Non-Renewable Resources and Sustainable Resource Extraction: An Empirical Test of the Hotelling Rule’s Significance to Gold Extraction in South Africa

Abstract

The study sought to test the applicability of Hotelling’s rule to gold extraction in South Africa. In environmental economics, Hotelling’s rule has come to be a pillar of the exhaustible resources framework and in addition to this, it has presented essential insights into the consumption and extraction of non-renewable resources. According to Hotelling’s Rule, the extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations. The welfare of South Africa’s present population, particularly in the future, will be greatly determined by the stock of natural resources available. Currently, the production processes deplete natural resources in a way that is not sustainable. For instance, South Africa’s gold reserves are becoming depleted at a rate that, within 25 to 33 years, will mean the end of the industry on which South Africa’s economy has been built. This raises questions regarding how much of these non-renewable resources (gold) should be extracted today, and how much should be saved for future use or for future generations. Is gold being depleted more rapidly than the optimisation level suggested by Hotelling’s Rule? In order to empirically test Hotelling’s Rule, the study was guided by previous literature that had sought to test it, namely, the previously used graphical analysis and autoregressive distributed lag (ARDL) approach to assess the applicability of Hotelling’s Rule. The results showed that there seems to be no significant relationship between interest rates and gold processes. This shows that Hotelling’s Rule does not hold in South Africa. The results of the study suggested that the gold extraction in South Africa is not following a social optimal path. The study recommended that the government come up with measures that prolong the lifespan of the gold reserves. These included research and development to promote technological innovations in the mining sector.

1. Introduction

Economists have long been concerned with the extraction and efficient use of non-renewable resources [1,2]. The fact that non-renewable resources decrease as they are used has made economists worry that at some point, the world will run out of these resources. One question is of central importance: What is the optimal extraction path over time for any particular non-renewable resource stock? Hotelling’s Rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme. Hotelling’s Rule states that the market price for an exhaustible natural resource should rise at a rate equal to the interest rate in a market equilibrium [3]. In environmental economics, Hotelling’s Rule has come to be a pillar of the exhaustible resources framework [2,4,5,6] and in addition to this, it has presented essential insights into the consumption and extraction of non-renewable resources. Lamdry, Turner, and Dorfman [7] concur and state that Harold Hotelling [3] created a central and enduring paradigm of modern resource economics.

Hotelling formalised the equilibrium conditions for such a resource, which are equal when the price of an exhaustible resource grows at a rate equal to the rate of interest [8,9]. Its central result is that the extraction rate of an exhaustible resource is monotonously sinking, while its price is increasing. An implication of the continuously rising price is that the quantity extracted would be continuously falling until such time as the resource is exhausted. As the price rises, the demand for the resource is slowly choked off. Eventually, the price would be so high that demand would be eliminated altogether. The basic message of Hotelling’s Rule is that the profitable extraction path, both socially and economically, is one in which the price of the non-renewable resource increases at the same rate as the interest rate [10,11,12]. Hotelling’s Rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme. The extraction path in competitive market economies will, under certain circumstances, be socially optimal. An extraction path that is not socially optimal compromises the welfare of future generations.

The welfare of South Africa’s present population, and more especially, that of future generations, will be greatly determined by the stock of natural resources available and the quality of the environment. Currently, the gold production processes depletes natural resources. Concern regarding the supposed increasing scarcity of gold in South Africa, and the possibility of running out of gold, have become major concerns. South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at an alarming rate [13]. The declining importance of the gold sector is also shown by gold production data. Historical values of the gold index show the extent to which production has fallen. Gold production has continued to decline over the last ten years. It declined from 522.4 metric tons in 1995 to 342.7 metric tons in 2004, “the lowest level of production since 1931” [14]. In January 1980, the index was 359.0, while the volume of gold produced was far lower in January 2015, resulting in the low index of 48.4 [15]. In other words, South Africa produced 87% less gold in January 2015 compared with the same month in 1980. These statistics show that the gold sector is losing the prominent place it once had in the South African economy. This is reducing gold’s contribution to the South African economy. The metal contributed 3.8% to the gross domestic product in 1993, falling to 1.7% in 2013. In terms of sales, gold made up 67.0% of all mineral sales in 1980, falling to 12.5% in 2014 [15].

A number of concerns have been raised over the future of several leading gold mines in South Africa. Most mining operations are viable for a period of 30 years, depending on the mineral extracted and the available reserves [16]. Most reserves are already exhausted, and the costs involved in mining lower grade ore, as well as deposits located very deep in the earth, are becoming excessive. Mantashe [14] notes that the “depth at which gold deposits are found in South Africa is a further complicating factor. The closure of marginal mines is accelerating the decline, visible in the 8.8% decline in gold production between 2003 and 2004.” Several gold mines have already shut down. The North West, the Savuka, the Kloof, the Great Noilgwa, Ergo, Tau Tona, and St. Helena mines have been all closed down [17]. In addition to this, Harmony Gold Mining, a mining company which is ranked third in gold production in South Africa, has, in the last couple of years, closed several mine shafts. In 2009, it closed the Evander shaft numbers 2, 5, and 7 in the Mpumalanga province and several other shafts in its mines in the Free State province [18]. Moreover, the rate of decline in the reserves of several mines owned by the three giants gives them less than ten years of continued production; moreover, about one-tenth of these reserves are in the form of mine dumps from which gold is being recovered [16]. South Africa’s gold reserves (gold in the ground that can be extracted profitably) are becoming depleted at a rate that, within 25 to 33 years, will mean the end of the industry on which South Africa’s economy has been built [13,15,19,20]. This raises questions concerning how much of these non-renewable resources (gold) should be extracted today and how much should be saved for future use or for future generations. Is gold being depleted more rapidly than the optimisation of Hotelling’s Rule? In light of this, this study seeks to test the applicability of Hotelling’s Rule in South Africa.

Given the importance of the gold industry to the South African economy, a study of the optimum extraction path in the gold industry was especially valuable. There are no records of similar studies conducted in South Africa. Recognising a gap in South African literature to test the applicability of Hotelling’s Rule was one of the driving forces for conducting this study. This study made an original contribution towards the broader scope of environmental economics in the South African gold mining sector.

2. Literature Review

This section examines theories and empirical work associated with the examination of sustainable resource extraction and optimal exhaustible resource use. The focus will be on certain key theoretical and empirical issues which lie at the heart of any analysis of sustainable and optimal exhaustible resource use. The task of literature scrutiny is to develop a well-founded judgement that can guide to a reasoned decision on the issues of the optimum extraction path and sustainability.

2.1. Theoretical Literature

The theoretical section of this study discusses the theories that sought to explain how sustainability can be achieved and how an optimum extraction path can be established. Although economists have long been concerned with the extraction of natural resources, there is no theoretical consensus on how to obtain an optimum extraction path. The efficient use of scarce natural resources, both renewable and non-renewable, has long been a concern of natural resource economics [1,21].

2.1.1. Hotelling’s Rule

The basic message of Hotelling’s Rule is that the profitable extraction path, both socially and economically, is one in which the price of the non-renewable resource increases at the rate of the interest rate [22]. In other words, Hotelling’s Rule illustrates the time path of non-renewable resources’ extraction which maximises the value of the natural resource stock. Hotelling’s Rule states that the price of an exhaustible resource must increase at the same rate as the interest rate. Hotelling’s Rule is a necessary efficiency condition that must be satisfied by any optimal extraction programme. Hotelling’s rule states that in a competitive market, the price of a depletable resource must increase at the same rate as the discount rate. Arbitrage will remove any deviation of the future prices. The theory for this special case was worked out in the classic paper by Hotelling [3]. Krautkraemer’s [23] notes that “Hotelling’s formal analysis of non-renewable resource depletion generates some basic implications for how the finite availability of a non-renewable resource affects the resource price and extraction paths.”

2.1.2. Hartwick Rule

The Hartwick Rule, in contrast, was formulated for a production economy where consumption at any point of time t depends not only on the extraction of natural capital, but also on the stock of man-made capital available at t. Hartwick [24] showed that, given Hotelling’s Rule as condition for local efficiency, a zero value of aggregate net investment will entail constant consumption over time. This result was the heart of what was later called the Hartwick rule. The Hartwick Rule states that the market should “keep a country’s total capital stock at least constant by investing in all forms of capital at the same level of all forms of capital consumption to allow for sustained consumption over time” [25].

Hartwick’s Rule states that if it is on an efficient path, the value of net investments is zero at each point in time, and utility is constant. This rule was established for a very general class of models in an elegant and important piece of work by Dixit et al. [26]. Regarding one consumption, a good economy endowed with two stocks, a stock of an exhaustible non-renewable resource and a stock of man-made capital, Hartwick’s Rule means that if the accumulation of man-made capital always exactly compensates in value for the resource depletion, then consumption remains constant at the maximum sustainable level. The Hartwick Rule [24] offers a rule of thumb for sustainability in exhaustible-resource economies—a constant level of consumption can be sustained if the value of investment equals the value of rents on extracted resources at each point in time.

2.1.3. Marxism

The environmental Marxist perspective questions the very possibility of an environmentally sustainable capitalist economy, arguing that economic growth relies upon exploitation of natural and social capital and the avoidance of wealth redistribution (or equity), both at the national and international level [27]. Therefore, by its very nature, capitalist development does not foster the goals of environmental sustainability, cultural diversity, or more equitable social development, where poverty is eradicated. The Marxian understanding of the environmental–economic relationship is crucial for a complete discussion of the ecological destruction occurring in society today. Several theories in environmental economics do not challenge the basic premises of capitalism, and as such, the solutions offered by these approaches cannot ameliorate the ecological effects of the system [28]. For Marx and his followers, to understand the specificity of ecological destruction in society, it is necessary to examine the historical materialist conditions, modes of production/reproduction, and the nature of capital within society.

2.1.4. Non-Declining Natural Capital Stock Approach

Another different approach to the limited degree of substitutability between natural capital (Kn) and man-made capital (Km) is the approach suggested by Pearce et al. [29]. Here, the view is taken that, whilst some substitution is possible between certain elements of natural capital and human capital (for example, better machinery, meaning that less raw materials are used to produce certain products), many elements of natural capital provide non-substitutable services to the economy. The idea here is that, if it is necessary to maintain some amount of the natural capital stock constant in order to allow future generations to reach the same level of utility as the average held by this generation, this holding constant of the natural capital stock becomes a rule for sustainable development [30].

2.2. Empirical Literature

Halvorsen and Smith [31] utilized a generalised Cobb–Douglas cost function to look at the Canadian metal mining sector as a whole. They strongly rejected Hotelling’s Rule. They recommended that further study be done on disaggregated data and uncertainty in an imperfect arbitrage scenario. Moazzami and Anderson [32] estimated an error-correction model and discovered U-shaped price pathways, but Berck and Roberts [33] evaluated both difference and trend–stationary models and discovered U-shapes in the former, but not the latter. Chermak and Patrick [34] used monthly data from 29 tight gas sand wells to study the natural gas market in the United States. They used a Cobb–Douglas cost formula that calculated monthly expenses as a function of gas produced, remaining reserves, and time trend. They also took into account cost disparities between firms. They discovered that Hotelling’s Rule cannot be disregarded because of high interest rates, which they suggest might apply to the enterprises in question. They proposed including uncertainty into the firm’s decision issues for future study. Banks [35] discovered data that refuted Hotelling’s Rule; the study’s findings revealed that the Hubbert curve approach was far more significant than Hotelling’s Rule in describing the behavior of non-renewable resource pricing. Andre and Smulders [36] developed expansions to Hotelling’s Rule and demonstrated that it was still applicable.

Livernois, Thille, and Zhang [37] looked at non-renewable old-growth timber and used stumpage price bids at timber auctions to calculate shadow prices. The results of their structural testing backed Hotelling’s theory. Gaudet [38] looked at US price data from 1870 to 2004 for copper, lead, zinc, coal, and petroleum; 1880 to 2004 for tin; 1900–2004 for aluminum and nickel; and 1920–2004 for natural gas, plotting the rate of change in price for each of those seven non-renewable minerals and three non-renewable fossil fuels. The rate of change of such prices was found to be quite volatile, according to the findings. However, perhaps more importantly, the volatility looked to be centered around zero. In reality, the mean rate of change in price in none of the ten situations was substantially different from zero. It was difficult to identify any pattern in the real price levels of such resources. Overall, it was difficult to tell whether resource costs normally climbed or declined over time. This neither supported nor rejected Hotelling’s Rule. The basic Hotelling’s Rule, according to Kronenberg [39], does not hold in reality, since some of its assumptions are broken. He believed that departures from the simple Hotelling’s Rule were not a severe concern if they were driven by marginal extraction costs, which may be growing due to stock effects or dropping due to technological development. Under such circumstances, it is socially desirable to apply a modified Hotelling’s Rule, which is exactly what the market would do, resulting in an effective market solution. However, if the failure of Hotelling’s Rule was due to ambiguous property rights or strategic interaction, this was undesirable, since it meant that the market would not produce an efficient solution.

The findings of Chakravorty, Leach, and Moreaux [40] imply that resource pricing may display large structural fluctuations over time, driven by regulatory policy and market dynamics, resulting in alternating periods with secular upward or downward price swings. Resource prices are stagnant around deterministic trends, with structural breakdowns in slope and intercept, according to the researchers. In other words, prices may exhibit upward and downward trends, with the endogenous structural breakpoints interrupting these trends. They could not be rising or declining, as the traditional Hotelling model predicts. Their findings revealed that, when exposed to regulation and learning effects, the same Hotelling model may predict alternating bands of rising and dropping prices, rather than a secular trend, as is usually supposed. In this way, the findings had a direct impact on the literature that sought to empirically test the Hotelling model’s predictions. It was claimed that looking for a secular trend in pricing may be compared to trying out a faulty Hotelling model. The key relevance of their findings is that looking for secular price patterns as anticipated by the textbook Hotelling model might lead to erroneous conclusions about the theory of nonrenewable resource economics’ predictive potential.

The flaws of the Hotelling strategy are obvious in oil markets, according to Mason and Veld [41]. Real oil prices have remained relatively stable for almost a century, in stark contrast to predictions that rents would grow at the rate of interest [41]. A variety of theories have been proposed, including the consistent flow of freshly discovered resources and technology advancements that may have continuously altered the price path out, disguising what would have otherwise been a trend toward increasing prices. Ukani [42] investigated how Hotelling’s Rule has forecasted the evolution of crude oil prices over the previous 100 years, and examined whether the rule may be used to forecast future resource prices. During the previous few decades, Hotelling’s Rule has been viewed as both outmoded and relevant. A previous study has found that resource price trends are more complicated than Hotelling expected. Tests of factors such as interest rates, time spans, and extraction costs were used to conduct the analysis. The notion of resource costs growing exponentially has also been tested. The results reveal that the Hotelling Rule’s capacity to anticipate future prices has no broad support.

Van Veldhuizen and Sonnemans [12] investigated a fresh cause for the lack of empirical evidence for Hotelling’s Rule for nonrenewable resources using a laboratory experiment. They investigated whether producers with enormous resource stocks pay less attention to the dynamic component of their extraction decisions, causing them to shift extraction to the present and concentrate on strategic behaviour. According to their findings, producers with big stockpiles pay less attention to dynamic optimisation and shift extraction to the present, causing them to overproduce in comparison to Hotelling’s Rule. Ferreira da Cunha and Missemer [9] were able to confirm that it is possible to obtain bell-shaped trajectories for supplies and U-shaped ones for prices, as described by Hotelling, at least for given values of the parameters. Uberman’s [43] study revealed no support for Hotelling’s Rule.

The empirical literature above showed that researchers, looking at different resources or different time periods, have come up with a variety of results. There is no clear picture of whether resource prices follow Hotelling’s Rule. It was found that very little research has been done in developing countries on the relevance of Hotelling’s Rule. It can thus be said that the ability of the theory of exhaustible resources to describe and predict the actual behaviour of resource markets remains an open question in countries in the developing world, such South Africa. In light of this, this study makes an attempt to validate Hotelling’s Rule (and other associated aspects of the resource depletion theory) within a South African context. To the author’s knowledge, this is the first study to investigate the validity of Hotelling’s Rule in South Africa.

3. Methodology

3.1. Data Sources

The study used secondary quantitative data for estimation purposes. Data for the study was obtained mainly from secondary sources, including Stats SA, the South African Reserve Bank, the Department of Trade and Industry, and other relevant sources. Nominal figures were used for the study. The study employed monthly South African data for the period of 1990–2017. The data frequency selected was monthly so as to ensure an adequate number of observations.

3.2. Estimation Techniques

The study used applicable econometric approaches to conduct this research, which complement and enhance those previously used in the literature. According to Neumann [44], three main types of testing methodologies have been used in literature:

(i)

First, there are descriptive studies which examine the price behaviour.

(ii)

Second, a specific model can be tested by estimating equations. This approach relies on econometric estimations.

(iii)

The third approach refers to a reformulation of Hotelling’s Rule in the form of the HVP.

This study focused on the first (descriptive) and second (econometric estimation of equations) approaches.

3.2.1. Descriptive Statistics

The study used descriptive analysis to examine the price, production, and consumption trends of the gold variable. Descriptive statistics is the name given to a type of data analysis that helps to explain, illustrate, or summarize data in a comprehensible way so that patterns might emerge [45]. They are just a means of describing data. The majority of descriptive studies have looked at how mineral commodity prices have changed through time [46]. The reason for utilizing descriptive statistics in this study is that it will be simpler to determine whether or not these resources are subject to growing degrees of resource scarcity by describing the actual attributes of the data series. According to Hotelling [3], there are three things we can say about resource extraction for a finite resource:

• Firms will always try to extract low-cost resources before high-cost resources, causing resource extraction costs to increase over time.
• In general, greater scarcity caused by in situ reserves increases the value of a resource, causing the price to increase over time.
• Since the price of a resource increases over time, then demand and production should decrease over time.

This study made use of descriptive statistics to understand the nature of the gold price, production, and consumption paths. Understanding the nature of resource price, production, and consumption paths was important because knowing the correct time series behaviour of natural resource prices can be vital to testing the validity of Hotelling’s Rule. In order to test whether (i) the gold price increases over time and (ii) demand and production decrease over time, the study made use of the Hodrick–Prescott (HP) filter. The presence/absence of a trend in the mean was examined by applying a Hodrick–Prescott filter to the time series. The Hodrick–Prescott filter is a smoothing method that is widely used among macroeconomists to obtain a smooth estimate of the long-term trend component of a series [47]. The method was first used in a working paper (circulated in the early 1980s and published in 1997) by Hodrick and Prescott to analyse post-war US business cycles. If the result is a series that does not resemble a roughly flat, horizontal line, then a trend in mean is present in the initial series.

3.2.2. Inferential Statistics: Econometric Estimation of Equations

The study used the ARDL model for estimation purposes. Unit root tests showed that there were variables that were stationary at some levels, and some variables that were stationary after being different once. As a result, it was appropriate to use the ARDL model. This technique, suggested by Pesaran, Shin, and Smith [48], is used for investigating long-run relationships between variables based on F-test or t-test standards. In regression analysis, if a model includes both current and lagged values for independent variables, it is called a distributed lags model, and if a model also includes lagged values for dependent variables, it is called an autoregressive model [49]. According to Pesaran et al. [48]:

(i)

The autoregressive distributed lags method allows us to express the cointegrated behaviour of variables which have a different order of integration.

(ii)

The ARDL procedure is irrespective of whether variables used in a model are I(0), I(1), or mutually cointegrated [48].

The ARDL was used for two reasons: the variables had different orders of integration, and some were I(0) variables, while some were I(1) variables. This justified the use of ARDL in the study. The ARDL model has the advantage of simultaneously correcting for residual serial correlation and the problem of endogenous regressors, enabling ARDL to have an edge over other approaches to cointegration, as it yields robust results [50]. The ARDL model takes preference because of the incomparable power of its estimates that are more effective and reliable in small samples than those from the Johansen technique (Banerjee et al. 1993). In the short run, the variables may be in disequilibrium; therefore, due to this aspect, an error correction model (ECM) was specified.

The study adopted the methods of Ghosh et al. [51]. Ghosh et al. [51] analysed monthly gold price data from 1976 to 1999 using cointegration regression techniques. Their study provided empirical confirmation that gold can be regarded as a long-run inflation hedge, and that the movements in the nominal price of gold are dominated by short-run influences. Their basic model was:

$$P_g=f\left(P_{usa},P_w,R_g,Y,{\beta }_g,er,\theta \right)$$

(1)

where Pg is the nominal USD price of gold, Pusa is the US price index, Pw is the world price index, Rg is the gold lease rate, Y is world income, βg is gold’s beta, er is the dollar/world exchange rate, and θ are random financial and political shocks that impact on the price of gold. This study modifies Ghosh et al.’s [51] model by replacing some variables. This study modifies Equation (1) by adding some additional variables that influence gold prices. The model of this study will then have the following function:

GP = f (INT, PG, M, Y)

(2)

where Rand denominated gold price (GP) will be a function of interest rates (R), gold production (PG), money supply (M), and world income (Y).

4. Presentation of Results

4.1. Descriptive Statistics

The study used descriptive analysis to examine the price, production, and consumption trends of the gold variable. The descriptive statistics are presented in this section.

4.1.1. Gold Price Trends

The first descriptive analysis was done to check the behaviour of gold prices over time. The graphical results from the Hodrick–Prescott filter are displayed in Figure 1.

From Figure 1, it can be seen that the gold price series appears to be trending upward. The gold price series shows that the constant variance condition for stationarity is being violated. The vertical fluctuation of the series appears to differ from one portion of the series to the other, indicating that the mean is not constant. Furthermore, an upward trend is a violation of the requirement that the mean is the same for all periods. It can thus be said that the gold price series is violating the following:

$$\mathrm{E}\left(y_t\right)=\mu \left(\mathrm{constant}\mathrm{mean}\right)$$

(3)

The analysis shows that the series is following a upward trend, and this is a deterministic trend. The changing mean of a non-stationary process or trend can be represented by a deterministic function of time. These models for the trend imply that the series trend evolves in a perfectly predictable way; therefore, they are called deterministic trend models. In Figure 1, it can be seen that the series is not stationary, and it has a deterministic trend. Using a related methodology—Kalman filter methods—Pindyck [52] estimated a model where prices revert to a quadratic trend that shifts over time. On the other hand, Cuddington and Nülle [53] used band filters to assess the behaviour of commodity prices and found that there is no “general tendency” in the negative or positive direction of long-run mineral commodity price trends. While there are examples therein which are illustrative of the Hotelling, Prebisch–Singer, and Pindyck/Heal/Slade U-shape models and expectations of long-term price trends, none of the seminal models emerge as preeminent.

According to Neumye [54], rising resource rents would indicate rising scarcity; whereas, falling resource rents would indicate falling scarcity, and no rise or fall would suggest no change in scarcity. A review of the graphical trends of the gold price series clearly showed that the series had an upward trend. This confirms Hotelling’s Rule and is also consistent with empirical literature. According to the literature [55], as price pulls away from marginal extraction cost, the rate of increase in price will approach the rate of interest. It is clear that in such a model, price does not revert to a fixed mean. It is also clear that such a model implies systematic increases in real price over time. However, price movement is still systematic and may be modelled appropriately as a deterministic trend. This supports the present study’s findings.

4.1.2. Gold Production

The second descriptive analysis was done to inspect the behaviour of gold production over time. The trend of gold production in South Africa was examined through the Hodrick–Prescott filter, shown in Figure 2 below.

The Hodrick–Prescott filter shows that gold production has been declining, as shown by the declining gold production trend line in Figure 2. This shows that there has been a decrease in gold production over time in South Africa. This is in line with Hotelling’s Rule, which states that resource production should decrease over time to reflect scarcity. However, some studies have found the opposite. For example, Scott and Pearse [56] and Simon [57] show that all of these theoretical trends have not occurred. Costs of extraction and prices of natural resources have mostly decreased over time, not just in recent years, but in many cases, for decades. Quantities of most natural resources extracted and produced have increased over the same long time frame.

The question is, is diminishing gold production indicative of Hotelling’s recommended socially optimum path? Is Hotelling’s Rule supported by diminishing gold production? The reduction in output is mostly due to the extraction of lower-grade ore, which has been affected by increased Rand gold prices, as well as the temporary closure of shafts to repair infrastructure [15]. South African gold production (extraction) has declined by 71% over 29 years, from 675 tons in 1980 to 198 tons in 2009. This follows Hotelling’s Rule, which states that resource output should decline over time to represent scarcity. The conclusions are also supported by actual evidence. Mudd [58] showed that long-term trends for copper, gold, nickel, lead, silver, and zinc ore grades in Australia are declining. In many cases, high quality ores have largely been exploited, and ores that require more complex processing remain.

At current production levels, South African gold resources will be exhausted in only 33 years [15]. This is supports Hotelling’s Rule, which argues that:

(i)

In general, greater scarcity caused by in situ reserves increases the value of a resource, causing the price to increase over time.

(i)

Since the price of a resource increases over time, then demand and production should decrease over time [59].

The second principle has been observed in South Africa. The resource prices and the production levels have been going down. The monthly gold production index has fallen over the years. In January 1980, the index was 359.0, while the volume of gold produced was far lower in January 2015, resulting in the low index of 48.4 [15]. In other words, South Africa produced 87% less gold in January 2015 compared with the same month in 1980. General historical trends show that gold has lost the prominent place it once had in the South African economy. On the other hand, the price for gold has been increasing. This is consistent with Hotelling’s Rule.

4.1.3. Gold Consumption

The third analysis was conducted to examine whether or not gold consumption has been declining over time. Hotelling’s Rule argues that in the social optimum, the price of a non-renewable resource should be rising at the rate of interest [46]. Furthermore, resource consumption should decline over time, asymptotically falling to zero [60]. This will result in an extraction path that is socially optimal, according to Hotelling. The results of domestic gold consumption are shown in Figure 3 below.

The Hodrick–Prescott filter shows that there is a rising trend in domestic gold sales (gold consumption) in South Africa. This is illustrated by the trend line, which has been rising steadily since 1995. The trend line shows that gold sales were slowly declining from 1995 until 2001, when they began to rise. From 2001 on, there was a gradual increase in gold sales in South Africa. This is not in line with Hotelling’s Rule, which states that the production and consumption of a resource should decline over time. The fact that gold consumption fell between 1994 and 2001 prompts the need to examine the growth rate under this period of investigation.

The above analysis shows that gold consumption is increasing, and this violates Hotelling’s Rule, which expects consumption to decrease over time. This shows that Hotelling’s Rule does not hold for gold consumption in South Africa. A more important question is whether the failure of this Hotelling’s Rule principle implies that the market is failing to produce a socially optimal resource consumption path.

4.2. Inferential Statistics

4.2.1. Unit Root Tests

Unit root tests showed that there were variables that were stationary at some levels and some variables that were stationary after being different once. As a result, it was appropriate to use the ARDL model. This technique, suggested by Pesaran, Shin, and Smith [48], is used for investigating long-run relationships between variables based on F-test or t-test standards. One more important thing in this technique is that it rules out pre-unit-root testing. The time series data can be stationary I(0), integrated of order one I(1), or mutually cointegrated. This is one of the main advantages of the bounds testing approach because the main variable can be stationary, whereas others variables can be non-stationary [61]. Moreover, it can be used if the data has trends. The ARDL technique also sets appropriate lags of variables. This was performed, and the AIC and FPE picked three lags.

4.2.2. Cointegration Test: ARDL Bound Test

The study employed the ARDL bounds test to test whether there is a long-run relationship among variables. The results are shown in

Table 1. Bound testing.

T Statistic	Value	K
F Statistic	4.8523	2
Critical value bounds
Significance	I(0) Bound	I(1) Bound
10%	2.1	3.13
5%	2.43	3.54
2.5%	2.74	3.61
1%	3.12	4.54

.

The test statistic value (4.8523) is greater than the I(1) bound tabulated values; hence, the null hypothesis of none of the long-run relationships is rejected. This shows that there is cointegration amongst the variables under investigation. Having found evidence of cointegration, the study proceeded to perform an ARDL test to estimate the long-run and short-run estimates.

4.2.3. ARDL Results

The presence of cointegration necessitated the use of the ARDL technique to calculate the elasticities. The long-run ARDL was estimated, and the results are presented in

Table 2. Long-run coefficients estimated through the ARDL approach.

Variable	Coefficient	Standard Error	t-Statistic	p-Value
GP	0.217066	0.028445	7.631162	0.0000
INT	0.303575	0.466545	0.650688	0.5168
LM3	−0.048382	0.008921	−5.423479	0.0000
LPG	0.108165	0.017013	6.357574	0.0000
LGDP	0.162778	0.078210	2.081287	0.0401

below.

The results shown in Table 2 indicate that the independent variables, such as M3, PG, and GDP, are significant in explaining gold prices; however, interest rate is not. The relationship between interest rates and gold process was seen to be insignificant. This shows that there is no relationship between interest rates and gold prices. This suggests that Hotelling’s Rule does not apply. The results showed that there is no relationship between gold price and interest rates. This is inconsistent with Hotelling’s Rule, which states that the price of a non-renewable resource should rise at the rate of the rise in the interest rate. A positive relationship should have been found if Hotelling’s Rule were to hold in the South African gold mining sector. Mason and Veld [41] discovered that the Hotelling technique has obvious flaws in oil markets. Real oil prices have remained relatively stable for almost a century, in stark contrast to predictions that rents would grow at the rate of interest [41]. The results from a study by Ukani [42] suggested that Hotelling’s Rule predicts price paths best when a short time-span is considered. Van Veldhuizen and Sonnemans [12] investigated a fresh cause for the lack of empirical evidence for Hotelling’s Rule for non-renewable resources using a laboratory experiment. They investigated whether producers with enormous resource stocks pay less attention to the dynamic component of their extraction decisions, causing them to shift extraction to the present and concentrate on strategic behaviour. Their research discovered that producers with big stockpiles pay less attention to dynamic optimisation and shift extraction to the present, causing them to overproduce in comparison to Hotelling’s Rule. Ferreira da Cunha and Missemer [9] were able to confirm that it is possible to obtain bell-shaped trajectories for supplies and U-shaped ones for prices, as described by Hotelling.

The global production of gold was seen as having a positive relationship with gold prices. This is inconsistent with Hotelling’s Rule. According to Hotelling’s Rule, an optimal extraction path can be attained if the price of a gold resource rises over time, forcing demand to decrease. This will then lead to a reduction in production. In this case, a negative relationship between the resource price and its production would be established. Since the price of a resource increases over time, then demand and production should decrease over time [3]. Growing resource rents would imply rising scarcity, while decreasing resource rents would indicate dropping scarcity, and no increase or decrease would indicate no change in scarcity [54]. An analysis of the gold price series’ graphical patterns revealed that the series was obviously trending upward. This supports Hotelling’s Rule, and is also supported by actual evidence.

The results also show that income has a positive relationship with gold prices. Money supply (M3) is found to have a negative relationship with gold prices. The short-run relationship results are displayed in

Table 3. ARDL—Short-run relationships.

Variable	Coefficient	Standard Error	t-Statistic	p-Value
ECM	−0.037720	0.01951	−1.93306	0.0593
D(INT)	−0.022048	0.00713	−0.00402	0.6871
D(LM3)	0.000338	0.00010	3.38427	0.0001
D(LPG)	−0.000187	9.88105	−1.89788	0.0824
D(LGDP)	−0.000287	0.00012	−2.29532	0.0321

.

In Table 3, the coefficients of LPC and LGDP are negative and lie between zero and one, indicating that these two variables converge to their long-run equilibrium. The coefficient of D (LGP) of −0.037720, as indicated in Table 3, shows that the speed of adjustment is approximately 3.77%. This indicates that if there is a deviation from equilibrium, and 3.77% is corrected as the variable moves towards restoring equilibrium.

4.2.4. Diagnostic Checks

Diagnostic tests were important in validating the parameter evaluation of the outcomes achieved by the model. The VAR was tested using the AR Roots test and serial correlation, and the results are indicated in Figure 4.

From the

Table 4. Heteroskedasticity test.

Heteroskedasticity Test
Chi-Sq	Df	Prob
183.2053	180	0.4196

Source: Author’s computation based on EViews 7.

below, we can conclude that the VAR model is stable, since all roots lie within the circle and are less than one. If the VAR model is not stable, results such as impulse response standard errors will not be valid. White heteroskedasticity was carried out in this study. The presence of heteroskedasticity means that the model has misspecifications; hence, conclusive results cannot be derived from such a model. Results shown in Table 4 summarise the results of heteroskedasticity using the White test.

The test with no cross terms produced a chi-square of 183.2053 and a probability of 0.4196. In this study, based on the results above, the null hypothesis, which assumes that there are no misspecifications, will not be rejected, and the model will be relied on. The Breusch–Godfrey serial correlation test was performed to test for serial correlation. The results are shown in

Table 5. Breusch–Godfrey serial correlation LM test.

Breusch-Godfrey Serial Correlation LM Test
F Statistic	0.008002	Prob.F	0.9303
Obs * R Squared	0.025443	Prob.Chi-Squared	0.8733

Source: Author’s own rendering; results obtained from Eviews 10.

.

Results show that there is no correlation in the model. The decision rule states that the null hypothesis (H₀) should be rejected if the p-value of observed R-squared is less than the 0.05 level of significance [49].

5. Conclusions and Recommendations

This study sought to test the applicability of Hotelling’s Rule in South Africa. The study used graphical analysis to assess the applicability of Hotelling’s Rule. A review of the graphical trends of the gold price series clearly showed that the series had an upward trend. This confirms Hotelling’s Rule and is also consistent with the empirical literature. As price pulls away from marginal extraction cost, the rate of increase in price will approach the rate of interest. It is clear that in such a model, price does not revert to a fixed mean. It is also clear that such a model implies systematic increases in real price over time. It can thus be said that the scarcity of gold in South Africa and the rising price of gold seem to be consistent with Hotelling’s Rule. The gold price trends have shown a steady upward climb, in line with Hotelling’s Rule.

The study also conducted a review of the gold production trends in South Africa. The objective was to identify the trend properties of the South African gold production to see if they follow the trend according to Hotelling’s Rule. The results showed a declining gold production trend. This shows that there has been a decrease in gold production over time in South Africa. Lastly, a review of gold consumption in South Africa was performed. The findings showed that gold consumption is increasing. This was also supported by qualitative sources, such as previous studies. The rising consumption of a non-renewable resource violated Hotelling’s Rule. Hotelling’s Rule claims that demand and consumption should decrease over time because the price of a resource increases over time. Conventional classical economic wisdom suggests that an increase in the price of a commodity is supposed to depress its demand. The same applies to non-renewable resources. This leads to some inconsistency on the theoretical aspect of the optimal depletion of the gold resource. The failure of Hotelling’s Rule to hold on consumption has been highlighted by other researchers. For example, Mikesell states that supply and demand conditions in individual countries do not conform to world conditions of relative mineral scarcity.

Based on these findings, this study concludes that the operation of Hotelling’s Rule would not result in an optimum path for achieving national sustainability. The implication of this is that gold extraction is following a path that is not socially optimal. Consumption of gold is likely to increase in the next couple of years because of global demand. There have been several emerging market economies, including China and India, which have been expanding in terms of production. These countries have also been demanding more gold in the last decade. An increase in demand and consumption of gold will lead to more production, and this may lead to the rapid depletion of gold. The depletion is moving at a faster rate, and this might lead to the South African mining sector running out of gold sooner (The study cannot ascertain when South Africa may run out of gold reserves because it did not do an empirical forecasting regarding when the current gold reserves might be depleted. However, official private and government statistics show that South Africa may run out of gold in the net 30–40 years.). It can thus be said that gold production is currently unsustainable, and this raises the spectre of an imminent resource depletion.

The fact that gold depletion is occurring at a faster rate requires the government to intervene and ensure that there are new discoveries in the gold mining sector. There is a need for new discoveries to be made so that the gold reserve base can increase. There is thus a need to generate scientific knowledge and methods to discover new reserves. The government should also spend more funds to promote research and development. This could bring about more technological innovations in the mining industry. Gold reserves could be effectively extended through regulatory interventions by government or private entities, leading, for example, to technological development that would allow for profitable access to lower-grade ores.