The use of Expected Utility Theory (EUT) in Taxpayers Behaviour Modelling

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1 American Journal of Applie Sciences Original Research Paper The use of Expecte Utility Theory (EUT) in Taxpayers Behaviour Moelling Fari Ameur an Mohame Tkiouat Stuies an Research Laboratory in Applie Mathematics (LERMA), Mohammaia School of Engineering, Mohame V University, Rabat BP 765, Morocco Article history Receive: Revise: Accepte: Corresponing Author: Fari Ameur Stuies an Research Laboratory in Applie Mathematics (LERMA), Mohammaia School of Engineering, Mohame V University, Rabat BP 765, Morocco Tel: ameur_fari@yahoo.fr Abstract: In this stuy, we analyze taxpayers behaviour regaring tax system. We present a theoretical stuy of a moel pre establishe by other authors base on the expecte utility theory; taxpayer's behavior is assume to be risk-averse. We have release some conitions of this moel an we have introuce a new parameter reflecting the efficiency of tax control; we foun that the efficiency of a fiscal control have an important effect on these interactions. Previous stuies are base on a maximal efficiency of tax control, which is a particular case of our moel. We foun that for Moroccan case, the frau is relate to the size of companies; it s more important in the big companies than small an meium enterprises. This result can be use as a tool to reconsier aministrative approaches of tax compliance. Keywors: Expecte Utility Theory, Prospect Theory, Survey, Tax Frau, Tax Auit, Tax Compliance, Taxpayers, Behaviour, JEL Classification Coes: H3, C5 Introuction A recent stuy of the eterminants of fiscal policy has been publishe by the Organization for Economic Co-operation an Development (OECD), shows that the tax reforms that have been implemente are esigne to respon not only to the nee to improve The performance of the economy but also to counter the phenomenon of tax frau. As for Morocco, the government is unergoing many changes in the tax law. The challenge is to have a competitive an efficient tax system that helps to improve the economic an social environment an tackle the scourge of tax evasion. The role of tax aministration is to en such behavior which changes the social contract. In fact, there is always a ifference between the tools an methos of tax frau an tax auit. However, in orer to reuce the cost of this unequal conflict, tax aministrations have to be intereste in analyzing the behavior of taxpayers so that they can esign an implement a more effective set of responses which aress the causes of non compliance with tax law. In this stuy, we examine this phenomenon base on the moel of Allingham an Sanmo (1972) improve by numerous authors such as (Yitzhaki, 1974; Koskela, 1983; Caplin an Leahy, 2001; Bazart, 2002; Ameur an Tkiouat, 2012; 2014; 2015) (the list is not exhaustive). The literature on tax frau has shown controversial results. In fact, the proportional taxation of eclare income associate with a penalty on issimulate income q*(i-x) is the funamental hypothesis of the moel of Allingham an Sanmo (1972). As such, the taxpayer selects the amount of income to eclare, x, in orer to maximize his expecte utility. The results show that increasing the penalty has a positive impact on the honesty of taxpayer on his tax report. However, the ifference in eclare income compare to the taxation s level t is unetermine in the Moel of Allingham an Sanmo (1972). The question is: Does the proportion of reporte income increases as isposable income? This inetermination was lifte by Yitzhaki (1974) who consiere the problem of tax frau as the one efine by Allingham an Sanmo (1972), but in which the penalty, enote q, concerns mainly the evae tax: t*(i-x). The result obtaine by Yitzhaki (1974) reveals that the moel of expecte utility theory forecasts a negative relationship between tax rates an evasion when two conitions are satisfie. First, fines are impose. Secon, the preferences of taxpayers satisfy the ecreasing absolute assumption of risk aversion. Several researches consier that such result isagree with the intuition; it was calle the Yitzhaki 2017 Fari Ameur an Mohame Tkiouat. This open access article is istribute uner a Creative Commons Attribution (CC-BY) 3.0 license.

2 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): paraox. An empirical literature (Cebula an Feige, 2011) reveals that there is a positive relationship between tax rate an tax frau. Kahneman an Tversky (1979) evelope a new theory calle the Prospect theory base on experimental work. This theory criticizes the expecte utility theory (Piolatto an Rablen, 2013; Dhami an Al-Nowaihi, 2007). In fact, the PT provies closer results to the reality than EUT. Some authors argue that PT can reverse the Yitzhaki paraox, base on experimental finings; which show a positive relationship between evasion an tax rates. Dhami an Al-Nowaihi (2007) claim that the prospect theory can reverse the Yitzhaki puzzle. However, the result of (Piolatto an Rablen, 2013) shows that the reference epenent moel cannot reverse Yitzhaki puzzle, when consiering that the utility is homogenous. Piolatto an Rablen (2013; Dhami an Al-Nowaihi, 2007), expan their moel to inclue a cost calle stigma, which is relate to the possibility of etecting frau. They conclue that when stigma is equal to zero, the prospect theory cannot reverse the Yitzhaki puzzle. Also, the Yitzhaki puzzle can be inverse when the moel of expecte utility theory is expane with stigma. In the moel of Allingham an Sanmo (1972) an in other moels evelope later, it is suppose that after tax auit, the tax aministration has a comprehensive knowlege of the real value of the income chosen by taxpayer. However, in reality, the tax aministration is not able to etect all errors an frau that can be mae by a taxpayer in orer to reuce his revenue eclaration. We prove that the importance of tax frau, regaring taxpayer income, is relate to the penalty q an the effectiveness of tax auit which we call r. In this research, we are going to examine the question of how can EUT or PT explains the frauulent behavior of taxpayers. Our objective is to be able to ientify which Moel can better explain the behaviour of taxpayers. This paper is organize as follows: After the introuction in section 1, we analyze in section 2 the results of some previous stuies one by authors who worke on the frauulent taxpayers behaviour base on EUT an PT. In section 3, we present our contribution an iscussions of the results. We use some examples to show that the result of PT moel is not always true. In section 4, we outline the consequences of our theoretical work projecte on the Moroccan case to assess the relevance of the last fiscal legislative ecisions. In section 5, we conclue this paper by presenting our results an by proviing some recommenations that can help in a better unerstaning of taxpayer s behaviour an improving the effectiveness of tax auit. Previous Research The phenomenon of tax frau was stuie by Allingham an Sanmo (1972) base on the expecte utility theory, which was evelope in 1944 by John von Neumann an Oskar Morgenstern. The assumptions of Allingham an Sanmo s (1972) moel were progressively release by numerous authors, Yitzhaki (1974; Koskela, 1983; Caplin an Leahy, 2001; Bazart, 2002) (the list is not exhaustive). A methoological choice, which is base on observation, represents the main characteristic of those assumptions. This methoology argues that tax evasion s ecision is mae uner uncertainty. The agreement also seems on the parameters which affect the optimal ecision of an iniviual taxpayer. Yitzhaki (1974) foun that, when two conitions are satisfie, the expecte utility theory s moel preicts a negative relationship between tax rates an evasion. First, fines are impose an secon, the preferences of taxpayers satisfy the eclining absolute assumption of risk aversion. Several works consier that there is a contraiction with intuition an this result which was calle the Yitzhaki paraox or Yitzhaki puzzle. Kahneman an Tversky (1979) evelope a new theory calle the Prospect theory base on experimental work. This theory criticizes the expecte utility theory (Piolatto an Rablen, 2013; Dhami an Al-Nowaihi 2007). In fact, the PT provies closer results to the reality than EUT. Some authors argue that PT can reverse the Yitzhaki paraox, base on experimental finings; which show a positive relationship between evasion an tax rates. Accoring to Dhami an Al-Nowaihi (2007), the prospect theory has explaine the issue of tax evasion in a proper way. Hashimzae et al. (2012) argues that the tax effect s irection is not reverse when applying the prospect theory. Only the selection of tax s level can affect its irection. In orer to stuy the alternatives of a reference-epenent moel with the tax evasion s ecision. Piolatto an Rablen (2013) vary the prospect theory s elements that are fixe, the reference of tax level an the auit s probability that may epen on taxpayers eclaration. They then ivie the prospect theory into four main elements which are: Reference epenence; the outcomes are referee accoring to a reference level of wealth. Then, ecreasing sensitivity: It implies a convex preference above the outcomes that are below the reference level an concave preference above the outcomes which are over the reference level. The thir element is the isutility of a loss surpasses the utility of a gain. The last element is probability weighting when objectives probabilities are converte to ecision weights. 246

3 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): This ecomposition of the prospect theory allows ientifying the elements that can inversion the Yitzhaki pulzze. The results show that the Yitzhaki pulzze is not reverse by only introucing the reference epenence when holing the probability of the auit an the reference level fixe. However, both the reference epenence an ecreasing sensitivity reverse the Yitzhaki pulzze if the payoff is below the reference level. During the analysis process, probability weighting an loss aversion showe that they have no effect to ownturn the Yitzhaki pulzze. Besies, the reference level is enough to reverse the Yitzhaki pulzze if the reference level is sensitive enough to the level of tax rate. However, the Yitzhaki pulzze is reverse in case if the reference level is insensitive to the tax rate an when both the ecreasing sensitivity an reference level are suppose. Accoring to Piolatto an Rablen (2013), there are some terms of the reference level which are not sensitive enough to the tax rate to inverse the Yitzhaki pulzze when taking into consieration only the reference epenence. However, those specifications can be sensitive to the tax rate an reverse the Yitzhaki pulzze when combining ecreasing sensitivity with reference epenence. Among the specifications of the reference level is when the post-tax wealth of the taxpayer. The reference epenent moel cannot reverse the Yitzhaki pulzze when utility is set to be concave or to show ecreasing sensitivity. These finings are strong in a set of specifications of the reference level like the tax gamble s expecte value which permits the epenency of eclaration of the taxpayer. Dhami an Al-Nowaihi (2007) claim that the prospect theory reverses the Yitzhaki pulzze, but Piolatto an Rablen (2013), when consiering that the utility is homogenous, the result was that the reference epenent moel cannot reverse Yitzhaki pulzze. Piolatto an Rablen (2013; Dhami an Al-Nowaihi, 2007), expan their moel to inclue a cost calle stigma relate to the possibility of etecting the cheating. They conclue that: The prospect theory cannot reverse the Yitzhaki pulzze when stigma is equal to zero. Also, when the moel of expecte utility theory is expane with stigma, it can inverse the Yitzhaki pulzze. Therefore, one cannot conclue that the capacity of reference epenent moel to reverse the paraox is greater than the one of the moel of expecte utility theory. The authors then argue that the application of the prospect theory to tax evasion fall short when tax evasion increases in the marginal tax rate. New approaches to specify the reference level are then neee. Our Contribution an Results Discussion In this section, we present our methoology an the results obtaine. We present our theoretical results; base on previous EUT moel. With some moifications of Allingham an Sanmo Moel (AS), we argue that espite critics to EUT, PT moel isn t more important than EUT. Critics to Some Previous Results: PT Moel Against EUT Moel All previous researches that criticize the EUT moel base their analysis on the fact that the result obtaine by the EUT moel is against intuition an it is inconceivable that frau is ecreasing as a function of tax rates (Piolatto an Rablen, 2013; Dhami an Al- Nowaihi, 2007). The position of these researchers was motivate by some surveys an investigations. Inee, if we consier that the result obtaine by the EUT is against intuition, it means that all taxpayers have the same behaviour; they suppose that tax rate is the most important parameter that influences their behaviour regarless of the egree of tax compliance of each taxpayer. The following example can escribe more this point: We consier two taxpayers C1 an C2, the first is known by his honesty an tax compliance. All ajustments that C1 i after ifferent tax auits were the results of errors or omissions, no frau was raise. C1 is satisfie that these contributions allow the state to provie services to citizens an therefore an increase in tax revenues that automatically create more services. He is willing to contribute as far as the contribution oes not excee a given limit. The secon taxpayer consiers that the tax is a violation of his rights because the state oes not give him a real part against his contribution. C2 always seeks the opportunity to minimize his contribution; in particular a ecrease in the amount of the penalty may encourage him to increase his frau. If we place a policy to reuce tax rate: For C1: The state will lose some of these revenues without any effect on the behaviour of the taxpayer. For C2: The state will lose some of these revenues since the effect of the ecrease in tax penalty encourages him to increase his frau. We conclue that more a value of tax rate (that we name optimum rate top); tax frau increase as a function of tax rate. However, tax frau ecrease or oesn t change in function of tax rate. We can schematize this result in the following graph: EUT Moel with Some New Assumptions EUT Moel To use the avance of the moel of Allingham an Sanmo (1972), taxpayer's behavior is consistent with the axioms of von Neumann-Morgenstern utility function an is solely epenent on isposable income. The taxpayer is assume to be risk-averse thus this function has a positive marginal utility an strictly ecreasing. 247

4 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): Fig. 1. Tax frau as a function of tax rate for C1 an C2 Fig. 2. Tax frau as a function of income where rq<1 an rq> = 1 The moel of Allingham an Sanmo (1972) is given by: EU = (1 p) U ( I ) + pu ( I ) (1) an With: n I = I tx q( I x) In = I tx While: I = Real income of the taxpayer, here is an exogenous variable an is known but ignore by the taxpayer of the tax aministration I n = Disposable income where the taxpayer is not foun in the frau I = Disposable income after the tax auit of the taxpayer x = Income eclare ecision variable of the taxpayer t = Tax rate, constant on the amount of reporte income, x q p = The rate of penalty for unreporte income = The probability of etection. It is assume that after the fiscal control, tax aministration has a comprehensive knowlege of the actual amount of taxpayer's income Previous Results are a Special Case of our Contribution Some previous stuies base on EUT has shown controversial results, the hypotheses of proportional taxation of eclare income associate with a penalty on issimulate income q(i-x) are the essential hypothesis of the moel of Allingham an Sanmo (1972). In this context, the taxpayer chooses the amount of income to eclare, x, in orer to maximize his expecte utility. The results obtaine show that increasing the penalty has a positive incentive on taxpayer to be honest in his tax report. However, the variation in eclare income compare to the level of taxation t is unetermine in the Moel of Allingham an Sanmo (1972). The question is: Does the proportion of reporte income increases as isposable income? This inetermination was lifte by (Yitzhaki 1974), he consiere the problem of tax frau as a framework similar to that efine by Allingham an Sanmo (1972), but in which the penalty, enote q, concerns specifically the evae tax: t*(i-x). the result obtaine by Yitzhaki shows that tax frau ecrease when the tax rate increase. But empirical literature (Cebula an Feige, 2011) shows that there is a positive relationship between tax rate an tax frau. Base on the assumptions of the moel of Allingham an Sanmo (1972; Bazart, 2002) showe that tax frau ecreases when real income rises. But tax aministration cannot etect all the anomalies or omissions of taxpayers. This result represents a special case for our proposal moel with an effectiveness of 100% or r =

5 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): Table 1. (Previous Moels) Matrix q*r (penalty rate *tax auit effectiveness) Q R r*q Table 2. (Our moel) Matrix q*r (penalty rate *tax auit effectiveness) q/r The moel of Allingham an Sanmo (1972) as it is given in Equation 1 became: EU = (1 p) U ( I ) + pu ( I ) (2) an: With: n I = I tx rq( I x) In = I tx The taxpayer chooses the amount of income to report, x, in orer to maximize his expecte utility an the conitions for maximum are: (The secon orer conition is enote D): t[ (1 p) U '( I ) + p( rq 1) U '( I )] = 0 (3) n D = t [(1 p) U ''( I ) + p( rq 1) U ''( I ) (4) 2 2 n Proposal: For a given level of penalty q an given an effectiveness of tax auit r, the tax frau woul ecline when real income rises if (rq> = 1) an it increases in function of income in the opposite case. Demonstration: We can easily prove that: [ ] x t = p U I A I rq A I I D ' (1 ) ( n ) ( n ) (1 ) ( ) With respect to the conition of the moel, if (rq 1), x so we have: 0 I We conclue that for a given level of penalty q an given an efficiency of tax auit r, the tax frau woul ecline when real income rises if rq 1 (see Fig. 2) an it increases in function of income in the opposite case. From Table 1, we can notice that in previous moels, the effectiveness r is equal to 1 (100%) which represent a special case of our moel (Table 2), the value of r is between 0 an 1. Application-Moroccan Case We project our theoretical results on the Moroccan case to assess the effectiveness of the last legislative ecisions in fiscal terms. Taking the case of Morocco, for each correction of the tax base after fiscal control, besies the payment of the tax evae, taxpyers will pay as a minimum 30% of the evae tax. However, if we increase the penalty an keep the same level of effectiveness of tax auits, taxpayers who have high income are more honest than those with lower incomes. This result is quite logical; for a low income, even if we increase the punishment, its effect on isposable income of the taxpayer frau is minimal. Generally, in morocco, base on experts confirmation from tax epartment, the effectiveness of fiscal control is less than 80%, so regaring our theoretical result, tax frau increases with income. Which mean that the Moroccan government shoul focus their effort on big companies in orer to reuce the effect of tax frau. However, among the latest legislative ecisions of Moroccan government is the ecrease of tax rate from 30 to 10% for very small companies. We notice that meium an big companies are not concerne by this ecision. We conclue that if the target of the government is increasing tax revenue ue to tax auit, the government shoul select big an meium companies for control. 249

6 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): However, if the target is enlarge tax base an attract the informal sector to integrate the formal economy, the legislative ecision shoul take time in consieration; instea of very small an meium companies, the reuce of tax rate from 30 to 10% must concern new companies. Tax frau is the emerging issues for concern where this issue is becoming a global phenomenon that shoul be a concern for the state authorities, in particular the tax authorities, because it woul threaten state tax revenues. For that reason, it is necessary for the tax authorities to carry out effective strategies to combat an prevent tax frau. Tax frau has become one of the enemy who must be the primary concern of a state tax authorities for possible onshore materially reuce tax revenues. Therefore, it is first important to unerstan the meaning of tax frau. In taxation, there are a number of negative behaviors of taxpayers who may be performe to obtain tax benefits. Tax Actors Tax evasion remains a share responsibility between ifferent tax actors that tax authorities must take into account: Business people an stakeholers are able to control themselves each to the lack of benefits illegally. Supposely the company's internal accountants an public accountants remain objective an inepenent an not affecte by the management. Internal accountant shoul be responsible irectly to the owner an not its management company, as this can reuce the pressure face by internal accountants. The evelopment of social responsibility: Business persons are require to care about the state of society. Thus, uner any circumstances the businesses shoul be able to evelop an manifest the attitue of responsibility towars the local community in their business environment. The importance of ethics eucation for accountants as a provision in the face of potential frau: Ethics violations will continue to occur if there is no eep unerstaning of the importance of accountants to ahere to professional ethics. It coul be that they o not know the impact of the frau which they i. One way to reuce the number of accountants who eviate an instill awareness of the importance of applying the coe of ethics is to o intensive socialization on professionalism an coe of ethics of accountants in the work environment. The Government of Morocco The government shoul tighten supervision of tax to companies large an not selective in resolving tax evasion. The government shoul implement severe penalties for companies that arken taxes an severely punish the persons who receive bribes an companies shoul be aware of their tax obligations. Multinational corporations who intentionally prove not fulfill the obligations of economic, legal an social operating license can be revoke an banne from operating in Morocco. The first important thing in orer to successfully fight against tax frau is a goo an strong cooperation between the authorities of the State. This means that not only the cooperation between the tax authorities, but also the cooperation between the tax authorities with other authorities, such as the National Police, Bank, Customs an Excise. Moreover, for intergovernmental cooperation, it woul also be beneficial if there is cooperation between the government an other parties that have information about tax frau, such as employees of a company that oes the tax frau. Law Enforcement If the law is applie effectively, both the taxpayer an the government will be reluctant to act against the law. On the other han, in an environment of weak law enforcement, taxpayer rogue will try to fin loopholes in the law an abuse. Furthermore, the authorities, such as tax officials, police or other authorities, also will try to take avantage of the situation to their own avantage, thus, it will create an environment conucive to collusion an corruption. For that reason, it is necessary to have a well-establishe law enforcement to tackle an prevent tax frau. Summary an Concluing Remarks The Results of our stuy o not show that EUT Moel is better than PT Moel contrary to what it is state by some other authors. We conclue that each Moel can help to unerstan taxpayers behavior base on its own initial assumptions. We notice that there is complementary relationship between those two Moels. The moels state above concerning the EUT, represent a special case of our moel. Where tax auit effectiveness is equal to 1 (100%), our moel give the same results as others moel, but in the reality tax auit effectiveness can t be at its maximal value. Tax aministration is always trying to fin an control companies that represent a major risk in terms of tax frau. The result of our work will be a guie for the selecte companies that will be controlle by referring to the parameters of the tax system that is in place. Moreover, base on this fining an by applying it to the Moroccan case that represent a low effectiveness in terms of tax auits an that sanction policy are fairly flexible. It is important to aress the control to big businesses. Yet, such companies represent a negligible percentage of the overall tax population an a concentrate an continuous auiting will isrupt their evelopment an their growth, especially that their 250

7 Fari Ameur an Mohame Tkiouat / American Journal of Applie Sciences 2017, 14 (2): contribution excees 80% of total tax revenues. On the other han, the auit of small an very small enterprises is expensive for the tax aministration because it nees to increases the number of files to auit an increase also the number of auitors as well. We can also notice that tax auit is not enough to avoi tax evasion, tax authorities must look for other tools to struggle frau, especially using avance tools of risk analysis for planning files to be controlle. We propose that tax authority shoul perceive the frauulent taxpayers not only as robbers but also as clients; we suggest the improvement of the relationship between taxpayers an the government in orer to create a climate of cooperation an trust. Acknowlegement We are grateful to anyone who has contribute in any way to the realization of this work. In particular our colleagues from General Directorate of Taxes of Morocco. Funing Information Our proposal moel represent a solution to Ytzhaki puzzle. For a given level of penalty q an given an effectiveness of tax auit r, the tax frau woul ecline when real income rises if (rq> = 1) an it increases in function of income in the opposite case. Author s Contributions This stuy is the result of the full an equal collaboration of all the authors: Fari Ameur: Ieas generation; literature review an moel an mathematical esign an equal contribution to result valiation an iscussion. Mohame Tkiouat: Ieas generation, Designing the methoology, mathematical valiation an equal contribution to result valiation an iscussion. Bazart, C., «The behavior of tax frau: Taxpayers facing tax aministration». French J. Econom., 16: Cebula, R. an E.L. Feige, America s unergroun economy: Measuring the size, growth an eterminants of income tax evasion in the U.S. Munich University Library. Dhami, S. an A. Al-Nowaihi, Why o people pay taxes? Prospect theory versus expecte utility theory. J. Econom. Behavior Organ., 64: DOI: /j.jebo Ameur, F. an M. Tkiouat, Taxpayers frauulent behavior moeling the use of atamining in fiscal frau etecting Moroccan case. Applie Math., 3: DOI: /am Ameur, F. an M. Tkiouat, Expecte utility theory vs prospect theory taxpayers frauulent behaviour moelling-moroccan case. Int. Res. J. Finance Econom., 121: Ameur, F. an M. Tkiouat, Determinants of tax frau: Experience from Morocco. Eur. J. Econom. Finance Amin. Sci., 78: Hashimzae, N., G.D. Myles an B. Tran-Nam, Applications of behavioural economics to tax evasion. J. Econom. Surveys, 27: DOI: /j x Kahneman, D. an A. Tversky, Prospect theory: An analysis of ecision uner risk. Econometrica, 47: DOI: / Koskela, On the shape of tax scheule, the probability of etection an the penalty schemes as eterrents to tax evasion. Public Finance, 38: Piolatto, A. an M.D. Rablen, Prospect theory an tax evasion: A reconsieration of the yitzhaki puzzle. Theory Decis. Yitzhaki, S., A Note on income tax evasion: A theoretical analysis. J. Public Econom., 3: DOI: / (74) Conflict of Interest The author confirms that this article content has no conflict of interest. References Allingham, M.G. an A. Sanmo, Income tax evasion: A theoretical analysis. J. Public Econom., 1: DOI: / (72) Caplin, A. an J. Leahy, Psychological expecte utility theory an anticipatory feelings. Q. J. Econom., 116: DOI: /