2.1. The dependent variable

The variable ${\rm Growth}$ is the dependent variable. This variable refers to the average log-growth of real (PPP in constant dollars) GDP per capita between 1980 and 2014. The Penn World Table 9.0 provides five GDP estimates: here we use real GDP calculated using national accounts growth rates, as recommended for growth regressions by Feenstra et al. (Reference Feenstra, Inklaar and Timmer2015).Footnote ⁸

2.2. The explanatory variables

This paper tries to disentangle resource-abundance effects from resource-dependence ones, in a way that follows Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008). In all our regressions, we consequently include a resource-abundance variable together with a resource-dependence variable as regressors. In addition, we include different variables capturing the institutional quality, the level of investment, human capital and population growth, as well as the initial GDP. All of these explanatory variable are described hereafter.

We use alternatively two indicators of resource abundance (RA). ${\rm RA}_{1}$ is the log of the World Bank subsoil asset natural capital per capita indicator averaged over the period. Natural capital includes the valuation of numerous minerals and fuels. This includes exhaustively bauxite, copper, hard coal, iron, lead, lignite, natural gas, nickel, oil, phosphate, silver, tin and zinc, and is measured as the discounted sum of the value of rents generated over the lifetime of the resource stock. Values are measured at market exchange rates in constant 2014 US$, using a country-specific GDP deflator.Footnote ⁹ ${\rm RA}_{2}$ is the natural resources rents as a share of GDP estimated by the World Bank. Rents are calculated as the difference between the market price of a commodity and its cost of production. We averaged rents over the period to obtain an index of revenues generated by natural resources exploitation in a country during the observation period. While ${\rm RA}_{1}$ may be seen as a measure of the stock value in the ground, ${\rm RA}_{2}$ is an estimation of the revenues generated by such stocks along the period.

Concerning resource dependence, we use three alternative proxies. ${\rm RD}_{1}$ is the average GDP share of mineral exports (the sum of mineral fuels, ores and metal exports).Footnote ¹⁰ The famous work of Sachs and Warner (Reference Sachs and Warner1995, Reference Sachs and Warner1999, Reference Sachs and Warner2001) uses this proxy as a resource abundance variable. Numerous authors criticize this choice and suggest that it is more a proxy for resource dependence (Stijns, Reference Stijns2006; Brunnschweiler and Bulte, Reference Brunnschweiler and Bulte2008; Lederman and Maloney, Reference Lederman and Maloney2008). They also argue that evidence for a resource curse rests strongly on this poor choice. In the present paper, ${\rm RD}_{1}$ is our favorite proxy for resource dependence. ${\rm RD}_{2}$ is the average share of mineral exports in total exports. It shares a lot of characteristics with ${\rm RD}_{1}$ but often leads to somewhat more robust results (Sachs and Warner, Reference Sachs and Warner1995). Those variables are calculated by the World Bank using the Comtrade database (United Nations Statistics Division). ${\rm RD}_{3}$ represents the net exports of mineral resources per worker, averaged over the period. Leamer (Reference Leamer1984) and Lederman and Maloney (Reference Lederman and Maloney2008) recommend the use of this variable to proxy resource dependence. They argue that it is the more appropriate measure of resource dependence according to the Heckscher-Ohlin model of international trade. Moreover, taking the net value of resource exports obviates countries appearing as resource-abundant economies due simply to large imports of raw materials that are immediately re-exported. Singapore is the typical example of such a country (Lederman and Maloney, Reference Lederman and Maloney2008). This variable can be thought of as the resource-dependence variable that is best suited to capture abundance of resources when we do not have resource-abundance variables as such. Fortunately, in the present work, resource abundance is already captured by our RA variables. We thus introduce ${\rm RD}_{3}$ as a resource dependence variable mainly to verify the consistency of our results.

We measure institutional quality using two alternative proxies. Our preferred one, ${\rm Rule}$, is the well-known ‘Rule of law’ indicator popularized by Kaufmann et al. (Reference Kaufmann, Kraay and Mastruzzi2011) which captures the effectiveness of contract enforcement, police and the courts, and the likelihood of crime and violence. We averaged it over the period to better represent ‘average’ institutional quality over the period considered. As an alternative proxy, we use ${\rm GovEffect}$, Kaufmann's et al. (Reference Kaufmann, Kraay and Mastruzzi2011) popular Government Effectiveness indicator. It captures how the people perceive ‘the quality of public services, the quality of the civil service and the degree of its independence from political pressures, the quality of policy formulation and implementation, and the credibility of the government's commitment to such policies’. We use this indicator for robustness check purposes. Both institutional quality measures are obtained through large surveys and take values between $-2.5$ and 2.5.Footnote ¹¹

${\rm Inv}$ is a variable that represents the gross formation of fixed capital, i.e., investments, as a share of GDP. We use the average share of investment over the period. ${\rm human}_{t=0}$ is a measure of human capital. We use the Barro and Lee (Reference Barro and Lee2013) average years of total schooling for people over 25 years old in 1980. ${\rm popgrowth}$ is the annual population growth rate. Finally, initial GDP is introduced following the recommendation in Feenstra et al. (Reference Feenstra, Inklaar and Timmer2015). We thus take log of real GDP in current PPP in 1980. This choice limits the bias that may be introduced by the ‘constant PPP correction’ and is the best measure of initial GDP.

2.3. Instrumental variables

As will be discussed later, and given the specification of the model we estimate, some of the explanatory variables presented above are potentially endogenous and may result in a biased estimates of model parameters. We hereafter describe the instrumental variables we use to tackle this issue. More details on the estimation procedure will be provided in section 3.2.

${\rm pres}_{t=0}$ is a dummy variable for the regime being Presidential (1) or Parliamentary (0). The first entry in 1980 is retained. ${\rm open}$ is a historical trade-openness variable calculated as the average real (current PPP) GDP share of imports and exports over the 1970s. We do not consider previous periods in order to maximize the number of observations in the database. Finally, ${\rm latitude}$ is the country capital's latitude in absolute value, divided by 90 to produce a figure between 0 and 1.

The summary statistics of our dataset are displayed in table 2.

Table 2.

Descriptive statistics

Notes : We provide here the sources where we actually obtain the data.${\rm RD}_1$ refers to the average GDP share of mineral exports. ${\rm RD}_2$ is the average share of mineral exports in total export. ${\rm RD}_3$ represents the net exports of mineral resources per worker. ${\rm RA}_1$ is the log of subsoil asset per capita. ${\rm RA}_2$ is the natural resources rents as a share of GDP. ${\rm Rule}$ is the ‘Rule-of-law’ indicator while ${\rm GovEffect}$ represents the government effectiveness. ${\rm lngdp}_{t=0}$ is the log of real GDP in current PPP in 1980. ${\rm Inv}$ is the investment-to-GDP ratio. ${\rm human}_t=0$ is the average years of total schooling for people over 25 years old in 1980. ${\rm popgrowth}$ represents the annual population growth rate. ${\rm pres}$ is a dummy variable for the regime being Presidential (1) or Parliamentary (0). ${\rm open}$ is a historical trade-openness variable.

3.1. The threshold regression model

We extend the linear model in Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008) by introducing non-linearity. Wealso introduce additional regressors, namely human capital, investment, and population growth, to be consistent with the literature on growth. The main equation in the linear model of Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008) is very similar to the following:Footnote ¹²

(1)$$\begin{align}{\rm Growth}_{i}& =\beta_{0}+\beta_{1}{\rm RD}_{i}+\beta_{2}{\rm RA}_{i}+\beta_{3}{\rm Rule}_{i}+\beta_{4}{\rm gdp}_{t=0,i}+\beta_{5}{\rm Inv}_{i}+\beta_{6}{\rm human}_{t=0,i} \\ & \quad +\beta_{7}{\rm popgrowth}_{i}+\varepsilon_{i}. \end{align}$$

This regression can also be written as:

$$\begin{equation}{\rm Growth}_{i}=\Psi X_{i}+\varepsilon_{i},\end{equation}$$

where

$$\Psi =(\beta_{0},\beta_{1},\beta_{2},\beta_{3},\beta_{4},\beta_{5},\beta_{6},\beta_{7})$$

and

$$X_{i}=(1,{\rm RD},{\rm RA},{\rm Rule},{\rm lngdp}_{t=0},{\rm Inv},{\rm human}_{t=0},{\rm popgrowth})^{\prime }.$$

We look for a possible nonlinear effect of initial GDP per capita (i.e., in the starting period). The choice of the transition variable among the explanatory variables for threshold models is key. In many papers, this choice comes from economic theory. Here we appeal to the literature on convergence clubs to identify initial real GDP per capita as the threshold variable. The idea is to show that there are different growth trajectories, depending on initial GDP. We believe that these differences can be measured by the asymmetry of long-run GDP growth relative to initial GDP.Footnote ¹³ Hansen (Reference Hansen2000) uses initial GDP as the threshold variable in growth regression to distinguish multiple equilibria. This idea was inspired by Durlauf and Johnson (Reference Durlauf and Johnson1995), who suggest that cross-section growth may be determined by initial conditions. Clootens and Kirat (Reference Clootens and Kirat2017) uncover some evidence that countries do react differently to an increase in resource dependence or abundance by their initial level of GDP. We thus consider the following threshold-regression model:

(2)\begin{equation} {\rm Growth}_{i}=\left\{ \begin{array}{c} \Psi ^{1}X_{i}+\varepsilon_{i} \ \ \ if \ \ {\small {\rm gdp}}_{t=0,i}\leq q \\ \Psi ^{2}X_{i}+\varepsilon_{i} \ \ \ if \ \ {\small {\rm gdp}}_{t=0,i}>q \end{array} \right. , \end{equation}

where $\Psi ^{1}=(\beta_{0}^{1},\beta_{1}^{1},\beta_{2}^{1},\beta_{3}^{1},\beta_{4}^{1},\beta_{5}^{1},\beta_{6}^{1},\beta_{7}^{1})$ and $\Psi ^{2}=(\beta_{0}^{2},\beta_{1}^{2},\beta_{2}^{2},\beta_{3}^{2},\beta_{4}^{2},\beta_{5}^{2},\beta_{6}^{2},\beta_{7}^{2})$. The threshold parameter $q$ is considered as unknown. It is convenient to rewrite (2) as:

(3)\begin{equation} {\rm Growth}_{i}=\Psi ^{2}X_{i}+\lambda X_{i}\mathbb{1}_{gdp_{t=0,i}\leq q}+\varepsilon_{i}, \end{equation}

where $\lambda =\Psi ^{1}-\Psi ^{2}$. We want to estimate $\Psi ^{1}$, $\Psi ^{2}$ and $q$ if the null hypothesis of linearity is rejected, i.e., $H_{0}:\ \lambda =0$ in equation (3).

We first examine this null hypothesis of linearity in equation (3), $H_{0}:\ \lambda =0$. Without an a priori fixed value of $q$ in regression (3), it is not easy to carry out statistical inference regarding $\lambda$. In this case $q$ is a nuisance parameter that is not identified under the null hypothesis. Hansen (Reference Hansen1996) avoids this problem via a simulation technique producing a p-value statistic for the inference of $\lambda$. His approach does not require fixing an a priori value of $q$ and allows for possible heteroskedasticity in (3). The calculation of the threshold estimate $\widehat {q}$ uses the concentrated sum of squared errors function from (3):

\[ S(q)=\sum_{i=1}^{N}( {\rm Growth}_{i}-\widehat{\Psi ^{2}}(q)X_{i}-\widehat{ \lambda }(q)X_{i}(q)) ^{2},\]

and the threshold estimate $\widehat {q}$ is the value that minimizes $S(q)$:

\[ \underset{q\epsilon \Gamma }{\widehat{q}=\arg \min }S(q),\]

where $\Gamma$ is a bounded set of elements of $\{gdp_{t=0,i},i=1,\ldots ,N\}$ and can be approximated by a grid (see Hansen, Reference Hansen2000). Finally, the slope estimates in the threshold model (2) can be calculated using $\widehat {\Psi ^{2}}(\widehat {q})$ and $\widehat {\lambda }(\widehat {q})$. Hansen (Reference Hansen2000) and Caner and Hansen (Reference Caner and Hansen2004) have also developed asymptotic-distribution theory for the threshold estimate $\widehat {q}$, and propose asymptotic confidence intervals by inverting the likelihood-ratio statistic. This approach also allows for possible heteroskedasticity in (3).

3.2. Dealing with endogeneity

Endogeneity is a central issue in threshold models. Threshold regression requires the exogeneity of regressors in equation (1), otherwise the estimates will be biased. In their paper, Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008) identify a number of sources of endogeneity.Footnote ¹⁴ For instance, taking institutional quality and resource dependence as exogenous variables may lead to biased outcomes. Institutional quality might be linked to variables such as culture or other omitted variables that also determine growth. Moreover, resource dependence is not a proper explanatory variable in growth regressions. Resource dependence is, to a large extent, determined by the comparative advantage of the resource sector which in turn is determined by government choices. There is little doubt that those choices also determine growth.

Another concern is the exogeneity of the resource-abundance variables. We believe that ${\rm RA}_{1}$ may be reasonably thought of as exogenous. Obviously, the exploration and evaluation of resource stocks is a technologically-intensive process that is not independent of countries’ technological levels. Nevertheless, thanks to their economic potential, mineral deposits have been explored and estimated by large multinational firms regardless of the local conditions. While ${\rm RA}_{1}$ is not free from criticism,Footnote ¹⁵ we believe that it constitutes a significant improvement with respect to the standard measure popularized by Sachs and Warner (Reference Sachs and Warner1995). Our second resource abundance variable $RA_{2}$ is the natural resources rents as a share of GDP. It thus captures the actual rent that has been realized during the period. Broadly speaking, it is calculated as the difference between the resource price and the extraction cost, multiplied by extracted quantities. Finally, the scaling exercise supposes that the rent is divided by the GDP. To some extent, resource prices are determined on world markets and can be seen as exogenous.Footnote ¹⁶ The extraction costs are determined by the deposit quality. Clearly they can also be affected by the level of technology. However, mining deposits are often operated by large multinational firms that have access to the same technology. We thus believe that the unitary rent may reasonably be considered as exogenous. More suspicions can be put on the quantity extracted, and the scaling exercise, which are affected by government decisions. Still, while we acknowledge that this second resource-abundance variable is more prone to generate endogeneity issues, we consider it exogenous, and we use it mainly for robustness check purposes.

The literature has typically used three alternative instruments to control for the endogeneity bias introduced by institutions: latitude, the fraction of population speaking a Western-European language (Hall and Jones, Reference Hall and Jones1999) and the logarithm of settler mortality (Acemoglu et al., Reference Acemoglu, Johnson and Robinson2001). Latitude and the fraction of population speaking a Western language are measures of the extent to which the economy has been influenced by Western Europe, as this was the first area to introduce institutions supporting production. Nevertheless, these variables are not affected by current economic performance.Footnote ¹⁷

According to Acemoglu et al. (Reference Acemoglu, Johnson and Robinson2001), settler mortality is also a good instrument for institutions, as there were various types of colonization ranked from ‘extractive states’ to ‘neo-Europes’ (Crosby, Reference Crosby2004). The feasibility of settlements affected the colonization strategies such that ‘neo-Europes’ appeared where settler mortality was low. As past institutions are a major determinant of current institutional quality, settler mortality seems to be a good instrument for institutions. Here we use latitude to instrument institutions, as it is likely that mineral abundance promoted the establishment of extractive states.

We distinguish two institutional perspectives, following Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008). First, institutions can be seen as persistent constitutional variables (Presidential vs. Parliamentary regimes, electoral rules, etc.) and refer to the ‘deep and durable’ characteristics of a society (Glaeser et al., Reference Glaeser, La Porta, Lopez De Silanes and Shleifer2004). On the other hand, institutions can also refer to the policy outcomes in property-rights enforcement, the fight against corruption and so on (Rodrik et al., Reference Rodrik, Subramanian and Trebbi2004). Our variables ${\rm Rule}$ and ${\rm GovEffect}$ are of the second type, and may be endogenous when used in the second-step estimation. We therefore need to instrument them in a first step.

Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008) show that deep and durable institutions can be used to instrument resource dependence. They use a dummy variable (for the country having a Presidential regime in the 1970s) as a proxy for institutions. Presidential regimes are often associated with public expenditures that are biased in favor of private interests (including the primary sector), as the decision maker does not have to rely on a stable majority. They also show that past trade openness is a good instrument for ${\rm RD}$.Footnote ¹⁸

To avoid endogeneity issues in threshold estimation, we use here the predicted values of the ${\rm RD}$ and ${\rm Rule}$ variables from instrumental equations (or first-step instrumental-variable estimations) instead of their observed values. The instrumentation procedure that we use here follows that in Brunnschweiler and Bulte (Reference Brunnschweiler and Bulte2008).