Thursday, October 21, 2021

The Environmental Kuznets Curve: 2021 Edition

The second encyclopedia chapter. First one is here.

Introduction 

The environmental Kuznets curve (EKC) is a hypothesized relationship between various indicators of environmental degradation and countries’ gross domestic product (GDP) per capita. In the early stages of a country’s economic development, environmental impacts and pollution increase, but beyond some level of GDP per capita (which will vary for different environmental impacts) economic growth leads to environmental improvement. This implies that environmental impacts or emissions per capita are an inverted U-shaped function of GDP per capita, whose parameters can be statistically estimated. Figure 1 shows a very early example of an EKC. A large number of studies have estimated such curves for a wide variety of environmental impacts ranging from threatened species to nitrogen fertilizers, though atmospheric pollutants such as sulfur dioxide and carbon dioxide have been investigated most. Panayotou (1993) was the first to call this relationship the EKC, where Kuznets refers to the similar relationship between income inequality and economic development proposed by Nobel Laureate Simon Kuznets and known as the Kuznets curve. The EKC can be seen as an empirical version of the interpretation of sustainable development as the idea that development is not necessarily damaging to the environment and, also that poverty reduction is essential to protect the environment (World Commission on Environment and Development, 1987).

Figure 1. An Environmental Kuznets Curve 

The EKC has been the dominant approach among economists to modeling ambient pollution concentrations and aggregate emissions since Grossman and Krueger (1991) introduced it in an analysis of the potential environmental effects of the North American Free Trade Agreement. The EKC also featured prominently in the 1992 World Development Report published by the World Bank and has since become very popular in policy and academic circles and is even found in introductory economics textbooks. 

Critique 

Despite this, the EKC was criticized almost from its beginning on empirical and policy grounds, and debate continues. It is undoubtedly true that some dimensions of environmental quality have improved in developed countries at the same time that they have become richer. City air and rivers in these countries have become cleaner since the mid-20th Century and, in some countries, forests have expanded. Emissions of some pollutants such as sulfur dioxide have clearly declined in most developed countries in recent decades. But there is more mixed evidence for other pollutants such as carbon dioxide. Carbon emissions have fallen in the last 40 years in some developed countries such as the United Kingdom or Sweden, while they have increased in others such as Australia or Japan. There is also evidence that emerging countries take action to reduce severe pollution. For example, Japan cut sulfur dioxide emissions in the early 1970s following a rapid increase in pollution when its income was still below that of the developed countries (Stern, 2005) and China has also acted to reduce sulfur emissions in recent years. As further studies were conducted and better data accumulated, many of the econometric studies that supported the EKC were found to be statistically fragile. 

Initially, many understood the EKC to imply that the best way for developing countries to improve their environment was to get rich (e.g. Beckermann, 1992). This alarmed others (e.g. Arrow et al., 1995), as while this might address some issues like deforestation or local air pollution, it would likely exacerbate other environmental problems such as climate change. Even if there is an EKC for per capita impacts, environmental impacts would increase for a very long time if the majority of the population is on the rising part of the curve and/or the population is also growing (Stern et al., 1996). 

Explanations 

The existence of an EKC can be explained either in terms of deep determinants such as technology and preferences or in terms of scale, composition, and technique effects, also known as “proximate factors”. Scale refers to the effect of an increase in the size of the economy, holding the other effects constant, and should increase environmental impacts. The composition and technique effects must outweigh this scale effect for pollution or other environmental impacts to fall in a growing economy. The composition effect refers to the economy’s mix of different industries and products, which differ in pollution intensities. Finally, the technique effect refers to the remaining change in pollution intensity. This will include contributions from changes in the input mix, for example substituting natural gas for coal; changes in productivity that result in less use, ceteris paribus, of polluting inputs per unit of output; and pollution control technologies that result in less pollutant being emitted per unit of polluting input. 

Over the course of economic development, the mix of energy sources and economic outputs tends to evolve in predictable ways. Economies start out mostly agricultural and the share of industry in economic activity first rises and then falls as the share of agriculture declines and the share of services increases. We might expect the impacts associated with agriculture, such as deforestation, to decline, and naively expect the impacts associated with industry, such as pollution, would first rise and then fall. However, the absolute size of industry rarely does decline, and it is improvement in productivity in industry, a shift to cleaner energy sources, such as natural gas and hydro-electricity, and pollution control that eventually reduce some industrial emissions. On the other hand, offshoring of pollution probably plays only a small role in cutting emissions in developed economies (Kander et al., 2015). 

Static theoretical economic models of deep determinants, that do not try to also model the economic growth process, can be summarized in terms of two parameters: The elasticity of substitution between dirty and clean inputs, which summarizes how difficult it is to cut pollution; and the elasticity of the marginal utility of consumption with respect to consumption, which summarizes how hard it is to increase consumer well-being with more consumption (Pasten and Figeroa, 2012). It is usually assumed that these consumer preferences are translated into policy action. Pollution is then more likely to increase as the economy expands, the harder it is to substitute other inputs for polluting ones and the easier it is to increase consumer well-being with more consumption. If these parameters are constant, then either pollution rises or falls with economic growth. Only if they change over time will pollution first rise and then fall. The various theoretical models can be classified as ones where the EKC is driven by changes in the elasticity of substitution as the economy grows or models where the EKC is primarily driven by changes in the elasticity of marginal utility. 

Dynamic models that model the economic growth process alongside changes in pollution are harder to classify. The Green Solow Model developed by Brock and Taylor (2010) explains changes in pollution as a result of the competing effects of economic growth and a constant rate of improvement in pollution control. Fast growing middle-income countries, such as China, then having rising pollution, and slower growing developed economies, falling pollution. An alternative model developed by Ordás Criado et al. (2011) also suggests that pollution rises faster in faster growing economies but that there is also convergence so that countries with higher levels of pollution are more likely to reduce pollution faster than countries with low levels of pollution. 

Recent Empirical Research 

Recent empirical research builds on these dynamic models to paint a subtler picture than early EKC studies did (Stern, 2017). We can distinguish between the impact of economic growth on the environment and the effect of the level of GDP per capita, irrespective of whether an economy is growing or not, on reducing environmental impacts. We can also distinguish between the effects of economic growth and the simple passage of time. Economic growth usually increases environmental impacts, but the size of this effect varies across impacts and the impact of growth often declines as countries get richer. However, richer countries are often likely to make more rapid progress in reducing environmental impacts. In econometric terms, the time effect – the change in emissions if economic growth is zero – may be higher in richer countries. Rapid growth in middle-income countries, such as China or India, is more likely to overwhelm the time effect in those countries as suggested by Brock and Taylor (2010).

Finally, there is often convergence among countries, so that those that have relatively high levels of impacts reduce them faster or increase them slower than countries with low levels of impacts. These combined effects explain more of the variation in pollution emissions or concentrations than either the classic EKC model or models that assume that either only convergence or growth effects alone are important. Therefore, while being rich means a country might do more to clean up its environment, getting rich is likely to be environmentally damaging. 

References 

Arrow, K., Bolin, B., Costanza, R., Dasgupta, P., Folke, C., Holling, C. S., Jansson, B.-O., Levin, S., Mailer, K.-G., Perrings, C., Pimental, D., 1995. Economic growth, carrying capacity, and the environment. Science 268, 520–521. 

Beckermann, W., 1992. Economic growth and the environment: whose growth? Whose environment? World Development 20, 481–496. 

Brock, W. A.,Taylor, M. S., 2010. The green Solow model. Journal of Economic Growth 15, 127–153. 

Grossman, G. M., Krueger, A. B., 1991. Environmental impacts of a North American Free Trade Agreement. NBER Working Papers 3914. 

Kander, A., Jiborn, M., Moran, D. D., Wiedmann T. O., 2015. National greenhouse-gas accounting for effective climate policy on international trade. Nature Climate Change 5, 431–435. 

Ordás Criado, C., Valente, S., Stengos, T., 2011. Growth and pollution convergence: Theory and evidence. Journal of Environmental Economics and Management 62, 199–214. 

Panayotou, T., 1993. Empirical tests and policy analysis of environmental degradation at different stages of economic development. Working Paper, Technology and Employment Programme, International Labour Office, Geneva, WP238. 

Pasten, R., Figueroa, E., 2012. The environmental Kuznets curve: A survey of the theoretical literature. International Review of Environmental and Resource Economics 6, 195–224. 

Stern, D. I., 2005. Beyond the environmental Kuznets curve: Diffusion of sulfur-emissions-abating technology. Journal of Environment and Development 14(1), 101–124. 

Stern, D. I., 2017. The environmental Kuznets curve after 25 years. Journal of Bioeconomics 19, 7–28.

Stern, D. I., Common, M. S., Barbier, E. B., 1996. Economic growth and environmental degradation: the environmental Kuznets curve and sustainable development. World Development 24, 1151–1160. 

World Commission on Environment and Development, 1987. Our Common Future. Oxford: Oxford University Press.  

Energy and Development

The first of two book chapters for Elgar encyclopedias I recently wrote.

What is the Role of Energy in Economic Activity?

The economic system must operate within the constraints determined by the laws of physics and human knowledge of technology. Production, including household production, requires energy to carry out work to convert materials into desired products and to transport raw materials, goods, and people. The second law of thermodynamics implies that energy cannot be recycled and that there are limits to how much energy efficiency can be improved. Therefore, energy is an essential factor of production, and continuous supplies of energy are needed to maintain existing levels of economic activity as well as to grow and develop the economy (Stern, 1997). The first law of thermodynamics states that energy cannot be created and so energy (and matter) must be extracted from the environment. Also, energy must be invested in order to capture useful energy (Hall et al., 1986). Before the Industrial Revolution, economies depended on energy from agricultural crops and wood as well as a smaller amount of wind and waterpower, all of which are directly dependent on the sun (Kander et al., 2015). This is still largely the case in the rural areas of the least developed countries. While solar energy is abundant and inexhaustible, it is very diffuse compared to concentrated fossil fuels. This is why the shift to fossil fuels in the Industrial Revolution relaxed the constraints on energy supply and, therefore, on production and growth (Wrigley, 1988).

How Does Energy Use Change with Economic Development?

Figure 1 shows that energy use per capita increases with GDP per capita, so that richer countries tend to use more energy per person than poorer countries. The slope of the logarithmic regression line implies that a 1% increase in income per capita is associated with a 0.8% increase in energy use per capita. As a result, energy intensity – energy used per dollar of GDP – is on average lower in higher income countries. These relationships have been very stable over the last several decades (Csereklyei et al., 2016). Energy intensity in today’s middle-income countries is similar to that in today’s developed countries when they were at the same income level (van Benthem, 2015).

Figure 1. GDP and Energy Use per Capita 2018

Energy intensity has also converged across countries over time, so that countries that were more energy intensive in the 1970s tended to reduce their energy intensity by more than less energy intensive countries, and the least energy intensive countries often increased in energy intensity. Though data are limited to fewer and fewer countries as we go back further in time, these relationships also appear to hold over the last two centuries – energy use increased, energy intensity declined globally, and countries converged in energy intensity (Csereklyei et al., 2016). Though data is even more limited, it seems that the share of energy consumption expenditure and production costs also declines as countries develop (Csereklyei et al., 2016; Burke et al., 2018).

The mix of fuels used changes over the course of economic development. Figure 2 shows the average mix of energy sources in each of five groups of countries ordered by income per capita in 2018. In the lowest income countries in the sample (approximately below $5,000 per capita in 2017 purchasing power parity adjusted dollars), traditional use of biomass such as wood and agricultural waste dominates and oil use for transportation as well as electricity generation and other uses is the second most important energy source. As we move to richer countries, the relative role of biomass declines radically, and first oil and then natural gas and primary electricity increase in importance. Note that biomass use per capita in the richest quintile (above $40,000 per capita) is actually greater than in the lowest quintile, as total energy use increases with income. The ways in which this biomass is used will of course be quite different. Higher quality fuels are those that provide more economic value per joule of energy content by being converted more efficiently, being more flexible or convenient to use, and by producing less pollution. We would expect that lower income households would be more willing to tolerate the inconvenience and pollution caused by using lower quality fuels to produce energy services. So as household income increases, we would expect households to gradually ascend an “energy ladder” by consuming higher quality fuels and more total energy. Recent studies often find a more ambiguous picture where multiple fuels are used simultaneously as modern fuels are added to the use of traditional fuels (Gregory and Stern, 2014). 

Figure 2. Fuel Mix and Development 2018

 

In 2016, approximately one billion people remained without access to electricity at home (International Energy Agency, 2017). Around 85% of these people lived in rural areas. There has been rapid progress in electrification in recent years with both grid expansion and the spread of off-grid systems (Burke et al., 2018; Lee et al., 2020). Due to the complexity and costs of electricity-sector management and constrained and weak institutions, power supply is usually less reliable in developing countries than in developed countries (Figure 3) and electricity theft is also more common (Burke et al., 2018). Best and Burke (2017) found that countries with higher levels of government effectiveness have achieved greater progress in providing access to reliable electricity. Industry and other electricity consumers, therefore, often rely on self-generation of electricity, but this is a costly solution (Fingleton-Smith, 2020). 

 Figure 3. Electricity Reliability and Development 2017

 

Does Energy Use Drive Economic Growth?

Economic growth refers to the process that results in increasing GDP per capita over time while development refers to a broader range of indicators including health, education, and other dimensions of human welfare. However, GDP per capita is highly, although not perfectly, correlated with broader development measures (Jones and Klenow, 2016) and so it is worth considering what the role of energy is in economic growth.

Mainstream economic growth models largely ignore the role of energy in economic growth and focus on technological change as the long-run driver of growth. On the other hand, there is a resource economics literature that investigates whether limited energy or other resources could constrain growth. By contrast, many ecological economists believe that energy plays the central role in driving growth and point to the switch traditional energy sources to fossil fuels as the cause of the industrial revolution (Stern, 2011). 

To reconcile these opposing views, Stern and Kander (2012) modified Solow’s neoclassical growth model (Solow, 1956) by adding an energy input that has low substitutability with capital and labor. Their model also breaks down technological change into those innovations that directly increase the productivity of energy– energy-augmenting technical change and those that increase the productivity of labor – labor-augmenting technical change. In this model, when energy is superabundant the level of the capital stock and output are determined by the same functions of the same factors as in the Solow model. But when energy is relatively scarce, the size of the capital stock and the level of output depends on the level of energy supply and the level of energy-augmenting technology. Therefore, in the pre-industrial era and possibly when energy was scarce – and possibly in developing countries today – the level of output was determined by the supply of energy and the level of energy augmenting technology. Until the industrial revolution, output per capita was generally low and economic growth was not sustained (Maddison, 2001). After the industrial revolution, as energy became more and more abundant, the long-run behavior of the model economy becomes more and more like the Solow growth model. If this model is a reasonable representation of reality, then mainstream economists are not so wrong to ignore the role of energy in economic growth in developed economies where energy is abundant, but their models have limited applicability to both earlier historical periods and possibly to today’s developing countries. McCulloch and Zileviciute (2017) find that electricity is often cited as a binding constraint on growth in the World Bank’s enterprise surveys. Energy is expensive relative to wages in developing countries. The price of oil is set globally, and the share of electricity in costs or expenditures can be very high in middle income countries (Burke et al., 2018).

Electricity and Development

Access to energy and electricity, in particular, is a key priority for policymakers and donors in low-income countries. For example, the United Nations’ Sustainable Development Goal 7 targets universal access to modern energy by 2030. Electrification can allow poor households to have easy access to lighting for evening chores or studying and power for phone charging and for a range of new small business activities, both on and off the farm (Lee et al., 2020). Electricity access allows a reallocation of household time, especially for women, away from obtaining energy, for example by collecting firewood, and towards more productive activities. Electricity could also provide health benefits by allowing deeper wells, refrigeration, reduced exposure to smoke etc. (Toman and Jemelkova, 2003).

The micro-level effect of electrification is a growing area of empirical research (Lee et al., 2020). While micro studies typically suggest positive impacts of electrification on income and other development outcomes, more recent quasi-experimental approaches such as randomized controlled trials typically find a smaller impact for electrification than earlier studies did (Lee et al., 2020). Estimates of the effect of electricity infrastructure on economic growth are typically small. One of the best studies (Calderón et al., 2015) estimates the elasticity of GDP with respect to electricity generation capacity as 0.03 (Burke et al., 2018).

Lee et al. (2020) argue that providing poor households with access to electricity alone is not enough to improve economic and noneconomic outcomes in a meaningful way. Complementary inputs are needed, which will accumulate very slowly. Imagination and role models are also important in understanding how to exploit electricity to develop businesses (Fingleton-Smith, 2020). When electricity becomes available in rural areas of sub-Saharan Africa, it is often not used to power agricultural or other productive activities (Bernard, 2012). Institutions are also vital for attaining broad-based benefits from electricity in developing countries. Many developing countries have reformed their electricity sectors during the last few decades, mostly towards market liberalization and corporatization. These efforts have only been partially successful in promoting efficient pricing and greater electricity access (Jamasb et al., 2017). Studies assessing the economic effects of these reforms are scarce. The effects on economic growth seem positive, while the effects on poverty are mixed (Jamasb et al., 2017). In this context, technology transfer and development finance will be critical for increasing the use of electricity in developing countries (Madlener, 2009).

Burke et al. (2018) examined electrification success stories - countries that, from a low level of economic development, have now achieved near-universal electricity access as well as relatively high levels of electricity use. These countries are South Korea, China, Thailand, Vietnam, Egypt, and Paraguay. The first four are well-known development success stories too. Paraguay has abundant hydroelectricity and both Paraguay and Egypt have had relatively strong economic growth. Egypt has been less successful in providing a reliable electricity supply. The most successful countries in increasing access in Sub-Saharan Africa have been South Africa and Ghana, which both suffer from unreliable electricity, which constrains economic activity.

References

Bernard, T., 2012. Impact analysis of rural electrification projects in Sub-Saharan Africa. World Bank Research Observer 27(1): 33–51.

Best, R., and P. J. Burke, 2017. The importance of government effectiveness for transitions toward greater electrification in developing countries. Energies 10(9): 1247.

Burke P. J., D. I. Stern, and S. B. Bruns, 2018. The impact of electricity on economic development: a macroeconomic perspective. International Review of Environmental and Resource Economics 12(1): 85–127.

Calderón, C., E. Moral-Benito, and L. Servén, 2015. Is infrastructure capital productive? A dynamic heterogeneous approach. Journal of Applied Econometrics 30: 177–198.

Csereklyei Z., M. d. M. Rubio Varas, and D. I. Stern, 2016. Energy and economic growth: The stylized facts. Energy Journal 37(2): 223–255.

Fingleton-Smith, E., 2020. Blinded by the light: The need to nuance our expectations of how modern energy will increase productivity for the poor in Kenya. Energy Research & Social Science 70: 101731.

Gregory, J. and D. I. Stern, 2014. Fuel choices in rural Maharashtra. Biomass and Bioenergy 70: 302–314.

Hall, C. A. S., C. J. Cleveland, and R. K. Kaufmann, 1986. Energy and Resource Quality: The Ecology of the Economic Process. New York: Wiley Interscience.

International Energy Agency, 2017. Energy Access Outlook 2017: From Poverty to Prosperity. World Energy Outlook Special Report.

Jamasb, T., R. Nepal, and G. R. Timilsina, 2017. A quarter century effort yet to come of age: a survey of electricity sector reform in developing countries. Energy Journal 38(3): 195–234.

Jones, C. I., and P. J. Klenow. 2016. Beyond GDP? Welfare across countries and time. American Economic Review 106(9): 2426–2457.

Kander, A., P. Malanima, and P. Warde, 2014. Power to the People: Energy in Europe over the Last Five Centuries. Princeton University Press.

Lee, K., E. Miguel, and C. Wolfram, 2020. Does household electrification supercharge economic development? Journal of Economic Perspectives 34(1): 122–144.

Maddison, A., 2001. The World Economy: A Millennial Perspective. Paris: OECD.

Madlener, R., 2009. The economics of energy in developing countries. In: L. C. Hunt and J. Evans (eds.), International Handbook on the Economics of Energy, Edward Elgar.

McCulloch, N., and D. Zileviciute, 2017. Is electricity supply a binding constraint to economic growth in developing countries? EEG State-of-Knowledge Paper Series 1.3.

Solow, R. M., 1956. A contribution to the theory of economic growth. Quarterly Journal of Economics 70: 65–94.

Stern, D. I., 1997. Limits to substitution and irreversibility in production and consumption: a neoclassical interpretation of ecological economics. Ecological Economics 21: 197–215.

Stern, D. I., 2011. The role of energy in economic growth. Annals of the New York Academy of Sciences 1219: 26–51.

Stern, D. I., and A. Kander, 2012. The role of energy in the industrial revolution and modern economic growth. Energy Journal 33(3): 125–152.

Toman, M. A., and B. Jemelkova, 2003. Energy and economic development: An assessment of the state of knowledge. Energy Journal 24(4): 93–112.

van Benthem, A. A., 2015. Energy leapfrogging. Journal of the Association of Environmental and Resource Economists 2(1): 93–132.

Wrigley, E. A., 1988. Continuity, Chance, and Change: The Character of the Industrial Revolution in England. Cambridge: Cambridge University Press.

Wednesday, October 20, 2021

Our COVID-19 Paper

Publishing papers on COVID-19 is very popular: 

and we couldn't resist joining the bandwagon. Late last year, Xueting Jiang, my PhD student, and I did a quick literature survey to identify a gap. Though there was a lot of research on how pollution emissions evolved over the course of the pandemic and recession, there was little putting that into the historical context of past recessions. Last year, I worked with Kate Martin, a masters student, on the relationship between carbon emissions and economic activity over the business cycle. We decided to extend that analysis. 

Our new paper uses U.S. monthly data from January 1973 to December 2020. We look at how the relationship between carbon emissions and GDP varies between recessions and expansions, but we also look at individual recessions and how emissions from different sectors vary over the business cycle. 

Like Sheldon and others, we find that, in general, the emissions-GDP elasticity is greater in recessions than in expansions, but we find that this is largely because of sharp falls in emissions associated with negative oil market shocks. The 1973-5, 1980, and 1990-1 recessions were associated with negative oil supply shocks. In 2020, there was instead a negative oil demand shock due to the pandemic. These recessions have emissions-GDP elasticities that are significantly larger than the elasticity in expansions. The elasticities in the 1981-2, 2001, and 2008-9 recessions are no larger than in expansions.

The graph shows NBER recessions in light blue stripes and nominal and real oil prices. The big spike in oil prices in 2008 came at the end of an extended increase associated with rising demand for oil. Of course, supply was constrained during this period but there wasn't a sudden supply crisis. In 1981-82 the price of oil was already falling when the recession started and it is usually regarded as having been caused by the Federal Reserve under Paul Volcker dramatically raising interest rates.

When we regress the growth of sectoral carbon emissions on the growth of national GDP, we find that the asymmetry is present in the industrial and particularly in the transport sector, which are the two largest users of oil in the US economy, using 28% and 66% of the total, respectively.

When we control for oil use, the asymmetries disappear. 

So, though the cause of the COVID-19 recession was unusual the carbon emissions outcome was similar to past recessions associated with oil crises. More importantly, we learned something new about what happens to emissions in recessions, at least in the US.


Tuesday, October 12, 2021

How Large is the Economy-Wide Rebound Effect in Middle Income Countries? Evidence from Iran

 


We have a new working paper in our rebound effect series. Previous papers reviewed the literature on the economy-wide rebound effect, estimated the economy-wide rebound effect for the United States, and estimated it for some European countries (as well as the United States). The new paper is about Iran. This is a middle income country with a resource intensive and quite regulated economy. Is it a lot different to the developed economies we have already looked at?

The rebound effect is large in Iran too. A major difference between Iran and the developed economies is that energy intensity has been rising in Iran:

 

Total energy use tripled from 1988 to 2017, which is the sample period used in our econometric analysis (quarterly data):


The econometric model is the same as that used in the US paper that is now published in Energy Economics, except we only use the distance covariance method for the independent component analysis in this paper. The next figure shows the estimated impulse response functions of energy, GDP, and the price of energy to energy efficiency, GDP, and price shocks:

The top left panel shows the rebound effect. Initially, there is a large drop in energy use, but this diminishes over time. We estimate that the rebound is 84% after six years. The confidence interval is wide and includes 100%.

On the other hand, the GDP shock has large positive effects on energy (top middle panel) and GDP (middle). These are similar in size. By contrast, in the US, the effect on energy is much smaller than on GDP. This seems to be "why" energy intensity falls in the US but rises in Iran.

In this paper we also conduct a forecast error variance decomposition:

This shows how much each of the shocks explain each of the variables at different time horizons. Energy efficiency shocks explain most of the forecast error variance in the first few quarters after a shock. But over time, the GDP shock comes to explain most of the forecast error variance. This is why I argue that the relative GDP shocks are what drives energy intensity.

The paper is coauthored with Mahboubeh Jafari at Shiraz University and Stephan Bruns at University of Hasselt.