s2fieldsofstudy: Economics History

text:
Measuring Intra-City Eco-Efficiency Variations of Urban Infrastructures in Jeddah

Corresponding Author: Mohammed Aljoufie Department of Urban and Regional Planning, King Abdulaziz University, Saudi Arabia Email: maljufie@kau.edu.sa; aljoufie@itc.nl Abstract: Saudi cities are experiencing construction booms linked to urban infrastructure services and the Kingdom’s second largest city, Jeddah, is not an exception. As these booms are associated with urban expansion and rapid population growth, the major challenge confronting urban planners is the ensuring of resource efficiency given the offered infrastructure. In fact, reducing the consumption of resources and the impact of consumption on the environment is a serious concern with respect to the improved value of sustainable urban development as well as society. This paper attempts to measure intracity spatial eco-efficiency variations of the major urban infrastructures of Jeddah. These infrastructures include water supply, public transportation, social businesses, energy consumption, solid waste generation and green areas, all of which are assumed to be offered as a skeleton for upcoming urban environmental plans that will then lead to the reconfiguring, retrofitting or replacing of infrastructures in the city, thus driving it towards a green economy.

Introduction
Measuring or assessing (Kuosmanen, 2005) is the secret to established management practices. Measuring the sustainability of cities contributes to overall good city management as sustainability indicators and composite indices are recognised as effective tools for policy making (Singh et al., 2009).
Assessing eco-efficiency inspires urban planners and decision makers to search for the least costly and most environmentally friendly alternatives available (Ribarova et al., 2013). While urban environments drive economic development, their avid hunger for growth combined with their size, results in an alarming increase in resource consumption in dense areas of cities (Schaffer and Vollmer, 2010).
In fact, sustainability does not prevent resource consumption, but rather, it aims to efficiently consume resources. While material and resource flows are inherent to and incurred by the cities' infrastructure, eco-efficiency is the indicator to promote transformation towards sustainability. However, there is a considerable lack of research regarding the development of this indicator. In particular, there is a considerable absence in the literature on the development of such an indicator to analyse intracity eco-efficiency variations in urban infrastructures.
Sustainability of Urban infrastructure is crucial for urban environment (Choguill, 1996) because they regulate flow of natural and artificial resources consumed in the urban areas. The eco-efficiency of urban infrastructure has significant importance with respect to rapidly urbanising and globalising cities such as Jeddah, where urban infrastructure development choices made today determine the success of cities to deliver services to its stakeholders while growing competitively within a protected environment for decades to come (UNESCAP, 2011).
Hence, this paper attempts to develop a measure for intra-city spatial eco-efficiency of selected urban infrastructure amenities in Jeddah such that the amenities can be strategically planned to offer sustainable reconfiguring and retrofitting.

Eco-Efficiency of Urban Infrastructure: Theoretical Background
Brunt land Commission suggested sustainable development as a development paradigm that aims to meet the needs of the present generation without compromising the capabilities of future generations (WCED, 1987). Saudi cities have recently begun focusing on sustainability because of the increasing awareness that economic growth usually comes at the cost of environmental impact, such as the consumption of the earth's resources has surpassed the earth's available resources. In 2012, the UAE launched 'The Arab Green Economy Initiative", which guides their economy from a virtual to a real sustainability perspective (UNDP, 2012). The environmental and climate changes impact related burdens as the production and consumption of resources call for a more efficient use of environmental resources. The concept of eco-efficiency was initially developed as a business link to sustainability (Schaltegger and Sturm, 1990;Freeman et al., 1973). It was later adopted by the WBCSD (2000) with the slogan, 'doing more with less' or 'creating more value with less impact'. Eco-efficiency suggests a substantial change from non-sustainability to sustainability (Mickwitz et al., 2006). Eco-efficiency offers solutions such as optimising resource values by reducing the use of resources and thereby reducing the environmental impact Eco-efficiency promotes the development of a cyclic economy that is resource conservative in nature rather than a traditional linear economy that consumes resources and produces waste (Byström, 2012). A paradigm shift from conventional environmental reporting to sustainability reporting or ecoefficiency reporting, which comprises the Triple Bottom Line (TBL)-social, economic and environmental aspectshas been evidenced in the last few years (Fet, 2003). Ecoefficiency reporting advises cities' economies to reconfigure their infrastructure towards a low-carbon transition plan (Bulkeley et al., 2014).

Study Area
Jeddah is the second largest city in the Kingdom of Saudi Arabia with a population of 3.4 million in 2014. The population is expected to grow to over 5 million by 2029 (JM, 2009), when the city will then rank 5th, based on size, among all Arabian cities (UN-HABITAT, 2012a). Jeddah is located on the west coast of the Kingdom in the middle of the eastern shore of the Red Sea and it is surrounded by the plains of the Tahoma to the east (Fig. 1). Being a coastal city, its location is more environmentally sensitive to the kingdom. Furthermore, the city is experiencing a transition as many mega infrastructural amenities designed to provide the city's residents a better quality of life are either provisioned for or planned. Jeddah's history, location and unique role in relation to Hajj have contributed to shaping its urban form and demographic profile. Attracting migrant workers and pilgrims from the entire Islamic world, the city is perceived as a place of opportunity. The rapid growth in population (natural and migratory) in the last four decades has coincided with the Kingdom's enormous increase in wealth, which, in turn, has resulted in Jeddah's unprecedented rate of physical expansion. The urban area of Jeddah has exceeded the current capacity of its infrastructure, thus leading to structural problems with respect to city's ability to provide adequate water, sewage and roadways. This growth has also left the city with a number of structural challenges, including numerous areas of vacant land as well as a dependency on private cars for transportation.

Data Collection and Preparation
In this study, six key urban infrastructure resources have been chosen in varying units to determine environmental cost, namely, water, energy, solid waste, green cover, public transport and social business areas (mall in the case of Jeddah). These constitute major urban infrastructure, all of which are pertinent for environmental betterment and improved quality of life in a city.
The analysis was conducted at the district level because of the homogenous character of districts in Jeddah. A simple random sampling technique was applied to obtain household level water, energy and solid waste related data at the district level. The remaining infrastructure data, including green infrastructure, public transport route length and social business areas, were first extracted from satellite imageries in conjunction with secondary data A GIS-based approach was then used to disaggregate the extracted data regarding green infrastructure, public transport route length and social business areas at the district level.

Eco-Efficiency Indicators
Though numerous indicators have been recommended by scholars and agencies to measure sustainability and eco-efficiencies (Singh et al., 2009) the UN (2009) adheres to the following equation:

Environmental Cost Eco efficiency
Economic Output

− =
As previously indicated herein, environmental cost may refer to pollution emissions, resources used or costs associated with environmental burden, while economic output can be expressed in value added through benefits, units of product or service or costs associated with environmental burden. In this study, environmental cost refers to urban infrastructure resources used, while the economic output refers to the service area expressed as per hectare (10,000 square meters) of land parcel. Hence:

Infrastrcture resource uses Eco efficiency
Service area After computing the eco-efficiency of each infrastructure resource at the district level, the resources were categorised on the basis of natural breaks (jenks) and a weight was assigned to each infrastructure resource ranging from very low (0) to very high (5).
Accordingly, to calculate the eco-efficiency for public transport (EEtr):

Length of publictransport routes in meters EEtr
Geographical area of district in hectares = Allocated weights for public transport ecoefficiencies (EEtr) are depicted in Table 1.
To calculate the eco-efficiency for water supply (EEwt):

Watersupply in killoleters EEwt
Geographical area of district in hecatres = Allocated weights for water supply eco-efficiencies (EEwt) are presented in Table 2.
To calculate the eco-efficiency for energy (electricity):
To calculate the eco-efficiency for solid waste generation (EEsw):

Daily solid waste generationin quintals EEsw
Geographical area of district in hecatres = Allocated weights for solid waste generation ecoefficiencies (EEsw) are presented in Table 4.
To calculate the eco-efficiencies for green infrastructure (EEgi):

Green area in square meters EEgi
Geographical area of district in hecatres = Allocated weights for green infrastructure ecoefficiencies are presented in Table 5 (EEgi).
Allocated weights for social businesses ecoefficiencies (EEsb) are presented in Table 6. After determining the infrastructure resource ecoefficiencies, a composite index was developed at the district level. The index depicts the overall spatial sustainability performance of a district. Then, after calculating the sustainability performance, the following formula is applied: where, EEIi is the eco-efficiency index for the 'i'th district; EEtri, EEwti, EEgii, EEeni, EEswi and EEsbi are the weighted eco-efficiencies for the 'i'th district for public transport, water supply, green infrastructure, energy, solid wastes and social businesses, respectively; and Cui denotes the number of classes of the urban infrastructures.
Additionally, a city-level eco-efficiency index was created and classified to denote district level variations of eco-efficiencies for Jeddah as depicted in Table 7.
It is statistically noteworthy, as evidenced in Table 7, that the highest possible eco-efficiency in a district 5 '5', while the lowest is '1'.

Results
Sustainable infrastructure ensures the prosperity of a city (UN-HABITAT, 2012b), while huge environmental resource consumption and limited availability of green and open spaces hampers carrying capacities in urban areas (Mitlin and Satterthwaite, 1996). Accordingly, measuring eco-efficiency becomes more important for the sustainable planning of a city's environment. The findings of this study with respect to eco-efficiency of a city are as follows.

Eco-Efficiency of Public Transport
The importance of an efficient public transport system is not debatable and the need to develop such a system is crucial for decreasing the carbon footprint of a city. However, such development is lacking in Jeddah, as Aljoufie et al. (2013) have indicated the dominance of the car as a means of transportation and a decline in the emphasis placed on public transportation. The share of daily car trips in Jeddah was 96% in 2012. Conversely, public transportation, walking and cycling jointly represented only 4% of the total trips in the city (AECOM, 2012). At present, adequate public transport is available in only a few districts. Figure 2 shows the district level eco-efficiency of public transportation infrastructure in Jeddah. Of the 70 reporting districts in Jeddah, 25 do not have a single meter of public transportation routes, while only three districts-Al Sabeel, Al Balad and Al Sahefah have transportation routes of more than 35 kilometres per hectare, which is considered very high with respect to eco-efficiency. The districts that demonstrate high eco-efficiency are located in the city centre. District level eco-efficiency of public transport infrastructure is presented in Table 8.
The factors that likely obstruct the sustainable development of public transportation in Jeddah include poor service offered by the current public transportation system, cheap fuel prices, cheap automobiles and low social acceptability. Nonmotorised transport modes, such as walking and cycling, are also not well received in the city because of the adverse climate conditions and the absence of adequate supporting road features (secured pedestrian sidewalks and bicycle tracks).

Eco-efficiency of Water Supply
Water is both an economic and an ecological resource (Huang et al., 2013) and in urban areas, the demand for this resource ensues due to the use of alternative hydro-systems (Grimm et al., 2008). Figure 3 and Table 9 show the district level ecoefficiency of water supply in Jeddah. It is noted that eco-efficiency of water supply is high and very high, cumulatively, in approximately 55.7% of the districts located in the urban peripheries where there are new districts and low population density. On the other hand, the eco-efficiency of three districts concentrated in Jeddah's city centre was very low.
Urbanisation consistently increases water-related environmental vulnerabilities, which include water pollution, urban floods, the depletion in the quantity and quality of groundwater, etc. Jeddah's groundwater is highly polluted because of high concentrations of nitrates resulting in the water being declared unusable. The daily water consumption of Jeddah is 1 million cubic meters, 85% of which is supplied through a piped distribution system while the remaining 15% is supplied via water tankers. The analysis further reveals that per capita water consumption averages 190 litters per day and ranges from 90 litters in the lowest use cases to 275 litters in the highest use cases. Unaccounted for water due to leakage and other factors is 30%, which is equal to 191 thousand cubic meters per day (Al-Sefry and Sen, 2006), a factor that negatively affects the eco-efficiency of the water supply. It is further noteworthy that the entire water supply of the city is cycled through hydrocarbon fuelled desalination plants. This means that the consumption of water in the city is, in essence, the indirect consumption of fossil fuel. Undoubtedly, continuing to supply water in this manner will increase the negative environmental impacts and impede the greening of the city's economy. Ecoefficiency of Water infrastructure is also crucial because of its multiplier effects which can be either of positive or negative, for instance if water is consumed in an inefficient way it could lead problems for wastewater infrastructure hampering city's sustainability (Beck and Cummings, 1996) more adversely.   Kambites and Owen (2006) defined green infrastructure as the connected networks of multifunctional, predominately unbuilt space that supports both ecological and social activities and processes. As such, green infrastructure is multifunctional as it can solve many urban problems almost simultaneously. For example, it can absorb carbon emissions from automobiles, contribute to environmental improvements, enhance urban health, sustain place making and leisure activities, decrease the urban heat island effect, increase social cohesion and interactions, etc. Because of the many potential benefits, urban professionals' concern regarding green infrastructure has increased in recent years (Krellenberg et al., 2014, Schäffler and Swilling, 2013, Alberti et al., 2003. Figure 4 and Table 10 depict the district level ecoefficiency of green infrastructure in Jeddah. It is evidenced that very low and low eco-efficiencies are dominant in Jeddah, while high and very high ecoefficiencies comprise collectively a low percentage. Thus, there is a significant need for green infrastructure in most of the districts of Jeddah Unfortunately, however, green infrastructure in Jeddah faces many challenges, two of which are the arid climate and the lack of water, both of which deter the development of green infrastructure in the city.

Eco-Efficiency of Energy Infrastructure
Similar to water supply, electricity supply in Jeddah depends on hydrocarbon based fuels. As most of the electricity is used for air-conditioning, the production and consumption of electricity in the city generates higher carbon emissions, which translate into a larger ecological footprint. With respect to Beijing, Zhang et al. (2013) proposed the expansion of green spaces as a tool for energy savings and emissions reduction. Table 11 and Fig. 5 indicate high consumption of electric energy in 20 districts, thus leading to an extremely low eco-efficiency, while eco-efficiency is comparatively very high in 19 districts of the city. It is noted that low, very low and moderate ecoefficiencies are concentrated in the city centre of Jeddah and in the highly dense areas of the city. The rationalisation of energy consumption in conjunction with climate conditions are the main challenges facing energy infrastructure not only in Jeddah but in all Saudi cities.

Eco-Efficiency of Solid Wastes
Massive amounts of municipal solid waste and its improper handling and management negatively impacts human and environmental health as well as sanitation in many of the world's cities (Da Silva et al., 2005;Diaz et al., 2005;Rotich et al., 2006;Rouse, 2006). Urbanisation, rapid population growth and unsustainable resource use patterns in cities has worsened the problems associated with the proper handling of the solid wastes generated by cities (Suocheng et al., 2001). The average amount of daily per capita generated solid waste in Jeddah is 1.2 kilograms, though its spatial generation varies. Figure 6 and Table 12 depict the district level ecoefficiency of solid waste generation in Jeddah. The ecoefficiency of solid wastes was found to be very low in two districts of Jeddah where generated waste equalled more than 47 quintals per hectare of land, while it was below 3.8 quintals per hectare of land in 20 districts. Recycling and solid waste management are the main challenges facing solid waste generation in Jeddah.

Eco-Efficiency of Social Business
Malls are now inseparable features of any city environment. As such, they offer a social space especially for the families and children within the city's boundaries.
Hence, their efficiency or sufficiency is worth measuring. Richard et al. (1989) concluded that malls are the most preferred place for social interaction and shopping and accordingly, these social business areas offer improved quality of life and prosperity to city residents. Figure 7 and Table 13 depict the district level ecoefficiency of social businesses in Jeddah. The social businesses in approximately 85% of Jeddah's districts demonstrate low eco-efficiency, whereas three districts receive an eco-efficiency rating of very high. There is an unequal distribution as well as a dispersed pattern of moderate to very high eco-efficiency with respect to social businesses in Jeddah, which is escalated by the absence of a strict urban centre hierarchy in Jeddah.    Figure 8 and Table 14 depict the intra-city ecoefficiencies of urban infrastructure resources in the various districts of Jeddah. Table 14 indicates that the eco-efficiency of 5.41% of the districts of Jeddah was very low, while the ecoefficiency of the urban infrastructure of 54.05% of the districts was found to be low, an issue of serious concern for decision makers and planners. The eco-efficiency level in the remaining 40.54% of the districts in Jeddah was determined to be moderate. No districts in Jeddah were found to be highly or very highly eco-efficient.

Intra-City Eco-Efficiency Index
Areas deemed to be very low with respect to urban infrastructure eco-efficiency were distributed in a rather dispersed pattern in the city centre and drawn areas. Low-efficiency areas were distributed throughout the city in highly dense locales, while moderate eco-efficient areas were distributed in the urban peripheries that were comprised of new, low-density districts.

Eco-Efficiency and Population Density
Although this paper attempts to measure ecoefficiencies in spatial reference, it must also determine if there exists a relationship between eco-efficiencies and population. To determine the measured 'r' (correlation coefficient), population serves as the independent variable (x) and the infrastructure resources serve as the dependent variables. As shown in Table-15, a strong relationship was found between a district's population and available transportation routes (r = 0.76), energy consumption (r = 0.88), waste generation (r = 0.91) and water consumption (0.85). On the other hand, no association was found between population and social business areas (0.05) and a weak association (r = 0.4) was found between population and green infrastructure availability.
A strong positive correlation between population and public transportation routes indicates that eco-efficiency increases as the population increases, while it decreases in terms of dense population in the case of energy use, water consumption and solid waste generation. No correlation between population and social business indicates that malls are not necessarily located in dense, deserted or newly expanded areas; hence, we cannot link a mall's eco-efficiency to population density. The weak association between population and green infrastructure reveals that eco-efficiency in reference to green infrastructure generally increases with the increase in population density, though there are exceptions.

Eco-Efficiency Applicability for Urban Infrastructure in Jeddah
Worldwide debates on sustainability indicate that eco-efficient, socially inclusive urban infrastructure is a perquisite for building competitive and liveable cities (UNESCAP, 2011). Eco-cities such as Dongtan (China) and Masdar (UAE) are the first two global cities that promise to offer excellent eco-efficiency by ensuring a zero carbon level (Premlatha et al., 2013). Though in a broad scenario, a closed materials cycle is likely difficult to enact in any city, this concept does not lead towards rejection but rather it encourages urban planners and decision makers to minimise resource waste, thereby lowering carbon emissions (Li, 2014) and to maximise their economic and environmental values by innovative urban designs and ideas. In this respect, eco-efficiency is a pathway that leads towards integrated resource management. Thus, this paper adopts a simpler method to compute eco-efficiency and it offers an inspiration -as simpler is better; it proves also to be easier for the residents of Jeddah.
Major barriers in Jeddah from an eco-efficiency perspective include the following: Not only is there is a limited availability of public transportation routes, but public transportation is not perceived as a popular means of transportation among the city residents as it is not reliable and it is inadequate and uncomfortable. Nonetheless, it has been used widely by migrant workers because of it is a more affordable means of transportation. Thus, to address this problem, land uses in Jeddah should be well integrated with its transportation planning (Aljoufie, 2014). Further contributing to the problem is the fact that Jeddah is not a pedestrian friendly environment, a factor that negatively affects the city's liveability as walkability in a city not only improves its eco-efficiency, but it apparently also improves urban health and liveability (Shamsuddina et al., 2012;Bhattacharyyaa and Mitra, 2013;Ariffin and Zahari, 2013). Walkability in a city supports a mass rapid public transportation system, which cumulatively contributes to a decrease in the carbon footprint and increase in eco-efficiency. The same is true for bicycle riding. Given the benefits of enhancing a city's walkability, Jeddah's strategic plan should include Transit Oriented Development (TOD) as it may contribute to achieving public transport linked eco-efficiency (Wey and Chiu, 2013). However, this must be supported by an efficient public transportation system in conjunction with restrictions on private vehicle use.
As water and energy in the city of Jeddah are acquired by hydrocarbons, their linear consumption can have a greater negative impact on the environment, which means a notable decrease in eco-efficiency. The arid climate of the city creates a greater demand on energy for air-conditioning, while increased water consumption produces a series of consequences including the generation of greater amounts of wastewater, which must be treated, thus using more energy. Hence, energy intensive (a special reference to fossil fuel) approaches to the provision and extension of the infrastructure is not sustainable. Accordingly, a holistic water and energy management approach is critical for Jeddah, A higher environmental cost is involved in seawater desalination which can be minimised by maximising renewable energy uses leading into improved eco-efficiency performance of both Water and Energy Infrastructure resources (Purnamaa et al., 2005;García-Rodríguez, 2002).
The increased amount of solid waste generated in some districts is a critical factor that hampers environmental sustainability to a large extent as resource recovery, recycling, reducing and reusing is not often practiced in the city. Thus, separation (Mbiba, 2014) of solid waste at the source is vital as it results in 3R (reduce, reuse and recycle) actions.
Though social business areas in the city are adequately provisioned, there are variations at the district level and many districts still require more social spaces to enhance their eco-efficiency. Thus, an efficient urban centre hierarchy system that promotes social justice is highly recommended.
Finally, eco-efficiency of green infrastructure is significant as Jeddah does not have an adequate amount, partly due to the challenges presented by the arid climate. The expansion of green spaces improves the eco-efficiencies of many infrastructure resources as it consumes organic waste after the recycling of solid waste and it contributes substantially to the cooling of the city, which leads to energy savings and promotes walkability in the city by providing shade and protection from the sun and arid weather while absorbing carbon emission from automobiles. Accordingly, the expansion of green infrastructure in Jeddah, implemented on a priority basis, offers multiple advantages.
Improvements in infrastructure resource efficiency are often considered the first step towards sustainable resource management (Hawken et al., 2010;Von Weizsäcker et al., 2009;Natalia and Kennedy, 2008).
Adopting technological innovations, strengthening local institutions (Chan et al., 2013) and enhancing the efficient capacity building are important strategies as Jeddah transitions towards eco-efficiency and low-carbon emission. As eco-efficiency in Jeddah cannot be planned and achieved in isolation, there is an urgent need to prepare an integrated strategic plan for the city to tackle the sustainability challenges that the city's infrastructure is currently facing.

Conclusion
Urban infrastructures in Jeddah are in a transitional phase as they continue to experience rapid growth. At this juncture, measuring the sustainability of these infrastructures with the help of eco-efficiency indicators has greater importance because eco-efficiency is vital for integrated and sustainable infrastructure resource management.
Eco-efficiency indicators at the city level were developed to measure the intra-city spatial eco-efficiency of selected urban infrastructure amenities in the city of Jeddah. Results indicate that low eco-efficiency dominates Jeddah's urban infrastructure and that there is an emerging need for an integrated strategic plan for the city to tackle sustainability challenges with respect to urban infrastructure, it paves the framework for the retrofitting, replacing and expansion of infrastructure whatever and wherever required.
Eco-efficiency paves the way for decoupling economic benefits from environmental improvements, which is a perquisite to establishing a liveable and competitive city. Eco-efficiency intimates a notion for urban planners, designers and policymakers to work together for the city's branding as a green place. Furthermore, it calls for more in-depth investigations regarding resource efficiency deficits.


extfieldsofstudy:
Mathematics
Economics
Computer Science

s2fieldsofstudy: Economics Mathematics

text:
A two-step approach to account for unobserved spatial heterogeneity

Empirical analysis in economics often faces the difficulty that the data is correlated and heterogeneous in some unknown form. Spatial parametric approaches have been widely used to account for dependence structures, but the problem of directly deal with spatially varying parameters has been largely unexplored. The problem can be serious in all those cases in which we have no prior information justified by the economic theory. In this paper we propose an algorithm-based procedure which is able to endogenously identify structural breaks in space. The proposed algorithm is illustrated by using two well known house price data sets.

Introduction and literature review
It is a well-established fact that if spatial models are correctly specified then they can also be consistently and efficiently estimated by the commonly used estimators. However, incorrect functional forms, correlated omitted variables, models with near unit roots and row-normalized weighting matrices, and so on, typically produce spurious spatial autocorrelations (Fingleton, 1999;McMillen, 2003, Lauridsen andKosfeld, 2006;Lee and Yu, 2009;Lauridsen and Kosfeld, 2011), which can lead to inconsistency of the usual estimators. Spatial heterogeneity is a particular form of heterogeneity, usually unobserved, that is related to geo-referred data sets and would lead to misspecification of the model if not account for.
Empirical analysis in economics often faces the difficulty that the data are correlated and heterogeneous in some unknown form. A first attempt to explicitly model discontinuities in space is for example the work by McDonald and Owen (1986), which procedure has been then used by McMillen (1994) to study potential discontinuities in the population density of Chicago in 1980. As Anselin (1988a, p. 119) stressed, there are two distinct aspects that pertain to spatial heterogeneity: the former is the structural instability as expressed by changing functional forms or varying parameters, the latter is the heteroscedasticity which follows from missing variables or other forms of misspecification that lead to error terms with non-constant variance. In this paper, we are going to deal with the idea that coefficient estimates can vary over space leading to a spatial structural instability, i.e. when its parameters take on distinct values in subsets of the spatial sample.
Moreover, if spatial heterogeneity can be categorized into a small number of regimes, each represented by different values for the regression coefficients, the phenomenon is also known as spatial regimes. In this case, if spatial heterogeneity is present the functional form of the model will be misspecified because of the wrongly assumed constant relationships between dependent variables and regressors. The following Anselin's (2010, p. 5) statement is useful to understand "Spatial heterogeneity becomes particularly challenging since it is often difficult to separate from spatial dependence. This is known in the literature as the inverse problem. It is also related to the impossible distinction between true and apparent contagion. The essence of the problem is that cross-sectional data, while allowing the identification of clusters and patterns, do not provide sufficient information to identify the processes that led to the patterns." The problem of spatial heterogeneity in terms of spatially varying parameters has been largely unexplored by spatial econometricians, typically because of the main purpose of controlling only for spatial spillover effects. As Postiglione et al. (2013, p. 171) stressed "the problem of spatial heterogeneity is often neglected in empirical analysis of geographic data and this negligence can affect sensibly model estimates". Some authors have attempted to detect the presence of spatial heterogeneity by constructing statistical tests that are typically based on the LM statistic (Anselin, 1988b;de Graaff et al., 2001;Lauridsen and Kosfeld, 2006;Lauridsen and Kosfeld, 2011;Pede et al., 2014;among others). Unfortunately, once detected the presence of spatial heterogeneity no test is able to suggest how to correctly model our spatial data set and in which direction we have to proceed for further analyses. Recently, Ibragimov and Müller (2010) have derived the small and large sample properties of the t statistic, also in the context of spatially correlated data, by assuming a reasonable partition in q groups of the data. As Ibragimov and Müller (2010, p. 454) emphasized "some a priori knowledge about the correlation structure is required …". However, in practical cases, there is usually no reason to accept one partition instead of another, which is in some way justified by the economic theory.
Following a parametric approach, the typical starting point to estimate a spatial econometric model is usually based on the choice of a row-standardized spatial weighting matrix, , which is able to specify the relationship between neighboring observations. In some cases the significance of the spatial spillover effects through the autoregressive coefficient might be simply due to an omitted spatially-correlated regressors problem, which can easily justifies the use of the well-known more flexible spatial Durbin models (see e.g. Corrado andFingleton, 2011, LeSage, 2014, for comprehensive discussions). However, neighborhood influence is not calibrated in terms of the data but is prescribed by the specification of W 2 . Imposing a predefined spatial structure of the data can be sometimes too restrictive in practical cases and it can bias results when inappropriate 3 , so that McMillen (2012), among others, has 2 See the papers of LeSage and Pace (2014), Getis (2009Getis ( ,2007 for considerations on the spatial weight matrix and the autocorrelation coefficient. 3 Recently, both from a theoretical and a computational perspective, some excellent works on the definition of the W matrix has been proposed (see LeSage and Pace, 2007;Seya et al., 2013;Bhattacharjee and Jensen-Butler, 2013;Qu and Lee, 2015). In particular, Qu and Lee (2015) defined a particular endogenous W matrix (where the usual exogenous W matrix can be considered a particular case) and showed the consequences on the estimates by considering commonly used estimators in SAR cross-sectional models when the true W is endogenous. criticized this approach. Although our purpose is not to criticize the parametric approach, it is reasonable to assume that for some economic phenomena there is no reason, justified by the economic theory, to choose a priori a particular spatial structure of the underlined spatial process.
The main purpose of the present paper is then to propose a possible partition of the spatial data, i.e. a classification of the data due to unobserved heterogeneity, with no a priori information of the true dependence structure.
For instance, the advanced recent literature in hedonic house price models accounts for spatial spillover effects but still ignore the possibility of a spatial heterogeneity effect (Holly et al., 2010;Holly et al., 2011). Some researchers are then recognizing that the spatial structures can be sufficiently different that the data should not be pooled and estimated together and global spatial regression models usually fail in taking into account any potential variations over space, with the consequences of biased resulting estimates. Along the same line, one of the purposes of the present paper is to show how the presence of spatial heterogeneity might modify (and generally reduces) the significance of the spatial effects in a global spatial autoregressive model by simply estimating spatial autoregressive models with spatial regimes (which introduce a sort of flexibility in spatial autoregressive models). This can be interpreted in the fact that the spatial heterogeneity might generates part of the spatial autocorrelation effect, or in other words that the autoregressive coefficient is sometimes overestimated. In line with this view is the work of Basile et al. (2014). In order to simultaneously account for spatial dependence, unknown functional form and unobserved heterogeneity, they proposed the use of the so-called Spatial Autoregressive Semiparametric Geoadditive Models, which are based on a combination between spatial parametric autoregressive models and unknown smooth functions.
Semiparametric and nonparametric estimation methods, such as geographically weighted regressions (GWRs) (Brunsdon et al., 1996), are proving to be valid alternatives to parametric approaches and should be used as diagnostic tools to detect the presence of spatial heterogeneity 4 .
The above methods allow coefficient estimates to vary over space by calibrating the global model separately for each spatial units in order to produce n sets of parameter estimates, with the behind basic idea that simple econometric models represent the data best in small geographic areas. They indeed have the attracting advantage to control for misspecified spatial effects while using highly flexible functional forms, with the only condition that nearby observations need more weight when constructing an estimate for a target point. McMillen and Redfearn (2010) showed that the GWR specification can be viewed as a special case of the already known locally weighted regression (LWR) method 5 . GWRs or Geoadditive Models usually interpret the spatially varying parameter problem as a smooth changing over space. As a matter of fact, pairs of beta coefficient GWR estimates that are proximal in space could not exhibit statistically significant differences. As Anselin (2010, p. 17) underlined "…in models of spatial heterogeneity, the spatial regimes or spatially varying coefficients show evidence of the heterogeneity, but do not explain it. Ideally, one would want to make the structure of dependence and/or the structure of heterogeneity endogenous". This is the aim of the present paper. Our purpose is to iteratively find, in a way that spatial parameter variations can be described by breaks in continuity over space (or spatial regimes).
In the spatial statistics literature an adaptive weights smoothing (AWS) algorithm have been recently proposed by Spokoiny (2000, 2006) to describe, in a data-driven iterative way, a maximal possible local neighborhood of every point in space in which the local parametric assumption is justified by the data. The basic assumption of the proposed approach is that for every point there exists a vicinity of in which the underlying model can be well approximated by a parametric model with the constant set of parameters. Their method has been applied in the field of image analysis and it is based on both a successive increase of the local neighborhoods around every point and on a description of the local models by assigning weights to every spatial unit that 4 A valid alternative to the GWR approach is the NCSTAR model as pointed out by Lebreton (2005). 5 The main difference pertains the way of thinking the distance measure. In GWRs, distance is thought as a mere geographic distance (Euclidean, great circle, etc.), whereas in LWRs an economic interpretation can be also assigned. depends on the result of the previous step of the procedure. The potential of this method in an econometric environment concerns the possibility of endogenously obtaining cluster of observations due to unobserved spatial heterogeneity (i.e. spatial regimes) exhibiting similar coefficient estimates. Andreano et al. (2016) defined a first algorithm based on the work by Spokoiny (2000, 2006) for the identification of economic convergence clubs. In this paper we substantially modify the previous contribution proposing a two-step procedure (see Section 3 for further details and comparisons), which is based on the conjunction between the LWR approach and the AWS procedure. A two-step procedure to deal with both spatial dependence and spatial heterogeneity within the estimation of hedonic house price functions has been proposed for instance by Beron et al. (2004). However, their method focused on the estimation of a first set of parameters related to environmental characteristics in the first step, whereas it proposed a spatial econometric model that accounts for both spatial dependence and spatial heterogeneity in the second step, assuming a spatial trend as a quadratic form of latitudes and longitudes for the heterogeneity effects. In our two step procedure, instead, we propose a first step that focuses on the estimation of unobserved discrete spatial heterogeneity (i.e. spatial regimes) and a second step that estimates the effects of both spatial dependence and the identified spatial regimes. Our purpose is based on the idea that we can combine the potential of local estimation with the usefulness of a modified AWS procedure, which is able to identify spatial regimes, i.e. subsamples over space with an estimated set of beta coefficients for each of them.
The paper is structured in the following way. In section 2 we introduce the LWR and the GWR as a special case. In section 3 we explain the first step of our procedure, i.e. the algorithm, whereas section 4 explain the second step to estimate both spatial dependence and spatial regimes. Section 5 illustrates the data set used and their main estimation results in terms of the marginal effects obtained by using different spatial econometric models. Finally, section 6 concludes.

Locally Weighted Regressions
Spatial econometric models may be not appropriate in the presence of (unobserved) spatial heterogeneity. Locally weighted regressions (LWRs) (Cleveland and Devlin, 1988) or Geographically weighted regressions (GWRs) (Brunsdon et al., 1996;Fotheringham et al., 1998, Fotheringham et al., 2002, which are recognized to be natural evolutions of the expansion method (Casetti, 1972), allow us to estimate local rather than global parameters.
Residual terms usually exhibit a different from zero spatial autocorrelation parameter that, actually, might be not statistically different from zero if the true reason of error autocorrelation is different from a true contagion process (i.e. spurious autocorrelation). The first law of geography (Tobler, 1970, p. 236) states: "everything is related to everything else, but near things are more related than distant things". The goal should be to detect the reason why the closest things are related. The basic idea behind local geographical estimation is that simple linear functions may fit well for observations close to a site, say i, but probably they will be inappropriate when more distant observations are included. Limiting the estimation to a neighborhood of observation i eliminates much of the heteroscedasticity and autocorrelation that is endemic to spatial data set. Therefore, simple linear functions can be written to account for local parameter estimates in the following way where is an -dimensional column vector, is an by + 1 matrix with i-th row = ( 0 , 1 , 2 , … , )′, ⊙ is the Hadamard product operator in which each element of is multiplied by the corresponding element of the i-th row in , = ( 0 , 1 , 2 , … , ), is a ( + 1) column vector of ones, and is an -dimensional column vector of innovations. The idea is that, in order to estimate a set of parameters for a given point i, one can approximate the model in [2.1] in the neighborhood of i by using a simple linear model, and perform least squares with a subset of points that are closed to i. The objective function, for each local regression i, takes the following where is an n-dimensional diagonal square matrix whose diagonal elements, ( 1 , 2 , … , , … , ), denote the weights (in our case geographic distances) of each of the n observed data for regression point i. We will therefore have n diagonal spatial weighting matrices and n sets of local parameter estimates that correspond to the local marginal effects. Then, a locally weighted least squares (LWLS) estimator is simply obtained by repeated weighted least squares Initial Kernel weighting functions have to be specified to define the matrices. Such functions are typically the exponential, the Gaussian, the bi-square, the tri-cube, and they seem to be similar in placing higher weight on nearby observations and lower weight on the distant ones, but they differ according to the type of bandwidth (b).
The choice of the bandwidth value is then crucial: the neighborhood of observation i is defined by the value of b which then determines the number of observations (i.e. a subsample) that receive a weight in constructing the estimate for i, and how rapidly these weights decline as distance increases. So, an important question could be how close to i should points be considered, or in other words in which way we can define a proper neighborhood for i. The observations are used several times with a maximum equals to n 2 . Every local ̂ can be based on the same set of n observations, but in this case the local estimates would be the same. The minimum number of observations to be used for each local estimation is instead + 1, but then the ̂' s would be not significant. The point is then to choose an ideal subsample of observations for each local estimation, i.e. b should be somewhere in between n and + 1 such that we have sufficient observations for each ̂ and part of them will be significant. This problem is referred as a bias-variance trade-off in choosing the value of b (Brunsdon et al., 1996). Since the LWLS estimate for point i, ̂, is only an approximation of the true value in the same point, one can consider observations very closed to i with the justification that it is reasonable to assume a lower magnitude of difference in the beta values. However, because of the sample size reduction, the standard error of ̂ will increase (i.e. ̂ are not significant). The opposite will occur if we increase the sample size. To solve the problem of choosing an optimal bandwidth value, , a cross-validation (CV) method has been widely used, which minimizes the overall residual sum of squares obtained when observation i is deleted (i.e. the target point). A different and more general approach based on a trade-off between goodness of fit and degrees of freedom is the AIC 6 (Fotheringham et al., 2002, p. 61) = min = min 2 ln(̂) + ln (2 )  Another important issue is that the bandwidth value can be defined as fixed or variable/adaptive.
Since that adaptive bandwidths suit highly irregular sample configurations and they ensure sufficient (and constant) local information for each local calibration, the adoption of an adaptive bandwidth seems to be preferred to a fixed bandwidth for analyzing spatial data. The choice of an adaptive bandwidth is then useful for two reasons: (i) it guarantees the same number of observations (i.e. the same amount of information) for each local estimation, (ii) it can potentially reduce the edge effects in spatial data analysis. Therefore, in this paper we calculate an adaptive bandwidth following the nearest neighbor approach and we define, for each used kernel weighting function, the optimal variable bandwidth or window size, , by using the minimizing the AIC criterion in [2.4]. The bandwidth value (b) selects the b-smallest distances for each initial local estimation. Each of the elements of the geographical distances are then normalized through the maximum distance, so that it does not matter how far is the most distant point within the optimal neighborhood defined by b for each local estimation. In this way, through an appropriate kernel function, the weights that contribute to each local estimation do not depend on the effective position of the points in space. In the following two paragraphs we intend to explain our two-step procedure. The first step (i.e. Section 3) is an algorithm that is able to endogenously identify spatial regimes, whereas the second step (i.e. Section 4) is based on the specification and estimation of two spatial autoregressive models with the identified spatial regimes.

The first step: an algorithm to deal with unobserved spatial heterogeneity
In this section we intend to explain our iterative procedure, which enters as a first step of the entire estimation approach. The idea comes from the adaptive weights smoothing (AWS) procedure first proposed by Polzehl and Spokoiny (2000) is the variance-covariance matrix of ̂ and Σ j is the same matrix for ̂. This variance-covariance matrix is different from that in Andreano et al. (2016) in order to preserve degrees of freedom.
Each vector ̂ for = 1, … , , at iteration , is obtained from the LWLS problem in [2.3] by only using a subsample of observations whose size is defined by a mix of one of the possible kernel functions and a bandwidth value. If the number of observations is reasonably large in all defined subsamples (which contribute to different beta vector estimations), the approximate multivariate normality is a standard result ̂~( , Σ i ) (see Ibragimov andMüller, 2010 andBester et al., 2011 is the − of the chi-square distribution (for details see Polzehl and Spokoiny, 2006 where ∈ (0,1) is a control parameter (also called memory parameter in Polzehl and Spokoiny, 2006) which is used to stabilize the convergence procedure. We set = 0.5, so that we consider the exact arithmetic mean between the weights at the ( − 1)-th and the -th iterations. In this way, the new weights are smoothly or gradually introduced to avoid potential convergence problems due to discontinuities in the iterative process. During the convergence procedure, it is important to provide enough observations for each formed group. Because of the identification problems, groups characterized by a limited number of observations (i.e., less than the number of parameters to be estimated) will be automatically excluded from the analysis and treat as outliers. A final useful definition for the description of the convergence procedure is the weights variation function which tends to zero as the convergence procedure stabilizes (see Figure 3). This procedure does not impose any restrictions and it is fully adaptive in the sense that no prior information about the spatial structure is required. To summarize, the convergence procedure is based on the following steps  Define initial weights with a kernel that is a function of distances between pairs of units in space and an optimal bandwidth value (the econometric model must be assumed to be the true one) and use these weights in equation [

The second step: spatial autoregressive models with spatial regimes
It is already well-known that (first-order) autoregressive spatial model with (first-order) autoregressive disturbances (SARARs) models and spatial Durbin models (SDMs) provide general starting points for spatial analysis, since they subsume, in different ways, both spatial autoregressive error (SEM) and spatial autoregressive (SAR) models (LeSage and Pace, 2009). The two spatial models are defined as where is an n by p+1 matrix of regressors representing own-region characteristics with a p+1 by 1 vector of parameters , ̆ is the same matrix without the intercept and is the corresponding p vector of parameters, is the autoregressive parameter, is an n by 1 vector of autoregressive error terms with spatial coefficient and spatial weight matrix 2 , is an n by 1 vector of i.i.d. error terms. 1 is the commonly used n by n spatial weighting matrix which can be different or equal to 2 . In this paper we set 1 = 2 = and we define as a k-nearest neighbor weight matrix with = 10 and geographical distances. The squared weighting matrix has the diagonal elements wii equal to zero, the rows and columns uniformly bounded as n goes to infinity, and it is then normalized, so that the admissible parameter spaces of and are known and less than unity in absolute value.
It is worth noting that, although both the weighting matrix used in this section, i.e. , and the one neighbor criterion (i.e. based on the optimal adaptive bandwidth value) is only used to define the initial set of weights in , so that this is an issue only for the first set of local estimates within the iterative procedure. Finally, there is no need of normalization to ensure admissible parameter spaces of autoregressive coefficients in the case of 8 .
Recently it has been emerged that SDMs are useful model specifications to overcome the omitted variable problem especially with hedonic house price data (Gerkman, 2012). In order to show how estimating models with spatially varying parameters can produce substantial differences in terms of the autocorrelation effects, in this paper we estimated different global models (GMs): OLS, SAR, SEM, SARAR, and SDM. Those models are then compared with the same models adding spatially 8 The weights in the diagonal of have the role, at first, of selecting the observations that contribute to local estimations trough local weighted least squares estimations, whereas the weights in permits, trough the reduced form of the model, the expansion of the infinite number of cross-sectional effects in the entire system (i.e. global spillover effects).
varying coefficients, after using the ILWR approach to identify the number of clusters in space. We called these model specifications Endogenous Spatial Regime models (ESRMs where, in both cases, ∼ (0, 2 ), = 1, … , , and is the unknown number of clusters in space. After having defined these unknown clusters through the first step procedure, we proceed with the estimation of models in [3.7] and [3.8], which can be interpreted as spatial autoregressive models with structural breaks in space (also known in the literature as spatial regimes).

Data sets and results
In order to detect the presence of unobserved spatial heterogeneity in the form of spatial regimes and to prove the usefulness of the above two-step approach, we use baltimore and house data sets 9 which summarizes the information on house sales prices in Baltimore, MD, and Lucas County, Ohio, respectively (see Table 1). Baltimore data set was first analyzed by Dubin (1992) who emphasized the problem of spatially varying parameters. Because of the computational burden of our algorithm in the first step we selected the central subsample of the cross-sectional house data set in 1993 (see Figure 1).
INSERT with subsamples 1 = 101 and 2 = 110, mostly dividing the central and the northwest areas from the south and the northeast ones (Figure 2(a)). Considering AIC values, ESRMs are always to be preferred over GMs and in both situations the SAR specification seems to fit the data best. Then, in this case positive spatial neighbor effects seem to persist despite the presence of two spatial regimes. However, if we see the results of SDM with spatial regimes (SDM-SRs) we can confirm the hypothesis that most of the spatial autocorrelation is induced by the omitted variable problem of not considering the lagged covariates. In this case the presence of spatial regimes has a "pure" informative role: the SDM-SR specification (with lowest AIC) is more useful than the others since it can be used to guide zone-specific policies. INSERT TABLE 2 HERE   INSERT TABLE 3 HERE   Tables 4 and 5 show GMs and ESRMs estimates for house data set, instead. The bandwidth value corresponds to 19 nearest neighbors, = 19, over 382 number of observations. The first step identified 4 homogeneous clusters ( = 4) with subsamples 1 = 57, 2 = 141, 3 = 58, 4 = 126 (Figure 2(b)). Conclusions are a bit different from those obtained for Baltimore: not only ESRMs provide better results in terms of AIC values, but also spatial spillover effects seem to be attenuated by the presence of the spatial regimes. This is particularly clear in the comparison between a global SDM and an SDM-SRs where the autocorrelation coefficient goes down from 0.655 to 0.248. In this case the additional information of the identified spatial regimes makes us able to split the apparent contagion (in Anselin's words) into the true contagion (the spillover effects), the part due to the lagged covariates, and the part due to the presence of spatial heterogeneity.

INSERT FIGURE 2 HERE
INSERT It is then interesting to note that estimating spatial models with spatial regimes (endogenously identified with the first step of our procedure) can be not only useful to account for both spatial dependence and spatial heterogeneity giving more flexibility to our models, but also to provide zone-specific economic results. Considering for instance Baltimore results (Tables 2-3), we can observe that some regressors in ESRMs are highly statistically significant in the first zone (i.e., central and northwest areas) whereas not in the second (i.e., the south and the northeast areas).
Therefore, for the same model a significant global parameter estimate should be mainly due to the statistical significance of the same parameter in central and northwest areas.
It is well known in the literature that house prices do not necessarily change at a uniform rate throughout an urban area. Several papers that attempt to smoothly describe a spatial price variation or to identify housing submarkets within cities have been published (see e.g. McMillen, 2013, for a recent exhaustive review). The identification of regimes in housing markets allows us to identify a set of discrete neighborhoods with constant coefficients within each subarea and discrete changes across boundaries. Therefore, this procedure could be viewed as a solution for the identification of the potential number of submarkets (see e.g. Watkins, 2001) within an urban area (e.g. a city) especially when no prior knowledge on the geographical structure is available.

INSERT TABLE 6 HERE
INSERT FIGURE 3 HERE Table 6 shows the number of iterations of the algorithm and the time required to ensure the convergence (see Figure 3). Although the computational time seems to be still reasonable as long as the number of observations are lower than 400, we can note that the time is dramatically increased by an augmentation of only around 100 of observations, and the number of iterations are twice as much those required for baltimore data set. Conversely, the number of explanatory variables seems not to change the time required by our algorithm. Finally, in Figure 3 we can see how the convergence procedure works: after an initial period of "instability", the weights tend to zero as the number of iterations increased. The most significant and rapid decrease is between the interval of iterations (5 th -15 th ) for baltimore and (15 th -30 th ) for house.

Conclusions and future developments
Spatial heterogeneity is one form of unobserved heterogeneity, which leads to model misspecification problems. Geographically weighted regressions or geoadditive models are surely promising alternatives to account for spatially varying parameters, in which the parameter surface is not assumed to be constant over space. However, economic studies usually suggest a form of spatially varying parameters, which can be interpreted as the presence of discrete spatial heterogeneity (or spatial regimes). In this paper we then define a two-step approach able to identify these regimes in a first step and to simultaneously estimate spatial dependence and heterogeneity in a second step.
By using two house price data sets, we found that our procedure was able to identify clusters and that spatial econometric models estimated on that partition were to be preferred. Most of the results showed that spatial neighbor effects are present in our data sets but in a reduced form, and probably part of the neighborhood effects is not only due to an omitted variable problem but also to the unobserved spatial heterogeneity. This firstly suggested that accounting for both spatial dependence and some form of spatial heterogeneity (e.g. the spatial regimes, with the use of some algorithmbased approach to identify them) is a fundamental step. The additional information derived from the identified spatial regimes makes us able to split the apparent contagion into three parts: the true contagion (the spillover effects), the lagged covariates (which justifies the use of the spatial Durbin model), and the presence of spatial heterogeneity. Moreover, zone-specific economic results can be provided with these more flexible spatial models.
As expected, its main drawback is the computational time required for the convergence procedure, which we suppose can become infeasible with very large data sets. The need to overcome the ILWR computational problems is straightforward. Unobserved spatial heterogeneity is still a problem in spatial econometrics. Many author are still trying to test the presence of spatial heterogeneity, but the prospect of considering algorithm-based methods is becoming a successful way to follow in order to solve practical problems with several data sets and to consider higher flexibility in our models.
The first step of our two-step procedure does not impose any restrictions and is fully adaptive in the sense that no prior information about the spatial structure is required. It can be easily extended to any other model which can be locally estimated by weighted least squares, and with different definition of the weights (e.g. economic definitions rather than mere geographic distances).
Moreover, two possible and interesting modifications of this algorithm can be the one that permits the simultaneous consideration of both spatial dependence and local marginal effect estimation inside the iterative procedure and the extension to panel data sets to also deal with time variations.
These will be accounted for in future works.    Table 3 Parameter estimates of models with spatial regimes in the baltimore data set based on the partition in Figure 2(a).  Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Table 5 Parameter estimates of models with spatial regimes in the house data set based on the partition in Figure 2(b).


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A"Social Bitcoin"could sustain a democratic digital world

A multidimensional financial system could provide benefits for individuals, companies, and states. Instead of top-down control, which is destined to eventually fail in a hyperconnected world, a bottom-up creation of value can unleash creative potential and drive innovations. Multiple currency dimensions can represent different externalities and thus enable the design of incentives and feedback mechanisms that foster the ability of complex dynamical systems to self-organize and lead to a more resilient society and sustainable economy. Modern information and communication technologies play a crucial role in this process, as Web 2.0 and online social networks promote cooperation and collaboration on unprecedented scales. Within this contribution, we discuss how one dimension of a multidimensional currency system could represent socio-digital capital (Social Bitcoins) that can be generated in a bottom-up way by individuals who perform search and navigation tasks in a future version of the digital world. The incentive to mine Social Bitcoins could sustain digital diversity, which mitigates the risk of totalitarian control by powerful monopolies of information and can create new business opportunities needed in times where a large fraction of current jobs is estimated to disappear due to computerisation.

Nowadays we are facing a number of serious problems such as financial instabilities, an unsustainable economy and related global warming, the lack of social cooperation and collaboration causing the rise of conflict, terrorism and war. Traditional approaches to remedy such problems are based on top-down control. Whereas in the past this way of thinking worked reasonably well, the high interconnectivity in modern systems will eventually but unavoidably lead to its failure as systems become uncontrollable by central entities due to stronger internal effects, leading to often unpredictable cascading behavior [1] and catastrophic failures [2].
Instead of entirely top-down based approaches, designing mechanisms to promote desired results like increased cooperation, coordination, and better resource efficiency could help to deal with current socio-economic challenges. Importantly, a multidimensional incentive system is needed to design the desired interactions and appropriate feedback mechanisms [3,4]. Such incentives have to be implemented in a bottom-up way, allowing systems to self-organize [5] and thus promoting creativity, innovation, and diversity [6].
Diversity acts as a motor of innovation, can promote collective intelligence [7], and is fundamental for the resilience of society [8,9]. This renders socio-economic and cultural diversity equally important as biodiversity. The importance of diversity, however, is not restricted to in-dividual, cultural, social, or economic domains. For instance, diversity among digital services in competition for the attention of users can mitigate the risk of totalitarian control and manipulation by extremely powerful monopolies of information. As we explain in Sec. III C, the loss of diversity in the digital world can lead to a systematic and irreversible collapse of the digital ecosystem [10,11], akin to the loss of biodiversity in the physical ecosystem. Such a collapse can have dramatic consequences for the freedom of information and eventually for the freedom of society. In this contribution, we show how such a catastrophic collapse could be avoided on a systematic level by introducing a multidimensional incentive system in which "Social Bitcoins" provide an incentive for individuals to perform certain tasks in their socio-digital environment.

II. A MULTIDIMENSIONAL FINANCIAL SYSTEM
The invention of money has led to unprecedented wealth and has provided countless benefits for society. However, the current monetary system is not appropriate any more to control highly interconnected dynamical complex systems like the ones our economy and financial system nowadays form. Whereas such systems are in general difficult to control and understand and nearly impossible to predict, they exhibit the tendency to self-organize [5,12]. New approaches to face todays challenges should therefore take advantage of this system intrinsic tendency.
Central banks like the ECB can control the amount of money in the market by means ranging from adjusting interest rates to quantitative easing. Recently, the ECB has lowered interest rates to the lowest value of all time (even introducing negative rates for some bank deposits [13]) and has further increased its efforts to buy government bonds [14]. These measures are intended to boost economy and increase inflation in the Euro zone to the target of 2%. Despite these efforts, inflation has remained close to 0%, raising doubts about the capacity to act and the credibility of the ECB [15]. Furthermore, liquidity pumped into the market does not reach efficiently enough the real economy. As a consequence recently "helicopter money" has been discussed as a possible solution [16,17]. Importantly, these problems are not limited to the Euro zone. For example, due to the interconnected nature of our economic and financial systems, the state of the global economy limits the decisions the Fed can take concerning a raise of interest rates, as such a raise could pose a threat for the global economy [18].
The problem is that the current monetary system provides only a one-dimensional control variable. Let us consider the human body and how it self-organizes as an example. To ensure its healthy function, it is not enough to adjust only the amount of water one drinks. Instead, the body needs water, air, carbohydrate, different proteins and vitamins, mineral nutrients and more. None of these needs can be replaced by another. Why should this be different in systems like our economy, the financial system, or society?
Indeed, a multidimensional currency system could help to solve the problems mentioned above, where the different dimensions can be converted at a low (or negligible) cost. Such multidimensional incentive system could be used to promote self-organization of financial and economic systems in a bottom-up way [19]. This opens the door to "Capitalism 2.0" and "Finance 4.0" (see [20][21][22][23] for details).
A special case of a multidimensional incentive system is "qualified money". The concept was first introduced by Dirk Helbing in [19,22]. Instead of a scalar (onedimensional) quantity, like the Euro or any other currency, money could be multidimensional and earn its own reputation. To illustrate this, consider the example that there were two dimensions of money. By law, the first could only be invested into real values, but not into financial products. Instead, the latter dimension could. There would be an exchange rate (and cost) to convert one dimension into the other. As a consequence, the ECB could increase the amount of money for real investments directly, hence avoiding the problem mentioned earlier.
In other words, the decision space on which institutions like the ECB can act would considerably increase without them acting outside of their mandate. Qualified money, which could be realized in a Bitcoin-like [24] way 1 , could earn its own reputation depending on how and where it was created and what businesses it supports. The reputation then can give the money more or less value, which can lead to a more sustainable economy as sustainability would become measurable and transparent to individuals (for details see [20,22]). The concept of qualified money is not limited to the above described two dimensions. Instead, everything people care about can be represented by a dimension in the currency vector. As we explain in the following, one dimension of qualified money could be socio-digital capital that can be acquired in the digital world.
Modern information and communication technologies play an important role in facing todays challenges. Indeed, nowadays the digital and physical world are strongly interdependent and cannot be treated in isolation any more [1]. The huge success of Web 2.0 and online social networks is changing the way humans interact at a global scale. They promote cooperation and collaboration on unprecedented scales, but at the same time powerful monopolies of information have the power to alter individuals' emotions and decisions [25,26]. Supercomputers nowadays perform a large fraction of all financial transactions, hence influencing the prices of important commodities, which can lead to starving, conflicts, war, etc. Information and communication technologies thus are both a crucial part of the problems society has to solve as well as a fundamental and promising piece of the solution.

A. Decentralized architectures
The existence of powerful monopolies of information like big IT-companies or even some governments can lead to the loss of control by individuals, companies, or states. Besides, the economic damage attributed to cybercrime is growing exponentially and is estimated to reach 2.1 trillion dollars in 2019 [27]. Hence, it is time to design more resilient information and communication technologies that-by design-cannot be exploited by single entities. Decentralized architectures naturally provide these benefits [28][29][30].

B. Social Bitcoins and Web 4.0
As explained earlier, the main idea behind qualified money is to price a broader spectrum of externalities. This means that it can be applied to, for instance, information. This can be realized in many different ways. The exact details would probably emerge in a self-organized way, depending on choices and preferences of individuals. But how could such a system look like and what benefits would it provide? Here, we discuss a possible vision in which one dimension of qualified money, sociodigital capital, can be priced in terms of Social Bitcoins that can be mined using online social networks and digital infrastructures. It is impossible to foresee the exact details of such a system, nevertheless, in the following we will sketch a possible vision of a future Internet and digital world in which individuals perform the routing of messages and information using their social contacts and technological connections rather than relying on service providers.
The use of the Internet has changed fundamentally since its invention. At first, it was a collection of static web pages. Then, Web 2.0 emerged as "a collaborative medium, a place where we [could] all meet and read and write" [31]. Consequently, Web 3.0 constitutes a "Semantic Web" [31], where data can be processed by machines. Let us refer to a digital world in which information is managed in a bottom-up way, free of central monopolies in control of the vast majority of information, as Web 4.0 2 . A digital democracy [28], if you will. Assume that this digital world was composed of many interacting, decentralized systems, which-in the absence of central control-compete for the attention of individuals [10,11]. As we explain in Sec. III C, such a state is possible but fragile. Now assume that, in the future of the Internet, each individual routes information using their social and technological connections rather than relying on service providers 3 . In decentralized architectures, this task has to be performed relying only on local knowledge. As shown in [33], this type of routing can be performed very efficiently and-most importantly-can be perfected if individuals actively use multiple networks simultaneously 4 . This fact constitutes an important starting point to design appropriate incentives to sustain digital democracy.
Assume that individuals could earn Social Bitcoins by routing information in the way explained above. These Social Bitcoins would form a dimension of qualified money [19,20,22] and could (with some additional cost) be exchanged and hence converted into other dimensions of the currency vector. Their exchange rate would depend on the trust individuals have in the system and how much they value their socio-digital environment.
The important point is that now individuals have an incentive to route information ("mining" Social Bitcoins). As a consequence, individuals will optimize to some ex-  Figure 1. Illustration of the incentive to mine Social Bitcoins. Social Bitcoins form one dimension of qualified money and can be mined by performing search and navigation tasks using social and technological connections in a future digital world. Hence, acquiring Social Bitcoins constitutes an incentive to perform routing. Individuals optimize their strategy to route information and will be active simultaneously in more networks, as this (among other aspects [34]) increases routing performance [33]. Performing routing in less active networks could increase the reputation of the mined Social Bitcoins, providing an additional incentive to engage in less active networks. This then could sustain digital diversity [10,11] and at the same time increase the payoff for the individual performing routing. Icon credits: Mourad Mokrane, lastspark, and Joshua Jones from thenounproject.com (CC BY 3.0).
tend their capabilities to perform this action. As explained above and shown in [33], the routing success can be increased and even perfected if individuals actively use many networks simultaneously 5 . Hence, the introduction of a Social Bitcoin would constitute an incentive to be active in several networks, as illustrated in Fig. 1. In addition, search and navigation tasks taking place in less active networks could increase the reputation of the mined Social Bitcoins, providing further incentive to engage in less active networks. In other words, sustainability in the digital world could be priced and would become transparent to individuals who then could adjust their behavior accordingly. Importantly, as we explain in detail in the following, this optimization could make digital diversity robust and sustainable.

C. How a Social Bitcoin could sustain digital diversity
Here, we present a mathematical model to illustrate the potential effect of a Social Bitcoin. As mentioned earlier, many digital services compete for the attention of individuals. In this context, the attention of users can be considered a scarce resource and hence the digital world forms a complex ecosystem in which networks represent competing species. A concise description of the digital ecology was developed in [10]. In a nutshell, multiple online social networks compete for the attention of individuals in addition to obeying their intrinsic evolutionary dynamics. This dynamics is given by two main mechanisms, the influence of mass media and a viral spreading dynamics acting on top of pre-existing underlying offline social networks [35]. Importantly, the parameter that quantifies the strength of viral spreading, λ, determines the final fate of the network. If λ is below a critical value λ c , the network will eventually become entirely passive, with corresponds to the death of the network. On the other hand, for λ > λ c , the activity of the network is sustained [35,36]. The competition between multiple networks can be modeled assuming that more active networks are more attractive to users. Hence, the total virality, which reflects the overall involvement of individuals in online social networks, is distributed between the different networks as a function of their activities. More active networks obtain a higher share of the virality, which then makes these networks more active. Note that this induces a rich-get-richer effect. Interestingly, despite this positive feedback loop, diminishing returns induced by the network dynamics allows for a stable coexistence (digital diversity) of several networks in a certain parameter range (we refer the reader to [10] for details).
The system can be described by the following meanfield equations 6 where ρ a i denotes the fraction of active users in network i, λ is the total virality mentioned earlier, and k denotes the mean degree of the network, i.e. the average number of connections each node has. The weights ω i (ρ a ) depend on the activities in all networks, ρ a = (ρ a 1 , ρ a 2 , . . . , ρ a n ), and govern the distribution of virality between different networks. In [10] we used where σ denotes the activity affinity that quantifies how much more prone individuals are to engage in more active networks.
As mentioned earlier, assume that the introduction of Social Bitcoins incentivizes users to simultaneously use multiple networks in order to increase their capabilities to successfully perform search and navigation tasks and hence increase their expected payoff. The exact form of this incentive depends on the details of the implementation of the systems' architectures and Social Bitcoins, which comprises an interesting future research direction. Here, we model the additional tendency of individuals to engage in multiple (and less active) networks by shifting the weight of the distribution of the virality towards networks with lower activity, hence hindering the richget-richer effect described earlier. In particular, let us consider the following form of the weight function, where ξ is a parameter proportional to the value of Social Bitcoins and ρ a = 1 n n i=1 ρ a i denotes the mean activity among all networks.
The effect of the inclusion of the new term ("Social Bitcoin incentive") in Eq. (2) can change the behavior of the system dramatically if ξ is large enough, which we illustrate 7 for two competing networks. Let us first consider the case of ξ = 0.2. In this case, the qualitative behavior of the system is similar to the one in absence of Social Bitcoins as described in [10]. Below a critical value of the activity affinity, σ < σ c , coexistence is possible (solid green central branch in Fig. 2 Fig. 2 (middle, left)), but-once lost-cannot be recovered.

(top) & central green diamond in
To illustrate this, assume that we start with σ < σ c and the system approaches the coexistence solution (central green diamond in Fig. 2 (middle, left)). Then, we change σ to some value larger than σ c . Hence, the coexistence solution becomes unstable and the system eventually approaches the solution where either ρ 1 = 0 or ρ 2 = 0 (green diamonds in Fig. 2 (middle, right)). Now, after changing σ back to a value below σ c , the system does not return to the again stable coexistence state, but instead remains in the domination state, which is also stable (outer green diamonds in Fig. 2 (middle, left)). This example is illustrated in Fig. 2 (bottom), where we explicitly show the evolution of the fraction of active users for both networks 8 . To conclude, the system is fragile in the sense that an irreversible loss of digital diversity is possible-similar to the loss of biodiversity. 7 Here we present only a brief discussion of the dynamical system given by Eqns. (1) and (2). A more detailed analysis and the investigation of different forms of the incentive term in Eq. (2) is left for future research. 8 Note that here we describe an idealized system without noise.
Noise in real systems would speed up significantly the separation of the trajectories in Fig. 2 (bottom) shortly after the first dashed gray line. Interestingly, for a higher value of ξ the behavior of the system differs dramatically, which we illustrate here for ξ = 1. The solution corresponding to equal coexistence of two networks, hence ρ 1 = ρ 2 = 0, is stable as before for values of σ below some critical value σ c . However, in this regime now the domination solutions (ρ 1 = 0 or ρ 2 = 0, denoted by the red squares in Fig. 3 (middle, left)) are unstable. This means that, independently from the initial conditions, in this regime the system always approaches the coexistence solution. For σ > σ c the equal coexistence solution becomes unstable and new stable solutions emerge (green diamonds in Fig. 3 (middle, right)). These unequal coexistence solutions correspond to the case that one network has a significantly higher activity than the other, but the activities of both networks are sustained. Let us again consider the explicit example of two networks and start with σ < σ c . The system approaches the equal coexistence solution (green square in Fig. 3 (middle, left)). Then, we change σ to some value above σ c . Now, the system approaches the unequal coexistence solution (green diamonds in Fig. 3 (middle, right)), but now the activity in both networks is sustained. By lowering σ again below σ c , the system recovers the equal coexistence solution, in contrast to the previous case. This example is shown in Fig. 3 (bottom) where we present the fraction of active users in both networks. To conclude, in contrast to the case discussed before, the system is robust in the sense that an irreversible loss of digital diversity cannot occur.
To sum up, the introduction of a multidimensional incentive system in which one dimension represents sociodigital capital in terms of Social Bitcoins that can be mined by performing search and navigation tasks in a future digital world can make digital diversity robustgiven that the value of Social Bitcoins is high enough.

IV. OUTLOOK AND FUTURE RESEARCH DIRECTIONS
A multidimensional financial system offers manifold success opportunities for individuals, companies, and states. Top-down control alone is destined to fail in a hyperconnected world. Hence, we need a new approach that incorporates the bottom-up empowerment of society and the right incentives and feedback mechanisms to promote creativity and innovations. The initiative "A nation of makers" [37] in the US as well as the rise of citizen science [38] constitute promising starting points for such a development. Nevertheless, increasing financial instabilities emphasize the pressing need to redesign certain aspects of the financial system, hence the urge to create "Finance 4.0" [22].
In this perspective, multiple monetary dimensions could represent different externalities (negative ones like noise, environmental damage, etc. and positive ones such as recycling of resources, cooperation, creation of new jobs and so on). Building on this framework, appropriate feedback and coordination mechanisms could increase resource efficiency and lead to a more sustainable, circular, cooperative economy. This can be achieved in a bottom-up way in terms of an improved version of capitalism based on the abilities of self-organization intrinsically present in dynamical complex systems by accounting for externalities in a multidimensional incentive system. The Internet of Things and the blockchain technology underlying the Bitcoin architecture provide the technological requirements to realize "Finance 4.0" and "Capitalism 2.0" based on knowledge from the science of complex systems [20][21][22][23]39].
Nowadays, the digital and physical world are strongly interdependent. We have presented an example how a multidimensional incentive system, in particular a Social Bitcoin generated in a bottom-up way by performing search and navigation tasks in a possible future digital world can sustain digital diversity, which is essential for the freedom of information. Furthermore, a diverse digital landscape is expected to create business opportunities for individuals and companies [4,21,39] facing the disappearance of half of todays jobs [40]. The price of Social Bitcoins is crucial for the desired effect of sustaining digital diversity. This price, however, is determined dynamically by the market and may depend on other dimensions of the currency system. The development of a concise and general theory of this system and possible implementations comprise interesting future research directions.