johansen Test: An Illustration Using Data Based Monte Carlo Simulations,”Review of Economics and Statistics, Vol. 78 (November), pp. 726–32.

    • Search Google Scholar
    • Export Citation

    Kose, M. Ayhan, and AlessandroRebucci,2005, “How Might CAFTA Change Macroeconomic Fluctuations in Central America? Lessons from NAFTA,”Journal of Asian Economics, Vol. 16 (February), pp. 77–104.

    • Search Google Scholar
    • Export Citation

    Kose, M. Ayhan, and AlessandroRebucci, and AlfredSchipke,2005, “Macroeconomic Implications of CAFTADR” in Central America: Global Integration and Regional Cooperation, IMF Occasional Paper No. 243, ed. by MarkusRodlauer and AlfredSchipke (Washington;International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Macías, José Brambila, GuyMeredith, and Ivanna VladkovaHollar,2007, “Growth Performance,” in Economic Growth and Integration in Central America, IMF Occasional Paper No. 257, ed. by DominiqueDesruelle and AlfredSchipke (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Morales, R. Armando, and AlfredSchipke,2005, “Regional Integration and Financial Systems Issues” in Central America: Global Integration and Regional Cooperation, ed. by MarkusRodlauer and AlfredSchipke (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Rapoport, Hillel, and FredericDocquier,2005, “The Economics of Migrants’ Remittances,”IZA Discussion Paper No. 1531 (Bonn: Institute for the Study of Labor). Available via the Internet:

    • Search Google Scholar
    • Export Citation

    Roache, Shaun K., and EwaGradzka,2007, “Do Remittances to Latin America Depend on the U.S. Business Cycle?”IMF Working Paper 07/273 (Washington: International Monetary Fund).

    • Search Google Scholar
    • Export Citation

    Stock, James, and MarkWatson,1988, “Testing for Common Trends,”Journal of the American Statistical Association, Vol. 83 (December), pp. 1097–107.

    • Search Google Scholar
    • Export Citation

    Vahid, F., and R.F.Engle,1993, “Common Trends and Common Cycles,”Journal of Applied Econometrics, Vol. 8 (October–December), pp. 341–60.

    • Search Google Scholar
    • Export Citation

The common cycles method of Vahid and Engle (1993) applies the insights of cointegration to the analysis of stationary, or in this case, cyclical economic data.


The figures in this chapter refer to exports of goods and exclude services. Services are an increasingly important component of exports for some countries, particularly for economies with a large and developing tourist industry such as Costa Rica.


These results have been based largely on short-horizon data. Recent work (see Chinn and Meredith, 2005) suggests that the relationship may be stronger for long-term interest rates.


These figures exclude Panama because of the scale of that financial system’s offshore activities. These figures also exclude local lending by foreign banks that have acquired a presence in domestic banking systems.


Even before the large-scale entry of foreign banks, financial sector integration had gained momentum over the past few years, as some regional institutions that originally focused on the home market expanded regionally (see Morales and Schipke, 2005).


For a survey of theoretical models that describe remittance behavior, see Rapoport and Docquier (2005).


Countries include Argentina, Bolivia, Brazil, Chile, Colombia, Ecuador, Mexico, Paraguay, Peru, Uruguay, and Venezuela. Imports were used to interpolate the GDP series when quarterly data were not available.


Although the AIC possesses a nonzero limiting probability of overfitting a VAR model—that is, selecting too many lags—Gonzalo and Pitarakis (2001) have shown that this bias is a decreasing function of the system dimension and that the AIC outperforms other criteria in large dimensional systems. Also, Hecq, Palm and Urbain (2006) have shown that the inefficiencies of overfitting a common cycles model tend to be small.


The following terms describe the trend and cyclical factors, respectively:

α˜yt=α˜C(1)s=0εt-sαyt =α ′ C * (L)ϵt-s(11)

where α̃ is the (n x s) matrix of cofeature vectors and α is the (n x r) matrix of cofeature vectors. The trend and cycle for each series can then be recovered using the following expression, where the (n x s) matrix ã̃- and (n x r) matrix α- are formed from the partition of the inverse of the matrix [ãa’]’:



The cyclical contribution to GDP growth is approximated by the first difference in the cyclical series extracted above. Then, for each Central American country, the first-differenced cycle was estimated as the sum of: a constant γ (which should be zero in the long run); the first differenced U.S. cycle and the elasticity εUSC; the first differenced U.S. trend and the elasticity εUST; and a residual e that could reflect country-specific factors or linkages with other economies in the sample. Given the exogeneity assumption, this relationship—equation (13) below—may be estimated using ordinary least squares (OLS).


The codependent combination of variables eliminates the influence of past shocks. As a result, it should be possible to discard autoregressive terms or lags of the U.S. cycle. If such variables were incorrectly omitted from equation (13), the result would likely be strong serial correlation of the equations residuals, something that can be tested using well-known procedures.


Using the index for economic activity (IMAE) instead of GDP, the elasticity is about 0.4 in the case of Guatemala.


An application of the portfolio risk contribution is used to assess this. To describe this method, first recall that in our case, there are three common cycles and four common trends, which are scaled up by the factor loadings to yield the level of GDP. This implies that it is possible to write GDP as a factor model, where the (n x 1) vector f contains r cycles and s trends:


For any individual country, this can be written as:


The variance in this case can be written as:

var(yi)=Σj=1nΣk=1naijajk cov(fj , fk) j , k= 1 ,..., N(16)


For instance, Cubero and Sowerbutts (forthcoming) find that, in the case of Costa Rica, the elasticity of tax revenues with respect to GDP is about 1.1 (and much higher than that for income taxes).


Over the long run, the tax-to-GDP ratio should be expected to stabilize at some level, given an unchanged tax structure.


Ignoring absorption capacity constraints in the economy for simplicity could imply other consequences from higher spending, such as higher inflation and rapid real exchange rate appreciation.

    Other Resources Citing This Publication