2.1. Theoretical background

When modelling a renewable natural resource in an endogenous growth model, we find a substantial literature dealing with limited natural resources in growth theory (for example Barbier, Reference Barbier1999; Chambers and Guo, Reference Chambers and Guo2009). Several contributions base their model on the AK model. The AK model incorporates the aggregate production Y of the representative producer i with capital K that can be expressed as:

(1) $$Y_i = AK_i$$

where A is the marginal product of capital. Barbier (Reference Barbier2004) considers water as a public non-excludable good subject to congestion. He introduced a basic model of growth that can be represented as:

(2) $$Y_i = AK_i f(\hbox{water withdrawal}),\,\hbox{where}\,f^{\prime} \gt 0\,\hbox{and}\,f^{\prime \prime} \lt 0. $$

Economists widely use the Cobb–Douglas model with natural resources to illustrate the diminishing returns of capital. Bretschger and Smulders (Reference Bretschger and Smulders2007) also used the Cobb–Douglas framework to decouple growth from environmental degradation. We can use the Cobb–Douglas function as:

(3) $$Y = AK^{\alpha_1}L^{\alpha_2} W^{\alpha_3} P^{1\hbox{-}\alpha_1\hbox{-}\alpha_{2}\hbox{-}\alpha_{3}} $$

where W is the water resource, K is the capital, L is labour, P is water pollution, A is the total factor productivity and the production coefficients of the Cobb–Douglas production function are expressed as α _i , with i = 1, 2, 3 and the constraint $\sum \alpha_{i}= 1$ .

Assuming water is the only additional factor of production in the economy, and S is the stock of a renewable natural resources, the dynamics of the renewable water resources can be represented by $\dot{S} = \eta_{S}\lpar S\rpar - W$ , where η _S (S) is the rate of water generation; if consumption is greater than this rate, then the stock S declines and tends to reach zero, S → 0. But if consumption is less than the generating stock, then the stock of water resources increases. Bretschger and Smulders (Reference Bretschger and Smulders2007) commented on the concept in this model as it helps to illustrate the diminishing returns of capital and that there is a substitution between capital and pollution. The average productivity of capital per unit of output, together with the impact of extracted water and the pollution accompanying output, can be expressed as:

(4) $${Y \over K} = A \left({L \over K} \right)^{\alpha_2} \left({W \over K}\right)^{\alpha_3}\left({P \over K} \right)^{1\hbox{-}\alpha_{1}\hbox{-}\alpha_{2}\hbox{-}\alpha_{3}}\,\hbox{where}\,0\,\lt \alpha_{1}, \alpha_{2}, \alpha_{3}. $$

Owing to input substitution, the productivity of capital in the economy increases with water consumption, and is affected by pollution.

In our empirical model we are going to construct a linear model. The focus of the paper is on the empirical work rather than constructing a theoretical model. Nonetheless, the model does build on others in terms of the non-environmental variables we include. In the Romer–Stiglitz model of endogenous growth, resource scarcity and population growth determine the optimal level of ‘balanced’ growth for an economy. This endogenous growth literature has, in general, not been concerned with the contribution of natural resources to growth. However, Barbier (Reference Barbier1999) builds onto this the possibility of resource availability constraining the supply of innovation. To this we add considerations of the pollution of that resource.

2.2. The empirical model

Bretschger and Smulders (Reference Bretschger and Smulders2007) emphasized that the dynamics of the depletion of natural resources needs to be researched by natural economics. Our main interest is to explore the effect of water utilization and water quality on economic growth and GDP itself across countries. We analyse the role of the ratio of water utilization and water quality in endogenous economic growth. Water is expressed in the model as both the ratio of water utilization, which stands as a proxy for water scarcity,Footnote ¹ and as water quality, which stands as a proxy for the value of wastewater treatment. The ratio of water utilization is calculated as:

(5) $$\rho = {\hbox{Water withdrawal per capita} \over \hbox{Renewable water resources per capita}}. $$

The concept of water utilization intensity is not new; it was introduced by the United Nations Food and Agriculture Organization to classify areas that may be subjected to water shortages in the future (FAO, 1996; Sullivan, Reference Sullivan2002). The ratio of water utilization that stands for the scarcity of water is used by Barbier (Reference Barbier2004) as an indicator of relative water demand, and as a conceptual indicator of the amount of water utilized with respect to the available water resources in the economy. In addition to water utilization, we want to explore the effect of water quality on growth and GDP per capita; to apply this exploration we add biological oxygen demand (BOD) to our model.

Water quality/pollution is conceptually represented by BODFootnote ² in terms of kg per day. Both Crapanzano et al. (Reference Crapanzano, Pavan, Hunt, Markandya and Tamborra2005) and Barua and Hubacek (Reference Barua and Hubacek2008) use this as an indicator of water quality. Higher values indicate greater pollution. The reasons for using this indicator are many. An important one is the availability of credible data from the World Bank database. Another is, as already noted, the popularity of this indicator in much of the literature concerned with water pollution. Scientifically, BOD is used as an assessment of the damage caused by water pollutionFootnote ³ ; it reflects the quality of water. The costs of water treatment in general are shared among all of the economic sectors. However, BOD reflects only organic pollution and excludes the chemical and thermal causes of pollution (Crapanzano et al., Reference Crapanzano, Pavan, Hunt, Markandya and Tamborra2005). Nonetheless, it still measures an important aspect of water quality. Moreover, Gürlük (Reference Gürlük2009) does find a nonlinear relationship with GDP per capita, but fails to test for nonlinearity. The biggest sector impact on BOD in most countries is food, followed by textiles, paper and pulp, and chemicals. Apart from chemicals, these are found in all types of countries and hence, on these grounds, there is no obvious reason to link BOD with the level of development of a country. Nonetheless, this relationship between pollution and GDP per capita is one that warrants further analysis.

Generally, water quality here stands as a proxy for the value of waste- water treatment, which Briscoe (Reference Briscoe1996: 185) suggests measures the value of environmental quality. The water pollution variable reflects the waste accumulation and the irreversibility of the damage taking place in the environment and the ecosystem (Smulders, Reference Smulders and van den Bergh1999). Specifically we argue that pollution is bad for growth. Water is a factor of production, water pollution impacts adversely on the quality of this input and will, we argue, reduce both growth and GDP itself. Much of the previous literature linking water and economic growth neglected pollution. Thus they also ignored the depletion of natural resources during the modelling of economic growth, which contributed to the failure of water development projects whose effect on growth is one of the main dimensions of the environmental Kuznets curve (EKC). However, in modelling long-run endogenous growth under optimal policy designs, Mohtadi (Reference Mohtadi1996) used the environment as a factor of production in both the utility and the production functions. In doing so, he established that the optimal growth of any country is directly affected by environmental policies and regulations.

To set up the model, following the literature, the ratio of water utilization ρ (Barbier, Reference Barbier2004) and BOD as an indicator of water quality (Barua and Hubacek, Reference Barua and Hubacek2008), are used. Both are included in a quadratic form. The inclusion of ρ as a quadratic follows the approach of Barbier (Reference Barbier2004). It allows for either a flattening (or less likely, an explosion) of the curve, or a turning point. This can be regarded as incorporating both the direct and indirect effects of these variables on growth. The indirect effects come via their influences on other variables that consequently impact growth. It is to these that we now turn.

The analysis of growth encompasses a wide literature that analysed growth for different purposes. The additional explanatory variables here are chosen to increase the robustness of the analysis. Several elements of the literature (for example, Levine and Renelt, Reference Levine and Renelt1992; Sala-I-Martin, Reference Sala-I-Martin1999) explored the variables that are important determinants of growth. As we are examining growth, the explanatory variables widely used in the previous literature as affecting growth should also be included in our considerations. We chose these variables based on the availability of credible data that covers a sufficiently long period of time (1960–2009), and a substantial pool of countries that represent different continents and income per capita. These variables are included in a matrix X in the following equation:

(6) $$\hbox{Growth}_{it} = \beta_{0} + \beta_{1} \rho_{it} + \beta_{2} \rho_{it}^{2} + \beta_{3} \hbox{BOD}_{it} + \beta_{4} \hbox{BOD}_{it}^2 + \beta_5 \hbox{X}_{it} + \varepsilon_{it} $$

where i denotes the country and t time, and ε is a white noise error term of the regression. X _it includes GDP per capita, scholar primary enrolment, and scholar secondary enrolment. The first and second school enrolment rates variables are used as proxies for human capital; these variables have been used based on the original year to represent the initial stock of capital (Barro, Reference Barro1991; Sala-I-Martin, Reference Sala-I-Martin1999; Temple, Reference Temple1999; Barbier, Reference Barbier2004). School enrolments are used here as conceptual indicators to proxy the impact of human capital on growth.

We also include the impact of governance factors, including the political situation in individual countries. As for political and civil liberties, the higher the degree of democracy in the society, the greater the influence of the interest groups that focus on environmental protection and sustainability (Shafik and Bandyopadhyay, Reference Shafik and Bandyopadhyay1992). Democracy and good governance may, for example, act as a stimulus to innovation and investment, thus stimulating growth. The indicators that reflect political influence are an index of political rights that measures the rights to free elections, and the rights to the existence of different political parties, as well as the decentralization of the official power. Hence, we choose the variables corruption and political rights index. Corruption is used as an assessment of corruption within the political system.

In exploring the link between economic policy and environmental quality across countries, Shafik and Bandyopadhyay (Reference Shafik and Bandyopadhyay1992) argue that an open economy in higher income countries focuses on capital intensive, and consequently, more pollution-intensive activities, whereas an open economy in low income countries is more concentrated on labour intensive, and consequently, less polluting activities. At the same time, openness and competition tend to increase the investment in innovation and technology and thus stimulate growth and GDP. In our analysis we use trade as a percentage of GDP to indicate openness, and as a proxy for the rate of investments.

The explanatory variables include those which may impact growth, and those which moderate the impact of water shortage and quality of water on growth. The latter impact is our main focus and hence dictates this approach. Human capital does the latter; human capital is knowledge and the ability that humans have, which facilitates the efficient use of water. Humans negatively impact water quality with some of their actions, but that is different, although of course the primary impact of a human capital variable will be via its traditional impact on growth. This dual impact may also be true of other variables. We add the Gini index to the model to represent the effect of inequality on the allocation of natural resources and its effect on growth. The interaction between humans and the environment is a crucial part of sustainability theory (WCED, 1987). The inequalities in income increase the divisions in society that have an important impact on the nature of this interaction. Gylfason and Zoega (Reference Gylfason and Zoega2002) demonstrated that the distribution of natural resources proved to be linked to inequality in the distribution of wealth, i.e., inequality in the distribution of income, education or land is connected to the contribution and share of natural resources in the national income. In other words, inequality in income reflects an inequality in the distribution of natural resources. Morevover, various parts of the literature shed light on the relationship between environmental quality and inequality. Boyce et al. (Reference Boyce, Klemer, Templet and Wills1999) recorded the effects of power inequalities between winners and losers with respect to the pollution level. In our case, we are concerned that resource inequality limits the impact of aggregate resources, specifically with respect to water and water quality on growth, but we also wish to capture the other potential impacts of inequality on growth.

Inflation is added to the model because most of the literature links inflation negatively to growth. Here too inflation, particularly in developing countries, is linked to food prices and food prices to water availability. Food and water are of central importance in every society and are directly related to the availability of water resources, whether in irrigation, canning, manufacturing or transporting. Of course, there are potential endogeneity problems with including inflation, particularly with respect to growth as the left hand side variable. However, as long as we are modelling growth we cannot disregard the potential impact of inflation.

Population growth adds to the demand for water resources, hence, may again limit the impact of available water on economic growth, and is included in the analysis. The modelling of the effect of water utilization on growth deals with water as an economic input and as a public good. The more open, democratic and developed the society, the more efficient policies and institutions may be in managing the natural resource, and in facilitating growth per se.

2.3. Data, data sources and descriptive statistics

The water data are from the AQUASTAT (FAO, 2010) update of the renewable water resources and the total water withdrawal per capita. Previous studies such as Barbier (Reference Barbier2004) used the Gleick databases 1998 and 2006. The constraint in using just the Gleick database is due to the availability of only one year of data, not a series of years or time series data. We use the data from the AQUASTAT database supported by Gleick's water databases (Gleick, Reference Gleick1998, Reference Gleick2000; Gleick and Cooley, Reference Gleick and Cooley2006).Footnote ⁴ This allows us to substantially expand the data set.Footnote ⁵

The analysis is based on monitoring the effect of water utilization per capita and BOD on economic growth – as well as the level of GDP – across countries, using a panel analysis of 177 countries. The countries are listed in table A1, appendix A. The calculations of the ratio of water utilization are obtained by applying the definition given in equation (5) that is used by Barbier. This is derived by dividing the annual water withdrawal per capita for the individual country by the annual renewable water resources per capita for that country.

We based inflation on the GDP deflator due to the availability of accredited data in the World Bank Development Indicators database. The remaining variables are GDP per capita (in constant 2000 US$ ) and population growth (annual per cent), and are also obtained from the World Bank Development Indicators database.

We summarize all of the data definitions and sources in table 2. Table 3 contains the descriptive statistics of the explanatory variables. Missing observations are interpolated using STATA.Footnote ⁶ The variables we are interpolating are ones which change steadily over time rather than ones which are dominated by stochastic shocks, and hence the interpolations are likely to be reasonably accurate.

Table 2. Variables definitions

*Definition given by the World Bank

Table 3. Descriptive statistics

2.4. Estimation framework

The analysis is done on two different dependent variables, so that each group embodied two different sets of panels:

• • Panels for the effect of water utilization and BOD on per capita GDP at year t. GDP per capita is, of course, not growth, but represents the prosperity of a country. So equation (6) is used for two dependent variables:

  (7) $$Y_{it} = \beta_{0} + \beta_{1} \rho_{it} + \beta_{2} \rho_{it}^{2} + \beta_{3} \hbox{BOD}_{it} +\beta_{4} \hbox{BOD}_{it}^{2} + \beta_{5} \hbox{X}_{it} + \varepsilon_{it} $$
  where Y _it  = GDP per capita in the first regression, and $Y_{it} = \hbox{Growth}$ in the second regression. It is possible that the impact of variables such as water and pollution on GDP per capita may be different from growth. GDP per capita depends on the available resources and how efficiently they are used. Growth reflects any increases and/or decreases in resources, and may reflect increases in their efficiency of use and any growth of knowledge.

• • To see the effect on economic growth of ρ and BOD over a longer period, we build on Barbier's model (Reference Barbier2004) which used a range of five-year growth. In taking the rate of five-year growth, calculations are done by taking the percentage of growth from year t until year (t + 5) and regressed on ρ and BOD at year t. In the context of equation (7) we used the five-year growth as the basis for the analysis for three reasons. First, to see the effect over a longer period of time, over which the impact of an increase in an independent variable can be expected to have had a substantial impact. Five years tends to represent a single business cycle for many countries. Ten years would represent two business cycles. The second reason is to compare our analysis with the previous literature (e.g., Barbier, Reference Barbier2004). Thirdly, there is the argument that a five-year horizon reduces the fluctuations in the business cycle and allows a concentration on the fundamentals. Others have also tended to use a five-year average to present data (e.g., Barro and Lee, Reference Barro and Lee1993).

We used an unbalanced panel for 177 countries covering the period from 1960 until 2009. The equation for the fixed effects model becomes:

(8) $$\hbox{Growth}_{it} = \beta_{0} + \beta_{1} \rho_{it} + \beta_{2} \rho_{it}^{2} + \beta_{3} \hbox{BOD}_{it} + \beta_{4} \hbox{BOD}_{it}^{2} + \beta_{5} \hbox{X}_{it} + \alpha_i + \varepsilon_{it} $$

where $\alpha_{i}\lpar i = 1 \ldots n\rpar $ is the unknown intercept for each entity with n entity-specific intercepts. The attractiveness of the panel data analysis is found in the high number of observations and greater degrees of freedom due to more observations. This approach also allows a solution to the problem of omitted variables heterogeneity. Specifically, it can control for individual, specific, time-invariant characteristics and their unobserved heterogeneity, whose presence may lead to biased estimators in the standard ordinary least squares (OLS) estimator. We thus used fixed effects to study the impact of variables that vary over time. As such, we explore the relationship between the dependent and the explanatory variables, and omit the effects of time-invariant characteristics from the explanatory variables (Hausman and Taylor, Reference Hausman and Taylor1981). Moreover, the fixed effects picks up any significant difference between countries: ’the crucial distinction between fixed and random effects is whether the unobserved individual effect embodies elements that are correlated with the regressors in the model, not whether these effects are stochastic or not‘ (Greene, Reference Greene2008: 183). We also cannot ignore the influence of the geography and the region that is systematically affected by climatic influences and, for this as well as other reasons, may impact growth. The fixed effects model captures these individual countries’ effects, which can affect the regression results within the context of different models.

We estimate our models using a robust estimate for the standard errors to control for heteroskedasticity. The correlation coefficient test indicates the presence of a correlation between the x and the x ² (i.e., the two quadratic form variables) in the model, but the mean variance inflation factor gives an accepted value, as x ² is an interaction term of itself; x and x ² will obviously be reasonably collinear.

For this reason we just report the results with fixed effects. In our analysis, we are exploring the effect of water quality that is expressed by BOD as an exogenous variable in the endogenous growth model. There is potentially a causal effect between growth and BOD. It is almost a stylized fact that growth causes pollution; this can impact the regression results and may result in a biased estimator. That is why some of the regressors are correlated with the error term $\hbox{cov}\lpar x_{ik}\comma \; u_{i}\rpar \ne 0$ . In this case, the regression analysis needs further treatment to deal with the causality effect of the regressors on the dependent variable. To deal with the potential problems, we use the instrumental variable technique in the fixed effects model.Footnote ⁷

An important issue in our regression that we need to take into consideration is that we are using environmental variables and socio-economic variables. Thus, finding external instrumental variables is often a challenging task.Footnote ⁸ The variables that we have chosen affect the quality of the environment through the effect on greenhouse gases (GHGs). For this task, we have to identify the aspects,Footnote ⁹ in addition to their environmental impacts, that cause harm to the quality of the environment – whether directly or indirectly. In the case of water quality, these aspects could be the discharge of wastes in water, and the impact is the damage to the aquatic system.

We rerun the regression with the instrumental variables and use the Davidson–MacKinnon test to test for exogeneity after the fixed effects instrumental variable model. The acceptance of the null (p > 0.05) indicates that the model with the instrumental variables is not significant; in other words, the endogenous regressors do not affect the regression results in the fixed effects model, instrumenting BOD is not requiredFootnote ¹⁰ and the ordinary fixed-effects estimations in column 2 of the regression tables are consistent. The results of the tests are reported in tables 4 and 5.

Table 4. Regression analysis of water utilization and BOD with Log GDP per capita as a dependent variable

Notes: t statistics are in parentheses; ***significant at 1 per cent level, **significant at 5 per cent level, *significant at 10 per cent level.

Modified Wald test for groupwise heteroskedasticity in fixed effect regression model ( $H_{0}\colon \sigma \lpar i\rpar ^{2} = \sigma^{2}$ for all i) is 65937.73***, indicating a heteroskedasticity which is alleviated by using the heteroskedasticity-robust standard errors. The mean value of the variance inflation factors of the overall variables in the models is 9.86

The significance of R ² is based on F statistics.

Davidson–MacKinnon test of exogeneity: 0.0431282 F(1,1506) P−value = 0.8355

In column 2: Turning point ρ: 0.20, turning point BOD: 0.25.

RMSE: root mean squared error

Table 5. Regression analysis of water utilization and BOD with the rate of five-year growth as a dependent variable

Notes: t statistics are in parentheses; ***significant at 1% level, **significant at 5% level, *significant at 10% level.

Modified Wald test for groupwise heteroskedasticity in fixed effect regression model ( $H_{0}\colon \sigma\lpar i\rpar ^{2} = \sigma^{2}$ for all i) is 89498.23***, indicating a heteroskedasticity which is alleviated by using the heteroskedasticity-robust standard errors. The mean value of the variance inflation factors of the overall variables in the models is 8.73.

The significance of R ² is based on F statistics.

Davidson–MacKinnon test of exogeneity: 0.4395 F(1,925) P−value = 0.5075

In column 2: Turning point ρ: 0.24, turning point BOD: 2.677.

RMSE: root mean squared error

For better illustration of the model we use two specifications. The first specification introduces the model with the ratio of water utilization (ρ and ρ²) that is present in column 1 in tables 4 and 5. We use this specification to compare our results with Barbier's (Reference Barbier2004). The second specification includes both (ρ + ρ²) and water quality (BOD and BOD²) to see the effect of different specifications within the model context (column 2 in tables 4 and 5). We calculated the turning pointsFootnote ¹¹ of ρ and BOD using the models in column 2 (tables 4 and 5), where it represents the peak impacts of ρ and BOD in the same fixed effects model.

To test the robustness of our model, we rerun the regression excluding the countries that are excluded by Mankiw et al. (Reference Mankiw, Romer and Weil1992), these being the oil producing countries.Footnote ¹² We get similar results with a negligible change in the coefficients of the variables. We also exclude inflation from our model due to potential endogeneity between growth and inflation; we again get similar results. Our main focus is on the impact of the environmental variables; nonetheless, we further replaced the inflation with a proxy variable, the international rate of inflation, and again got similar results.