Linking Wealth and Productivity of Natural Capital for 140 Countries Between 1990 and 2014

Abstract

This study explores the relationship between inclusive wealth, economic growth, and productivity of natural capital (including forestry, fishery, fossil energy reserves and minerals) for 140 countries between 1990 and 2014. For this objective, a Malmquist productivity index is developed, and regression analysis is performed. The results are threefold. First, we found that natural capital deterioration constituted the main driving force of declining wealth per capita following fossil fuel extraction. Second, the adjustment to a conventional productivity growth measure depends on GDP growth and an endowment growth shift of natural capital relative to other input factors. Third, we also found that the initial phase of GDP growth was accompanied by slower natural capital utilization followed by a phase of deterioration as these countries continue to develop economically. With further economic development, enhanced technology and effective natural resources utilization limit the material basis and result in reduced natural capital extraction. These results imply that natural capital extraction management for a broader income level can be implemented for sustainability in both the short and long term.

Appendix

1.1 Wealth Accounting Method

The Brundtland Commission defines sustainable development as ‘development that meets the needs of the present without compromising the ability of future generations to meet their own needs’ (World Commission on Environment and Development 1987). Many previous studies, such as Arrow et al. (2004), define sustainable development as non-declining well-being in the future:

$${\text{Vt}} = \mathop \smallint \limits_{t}^{\infty } U\left( {C_{t} } \right)e^{{ - \delta \left( {t - 1} \right)}} d\tau \quad and\quad \frac{dV}{dt}\, \ge \,0\quad for\;all\;t,$$

(1)

where V, U, C and $\delta$ represent well-being, current well-being, consumption, and the social discount rate respectively.

The direct measurement of well-being, V, might be a suitable approach in assessing sustainability, along with Eq. (1). However, because of the difficulty of observing well-being, Arrow et al. (2004) proposed for an alternative approach, namely measuring the productive base of V based on the determinants of well-being. This aggregated capital of productive based is termed as Inclusive Wealth (IW). It is includes produced capital, human capital, natural capital, and intangible capital, such as knowledge and institutions. Accordingly, we can define IW at time t.

$${\text{I}}\varvec{W}\left( \varvec{t} \right) = \varvec{P}_{{\varvec{PC}}} \varvec{PC}\left( \varvec{t} \right) + \varvec{ P}_{{\varvec{HC}}} \varvec{HC}\left( \varvec{t} \right) + \varvec{P}_{{\varvec{NC}}} \varvec{NC}\left( \varvec{t} \right)$$

(2)

Each P is shadow price of the capital asset, defined as δW_t/δC, where K is each capital which is PC(t), HC(t) and NC(t) represent produced capital, human capital and natural capital at time t, respectively. We utilize gross domestic product (GDP) as the desirable output. This calculation is based on millions of constant 2005 US$.

1.2 Productivity Measure

There are several method to calculate productivity growth, such as data envelopment analysis, parametric methods or econometric methods. Several methodological issues emerge when TFP is estimated using traditional methods, i.e. by applying ordinary least squares (OLS) to a panel of (continuing) firms. First, because productivity and input choices are likely to be correlated, OLS estimation of firm-level production functions introduces a simultaneity or endogeneity problem. We used a deterministic nonparametric analysis called Malmquist Productivity Index, based on the Data Envelopment Analysis (see review for Färe et al. 1994, Kerstens and Managi 2012). The index is suitable for assessing the relation between multivariate inputs and outputs. In addition, the measurement takes into account the efficiency of resource use and productivity changes. DEA is an established method in order to measure the relative efficiency of decision-making unit based on input and output in the sample (Mizobuchi 2014).

We apply physical, human and natural capital as a separate unit, each capital as an input and GDP as an output in our calculating of TFP. Using the distance function specification for the index, we can formulate our problem as follows:

$$T\left( t \right) \equiv \left\{ {\left( {x_{t} ,y_{t} } \right):x_{t}\, can \,produce \,y_{t} } \right\}.$$

(3)

Let x = $\left( {x^{1} , \ldots x^{M} } \right) \in R_{ + }^{M}$and y = $\left( {y^{1} , \ldots y^{N} } \right) \in R_{ + }^{N}$ be the input and output vectors, respectively. The technology set, defined by Eq. (3), consists of all feasible input vectors, x_t, and output vectors, y_t, at time t, and satisfies certain axioms that are sufficient to define meaningful distance functions. The distance function is defined as:

$$d\left( {x_{t} ,y_{t} } \right) = max\left\{ {\delta ;\left( {x_{t} ,y_{t} /\delta } \right) \in T\left( t \right) } \right\}$$

(4)

where $\delta$ is the maximal proportional amount to which y_t can be expanded, given technology T(t). In this analysis, we characterize production technology as having constant returns to scale. This formulation produces an output-oriented distance function. Equation 5 is a formulation of the Malmquist Productivity Index (M as TFP to inclusive investment), as follows:

$$\begin{aligned} & M\left( {GDP_{i,t} ,HC_{i,t} ,PC_{i,t} ,NC_{i,t} ,GDP_{i,t + 1} ,HC_{i,t + 1} ,PC_{i,t + 1,} NC_{i,t + 1} } \right) \\ & \quad = \left[ {\frac{{d^{t} \left( {GDP_{i,t + 1} ,HC_{i,t + 1} ,PC_{i,t + 1,} NC_{i,t + 1} } \right)}}{{d^{t} \left( {GDP_{i,t} ,HC_{i,t} ,PC_{i,t} ,NC_{i,t} } \right)}} \times \frac{{d^{t + 1} \left( {GDP_{i,t + 1} ,HC_{i,t + 1} ,PC_{i,t + 1,} NC_{i,t + 1} } \right)}}{{d^{t + 1} \left( {GDP_{i,t} ,HC_{i,t} ,PC_{i,t} ,NC_{i,t} } \right)}}} \right]^{1/2} \\ \end{aligned}$$

(5)

where d is the geometric distance to the production frontier caused by production inefficiency, while the frontier denote the best available technology from the given inputs and outputs; i refers to the country under analysis, running i from 1 up to 140 nations in our sample; GDP is the corresponding value of gross domestic product; HC stands for human capital; PC represents produced capital; NC represents natural capital. Thus we capture the productivity change from the variations in inefficiencies between two years.

1.3 Kuznets Curve Relationship: Natural Capital Productivity and Income Level

According to the EKC literature (see Dinda 2004; Stern et al. 1996), it is expected that per capita income has a negative relation with environmental degradation. After a sufficiently high per capita income is reached, further increment in income is expected to reduce environmental degradation. We follow Dinda (2004), Galeotti and Lanza (2005), and Akbostancı et al. (2009) which develop the equation for cubic model to test the EKC hypothesis as revealed below:

$${\text{Y}}_{\text{it}} = \alpha_{\text{it}} + \beta_{1} {\text{X}}_{\text{it}} + \beta_{2} {\text{X}}_{\text{it}}^{2} + \beta_{2} {\text{X}}_{\text{it}}^{3} + {\text{u}}_{\text{it}}$$

(6)

In this equation, Y denotes natural capital productivity, X represents GDP per capita, u_it is traditional error term, i symbolizes individuals and/or groups, and t is time. The signs of the coefficients of X, X², and X³ determine the shape of the curve.

We employ panel regression techniques to estimate Eq. (6). Panel data approach encompasses data across cross-sections and over time series, thus provides a comprehensive analysis to examine variables of interest. However, the use of panel data and dynamic specifications make this problem more complex. Alternatively, to eliminate the serial correlation problem, Zhengfei and Lansink (2006) suggest the use of a dynamic generalized method of moments (GMM) model to analyze TFP measures estimated by DEA. Therefore, we employ system GMM to analyze productivity change in this article.