Chapter 3. Benchmarking Sub-Saharan African Trade Performance

Sanjeev Gupta, Kevin Carey, and Ulrich Jacoby
Published Date:
October 2007
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Many studies have investigated whether regions or countries undertrade or overtrade relative to a benchmark model of trade flows.18 Gravity models are commonly used for setting this benchmark; they derive the level of bilateral trade (exports and imports) from natural determinants: in its simplest specification, trade between any two countries is expected to be directly related to their economic size (GDP) and level of development (GDP per capita) and inversely related to the distance between them. When the observed level of trade exceeds the model’s prediction, the country pair is considered to overtrade; when it falls below the prediction, they are said to undertrade.

Undertrading is influenced by all barriers to trade, including structural and policy-induced impediments. The difference between actual and predicted trade—the residual—is the unexplained portion of bilateral trade flows. The estimation includes as many of the natural determinants of trade flows as possible. In addition to the core variables of size and distance, they include geographic characteristics (for example, landlocked versus coastal), participation in customs or currency unions, and historic linkages between trading partners. The residual then captures the impact of trade policy and such impediments to trade as infrastructure, trade facilitation, and business climate. Overtrading probably reflects structural aspects not captured by the gravity model, such as the emergence of intra-industry trade (see below). An alternative approach is to include additional determinants of trade in the gravity model. For example, Broadman (2007) adds indicators for export and import customs procedures, port quality, domestic business procedures, and quality of utilities to the base gravity model specification. Some variables, such as the number of customs and business procedures, are found to have a substantial negative impact on sub-Saharan African trade; these would represent components of undertrading if they were not included in the model. However, it is difficult to assign precise influence to specific sets of included variables, because they could be correlated with other omitted variables that also have an impact on trade flows. The remainder of this study therefore adopts the more parsimonious gravity model specification.

Benchmarking trade using the gravity model has limitations. First, the model is not a comprehensive economic model of trade flows. It has no role for factor proportions, comparative advantage, exchange rates, or other determinants of patterns suggested by international trade theory. Second, gravity models can be highly unstable in predicting the influence of variables like distance and degree of development. Because these are part of any economy’s structure, the instability of their coefficients suggests that the gravity model is affected by variables beyond those at the model’s core. Finally, because gravity models use data on merchandise trade, they do not take into account trade in services, which has been growing recently. Nevertheless, its parsimonious specification and extensive track record of applications have established the gravity model as an accepted tool for analyzing trade flows.

Estimation Results

An IMF study of global trade in the late 1990s found modest overtrading for sub-Saharan Africa (IMF, 2002).19 It estimated a gravity model for bilateral flows from 1995 through 1999. East Asia overtraded by more than 40 percent relative to the model’s prediction and sub-Saharan Africa by about 5 percent. In contrast, developing countries in the Western Hemisphere undertraded by about 10 percent and in South Asia and the Middle East and North Africa (MENA) by about 40 percent. Moreover, sub-Saharan Africa’s overtrading may have been a modest 5 percent globally, but it was 50 percent when both partners were in sub-Saharan Africa.

A gravity model was estimated covering the period of the recent African trade boom. The specifications and data for estimating the model are an extension of those in Rose (2002). He estimates a global gravity model for 178 countries using data spanning 1948–99. The data set has more than 12,000 country pairs and contains a full range of right-hand-side variables, including real GDP, GDP per capita, distance, land area, geographic and relevant colonial characteristics, and presence in a currency union. For new estimates, the macroeconomic variables were updated to 2005 from the IMF Direction of Trade Statistics and World Economic Outlook databases, deflated to 2000 U.S. dollars.20 Because the regression technique is ordinary least squares, it does not make any adjustment for possible endogeneity of explanatory variables.

The new estimates cover relatively short periods. Using longer periods in a single sample runs a variety of risks, including subsample instability and divergent trends across different countries (Baldwin and Taglioni, 2006). Four regressions were estimated. First, as a check that the method could reproduce existing estimates, Rose’s estimates were replicated on a subset of his data covering 1990–99, but using the new GDP data to take into account revisions and updated deflators.21 Second, an equation identical to the first regression was estimated with data for 2000–05; this is the main regression used in the benchmarking calculations. Two additional equations were estimated as robustness checks, one allowing for selectivity in bilateral pairs that report zero trade and one allowing for random effects across trading pairs. All regressions contain dummies for year to control for influences on trade common to all countries in each year (for example, global business cycle effects). The regressions also control for geographic characteristics, including whether either trade partner had resource-intensive exports or was landlocked and whether a pair has a common border. Residuals can then be averaged across groups; for example, in terms of coastal, landlocked, and resource-intensive for sub-Saharan African countries. Thus the residuals will indicate whether, relative to the global prediction for the impact of the included characteristics, sub-Saharan African countries tend to trade more or less than the model predicts.

The estimates are relatively stable but there are notable cases of individual parameter instability. Table 10 reports the coefficients on some key variables from the regressions for 2000–05 (columns B, C, and D) along with a Rose-type regression covering 1990–99 for comparison purposes (column A). Although the coefficients on distance, GDP per capita, presence of regional trade agreements (RTAs), and the geographic variables are broadly similar, the coefficients on GDP and currency union fall substantially, whereas that on common border rises. The currency union variable is estimated to be negative in the B, C, and D regressions, although the effect is not significant.22 Of particular interest is the shifting relative influence of GDP and GDP per capita; the impact of the latter on trade increases relative to the former in more recent regressions.23 Thus, other things being equal, the combined economic size of a trading pair has a smaller impact over time on bilateral trade relative to their combined per capita income. This aspect of the estimates is discussed further below.

Table 10.Coefficients on Selected Variables from the Global Gravity Model(Dependent variable as average of log trade flows)
Pair GDP0.510.390.40.24
(log product)(0.01)**(0.01)**(0.01)**(0.01)**
Pair GDP per capita0.470.420.440.39
(log product)(0.02)**(0.02)**(0.01)**(0.01)**
Currency union0.61–0.2–0.16–0.28
Regional trade agreement0.340.350.360.37
Land area0.
(log product)(0.01)**(0.01)**(0.01)**(0.01)**
Common border1.
Colonial link1.
Observations (pairs)52,904 (8,528)31,486 (6,168)47,21431,486 (6,168)
Sources: Rose (2002); and IMF staff calculations.Note: Standard errors robust to clustering by pairs are in parentheses, with significance indicated at 1 (**) percent.Regression A replicates the regression from Rose (2002) on a subsample of Rose’s data, but with updated GDP data; it is presented for purposes of comparison. The main regression is B, which forms the basis of the trade benchmarking calculations. Column C reports a Heckman two-step estimator of the same model as in B, with a selection equation for observations that have zero bilateral trade. Column D reports a panel regression of the gravity model that allows for random effects across bilateral pairs. All regressions also include dummies for year, and the last three regressions have dummies for countries whose exports are dominated by fuel or nonfuel primary exports.
Sources: Rose (2002); and IMF staff calculations.Note: Standard errors robust to clustering by pairs are in parentheses, with significance indicated at 1 (**) percent.Regression A replicates the regression from Rose (2002) on a subsample of Rose’s data, but with updated GDP data; it is presented for purposes of comparison. The main regression is B, which forms the basis of the trade benchmarking calculations. Column C reports a Heckman two-step estimator of the same model as in B, with a selection equation for observations that have zero bilateral trade. Column D reports a panel regression of the gravity model that allows for random effects across bilateral pairs. All regressions also include dummies for year, and the last three regressions have dummies for countries whose exports are dominated by fuel or nonfuel primary exports.

New estimates for 2000–05 find substantial changes in regional patterns of undertrading or overtrading (Table 11).24 These numbers are based on the residuals from the B regression in Table 10. They not only confirm the conclusion of IMF (2002) and others that East Asia is a large overtrader; they also show that the extent of overtrading has almost doubled since the 2002 study. Sub-Saharan Africa switches on average from modest overtrading to undertrading by more than 20 percent. In intraregional trade, sub-Saharan Africa’s performance has improved but is now just at the predicted level.

Table 11.Undertrading in Developing Countries, 2000–05(Average difference between actual and predicted trade, in logarithms)
Trade Partners
Sub-Saharan Africa–0.21–0.04
South Asia0.140.12
East Asia0.821.68
Latin America and Caribbean–0.030.43
Middle East and North Africa–0.400.04
High-income countries–0.060.12
Source: IMF staff estimates.Note: Based on a gravity equation estimated on annual data. A negative number indicates a negative residual and thus undertrading; similarly, a positive number indicates overtrading.
Source: IMF staff estimates.Note: Based on a gravity equation estimated on annual data. A negative number indicates a negative residual and thus undertrading; similarly, a positive number indicates overtrading.

The results confirm the continuation of trends identified earlier. IMF (2002) supplemented the analysis of 1995–99 by benchmarking trade performance for five-year subperiods for 1980 through 1999. This demonstrated that sub-Saharan Africa’s tendency to overtrade was declining sharply, from nearly 30 percent in 1980–84 to just 5 percent in 1995–99. East Asia’s overtrading declined in the 1980s to 19 percent before increasing again, and South Asia’s undertrading was diminishing. Coe and Hoffmaister (1999) also found that the degree of sub-Saharan Africa’s overtrading was falling over time. Although consistent with these trends, the results may also indicate that the basic gravity model does not fully capture the impact of transport costs on African trade; note that sub-Saharan Africa, along with MENA, is also unusual in terms of its low level of intraregional trade relative to the benchmark. Limão and Venables (2001) find that including direct measures of transport costs in the gravity model absorbs much of the estimated underperformance of intraregional and external trade for sub-Saharan African countries.

The new results are partly attributable to the stronger role of the level of development in explaining trade patterns than previously assigned by the gravity model. The new estimates find a smaller role for GDP and a larger role for GDP per capita than in IMF (2002). As the 2002 study explains, global trade patterns are increasingly driven by the fact that demand for product variety rises with economic growth, and specialization is the most efficient cost structure. Thus consumers in rich countries demand an ever-wider variety of products, which are produced by vertically integrated structures spread across many countries. This link between product demand patterns and trade probably lies behind the rising influence of per capita incomes in the model. The systematic differences by region indicate that regions are differently placed in their ability to take advantage of this kind of trade. However, for trade within sub-Saharan Africa, the variation in level of development is not as dominant because most countries are lower income, so trade values come much closer to the model’s prediction.

Landlocked countries within sub-Saharan Africa have been rising to the benchmark in the past two or three years. However, coastal and resource-intensive groups have remained large undertraders since 2000. Figure 8 breaks down the deviations of observed from predicted trade for each geographic group by year. The performance of landlocked countries trended upward, moving from undertrading consonant with the other groups in 2000 to overtrading by nearly 10 percent in 2004 and 2005.25 No change is evident for the other groups, for which year-by-year gaps hew to the average. The shortfall shows no sign of having narrowed during the commodity export boom, suggesting that much of the growth in trade can be explained by global factors and predetermined country characteristics (for example, whether the country exports fuel).

Figure 8.Sub-Saharan Africa: Undertrading by Geographic Subgroup, 2000–05

(Average difference between actual and predicted trade, in logarithms multiplied by 100)

Source: IMF staff estimates.

Note. Based on a gravity equation estimated on annual data. Regression residuals were multiplied by 100 to express the results as approximate percentage deviations. The interpretation of the signs remains as in Table 8.

The sub-Saharan African groups on average overtrade with East and South Asia and undertrade with Latin America and the Caribbean (LAC) and MENA. Table 12 breaks down the gravity model residuals by sub-Saharan African subgroup and non–sub-Saharan African region. The results reflect the earlier analysis in that the regions with general overtrading—South and East Asia—tend to overtrade with sub-Saharan African subregions as well; the converse is true for undertrading. Not surprisingly, because the two groups have similar endowments, resource-intensive sub-Saharan African countries have significant undertrading with MENA. Significant overtrading between coastal countries and South Asia may partially reflect the presence of ethnic Indian communities in several eastern and southern sub-Saharan African countries.

Table 12.Undertrading in Sub-Saharan Africa, 2000–05(Average difference between actual and predicted trade, in logarithms)
Trade Partners
South Asia0.660.420.14
East Asia0.680.640.85
Latin America and Caribbean–1.20–0.98–0.44
Middle East and North Africa–1.07–0.78–1.32
United States–0.65–0.150.62
High-income countries–0.38–0.25–0.46
Source: IMF staff estimates.Note: See Table 8.
Source: IMF staff estimates.Note: See Table 8.

At the subregional or country level, the sub-Saharan African subgroups have modest undertrading with the EU-15, large overtrading with China, and, except for resource-rich countries, undertrading with the United States. Because the calculations in Table 12 reflect characteristics of a trading pair, they cannot be exclusively interpreted in terms of the sub-Saharan African trading partner.26 For example, sub-Saharan Africa’s large overtrading with China is a reflection of China’s high participation in global trade, although the calculation does plausibly indicate that overtrading is highest with the resource-intensive group. The results for the United States again point to resource-driven trade, although the big difference between calculated undertrading for coastal versus landlocked countries likely reflects the relative success of AGOA in promoting exports from landlocked countries. Trade is quite close to the gravity benchmark for all groups with the EU-15 countries, although the magnitude of the shortfall is largest for coastal countries—which again indicates their lack of participation in global trade despite relatively favorable circumstances.

The boom in sub-Saharan African trade has done little to offset the region’s lack of integration into global trade. Relative to the global pattern, the sharp increase in exports from resource-intensive sub-Saharan African countries has not closed their shortfall in trade compared with countries with similar characteristics in other regions. Similarly, coastal sub-Saharan African countries, the model implies, have not been able to exploit their advantages of lower transportation costs and shorter distance to global markets.

Alternative Estimation Methods

Alternative methods have been proposed for checking the robustness of the findings from the basic gravity model. A key concern with the estimation of the model is the treatment of trading pairs where zero trade flows are reported. These observations are discarded by default in a gravity model because it is expressed in logarithms, and thus a trade value of zero cannot be calculated. Researchers have recommended various procedures for dealing with this problem. One common approach is to add a small positive constant to each zero trade flow so that the logarithm can be evaluated, and then use a Tobit method to account for the bunching of values around this new cutoff value.27 However, other studies question whether the Tobit method is consistent with the underlying interpretation of the gravity model (Linders and de Groot, 2006). They argue that using the Tobit implies that in some cases trade would be negative if it could be observed.28 Alternatively, zero reported trade may represent mismeasurement of actual flows, in which case incorporating them in the estimation runs the risk of bias due to measurement error. One compromise among these various considerations is to use a Heckman model, because it estimates a separate selection equation for the zero-valued (or missing) trade data while leaving open the precise interpretation of why trade is not always observed. The number of such values is substantial: the sample size increases from 31,500 in the least-squares regression to 47,200 when the Heckman method is used. A second alternative allows additional controls for country-pair effects; this is implemented through a random effects panel regression.29

Alternative estimation methods confirm that the gravity model parameters are fairly robust. The Heckman estimates are reported in column C of Table 10 and the random effects estimates in column D. The main challenge in implementing the Heckman method is the need to specify instruments for the selection equation; that is, variables that explain the probability of positive trade flows while being weakly correlated with the level of trade. These are difficult to find because in principle the gravity model itself should encompass all determinants of trade flows. The chosen instruments are the levels of GDP per capita for each trade partner. These variables enter the gravity equation only as a product; arguably, they have a separate role in specifying a minimal level of development for trade to occur, or to be properly recorded. The resulting gravity coefficient estimates are very close to the earlier specification.30 The currency union variable is again negative and is now borderline significant. The Heckman method sheds some light on why this is the case. In the underlying selection equation, which predicts the probability that positive trade flows will be observed, the currency union variable has a strong positive effect. Thus one aspect of being in a currency union is that it makes measured trade more likely, which may reflect the superior data quality when trade flows are being monitored by a regional institution. Conventional least-squares estimates of the currency union effect may therefore compound measurement of trade with the true impact of a common currency, imparting some instability to the parameter as the sample changes. The main difference between the random effects method and the others is the somewhat lower weight it attaches to GDP and the higher weight to a colonial link between countries.

The estimates of undertrading using alternative techniques are also similar to those reported earlier. This is not surprising given the stability of the parameter estimates. The Heckman estimates find undertrading for sub-Saharan Africa of 10.3 percent, compared with 20 percent in Table 11. For East Asia overtrading is now 91 percent, and for South Asia 22 percent. MENA undertrading is 32 percent, whereas the Latin American countries, which had undertraded according to the earlier estimate, now have modest overtrading of 7 percent. The Heckman method also finds that for intraregional trade, sub-Saharan Africa overtrades by 10 percent; this was calculated as slight undertrading using the least-squares method. On balance, therefore, though including zero-valued trade flows does not lead to big changes in magnitude relative to the benchmark, it does produce a slightly improved assessment of sub-Saharan African trade performance. The random effects estimate of global sub-Saharan African undertrading is smaller—about 7 percent—but the direction of the effects is very close to that found by the other estimates. It is likely that the random effects absorb some of the estimated undertrading from the other models into the country effects, thus reducing the gap between actual and predicted trade that needs to be explained.


IMF (2002, Chapter III) provides extensive discussion and references.


The estimation is built on a background study by Rose (2002).


Rose deflates Direction of Trade Statistics data to constant 1982–84 dollars, and his GDP data were taken from World Development Indicators 2000 or the Penn World Tables version 5.6 (Heston and others, 1995) when the former were missing. Baldwin and Taglioni (2006) emphasize that the impact of an inappropriate deflator is magnified in long-horizon regressions.


The dependent variable for the new regressions was calculated slightly differently from Rose (2002). As recommended by Baldwin and Taglioni (2006), it is calculated as the average of log exports plus log imports, rather than the log of the average of exports and imports. Calculations not reported confirm that this change alone makes little difference to the results.


Tsangarides, Ewenczyk, and Hulej (2006) find a currency union effect much closer to the sizable positive effect found by Rose (2002), although they do not report estimates for later subperiods in their sample (1948–2002). Because of indications that large valuation effects induced by euro-dollar volatility affect the post-2000 sample, the regressions include an interaction of country and year effects for euro-linked countries, including those in the CFA zone.


IMF (2002) reported an even smaller coefficient, 0.27, on GDP per capita than that found by Rose (2002).


The regression is based on logarithms of trade and GDP. Thus multiplication by 100 approximates the percentage difference between actual and predicted trade.


This of course does not mean that landlocked countries were outperforming coastal countries, which still have their advantage of better access to global markets. It means that taking account of the poorer access of landlocked countries, their trade performance was relatively good in the later years of the sample.


The calculations of overtrading or undertrading are based on estimated residuals from a regression, and thus are subject to statistical uncertainty. This uncertainty grows progressively larger as the sample size over which the group averages are calculated gets smaller. Standard error bands around the individual country rows in Table 12 would be relatively large.


This is one of the many robustness checks implemented by Rose (2004). Tsangarides, Ewenczyk, and Hulej (2006) discuss the role of the treatment of zeroes and endogeneity of the currency union variable in estimating the impact on trade of currency unions. Estimates that use observations of zero bilateral trade (which the basic gravity model cannot do because it takes logs) deliver broadly similar implications for the impact of currency unions on trade as the least-squares estimates.


The Tobit estimator deals with data on a dependent variable where it is known that a set of values above or below a certain threshold was reported as being at that threshold; for example, a survey that recorded only whether incomes were at least at a certain level. However, a Tobit model with a cutoff at zero (or its replacement value after taking logs) could be interpreted as modeling a range of potential trade values that are not large enough to overcome fixed costs of exporting.


Country-pair fixed effects, as opposed to random effects, are collinear with variables already in the regression that do not vary over time for a country pair (for example, the geographic variables).


Although it is conceptually useful to think of the Heckman method as a two-step approach, the reported estimates come from maximum likelihood estimation of the two equations jointly. The standard likelihood ratio test that the correlation between the error in the selection equation and the regression equation is zero is rejected, indicating that the Heckman method is warranted.

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