RDP 2004-11: Trade Openness: An Australian Perspective 3. The Openness Equation

The above analysis suggests that the gravity model can yield contrasting answers when used to consider the question of whether countries trade more or less than would be expected, based on a number of economic and geographic variables that are important determinants of trade. These conflicting results suggest that it might be instructive to consider other approaches to the question of explaining the total level of a country's trade. Accordingly, in the remainder of this paper we estimate equations for total trade using data for 1971–2000. However, our interest is not in explaining the nominal value of countries' trade, but the level of their trade relative to their GDP. We therefore estimate an equation for openness – defined as exports plus imports as a proportion of GDP.

3.1 Specification

Theory provides only very limited guidance as to the type of equation that could be expected to explain the openness of countries: we are aware of no general theoretical model explaining openness. However, individual authors have proposed particular effects that we should expect to find in the data. For example, models of differentiated goods and increasing returns to scale suggest that countries will specialise in particular goods, and the amount of trade they undertake will be inversely proportionate to their size. In a world with no barriers to trade and where all goods are both final and tradable, a country which represents x per cent of world production would have imports and exports each equivalent to 100–x per cent of GDP (see, for example, Haveman and Hummels 2004). Alternatively, in a highly stylised Heckscher-Ohlin world (with constant returns to scale), Leamer (1988) shows that in the absence of barriers to trade, openness ratios should be a function of ‘resource distinctiveness’ or the ‘peculiarity of the resource supply vector’. Given data limitations, it is not clear that this notion can be seriously tested. More generally, problems of data availability preclude us from including some of the resource endowment variables that might be suggested by trade theory, but we make some modest attempts to include such variables in our robustness tests.

Instead, our empirical model for openness draws on many of the insights of earlier empirical work with the gravity model. We conjecture that openness will be related to various economic, geographic and policy factors. We do not claim to be estimating a structural model and are aware that causality between the left-hand-side variable and right-hand-side variables may go in both directions, and that there may be causality between the right-hand-side variables.^[8] Nor do we test any specific theoretical model of international trade. Instead, the regressions should be interpreted as an attempt to identify which variables are most correlated with the openness of countries. The relative paucity of work explaining the openness of countries suggests that such an exercise may be worthwhile.

We begin by proposing a fairly parsimonious equation with five explanatory variables. The selection of variables is based largely on the availability of data and our desire to maintain as large a sample size as possible. Three of the variables can be viewed as possible economic or geographic determinants of openness: the population and total area of each country, and the level of economic development (using GDP per capita as a proxy). The two other variables are measures of the existence of either natural or policy-induced barriers to trade: we use a measure of the location of each country relative to economic activity in the rest of the world as a proxy for natural barriers to trade and a trade-policy index as a proxy for policy-induced barriers.

Besides the trade-policy measure, all the variables are in logs, and the equation estimated is:

The openness, area, population and GDP per capita variables are defined in the usual manner.^[9] The economic location and trade-policy variables are specifically constructed and are described in greater detail below.

The most straightforward definition for an economic location variable would be a simple weighted-average of distance to all possible trading partners, termed remoteness:

where distance is the Great World Circle distance (the shortest path following the surface of the globe) between the capital cities of two countries, J is the sample of countries, i is the home country, j is the potential trading partner, and w_j is the weight of country j in world GDP (excluding the GDP of country i).^[10] This variable for the average distance to all potential trading partners has a mean value of 8,320 kilometres for the 172 countries for which it can be constructed. It shows western European countries to be the least remote, with weighted-average distance to potential trading partners as low as 5,500 kilometres. By contrast, Australia and New Zealand are shown as the most remote countries, with an average distance to potential trading partners of 13,700 and 14,000 kilometres respectively.^[11]

However, a transformation of the gravity model (see, for example, Ewing and Battersby 2003) suggests an alternative measure of remoteness, which we term economic location, which is given by:

The variable α in Equation (4) corresponds to the absolute value of the coefficient on the distance term in a gravity model (β₂). Most empirical estimates put β₂ between about −0.5 and −1.0 (Disdier and Head 2003). In preliminary regressions the overall fit of the equation was little different with values for α of 0.5 and 1.0, so for simplicity all the estimated equations use α equal to 1.0. Given that it uses the reciprocal of distance, countries with a more favourable economic location (that is, closer, on average, to the rest of the world) will have a higher value. As such, we expect this measure of economic location to be positively related to openness.

The trade-policy variable was constructed from the trade-policy component of the Economic Freedom of the World Index produced by the Institute for Economic Freedom (IEF). The IEF's summary measure is based on five separate indicators of countries' openness to trade. However, one of these – the ratio of actual trade to predicted trade (based on a simple openness equation)^[12] – is clearly inappropriate for inclusion in our openness regressions, and is accordingly omitted. Therefore, our measure of trade policy is the average of four components – taxes on international trade, the existence of regulatory trade barriers, the difference between the official and black market exchange rates, and the existence of international capital controls.^[13] We calculate a simple average (the same method used for the composite index) of these four components. The index is available at five-year intervals from 1970 and scaled from 1 to 10; a higher score indicates a more liberal trade regime.^[14]

3.2 Empirical Analysis

To simplify the analysis and reduce the noise in annual trade data, the thirty years of data (1971–2000) are averaged over six five-year time periods: 1971–1975, 1976–1980 and so on. We estimated regressions for each of these time periods and also estimated a pooled cross-section regression with the full sample of countries available in each time period.^[15] Time dummies were included for the last five time periods. Dummies are also included for Hong Kong and Singapore in each regression. As re-exports are a significant proportion of their total trade, the openness ratios for these countries will be substantially higher than for other countries (315 per cent and 273 per cent for average 1996–2000 respectively, the two most open countries in our sample).^[16] The results of the regression are reported in Table 2.

The results in Table 2 are encouraging. All five variables are significant at the 1 per cent level in the pooled cross-section regression, and most are significant in the individual cross-sections.^[17] With the possible exception of the result for GDP per capita (which is considered in detail in Section 3.3), the parameter estimates have the expected sign in the pooled cross-section and all individual cross-sections.

The coefficient values on the time dummies (not shown) are significant and increase over time, consistent with the general increase in openness over time. The Hong Kong and Singapore dummies (not shown) are also consistently significant.

Although the decline in adjusted R² over time is puzzling, the overall fit of the regression is quite good.^[18] Yet, unlike the case of the gravity model, the goodness of fit of the openness equation is not boosted by a scale effect from nominal GDPs. Indeed, if we reformulate the openness equation with country trade as the dependent variable, and country GDP as one of the independent variables, the adjusted R² jumps to around 0.96 in each of the cross-section regressions, which is higher than the normal bilateral gravity model (albeit on a different regressand).

We now discuss the parameter estimates, in order of their marginal significance in the pooled cross-section regression. The most important variable in explaining openness is population. Countries with smaller populations have higher levels of external trade (relative to GDP), presumably because they have fewer opportunities for within-country trade.

The second most important variable is economic location, which has a positive coefficient. Countries which are located closer to the rest of the world tend to trade more and be more open than countries with a less favourable location, presumably for the same reasons that the distance variable in the gravity model has a negative sign.^[19] Indeed, Clark, Dollar and Micco (2004) note that, with the decline of regulatory trade barriers such as tariffs, transport costs may in many cases now represent a larger effective rate of protection than trade-policy restrictions. However, it is sometimes argued that as transport costs have declined over time the negative impact of distance on trade should have fallen over time. To test for this, we interacted our economic location variable with time dummies and found that the impact of the location variables fell by 0.04 between 1971–1975 and 1996–2000. These results suggest that an unfavourable economic location is having a smaller detrimental effect on trade over time, which is consistent with declining transportation costs. On the other hand, the results from the individual cross-sections suggest the opposite conclusion. Similarly, other work investigating the ‘death of distance’ (e.g., Coe et al 2002, and Disdier and Head 2003) also finds conflicting results.

The third most important variable is our measure of trade policy. The variable takes the expected sign, and indicates a positive correlation between the degree of liberalisation of a country's trade-policy regime and how much it trades. It seems reasonable to expect that much of the causality runs from trade policy to trade – that a liberal trade regime stimulates trade. However, it is possible that there is also some reverse causation. For example, countries with high levels of trade may have constituencies pushing for low trade barriers. Alternatively, to the extent that trade is a potential source of budget revenue, countries with low trade levels might levy higher taxes on trade.

The parameter estimates on the per capita GDP variable are always negative, but sometimes not significant in individual cross-sections. The negative sign suggests that countries with larger per capita GDP tend to have a lower level of openness. This is contrary to the conventional wisdom that much trade is intra-industry or in differentiated products, that rich countries do more of such trade, so rich countries trade more. Gravity model researchers typically summarise their finding that per capita GDP has a significant positive sign to the effect that ‘richer economies trade more’ (see, for example, Frankel and Wei 1998, p 193, and Rose 2004, p 103). Our finding is also contrary to the result in the basic gravity model in Table 1. We consider this result further in the next section.

The least significant variable in the regression is total area. Similar to the results of the gravity model, there is a negative relationship between total area and openness, confirming that geographically larger countries are less open. In some respects this may appear somewhat counter-intuitive. In particular, holding population constant, population density falls as area rises, and the costs of internal trade increase. This might be expected to increase the level of external trade: it becomes more likely that people on one side of a country will trade with a neighbouring country rather than their own countrymen. However, this effect is clearly dominated by other factors, and an obvious one is that countries that are geographically larger may have a wider range of resource endowments and climatic variation, and so are able to produce a more diversified range of products internally and thus have less need for external trade.

3.3 The Relationship between GDP Per Capita and Openness

As noted, the finding that GDP per capita has a negative relationship with openness is somewhat unexpected. In this section we examine some possible explanations for why our result differs from the conventional wisdom.

We first consider the possibility that the conventional wisdom is flawed because it ignores one or more important omitted variables. Column (1) of Table 3 shows that the correlation between openness and GDP per capita is significantly positive in a simple regression that also includes the dummy variables for time, Hong Kong and Singapore. However, the explanatory power of GDP per capita for openness is fairly modest: when it is added to a regression already including the dummy variables the adjusted R² increases only from 0.17 to 0.20. Furthermore, the coefficient on GDP per capita falls close to zero when population, economic location and total area are added to the regression, as is shown in column (2). And when the trade-policy variable is added to the regression (column (3)), the coefficient on GDP per capita turns negative and significant. These results suggest that after controlling for some other important determinants of openness, notably trade policy, there is no evidence that richer countries tend to trade more than poorer countries.^[20]

The results from the gravity model provide further evidence on this point. Column (2) of Table 1 shows the parameter estimates from a standard gravity model which also includes a variable for the average of the trade-policy variables for each country pair.^[21] The parameter estimate on this additional variable is positive and significant at the 1 per cent level. Furthermore, the coefficient on the product of GDP per capita is now only significant at the 10 per cent level and falls from 0.19 to −0.03. This strongly suggests that the relative restrictiveness of trade policies is an important variable in explaining bilateral trade outcomes. In addition, after controlling for differences in trade-policy regimes, there is no evidence from the gravity model that countries with higher GDP per capita tend to trade relatively more than countries with lower GDP per capita.^[22]

A second possible explanation is that the result for GDP per capita reflects the use of market exchange rates in calculating the openness ratio. While it is conceivable that the price of tradables across countries will approximately follow the law of one price, there is ample evidence that this does not hold for the price of non-tradables. In particular, non-tradable prices tend to be substantially lower in developing countries than in developed countries (see, for example, Kravis, Heston and Summers 1982). To illustrate the implications for openness ratios, assume that all economies produced the same proportion of tradable and non-tradable goods. However, the fact that non-tradable prices are lower in developing countries will mean that the value of the non-tradable sector will be lower, which will reduce their GDPs measured at market exchange rates and boost their openness ratios relative to developed countries. This would result in a negative coefficient on per capita GDP.

To test for this, we included a variable in the pooled cross-section regression for each country's price level relative to the US, taken from the Penn World Tables. The results are shown in column (4) of Table 3. As expected, the price level variable takes a negative sign: countries with a higher price level have lower openness, presumably because price level effects boost their measured GDP. Furthermore, after controlling for price levels, the coefficient on GDP per capita becomes positive.

To check the robustness of this result, in column (5) we replace GDP per capita measured at market prices with a purer measure of real incomes from the Penn World Tables, namely real income (measured relative to the US) with all output measured at PPPs. The parameter estimates again show a strong negative coefficient on the price level variable. The coefficient on the alternative income level variable is negative, but only significant at the 10 per cent level. Overall, we conclude that the use of market exchange rates in calculating GDPs and openness ratios is a significant factor in the finding that openness is negatively related to GDP per capita.^[23]

Finally, we investigated the possibility that the negative coefficient for GDP per capita masked the existence of a non-linear relationship by adding a GDP per capita squared term to the basic regression (including the country price level variable). The results from this regression are reported in column (6) of Table 3. Both the linear and squared terms are significant at the 1 per cent level. The positive coefficient on GDP per capita and negative coefficient on GDP per capita squared suggest that the relationship between openness and GDP per capita is indeed non-linear, approximating an inverse U shape.^[24]

These results suggest that, to properly understand the relationship between economic development and openness, it is necessary to also allow for the relationship between trade policy and openness, as our initial specification does. In addition, the results suggest that it is important to account for the impact of a country's price level on its measured openness ratio and for possible non-linearity in the relationship between openness and GDP per capita. As such, both of these variables are included in the robustness checks reported in the next section.

3.4 Robustness Checks

To further examine the robustness of the above results, a number of geographical variables and policy variables were added to our basic regression. In addition, we also attempt to test, albeit crudely, for the impact of variables measuring resource endowments.

3.4.1 Geographical variables

We include several variables to test for the effects of a country's own geography and its position in the world on its level of trade, and also to assess the robustness of the correlations identified in Table 2. The results from these tests are shown in Table 4 and they indicate that the coefficients and significance of our key variables are robust to the inclusion of the additional variables.

First, since numerous authors (see, for example, the literature on regional trading blocs in Frankel 1998) have argued that there are regional effects in the level of trade, we included separate dummies for the major regions of the world. Column (2) of Table 4 shows the results with the two most significant dummies: east Asia, which has higher than expected openness (even after the inclusion of the dummy variables for Hong Kong and Singapore) and central and South America, which has lower than expected openness. The significance of these regional dummy variables suggests that there are some common factors which are not captured by the variables in the basic equation. However, the inclusion of the most significant regional dummies increases the adjusted R² by only 0.05. Together with the fact that the parameter estimates are mostly little changed following the inclusion of regional dummies, this suggests that the regression based purely on economic, geographic and policy variables is doing a reasonably good job in explaining the openness of countries.

Second, following the tradition of the gravity model, we included a dummy variable for whether a country is landlocked. A number of studies, including Limao and Venables (2001), have shown that the per-kilometre cost of land freight is far higher than the equivalent cost of shipping, implying that landlocked countries face higher transport costs in foreign trade because of their absence of seaport facilities. Hence, the expectation is that the parameter estimate on this variable would be negative, with landlocked countries less open than countries with a coastline. The results show that this dummy was indeed significant and negative, but again, did not disturb the parameter estimates for the core variables (column (3) in Table 4).

Our third variable is motivated by the fact that Rodriguez and Rodrik (2001) have shown in another context – the relationship between trade and growth – that crosscountry empirical results can be extremely sensitive to the inclusion of a variable for the proportion of land in the tropics. The coefficient on this variable was significant, but the coefficients on the other variables were robust to its inclusion (column (4) in Table 4).^[25]

Fourth, to further examine the importance of a country's position in the world for its trade, we added a variable for the average trade-policy liberalisation of a country's natural trading partners. The measure is a weighted average of the trade policy of all other countries, with weights that are highest for nearby and large countries. The variable is calculated as:

where w_j is defined (as in Equations (3) and (4)) as the weight of country j in world GDP (excluding the GDP of country i). Although the expectation is that this variable should show a positive sign – countries should trade more if their larger neighbours have liberal trade regimes – the parameter estimate was negative and significant at the 5 per cent level.^[26]

3.4.2 Policy variables

Our second set of robustness checks examined the impact of a country's economic and other policies on its trade. The results are reported in Table 5. We first test the possibility that the significance of the trade-policy variable might be acting as a proxy for broader aspects of policies or institutions. Accordingly, we tested the significance of a variable that measures the overall quality of a country's legal and property rights (taken from the IEF's Economic Freedom of the World Index). This variable is indeed quite highly correlated with our trade-policy measure, with a correlation coefficient of 0.64. Column (1) of Table 5 reports the results of our basic pooled cross-section regression. Column (2) reports the results also including the legal and property rights measure, which is found to be positive and significant at the 10 per cent level. In column (3), we drop the trade policy measure and just include the legal and property rights measure. The measure is positive, as expected, and significant at the 10 per cent level. Yet comparing columns (1) and (3) strongly suggests that trade policy has a greater impact on openness than institutional factors such as legal and property rights.

In addition, we tested for a relationship between the quality of a country's transport infrastructure and the level of its trade. Limao and Venables (2001) and Clark et al (2004) show that port inefficiency is a major component of transport costs and is accordingly associated with lower levels of bilateral trade in gravity regressions. The data we use is for the quality of transport infrastructure from the World Economic Forum's Global Competitiveness Report, which provides measures of port and air transport infrastructure quality. The measure takes values from 1 (least efficient) to 7 (most efficient). The prediction is that the parameter on these variables will be positive, with more efficient infrastructure (and low transport costs more generally) being associated with higher trade. The 1998 Report contains data for 51 countries in our sample. We imputed values for a further 29 countries using the data from 2002–2003 Report.

When the two infrastructure measures are added to the basic regression for 1996–2000 (columns (5) and (6)), both measures are significant. This is not surprising: efficient transport infrastructure presumably boosts trade, though the correlation between these variables may go both ways, since countries which trade heavily have greater incentives to improve their infrastructure.

3.4.3 Resource endowment variables

In the final set of robustness checks, shown in Table 6, we look for any evidence that the openness of countries is influenced by their resource endowments. The rationale for this is the idea noted above that in a Heckscher-Ohlin world, the amount of a country's trade should be related to its' ‘resource distinctiveness’ or the ‘peculiarity of the resource supply vector’. For example, countries with ‘balanced’ resource endowments might be able to meet many of their needs internally and might not trade much. By contrast, countries with resource endowments that are very different from the average may trade intensively, importing to get access to goods that they cannot produce internally, and exporting goods which are intensive in those factors in which they are abundant. To give effect to this, all of our measures of resource endowment are expressed as absolute deviations from the mean. The rationale is that countries with an abundance of a particular resource will trade more (exporting the surplus), as will countries with a relatively small supply of the resource (as they import to offset the particular shortage).

It is clearly difficult to find suitable variables to represent differences in resource endowments, so the variables used are necessarily imperfect.^[27] Our first measure of resource endowments is a variable for the amount of land suitable for agriculture on a per capita basis (expressed as the absolute difference in a country's ratio from the mean ratio). While the coefficient is positive as expected, it is not significant.

Our other resource endowment variables attempt to capture the impact of absolute differences in labour or capital endowments on trade (and are also expressed as deviations from the mean of the sample). We would expect trade to be greater for countries with either a very high capital-labour ratio (which should export capital-intensive goods) or a very low capital-labour ratio (which should export labour-intensive goods). Consistent with this, the estimated coefficient is positive and significant at the 1 per cent level. Similarly, the absolute difference in human capital per worker (relative to the mean) is also positive, although it is not significant. Surprisingly, the coefficient on the average years of secondary schooling of the population aged over 25 (expressed as the absolute deviation from the mean) was estimated to be negative, although not significant.

Overall, the empirical results provide only limited evidence for a role for resource endowments in influencing openness. Although three of the four parameter estimates take the expected sign, only one is significant. This may reflect the relatively crude nature of the measures of resource distinctiveness, but our results are consistent with a range of earlier work (see, for example, the summary in Davis and Weinstein 2001) showing that the data provide limited support for models of trade that are based on resource differentials.

Footnotes

The standard approach to draw out causal effects in these circumstances would be to use instrumental variables, but it is unclear that suitable instruments (for example, variables that influence trade policy but do not influence trade) exist. [8]

The use of the log of openness seems appropriate given its distribution – bounded below at zero with no upper bound due to the existence of entrepôt trade. In addition, the Box-Cox test suggests that the log functional form is preferable to the linear form. The data are in current US$ and taken from Penn World Tables 6.1, as are the data for GDP per capita and population. Area is defined as the total area (land and water) of a country in square kilometres, taken from the Central Intelligence Agency World Factbook. [9]

Consistent with common practice in gravity model regressions, Chicago was used as the ‘capital’ for the United States and Shanghai for China. The GDP data used to calculate the various remoteness/economic location measures, measured by market exchange rates, were taken from the IMF World Economic Outlook Database as it has greater coverage than the Penn World Tables. [10]

These values are somewhat higher than Ewing and Battersby (2003, p 21) who report remoteness for Australia and New Zealand of 10,183 and 12,312 kilometres, respectively. The difference appears to be due to our use of GDP measured using market exchange rates and their use of GDP measured at purchasing power parities (PPPs), which markedly increase the weight of China and India in world GDP so that Australia appears less remote. Since market exchange rates determine countries' ability to purchase goods and services in international trade, the former is a more relevant weighting system for explaining current levels of trade. [11]

The independent variables in the openness equation used by the IEF are remoteness, population, total area, length of coastline, a dummy for landlocked countries, and time dummies. In the results that follow we include two additional determinants of openness (the trade-policy regime and level of economic development) and a location variable that is theoretically and empirically preferable to a simple remoteness variable. [12]

All measures are cardinal and based on quantitative assessment: a detailed discussion of the variables is available at <http://www.freetheworld.com/2003/1EFW2003ch1.pdf>. [13]

We include the 1970 value of the trade-policy variable in the 1971–1975 regression, the 1975 value in the 1976–1980 regression, and so on. Some early values of this variable were missing and were imputed using a regression of the index against its value in the next period. The results were robust to a ‘nearest neighbours’ imputation and also to using regional averages. For the 1971–1975 cross-section, 31 of 101 observations were imputed; the number of imputations falls moving forward. [14]

An alternative approach would be to estimate across time with a fixed-effects panel: this effectively involves country-specific dummy variables for every country. However, such an approach is problematic as one of our variables (total area) is constant over time, while the others change only slowly over time. As a result, it is either impossible or difficult to get good parameter estimates for the explanatory variables in a fixed-effects panel. Our compromise is to include dummy variables for only those two countries (Hong Kong and Singapore) which are clearly special cases. However, it should be noted that the coefficient estimates for the variables that can be estimated in a panel regression (population, GDP per capita, economic location and trade policy) are quite similar to the coefficient estimates we obtain from the pooled regression. [15]

The standard test for identifying outliers, the Welsch and Kuh DFITS test, suggests that Singapore was an outlier in all six of the cross-section regressions and Hong Kong in four. No other country showed up as an outlier in more than two of the cross-sections. [16]

The fact that total area is not strongly significant in any of the cross-sections and that GDP per capita is significant in only some of the cross-sections appears to be the result of the relatively low sample size in the individual cross-sections: it is noteworthy that the parameter estimates for the different cross-sections are fairly similar. [17]

The adjusted R2 of our equations is substantially higher than the values of around 0.30–0.40 obtained by Jansen and Nordås (2004): the difference appears to largely reflect our inclusion of variables for economic location and total area. [18]

See Venables (2001) for an overview of the role of location in influencing trade, and Anderson and van Wincoop (2004) for a survey of work on trade costs, broadly defined. [19]

This finding is consistent with some other recent research: see, for example, Anderson and Marcouiller (2002) and De Groot et al (2004). [20]

The trade-policy variable is not available for 53 of the 173 countries in the Rose database. To preserve the same sample used in column (1) of Table 1 we interpolate the missing values based on the average value of the trade-policy variable for the region where the country is located. We obtain very similar results – the significance of the per capita GDP variable disappears entirely – when we use a smaller sample of the 120 countries for which our trade-policy variable is available. [21]

Jansen and Nordås (2004) find a similar result for gravity models that include a variable for the average bilateral tariff rate. [22]

An additional explanation for the negative correlation between GDP per capita and openness might be that the non-traded sector (especially the services sector) is larger in developed economies. Unfortunately, this proposition cannot be tested directly, due to the unavailability of cross-country data on the size of the services sector. However, as government expenditure is predominantly in the non-traded sector (Froot and Rogoff 1991), we attempted to test for the importance of this sector by reformulating the openness ratio excluding government from the calculation of GDP in the denominator. However, the parameter estimate on per capita GDP was little changed. Subject to the caveat of the imperfect proxy for the non-traded sector, we tentatively conclude that this is less of a factor in affecting openness ratios than the other factors identified. [23]

We also tested for the existence of a non-linear relationship between openness and the other explanatory variables, but the evidence is much weaker. [24]

The data are from the Centre for International Development at Harvard University, and are available at <http://www.cid.harvard.edu/ciddata/ciddata.html>; a few missing values were filled in. We also separately included a variable capturing a country's distance from the equator: not surprisingly, the coefficient was negative (and significant), although the estimates for our main variables were robust to its inclusion. [25]

We also tested for the significance of the variable for the proportion of world GDP in any free trade agreements to which a country belongs. The parameter estimate was positive, as expected, although not significant. [26]

The data for the proportion of arable land are from the CIAWorld Factbook; the data for the capital-labour ratio are from Penn World Tables 5.6; the data for human capital per worker are from Hall and Jones (1999); and data for average years of secondary schooling are from the Centre for International Development at Harvard University. [27]