Parameter estimates for the model in Eq. (1) fitted on daily observations from January 2015 to June 2017.
\r\n\tThe study of populations and plant communities in their different aspects; ecological, structural, functional and dynamic, it is essential to establish a posteriori models of forest and agricultural management.
\r\n\r\n\tFor this, the methodological approaches on the type of sampling are considered essential, since there are differences between the purely ecological and the phytosociological methods, despite the fact that both pursue the same objective.
\r\n\tAlthough the ecological method for the knowledge of the vegetation is widely extended, the phytosociological one is no less so, since in the European Union it has been developed as a consequence of policies on sustainability, through which regulations have been issued, such as the habitats directive.
\r\n\tOn the other hand, research on plant dynamics and knowledge of the landscape in an integral way, have multiplied in the last 30 years, which has favored a deep knowledge of the floristic and phytocenotic wealth, which is fundamental for agricultural management, livestock and forestry.
",isbn:"978-1-83969-386-1",printIsbn:"978-1-83969-385-4",pdfIsbn:"978-1-83969-387-8",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"0abf2a59ee63fc1ba4fb64d77c9b1be7",bookSignature:"Dr. Eusebio Cano Carmona, Dr. Ricardo Quinto Canas, Dr. Ana Cano Ortiz and Dr. Carmelo Maria Musarella",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9662.jpg",keywords:"Climatic Factors, Bioclimate, Thermotype, Flora, Conservation, Phytocenosis, Plant Dynamics, Landscape, Cartography, Vegetation Series, Crops, Reforestation",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 23rd 2020",dateEndSecondStepPublish:"January 25th 2021",dateEndThirdStepPublish:"March 26th 2021",dateEndFourthStepPublish:"June 14th 2021",dateEndFifthStepPublish:"August 13th 2021",remainingDaysToSecondStep:"a month",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,biosketch:"Dr. Cano Carmona and colleagues have directed 12 doctoral theses and more than 200 publications among articles, books, and book chapters. He has participated in national and international congresses with about 250 papers. He has held a number of different academic positions, including Dean of the Faculty of Experimental Sciences at the University of Jaen, Spain, and founder and director of the International Seminar on Management and Conservation of Biodiversity.",coeditorOneBiosketch:"Ricardo Jorge Quinto Canas is currently an Invited Assistant Professor in the Faculty of Sciences and Technology at the University of Algarve – Portugal, and a member of the Centre of Marine Sciences (CCMAR), University of Algarve. His current research projects focus on Botany, Vegetation Science (Geobotany), Biogeography, Plant Ecology, and Biology Conservation, aiming to support Nature Conservation.",coeditorTwoBiosketch:"Ana Cano Ortiz's fundamental line of research is related to botanical bioindicators. She has worked in Spain, Italy, Portugal, and Central America. It presents more than one hundred works published in various national and international journals, as well as books and book chapters; and has presented a hundred papers to national and international congresses.",coeditorThreeBiosketch:"Carmelo Maria Musarella is a biologist, specialized in Plant Biology. He is a member of the permanent scientific committee of the International Seminar on “Biodiversity Conservation and Management” guested by several European universities. He has participated in several international and national congresses, seminars, and workshops and presented oral communications and posters.",coeditorFourBiosketch:null,coeditorFiveBiosketch:null,editors:[{id:"87846",title:"Dr.",name:"Eusebio",middleName:null,surname:"Cano Carmona",slug:"eusebio-cano-carmona",fullName:"Eusebio Cano Carmona",profilePictureURL:"https://mts.intechopen.com/storage/users/87846/images/system/87846.png",biography:"Eusebio Cano Carmona obtained a PhD in Sciences from the\nUniversity of Granada, Spain. He is Professor of Botany at the\nUniversity of Jaén, Spain. His focus is flora and vegetation and he\nhas conducted research in Spain, Italy, Portugal, Palestine, the\nCaribbean islands and Mexico. As a result of these investigations,\nDr. Cano Carmona and colleagues have directed 12 doctoral theses\nand more than 200 publications among articles, books and book\nchapters. He has participated in national and international congresses with about\n250 papers/communications. He has held a number of different academic positions,\nincluding Dean of the Faculty of Experimental Sciences at the University of Jaen,\nSpain and founder and director of the International Seminar on Management and\nConservation of Biodiversity, a position he has held for 13 years. 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His current\nresearch projects focus on Botany, Vegetation Science (Geobotany), Biogeography,\nPlant Ecology and Biology Conservation, aiming to support Nature Conservation.\nDr. Quinto Canas has co-authored many cited journal publication, conference articles and book chapters in above-mentioned topics.",institutionString:"University of Algarve",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"3",totalChapterViews:"0",totalEditedBooks:"0",institution:null},coeditorTwo:{id:"203697",title:"Dr.",name:"Ana",middleName:null,surname:"Cano Ortiz",slug:"ana-cano-ortiz",fullName:"Ana Cano Ortiz",profilePictureURL:"https://mts.intechopen.com/storage/users/203697/images/system/203697.png",biography:"Ana Cano Ortiz holds a PhD in Botany from the University of\nJaén, Spain. She has worked in private enterprise, in university\nand in secondary education. She is co-director of four doctoral\ntheses. Her research focus is related to botanical bioindicators.\nDr. Ortiz has worked in Spain, Italy, Portugal and Central America. She has published more than 100 works in various national\nand international journals, as well as books and book chapters.\nShe has also presented a great number of papers/communications to national and\ninternational congresses.",institutionString:"University of Jaén",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"University of Jaén",institutionURL:null,country:{name:"Spain"}}},coeditorThree:{id:"276295",title:"Dr.",name:"Carmelo Maria",middleName:null,surname:"Musarella",slug:"carmelo-maria-musarella",fullName:"Carmelo Maria Musarella",profilePictureURL:"https://mts.intechopen.com/storage/users/276295/images/system/276295.jpg",biography:"Carmelo Maria Musarella, PhD (Reggio Calabria, Italy –\n23/01/1975) is a biologist, specializing in plant biology. He\nstudied and worked in several European Universities: Messina,\nCatania, Reggio Calabria, Rome (Italy), Valencia, Jaén, Almeria\n(Spain), and Evora (Portugal). He was the Adjunct Professor\nof Plant Biology at the “Mediterranea” University of Reggio\nCalabria (Italy). His research topics are: floristic, vegetation,\nhabitat, biogeography, taxonomy, ethnobotany, endemisms, alien species, and\nbiodiversity conservation. He has authored many research articles published in\nindexed journals and books. He has been the guest editor for Plant Biosystems and a\nreferee for this same journal and others. He is a member of the permanent scientific\ncommittee of International Seminar on “Biodiversity Conservation and Management”, which includes several European universities. He has participated in several\ninternational and national congresses, seminars, workshops, and presentations of\noral communications and posters.",institutionString:'"Mediterranea" University of Reggio Calabria',position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"6",totalChapterViews:"0",totalEditedBooks:"1",institution:null},coeditorFour:null,coeditorFive:null,topics:[{id:"5",title:"Agricultural and Biological Sciences",slug:"agricultural-and-biological-sciences"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"247865",firstName:"Jasna",lastName:"Bozic",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/247865/images/7225_n.jpg",email:"jasna.b@intechopen.com",biography:"As an Author Service Manager, my responsibilities include monitoring and facilitating all publishing activities for authors and editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"878",title:"Phytochemicals",subtitle:"A Global Perspective of Their Role in Nutrition and Health",isOpenForSubmission:!1,hash:"ec77671f63975ef2d16192897deb6835",slug:"phytochemicals-a-global-perspective-of-their-role-in-nutrition-and-health",bookSignature:"Venketeshwer Rao",coverURL:"https://cdn.intechopen.com/books/images_new/878.jpg",editedByType:"Edited by",editors:[{id:"82663",title:"Dr.",name:"Venketeshwer",surname:"Rao",slug:"venketeshwer-rao",fullName:"Venketeshwer Rao"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"59478",title:"Optimal Taxation of Consumption in the Scope of Changing",doi:"10.5772/intechopen.74378",slug:"optimal-taxation-of-consumption-in-the-scope-of-changing",body:'\nTax is the main source of income, which is collected based on the sovereign authority of the government. In this context, taxation is one of the primary political tools that states use in order to obtain economic, social, and political goals. Taxation as a fiscal policy tool allows states to make effective practices in achieving their goals in macroeconomic terms. The role of tax policies in the matter of obtaining the aforementioned macroeconomic goals reveals that taxation is one of the effective economy policy tools in the hands of the state. In accordance with the social state approach, taxation emerges as a transfer mechanism. Enabling equality/justice for each individual is accepted to be at the helm of the duties of states toward their citizens.
\nCitizens belonging to all income groups in a country to be able to benefit from public services within the context of equality and justice principle on the other hand can only be possible by the state to transfer the resource, which is collected from the higher income group via taxation to lower income groups as public services. Within this framework, taxation is the most important element of the transfer mechanism between income groups.
\nHow to design taxes, which are the most important policy tools of the state in reaching the goal of effectiveness and equality, has been comprehensively discussed in the optimal taxation literature. Optimal taxation is a taxation, which reflects the preferences between the society’s rivaling aims of equality and economic efficiency and which has maximizing social wealth as the starting point.
\nIn today’s conditions, in which the state has asymmetrical information about the individual’s social and economic characteristics, the goal of income redistribution can be possible through the use of distortionary taxes. The state can assure income justice by using distortionary taxes only by conceding economic efficiency. Because of this reason, optimal taxation lays emphasis on tax subject, tax rate, and tax base, which will minimize thrashing in securing a certain amount of tax revenue.
\nIn this context, two main studies exist in the optimal taxation literature with regard to tax subject. In his study, Ramsey [1] approached optimal tax subject on the basis of consumption, and in the second fundamental study, Mirless [2] identified revenue as the tax subject. In both studies, ideal tax rates were searched within the context of the determined tax subject.
\nIn the Ramsey approach to optimal taxation, since the needed budget revenue is possible to be obtained only by distortionary taxes under the assumption that it is not possible for governments to resort to lump sum taxes, it will bring along a wealth loss in terms of economic efficiency and will move away from the optimal solution. Within this framework, Ramsey emphasizes on the tax subject and rate that will minimize efficiency loss. In Ramsey approach, it is generally agreed that the government can impose a linear income tax besides commodity tax [3].
\nOptimal commodity taxation, which was proposed in 1927 by Ramsey and whose theoretical structure has developed through today’s modern approaches, is based on the inverse elasticity rule, which claims goods with low demand elasticity to be taxed at a higher rate will reduce efficiency loss, and Corlett-Hauge Rule [4], which claims leisure complement goods that will change the preferences of consumers between working and leisure on behalf of working need to be taxed at a higher rate.
\nIn the inverse elasticity rule suggested by Ramsey, all goods are aimed to be affected equally from taxes by levying taxes at a high rate from goods with low demand elasticity and at a low rate from goods with high demand elasticity.
\nThe most important criticism toward this rule originates from the fact that necessity goods devoted to meet basic needs have low price elasticity of demand, and luxury goods on the other hand have high price elasticity. Taxing luxury goods at a lower rate compared to necessity goods under the assumption that consumers resemble each other is claimed to influence justice of taxation in a negative way.
\nThe assumption that luxury goods have high demand elasticity and necessity goods have low demand elasticity may change when short and long periods are in question and within the context of competition, which is the main incentives of market economy. In assuring the profit maximization, which is the main goal of firms competing in the market economy, their total revenues and demand elasticity for their products are important variables. Firms can increase their total revenues by decreasing the demand elasticity for their products. In this context, firms aim to reduce the vulnerability of the product they produce against price changes.
\nAs markets open to foreign countries, together with the liberalization in trade, magnitude of the market and innovation increases, and this may increase price elasticity of demand by increasing substitution possibility of especially necessity goods [5, 6, 7]. On the other hand against this risk, firms try to lower the demand elasticity of their products within the context of the brands they create and by increasing loyalty to these brands [8]. Especially, in product groups including luxury goods such as technological products and automobiles, brand loyalty reduces the sensitivity of consumers to the product’s price.
\nWithin this framework, changing market conditions changes demand elasticity of luxury and necessity goods, and this change on the other hand necessitates reassessing basic assumptions of optimal taxation and criticisms against optimal taxation.
\nThe most fundamental goal of economic and fiscal policies is to maximize wealth. This goal includes quite large sub-goals, such as providing stability, growth, efficient allocation of resources, and fair income distribution. Tax is the primary fiscal tool to be used in reaching the goals in question. Among the tax applications that are under the changing and developing state understanding, what type of taxation is the taxation that serves the goal of wealth maximization is considered in the literature especially in the framework of “Optimal Taxation” theory.
\nWhile within classical welfare economics understanding, optimal taxation theory considers taxes as effective tools in assuring resource allocation; new welfare economics’ view of utility measurement and impossibility of inter-personal comparisons caused economic area of interest to rotate to Pareto efficiency. This situation focused on substitution effect of taxes, creating efficiency loss and lasted until the study of Mirrlees [2], which targets resolution of equality and efficiency conflict.
\nIn this context, optimal taxation is the taxation that reflects the preferences of the society between equality and efficiency with rivaling goals, and that has social wealth maximization as the starting point. Within this scope, balance between the goals of justice (equality) in taxation and economic efficiency is tried to be redressed. On the other hand, trade-off between these goals created different approaches to the topic.
\nExistence of the relevant trade-off depends on the existence and influence of distortionary taxes. In today’s conditions, in which the state has asymmetrical information about the individual’s social and economic characteristics, the goal of income redistribution can be possible through the use of distortionary taxes. The state can assure income justice by using distortionary taxes only by conceding economic efficiency. Because of this reason, optimal taxation lays emphasis on tax subject, tax rate, and tax base, which will minimize efficiency loss in securing a certain amount of tax revenue.
\nIn general terms, distortionary taxes can be defined as taxes that will influence or change economic decisions of taxpayers. The main reason for distortionary taxation on the other hand is to assure redistribution of revenue, which is one of the fundamental functions of the state and thus to achieve a society structure more egalitarian than the one that could have been achieved via a uniform lump-sum tax [9].
\nThe state, which has a social aim of distributing the tax burden in a fair and balanced way within the scope of fiscal policy, needs distortionary taxes in order to realize this aim. State’s complete and absolute knowledge about the characteristics of each individual in the society underlies this need. In this context, use of distortionary taxes is a consequence of the aim to redistribute revenue in a world, where the state knows characteristics of individuals only incompetently [9]. Within this scope, in the assurance of justice (equality), individuals having the same ability to pay will be assumed to be in equal conditions, and same amount of taxes will be taken from them [10].
\nWhen different abilities to pay are at stake, the state redistributes revenue in a way to load a greater amount of public expenditures to higher income groups. Different societies may have different preferences on equality and efficiency. These differences bring along different tax systems in practice. Discussions on how progressive tax structure should be in order to enable equality are a result of value judgments about equality. In this context, inequality reduced through progressive tax structure can only be possible by the acceptance of a certain amount of efficiency loss.
\nAccording to Diamond and Mirrless [11], administratively, it is not possible for the state to realize its revenue distributer goal on the grounds of social justice and revenue creator goal on the grounds of public finance, through lump-sum taxes. Since lump-sum tax is not appropriate, optimal taxation will only be a taxation that will not impair the efficiency of production. This on the other hand is only possible if the taxation on the final production can be diversified between products at no cost [12].
\nIn the light of these explanations, optimal tax structure is defined as the tax structure, which reflects the preferences of the society between the balance of efficiency loss and equality and maximizes social wealth. Optimal taxation theory seeks answers basically to the following questions:
On what will the tax be taken from (income-consumption-wealth)?
If the tax will be taken on consumption, is it going to be at a fixed rate?
If the tax will be taken on wealth, how will the tax base be? [13]
In the following parts of this study, optimal taxation will be taken on consumption.
The main topic of discussion in the literature regarding optimal commodity taxes, which are approached under the heading of optimal taxation, is about the proportional structure of the taxes in question. In this context, literature searches which tax rates, single rate or varying, will create optimal results in the construction of optimal commodity taxes. Within this scope, while on one side, there is the view arguing that a single rate tax will not damage market forces and will be synonymous with a fixed rate tax on income [14]; on the other side, optimal commodity taxes within the context of Ramsey and varying rates take place.
\nRamsey rule involves taxing commodity and zero capital taxes in the long run [15] for minimizing the deadweight loss. For public choice theory, equilibrium taxes and feasible tax structure apart from Ramsey analysis are important subjects because tax system can cause rent seeking when it is used as an income distribution tool [16, 17].
\nOptimal commodity taxation, which was proposed in 1927 by Ramsey and whose theoretical structure has developed through today’s modern approaches, is based on the inverse elasticity rule, which claims goods with low demand elasticity to be taxed at a higher rate will reduce efficiency loss, and Corlett-Hauge Rule, which claims leisure complement goods that will change the preferences of consumers between working and leisure on behalf of working need to be taxed at a higher rate.
\nAs seen in \nFigure 1\n, tax application may cause a decrease in social wealth by changing price before and after tax. The reason behind this is the decline of production under the amount before tax because of the change in price. Minimization of this efficiency loss, which is also called excess tax burden or deadweight loss (DWL), is the purpose of the tax systems.
\nDeadweight loss of taxation. Source: Ref. [44].
Under the assumption that characteristics of individuals can only be known deficiently and thus lump-sum taxes are not applicable, Ramsey searched the tax structure that will minimize efficiency loss (deadweight loss) associated to the collection of a specific amount of tax revenue. Excess tax burden is caused by the reduction in equilibrium quantity because individuals change their behaviors and consume taxed product less. Decrease in the quantity of the product depends on demand elasticity. According to Ramsey rule, tax rate imposed on the good with high elasticity should be lower than the tax rate imposed on the good with low elasticity [18]. In this way, as seen in \nFigure 1\n, decrease in the equilibrium quantity of goods would be minimized.
\nUnder the assumption that people resemble each other, Ramsey taxes are expressed as the sum of the inverses of supply and demand elasticity.
\nIn this equation, t represents tax rate per unit, p represents price after tax, \n
In the inverse elasticity rule suggested by Ramsey, under the assumption that supply curve is finite or, in other words, a horizontal supply curve exists, tax is stated to be inversely proportional to compensated demand elasticity. Accordingly, all goods to be affected equally from taxes are aimed by collecting lower rates of taxes from goods with high price elasticity of demand and higher rates of taxes from goods with low price elasticity of demand.
\nWithin the framework of this purpose, Sandmo [19] expresses that Ramsey rule can be based on the following three hypotheses:
Being able to minimize efficiency loss, which occurs as a result of distortionary taxation, is possible through tax applications with a low substitution effect. Because of this reason, goods with prices that do not create substitution effect are the ideal subject of the tax. In other words, in cases where lump-sum taxes cannot be imposed, commodity taxes with similar effects should be imposed.
Goods, which will be taxed at high rates, should have a high leisure complementary level.
Elasticity of substitution between goods and leisure lies behind the fact that single rate tax, which does not change the relative prices of goods and will not be different from the lump-sum tax that will be imposed on labor income, is not optimal [14].
However, according to Corlett-Hague Rule, varying tax rates, in which leisure complementary goods that will change the preferences of consumers between working and leisure in favor of working will be taxed at higher rates, serve for the assurance of optimality in commodity taxes. In this context, Diamond [11] proposed leisure complementary goods to be taxed at relatively higher rates intended to the efficiency purpose.
Tax rates are expected to be inversely proportional with uncompensated own-price elasticity of demand.
The most important criticism toward the Ramsey rule composed of above-mentioned hypotheses is caused by the fact that necessity goods devoted to meet basic needs to have low price elasticity of demand and luxury goods to have high price elasticity. Under the assumption that consumers resemble each other, taxation of luxury goods at a lower rate compared to necessity goods is claimed to influence justice of taxation negatively.
Ramsey taxes, which were pointed out in the above section in detail, are criticized because of its current assumptions and negativity they might create in income distribution.
\nAt this point, first main criticism to Ramsey analysis is the assumption that all individuals resemble each other. The fundamental reason for the state to use distortionary taxes instead of lump-sum taxes is to have redistribution goals, which are not possible to attain in another way. In case this assumption is valid, there are no causes of the state for not imposing lump-sum taxes.
\nNevertheless, when taxes are imposed within the context of inverse elasticity rule, an equal amount of decrease in demand in all goods will be caused by collecting lower rates of taxes from goods with a high possibility of change in demand amount and at higher rates from goods with a low possibility of change in demand amount; and thus, efficiency loss will be minimized. According to this approach, taxation of necessity goods, which have low compensated demand elasticity and have a large share in the consumer’s budget, at a higher rate than luxury goods comes to the fore [9].
\nGenerally, price elasticity of demand for good, which are consumed with the purpose of meeting basic needs, is low, while price elasticity of demand for luxury goods is high. Based on this rule, tax rate to be imposed on basic necessity goods will be high, and tax rate to be imposed on luxury goods will be low. What needs attention here is the assumption that consumers are alike. However, since income distribution and demand for different products will vary, such a rule will create negative results in terms of tax equity especially in developing countries.
\nRamsey defended this rule by placing economic efficiency to forefront. Therefore, although theoretically consistent, this analysis becomes contradictive in practice with the influence of socio-political reasons [20].
\nIn short, when Ramsey’s suggestion is applied, low-incomers, who relatively allocate majority of their income to necessity goods, have to face a high tax burden. Therefore, a conflict between the goals of decreasing the efficiency cost of tax and equitable tax emerges. Ramsey rule puts forward what needs to be done when efficiency purpose is desired to be pursued. Goal of justice is not within this rule’s field of interest [18].
\nAs a result in optimal commodity taxation, Ramsey’s analysis requires a careful analysis of: the constraints on taxation; the elasticities of demand and supply; and the structure of the economy [21].
\nCriticisms done within the context of the basic assumptions of Ramsey taxes’ inverse elasticity rule become more serious especially on the topic of income redistribution. Inverse elasticity rule creates a conclusion in line with efficiency but to the detriment of equality by suggesting taxation of necessity goods, which occupy a heavy place in the consumption basket of lower income groups, at a high rate and goods appealing to higher income groups at lower rate depending on demand elasticity.
\nBesides the assumptions in inverse elasticity rule mentioned above that are subject to criticisms, another topic to be emphasized is whether demand elasticity varies within the framework of macroeconomic and microeconomic variables.
\nA change that may occur in demand elasticity of luxury and necessity goods may build a fairer structure for the inverse elasticity rule in terms of income distribution, and the abovementioned taxes criticized in practice within the context of enabling justice in income distribution, which is among the main functions of the state, may be reassessed as part of changing demand elasticity. Under this assumption, in this part, changes in elasticity of luxury and necessity goods that could be created by macrovariables and microvariables within the changing economic conjuncture will be addressed.
\nExistence of substitution possibility is the primary element affecting demand elasticity. Existence of close substitutes for some goods increases price elasticity of the demand in question. As seen in \nFigure 2\n, since development of substitution opportunities take time, while in short term, price elasticity of demand for many products is low, elasticity may increase in the long term [22]. Durable consumer goods have a different structure compared to other goods in short and long term elasticity. Despite the fact that elasticity differences are observed between terms in these goods as well, price elasticity of demand is more elastic for these goods in the short term, while it weakens in the long term [23].
\nChanging demand elasticity.
At this point, the most basic example is the price elasticity of demand for oil changing in short and long terms against OPEC cartel shock in 1970s. Sudden price increase experienced in the so-called period was received with highly inelastic price elasticity of demand at a level that did not cause a change in the amount demanded in the short term; however, fuel efficient solutions with the technology developed in the long term allowed price elasticity of demand to increase.
\nIn this way, short and long term price elasticity of demand for products with substitutes that need time to be developed may differ. Because of this reason, although goods with low price elasticity of demand are advised to be taxed at higher rates in Ramsey taxes within the tax structure that will not damage efficiency, in the long term, price elasticity of demand for many goods including necessity goods increases. In such a case, since tax rates will decline as part of increased elasticity, it will be difficult to achieve the budget revenue planned in the beginning without negatively affecting efficiency.
\nCriticism of Ramsey taxes, which will be applied within the scope of the inverse elasticity rule because luxury goods have high demand elasticity and necessity goods have low demand elasticity, because of its elasticity assumptions may change as part of competition, which is the main abettor of market economy today. Total revenue and demand elasticity for products are important variables in providing profit maximization, which is the principal purpose of firms competing in market economy.
\nFirms can increase their total revenues by decreasing the demand elasticity for their products. In this context, firms aim to decrease the vulnerability of the products they produce against price changes. Thus, they can increase their total revenues by raising product prices [24]. Yet, together with the increased competition, efficiencies [25, 26] increase, and together with liberalization, market size [27] increases.
\nEspecially, liberalization in commerce influences export and import performances of industries, declines in tariffs cause scale increases [28], and thus, competition escalates [29]. As supported by quite a few studies, high protectionism in commerce leads firms to produce under optimal scale, and output increases to be negatively affected [30].
\nCommercial liberalization on the other hand allows the tariff structure to soften, large-scale firms to rise together with the increase in competition, and output levels of small-scale firms to rise [29]. Diversity increased in the market structure that grew by this means enhances the substitution opportunity between goods and thereby increases price elasticity of demand. By this way, the scale that increased through liberalization and competition raises diversity of goods and services and therefore their substitutability and serves for the increase of price elasticity of demand of all necessity and luxury goods.
\nIn one of the first studies investigating the relationship between market size and innovation, Griliches [31] put forward in 1957 the existence of a significant relationship between technological change and technological adaptation and profitability and market size. In other studies analyzing different sectors following this study, a significant relationship between market size and innovation and innovation elasticity was exhibited [32, 33, 34]. In this context, the innovation process, which improves as market size grows, increases price elasticity of demand by supporting the increase of product range [35].
\nIn the light of these analyses, macroeconomic variables, such as short and long term structures, commerce liberalization and competition, market size, and innovation, affect and change the price elasticity of demand for luxury and necessity goods. This change generally reveals itself as the increase of price elasticity of demand for goods. This macrochange of demand elasticity in both luxury and necessity goods composes a risk for firms in microterms. On the other hand against this risk, firms try to decrease the demand elasticity for their products by creating brands and increasing loyalty to these brands [8].
\nBrand loyalty decreases the sensitivity of consumers to the prices of products especially in product groups such as technological products and automobiles. At this point, it is useful to mention about brand loyalty as a microvariable effective on price elasticity of demand.
\nWhile price elasticity of demand increases as part of macrovariables, this increase in elasticity requires different precautions to be taken, since it would negatively influence profit maximization goal. One of the fundamental elements for the firms to obtain their profit maximization goal is to be able to increase total revenue with price increases they gathered by decreasing substitutability opportunities and price elasticity of demand for their products [24]. Within this scope, primary methods for dropping price elasticity of demand for the firms’ products at microlevel are creating or strengthening brand loyalty.
\nAccording to Palumbo and Herbig [36], brand loyalty, which has different definitions in literature, is in the most general sense a situation, in which consumers continuously tend to seek and purchase only a certain brand even when competitor businesses offer lower prices and sales promotions.
\nBrand loyalty to be also high in high-priced products [37] leads the consumer, whose brand loyalty increased, to be less sensitive to price changes. Firms, with a purpose of increasing market share and profitability, try to reduce the vulnerability of their products against substitution opportunities and price changes by raising loyalty to their brands. Within this framework, a close relationship between market share and purchase possibilities of brand loyal consumers, who do not respond to price changes, is in question [38].
\nBrand loyalty provides some advantages to firms against competition. These advantages can be listed as follows:
Creating brand loyalty decreases an important amount of advertising and promotion costs [39]. Together with the fall in costs, consumers loyal to brand will be loyal to the brand and not be sensitive to price changes as long as they resolve problems they experience about the product.
Brand loyalty ensures competitive advantage to businesses. It builds a large entrance barrier to new entrant businesses. These barriers lower price elasticity of demand by complicating substitution of products firms produce.
Brand loyal consumers do not oppose to pay a higher price for the products and services the business offers, and this increases the profitability of the business in short and long term.
They do not abandon the brand immediately after they experience a negative situation about the brand.
All these advantages enabled by brand loyalty on the other hand serve price elasticity of demand for the product to fall.
\nBrand loyalty with regard to Ramsey taxation has importance especially in terms of decreasing price elasticity of demand for luxury goods. Brand loyalty to be high especially in luxury goods [40] drops price elasticity of demand to the so-called goods by weakening substitution possibilities and thus weakens the sensitivity of consumers of luxury goods the price changes of these goods.
\nAll these macrovariables and microvariables change price elasticity of demand for luxury and necessity goods as part of differential tax rates in optimal commodity taxes. Additionally, they give way to Ramsey’s inverse elasticity rule to be re-evaluated as part of criticisms it receives about income distribution. At this point, price elasticity of demand for luxury and necessity goods rises depending on short and long term effect, commercial liberalization, and increased competition and innovation, which are all macroeconomic variables.
\nThus, demand elasticity of necessity goods, which have a large share in the consumption spending of lower level income groups, increases as part inverse elasticity rule; and therefore, tax rates decrease in line with the increase in elasticity. A decline in the tax rate, which the lower income level group will be exposed to as part of inverse elasticity rule, may create a more agreeable result in income distribution.
\nThe influence microvariables have on price elasticity of demand on the other hand is important especially for luxury goods. Firms, aiming to increase their total revenues by reducing demand elasticity for their products, have the purpose of decreasing the vulnerability of their products against price changes. Since brand loyalty, which is one of the primary microvariables firms use within this framework, is high especially in luxury goods as mentioned above, it affects price elasticity of demand for the goods.
\nCreated brand loyalty prevents change in consumer preferences by reducing substitution possibilities of luxury goods and decreasing price elasticity of demand. By this way, in a tax that will be applied as part of inverse elasticity rule, luxury goods will be subject to high-rate taxes because of low demand elasticity. And therefore since aforementioned goods share in the consumption basket is very low for lower level income groups and high for higher level income groups, effect of this taxation, which is applied by considering elasticity, might be positive on income distribution.
\nWithin this scope, while justice in income distribution is served on one hand, a certain budget revenue of optimal taxation goal is achieved through taxing goods with low demand elasticity at a high rate, and this goal is achieved without damaging any economic decisions or in other words without spoiling economic efficiency. Both inverse elasticity rule and leisure complementary goods, which will change preferences of consumers between working and leisure in favor of working, to be taxed at higher rates play a role. The fact that luxury goods are mostly substitutes of leisure lead to this conclusion.
\nBeginning from this century, labor market and accordingly preferences between leisure and working started to change. In this context, leisure industry has boomed. In many societies, leisure was equalized with luxury goods such as motor sports and traveling and became a symbol of postmodernity [41].
\nThus, luxury goods have been effective in the change of the decision for working as a complementary of leisure. While luxury goods with a declined price elasticity of demand as part of brand loyalty are taxed at a higher rate with regard to inverse elasticity rule; at the same time, preferences of individuals in favor of working were strengthened by imposing taxes on leisure complementary goods and thus raising the cost of leisure.
\nKeeping in mind that criticisms Atkinson and Stiglitz [42, 43] made with regard to differential consumption taxes in terms of economic efficiency, the assumption that the single rate consumption tax will result efficiently in terms of optimal taxation, and under the agreement that other assumptions of Ramsey rule remain the same, demand elasticity of necessity and luxury goods, which changed with the influence of macrovariables and microvariables, will be able to serve in enabling the aimed public revenue without contradicting justice in income distribution under inverse elasticity rule.
\nOn the basis of an imperative tradeoff between equality and efficiency assumption, optimal taxation literature which claims that egalitarian redistribution policies of the state will create negative results oppose redistribution policies of the state because of equality-efficiency dilemma. The main starting point on this topic is not being able to enable a certain budget revenue goal via lump-sum taxes because of the asymmetrical information between state and individual and the need for distortionary taxes. In this context, one of the propositions for resolution in the literature is optimal commodity tax application.
\nIn optimal tax application with the aim of efficiency, discussion of single rate or differential tax application is in question.
\nRamsey’s study on optimal commodity taxes, which suggest goods to be taxed inversely proportional with price elasticity of demand, is one of the primary studies in the literature. While Ramsey rule basically proposes goods with low price elasticity of demand to be taxed at higher rates, its purpose is to preserve individuals’ decisions about the consumption of goods with increasing prices unchanged as part of low elasticity, or in other words, a deadweight loss or wealth loss not to be formed in the economy. This rule, in which economic efficiency concern dominates, faces the biggest criticism because of the unjust distribution emerging as a result of the assumption that all individuals resemble each other.
\nWith the inverse elasticity rule, Ramsey suggests necessity goods, which occupy a large share in the consumption basket of lower income groups, to be taxed at higher rates and goods, which appeal to higher income groups, to be taxed at lower rates due to demand elasticity. What is important in this context is whether price elasticity of demand for goods change or not as part of macrovariables and microvariables.
\nPrice elasticity of demand for luxury and necessity goods rises depending on short and long term effect, commercial liberalization, and increased competition and innovation, which are all macroeconomic variables. On the other hand, since brand loyalty, which is the leading microeconomic variable, is high especially for luxury goods, it affects price elasticity of demand for the aforementioned goods.
\nAdditionally, luxury goods to be taxed at higher rates under the assumption that they are leisure complementaries may affect the decisions of individuals on behalf of working. In this context, the criticisms brought about by Ramsey’s rule in terms of economic efficiency at the differential taxation, it can be seen that the rule of inverse elasticity on equality can be reconsidered.
\nBitcoin is a digital currency built on a peer-to-peer network and on the blockchain, a public ledger where all transactions are recorded and made available to all nodes. Opposite to traditional banking transactions, based on trust for counterparty, Bitcoin relies on cryptography and on a consensus protocol for the network. The entire system is founded on an open source software created in 2009 by a computer scientist known under the pseudonym Satoshi Nakamoto, whose identity is still unknown (see [1]). Hence, Bitcoin is an independent digital currency, not subject to the control of central authorities and without inflation; furthermore, transactions in the network are pseudonymous and irreversible.
\nBitcoin and the underlying blockchain technology have gained much attention in the last few years. Research on Bitcoin often deals with cybersecurity and legitimacy issues such as the analysis of double spending possibilities and other cyber-threats; recently, high returns and volatility have attracted research toward the analysis of Bitcoin price efficiency as well as its dynamics (see, among others, [2, 3, 4]). Moreover, many contributions claim that Bitcoin price is driven by attention or sentiment about the Bitcoin system itself; see [5, 6, 7, 8]. Possible driving factors for the sentiment about the Bitcoin system are the volume of Google searches or Wikipedia requests as in [5], or more traditional indicators as the number or volume of transactions, as suggested in [6]. In [9], the author suggests a time series model in order to identify the dynamic relation between speculation activity and price.
\nIn this chapter, after having introduced the basic concepts underlying Bitcoin, we sum up and describe to a broader audience the recent outcomes of the research reported in [10], by avoiding unnecessary technicalities. Some new insights are also given by looking at possible extensions in order to take into account the presence of bubble effects or the special feature of Bitcoin being traded in different online platforms (exchanges) that will be further investigated in our future research.
\nWe recall that Bitcoin was first introduced as an electronic payment system between peers by Satoshi Nakamoto (pseudonym) in [1]. Opposite to traditional transactions, which are based on the trust in financial intermediaries, this system relies on the network, on the fixed rules and on cryptography. Bitcoins can be purchased on appropriate websites that allow to change usual currencies in the cryptocurrency.
\nThe Bitcoin network has several attractive properties for its users:
No central bank authority for money supply and no regulator;
Transactions are 24/7 and without any country border;
Transaction cost are almost negligible with respect to traded amount;
Transaction are anonymous;
The security of each transaction is guaranteed by cryptography and digital signature;
The security of the whole network is guaranteed by construction unless more than 50% of the network nodes agree on a deceptive action.
As a digital payment system, Bitcoins may be used to pay for several online services and goods. Special applications have been designed for smartphones and tablets for transactions in Bitcoins and some ATMs have appeared all over the world (see Coin ATM radar) to change traditional currencies in Bitcoins. Accepting Bitcoins as a payment method is also related to an advertisement opportunity for companies. However, the high returns achieved in the last few years have transformed Bitcoin in a speculative asset affecting its use as a form of payment.
\nThe Bitcoin system has been subject to many cracks but has proven to be very resilient as the value of the cryptocurrency was able to rise again after all the falls. Nevertheless, at the time of writing, Bitcoin was experiencing a fall in its exchange rate with main fiat currencies.
\nTwo of the main crackdowns were China enforcement in December 2013 and Mt. Gox bankruptcy in February 2014.
\nBesides technical and regulation issues, the Bitcoin system also faces reputational concerns.
\nIn fact, the ambiguity of anonymous transactions has blamed the network of allowing several criminal activities such as buying illegal goods, money laundering or the financing of terrorism actions. As a representative example, we recall that The Silk Road was a website that started selling narcotics and illegal drugs in 2011, payable in Bitcoins. The website was finally shutdown by 2013 and the owner was arrested and sentenced to life in prison. Again, anonymous transactions make it possible to use huge quantities of money, exchanged in Bitcoins, without declaring its origin, hence allowing for possible money laundering. However, according to a research performed by the UK government, the highest score related to money laundering is still cash, followed by the bank, accountancy and legal service providers (see
It is worth noticing that while counterparties are represented by secret addresses and are anonymous, all transactions are recorded and might be traced. Investigation is hence favored by this feature of the network.
\nDespite the flaws in the system, Bitcoin has achieved a notwithstanding rise in recent years.
\nIn Figure 1, we report Bitcoin price and returns from January 2012 to December 2017 (source
Bitcoin price (top) and returns (bottom) from January 2012 to December 2017.
The model we suggest in what follows is motivated by findings in [5, 6, 8, 11] where it is showed that Bitcoin price is related to investors’ attention measured by the trading volume and/or the number of searches in engines such as Google and Wikipedia. Bitcoin is treated as a financial stock as suggested in [12] and the suggested model may be applied in principle to other assets that are proven to depend on market attention.
\nConsider a probability space \n
Let us denote the Bitcoin price process as \n
where \n
It is well known that the above dynamics for the attention factor is a geometric Brownian motion, the solution of which is given by \n
We collect in this subsection the properties of the logarithmic returns obtained by the price process defined in Eq. (1).
\nConsider the discrete process \n
Theorem 2.1. The random vector \n
Proof. In order to prove the theorem it suffices to remind that, for i = 1, 2, …, n, the random variable \n
As for the unconditional distribution, it is easy to obtain, for \n
where \n
Proposition 2.2. The joint probability density of the vector \n
where \n
The proof follows from Bayes’ rule and application of Theorem 2.1.
\nIt is worth to remark that the probability density \n
Precisely, we have that \n
We apply the outcomes above in order to estimate model parameters according to the maximum-likelihood method (see for example [14, 15]) where the likelihood is approximated by applying the Levy approximation [13].
\nParameter estimates are obtained as
\nwhere
The first step in our procedure is to identify possible measures of investors’ attention. As already mentioned in the introduction, we consider the total trading volume on Bitcoin available from
The trading volume of exchange is a classical measure of the attractiveness of a traded asset for an investor; besides, in [16], the authors find evidence that the latter captures the attention of retail/uniformed investors.
\nWe consider daily data from January 1, 2015, to June 30, 2017, for the total volume and the SVI Index. As for the daily value of the Bitcoin, we have considered the average mean across main exchanges represented by the Index in
In Table 1, the outcomes for parameter estimates, obtained by maximizing the approximate likelihood given the observed time series, are summed up.
\n\n | \n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|
A = Vol | \n0.9571 | \n1.1346 | \n0.0218 | \n0.0829 | \n
A = SVI | \n1.3584 | \n1.0687 | \n0.0743 | \n0.1559 | \n
Parameter estimates for the model in Eq. (1) fitted on daily observations from January 2015 to June 2017.
In this section, we show how to characterize the price of European call options on Bitcoins in the underlying market model. Let us fix a finite time horizon \n
where \n
Lemma 3.1. Every equivalent martingale measure \n
where \n
The proof can be deduced from that of Lemma 1.4 in [10], where they also account for a possible delay between the attention factor and its effect on Bitcoin prices trend. The process \n
is an \n
Equivalently, we can write the discounted Bitcoin price process \n
Clearly, under the minimal martingale measure \n
where \n
Remark 3.2. Note that, under any equivalent martingale measure that keeps the drift of the attention factor dynamics linear in \n
Now, we compute the fair price of a Bitcoin European call option via the risk-neutral evaluation approach, so it can be expressed as expected value of the terminal payoff under the selected pricing measure, that is, the minimal martingale measure. Let CT = (ST − K)+ be the \n
where
\nand \n
Here, \n
The following result provides the risk-neutral price of the option under the minimal martingale measure \n
Proposition 3.3. The risk-neutral price \n
where the function \n
Hence, the resulting risk-neutral pricing formula when evaluated in \n
In order to appreciate the performance of the pricing formula in Eq. (19), we compute model prices for option traded on the online platform
T-K | \nMarket bid | \nMarket ask | \nModel volume | \nModel Google SVI | \nBenchmark BS | \n
---|---|---|---|---|---|
Aug-2200 | \n0.1662 | \n0.2318 | \n0.2029 | \n0.2282 | \n0.1967 | \n
Aug-2300 | \n0.1670 | \n0.2072 | \n0.1737 | \n0.2032 | \n0.1655 | \n
Aug-2400 | \n0.1390 | \n0.1845 | \n0.1469 | \n0.1802 | \n0.1369 | \n
Aug-2500 | \n0.1142 | \n0.1638 | \n0.1228 | \n0.1591 | \n0.1112 | \n
Aug-2600 | \n0.0922 | \n0.1376 | \n0.1014 | \n0.1399 | \n0.0887 | \n
Aug-2700 | \n0.0749 | \n0.1202 | \n0.0828 | \n0.1226 | \n0.0695 | \n
Aug-2800 | \n0.0572 | \n0.1047 | \n0.0684 | \n0.107 | \n0.0535 | \n
Aug-2900 | \n0.0442 | \n0.0983 | \n0.0549 | \n0.0931 | \n0.0405 | \n
Sept-2200 | \n0.1991 | \n0.2648 | \n0.2546 | \n0.3204 | \n0.2173 | \n
Sept-2300 | \n0.1766 | \n0.2432 | \n0.2321 | \n0.3019 | \n0.1906 | \n
Sept-2400 | \n0.1890 | \n0.2230 | \n0.2113 | \n0.2844 | \n0.1662 | \n
Sept-2500 | \n0.1375 | \n0.2042 | \n0.1919 | \n0.2679 | \n0.1439 | \n
Sept-2600 | \n0.1207 | \n0.1828 | \n0.1741 | \n0.2523 | \n0.1239 | \n
Sept-2700 | \n0.1120 | \n0.1668 | \n0.1576 | \n0.2377 | \n0.1060 | \n
Sept-2800 | \n0.0953 | \n0.1504 | \n0.1463 | \n0.2239 | \n0.0903 | \n
Sept-2900 | \n0.0848 | \n0.1422 | \n0.1325 | \n0.2109 | \n0.0764 | \n
Motivated by empirical evidences (see for example [21, 22]), we discuss a generalization of the model introduced in Section 3.1, which is capable to describe speculative bubbles in Bitcoin markets.
\nPrecisely, we fix a finite time horizon \n
Without loss of generality, we assume that the interest rate is fixed and equal to zero. In this setting, the discounted Bitcoin price trend and the market attention factor dynamics are described by
\nwhere we have set \n
By simulating trajectories for the asset price \n
Simulated trajectories with n = 250 daily observations for the attention process (red) and the corresponding Bitcoin price dynamics for \n\nρ\n=\n0\n\n (black), \n\nρ\n=\n0.5\n\n(green), and \n\nρ\n=\n1\n\n (blue).
Indeed, we will show formally that the possibility of Bitcoin speculative bubbles is related to the sign of the correlation parameter \n
The mathematical theory of financial bubbles is developed, among others, in [23, 24, 25]. Precisely, we introduce the following definition from [23].
\nDefinition 4.1. The Bitcoin price process \n
The term strict \n
Recall that the absence of arbitrage opportunities is “essentially” equivalent to the existence of a probability measure \n
Remark 4.2. Note that stock bubbles arise if \n
Then, to exclude arbitrage opportunities from the market, we define the process \n
where \n
To ensure that \n
and we can consider the corresponding family of equivalent (local) martingale measures \n
where the \n
\n\n
Now, suppose that the risk perception process is zero, that is, \n
is a true \n
Proposition 4.3. In the model outlined in Eq. (24), the Bitcoin price process \n
The proof is based on the application of some of Sin’s results given in [27], where the existence of risk-neutral measures for the Hull-White stochastic volatility model [19] and for similar frameworks is determined by the possibility of explosion in finite time for solutions of certain auxiliary stochastic differential equations. Precisely, it is possible to show that the martingale property of the discounted stock price \n
Let us generalize the model introduced in Eq. (1) by assuming a possible delay \n
where \n
Analogous results as those in Section 2 can be derived by similar computations, and model parameters, for a fixed delay, can be estimated by means of the maximum likelihood method. In order to estimate the delay parameter, we maximize the profile likelihood as defined in [15]. Details of this procedure can be found in [10]. The estimation results of model in Eq. (27) on the same daily data considered in Section 2 are summed up in Table 3.
\n\n | \n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
A = Vol | \n1 day | \n0.4881 | \n1.0459 | \n0.0282 | \n0.0924 | \n
A = SVI | \n7 days | \n1.0964 | \n0.9946 | \n0.1005 | \n0.1885 | \n
Parameter estimates for model in Eq. (27) fitted on daily observations from January 2015 to June 2017.
In Figure 3, we plot simulated trajectories of the price process in Eq. (27) by letting the delay parameter vary.
\nSimulated trajectories of n = 250 daily observations of the attention factor (red) and the Bitcoin price according to model in Eq. (27) when the delay parameter is \n\nτ\n=\n1\n\n day (black) and \n\nτ\n=\n10\n\n days (blue).
The different delays result in a shift to the south-east between the faster and slower reacting trajectories; in the picture, this behavior is sharp since the other model parameters are kept constant. By looking at the picture, the idea to model the price of Bitcoin in different exchanges by the same model in Eq. (27) but allowing different parameters naturally arises.
\nIn particular, considering for instance two exchanges, we have
\nwhere \n
Note that within this model, prices for Bitcoin traded in different exchanges are perfectly correlated. Indeed, this is what happens in observed data; considering daily prices from January 2015 to June 2017 for Bitstamp, Kraken, Cex.io, Gdax, and The Rock exchanges we get cross-correlation values larger than 0.999.
\nWe fit model in Eq. (28) for the Bitstamp and Gdax exchanges on daily observations of Bitcoin price from January 2015 to June 2017 obtaining the outcomes reported in Table 4, when the attention is measured by the trading volume, and in Table 5, when attention is measured by the Google SVI index.
\nExchange | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
Bitstamp | \n1 | \n0.4994 | \n1.0461 | \n0.0281 | \n0.0896 | \n
Gdax | \n2 | \n0.4997 | \n1.0420 | \n0.0326 | \n0.1036 | \n
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the trading volume.
Exchange | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n\n\n | \n
---|---|---|---|---|---|
Bitstamp | \n7 days | \n1.0934 | \n0.9946 | \n0.0992 | \n0.1782 | \n
Gdax | \n7 days | \n1.0964 | \n0.9946 | \n0.1160 | \n0.2087 | \n
Model fitting with delay parameter: outcomes for Bitstamp and Gdax exchanges when attention is measured by the SVI index.
It is evident from the outcomes in Table 4 that the model parameters are not significantly different while the delay might be quite different as if the reaction to the attention factor is faster for some exchanges and slower for others. On the contrary, when attention is measured by the Google SVI Index, the delay is unchanged, but the difference between estimated parameters for the price dynamics is nonnegligible.
\nBy analyzing the outcomes and considering the shift effect as depicted in Figure 3, it is tempting to conjecture that the faster reaction determines the leader exchanges and that the slower exchange will then follow. If we could forecast that the next day price of the slower exchange will reach the price today for the faster one, we could obtain a profit by suitably investing in the two exchanges. However, it is worth noticing that the estimation of the delay parameter is obtained by maximizing the likelihood over a whole time series and is a product of averaging so arbitrage cannot be achieved in a direct way.
\nNevertheless, in a multivariate setting as ours, the theory guarantees that arbitrage opportunities are ruled out if the market price of risk in the market is unique. Without entering technical details and assuming \n
It is evident that these values are not equal if we plug parameter estimates in Eq. (30); hence, arbitrage opportunities are not ruled out at least from a theoretical point of view. We will address this issue more precisely in future research.
\nIn this chapter, we have introduced a model in continuous time in order to describe the dynamics of Bitcoin price depending on an exogenous stochastic factor, which represents market attention on the Bitcoin system. Market attention is measured either by the total trading volume in Bitcoins or by means of the Google Search Volume Index, which, as suggested in [16], is a direct measure of the revealed attention for uniformed retail investors. More precisely, the attention factor affects directly the instantaneous mean and volatility of logarithmic returns; in addition, it may be also correlated with the price changes. An estimation procedure to fit the model to observed data is also suggested and, under the assumption of no correlation, a closed formula for standard European option prices on Bitcoin is provided.
\nBy applying outcomes within the mathematical theory of bubbles [23, 24, 25, 27], we are able to show that Bitcoin boosts in a bubble if and only if there is a positive correlation between changes in the price and in the attention factor. This finding is reasonable and claims that a stronger positive dependence between the two processes in Eq. (21) may result in an explosion of the price process.
\nFinally, we allow for a delay on the effect of market attention on the Bitcoin price, and, based on this generalized model, we introduce a multivariate setting for our model (Eq. (28)) in order to take into account the special feature of multiple exchanges where it is possible to trade in Bitcoins. Preliminary results indicate that arbitrage opportunities may arise in two exchanges that are characterized by different delays.
\nWe gratefully acknowledge Marco Patacca for having provided the routines in Matlab® to develop the empirical sections of the paper and for useful suggestions and comments. We also acknowledge funding from Fondazione Cassa di Risparmio di Perugia (Grant 2015:0459013) and Bank of Italy (Grant 407660/16).
\nThe authors declare no conflict of interest.
Gianna Figà-Talamanca gratefully acknowledges interesting discussions on the topic of this chapter with colleagues of the Department of Finance and Risk Engineering where she was visiting professor while preparing this research. The authors also wish to thank Stefano Bistarelli for having introduced them to the intriguing and worth to explore world of cryptocurrencies.
\nOve Odredbe i uvjeti ističu pravila i regulacije u svezi korištenja IntechOpenove stranice www.intechopen.com i svih poddomena u vlasništvu IntechOpena, tvrtke sa sjedištem u 5 Princes Gate Court, London, SW7 2QJ, Ujedinjeno Kraljevstvo.
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\n\nBez prethodne privole i izričite pisane dozvole, ne možete stvarati okvire oko naših stranica ili koristiti druge tehnike koje na bilo koji način mogu promijeniti prezentaciju ili izgled naše stranice.
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\n\nOve Odredbe i uvjeti su sastavljeni u skladu s odredbama prava Ujedinjenog Kraljevstva, a za sve sporove nadležan je sud u Londonu, Ujedinjeno Kraljevstvo.
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